The Oxford Handbook of Science and Medicine in the Classical World 9780199984657, 9780190878825, 9780190878832, 9780199734146, 0199984654

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T h e Ox f o r d H a n d b o o k o f

SCIENCE AND M E DIC I N E I N T H E C L A S SIC A L WOR L D

The Oxford Handbook of

SCIENCE AND MEDICINE IN THE CLASSICAL WORLD Edited by

PAUL T. KEYSER with

JOHN SCARBOROUGH

1

3 Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and certain other countries. Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016, United States of America. © Oxford University Press 2018 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by license, or under terms agreed with the appropriate reproduction rights organization. Inquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above. You must not circulate this work in any other form and you must impose this same condition on any acquirer. Library of Congress Cataloging-in-Publication Data Names: Keyser, Paul T. (Paul Turquand), 1957– editor. | Scarborough, John, editor. Title: The Oxford handbook of science and medicine in the classical world / edited by Paul T. Keyser and John Scarborough. Other titles: Handbook of science and medicine in the classical world Description: New York, NY: Oxford University Press, [2018] | Series: Oxford handbooks | Includes bibliographical references and index. Identifiers: LCCN 2017049555 (print) | LCCN 2017059389 (ebook) | ISBN 9780199984657 (oso) | ISBN 9780190878825 (updf) | ISBN 9780190878832 (epub) | ISBN 9780199734146 (cloth : alk. paper) Subjects: LCSH: Science, Ancient. | Medicine, Ancient. Classification: LCC Q124.95 (ebook) | LCC Q124.95 .O94 2018 (print) | DDC 509.37—dc23 LC record available at https://lccn.loc.gov/2017049555 1 3 5 7 9 8 6 4 2 Printed by Sheridan Books, Inc., United States of America

Contents

Abbreviations  Contributors Introduction  Paul T. Keyser

xi xiii 1

A .   A N C I E N T S C I E N T I F IC T R A DI T ION S B E YON D G R E E C E A N D ROM E 1. Mesopotamia 

9

a. Mesopotamian Mathematics  Jens Høyrup

11

b. Astral Sciences of Ancient Mesopotamia  Francesca Rochberg

25

c. Mesopotamian Beginnings for Greek Science?  JoAnn Scurlock

35

2. Egypt 

47

a. Mathematics in Egypt  Annette Imhausen

49

b. Astronomy in Ancient Egypt  Joachim Friedrich Quack

61

c. Egyptian Medicine  Rosalie David

71

3. India 

81

a. Mathematics in India until 650 CE  Toke Lindegaard Knudsen

83

b. Sanskrit Medical Literature  Tsutomu Yamashita

95

vi   Contents

4. China 

105

a. Ancient Chinese Mathematics  Alexei Volkov

107

b. Astral Sciences in Ancient China  Xu Fengxian

129

B.   E A R LY G R E E K S C I E N C E  1. Pythagoras and Plato  Andrew Gregory

147

2. Early Mathematics and Astronomy  Leonid Zhmud

171

3. Early Greek Geography  Philip G. Kaplan

195

4. Hippocrates and Early Greek Medicine  Elizabeth Craik

215

C .   H E L L E N I ST IC G R E E K S C I E N C E 1. Aristotle, the Inventor of Natural Science  Jochen Althoff

235

2. Epicurus and His Circle: Philosophy, Medicine, and the Sciences  Teun Tieleman

257

3. Hellenistic Mathematics  Fabio Acerbi

269

4. Hellenistic Astronomy  Alan C. Bowen

293

5. Hellenistic Geography from Ephorus through Strabo  Duane W. Roller

315

6. Mechanics and Pneumatics in the Classical World  T. E. Rihll

337

7. Medical Sects: Herophilus, Erasistratus, Empiricists  Fabio Stok

359

Contents   vii

8. Astrology: The Science of Signs in the Heavens  Glen M. Cooper

381

9. The Longue Durée of Alchemy  Paul T. Keyser

409

10. Paradoxography  Klaus Geus and Colin Guthrie King

431

11. Music and Harmonic Theory  Stefan Hagel

445

12. Ancient Agronomy as a Literature of Best Practices  Philip Thibodeau

463

13. Optics and Vision  Colin Webster

481

14. Pharmacology in the Early Roman Empire: Dioscorides and His Multicultural Gleanings  John Scarborough

519

15. Dietetics: Regimen for Life and Health  Mark Grant

543

16. Greco-​Roman Surgical Instruments: The Tools of the Trade  Lawrence J. Bliquez

555

D.  G R E C O -​ROM A N S C I E N C E 1. Traditionalism and Originality in Roman Science  Philip Thibodeau

593

2. Science for Happiness: Epicureanism in Rome, the Bay of Naples, and Beyond  Pamela Gordon

615

3. Roman Medical Sects: The Asclepiadeans, the Methodists, and the Pneumatists  Lauren Caldwell

637

4. Science and Medicine in the Roman Encyclopedists: Patronage for Praxis  Mary Beagon

655

viii   Contents

5. Stoicism and the Natural World: Philosophy and Science  Teun Tieleman

677

6. Scribonius Largus and Friends  John Scarborough

699

7. Distilling Nature’s Secrets: The Sacred Art of Alchemy  Kyle Fraser

721

8. Physiognomy  Mariska Leunissen

743

9. Galen and His System of Medicine  Ian Johnston

765

10. Ptolemy  James Evans

789

11. Science in the 2nd and 3rd Centuries ce: An Aporetic Age  Paul T. Keyser

829

E .   L AT E A N T IQU E A N D E A R LY BYZANTINE SCIENCE 1. Plotinus and Neoplatonism: The Creation of a New Synthesis  Lucas Siorvanes

847

2. Greek Mathematics and Astronomy in Late Antiquity  Alain Bernard

869

3. The Greek Neoplatonist Commentators on Aristotle  Michael Griffin

895

4. Byzantine Geography  Andreas Kuelzer

921

5. Byzantine Alchemy, or the Era of Systematization  Cristina Viano

943

6. Byzantine Medical Encyclopedias and Education  Svetla Slaveva-​Griffin

965

Contents   ix

7. Late Encyclopedic Approaches to Knowledge in Latin Literature  David Paniagua

987

8. Medical Writing in the Late Roman West  Louise Cilliers

1013

Index 

1035

Abbreviations

DK

Diels, H., and W. Kranz. Die fragmente der Vorsokratiker. 6th ed. 2 vols. Zürich and Berlin, 1951. Cited by section and fragment number.

EANS Keyser, Paul T., and Georgia L.  Irby-​Massie, eds. Encyclopedia of Ancient Natural Scientists. London, New York, 2008. FGrHist Jacoby, F, ed. Fragmente der griechischen Historiker. Leiden, 1923–​. Cited by number, not volume and page. Kühn

Kühn, Karl Gottlob. Claudii Galeni Opera omnia, 20 vols. Leipzig 1821–​1833; repr. Hildesheim 1964–​1965 and 1986; cited by volume.page.

OLD

Glare, P. G. W., ed. Oxford Latin Dictionary. 2nd ed. 2 vols. Oxford, New York: Clarendon Press, 2012.

RE

Wissowa, G.  et  al., eds. Paulys Realencyclopädie der classischen Altertumswissenschaft. 85 vols. Including 15 supplements. Stuttgart, 1893–​1978.

SAM

Scarborough, John et  al., eds. Studies in Ancient Medicine. Vol. 1. Leiden, 1990—​.

SIG

Dittenberger, W., and F.  H.  von Gaertringen, eds. Sylloge Inscriptionum Graecarum. 3rd ed. 4 vols. Leipzig, 1915–​1924. Reprint Hildesheim, 1960.

Contributors

Fabio Acerbi, CNRS, UMR8167 “Orient et Méditerranée,” Paris, France Jochen Althoff, Institut für Altertumswissenschaften, Arbeitsbereich Klassische Philologie/​Gräzistik, Johannes Gutenberg-​Universität Mainz, Germany Mary Beagon, Department of Classics and Ancient History, University of Manchester, Manchester, England Alain Bernard, Centre A. Koyré, Paris Est Créteil University, France Lawrence J. Bliquez, Classics, University of Washington, Seattle, WA, USA Alan C. Bowen, Institute for Research in Classical Philosophy and Science, Baysville, ON, Canada Lauren Caldwell, Departments of History and Classics, Trinity College, Hartford, CT, USA Louise Cilliers, Department of English and Classical Languages, University of the Free State, Bloemfontein, South Africa Glen M. Cooper, Independent Scholar, Springville, UT, USA Elizabeth Craik, School of Classics, University of St. Andrews, St. Andrews, Scotland, UK Rosalie David, Centre for Biomedical and Forensic Studies in Egyptology, University of Manchester, Manchester, England James Evans, University of Puget Sound, Tacoma, WA, USA Kyle Fraser, University of King’s College, Halifax, Nova Scotia, Canada Klaus Geus, Freie Universität Berlin, Friedrich-​ Meinecke-​ Institut, Historische Geographie des antiken Mittelmeerraumes, Berlin, Germany Pam Gordon, Department of Classics, University of Kansas, Lawrence, KS, USA Mark Grant, Independent Scholar, Bruton, UK Andrew Gregory, Department of Science and Technology Studies, University College, London, England

xiv   Contributors Michael Griffin, Departments of Philosophy and Classical, Near Eastern, and Religious Studies, University of British Columbia, Vancouver, BC, Canada Stefan Hagel, Institute for the Study of Ancient Culture, Austrian Academy of Sciences, Vienna, Austria Jens Høyrup, Section for Philosophy and Science Studies, Roskilde University, Roskilde, Denmark Annette Imhausen, Historisches Seminar und Exzellenzcluster Normative Orders, Goethe Universität Frankfurt, Frankfurt am Main, Germany Ian Johnston, Independent Scholar, Tasmania, Australia Philip G. Kaplan, Department of History, University of North Florida, Jacksonville, FL, USA Paul T. Keyser, Independent Scholar, Chicago, New York, and Pittsburgh, USA Colin Guthrie King, Department of Philosophy, Providence College, Providence, RI, USA Toke Lindegaard Knudsen, Department of Cross-​Cultural and Regional Studies, University of Copenhagen, Copenhagen, Denmark Andreas Kuelzer, Austrian Academy of Sciences, Institute for Medieval Research, Division of Byzantine Research, Vienna, Austria Mariska Leunissen, Department of Philosophy, The University of North Carolina at Chapel Hill, Chapel Hill, NC, USA David Paniagua, Dpto. Filología Clásica e Indoeuropeo, Universidad de Salamanca, Salamanca, Spain Joachim Friedrich Quack, Ägyptologisches Institut, Heidelberg, Germany Tracey Rihll, Department of History and Classics, Swansea University, Wales, UK Francesca Rochberg, Near Eastern Studies, University of California, Berkeley, USA Duane W. Roller, Professor Emeritus of Classics, the Ohio State University, USA John Scarborough, Professor Emeritus, Department of History and School of Pharmacy, University of Wisconsin, Madison, WI, USA JoAnn Scurlock, Professor Emerita of History, Elmhurst College, Chicago, IL, USA Lucas Siorvanes, Department of Greek and Latin, University College, London, England Svetla Slaveva-​Griffin, Department of Classics, Florida State University, Tallahassee, USA Fabio Stok, Dipartimento di Studi letterari e filosofici, Università di Roma Tor Vergata, Rome, Italy

Contributors   xv Philip Thibodeau, Department of Classics, Brooklyn College, Brooklyn, NY, USA Teun Tieleman, Department of Philosophy and Religious Studies, Utrecht University, Utrecht, The Netherlands Cristina Viano, Centre Léon Robin, CNRS, Université de Paris IV -​Sorbonne, Paris, France Alexei Volkov, Center for General Education, National Tsing-​ Hua University, Hsinchu, Taiwan Colin Webster, Classics Program, University of California, Davis, CA, USA Xu Fengxian, Institute for the History of Natural Science, Chinese Academy of Sciences, Beijing, China Tsutomu Yamashita, Department of Business Administration, Kyoto Gakuen University, Kyoto, Japan Leonid Zhmud, Institute for the History of Science, St. Petersburg, Russia

I n t rodu ction Paul T. Keyser

What goes first comes last: only a Stoic Sage or a Daoist Master could write an introduction to a work before the work was completed. We, the two editors, are far short of such ascended masters, so only now do we look back and see what we have done. You have before you a collection of essays on ancient sciences intended to provide a synoptic synthesis of how scholars currently understand those sciences. Our focus is the classical world, that is, Greco-​Roman antiquity, up to ca 650 ce. But that set of descriptive terms raises a host of problematic queries, at least a few of which must be confronted: What is “science”? How, or using what categories, shall we study it? What role do the essays on Egypt, Mesopotamia, India, and China play in this book? We are in agreement that there is such a thing as science and, indeed, that there was such a thing in Greco-​Roman antiquity (Keyser 2013). That is, we take it as given that (a)  the world we observe does exist and can be known; moreover, (b)  we can share knowledge about the world; and finally, (c) there is a way that the world is, and it is both meaningful and even possible to say that some models of the world, or reports about the world, better represent that way than do others. Two illuminating examples from Greco-​Roman antiquity are (1) the observation that opium-​poppy sap and willow-​bark infusion each genuinely alleviate pain; and (2) the spherical-​earth theory, namely that the earth is not a flattish expanse on whose “top” we live, but rather a globular mass, on whose outside we live. In using the modern word “science,” we are naturally aware that we are using a modern word: we are after all, writing in English, not in Greek or Latin, much less in Egyptian or Sanskrit, among others. That, of course, means that we—​the editors and the contributors—​are translating ancient concepts into modern ones. We can only think about ancient categories and practices at all by first mapping them onto modern categories—​keeping in mind that our mappings will be rough and raw. It is no more anachronistic to employ the modern term “science” (or Wissenschaft, or 科学, kē xué) than it is to apply any modern term—​such as “book” or “city,” or “food” or “school”—​to a corresponding ancient Greek concept or practice. Scholars employ modern terms, such

2   Introduction as “astronomy,” to encompass what ancient Greeks or others included in their study of the heavens, and so also for “mathematics” or “medicine” or the rest. For any of us to attempt to speak or reason about ancient science without translating would be a comic futility, of the sort that Jonathan Swift might mock. But attempts at translation may fare better or worse—​do ours pass muster? Among the ancient Greeks, terms such as epistēmē, theōria, pragmateia, tekhnē, phusiologia, and “natural philosophy” were commonly used to cover a semantic range largely overlapping the modern English “science.” To label the work of ancient mathematicians, astronomers, doctors, and the like as science is valid: on the basis of shared goals, namely, comprehending, explaining, and sometimes predicting natural phenomena. We the editors firmly intended to be inclusive of science generally, that is, to include all the sciences that could reasonably be so designated. Some of those, notably alchemy and astrology, would not pass muster in the world of Einstein and Fermi as sciences. But all that we include herein was validly science for the ancient practitioners and theorists—​that is, all that we include involve attempts to understand how the world of nature worked and to construct models of that world to convey insight into its workings. If one excluded astrology and alchemy from the study of ancient science on the grounds their foundations and results have been invalidated (as indeed they have), we would also need to exclude ancient astronomy (which was highly geocentric) and ancient medicine (which was firmly humoral). If we can accept as somehow scientific a geocentric cosmos populated by livings beings constituted of humors, we must likewise accept stellar influences and material transmutation. We the editors also firmly wanted to include some material on other ancient cultures to see the science of the Greco-​Roman  (“classical”), world in its wider context. We wanted to do so, however, without losing our chosen focus on Greco-​Roman science. Our intent may be clarified by considering the analogy of the hypothetical “Oxford Handbook of Science and Medicine in the Sanskrit World” (or “Mesopotamian World”). Surely such a volume (highly desirable in its own right) would be rendered all the more insightful and valuable if it were to include some similar context-​setting essays, on other cultures of antiquity, and especially on the Greco-​Roman world. Attentive readers will note that the essays of the first section, on other ancient cultures, mostly focus on mathematics, astral sciences, and medicine, and that not all such sciences are covered for each of the four cultures, Egypt, Mesopotamia, India, and China. Would that we had been able to find contributors to cover the missing topics! As our editor at Oxford University Press can attest, we exerted lengthy and considerable effort, and greatly regret that our success was partial—​as, indeed, fate will have it for any effort in our actual and contingent world. And it need hardly be said that we are aware that many other cultures, other than or even prior to those we have touched upon here, must also have had some science—​but because science refers to a conceptual framework, we require texts to study, and those alas we lack, or they are few and not yet fully decoded. Given then that our central focus is on Greco-​Roman science, how shall we study that evolving system of concepts, across 13 or more centuries, from ca 650 bce to ca 650 ce?

Introduction   3 There have been typically two approaches, susceptible of being designated “reception studies” and “antiquarian studies,” both of which are burdened with what may be called the “great weight of the past.” Some scholars have studied ancient science as if collecting antiquarian oddities, of no larger or current relevance: this approach subjects the ancient ideas to the authority of our modern views. Others have studied ancient science as if elucidating the reception of its ideas by later writers, whether themselves also ancient or later: this approach subjects the ancient ideas to the authority of their prior texts (so that Plato is preferred over Plotinus, Hippocrates over Galen, and Aristotle over Alexander of Aphrodisias). Those two modes of scholarship on ancient science reflect the literary and philosophical debate that flared in the Renaissance, known as the “quarrel of the ancients and moderns.” Those who favored the ancients were favoring authority and adhered to a model of history as a process of decay, a view that emerges in Hesiod and the Hebrew scriptures, but persists in, for example, John Donne (see Hesiod, Works and Days 109–​ 201; Isaiah 51.6; Psalm 102.25–​27; Lucretius 2.1105–​1174; D.L. 7.141; Donne 1611; Lowenthal 2015, 226–​232). The opposing party, in favoring the moderns, was advocating that progress in some form was possible, and, in particular, they were arguing that people “now” could exceed the achievements of the ancients (see Vesalius 1543; Gilbert 1600; Bacon 1623, sec.4.2; Swift 1704). Perhaps we may step aside from that debate if we can conceive of science as an organic evolving whole, so that there is no question of subjecting the ancient ideas to any authority. Instead, let us humbly take the ancient ideas for what they are and study them as a system that changed and grew over time, leading in an unbroken series of small changes to our era (Keyser 2013). However alien the ideas of ancient Greeks—​or indeed ancient Chinese or ancient Egyptians—​may have been, those ideas were ideas about the same world in which we also live and were attempts to achieve the same goal that modern scientists have, the goal of understanding (Lloyd 1996; 2002). No radical break is possible, and science cannot have emerged suddenly, sometime, and somewhere, as if from the brow of Athena (Lloyd 2009, chap. 9, 159–​160). That outlook in turn throws some light on the somewhat unusual position of Greco-​ Roman science in world history. In the four cultures surveyed briefly (all too briefly) in the first section of essays, we may observe that the role of classic texts and the scholars who studied them was very much an effort of reception studies. That is most apparent in the history of Chinese science and literature from the early Han dynasty (ca 100 bce) onward, where a “classic” (jing, 经) was a text of a certain age, attributed to an honored founder, around which an interpretive tradition flourished that attracted students and inspired teachers; among the jing were the main scientific texts from ancient China. The teachers and students formed a “lineage” (jia, 家), within which students owed respect and deference to the teacher, and the most excellent student would succeed the teacher when he died. The lineage copied, memorized, and commented upon the text, ensuring its survival and elucidating the “veiled meanings or hidden dimensions” in the founder’s discourse, so that they could be “applied variably to new situations” (Sivin 1995; Lewis 1999, 53–​97; Lloyd and Sivin 2002, 42–​61).

4   Introduction The Sanskrit tradition, from the Maurya era (ca 300–​200 bce) onward, offers a very similar structure, in the succession (paramparā) of teacher (ācārya) and pupil (shishya) in a Vedic intellectual tradition, passing on knowledge and practice, and preserving the text around which the succession formed; the scientific texts of ancient India were preserved in this system. Here also the student began by memorizing the text that formed the basis of the tradition and owed his teacher the duty of preserving the tradition into which the teacher had initiated him. The work of the lineage was to produce exegetical commentaries on the text that defined the lineage (Hara 1980; Roelcke 1987; Jacobsen 2011). In the scribal traditions of both Mesopotamia and Egypt, from the second millennium bce onward, the scribe was an honored and revered figure, who, among other duties, passed on the wisdom of bygone ages. In Egypt, the texts that played the largest role in this tradition seem to have been ethical precepts attributed to specific, named ancient sages, although probably the scientific texts that survive were propagated in a similar way (Williams 1972; Assmann 1991, 476–​478; Piacentini 2001). In Mesopotamia, the Assyrian and Babylonian scribes preserved, translated, and commented on the classic texts of Sumerian literature, including science. Here the text tradition only gradually achieved stability of content and form, and the precise wording, unlike in the other three traditions, was fluid (Olivier 1975, 49–​54; Rochberg-​Halton 1984, 127–​137). As argued by Rochberg-​Halton (1984, 133–​134 /​2010, 72–​73), these “classic” traditions, dedicated to preserving a text and its attendant reinterpretations, tended to preserve and conserve their content, rather than prompting debate or development. The preservative path is not the only path for readers of classic texts, and “interpretive communities” can become actively innovative, as argued by Fish (1980, 338–​371). The traditions of China and India, and to a lesser degree those of Egypt and Mesopotamia, thus provide an analogy with certain literary and scientific traditions within Greek scientific writing, pointing out both the preservative nature of such lineages and yet also showing how Greek science pressed against its “classic” boundaries. Plato’s dialogues served as the classic text of the Academy; whereas much later (from  the 1st and 2nd centuries CE), Aristotle’s essays also served much the same function for philosophers, especially for the Neoplatonists. The school founded by Epicurus treated his letters and longer works as classics, which later Epicureans studied. The medical schools founded in the first half of the 3rd century BCE by Herophilus and Erasistratus preserved and interpreted the texts of their founders. When those three schools withered away in the 1st and 2nd centuries CE, their texts soon afterward became lost, except for quotations, sometimes extensive, by outsiders. A final example from the Greek world is the fellowship imagined in the Hippocratic Oath (cf. Lloyd and Sivin 2002, 112), in which the student swears to pass on the teacher’s knowledge only within the Hippocratic lineage. In the end, the study of ancient Greco-​Roman science, like any study, is undertaken for its own sake and cannot be justified by an appeal either to some basis upon which it is founded or to some benefit which it may confer. This situation is like the study of any ancient or foreign discipline—​music, painting, philosophy, poetry—​those practitioners

Introduction   5 were doing what we do, we think (see above on translation), and their efforts are worthy of appreciation and study in their own right. So also science: humani nil a me alienum puto (Terence, Heautontimoroumenos, 77). The volume before you is made up of five parts. The first offers essays on the sciences of ancient Egypt, Mesopotamia, India, and China. In the second part, the contributors have sketched what we know of the science of the period up through Plato and the early Academy. The third and largest part focusses on the science of Aristotle, the Peripatetic school, and the long Hellenistic era generally. The fourth part, somewhat overlapping with the third, treats the science of the Greco-​Roman period. The last part offers essays on the science of Late Antiquity, including the very earliest phase of the Byzantine Empire. These divisions seemed to us the “natural joints” of our material, as did the individual topics of the dozens of essays. We strove to employ ancient actors’ categories, suitably translated, insofar as we could, rather than retrojecting modern categories in an eisegetical way. But as always, we translate when we analyze, and our syntheses are limited by our imperfect insight. Last, but never least, let us now thank helpful people. A work such as this depends not only on its many contributors but also on scholars who gave advice, read drafts, wrote referee’s reports, or (especially) helped us find contributors. Among those, we pick out for note these five: David Creese (Newcastle), Wiebke Denecke (Boston), Marco Formisano (Utrecht), Susan Mattern (Atlanta), and Karine Chemla (Paris). The work is better for their efforts, but they are in no way to be held responsible for its defects. Readers please also note that the bibliographic closing date of this volume was November 31, 2016—​items appearing after that date could only be cited or used in exceptional cases.

Bibliography Assmann, Jan. “Weisheit, Schrift und Literatur im alten Ägypten.” In Weisheit, ed. Aleida Assmann, 475–​500. München: Fink, 1991. Bacon, Francis. De Augmentis Scientiarum. London: Haviland, 1623. Donne, John. Anatomie of the World. London: Macham, 1611. Fish, Stanley. Is There a Text in This Class? The Authority of Interpretive Communities. Cambridge, MA: Harvard University Press 1980. Gilbert, William. De Magnete. London: Short, 1600. Hara, Minoru. “Hindu Concepts of Teacher: Sanskrit Guru and Ācārya.” In Sanskrit and Indian Studies: Essays in Honour of Daniel H. H. Ingalls, ed. Masatoshi Nagatomi, B. K. Matilal, J. M. Masson, and E. C. Dimock, Jr., 93–​118. Dordrecht and Boston: Reidel, 1980. Jacobsen, Knut A. “Gurus and Ācāryas.” In Brill’s Encyclopedia of Hinduism, ed. Knut A. Jacobsen, vol. 3, 227–​234. Leiden: Brill, 2011. Keyser, Paul T. “The Name and Nature of Science:  Authorship in Social and Evolutionary Context.” In Writing Science: Medical and Mathematical Authorship in Ancient Greece, ed. Markus Asper, 17–​61. Berlin and Boston: de Gruyter, 2013. Lewis, Mark Edward. Writing and Authority in Early China. Albany:  State University of New York Press, 1999.

6   Introduction Lloyd, G. E.  R. Adversaries and Authorities:  Investigations into Ancient Greek and Chinese Science. Cambridge: Cambridge University Press, 1996. —​—​—​. The Ambitions of Curiosity:  Understanding the World in Ancient Greece and China. Cambridge: Cambridge University Press, 2002. —​—​—. Disciplines in the Making:  Cross-​ Cultural Perspectives on Elites, Learning, and Innovation. Oxford: Oxford University Press 2009. Lloyd, Geoffrey, and Nathan Sivin. The Way and the Word. New Haven, CT: Yale University Press, 2002. Lowenthal, David. The Past Is a Foreign Country—​Revisited. Cambridge: Cambridge University Press, 2015. Olivier, J. P.  J. “Schools and Wisdom Literature.” Journal of Northwest Semitic Languages 4 (1975): 49–​60. Piacentini, Patrizia. “Scribe.” Oxford Encyclopedia of Ancient Egypt, ed. Donald B. Redford, vol. 3, 187–​192. Oxford: Oxford University Press, 2001. Rochberg-​Halton, Francesca. “Canonicity in Cuneiform Texts.” Journal of Cuneiform Studies 36.2 (1984): 127–​144; repr. as chap. 3 in her In the Path of the Moon: Babylonian Celestial Divination and Its Legacy, 65–​84. Leiden: Brill, 2010. Roelcke, Volker. “Medical Thought in Ancient Greece and India: Comments on the Relation Between Social Organisation and Medical Ideology.” Cambridge Journal of Anthropology 12.3 (1987): 41–​66. Sivin, Nathan. “Text and Experience in Classical Chinese Medicine.” Knowledge and the Scholarly Medical Traditions, ed. Don Bates, 177–​204. Cambridge, New York: Cambridge University Press, 1995. Swift, Jonathan. An Account of a Battel Between the Antient and Modern Books in St. James’s Library. London: Nutt, 1704, 4th ed. 1705. Vesalius, Andreas. De humani corporis fabrica. Basel: Oporini, 1543. Williams, Ronald J. “Scribal Training in Ancient Egypt.” Journal of the American Oriental Society 92.2 (1972): 214–​221.

A

A N C I E N T S C I E N T I F IC T R A DI T ION S B E YON D G R E E C E A N D  ROM E

A1. Mesopotamia

chapter A1a

M esop ota mia n M athem at i c s Jens Høyrup

1.  Social Base and Role, and Gross Development The complex we now call “Mesopotamian mathematics” was shaped in the late fourth millennium bce (this, and all following dates use “middle chronology”) during the so-​ called proto-​literate period, alongside a logographic script. The only function of both was to serve in accounting. The context in which the complex emerged was the first formation of a bureaucratic state in southern Iraq around the city Uruk (map A1a.1). Writing, accounting, and calculation were the responsibility and privilege of the manager-​priests of the temples, who used the techniques in the calculation and control of land distribution to high officials, of rations in kind to workers, and of necessary ingredients in the production for instance of beer (one of the acceptable ways to make barley consumable for humans) (Nissen, Damerow, and Englund 1993). The mathematical techniques were based on notations for a counting sequence and for metrologies for lengths, for areas (geared to length measures), for capacity, and for time (namely, an administrative calendar used for the allocation of fodder and perhaps rations, decoupled from sun and moon). The number system had a base 60 (or rather, alternatingly 10 and 6, in the same sense as the Roman numeral system has alternating bases 5 and 2); the metrologies had step factors that were fairly convenient within the sexagesimal counting system (as the factor 12 between inch and foot) but were not themselves sexagesimal, which indicates that they had been created as normalizations of preexisting “natural” measures. We also have evidence of the computation of rectangular and near-​rectangular areas from the sides—​the former as inherent in the gearing

12    Ancient Scientific Traditions Beyond Greece and Rome

Map A1a.1  Sumerian and Babylonian sites. Ancient World Mapping Center.

of the metrologies, the latter by means of the “surveyors’ formula,” average length times average width. The evidence comes almost exclusively from discarded clay tablets that were used as filling material. This evidence is obviously incomplete yet complete enough to provide a good picture of mathematical practice. In particular it is clear that mathematics was taught in direct emulation of accounting routines: the only teaching texts we have are “model documents”—​texts that lack an official’s seal and have nicer numbers than could be expected in real-​life accounting but are otherwise indistinguishable from genuine accounting documents. Due to the pioneering efforts of Jöran Friberg (1978; 1979) and the computerized analysis of the complete corpus by Peter Damerow and Robert Englund (1987) we understand the numerical and metrological notations better than the linguistic aspect of the script. The temple-​centered Uruk state had an ill-​documented breakdown in the early third millennium. During the ensuing “Early Dynastic” period, a polycentric system of city-​ states emerged, in which political power was taken over by a king (a military leader) and the temples became subordinate. For a couple of centuries, written evidence is almost completely lacking, but around 2600 bce we find new accounting material from Ur (First Dynasty of Ur, famous for its Royal Tombs), and soon afterward much more from the city Shuruppak (shortly before that we also have the earliest royal inscription).

Mesopotamian Mathematics   13 It is clear from Ur and Shuruppak that neither the writing tradition nor the mathematical techniques had been extinguished—​their absence from the horizon during the intermediate centuries can only in part be due to rarefaction of the tradition. But Shuruppak (from whose epoch we also have the first literary texts, a proverb collection and a hymn [Biggs 1974]) tells us much more. First, scribes turn up as a particular profession (growing out of but also away from the class of temple managers), moreover with professional specializations (contracts written by one scribe refer to the presence of another one responsible for mensuration). We also find an innovation in mathematics education: “supra-​utilitarian” problems, that is, problems that seemingly deal with practice but would never turn up in real-​life scribal work. They do not represent theory. From a modern perspective they look like “mathematics for fun,” in the style of riddles; at the time, their function was rather to manifest professional identity through testing and display of the scope of a professional tool (just as the writing of literary texts tests the other main tool); and it would be mistaken to impose a dichotomy pure/​applied. One example asks for the distribution of the contents of a “granary”—​known to consist of 40∙60 “tuns” of 8∙60 “liters” each—​in rations of 7 “liters”; it exists in two copies, one of which is answered correctly, while the other calculation is either incomplete or wrong (Høyrup 1982). The merit of the problem is the division of a huge quantity by a factor that is at odds with the metrology (and which was never used in administrative practice). From Shuruppak we also have the first “table of squares”—​geometrical squares, given in area metrology, corresponding to sides given in length measure. We know Shuruppak (or rather its last year) so well because the city was destroyed in a military attack. The next informative phase is the “Old Akkadian period” (2335–​2193), during which first southern Iraq, and then for a while a much more extensive area, was united into or controlled by a single regional state established by Sargon of Akkad (the so far unidentified city in central Iraq which gave its name to the “Akkadian” language, of which Babylonian is a dialect). Scribes and scribal culture lost nothing of their importance because of the change. Literature, invented in the preceding period as an expression of scribal identity, was adopted as royal propaganda bolstering the legitimacy of the new state. Supra-​utilitarian mathematics could serve no similar purpose. However, the scale of administration and accounting grew (Foster 1982). Moreover, the epoch has left a number of supra-​utilitarian school problems about area calculation—​for instance, asking for one of the dimensions of a rectangle of which the area and the other dimension are known (Foster and Robson 2004). These problems are not “striking” or “funny,” and they may perhaps reflect autonomization of mathematics teaching from immediate practice rather than the formation of professional identity. In any case, they contain the rudiments of a specific vocabulary for problem solution (on which more below). In spite of the incipient introduction of supra-​utilitarian problems, Early Dynastic and Sargonic mathematics was first of all an accounting and mensurational technique, and thus centered on metrology. A  new weight metrology was created from scratch, with all step factors equal to 60—​except for the step between the “shekel” and the “barleycorn,” which differed by a factor 3∙60 (obviously because the barleycorn is

14    Ancient Scientific Traditions Beyond Greece and Rome a natural measure that could be normalized but not changed radically). The same trend of “sexagesimalization” can be seen in the upward and downward extension of existing metrologies. However, when a Sargonic “royal” capacity metrology was introduced—​probably not meant to replace the local metrologies but to serve royal administrative purposes—​the traditional structure was only modified to fit bureaucratic procedures, which were allowed to overrule the purely mathematical rationality of sexagesimalization. The next centralization of power, under the Third Dynasty of Ur (2112–​2004; or Ur III), overcame the contradiction between mathematical and bureaucratic rationality, and thereby did much more. The context was a centralized economy (established ca 2075, probably as part of a military reform); a large fraction of production was taken care of by workers’ troops managed by overseer scribes—​how large is disputed and probably undecidable because production outside state management would leave relatively few written traces. The scribes were responsible for the output of their crew, calculated according to fixed norms in units equivalent to 1/​60 of a working day, or corresponding amounts of grain or silver—​the debit being calculated from the number of workers (male, female, children) allotted to the overseer and borrowed from other crews, the credit from the yield and from the number of workers who were loaned to other scribes or who were ill, deceased, or in flight. The overseer’s yearly deficit was accumulated, and if at his death his family could not cover it, its members and household slaves would be thrown into the labor troops as slaves—​“that deficit is (therewith) resolved,” as one accounting text states (Englund 1991, 268). In its principles (Englund 1990, 13–​90), the accounting system was thus not far from double-​entry bookkeeping. Its use asked for a huge amount of calculations. As a simple illustration, we may think of the task of carrying the bricks of a certain type for a wall of given dimensions over a certain distance. Even if one knew how much a worker was supposed to carry a day, to find the corresponding number of working days would be prohibitively complicated if calculations were made in traditional non-​sexagesimal metrologies. The solution was the creation of a new numeral system: a floating-​point place-​value system with base 60, accompanied by “metrological tables” translating all units and relevant multiples into place-​value multiples of a basic unit for each metrological system, and by tables of technical constants telling, for example, how many bricks of a given type a man could carry a unit distance in one day (say, a), and how many of them went into a unit volume (say, b). Then the dimensions of our wall would have to be expressed in place-​value numbers and multiplied together, the product multiplied by b and next divided by a. The multiplications could be made by means of tables of multiples, and the division as a multiplication by the reciprocal of a (technical constants were always chosen so as to possess a finite reciprocal); both tables of multiples and of reciprocals were learned by heart. Obviously, this floating-​point system was only used for intermediate calculations; final results were written down in the traditional notation, in which the order of magnitude was well-​defined. The basic idea of place-​value sexagesimalization had been experimented on for centuries, but all texts preceding Ur III that try to make use of it contain errors (Powell

Mesopotamian Mathematics   15 1976), showing that the system was not yet there. Without the complete system, including metrological tables and tables of multiples, reciprocals and technical constants, place-​value computation was of no use. Addition and subtraction, indeed, had no need for place-​value operations: they had been performed on some kind of reckoning board known as a “hand” at least since Shuruppak (Proust 2000; Høyrup 2002b). The planned introduction of a complete technical system, mathematical or otherwise, has few parallels until recent centuries. The “place-​value system” was, indeed, not only mathematical but also eminently social: it could only work if its users were thoroughly trained in an adequate teaching institution. Of this institution we know nothing except through its continuation in the ensuing “Old Babylonian” period—​but it must have been there from the start; comparison with such systems as the Assyrian military machine or modern railway structures, also technical as well as social, is thus not off the mark. The implementation of a place-​value system within a single generation may be confronted with the millennium or more it took for the Chinese rod numerals to give rise through spontaneous development to a genuine place-​value notation (Martzloff 2006, 185–​188). The cost (which the creators of the system hardly considered a cost) appears to have been complete elimination of the culture of mathematical problems and of supra-​utilitarian mathematics (Høyrup 2002c). As in proto-​literate times, the only mathematics teaching texts we know from the period are model documents and arithmetical tables probably meant for training. The Ur III Empire lost control of its peripheral conquests in 2025, and the core itself dissolved into smaller states in 2004. The initially leading successor (Isin) attempted to continue Ur III ideologically; to a gradually lessening extent, centralized management also persisted, but in the 18th century we see both increased weight of private management and an ideological impact of this change. The private person steps forward in a way that was unknown before—​private letter writing, private seals, and even personal tutelary gods turn up. In scribal ideology (as known from the texts used to inculcate professional pride in the scribal school), an ideal of being particularly human appears. This “scribal humanism” emphasized supra-​utilitarian abilities: ability to read and speak Sumerian—​the dead prestige language of the scribal tradition—​and familiarity with occult meanings of cuneiform signs. Mathematics used in surveying and accounting also enter the list, but the texts are not specific beyond that. However, mathematical texts are more informative. Throughout the Old Babylonian epoch (2000–​1600) the place-​value system and all its appurtenant tables were trained together with the determination of simple areas and volumes; from the city Nippur the material suffices to reconstruct the complete syllabus (Robson 2002; Proust 2008). All the more strangely, that level of sophisticated supra-​utilitarian mathematics that is commonly known as “(Old) Babylonian mathematics” is virtually absent from Nippur, where Sumerian literature was taught at the same time as simple multiplications (as also elsewhere); we must conclude that sophisticated supra-​utilitarian mathematics was not part even of the full normal curriculum but was only practiced in specialized schools (the texts in question are in an indubitable school format).

16    Ancient Scientific Traditions Beyond Greece and Rome The first evidence for the appearance of this kind of mathematics comes from 19th or very early 18th-​century Ur in the south (Friberg 2000) and from contemporary Mari in the extreme northwestern periphery (Soubeyran 1984). The mathematics of the texts from Ur seem to descend primarily from the Ur III tradition, but with two conspicuous innovations: it sometimes serves for the creation of supra-​utilitarian problems; moreover, these problems are sometimes structured in a rudimentary problem format, asking the question by means of the logogram en.nam, “what,” and stating that the result is “seen.” Already the Old Akkadian texts had “seen” results; but since they had asked the question by means of the possessive suffix .bi, “its [length, etc.],” absent from the Ur problems, direct transmission through the Ur III school is unlikely. Mari had never been part of the Ur III Empire, but at some moment it must have borrowed the place-​value system, superimposing it upon and amalgamating it with its own decimal counting system (as happened in much of the Syrian area, cf. Chambon 2011). Most of the mathematical texts that have been found are tables of multiples, inverses, and inverse squares. One, however, is quite different, namely a calculation (without problem format) of the famous “grain on a chess-​board problem” (though ascending only to 30, which was usual until the invention of chess). It shows where Old Babylonian mathematics teachers could find inspiration for supra-​utilitarian mathematics:  namely from traditions of mathematical riddles carried by practitioners’ traditions (in the present case probably traveling merchants—​Mari was on an important trade route). The important step, however, seems to have been taken in Eshnunna, a state in mideastern Mesopotamia that had been subject to Ur III between 2075 and 2025, and which in general appears to have been the cultural center of central Mesopotamia around 1800 (before the rise of Babylonia). The earliest mathematical Eshnunna text, from ca 1790, contains a problem about the subdivision of a right triangle (Baqir 1950a). It uses a format sufficiently close to that of Ur to suggest a connection and sufficiently different to exclude direct descent. More interesting is a rather large group of texts from ca 1775 (Baqir 1950b; 1951; 1962; al-​Rawi and Roaf 1984; Gonçalves 2015; etc.). On one hand, it shows familiarity with almost all the main problem types that characterize mature Old Babylonian mathematics, in particular the so-​called “algebra” (on which more below). On the other, it displays rather elaborate formats, homogeneous in subgroups but varying between these and unequally developed—​implying that a canonical way to write problems was deliberately sought but agreement had not yet been reached. Inspiration for problems was taken in part from the Ur III computational tradition, in part from riddles circulating among nonscribal, probably Akkadian-​speaking surveyors. Eshnunna was conquered and destroyed by Hammurabi’s Babylon in 1761 (and Mari in 1758). After that we know of no mathematical texts from the area, and its cultural role was taken over by Babylon; Hammurabi’s famous law code could have been directly inspired by one produced in Eshnunna around 1790. Perhaps because the Old Babylonian strata of Babylon are covered by ruins from later epochs, we have no evidence that Hammurabi also brought mathematics or mathematics teachers to Babylon.

Mesopotamian Mathematics   17 However, we do have sophisticated mathematical texts from the subsequent period. Almost all of them come from illegal diggings, and therefore only internal evidence allows us to determine their origin. However, a first division of the corpus into distinct groups was made by Albrecht Goetze (1945) on the basis of orthography; analysis of the terminology allows further refinement (Høyrup 2002a, 317–​361). A number of texts were produced in the former Sumerian cities Uruk and Larsa between the 1740s and the 1720s (by 1720 the south had seceded, and literate culture appears to have withered away). An interesting text from Larsa (AO 8862), roughly contemporary with a dated text from 1749, shows evidence of belonging to the earliest phase of a local development—​especially a vacillating terminology. Other texts belonging to the same orthographic group confirm this. Two distinct groups from Uruk seem mature. Both are highly standardized, reflecting a deliberate effort to develop a canonical format. However, almost everywhere a choice is possible, the choices of the two groups differ. The most likely explanation appears to be conflict or competition between two schools or teachers. On one account, however, all of these texts, and all others from the south, agree: although an oblique reference shows the idiom to be familiar, they never state that a result is “seen,” as done not only in the Old Akkadian texts but also in the problem texts from Ur and in many of the Eshnunna texts. The avoidance must be deliberate: what may have been brought to Babylon was reformulated to demarcate the southern developments from what (probably) was done in Babylon. After 1720, perhaps before, many scholars from the south went north, and from the 17th century we have a number of sophisticated mathematical texts from northern Babylonia. Some of these may draw on traditions coming from the south, while a group from the town Sippar seems (according to terminology and closeness to practical surveying habits) to be local (and thus somehow related to the Eshnunna group). In 1595, Babylonia fell first to a Hittite raid and next to Kassite warrior tribes. During the following centuries, traces of literate culture are rare, and the scholarly scribal tradition seems to have been kept alive in “scribal families.” These families conserved and systematized traditions concerned with language studies (not least Sumerian), omens, and medicine cum incantation; sophisticated mathematics appears to have been disregarded. Place-​value computation and the appurtenant metrologies may have been remembered. In any case, the Assyrian king Assurbanipal not only collected the scholarship of the scribal families in his mid-​7th-​century library but also boasted of being able to multiply and find reciprocals. Less scholarly calculators probably also kept place-​value calculation alive while developing new metrologies closer to the cares and ways of actual agriculture. In the 5th century it seems that some of the scholar-​scribes who were involved in the development of mathematical astronomy were also aware that sophisticated mathematics ought to be part of their interest. We have a few texts of “algebraic” character (in the same sense as in the Old Babylonian period), but their way to find Sumerian equivalents for Akkadian terms shows that these were reinventions; so, once more the inspiration appears to have been riddles belonging to Akkadian-​(or, by now, Aramaic-​) speaking surveyors.

18    Ancient Scientific Traditions Beyond Greece and Rome Another couple of such texts were produced in the 3rd century within the same environment. Terminology, topics, and methods show that they do not descend from the 5th-​century texts. Some of their characteristic problems turn up in Demotic Egypt at the same time; by then, Assyrian, Achaemenid, and Macedonian armies with their surveyors and tax collectors had been familiar visitors or masters of Egypt for half a millennium. All we may conclude is thus that the scholar-​scribes this time borrowed from practitioners whose activity also made itself felt in Egypt. In summary, accounting and mensurational mathematics had been a key ingredient in the formation of the first Sumerian state, and even when royal military power took over leadership in the Early Dynastic and Sargonic state, the scribal carriers of mathematical competence retained a high prestige—​(cf. Visicato 2000). During Ur III, scribal competence, also in accounting mathematics, was something the king boasted of possessing—​irrespective of the unpleasant social situation of those actually responsible for the accounts. Even during the mature Old Babylonian period, where accounting justice no longer served as legitimization of power, mathematical competence was still part of the same scribal curriculum as Sumerian literature, and thus shared the prestige of scribes. In those phases where independent scribal professional identity existed, it also found expression in the devising of supra-​utilitarian mathematics. All this changed after the collapse of the Old Babylonian system. Subsequently, scribal scholarship and mathematical practice appear to have separated, being carried by distinct social groups. In the first millennium, when written evidence becomes abundant again, scholar-​scribes became ritual experts and omen interpreters for the Assyrian rulers, whose correspondences with the scholars have survived. Material plan­ning and accounting was certainly no less important for the Assyrian Empire, but the names of those who took care of such matters have not been preserved—​they had no more cultural distinction than the practical calculators of Greco-​Roman antiquity, and they wrote alphabetically on perishable material, not as the prestigious scholars in cuneiform on clay.

2  (Old) Babylonian Mathematics, and Afterlife What is normally presented in histories of mathematics as Babylonian mathematics is the supra-​utilitarian level of Old Babylonian mathematics, perhaps mixing in some Seleucid text without making any temporal distinction; this is also what is contrasted with, and sometimes connected to, Greek (theoretical) mathematics. Actually, the scope of the higher level of Old Babylonian mathematics was wider than this—​see for example the texts in Neugebauer 1935–​1937; Neugebauer and Sachs 1945.

Mesopotamian Mathematics   19 d

b

a

s

b

P

Q

d/2

d/2

s

Figure A1a.1  Babylonian rectangle problem, similar to Euclid, Elements II.6. Drawing by author.

Not everything is supra-​utilitarian; we also find utilitarian problems about carrying bricks, the amount of dirt needed for a construction project, and so on—​calculations an Ur III overseer scribe had been accustomed to perform. But supra-​utilitarian problems were certainly central. Some of these had to do with the properties of the sexagesimal system—​for instance, an elegant method for finding reciprocals of difficult numbers. Many more, however, belong with the so-​called “algebra”. (I here summarize some of the main results of Høyrup 2002a.) It appears that the starting point for this discipline was a set of four problems about rectangles with a given area, for which was also known one of (1) the length, (2) the width, (3) the sum of length and width, or (4) the difference between these. (1) and (2) had already been dealt with in the Sargonic school; the trick by means of which (3)  and (4)  could be solved was probably discovered between 2200 and 1900 in an Akkadian-​speaking lay surveyor’s environment, within which the problems are likely to have circulated as professional riddles. The trick to solve (4) is shown in figure A1a.1: the area of the heavily drawn rectangle ⊏⊐(a,b) is known to be A, while the known difference between the sides is d = a−b. First, the difference is bisected, and the part P is moved to Q so as to form a gnomon together with the unmoved part of the rectangle. This gnomon still has area A. In its corner, the shaded square □(d/​2) is fitted in. This produces a completed square with area A + □(d/​2), whose side s is found. Joining d/​2 to s gives the length a of the rectangle, removing it gives the width b. The same trick can be used to find the side of a square □(c) if the sum □(c)+c = A of the area and the side is known—​we just observe that □(c)+c = ⊏⊐(c+1,c). Even this seems to have existed as a surveyor’s riddle. The problem, as well as the procedure, is easily translated into equation algebra. In the square-​plus-​side version it becomes

c 2 + c = A ⇒ c 2 + c + ½ 2 = A + ¼ ⇒ (c + ½)2 = A + ¼ ⇒ c = A + ¼ − ½

20    Ancient Scientific Traditions Beyond Greece and Rome (omiting negative numbers, which the Babylonians did not have). This is the primary reason that it has been customary to speak of “Babylonian algebra.” However, there may be better reasons (whether they are sufficient depends on taste and definitions). Indeed, the square and rectangle problems themselves are almost absent from the record. What we find are mostly complicated problems which, with transformations that correspond to linear equation manipulations, can be reduced to the simple problems, and others that do not deal at all with geometric entities but can be translated (as we may translate geometric problems into algebraic pure-​number questions). One example (VAT 8520 #1, Neugebauer 1935–​1937, 1.346) dealing with igûm and igibûm, a pair of numbers from the table of reciprocals, states in literal translation that the 13th of the accumulation of igûm and igibûm to 6 I have repeated, from inside the igûm I have torn out, ½ it leaves –​in symbols, if a is the igûm and b is the igibûm (whence a∙b = 1)

a − 6 13 (a + b ) =

1

2

.

This is transformed into a rectangle problem of type (3),

 (7a, 6b ) = 42, 7a − 6b = 6 1 2 ,

from which a and b are easily found. In other problems, prices, areas or volumes are represented by linear magnitudes. When H.  S. Schuster and Otto Neugebauer discovered this “algebra” around 1930, they took the geometric terminology to be a purely arithmetical imagery (as with us a “square number”), and Neugebauer (1936, 250) thought the so-​called geometric algebra of Elements II to be a translation of a Babylonian arithmetical technique into geometry, undertaken in order to save its results from the philosophical threat or “foundation crisis” assumed to have resulted from the discovery of irrationality. Once it is realized that already the Babylonian technique was based on geometry, Babylonian inspiration seems even more plausible, despite Arpád Szabó (1969, 455–​456)—​as a matter of fact, the diagram in figure A1a.1 only differs from that of Elements II.6 by the absence of a diagonal by means of which Euclid performs the construction instead of just “moving around” a rectangle. (The diagram of rectangle problem (3) is equally close to that of Elements II.5.) However, some difficulties remain. First, could the Greeks have known the Babylonian technique? This was doubted by Szabó, but the difficulty is worse than he knew, since what Neugebauer had spoken about was an Old Babylonian technique that had disappeared a millennium before Thales’s times. (The Seleucid texts make use of diagrams that do not correspond to Elements II, and the 5th-​century problems, formulated in discordant area-​and length-​metrologies, are equally irrelevant.) Second, Elements II solves no problems, at most its theorems can be claimed to correspond to algebraic identities, in which Babylonian texts (Old or Late) show no interest; this was also seen by Szabó. Third, we find nothing in Greek mathematics that

Mesopotamian Mathematics   21 corresponds to the fully developed Old Babylonian discipline, only counterparts (transformed into “identities”) of the original riddles. We know, however, that the riddle tradition was still alive in the Islamic Middle Ages, and even reached medieval India (Høyrup 2001). It has also left traces in the pseudo‒Heronian Geometrica collections. It is more than plausible that archaic Greeks encountered it in the same Aramaic-​speaking region that gave them their alphabet. As the alphabet, it was probably not only adopted but also adapted; in any case, the earliest certain Greek evidence we have for it is precisely Elements II—​the fragment of Hippocrates of Chios constitutes a plausible but indirect and not very informative trace, and oblique references in the Platonic corpus (Høyrup 1990) are no more certain. What we find here is not a technique but, so to speak, a critique of this technique, putting things on a metatheoretically firm footing and thus determining its possibilities and limits (Möglichkeit und Grenzen, in Kant’s words). This had been the aim of the Old Babylonian teachers to a very restricted extent only—​in order to serve the professional identity of scribes, what they did had to remain supra-​utilitarian: that is, to look relevant to the task of the calculating scribe, which had always been to find the right numerical answer. The limited amount of critique we find appears to be connected to pedagogical concerns—​for instance, in explaining the method of rectangle problem (3) as above, to point out that a and b are found by moving the same piece d/​2 back to its original position, for which reason it has to be removed before it can be joined. Early texts, indeed, do as above, and add before they subtract (for the Babylonians, as for us, this was the normal order); mature texts respect the concreteness of the procedure, doing it the other (concretely meaningful) way around. On the elementary level, it is no wonder that the Greeks borrowed part of the metrology of their Phoenician trading partners, some of which was again an adaptation of Mesopotamian metrology. The sexagesimal place-​value system was borrowed (along with many planetary parameters and information about observations) and used in Greek mathematical astronomy, though only for the fractional part of numbers (whence our “minutes,” “seconds,” etc.). During the Middle Ages and the Renaissance, it inspired several attempts to implement decimal fractions—​ultimately successful in Simon Stevin’s De thiende from 1585.

Bibliography Al-​Rawi, Farouk N. H., and Michael Roaf. “Ten Old Babylonian Mathematical Problem Texts from Tell Haddad, Himrin.” Sumer 43 (1984): 195–​218. Baqir, Taha. “An Important Mathematical Problem Text from Tell Harmal.” Sumer 6 (1950a): 39–​54. —​—​—. “Another Important Mathematical Text from Tell Harmal.” Sumer 6 (1950b): 130–​148. —​—​—​. “Some More Mathematical Texts from Tell Harmal.” Sumer 7 (1951): 28–​45. —​—​—​. “Tell Dhiba’i: New Mathematical Texts.” Sumer 18 (1962): 11–​14, pl. 1–​3. Biggs, Robert D. Inscriptions from Tell Abū Ṣalābīkh. Chicago: University of Chicago Press, 1974.

22    Ancient Scientific Traditions Beyond Greece and Rome Chambon, Grégory. Normes et pratiques: L’homme, la mesure et l’écriture en Mésopotamie. I. Les mesures de capacité et de poids en Syrie Ancienne, d’Ebla à Émar. Gladbeck: PeWe-​Verlag, 2011. Damerow, Peter, and Robert K. Englund. “Die Zahlzeichensysteme der Archaischen Texte aus Uruk.” In Zeichenliste der Archaischen Texte aus Uruk, Band II, ed. M. W. Green and Hans J. Nissen, Kapitel 3, 117–​166. Berlin: Gebr. Mann, 1987. Englund, Robert K. Organisation und Verwaltung der Ur III-​ Fischerei. Berlin:  Dietrich Reimer, 1990. —​—​—. “Dairy Metrology in Mesopotamia.” Iraq 53 (1991): 101–​104. Foster, Benjamin R. “Archives and Record-​Keeping in Sargonic Mesopotamia.” Zeitschrift für Assyriologie und Vorderasiatische Archäologie 72 (1982): 1–​27. Foster, Benjamin, and Eleanor Robson. “A New Look at the Sargonic Mathematical Corpus.” Zeitschrift für Assyriologie und Vorderasiatische Archäologie 94 (2004): 1–​15. Friberg, Jöran. “The Third Millennium Roots of Babylonian Mathematics. I. A Method for the Decipherment, through Mathematical and Metrological Analysis, of Proto-​Sumerian and Proto-​Elamite Semi-​Pictographic Inscriptions.” Department of Mathematics, Chalmers University of Technology and the University of Göteborg, no. 1978–​9, 1978. —​—​—. “The Early Roots of Babylonian Mathematics. II: Metrological Relations in a Group of Semi-​Pictographic Tablets of the Jemdet Nasr Type, Probably from Uruk-​Warka.” Department of Mathematics, Chalmers University of Technology and the University of Göteborg, no. 1979–​15, 1979. —​—​—​. “Mathematics at Ur in the Old Babylonian Period.” Revue d’Assyriologie et d’Archéologie Orientale 94 (2000): 97–​188. Goetze, Albrecht. “The Akkadian Dialects of the Old Babylonian Mathematical Texts.” In Mathematical Cuneiform Texts, ed. O. Neugebauer and A. Sachs, 146–​151. New Haven, CT: American Oriental Society, 1945. Gonçalves, Carlos. Mathematical Tablets from Tell Harmal. Cham, Switzerland: Springer, 2015. Høyrup, Jens. “Investigations of an Early Sumerian Division Problem, c. 2500 b.c.” Historia Mathematica 9 (1982): 19–​36. —​—​—​. “Dýnamis, the Babylonians, and Theaetetus 147c7—​148d7.” Historia Mathematica 17 (1990): 201–​222. —​—​—​. “On a Collection of Geometrical Riddles and Their Role in the Shaping of Four to Six ‘Algebras.’” Science in Context 14 (2001): 85–​131. —​—​—. Lengths, Widths, Surfaces:  A Portrait of Old Babylonian Algebra and Its Kin. New York: Springer, 2002a. —​—​—. “A Note on Old Babylonian Computational Techniques.” Historia Mathematica 29 (2002b): 193–​198. —​—​—​. “How to Educate a Kapo, or, Reflections on the Absence of a Culture of Mathematical Problems in Ur III.” In Under One Sky: Astronomy and Mathematics in the Ancient Near East, ed. John M. Steele and Annette Imhausen, 121–​145. Münster: Ugarit-​Verlag, 2002c. Martzloff, Jean-​Claude. A History of Chinese Mathematics. Corrected Second Printing. Berlin: Springer, 2006. Neugebauer, O. Mathematische Keilschrift-​Texte. Vols. 1‒3. Berlin: Julius Springer, 1935–​1937. —​—​—. “Zur geometrischen Algebra (Studien zur Geschichte der antiken Algebra III).” Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik. Abteilung B: Studien 3(2) (1936): 245–​259. Neugebauer, O., and A. Sachs. Mathematical Cuneiform Texts. New Haven, CT:  American Oriental Society, 1945.

Mesopotamian Mathematics   23 Nissen, Hans J., Peter Damerow, and Robert Englund. Archaic Bookkeeping:  Writing and Techniques of Economic Administration in the Ancient Near East. Chicago:  Chicago University Press, 1993. Powell, Marvin A. “The Antecedents of Old Babylonian Place Notation and the Early History of Babylonian Mathematics.” Historia Mathematica 3 (1976): 417–​439. Proust, Christine. “La multiplication babylonienne:  la part non écrite du calcul.” Revue d’Histoire des Mathématiques 6 (2000): 293–​303. —​ —​ —​ . “Quantifier et calculer:  usages des nombres à Nippur.” Revue d’Histoire des Mathématiques 14 (2008): 143–​209. Robson, Eleanor. “More than Metrology: Mathematics Education in an Old Babylonian Scribe School.” In Under One Sky: Astronomy and Mathematics in the Ancient Near East, ed. John M. Steele and Annette Imhausen, 325–​365. Münster: Ugarit-​Verlag, 2002. Soubeyran, Denis. “Textes mathématiques de Mari.” Revue d’Assyriologie 78 (1984): 19–​48. Szabó, Arpád. Anfänge der griechischen Mathematik. München and Wien: R. Oldenbourg /​ Budapest: Akadémiai Kiadó, 1969. Visicato, Giuseppe. The Power and the Writing: The Early Scribes of Mesopotamia. Bethesda, MD: CDL Press, 2000.

chapter A1b

Astral Scienc e s of An cient Mesop ota mia Francesca Rochberg

1. Introduction The histories of modern astronomy and astrology can rightly be said to begin in the area of southern Iraq known as Babylonia, but evidence of such division that we make between astronomy and astrology in the sense of science versus pseudo-​science is not apparent in any of its surviving evidence. The astral sciences in ancient Mesopotamia were a major part of cuneiform intellectual culture. Accordingly, the bulk of the evidence comes in the form of scholarly compendia, observational records, and predictive ephemerides. In the periods from which most astral scientific texts were produced, that is, the 7th century and the period after 500 bce, astronomy and celestial divination were the province of highly trained scribes in the employ of the royal court in Assyria, or later, in the major temples of Babylonian cities, particularly the Esagil Temple of Marduk in Babylon and the Rēš Temple of Anu, the sky god, in Uruk. Astral, planetary, and lunar phenomena were objects of study both as signs of future events and as phenomena in their own right. Noncyclical aspects of the phenomena (color, brightness, lunar haloes, parhelia, meteors) were observed, and cyclical appearances (planetary and lunar first and last visibilities, stations, lunar and solar eclipses) were eventually calculated according to mathematical schemes. Weather phenomena were also of interest to the scholars who specialized in astral science, both in divinatory and observational contexts. Systematic study of heavenly phenomena seems to have arisen in a context of state-​sponsored divination where the phenomena, both cyclical and noncyclical, were understood as portents for the king, his army, the economic prosperity of the state, and the status of surrounding enemy lands. Cuneiform astral science continued to develop and change after the fall of the Assyrian Empire (after 612 bce), remaining an important part of the life of temple scribes well into Hellenistic and Parthian times, when the astronomical knowledge of the “Chaldeans” came to be known

26    Ancient Scientific Traditions Beyond Greece and Rome and admired by Greek and Greco-​Roman intellectuals (e.g., Diodorus Siculus 1.81, 2.30–​ 31; Strabo, Geography 16.1.6; Philo, On Abraham 69–​7 1; and Josephus, Antiquities of the Jews 1.154–​168). Cuneiform astral scientific texts were thus part of an intellectual tradition committed to the idea of the stars as signs from the gods, useful, therefore, in prognostication of events for human society. In the period after 500 bce, not long after the emergence of mathematical astronomy, nativities appear in texts similar to Greek horoscopes, where aspects and events of an individual’s life were predicted from the situation of the heavens on the date of birth (Rochberg 1998). Cuneiform astral sciences were thus consistent in certain respects with later premodern Western astronomy and astrology. The Hellenistic astronomer Ptolemy, whose Almagest (Greek Syntaxis Mathēmatikē:  Mathematical Treatise, 150 ce) was the authoritative treatise on mathematical astronomy of antiquity, and during the Middle Ages and Renaissance as well, also composed the astrological treatise Tetrabiblos (Four Books; Greek, Apotelesmatiká: effects). Astrology was not a pseudoscience until the modern era; it was part of science.

2.  The Compendia of Cuneiform Astral Science 2.1  Enūma Anu Enlil (EAE) The systematic study and recording of astral phenomena as signs can be said to begin in the Old Babylonian Period (ca 1800–​1600 bce; Rochberg 2006; George 2013, nos. 13 and 14). Extant Old Babylonian celestial omen tablets contain signs of the moon, sun, and weather. That planetary signs were already of interest is indicated by the Old Babylonian origins of the Venus Tablet of Ammiṣaduqa (EAE 63). The association of the text with King Ammiṣaduqa of the Hammurabi dynasty in the 16th century bce is the result of the appearance of part of the eighth-​year name of that king in place of one of the omen apodoses (omen 10). Since this discovery by F. X. Kugler in 1912, the Venus Tablet became and remains a linchpin in the establishment of ancient Near Eastern chronology in the second millennium (de Jong 2012–​2013). The omens of EAE 63 are constructed from a sequence of synodic phenomena of Venus over a period of 21 years (the length of the reign of Ammiṣaduqa) formulated as conditional statements: “If Venus . . . ” together with associated events “then . . . ” In its extant form, however, the tablet does not preserve a complete list of Venus observations from the Old Babylonian period, but is a composite text, and includes alongside a number of genuine observational data (in the first ten omens) computed values for the phenomena and the periods of invisibility that themselves have been copied and corrupted in the long manuscript transmission. EAE 63 demonstrates an awareness that

Astral Sciences of Ancient Mesopotamia    27 five synodic cycles of the appearances of Venus (as evening and morning star, that is, morning rise and set and evening rise and set) occur every eight years (that is, every 99 Babylonian months minus four days). The text begins as follows: (Year 1) If on the 15th of Month XI (Šabaṭu) Venus disappeared in the West (Evening Last), remained invisible 3  days, and reappeared in the East on the 18th day of Month XI: Catastrophes of kings; Adad will bring rains, Ea will bring floods, one king will send greetings to another king. (Reiner-​Pingree 1975, 29)

The standard celestial divinatory compendium Enūma Anu Enlil was composed in the Kassite period (ca 1600–​1200 bce), redacted during the neo-​Assyrian period (745–​ 612 bce) and copied until the last centuries bce. It contained roughly 7,000 omens in roughly 70 tablets (an exact count cannot be determined because of different recensions and tablet numbering conventions), divided into sections for lunar, solar, planetary, fixed star, and weather phenomena. Lunar omens comprise nearly a third of the whole, tablets 1–​22. Tablets 1–​13 are the “visibilities of the moon” (IGI.DU8.A.ME ša 30), concerned with appearances and disappearances, but mostly focused on the first appearance of the moon (ina tāmartišu “at its appearance”). These first tablets of Enūma Anu Enlil reflect the importance of the lunar syzygies, that is, around conjunction (between last and first visibility, or between the 27th and the first of the month) and the day(s) of opposition (days 14 or 15; Verderame 2002a; 2000b). Tablets 15–​22 concern lunar eclipses (Rochberg-​Halton 1988), followed by the solar omens, tablets 23(24) to 29(30) (van Soldt 1995), solar eclipses in tablets 31–​35(36), and 44–​49 are the weather omens (Gehlken 2012). The stellar and planetary omens begin with tablet 50 (51) (Reiner and Pingree 1981), and the remainder of the planetary omens are not well-​preserved (Reiner and Pingree 1998; 2005). Many tablets of Enūma Anu Enlil had commented texts, mukallimtu: lit. “the one that shows/​reveals”; as well as a series of excerpts, called rikis girri Enūma Anu Enlil: “guide to Enūma Anu Enlil”; and a separate serialized commentary entitled Sin ina tāmartišu: “If Sin [the moon] at its appearance,” of at least seven tablets (Koch-​Westenholz 1999; Gehlken 2007). Systematic celestial divination spanned a period of nearly 2,000 years, and cuneiform celestial omen texts have been found over nearly the whole of the ancient Near East, at Mari, Hattuša, Emar, Alalah, Qatna, Nuzi, Susa, and Ugarit.

2.2 MUL.APIN The astronomical compendium of the early first millennium bce is the two-​tablet series entitled MUL.APIN: The Plow Star (Hunger and Pingree 1989). It catalogues and systematizes a wide variety of celestial phenomena, beginning with the names and relative positions of fixed stars in areas of the sky called the Paths of Enlil, Anu, and Ea (which amount to bands of declination), the dates of the stars’ heliacal risings,

28    Ancient Scientific Traditions Beyond Greece and Rome simultaneous risings and settings of certain stars and constellations, stars that cross the meridian (ziqpu stars), stars in the Path of the Moon (18 ecliptical stars), astronomical seasons, luni-​solar intercalation rules with fixed stars, stellar calendar, appearances and disappearances of the five planets, periods of planetary appearance, length of day scheme, and a lunar visibility scheme. Despite its primary interest in the phenomena themselves, hence our classification of the text as astronomical, the final section of MUL.APIN (II.iii.16–​iv.12) is devoted specifically to astral—​not lunar, solar, or weather—​omens. Both Enūma Anu Enlil and MUL.APIN attest to early Babylonian astronomy’s employment of a schematic calendar (12 30‒day months = 1 year), for example, in MUL. APIN’s catalogue of stellar risings and settings, as well as its description of an intercalation scheme based on coordinating the date of the heliacal rising of the Pleiades with the first visibility of the moon (MA II Gap A 1‒7). The Old Babylonian schematic, or ideal, calendar placed the cardinal points of the year at the midpoints of months (in the traditional order) XII, III, VI, and IX. The Assyrian tradition shifted the calendar year so that the vernal equinox fell in month I (Nisannu). Various methods of regulating the calendar are attested, notably in MUL.APIN II.ii.12 and 16, in which an intercalary month was added every three years, or 37 months, thus 1 year = 12 1/​3 (actual, not schematic) months = 364 days. By the 8th century bce, it was known that this value was too low. For the later history of Babylonian month and year lengths, see Britton 2007a. Approximations of the length of the solar year became progressively better after the 6th century. With the adoption of the 19-​year (Metonic) cycle (235 months = 19 years = 254 sidereal months), the length of the solar year was derived as 12;22,6,18.  .  .  months, a parameter that underpinned the calculation of the planets and the moon in Late Babylonian mathematical astronomical texts.

3  Quantitative Predictive Models Babylonian astronomy is characterized by the use of mathematical models for the calculation of periodic phenomena. The Babylonians favored numerical sequences, not geometric diagrams, to represent variations in astronomical phenomena. We therefore infer that they were not invested in accounting for how the moon and planets moved within the celestial sphere, a concept they apparently did not have, but rather to calculate in advance the positions and dates of synodic phenomena by means of linear arithmetic methods. One predictive model employed throughout the history of Babylonian astronomy used the continuous linear zigzag function. The zigzag function tabulates values at equidistant time intervals (such as an ideal month, or the solar year, or the synodic period of a planet). The tabulated values vary linearly between two extrema (the maximum M and minimum m) with a constant difference (d). The sequence of tabulated values will repeat after a certain number (Π) of time intervals and a certain number of values (Z).

Astral Sciences of Ancient Mesopotamia    29 Later modified and refined in various ways in Babylonian System B, such as by truncations, for example, in the lunar theory column φ for variable lunar velocity and its contribution to the Saros cycle (Brack-​Bernsen and Steele 2011), the zigzag function was applicable to many periodic astronomical phenomena, especially for the calculation of longitudes. Appearing somewhat later was the model that employed a step function, based on parameters for various lunar or planetary periods. The model (System A) using step functions tabulates positions, or dates, of phenomena one time unit apart and divides the 360o of the zodiac into parts, or zones, (α) in which the body assumes different rates of progress (w). The number of occurrences of the phenomenon (Π) stands in relation to the number of times it makes a revolution of the zodiac (Z).

4.  Early Babylonian Astronomy 4.1 Astrolabes A fundamental corpus of early Babylonian astronomical texts are called Astrolabes (Horowitz 2014). The earliest exemplar stems from the Middle Assyrian period (reign of Tiglath-​Pileser I, 1115–​1077 bce). This was probably already a copy from an earlier, perhaps Old Babylonian source, and the text was still being copied in the Seleucid period (3rd century bce or later). The term Astrolabe is a misnomer from the point of view that the cuneiform exemplars are not planispheric, but they do map out fixed stars, constellations, and even planets in various parts of the sky for the twelve 30-​day months of an ideal year. The groups of stars are defined by their locations with respect to the horizon and in the three paths (ḫarrānu) mentioned above. The Astrolabe stars comprise a group of three stars per month, one per path, for a total of 36 stars. The monthly rising of an Astrolabe star represents the important seasonal reappearance of the star in the appropriate path following its period of invisibility. Another feature of the Astrolabe texts is a numerical sequence of values for the length of daylight throughout the ideal 360-​day year. The sequence describes a zigzag function such that M = 4 minas, m = 2 minas, d = 0;20 minas and P = 12 ideal months, or the ideal 360-​day year. This daylight scheme underlies the calculation of the duration of lunar visibility at night, as seen in EAE 14.

4.2  EAE 14 Enūma Anu Enlil tablet 14 belongs to a group of early astronomical texts concerning lunar visibility. It provides tabulated values for the length of visibility of the moon each night for the 30 days of the two equinoctial months (when day and night are of equal length as the sun crosses the equator). The interest in duration of lunar visibility

30    Ancient Scientific Traditions Beyond Greece and Rome is undoubtedly tied to the ominous nature of the moon when visible. This table, and a second table in the same tablet that gives a supplementary tabulation of lunar visibility coefficients allowing calculation of lunar visibility in other months of the year, is underpinned by the arithmetical scheme for the variation in daylight found in the Astrolabe, based on the ideal year and the ratio of longest to shortest daylight of 2:1. Values are tabulated for each day of a schematic 30-​day month, showing a geometrical progression at the two ends of the function (values in lines 1–​5 double their preceding value, with the same feature being restorable at the end of the table, each value being 1/​2 its preceding value in that case). The remainder of the values shows a constant difference of 12, that is, increments of 12 up to day 15 and decrements to day 25, the difference representing 1/​15 of the length of night on the equinoxes (taken to be the 15th day of months XII and VI) when day and night are of equal length (6 bēru = 12 hours). EAE 14 generates values for the duration of lunar visibility in other months of the year by dividing the length of night by 1/​15, as before: 1/​15 (= 4, i.e., 4/​60 in the sexagesimal system) is therefore a coefficient for the lunar visibility. This is stated as such in MUL.APIN II.iii.13: “4 is the coefficient for the visibility of the moon” (further details can be found in Hunger and Pingree 1999, 44–​50). Many of these early Babylonian predictive texts continued to be copied and preserved in the Late Babylonian period, even after development and refinement of mathematical methods in the Late Babylonian Systems A and B lunar and planetary tables and procedures.

5  Late Babylonian Astronomy The rediscovery of Babylonian astronomy in the late 19th century by the Jesuits Joseph Epping (1835–​1894), Johann Nepomuk Strassmaier (1846–​1920), and Franz Xaver Kugler (1862–​1929) was enormously consequential both for the history of ancient astronomy and the history of science more generally. Historical chronology also benefited from the study of the cuneiform astronomical texts, because contemporaneous dated Babylonian astronomical data helped establish a secure chronological foundation for the Hellenistic period. Otto Neugebauer ([1955] 1983)  published the entire corpus of cuneiform ephemerides and procedure texts (see now Ossendrijver 2012), and then (Neugebauer 1975) incorporated the material into a synthetic treatment of ancient mathematical astronomy together with Egyptian, pre-​Ptolemaic, and Ptolemaic Greek astronomy. Since Neugebauer’s time, and due largely to his efforts, the mathematical astronomical texts hold pride of place in the history of ancient science for their quantitative and predictive nature, their use of period relations and number-​theoretic functions in the construction of predictive models for calculating periodic lunar and planetary synodic phenomena, and for the direct influence they had on Greek astronomy. Late Babylonian astronomy emerged as the culmination of a long tradition in which knowledge of the heavens was of continuous interest for over two thousand years.

Astral Sciences of Ancient Mesopotamia    31 Tables for the planets and the moon were designated tērsītu (computed tables) in a number of colophons. The tērsītu tables were intimately related to a group of procedural texts stating the arithmetical rules (algorithms) used to calculate their various columns (Ossendrijver 2012). Extant table texts and procedures date to the period from the mid-​5th century to the mid-​1st century bce, with the bulk of preserved tablets dating to the 2nd century bce. But there are pre-​Seleucid tables, such as those concerning eclipse possibilities in accordance with the Saros cycle (223 lunar months = 18 years= 38 eclipse possibilities). The 38 eclipse possibilities per Saros cycle are spaced at six-​month (33 possibilities) and sometimes five-​month (five possibilities) intervals, discussed in Aaboe et al. 1991. One such table, the Saros Canon, begins with an eclipse possibility in the reign of Cambyses (527 bce) and ends in the early Seleucid period (257 bce). Seleucid tables represent a planetary theory aimed at the prediction of dates (expressed as months and 1/​30ths of lunar months, or tithis) and positions (expressed as degrees with the 12 signs of the zodiac) of the visible planetary heliacal phenomena, that is, first and last visibility; first and second stations; and acronychal rising of the planets, and a lunar theory aimed at predicting the moments of syzygies (new and full moons), eclipses, the variation in the length of daylight, and, in the final columns of a lunar table, the intervals (expressed as time degrees, 1 UŠ = 4 min. of time) between the rising and setting of the moon and sun around new and full moon known as the Lunar Sixes. The Lunar Six phenomena are the following: (1) At the beginning of the month in the evening, NA = the time interval from sunset to moonset, when the waxing crescent moon is first visible after conjunction; in the middle of the month. (2) ŠÚ = in the middle of the month, the interval from moonset to sunrise when the moon set for the last time before sunset. (3) na (Akkadian abbreviation) = in the middle of the month, the interval between sunrise and moonset when the moon set for the first time after sunrise. (4) ME = in the middle of the month, interval between moonrise to sunset when the moon rose the last time before sunset. (5) GE6 = in the middle of the month, the interval between sunset and moonrise when the moon rose the first time after sunset. (6) KUR = at the end of the month, in the morning, the time interval from moonrise to sunrise, when the waning crescent moon is last visible before conjunction (Brack-​ Bernsen 1997 and Huber 2003 for an assessment of observation versus calculation of Lunar Sixes). The Lunar Six intervals were observed for many centuries, together with the passage of the moon by ecliptical norming stars, planetary synodic appearances, and passages of the planets from one zodiacal sign to another. This program of astronomical observation is reflected in an archive of nightly observations from Babylon beginning in the 8th century bce. Roughly 1,500 observation reports (diaries) are extant, though none from the 8th century have survived (see Sachs and Hunger 1988; 1989; 1996; Hunger 2001; 2006). Despite this wealth of observational evidence, it is still less than clear how the Babylonian lunar and planetary theories were constructed on the basis of these records, or how exactly the periods and period relations that underlie the tables were derived from observational data. Recognition of period relations such as the 19-​year cycle (above), or the Saros, was the basis for Babylonian mathematical astronomy. In the tērsītu tables, two types

32    Ancient Scientific Traditions Beyond Greece and Rome of recursive mathematical steps (algorithms) were applied for calculation of the synodic arc: System A, typified by the application of the step function, and System B by the zigzag function. The construction of both systems took place early in the Seleucid era, with chronological priority going to System A (see Britton 2007b, 125; Ossendrijver 2012, 116). Each scheme was independent of a cosmological model, yet entailed an understanding that heliacal appearances were the result of the distance (elongation) of the planet or moon from the sun. An intimate connection, therefore, was found between synodic arc (Δλ), or progress in longitude made by the planet or moon per synodic phenomenon, and synodic time (Δτ), or the time required for the body to complete a synodic cycle between successive phenomena of the same kind (e.g., first visibility to next first visibility). Late Babylonian astronomy rests on many centuries of both observational and theoretical study of the synodic phenomena of the moon and planets. We should not imagine that mathematical astronomy replaced other kinds of inquiry about the heavens, such as celestial divination or astrology (horoscopic nativities), in an ever-​progressing evolution toward science as it would be defined today. The astral sciences, including celestial and natal divination, that is, omens and horoscopes, were parts of a scholarly discipline sustained over two millennia by cuneiform scribes in both Assyria and Babylonia, one which exhibited both conservativeness in the preservation of older traditions and innovation. Our understanding of the relationship between cuneiform astronomical and astrological texts, particularly in the late period, as well as their general cultural and social context is incomplete and ongoing. Whereas the integral nature of astronomy and astrology in Mesopotamian antiquity is clear, developments in Babylonian astronomy cannot be reduced to their practical application for omens or horoscopy.

Bibliography Aaboe, Asger, J. P. Britton, J. A. Henderson, O. Neugebauer, and A. J. Sachs. Saros Cycle Dates and Related Babylonian Astronomical Texts. Transactions of the American Philosophical Society, 81. Philadelphia: American Philosophical Society, 1991. Brack-​Bernsen, Lis. Zur Entstehung der Babylonischen Mondtheorie. Stuttgart:  Steiner Verlag, 1997. Brack-​Bernsen, Lis, and John M. Steele. “14-​Month Intervals of Lunar Velocity and Column Φ in Babylonian Astronomy: Atypical Text C.” In The Empirical Dimension of Ancient Near Eastern Studies, ed. Gebhard J. Selz and Klaus Wagensonner, 111–​130. Berlin: LIT, 2011. Britton, John P. “Calendars, Intercalations and Year-​Lengths in Mesopotamian Astronomy.” In Calendars and Years: Astronomy and Time in the Ancient Near East, ed. John M. Steele, 115–​ 132. Oxford: Oxbow Books, 2007a. —​—​—. “Studies in Babylonian Lunar Theory: Part I. Empirical Elements for Modeling Lunar and Solar Anomalies.” Archive for History of Exact Sciences 61 (2007b): 83–​145. Gehlken, Erlend. “Die Serie DIŠ Sîn ina tāmartīšu im Überblick.” Nouvelles Assyriologiques Brèves et Utilitaires 4 (2007): 3–​5. —​—​—. Weather Omens of Enuma Anu Enlil: Thunderstorms, Wind and Rain (Tablets 44‒49). Cuneiform Monographs. Leiden and Boston: Brill, 2012.

Astral Sciences of Ancient Mesopotamia    33 George, Andrew. Babylonian Divinatory Texts Chiefly in the Schøyen Collection. Cornell University Studies in Assyriology and Sumerology 18; Manuscripts in the Schøyen Collection, Cuneiform Texts 7. Bethesda, MD.: CDL Press, 2013. Horowitz, Wayne. The Three Stars Each:  Astrolabes and Related Texts. Archiv für Orientforschung: Beihefte 33. Vienna: Universität Wien, Institut für Orientalistik, 2014. Huber, Peter J. “Babylonian Short-​term Time Measurements:  Lunar Sixes.” Centaurus 42 (2003): 223–​234. Hunger, Hermann. Astronomical Diaries and Related Texts from Babylonia. Vol. 5: Lunar and Planetary texts. Vienna: Österreichische Akademie der Wissenschaften, 2001. —​—​—​. Astronomical Diaries and Related Texts from Babylonia. Vol. 6:  Goal Year Texts. Vienna: Österreichische Akademie der Wissenschaften, 2006. Hunger, Hermann, and David Pingree. MUL.APIN:  An Astronomical Compendium in Cuneiform. Archiv für Orientforschung, no. 24. Horn, Austria: Verlag Ferdinand Berger & Söhne, 1989. —​—​—. Astral Sciences in Mesopotamia. Leiden, Boston, Köln: Brill, 1999. De Jong, Teije. “Astronomical Fine-​Tuning of the Chronology of the Hammurabi Age.” Jaarbericht Ex Oriente Lux 44 (2012–​2013): 147–​167. Koch-​Westenholz, Ulla. “The Astrological Commentary Sîn ina tāmartīšu Tablet 1.” Res Orientales 12 (1999): 149–​165. Neugebauer, O. A History of Ancient Mathematical Astronomy. 3 vols. Berlin and New York: Springer Verlag, 1975. —​—​—​. Astronomical Cuneiform Texts. 3  vols. Sources in the History of Mathematics and Physical Sciences. London:  Lund Humphries, 1955; repr. 2nd ed. Berlin and New  York: Springer, 1983. Ossendrijver, Mathieu. Babylonian Mathematical Astronomy:  Procedure Texts. New  York, Heidelberg, Dordrecht, and London: Springer, 2012. Reiner, E., and David Pingree. The Venus Tablet of Ammiṣaduqa. Babylonian Planetary Omens 1. Malibu: Undena, 1975. —​—​—​. Babylonian Planetary Omens 2:  Enūma Anu Enlil Tablets 50‒51. Bibliotheca Mesopotamica 2. Malibu: Undena, 1981. —​—​—. Babylonian Planetary Omens 3. Groningen: Styx, 1998. —​—​—​. Babylonian Planetary Omens 4. Cuneiform Monographs 30. Leiden: Brill, 2005. Rochberg, Francesca. Babylonian Horoscopes. Transactions of the American Philosophical Society, No. 88. Philadelphia: American Philosophical Society, 1998. —​—​—​. “Old Babylonian Celestial Divination.” In If a Man Builds a Joyful House: Assyriological Studies in Honor of Erle Verdun Leichty, ed. Ann Guinan, Maria de J. Ellis, A. J. Ferrara, Sally M. Friedman, Matthew T. Rutz, Leonhard Sassmannshausen, Steve Tinney, and M. W. Waters, 337–​348. Cuneiform Monographs, 31. Leiden: Brill, 2006. Rochberg-​Halton, Francesca. Aspects of Babylonian Celestial Divination:  The Lunar Eclipse Tablets of Enūma Anu Enlil. Archiv für Orientforschung Beiheft 22. Horn: F. Berger, 1988. Sachs, A. J., and Hermann Hunger. Astronomical Diaries and Related Texts from Babylonia. Vol. 1: Diaries from 652 bc to 262 bc. Vienna: Österreichische Akademie der Wissenschaften, 1988. —​—​—. Astronomical Diaries and Related Texts from Babylonia. Vol. 2: Diaries from 261 bc to 165 bc. Vienna: Österreichische Akademie der Wissenschaften, 1989. —​—​—. Astronomical Diaries and Related Texts from Babylonia. Vol. 3: Diaries from 164 bc to 61 bc. Vienna: Österreichische Akademie der Wissenschaften, 1996. van Soldt W. H. Solar Omens of Enuma Anu Enlil: Tablets 23(24)—​29(30). Leiden: NINO, 1995.

34    Ancient Scientific Traditions Beyond Greece and Rome Verderame, Lorenzo. Le Tavole I‒VI della serie astrologica Enuma Anu Enlil. Nisaba 2. Rome: Grafica Cristal, 2000. —​—​—​. “Enūma Anu Enlil Tablets 1‒13.” In Under One Sky: Astronomy and Mathematics in the Ancient Near East, ed. John M. Steele and Annette Imhausen, 447–​457. Alter Orient und Altes Testament, 297. Münster: Ugarit Verlag, 2002.

chapter A1c

Mesop otam ian Be g i nni ng s f or Greek S c i e nc e ? JoAnn Scurlock

The great flourishing of Greek science did not take place in a vacuum. Long before the conquests of Alexander, there was a significant Greek presence in the Near East, beginning with the planting of colonies in the eastern Mediterranean and Asia Minor in the 8th century bce. Descendants of these colonists apparently encountered Assyrian expansion at least once, when the Yaunaya (Ionians, i.e. Greeks) sent tribute to Sargon II (721–​705) from Cyprus. Eusebius also quotes Abydenos to the effect that Sennacherib (704–​681) battled and defeated an Ionian Greek fleet (FGrH 685 F 5, §6; see also: Scurlock 2004a, 10; especially Röllig 1971, 643–​647; and Braun 1982b, 1–​31). Cultural contacts expanded dramatically with the founding of Naukratis to house Greek mercenaries. Greek armor was found at Carchemish (Braun 1982a, 49; Wiseman 1991, 230)  where the final battle of the fall of Assyria (614–​605 bce) was fought. Contacts between Greeks and non-​Greeks in the ancient Near East, particularly Egypt, intensified further as Athenians supported Egyptian revolts against the Persian Empire. A Babylonian named Berossos wrote a history of his land in Greek for the edification of his patron, Antiochus I (FGrH 680; Burstein 1978). From later periods, we have the so-​called Greco-​Babyloniaca, that is, texts in Akkadian (i.e. Assyro-​Babylonian) language but written using the Greek alphabet with a view to giving Greek scholars who wanted to learn Akkadian access to the rich literary and scientific tradition of ancient Mesopotamia (Geller 1997). That Egyptian sciences reached Greece is well established, and it is beginning to be realized just how much of ancient Greek mathematical astronomy has an ancient Mesopotamian foundation (see Rochberg, in this volume). Beginning already in the Persian period, the mix of cultures in the ancient Near East produced the Hellenistic science par excellence, and that was astrology, with its sister science of astrological medicine (Scurlock and al-​Rawi 2006), which allowed illness associated with conjunctions of the planets to be averted by using the right wood as a fumigant, the right plants and

36    Ancient Scientific Traditions Beyond Greece and Rome other ingredients as a salve, and wearing the right stone as a charm (Finkel 2000, 212–​ 217; Heeßel 2005).

1. Āšipu and Asû: Iatros and Pharmakopōlēs In ancient Mesopotamia, there were two separate medical experts who worked together to diagnose and treat illness; so, too, in Greece, the division of labor was quite similar (Scurlock 1999; 2005, 304–​306). The āšipu was, roughly speaking, the equivalent of the modern physician and the Greek iatros, whereas the asû corresponds to the modern pharmacist and the Greek pharmakopōlēs. These correspondences are not, however, exact. The modern physician does not think of himself as a philosopher, whereas the ancient Greek iatros did. The āšipu fell into the middle ground between these two poles, practicing medicine rather than philosophy but on occasion, as in the passage cited below, waxing philosophical about his craft. All physicians are frustrated that babies are hard to diagnose and that the impending death of elderly patients is all too clear. This inspired one ancient Mesopotamian physician to write this meditation on “evil death”: When a human being is born/​comes out of the womb, nobody can recognize its signs. [Only later] do they become apparent. It is as if they grow fat with him and grow tall with him. . . . The illness of that illness is a thing that can never be removed, the evils of that illness, of that false sleep. (Böck 2007, 223, lines 3–​7 with Scurlock 2011, 98–​99).

Like his modern colleague, the āšipu was the one expected to diagnose illnesses and, again like the modern physician, he prescribed medicines to be delivered to the patient by the pharmacist. However, modern physicians do not make a regular practice of directly providing patients with needed medicines, whereas the āšipu apparently frequently made up and administered medicinal preparations to his patients himself. Like modern physicians, he also gave a prognosis and, in hopeless cases, forbade his colleague the pharmacist from offering quack cures to desperate patients or their friends and relatives. For those who had simple problems not requiring diagnosis, or who knew from sad experience what was wrong, or who had gotten the ancient equivalent of a prescription from a physician, there was a second healing specialist known as the asû, the equivalent of the pharmakopōlēs and the European pharmacist. There were a thousand or so medicines known to ancient Mesopotamians, mostly plants or plant parts, but also animal and mineral substances; the asû needed information about supply, the right time to collect them, and how to store and process them for maximum efficiency. Like the physician, the pharmacist also had a stock of recitations to use to ensure the efficacy of

Mesopotamian Beginnings for Greek Science?    37 the treatments he sold customers. Like the physician, he experimented with his plants to determine the most efficacious for specific medical conditions. There were, of course, midwives and unofficial experts, many of them probably also women. It is unfortunate that we shall probably never know to what extent the temple of the goddess Gula at Isin (modern Išān al-​Baḥrīyāt in Iraq) provided an alternative locus of treatment. The site was under excavation but has now been completely destroyed (due to illicit excavations and looting in the wake of the 2003 American invasion). In ancient Greece, there was definitely an alternative to the Hippocratic iatros in the form of the asklepieion where patients came to spend the night and hopefully to receive the treatment of their dreams. Young boys from priestly families being groomed as physicians studied long hours in their own or relatives’ houses, passing through several grades of apprenticeship before being allowed to practice (Maul 2010). Along the way, much time was spent copying (Finkel 2000) and making commentaries on texts relevant to the discipline. So, too, Hippocratic physicians (Scurlock 2004b, 5–​7). It has been argued that Dioscorides was the “inventor” of the schema of organization of plants by medical use (Riddle 1985, 22–​24). In fact, the tradition goes back to the third millennium bce in the ancient Near East (Neumann 2010, 4). Neo-​Assyrian exemplars indicate that the pharmacist’s stock in trade included vademecum texts, that is, listings of plants with instructions for preparation. A typical entry from a vademecum text reads: pirʾi eqli is a plant to remove opaque spots in the eye. It is to be ground and [put] on the opaque spot. (BAM 423 i 9')

There are also two fragmentary works known to us by their ancient names, Šammu šikinšu (literally, the plant, its nature), which gave descriptions of plants, and URU. AN.NA, which was essentially an ancient plant glossary providing information on synonyms and substitutions. Šammu šikinšu prefixes to the medical use a description of the plant using the rudiments of a system of plant taxonomy (similar to Dioscorides, whose manuscripts add drawings). This allows an unknown plant to be described in terms of known plants with distinctive heads, leaves or seed pods. So, for example: The plant which resembles supālu and whose seed is red is called ellibu. It is good for removing limpness and numbness. You grind it and rub him gently with it (mixed) with oil. The plant which resembles duḫnu-​millet is called anunūtu. It is good for ears that produce pus. You grind it and pour it into his [ears] (mixed) with oil. (SpTU 3.106 i 1'-​4')

Some entries also give specific reference to habitat: The plant which resembles laptu-​ vegetable but which continually seeks out the front side (i.e., the plant turns to face the sunlight), and which comes up in irrigated fields and which when you pull it up, its root bends [is called] liddanānu. (SpTU 3.106 i 19'-​21')

38    Ancient Scientific Traditions Beyond Greece and Rome It is clear that these ancient Mesopotamian texts were written and read as practical manuals. In contrast to the Hippocratic iatros and more in line with the modern physician, the āšipu had a philosophy of “use whatever works”. A long tradition of experimentation revealed that many plants and other natural products have medicinal properties. Ancient Mesopotamians did not know that plants developed these properties to defend themselves against insects as, for example, by targeting their predators’ central nervous systems. What they did know was that plants could effectively be used to treat patients for quite a wide variety of diseases and conditions. Where plants are well attested, and we have some idea of what they were, we are in a position to understand just how sophisticated herbal medicine can be. For kamantu, which has some 97 references in ancient Mesopotamian therapeutic texts and which is probably henna, we can account for every medical use by the āšipu (Scurlock 2007). For example, in gynecological use, the āšipu ground the seed of kamantu, mixed it with first quality beer and used it in a potion “to have seed.” Hellenistic Greek physicians were in agreement with the āšipu that women and men had “seed” (Stol 2000, 8). Indeed, given Greek “folk” tradition which held that the woman was the oven where the man baked his loaves (as in the tale in Herodotus 5.92.η2–​3), it is not unlikely that the idea of women’s “seed” reached the Greeks from Mesopotamia (Scurlock 2006a, 175). What “having seed” meant in practical terms is that the woman had regular periods and was able to bear live children. Modern studies of henna have shown (Scurlock 2007, 517–​518) that it is an oxytocic drug. Oxytocic drugs stimulate uterine contractions and the ejection of milk, slightly lower blood pressure, and slightly dilate coronary arteries. In women who are not pregnant, they increase the tone, amplitude, and frequency of uterine contraction, thus bringing on menstruation. However, the uterus is resistant to oxytocic drugs during the first and second trimesters of pregnancy, which allows a fertilized egg to develop. As the pregnancy progresses, the susceptibility of the uterus also increases. What this means is that administering an oxytocic drug like kamantu in the third trimester of pregnancy will amplify uterine contractions, thus allowing the baby to be born (Scurlock 2007, 517–​520). Thus the āšipu’s use of herbal medicines to regulate female fertility was well-​founded. Similarly, ancient Mesopotamian physicians were quite right to prescribe date kernels, which contain plant estrogens, for irregular menstruation (BAM 237 i 25’); and to use šūmu-​garlic (Allium sativum L.), which is a vasodilator, in combination with zibû-​ black cumin (Nigella sativa L.), which is antihistaminic, to treat ghost-​induced tinnitus (roaring in the ears; for more details on the diagnosis and treatment of tinnitus see Scurlock and Stevens 2007).

2.  Diagnostic and Prognostic Series In division of specialties, uses of commentaries, and the practice of generating herbal handbooks, ancient Mesopotamia is in line with the Greek world. Numerous parallels

Mesopotamian Beginnings for Greek Science?    39 down to the level of language between ancient Mesopotamian therapeutic texts and the Hippocratic Corpus (Scurlock 2004a, 14–​15) strongly suggest some sort of meeting of the minds. The same may be said for the ancient Mesopotamian Diagnostic and Prognostic Series, a set of 2 tablets containing medical omens and a further 38 tablets explaining how to diagnose and prognosticate diseases and conditions on the basis of signs observed by the āšipu or symptoms described to him by his patients (Scurlock 2014, 13–​271). Tablet 36 of this series offers many predictions of the sex of a fetus, based on difficulties experienced by the expectant mother, that appear in later classical authors almost verbatim, albeit with the sexes reversed (Mesopotamian: Scurlock and Andersen 2005, 277–​279; classical: Hanson 2004, 298). The Diagnostic and Predictive Series had been systematized by the reign of the Babylonian king Adad-​apla-​idina (1068–​1047 bce). We know the name of the editor, Esagil-​kīn-​apli (Finkel 1988). Ancient Mesopotamian diagnosis was based on face-​ to-​face examination of the patient, soliciting symptoms by asking pertinent questions and noting signs by looking carefully at the patient’s color, general appearance and movement; examining his feces, urine and vomitus; listening to his breathing and bowel sounds; feeling his temperature and body configuration; and noting the odor of his breath and of infected wounds. (For more details and myriad examples, see Scurlock and Andersen 2005.) Ancient Mesopotamian āšipus generated a special vocabulary to describe medically significant signs (e.g., different types of pain, paralysis, spontaneous movement, and skin lesions). They knew how to tell whether a woman was pregnant by looking for what we understand to be chemical changes in the womb (Reiner 1982; Scurlock and Andersen 2005, 262) compared with inserting a garlic clove into the vagina and then checking to see whether her breath smelled of garlic—​a method favored by Hippocratic and Egyptian physicians (Hanson 2004, 296–​297). Ancient Mesopotamian physicians also devised a number of diagnostic maneuvers, for instance, what modern physicians call the Moro test, which is used to this day to evaluate the neurologic system of infants: “If you suspend an infant by his neck and he does not jerk and does not stretch out his arms, he was ‘gotten’ by the dust” (i.e. he will die) (Scurlock and Andersen 2005, 341). The Diagnostic and Prognostic Series contained information on the development of symptoms over the course of a disease, in some cases, day by day and in others five-​day period by five-​day period. There were also sections that helped the āšipu to distinguish one disease or condition from another similar disease or condition, what we call differential diagnosis (Scurlock and Andersen 2005, 575–​576). Of the 38 purely medical tablets in this series, 12 went systematically down the body in head to toe order, that is, signs and symptoms relating to the head were listed first, beginning with the patient who had been sick for one day and the top of whose head felt hot but whose temporal blood vessels were not pulsating. The listings continue with signs and symptoms of the neck and so on down the body to the toes ending with signs relating to the blood vessels of the feet. These listings were followed by tablets on fever, neurology, obstetrics and gynecology, and pediatrics (Scurlock and Andersen 2005, 575–​677, charts).

40    Ancient Scientific Traditions Beyond Greece and Rome On the neurology tablets, it is possible to recognize descriptions of what we call grand mal seizures, petit mal seizures, simple partial seizures, and complex partial seizures, in addition to sensory seizures, gelastic seizures, status epilepticus, and phases of seizures including the post-​ictal state, not to mention narcolepsy, cataplexy, stroke, and coma. Pseudo-​seizures were differentiated from the real thing. For example, complex partial seizures: If what afflicts him does so in close sequence and when it comes over him, he wrings his hands like one whom cold afflicts, he stretches out his feet, he jerks a lot and then is quiet, (and) he gazes at the one who afflicts him, “hand” of the binder. (Scurlock and Andersen 2005, 320–​322)

Then, gelastic seizures: [I]‌f when (a falling spell) falls upon him, he turns pale and laughs a lot and his hands and his feet are continually contorted, “hand” of lilû-​demon. (Scurlock and Andersen 2005, 322)

Third, pseudo-​seizures: If it afflicts him in his sleep and he gazes at the one who afflicts him, it flows over him and he forgets himself, he shudders like one whom they have awakened and he can still get up; alternatively, when they try to wake him, he is groggy, false “hand” of lilû. For a woman, a lilû; he can get up afterwards. (Scurlock and Andersen 2005, 435)

There is also a clinical description of what is now called Parkinson’s disease (similarly described by Parkinson in 1817): If his head trembles, his neck and his spine are bent, he cannot raise his mouth to the words, his saliva continually flows from his mouth, his hands, his legs and his feet all tremble at once, and when he walks, he falls forward, if . . . he will not get well. (Scurlock and Andersen 2005, 336–​337; with Scurlock 2010, 57)

Likewise, what appears to be Lesch-​Nyhan (described again in 1964): “If he chews his fingers and eats his own lips” (Scurlock and Andersen 2005, 163). A similar systematization of the therapeutic texts, with a matching series, also in head-​to-​toe order, seems to have taken place in the neo-​Assyrian period (943–​612 bce) (Scurlock 2014, 295–​336). Included in these therapeutic texts are everything from bandages for headaches, salves for fever, drops for sore eyes, fumigants for otitis media, distillate daubs for the lungs, enemas for intestinal gas, urethral irrigations for urinary tract problems, and tampons for irregular menstruation (Scurlock 2005, 310–​312; Heeßel et al. 2010, 45–​162; (Scurlock 2014, 361–​645). Making a distillate was devilishly simple. The plant mixture to be distilled went into a crescent-​shaped diqāru bowl, and a second, burzigallu, bowl with a hole bored into it was inverted over the top and sealed

Mesopotamian Beginnings for Greek Science?    41 round the rim with dough made from emmer flour. When the bottom bowl was put over a fire, the mixture boiled and distillate condensed onto the cool upper bowl where it was harvested by means of a straw inserted through the hole (Scurlock 2014, 465–​ 469, 480–​483).

3.  The Role of the Gods The problem, from our point of view, is that much of ancient Mesopotamian diagnosis was in terms of gods, ghosts, and demons and that the treatments included recitations, prayers, amulets, and even full-​fledged rituals alongside more conventional medical treatments. The āšipu also performed a variety of purification rituals for the community in connection with calendric rites or for individuals desiring success in business, an end to domestic quarrels, and other personal matters. We should not assume that the presence of supernatural causes is a sign of a pseudo-​ scientific approach and the dictation of inappropriate, even ridiculous, treatments as, for example, having the patient avoid food tabooed by Poseidon if you imagine him to have neighed like a horse during his seizure. This was, allegedly, the practice of ancient Greek sacred disease specialists (Scurlock 2004a, 12–​13). By contrast, the āšipu began by making a full assessment of his patient to determine whether or not he/​she had a case that he could treat. Having decided that he could treat it, he prescribed herbal medicines. The diagnosis ensured that the right medicines were going to the right patients and that whatever was causing the problem was forced or persuaded by the administration of the medicine to go away and leave her/​him alone. The parallel with modern germ theory is striking and, indeed, modern germ theory was greeted in some quarters as a revival of Babylonian demonology. For example, Jastrow states: This primitive germ theory has, in fact, a great advantage over the modern successor, for to the imagination of primitive man the germ is obliging enough to take on tangible shape. It does not hide itself, as the modern germ insists upon doing, so as to be discernible only when isolated and under the gaze of a powerful microscope, nor must its existence be hypothetically assumed. The ancient germ was not ashamed of itself; it showed its teeth and even its tail and its horns. The germ was a demon, an evil spirit that was sufficiently accommodating to sit for its portrait. (1917, 232)

The attribution of diseases to gods, ghosts, or demons was simply the āšipu’s way of subdividing broad categories of disease such as mental illness, neurological conditions, arthritis, skin diseases, heart and circulatory problems, illness due to trauma, and fevers. The result of the āšipu’s efforts was a system in which only a little over half of the syndromes could be assigned to already-​known spirits. Of the remainder, some were attributed to a malfunctioning body part, for instance “sick liver,” by which they meant what we call hepatitis. The rest were given a name based on some characteristic, for

42    Ancient Scientific Traditions Beyond Greece and Rome instance “stinking” for syndromes involving foul smell and grayish lesions in the mouth. (For more on this type of diagnosis, see Scurlock and Andersen 2005, 503–​506). As is the general rule in polytheistic religions, gods, ghosts, demons, malfunctioning body parts, or anything else that was causing trouble was believed to interact with humans in the hopes of being bought off. It is also generally the case, what we call omens (including the so-​called astrological omens) were not understood as causal factors triggering cosmic sympathies but as a language, or rather series of languages, whereby the spirits communicated with mankind (Farber 1995, 1899–​1900). It followed from this that the apparent omens represented by what we still call medical signs and symptoms were a code whereby a particular spirit could identify her-​or himself and his or her specific desires for offerings—​what we call medicines. In other words, if a particular spirit had a particular craving, he or she made someone ill through a particular set of symptoms known to the āšipu. Translated into our own “natural causes” idiom, what is happening in either case is that by producing symptoms, the body is telling you, as it were, in sign language, what is wrong so that you (or your doctor) can take appropriate action. The use of what we call “magic” was also of medical use to patients in that it treated the illness and the disease. In addition to diagnosing diseases and applying medicines, ancient Mesopotamian physicians also performed healing in a way that allowed the patient to see the doctor and his medicines in action and to personally participate in the healing process. Since it is the human body aided by the mind that is the single most important factor in medicine, this approach is not to be frowned upon. Magic is a self-​consistent system. The magical elements of Mesopotamian medicine were demonic magic (for details see Scurlock 2004a, 16–​20). Demonic magic is predicated on the notion that what makes rituals work is the more or less willing participation of sentient beings who operate by human logic and whose ways may be discerned by observation and experiment. Demonic magic is, then, a system of thought that, like polytheistic religion and modern “hard” science, is empirically rational, and a human universal in its general outlines. Mesopotamian physicians thus saw no contradiction (nor indeed was there any) in enlisting in the healing process, alongside more obviously medical pills, potions, bandages and enemas, also demonic “magic” and “religion.” The former (magic) included items such as historiolae (magic origin stories), threats and forced oaths, addresses in archaic or invented languages, and the employment of magical analogies. The latter (religion) involved sacrifices and respectful addresses in prayer asking for assistance to gods including patrons of magical and medical healing, such as the goddess Gula and the triad of gods Ea (god of freshwater and wisdom), Asalluḫi (god of medicine, equated with Marduk of Babylon) and Šamaš (sun god and god of justice). Indeed, preserved recitations are a mix of what to us is scientific knowledge and a no-​nonsense approach to treatment, with silly nonsense—​addressing the indwelling spirits in what we consider inanimate objects as if they were people, and appealing to gods in whose existence we do not believe. Witness the following charming recitations that describe (1) the process of digestion in ruminants, (2) human intestinal movement

Mesopotamian Beginnings for Greek Science?    43 (peristalsis) in a patient with intestinal bloating with gas, and (3)  the necessity for applying medicine and not just “magic” to medical problems. The sheep, when it vomits up [the grass], the mouth gives it to the karšu-​stomach, the karšu-​stomach to the riqitu-​stomach, the riqitu-​stomach to the rear; it falls as mere dung and the grass receives it. Grass which receives every evil receive mine from me and, grass, carry off my evil! (Scurlock and Andersen 2005, 117)

Human intestinal movements: The [.  .  .  are continually] loosened; the stomach is twisted; intestines are knotted . . . the darkness. Its face is like ditch water covered with algae. [Wind] from the steppe blows in, is put down, and roams the steppe. Its eyes (i.e., the greater and lesser omentum) are full; its “lips” continually dry out. It wriggles like a fish and makes itself bigger like a snake. When Gula, giver of life, brought mankind to the temple of Asalluḫi, merciful Marduk looked upon the young man and he belched and the young man got well. Either let the wind come out of the anus, or let it send out a belch from the throat. (Scurlock and Andersen 2005, 117–​118)

The need for medicine: The she-​goat is yellow; her kid is yellow; her shepherd is yellow; her chief herdsman is yellow; she eats yellow grass on the yellow ditch-​bank; she drinks yellow water from the yellow ditch. He threw a stick at her but it does not turn her back; he threw a clod at her but it did not raise her head. He threw at her a mixture of thyme and salt and the bile began to dissolve like the mist. The recitation is not mine; it is the recitation of Ea and Asalluḫi, the recitation of Damu and Gula. Recitation for pašittu. (Scurlock 2005, 313)

In short, the way to cure pašittu was not to throw sticks and clods at imaginary goats but to apply medicine reinforced by an appropriate recitation.

4. Conclusion In sum, ancient Greeks were familiar with ancient Mesopotamian medicine, and borrowed much from it. Unfortunately, it is also true that there would have been a lot less suffering over the course of the history of the Western world if the ancient Greeks had borrowed more than they did. All too often, Hippocratic physicians allowed their theories to dictate inappropriate and sometimes dangerous remedies, for example, using an anticoagulant to “stop” bleeding, cauterizing the armpits of athletes with dislocated shoulders after using a device similar to the torture rack to get the bones back into place, deliberately giving a patient acute pneumothorax to “treat” a pleural infection, or using a

44    Ancient Scientific Traditions Beyond Greece and Rome bow drill on a patient with a bruised bone to create a gap in the skull (!) (Majno 1975, 141–​ 206; Scurlock 2006a, 80–​81; cf. Scurlock 2004a, 24). Moreover, they rarely admitted the possibility of person-​to-​person transmission of disease (Scurlock 2004a, 25), something known in Mesopotamia since at least the second millennium BCE (Finet 1954–​1957, 129). Among Hippocratic treatments there is also a procedure that appears to have descended from a known Mesopotamian treatment for draining the lungs by making an incision and inserting a lead tube (Scurlock 2005, 312). But otherwise, in treating patients, the Hippocratic system was reductionist and minimalist, showing a strong preference for bleeding, purging and a starvation diet, after which nature was to be allowed to take its course. (For details, and comparison to ancient Mesopotamian regimens, see Scurlock 2004a, 13–​14.) However, there were ancient Greek doctors who based some of the finest medical observations ever penned on an ancient Mesopotamian foundation (Scurlock 2004a, 20–​24). And the biggest surprise is the partial acceptance of ancient Mesopotamian diagnoses with “supernatural” causes as a starting point for discussion—​minus, of course, the god, ghost, or demon originally in the text. So, for example, kausos is based, in conformity to expectations, on an ancient Mesopotamian diagnostic category without a supernatural cause. However, phrenitis is based on, of all things, “hand” of ghost (Scurlock 2004a, 14–​15, 27–​29). Indeed, one could argue that much of Greek medicine, including Aretaeus of Cappadocia and Soranus of Ephesus (Scurlock 2008, 195–​202), is incomprehensible without knowledge of the Mesopotamian texts to which ancient Greek scholars clearly had access.

Bibliography Böck, Barbara. Das Handbuch Muššuʾu “Einreibung”: Eine Serie sumerischer und akkadischer Beschwörungen aus dem 1.  Jt. vor Chr., Biblioteca del Próximo Oriente Antiguo 3. Madrid: Consejo Superior de Investigaciones Científicas, 2007. Burstein, Stanley M. The Babyloniaca of Berossus. Sources and Monographs from the Ancient Near East 1/​5. Malibu: Undena, 1978. Braun, T. F. R. G. “Greek Forces in Campaigns of the Saïte Dynasty.” In Cambridge Ancient History 3/​3, ed. John Boardman et al., 49–​52. Cambridge: Cambridge University Press, 1982a. —​—​—​. “The Greeks in the Near East.” In Cambridge Ancient History 3/​3, ed. John Boardman et al., 1–​31. Cambridge: Cambridge University Press, 1982b. Farber, Walter. “Witchcraft, Magic and Divination in Ancient Mesopotamia.” In Civilizations of the Ancient Near East, ed. Jack M. Sasson, 1895–​1909. New York: Scribner’s, 1995. Finet, André. “Les médecins au royaume de Mari.” Annuaire de l’Institut de Philologie et d’Histoire Orientales et Slaves 14 (1954–​1957): 123–​144. Finkel, Irving L. “Adad-​apla-​iddina, Esagil-​kīn-​apli, and the Series SA.GIG” In A Scientific Humanist:  Studies in Memory of Abraham Sachs, ed. Erle Leichty et  al., 143–​ 159. Philadelphia: University Museum, 1988. —​—​—​. “On Late Babylonian Medical Training.” In Wisdom, Gods and Literature: Studies in Assyriology in Honour of W.G. Lambert, ed. A. R. George and I. L. Finkel, 137–​223. Winona Lake: Eisenbrauns, 2000.

Mesopotamian Beginnings for Greek Science?    45 Geller, Markham J. “The Last Wedge.” Zeitschrift für Assyriologie 87 (1997): 43–​95. Hanson, A. E. “Aphorismi 5.28–​63 and the Gynaecological Texts of the Corpus Hippocraticum.” In Magic and Rationality in Ancient Near Eastern and Greco-​Roman Medicine, Studies in Ancient Medicine 27, ed. H. F. J. Horstmanshoff and M. Stol, 277–​304. Leiden: Brill, 2004. Heeßel, Nils P. “Stein, Pflanze, und Holz. Ein neuer Text zur ‘medizinischen Astrologie’.” Orientalia. New series 74 (2005): 1–​22. Heeßel, Nils P. et al. “Akkadische Texte des 2. und 1. Jt. v. Chr.” In Texte aus der Umwelt des Alten Testaments 5: Texte zur Heilkunde, ed. Bernd Janowski and Gernot Wilhelm, 8–​176. Gütersloh: Gütersloher Verlagshaus, 2010. Jastrow, Morris. “Babylonian-​Assyrian Medicine.” Annals of Medical History 1 (1917): 231–​257. Köcher, Franz. Die babylonisch-​assyrische Medizin in Texten und Untersuchungen. 6  vols. Berlin: W. de Gruyter, 1963–​1980. Majno, Guido. The Healing Hand: Man and Wound in the Ancient World. Cambridge: Harvard University Press, 1975. Maul, Stefan. “Tontafel Bibliothek aus dem sogenannten ‘Haus des Beschwörungspriesters.’” In Assur-​Forschungen, ed. S. Maul and N. Heeßel, 189–​228. Wiesbaden: Harrassowitz, 2010. Neumann, Hans. “Texte des 3.Jt. v.Chr.” In Texte aus der Umwelt des Alten Testaments 5: Texte zur Heilkunde, ed. Bernd Janowski and Daniel Schwemer, 3–​7. Gütersloh:  Gütersloher Verlagshaus, 2010. Reiner, Erica. “Babylonian Birth Prognoses.” Zeitschrift für Assyriologie 72 (1982): 124–​138. Riddle, John M. Dioscorides on Pharmacy and Medicine. Austin: University of Texas, 1995. Röllig, Wolfgang. “Griechen.” In Reallexikon der Assyriologie 3.4 (1971): 643–​647. Scurlock, JoAnn. “Physician, Conjurer, Magician: A Tale of Two Healing Professionals.” In Mesopotamian Magic: Textual, Historical and Interpretative Perspectives. Ancient Magic and Divination 1, ed. Tzvi Abusch and Karel van der Toorn, 69–​79. Groningen: Styx, 1999. —​—​—. “From Esagil-​kin-​apli to Hippocrates.” Le Journal des Médecines Cunéiformes 3 (2004a): 10–​30. —​—​—​. “The Hippocratic Treatise Humors, Chapter  1:  A Humerous Student Commentary,” Ktèma 29 (2004b): 5–​7. —​—​—. “Ancient Mesopotamian Medicine.” In A Companion to the Ancient Near East, ed. Daniel Snell, 302–​315. Oxford: Blackwells, 2005. —​—​—​. Magico-​Medical Means of Treating Ghost-​Induced Illnesses in Ancient Mesopotamia, Ancient Magic and Divination 3. Leiden: Styx-​Brill, 2006a. —​—​—​. Review of Marten Stol, Birth in Babylonia and the Bible: Its Mediterranean Setting. NIN 4 (2006b): 172–​180. —​—​—. “A Proposal for Identification of a Missing Plant:  Kamantu/​ÚÁB.DUḪ  =  Lawsonia inermis L./​‘henna.’” Festschrift für Hermann Hunger, Wiener Zeitschrift für die Kunde des Morgenlandes 97 (2007): 491–​520. —​—​—​. “Some Mesopotamian Medicine for a Greek Headache.” In Studies in Ancient Near Eastern World View and Society (Festschrift Marten Stol), ed. R. J. van der Spek, 195–​202. Bethesda, MD: CDL Press, 2008. —​—​—​. “Advantages of Listening to Patients: The First Descriptions of Parkinson’s.” Le Journal des Médecines Cunéiformes 15 (2010): 57. —​—​—​. “Ritual Rubbing Recitations from Ancient Mesopotamia.” Orientalia. New series 80 (2011): 83–​100. —​—​—​. Sourcebook for Ancient Mesopotamian Medicine. Writings from the Ancient World 36. Atlanta: Society of Biblical Literature, 2014.

46    Ancient Scientific Traditions Beyond Greece and Rome Scurlock, JoAnn, and Burton R. Andersen. Diagnoses in Assyrian and Babylonian Medicine: Ancient Sources, Translations and Modern Medical Analysis. Urbana: University of Illinois Press, 2005. Scurlock, JoAnn, and Farouk al-​Rawi. “A Weakness for Hellenism.” In If a Man Builds a Joyful House (Fs. Leichty), ed. Ann Guinan et al., 357–​382. Leiden: Styx/​Brill, 2006. Scurlock, JoAnn, and Dafydd Stevens. “A Ringing Endorsement for Assyro-​Babylonian Medicine: The Diagnosis and Treatment of Tinnitus in 1st Millenium BCE Mesopotamia.” Audiological Medicine 6 (2007): 4–​15. Stol, Marten. Birth in Babylonia and the Bible. Cuneiform Monographs 14. Groningen: Styx 2000. von Weiher, Egbert. Spätbabylonische Texte aus Uruk 3.  Ausgrabungen der deutschen Forscungsgemeinschaft in Uruk-​Warka 12. Berlin: Gebr. Mann, 1988. Wiseman, Donald J. “Babylonia 605‒539 b.c.” In Cambridge Ancient History 3/​2, ed. John Boardman et al., 229–​251. Cambridge: Cambridge University Press, 1991.

A2. Egypt

Chapter A2a

M athematics i n E g yp t Annette Imhausen

Egypt was among the first civilizations to develop a mathematical culture for which we still have written evidence today. Mathematics constituted an essential tool to administer available resources and was therefore pivotal to the development and success of Egyptian culture. This chapter begins with the invention of the script and number system—​both essential prerequisites for the development of more complicated mathematical techniques. This is followed by an overview of the characteristics of Egyptian reckoning techniques and examples from the main sources for our knowledge of Egyptian mathematics, the mathematical texts. However, mathematics also played a significant role within scribal culture, which is the focus of the following section. The chapter concludes with an overview of Egyptian mathematics in the Greco-​Roman periods, when Egyptian mathematical culture was connected with other mathematical cultures, most notably that of Mesopotamia.

1.  The Beginnings: Invention of Script, Numbers, and Metrological Systems As in later periods, evidence from Egypt usually originates from cemeteries (or temples), because these happened to be in desert areas, where excellent conditions existed for the preservation of artifacts. In contrast, only little evidence from cities has survived. Then, as in modern times, Egyptian settlements were located mostly in direct proximity to the Nile, that is, in proximity to water and humidity. Thus, modern settlements have been built on top of the ancient settlements and have rendered the latter unavailable for archaeological excavations. But even if this were possible, it is uncertain how much would have survived the moist conditions. Around the end of the fourth millennium bce, a social stratification of Egypt’s population can be traced based on evidence from cemeteries. Cemeteries from the late fourth

50    Ancient Scientific Traditions Beyond Greece and Rome millennium show large numbers of smallish-​sized one-​room tombs, fewer larger tombs with several rooms, and then some outstanding, large tombs with even more rooms. A good example of this variety of tomb sizes can be found at cemetery U at Umm el-​ Qa’ab, the necropolis of Abydos. And it is in this cemetery, in the artifacts of its largest tomb Uj, that the earliest evidence of writing in Egypt has been discovered (Dreyer 1998). It seems from the outset, writing was a tool used for the purposes of elites only. Early evidence suggests writing served to represent power and to administer goods when their amounts became too large to be overseen without a written record. Consequently, it is not surprising that numbers appeared with the first evidence of writing. The written evidence found in the tomb Uj is found on two types of objects. Ninety-​five vessels show one or two large format signs in ink (Dreyer 1998, 47), and 192 tablets (made from ivory, bone, and stone) bear either representations of quantities/​numbers or figurative signs that may possibly indicate their origins. The first evidence of the written representation of spoken language appears at the end of the Second Dynasty (evidence from tomb P of Peribsen at Umm el-​Qa’ab) around 2700 bce; the oldest extant papyrus originates from the tomb of Hemaka, an administrator under the First Dynasty pharaoh Den, but there was nothing written on it (Wilkinson 2001, 11)—​possibly Hemaka wished to take some writing material with him to the netherworld. The use of two writing systems continues in later Egyptian history with the hieroglyphic script, where signs were incised into stone objects, and also a cursive script (called hieratic), which was written with ink and a brush on papyrus, pottery shards, and other suitable surfaces. Hieroglyphs were used for monumental inscriptions, whereas hieratic was used for the kind of writing needed in daily life, like letters, administrative documents, literary and religious texts, and so forth. At the same time that the first writing appears, there is also evidence of writing numbers or quantities. The number system used in ancient Egypt can be described in modern terminology as a decimal system without positional (place-​value) notation. It used different signs for each decade from one to one million. Why the individual signs were attached to their specific numerical values seems somewhat arbitrary, however, some may have been the result of practice or observations. The number 1 is represented by a simple stroke , the sign for 10 is supposed to be the hieroglyph of a hobble for cattle . 100 is represented by a rope : from later periods, 100 cubits = 1 ḫt was used as a measure to determine the size of fields, a process shown in depictions in tombs of land measurements to be executed with a rope. 1,000 is represented by the hieroglyph of the lotus flower , 10,000 by the hieroglyph of a finger —​again, one could think of 10,000 as 10 times 1,000 and thereby create the association of our ten fingers. 100,000 was represented by the hieroglyph of a tadpole —​maybe from the observation that these appear in rather large numbers. The largest Egyptian sign for a number was that for 1,000,000, which was represented by a seated god with raised arms . Each of these signs was written as often as required to represent the specific number, for example, 205 would be written by writing the sign for 100 twice and the sign for 1 five times ( ). As in hieroglyphic script, the individual signs would be grouped appropriately. There was no sign for zero—​since the Egyptian number system was not positional. In a number like 205, it sufficed to leave out the symbol for 10 to indicate the absence of tens.

Mathematics in Egypt     51 The Egyptian number system was fully developed at the time of King Narmer (ca. 3000 bce; dates are according to Shaw 2000), as is documented by his ritual mace head, which was found at the temple of the god Horus at Hierakonpolis, the most important predynastic site in the south of Egypt. The object originated from a ceremonial context and the scenes represent King Narmer receiving a tribute consisting of bulls, goats, and captive prisoners. The numbers of each are indicated below them: 400,000 bulls, 1,422,000 goats, 120,000 captives. The symbols and method used to express these rather high numbers are the same as those employed later in hieroglyphic inscriptions. Thus, this mace head gives evidence for a fully developed number system before the First Dynasty (ca. 3000–​2890 bce). It also demonstrates that the number system was not only used for obvious administrative purposes but was also important in representational spheres of Egyptian culture. The period of the Old Kingdom (2686–​2160 bce) is usually considered to be the first cultural peak in the history of ancient Egypt, as documented by its output in art, architecture, and literature. It is hard to imagine that this could have taken place without the further development of mathematical techniques. The Great Pyramid of Giza, for example, which required several million limestone blocks for its construction, must have been a major logistic enterprise, hard to manage without the use of mathematics for architectural calculations (e.g., determining the relation of base, height, and inclination, or the amount of stones required). Furthermore, the logistics of a project of this scale (number of workers, rations of the workers and others) also obviously required some mathematics. Unfortunately, practically no information about mathematical techniques used at that time has survived. Despite this lack of direct evidence, however, there are several indications that mathematics did play a significant role during the Old Kingdom. Depictions in tombs regularly show scribes as administrators taking inventory of various goods. From these depictions it is obvious that literacy and numeracy were essential prerequisites for a bureaucratic career, as is also expressed in the scribal statues, a statue type found in the tombs of high-​ranking officials. This evidence documents the importance of scribes in the achievements of the Egyptian state, and at the same time their own awareness of their role. Depictions of market scenes, found in the decoration of a number of graves, inscriptions about land ownership found in another tomb, and two papyrus archives (Abusir and Gebelein) from the Old Kingdom prove the existence of several metrological systems, to measure lengths (e.g., of a piece of cloth), areas (of land), volumes (e.g., of grain, grain products, or beer), and weights. Another part of mathematics can be traced back at least as far as the Old Kingdom: fractions. The Egyptian concept of fractions, that is, parts of a whole, was fundamentally different from our modern understanding. This difference is so elementary that it has often led to a distorted analysis of Egyptian fraction reckoning viewed solely through the eyes of modern mathematicians, who marveled at the Egyptian inability to understand fractions as we do. However, the Egyptian system of fractional notations and their use in calculations can be understood by tracing the evolution of the Egyptian concept of fractions from its beginnings. The first Egyptian fractions consisted of a

52    Ancient Scientific Traditions Beyond Greece and Rome small group of specific fractions (3/4, 2/3, 1/2, 1/3 and 1/4) designated by individual special signs. These fractions are first attested within the context of metrological systems— that is, 3/​4 in 3/​4 of a finger (an Egyptian length measure), 1/​4 in 1/​4 of a sṯꜣt (an Egyptian area measure)—but they retain their notation in later times as abstract fractions (for a detailed account of these early fractional notations in Egypt and Mesopotamia see Ritter 1992). From this set of earliest fractions, a general concept of fractions seems to have developed. The list of earliest fractions comprises 1/​2, 1/​3, and 1/​4, and perhaps it may be inferred that, from this first set of specific fractions, all fractions generally came to be understood as the inverses of integers. As a consequence, the Egyptian notation of fractions did not consist of numerator and denominator, but only of the integer of which it was the inverse and a symbol indicating the inverse, that is, a fraction. The hieroglyphic sign that came to be used for this purpose was the sign for “part,” which was already used in the writing of 2/​3 and 3/​4. In order to designate a “general fraction” (always an inverse), it was placed above the integer of which the fraction was the respective inverse. In hieratic, this fraction-​marker was abbreviated to a dot. One of the first scholars of Egyptian fraction reckoning, Otto Neugebauer, devised a notational system that imitates this Egyptian notation (Neugebauer 1926): fractions (i.e., inverses of integers) are rendered by the value of the integer and an overbar to mark them as fractions. This notational system is close to the Egyptian concept and remains the best way of rendering Egyptian fractions. Following the concept of fractions as inverses of integers, the next step would have been to express parts that consist of more than one of these inverses. This was done by (additive) juxtaposition of different inverses, for example, what we write as 5/​6 was written in the Egyptian system as 1/​2 1/​3. The writing of any fractional number thus consisted of one or more different inverses written in descending order of size. Note that like our modern decimal notation of fractions, the Egyptian representation enabled a choice of the accuracy that was needed by considering only elements down to a certain size. It also allows for an easy comparison of the size of several fractions, for example, while the direct comparison of 5/​8 and 4/​7 only reveals that they are both a little more than 1/​2, their representation as Egyptian-​style fractions 1/​2 1/​8 and 1/​2 1/​14 allows for immediate comparison.

2.  Reckoning Techniques The Egyptian mathematical texts use specific technical terms for a number of operations. From these technical terms we can conclude that in Egyptian mathematics the following were distinguished: adding, subtracting, halving, doubling, multiplying, dividing, calculating a fractional part, squaring, and the extraction of a square root. For some of these operations several terms or variations of terms existed. The Egyptian mathematical texts allow us to follow the actual workings of multiplications and divisions, when they were carried out in writing. There is no evidence for the written execution of any of the other operations. Carrying out multiplications and divisions used the same formal

Mathematics in Egypt     53 scheme of two columns. Each multiplication begins with an initialization, marked by a dot in the first column, and one of the multipliers in the facing column. The multiplication is then carried out by using a series of techniques operating simultaneously on both columns so that the other multiplier is found by adding respective values in the first column of suitable rows; the sum of the corresponding entries in the second column will yield the answer to the multiplication. From row to row, one of a number of techniques is used, most prominently doubling, halving, and decupling. Divisions use that same formal layout of two columns. The first row (initialization) again holds a dot in the first column and the divisor in the second column. This first row is then manipulated with the same techniques used in multiplications until the addition of respective rows of the second column yields the dividend. The result of the division is obtained as the sum of the corresponding rows in the first column. Fraction reckoning constituted an intrinsically complicated part of Egyptian mathematics. How it was carried out in detail is not always clear to us. A number of tables survive that were used in fraction reckoning (most notably the so-​called 2÷N table that indicates the value of divisions, 2 by odd N, as a series of Egyptian fractions). Although mathematically the decomposition of 2÷N as a series of unit fractions is not unique, Egyptian mathematics seems to have settled on a specific set of decompositions as can be inferred from the existence of two specimens of the 2÷N table and the use of these decompositions within the mathematical texts. How exactly they were found has been a subject of much debate (cf. Neugebauer 1926; Vogel 1929; Bruins 1952;Gillings [1972] 1982; Bruckheimer and Salomon 1977; Gillings 1978; and most recently Abdulaziz 2008). Two general observations about the representations found in this table can be made: (1) the number of unit fractions is kept small within individual representations, and (2) preference is given to small numerators. Both of these obviously help make further calculations as easy as possible. They may also indicate that the 2÷N table is a result of experience and (presumably) trial and error rather than a systematic execution of a set of rules. In addition, Egyptian mathematics used red auxiliaries written next to fractions that would help carry out some operations involving fractions. The technique of using these auxiliaries works similarly to our modern usage of common denominators, albeit without explicitly noting the respective denominator.

3.  Mathematical Texts: Education and Mathematical Practices Our main sources for our knowledge of Egyptian mathematics are the so-​called mathematical texts. Not all texts that involve numbers are what we call “mathematical texts.” Using a definition from Eleanor Robson for Mesopotamian sources, mathematical texts are texts that “have been written for the purpose of communicating or recording a

54    Ancient Scientific Traditions Beyond Greece and Rome mathematical technique or aiding a mathematical procedure to be carried out” (Robson 1999, 7). The choice of writing material, papyrus, which is only preserved in extremely dry conditions, such as in the Egyptian desert areas where tombs and temples were located, has led to the destruction of most texts used in daily life. These presumably far more numerous texts were discarded in the towns, that is, in the proximity of the Nile (Ritter 2000, 115). Only six chance finds of mathematical texts have survived, all of which date (or are said to be linked) to the time of the Middle Kingdom (2055–​1650 bce). Therefore, the modern reader needs to be aware that the few mathematical texts extant from ancient Egypt are unlikely to give us a detailed picture of mathematics in Egypt. The individual sources are two larger papyri, the Rhind Mathematical Papyrus (with two inventory numbers BM10057 and BM10058 because it is in two pieces) and the Moscow Mathematical Papyrus (E4576), a Leather Scroll (BM10250), a set of mathematical fragments from the pyramid town Lahun called the Lahun Mathematical Fragments (UC32103D, UC32107A, UC32114B, UC32118B, UC32134A+B, and UC32159–​ 32162), two mathematical fragments now kept in Berlin (Berlin 6619), and two wooden boards (Cairo CG25367 and CG25368) with some mathematical content. All of these sources contain a collection of problems, tables, calculations, or a mixture of these. Problem texts (or procedure texts) present a mathematical problem followed by instructions for its solution. Table texts are regular arrangements of numbers used as aids in calculations. Extant table texts from Egypt include tables for fraction reckoning and tables for the conversion of measures. Of the six sources, the Rhind Mathematical Papyrus (RMP) and Moscow Mathematical Papyrus (MMP) are considered the most important due to the amount of preserved text. For editions of these sources see Peet 1923; Struve 1930; Imhausen and Ritter 2004; and Imhausen 2006; Clagett 2000 presents a collection of sources in one volume; Robins and Shute 1987 include color photographs of the entire RMP. Specialists have agreed that translation of Egyptian mathematics into modern mathematical terminology is misleading; for modern approaches see Ritter 1995; Ritter 2004; and Imhausen 2016. The context of the mathematical texts was that of education, more precisely, the education of scribes who would need mathematical abilities in their daily work when administering all kinds of goods. The aim of any Egyptian mathematical problem was the numeric solution of a given problem. Although some problems include geometric objects, a geometric construction is never executed or described. Drawings, which can be found within the group of geometric problems, are not to scale but have to be read with their annotations, which indicate the numerical values of their specific parts. The Egyptian mathematical texts provide access to various levels of Egyptian mathematics: arithmetic techniques and their auxiliaries, specific mathematical problems and their solutions, groups of problems (indicated as such by their terminology), and collections of strategies for their solution. As Jim Ritter has indicated, three basic formal features stand out. First, the text of the problem is rhetorical throughout; no symbolism for mathematical operations is used in setting the problem or in the procedure that solves it. Second, the solution is given as a procedure, a sequence of instructions that need to be followed to arrive at the solution (i.e., an algorithm). Third, the problem is set and solved with concrete numerical values,

Mathematics in Egypt     55 not with abstract placeholders. To highlight certain parts of the problem, especially the beginning of a new problem, red ink is used. The main body of the text is written in black ink. In addition to the textual parts, sections with only numbers are found in between the individual instructions, namely after multiplications and divisions. These show in written form how the respective operation (i.e., multiplication or division) is carried out. The technique of performing written multiplications or divisions reduces these operations to a sequence of steps, each of which can be carried out mentally. Since not a single example of a multiplication table for whole numbers has survived, perhaps it may be speculated that they were not used, due to the ease of carrying out multiplications in written form. Rewriting this kind of text into an algebraic equation obliterates all of these formal features, and thus may be misleading when it comes to a more detailed insight into the respective procedures or speculations how it may have been established. In order to avoid this, and to be able to analyze this kind of mathematical sources, Jim Ritter has proposed a method of rewriting the rhetorical procedure into a symbolic one, which brings out the procedural character of the text and enables an easier comparison of different problems and their respective procedures (e.g., Ritter 2004; this method was used to analyze hieratic mathematical problems in Imhausen 2003).

4.  Beyond the School: Mathematics in Daily Life, Literature, and Art Apart from the limited corpus of mathematical texts, mathematics is inextricably linked to the life of a scribe, as can be seen in a variety of sources from Egyptian scribal culture. One group of such texts from the New Kingdom (1550–​1069 bce) are the Late Egyptian Miscellanies (for translations see Caminos 1954 and Tacke 2001), which originated from the culture of scribal education. These texts include eulogies to scribal teachers, literary letters from fathers to sons (who should become a scribe and be placed in school), a composition known as Become a Scribe and others (most titles are modern inventions). Although none of them is explicitly “about” mathematics, they often include references to mathematical education or mathematical practices. The earliest literary text referring to the scribal profession is the Instruction of Khety, also known as The Satire of the Trades, which compares the profession of a scribe to other professions (for recent English translations of the text see Lichtheim 2006a, 184–​ 192; Parkinson 2009, 273–​283; or Simpson 2003; cf. also the recent German edition Jäger 2004). The text is extant in its entirety in Papyrus Sallier II and partially in pAnastasi VII, which were both written during the Nineteenth Dynasty (Lichtheim 2006a, 184–​ 185). Based on its supposed author, who also composed The Teaching of Amenemhet, the text is assumed to have been created during the Middle Kingdom (Parkinson 2009, 274); however, this is still under discussion (cf. Moers et al. 2013, and Stauder 2013).

56    Ancient Scientific Traditions Beyond Greece and Rome According to the introduction, the teaching imagines a father, presumably a scribe, who has brought his son to the school (at the pharaoh’s residence, i.e., the capital) to become a scribe. Coming from the context of scribal culture and probably scribal education, it is not surprising that the scribal profession is depicted as superior to any other. After a brief summary referring to the privileges of being a scribe (“the greatest of all callings”), various other professions are enumerated followed by their disadvantages, for example, the goldsmith (“he stinks more than fish roe”), the jewel-​maker (“his knees and back are cramped”), the barber (“he strains his arms to fill his belly”), the reed-​cutter (“mosquitoes have slain him”), the mason (“his loins give him pain”), and many more. The text ends with the statement of the superiority of the scribal profession, followed by a set of rules for the (apprentice) scribe. The theme of scribal superiority above all other professions is a well-​known element of the Late Egyptian Miscellanies (Simpson 2003, 431), and, in these texts, various implicit references to the numerate activities of scribes can be found. Papyrus Sallier I, 6, 1–​9 is a literary letter to an apprentice scribe who apparently had left his education at a scribal school and instead decided to become a farmer, spending his days working in the fields. Similar to The Satire of the Trades, the letter points out the disadvantages of the profession of a farmer, who keeps being hit by misfortunes and loses part (or rather most) of his harvest, and whose animals die from the strain of work. Then the scribe arrives to “reckon the tax” (Simpson 2003, 439). Since the farmer does not have the obligatory dues, he is then punished under the supervision of the scribe (“the taskmaster of everyone”). It is the numerate activity of calculating respective dues and work that puts a scribe in this superior position. A similar conclusion is drawn in Papyrus Lansing (pBM9994), a composition around the theme of becoming a scribe:  “instruction in letter-​writing made by the royal scribe and chief overseer of the cattle of Amen-​Re, King of Gods, Nebmare-​nakht for his apprentice, the scribe Wenemdiamun” (Lichtheim 2006b, 168). Apart from repeatedly pointing out the pleasures and beauty of writing, the numerate activity included is also mentioned: “The scribe, he alone, records the output of all of them” (Lichtheim 2006b, 170). The satirical letter of Papyrus Anastasi I, another New Kingdom document, includes direct references to mathematical problems (English translation: Gardiner 1911; more recent, German, translation and detailed commentary: Fischer-​Elfert 1986). The letter is fictional, from an imaginary learned debate between two scribes, namely Hori (the letter’s author) and Amenemope/​Mapu (the letter’s addressee). In response to a letter from Mapu, Hori proposes a scholarly competition covering various aspects of scribal knowledge, for example, the formal structure of an official letter, the geography of Syria and Palestine, but also several mathematical problems: the calculation of bricks needed to construct a ramp, the number of workers needed to transport an obelisk, the number of workers needed to move sand when a colossal statue has to be erected in a given time frame (including time for a lunch break), and the calculation of rations for a military excursion to Palestine. Although these problems are phrased like their earlier counterparts of the mathematical texts, the numerical information in pAnastasi I does not suffice to actually solve these problems. Therefore, it may be inferred that their aim was to remind

Mathematics in Egypt     57 the numerate reader of his mathematical education. Unfortunately, the fragmentary text does not allow definite conclusions about what lay behind the missing numerical information. For a modern reader, this text provides an idea of the variety of numerate tasks that a scribe had to master.

5.  Egyptian Mathematics in the Greco-​Roman Periods Only two New Kingdom ostraka survive, both incomplete with a few lines of text (Imhausen 2003, 9 fn. 14). With a long gap of over 700 years, a second corpus of mathematical papyri (Parker 1959; 1972; 1975; Jordan 2015)  and several ostraka (e.g., Belli and Costa 1981; Bresciani, Pernigotti, and Betrò 1983, no. 9; Devauchelle 1984, no. 3; and Wångstedt 1958, 70–​7 1) have survived from that date to the Greco-​Roman era (332 bce–​395 ce). It is from this corpus that a definite connection between the Egyptian and Mesopotamian mathematical cultures can be traced for the first time (for a comparison of their earlier mathematics see, e.g., Ritter 1995). The example par-​excellence cited (e.g., Parker 1972, 6; Høyrup 2002, 405–​406) to demonstrate this Mesopotamian influence is the group of “pole-​against-​a-​wall” problems (for a detailed discussion of this group of problems and their attestations see Melville 2004). From Mesopotamia, examples of this type of problem are extant from the Old Babylonian and the Seleucid periods (a gap of over a millennium); from Egypt, examples originate from the Greco-​Roman period only. An Egyptian example can be found in problem 24 of the Cairo Demotic Mathematical Papyrus (Cairo DMP). The problem describes the following situation: A pole is leaning vertically against a wall (of unknown and undetermined height). Then the foot of the pole is moved a given distance away from the wall, resulting in a lowering of the top of the pole against the wall, which is to be calculated. The solution uses the mathematical characteristic that the pole, the wall, and the ground form a right triangle, of which two sides (the hypotenuse and the shorter side) are provided as data. The procedure to solve this problem uses the Pythagorean rule (for the term Pythagorean rule cf. Høyrup 1999). A contemporary Mesopotamian example can be found in problem 12 of the Seleucid tablet BM34568. Within the history of Mesopotamian mathematical problems, this type of problem is also known from earlier Old Babylonian examples, for example, problem 9 of tablet BM85196. Exactly the same problem with an identical procedure/​algorithm can be found in another demotic pole-​against-​the-​wall problem, that is, problem 27 of the Cairo DMP. The two procedures are identical, apart from the wording of two steps in the procedure, indicated as “squaring” in the Mesopotamian text and as “multiplication of a number with itself ” in the demotic text. Therefore, it may be legitimate to assume that this type of the problem and its procedure were at some point transmitted from Mesopotamia to Egypt.

58    Ancient Scientific Traditions Beyond Greece and Rome Other problem types supply further evidence for a transmission from Mesopotamia to Egypt. The calculation of the circle, distinctly different in the hieratic Egyptian and Old Babylonian Mesopotamian texts undergoes a significant change in Egypt from hieratic to demotic problems. In the latter (e.g., in problem 30 of the Cairo DMP), we find a treatment of the circle that clearly resembles the Old Babylonian treatment (i.e., explicitly mentioning the circumference, which does not appear in hieratic Egyptian problems, as well as a constant of the numerical value 3 to indicate the relation between diameter and circumference). While hieratic Egyptian geometric problems are mostly straightforward calculations of the area of a simple geometric object (circle, triangle, rectangle), Old Babylonian and Demotic Egyptian problems include examples of calculating more complex geometric shapes, for example, circle segments (see, e.g., the Old Babylonian tablet BM15285 and problem 36 of Cairo DMP). The agrimensor1 formula, used in the Old Babylonian calculation of the area of a trapezium (YBC7290, published in Neugebauer and Sachs 1945, 44), is also used in the calculation of the area of a rectangle in the demotic BM10520 (problems 64 and 65 in Parker 1972). Finally, while multiplication tables constitute a significant number of the Mesopotamian mathematical texts, hieratic Egyptian tables include only those for fraction reckoning and the conversion of metrological units—​not a single multiplication table. The Demotic BM10520, however, includes a multiplication table for 64 from 1 to 16 (Parker 1972, 64–​65). When and how this transmission occurred is difficult to determine due to the lack of continuity within the source material. Apart from the fact that the mathematical texts from ancient Egypt are rare chance finds only, they fall into two distinct corpora of roughly half a dozen sources each, which are separated by over 1,000 years. For the earlier texts, Jim Ritter has demonstrated exemplarily that although both cultures were faced with similar problems, each developed their own mathematical strategy to deal with them (Ritter 1995). For the Egyptian Demotic texts, however, an influence from Mesopotamia cannot be denied.

Bibliography Abdulaziz, Abdulrahman A. “On the Egyptian Method of Decomposing 2/​N into Unit Fractions.” Historia Mathematica 35 (2008): 1–​18. Belli, Giula, and Barbara Costa. “Una tabellina aritmetica per uso elementare scritta in demotico.” Egitto e Vicino Oriente 4 (1981): 195–​200. Bresciani, Edda, Sergio Pernigotti, and Maria C. Betrò. Ostraca demotici da Narmuti. I (nn. 1–​33). Pisa: Giardini, 1983. Bruckheimer, M., and Y. Salomon. “Some Comments on R. J. Gillings’ Analysis of the 2/​N Table in the Rhind Papyrus.” Historia Mathematica 4 (1977): 445–​452. Bruins, Evert M. “Ancient Egyptian Arithmetic: 2/​N,” Koninklijke Nederlandse Akademie van Wetenschappen, Proceedings, Series A, Mathematical Sciences 14 (1952): 81–​91. Caminos, Ricardo A. Late Egyptian Miscellanies. Oxford: Oxford University Press, 1954.

1

  Agrimensor (also mensor agrorum or gromaticus) is the designation for Roman land surveyors.

Mathematics in Egypt     59 Devauchelle, Didier. “Remarques sur les méthodes d’enseignement du démotique.” In Grammata Demotika, ed. Heinz-​Joseph Thissen and Karl-​Theodor Zauzich, 47–​59. Würzburg: G. Zauzich Verlag, 1984. Dreyer, Günter. Umm el-​ Qaab I:  Das prädynastische Königsgrab Uj und seine frühen Schriftzeugnisse. Archäologische Veröffentlichungen 86. Mainz: Philipp von Zabern, 1998. Fischer-​Elfert, Hans-​Werner. Die Satirische Streitschrift des Papyrus Anastasi I.  Übersetzung und Kommentar. Ägyptologische Abhandlungen 44. Wiesbaden:  Otto Harrassowitz, 1986. Gardiner, Alan H. Egyptian Hieratic Texts. Series 1:  Literary Texts of the New Kingdom. Leipzig: J.C. Hinrichs, 1911. Gillings, Richard. “Response to ‘Some Comments on R. J. Gillings’ Analysis of the 2/​N Table in the Rhind Papyrus.” Historia Mathematica 5 (1978): 221–​227. —​—​—​. Mathematics in the Time of the Pharaohs. Cambridge, Mass and London: MIT Press, 1972. Reprint, New York: Dover, 1982. Høyrup, Jens. “Pythagorean ‘Rule’ and ‘Theorem’—​Mirror of the Relation Between Babylonian and Greek Mathematics.” In Babylon:  Focus mesopotamischer Geschichte, Wiege früher Gelehrsamkeit, mythos in der moderne, ed. Johannes Renger, 393–​ 407. Saarbrücken: Saarbrücker Druckerei und Verlag, 1999. —​—​—​. Lengths, Widths, Surfaces: A Portrait of Old Babylonian Algebra and Its Kin. New York: Springer, 2002. Imhausen, Annette. Ägyptische Algorithmen. Eine Untersuchung zu den mittelägyptischen mathematischen Aufgabentexten. Ägyptologische Abhandlungen 65. Wiesbaden: Harrassowitz, 2003. —​—​—​. “UC 32107A Verso: A Mathematical Exercise?” In The UCL Lahun Papyri: Accounts, ed. Mark Collier and Stephen Quirke, 288–​291. British Archaeological Reports International Series 1471. Oxford: Archaeopress, 2006. —​—​—​. “Zum Arbeiten mit hieratischen mathematischen Aufgabentexten.” In:  Translating Writings of Early Scholars in the Ancient Near East, Egypt, Greece and Rome. Methodological Aspects with Examples (Beiträge zur Altertumskunde 344), ed. Annette Imhausen and Tanja Pommerening, 281–​333. Berlin: de Gruyter, 2016. Imhausen, Annette, and Jim Ritter. “Mathematical Fragments: UC32114, UC32118, UC32134, UC32159–​UC32162.” In The UCL Lahun Papyri:  Religious, Literary, Legal, Mathematical and Medical, ed. Mark Collier and Stephen Quirke, 71–​96. British Archaeological Reports International Series 1209. Oxford: Archaeopress, 2004. Jäger, Stephan. Altägyptische Berufstypologien. Lingua Aegyptia. Studia monographica 4. Göttingen: Seminar für Ägyptologie und Koptologie2004. Jordan, Birgit. Die demotischen Wissenstexte (Recht und Mathematik) des pMattha. Tuna el-​ Gebel 5. Vaterstetten: Verlag Patrick Brose, 2015. Lichtheim, Miriam. Ancient Egyptian Literature. Vol. 1:  The Old and Middle Kingdoms. Berkeley: University of California Press, 2006. —​—​—​. Ancient Egyptian Literature. Vol. 2:  The New Kingdom. Berkeley:  University of California Press, 2006. Melville, Duncan. “Poles and Walls in Mesopotamia and Egypt.” Historia Mathematica 31(2004): 148–​162. Moers, Gerald, K. Widmaier, A. Giewekemeyer, A. Lümers, and R. Ernst, eds. Dating Egyptian Literary Texts. “Dating Egyptian Literary Texts” Göttingen, 9–​12 June 2010. Vol. 1. Lingua Aegyptia. Studia monographica 11. Hamburg: Widmaier Verlag, 2013.

60    Ancient Scientific Traditions Beyond Greece and Rome Neugebauer, Otto. Die Grundlagen der ägyptischen Bruchrechnung. Berlin:  Julius Springer, 1926. Neugebauer, Otto, and Abraham Sachs. Mathematical Cuneiform Texts. American Oriental Series 29. New Haven, CT: American Oriental Society, 1945. Parker, Richard A. “A Demotic Mathematical Papyrus Fragment.” Journal of Near Eastern Studies 18 (1959): 275–​279. —​—​—​. Demotic Mathematical Papyri. Providence, RI: Brown University Press, 1972. —​—​—​. “A Mathematical Exercise—​P. Dem. Heidelberg 663.” Journal of Egyptian Archaeology 61 (1975): 189–​196. Parkinson, Richard B. The Tale of Sinuhe and Other Ancient Egyptian Poems 1940‒1640 bc. Oxford: Oxford University Press, 2009. Peet, Thomas Eric. The Rhind Mathematical Papyrus. London: Hodder and Stoughton, 1923. Reprint, Nendeln (Liechtenstein): Kraus Reprint, 1970. Ritter, Jim. “Metrology and the Prehistory of Fractions.” In Histoire de fractions, fractions d’histoire, ed. Paul Benoît, Karine Chemla, and Jim Ritter, 19–​35. Basel: Birkhäuser, 1992. —​—​—​. “Measure for Measure:  Mathematics in Egypt and Mesopotamia.” In A History of Scientific Thought. Elements of a History of Science, ed. Michel Serres, 44–​72. Oxford and Cambridge, MA: Blackwell, 1995. —​—​—​. “Egyptian Mathematics.” In Mathematics Across Cultures: The History of Non-​Western Mathematics, ed. Helaine Selin, 115–​136. Dordrecht: Kluwer, 2000. —​—​—. “Reading Strasbourg 368:  A Thrice-​Told Tale.” In History of Science, History of Text, ed. Karine Chemla, 177–​200. Boston Studies in the Philosophy of Science 238. Dordrecht: Springer, 2004. Robins, Gay, and Charles Shute. The Rhind Mathematical Papyrus: An Ancient Egyptian Text. London: British Museum, 1987. Robson, Eleanor. Mesopotamian Mathematics 2100‒1600 bc:  Technical Constants in Bureaucracy and Education. Oxford: Clarendon Press, 1999. Shaw, Ian. The Oxford History of Ancient Egypt. Oxford: Oxford University Press, 2000. Simpson, William Kelly. The Literature of Ancient Egypt: An Anthology of Stories, Instructions, Stelae, Autobiographies, and Poetry. New Haven, CT: Yale University Press, 2003. Stauder, Andréas. Linguistic Dating of Middle Egyptian Literary Texts:  “Dating Egyptian Literary Texts” Göttingen, 9–​12 June 2010. Vol. 2. Lingua Aegyptia. Studia monographica 12. Hamburg: Widmaier Verlag, 2013. Struve, Wasili W. Mathematischer Papyrus des staatlichen Museums der schönen Künste in Moskau. Quellen und Studien zur Geschichte der Mathematik, Abteilung A:  Quellen 1. Berlin: Julius Springer, 1930. Tacke, Nikolaus. Verspunkte als Gliederungsmittel in ramessidischen Schülerhandschriften. Studien zur Archäologie und Geschichte Altägyptens 22. Heidelberg:  Heidelberger Orientverlag, 2001. Vogel, Kurt. Die Grundlagen der ägyptischen Arithmetik in ihrem Zusammenhang mit der 2/​ n Tabelle des Papyrus Rhind. Dissertation München, 1929. Reprint, Vaduz: Saendig Reprint Verlag, 1970. Wångstedt, Sten V. “Aus der Ostrakasammlung zu Uppsala III.” Orientalia Suecana 7 (1958): 70–​77. Wilkinson, Toby. Early Dynastic Egypt. London and New York: Routledge, 2001.

chapter A2b

Astronomy i n Ancient E g yp t Joachim Friedrich Quack

Although classical (Greek and Latin) sources tend to characterize Egypt as a culture with substantial astronomical (and astrological) knowledge, the actual Egyptian sources are much less obvious in this sense. This fact has led some scholars to say that Egypt has no place in the history of mathematical astronomy (Neugebauer 1975, 559). However, things are more complicated, and several important points have to be kept in mind (Quack 2016). First, in many cases, astronomical phenomena are integrated as parts of religious conceptions (von Lieven 2000). That makes them much more difficult to decode and often gives rise to suspicion by the historian of science. Second, our record of preserved Egyptian texts is seriously distorted in favor of material from tomb contexts, but pure astronomical texts are not among the most likely candidates to be found there. As soon as material from settlements is available in substantial numbers (especially for the Greco-​Roman period), astronomical texts tend to be present. Third, many of the sources are remnants of the practice without indicating the theory behind them, for example, lists of stars. This means that many of our overall conclusions are based on inference.

1.  Calendars and Constellations It can be assumed that some basic astronomical facts were known in Egypt from very early times, especially those directly relevant for timekeeping. The Egyptian calendar is, unlike most other ancient cultures’, not primarily based on the moon. Rather it has uniformly 365 days (without any intercalary days), divided into three seasons each of four months, with 30 days per month, and at the end of the year five special days outside

62    Ancient Scientific Traditions Beyond Greece and Rome of the normal structure. This is the closest fixed-​length approximation to the actual year-​length possible and likely based on astronomical observations of either the sun or the stars. It can be debated to what degree there was originally a lunar calendar in use in Egypt. For as far back as we have sufficient documentation, the civil calendar is dominant, although there is a lunar cycle, beginning on the day of the moon’s invisibility, and used for some aspects of religious life (especially temple service and a few festivals). Since there is no continuous count of years, and the lunar months are kept in close relation to their civil counterparts, it is not really justified to speak of a genuine lunar calendar. The waxing and waning of the moon was conceptualized as gods entering and leaving the celestial eye (von Lieven 2000, 127–​132). Since the lunar cycle had relevance for some religious feasts, it was observed in the temples and served, from the later Middle Kingdom (about 1850 bce) onward, as the organizing principle for temple service (with change of staff always on the second day of the lunar cycle). While for the older periods it is probable that it was based on actual observation, at least for the Greco-​Roman period there were schematic 25-​year cycles that worked well to keep the lunar cycle in line with the nonintercalated Egyptian year of 365 days. A famous example of a schema is Papyrus Carlsberg 9 (for the interpretation, see Depuydt 1998b), but there is good documentation that slightly different methods were also in circulation (Lippert 2009; Bennet 2008). Those schemes specify how 29-​ and 30-​day lunar months should follow each other, and when there would be a “big year” containing 13 lunar months. Celestial regions and stars play a substantial part already in the oldest corpora of religious texts preserved from ancient Egypt (Krauss 1997; Wallin 2002), but their location and identification with our star terminology is fraught with difficulties. The most important stars and constellations were Orion (connected with Osiris, the god who was killed by his brother), Sirius (connected with his sister and wife Isis), and the Big Dipper (connected with the murderer Seth). Sirius (called Sothis in Egyptian) had a special role because its heliacal rising coincided with the ideal Egyptian New Year day that was linked with the onset of the Nile inundation. It is likely that the specific phenomena of its appearance (like radiance, and in later periods planetary positions) were used for divinatory purposes, although unequivocal documentation exists only for the Roman period (Quack, forthcoming, a).

2.  Star Clocks and Decans The oldest explicitly astronomical monuments from Egypt are star clocks, attested by more than 20 copies, mainly on the inner side of coffin lids from the Eleventh and Twelfth Dynasties (ca 2050–​1900 bce) (Neugebauer and Parker 1960; Quack, forthcoming, a). They indicate, in principle, for each 10-​day interval of the year a sequence of 12 stars (or parts of constellations), with each star moving up one position in the table

Astronomy in Egypt   63 per interval. It is generally assumed that a significant astronomical position of the star (most probably its rising in the east) indicates the onset of a new hour of the night. The “hours” are rather short hours of about 40 minutes, so that a change by one “hour” for a star every 10 days corresponds more or less to astronomical reality. These stars (or parts of constellations) have a long history and still appear in some astrological treatises of classical antiquity. They are commonly called decans (as they are in Greek and Latin texts), while the Egyptian designation is baktiu “those connected with work”—​the “work” being the indication of the hours; often they are simply labeled in the texts as “stars” without further specification. The images seen in the sky by the Egyptians differ significantly from our modern tradition (mainly derived from Mesopotamia and Greece), and the identification of most of the Egyptian constellations is fraught with difficulties (a recent proposal is in Lull and Belmonte 2006). Observing the hours of the night was important mainly for the performance of some religious rituals. There are two basic types of the oldest star clocks, with some differences in the actual choice of decans and a divergent starting point. It is likely that this does not reflect different dates of invention (as supposed earlier by Neugebauer and Parker 1960); rather, both structures are equally schematic, with the one putting the heliacal rising of Sirius in the middle of the table, the other putting Sirius as the last regular star in the top line. A different type of star clock is constituted by the “Ramesside star clocks” (Neugebauer and Parker 1964; Leitz 1995, 117–​287; Depuydt 1998a). They are only attested in three royal tombs of the 11th century bce, but thought by astronomical considerations (especially the rising date of Sirius) to go back to the 15th century bce. They are also based on stellar position but show several refinements. The individual tables are no longer for 10 but for 15 days, which makes them more suitable for fixed hours of 60 minutes. They use the culmination as principal marker of hourly changes but allow also other positions, which are defined in terms of human anatomy (like “left eye” or “right ear”) and probably refer to a human statue set up directly opposite the observer as a marker of the meridian; so these would indicate positions of the star more or less distant from precise culmination. Only attested on one single monument from the 4th century bce is a type of stellar clock that divides the night only into three parts, based on the movements of the Big Dipper (Neugebauer and Parker 1969, 49–​52). The actual engraving shows serious corruption.

3.  The Book of Nut The most complex composition concerning celestial phenomena is constituted by the “fundamentals of the course of the stars” (von Lieven 2007), also known under the name Book of Nut. This composition is attested in three monumental versions (13th, 12th, and 6th centuries bce) as well as a number of papyri of the Roman period (2nd century ce), plus an excerpt of a short passage attested in some tombs of the Twenty-​Sixth Dynasty

64    Ancient Scientific Traditions Beyond Greece and Rome (Régen 2015); another short extract is attested on the ceiling of the temple of Athribis in the Ptolemaic period. Two of those papyri (Papyrus Carlsberg 1 and 1a) contain not only the basic text but also a translation into a more recent form of Egyptian, plus a commentary (not identical in the two sources). The monumental versions (and one papyrus with hieroglyphic writing) also show a picture of the sky goddess (Nut) lifted into the air by her father (Shu); the demotic papyri describe this image without drawing it. The first part consists of relatively short texts accompanying parts of the drawing. The first section of this part describes phenomena of the sun, especially its rising in the morning; the redness in the morning is equated to hemorrhage during a birth. This is followed by a short description of the outer parts of the sky where the sun does not shine. A substantial section treats the stars, especially the decans. They are pressed into a schematic template where each decan spends, after its heliacal rising, the first 80 days in the eastern part of the sky, then his culmination serves, for 120 days, to indicate nightly hours, and afterward, he spends 90 days in the western part of the sky, before being invisible for 70 days. This is obviously not to be taken as numerically exact, and it works with a rounded year-​length of 360 days (neglecting the final five days of the Egyptian year outside normal calendrical structure) in order to keep the calendar dates simple. Still, it shows that the Egyptian decans should be located in a celestial belt south of the ecliptic (Neugebauer and Parker 1960, 97–​100). The description of the cycle of the sun is resumed, this time focusing more on sunset and night, but continuing until sunrise. It is explained how the stars are following the sun. Finally, there is a section about the migratory birds which are understood as the souls of men, coming from the north to feed on the herbs of Egypt. The second part of the composition is contained in only one of the monumental versions, separated from the first part by passages about a shadow clock and a water clock, whereas the papyrus texts continue directly after the first part. The general style of the second part is more mythological than the first one, and there are longer connected texts. The disappearance of the stars is conceptualized as their consumption by a mother sow, their stay below the horizon as a purification. After the treatment of the stars, a section on the moon follows where the phases are mainly explained as interactions between different deities, for example, Horus and Seth. The final preserved section was understood as treating the moon and the planets by von Lieven (2007, 107–​119, 190–​201; 2012, 120f.), while Leitz (2008/​2009, 17–​19) preferred to see it as another treatment of exclusively the moon.

4.  Sky Ceilings There is a standard program for decorating astronomical ceilings of coffins, burial chambers, or temple rooms (and the outer sides of water clocks), which is attested by a few cases already from the Twelfth Dynasty (ca 20th century bce), and much better from both the New Kingdom and the Late Period (i.e., ca 1500–​150 bce) (Neugebauer and Parker 1969). The image is divided between a north and a south side. On the north side,

Astronomy in Egypt   65 in the center, a few northern constellations are shown, the most important one being the Big Dipper kept on a chain by a hippopotamus goddess, a crocodile, a lion, and a falcon-​ headed god. Left and right of them, there are deities who are perhaps personifications of days of the month (never a complete set), although in one late monument they are labeled as “circumpolar stars.” Sometimes, the months are also represented. The chaining of the Big Dipper refers to its never-​setting stars, and the constellation was understood as being unable to descend into the netherworld where Osiris is (von Lieven 2000, 24–​ 29). A spell invoking Thot, the god of time-​keeping, and threatening to reveal that he has slackened the chains so that the Big Dipper could actually go down in the west, might show the observation of the effects of precession, which led to some of its stars dipping below the horizon in southern Egypt from the late second millennium bce (Waitkus 2010, 179), even though the Egyptians did not formulate any theoretical model of the precession. On the south side, there is the sequence of the decans, often with their tutelary deities. A few of the more important decanal constellations are represented by images, especially the Ship, the Sheep, and the Two Tortoises. Also found on the south sides are depictions of the five planets known in antiquity. These distinguish the inner and the outer planets, but the outer ones are not arranged according to distance from the sun. The epithets given to them should not be understood as permanent ones but as valid for a specific situation, like “star of the southern sky” or “he walks backward”—​the latter showing observation of the phenomenon of retrograde movement. It seems as if a quite specific situation has served as model for future craftsmen even long after it had lost its pertinence. Attempts to date these depictions to specific historical moments have failed.

5.  Simple Formulae Beginning in the New Kingdom and attested still in copies dating from the 2nd century ce, there are examples of linear zigzag functions for defining the length of the day and night in different months of the year (Quack, forthcoming, b). The values used seem often more driven by the desire for numerically simple solutions than for precision. Thus, one has an increase of 2 hours per month, another one 1 1/​3 hours per month, which leads to extreme ratios of 18:6 or 16:8. A hieroglyphic inscription of the Late Period from Tanis gives some astronomical parameters (Clère 1949; Hoffmann 2016). The best preserved parts concern the length of day and night in 15-​day steps. The specific values seem to be borrowed from Mesopotamian traditions (Hoffmann 2016). Other parts correlate specific decans with the onset of night. Only in the late 2nd century ce do we have Egyptian-​language testimonies for a calculation of the divergences of day-​light from month to month which do not work in a linear way but indicate different fractions of change for each month (Naether and Ross 2008), going from 1/​16 to 1/​12.5.

66    Ancient Scientific Traditions Beyond Greece and Rome A papyrus of the Late Period (ca 650–​ 550 bce) from Elephantine (P. Berlin 23050)  indicates values (expressed in fractions) for the distance between different decans as well as within a decan constituted by several individual stars (Quack in press a). While the numerical values as such are not easily understandable, the system seems to show similarities to the Mesopotamian system of ziqpu-​stars where fractions of the volume of water in a water-​clock are used to indicate time-​and space-​distances.

6.  Materials of the Greco-​Roman Period In the Greco-​Roman period, Egyptian astronomy receives substantial impact from the Near East, but at the same time developed further what it received and probably played an important role in transmitting it to the Greeks (Greenbaum and Ross 2010, Quack, forthcoming, b). The most important new element was the zodiac. The first indications for its presence in Egypt can be found on a demotic ostracon (Strasbourg D 521) that correlates the Egyptian months with the zodiacal signs. The dates work best for the early Ptolemaic period, although palaeographically, the actual text is likely to be later. Another, still unpublished text from Roman period Tebtunis (Papyrus Carlsberg 769)  gives a correlation of months and zodiacal signs that works according to the Alexandrian calendar. Also, a number of constellations were taken over from other cultures and appear mixed with traditional Egyptian ones on the round and the rectangular zodiac of Dendara. They are more likely to come directly from Mesopotamia than from Greece (Quack, forthcoming, b against Leitz 2006). A  number of the specific Egyptian constellations attested on ceilings of temples appear also in the Greek and Latin lists of the so-​called sphere barbarica, that is, non-​Greek constellations. A late Ptolemaic papyrus gives, on one side, a list of lunar eclipses (Neugebauer, Parker, and Zauzich 1981) that are dated according to the fourth Callippic period (Jones 1999, 14). The other side correlates Egyptian calendar dates to the seasonal turning points (Parker and Zauzich 1981). It is stylized as a mathematical exercise text. The length of the respective seasons is given as 93, 90, 90, and 92 days. Especially for the Roman period, we have a situation in Egypt where Greek and demotic Egyptian language and script can be equally used for astronomical and astrological texts (Jones 1994; Jones 1999; Quack forthcoming, b). Sometimes, there is even clear evidence that manuscripts in Greek were actually used in the framework of Egyptian temples. Many of them use methods derived from Mesopotamian models (Jones 2001; Jones 2002; Hoffmann and Jones 2009) and are based on arithmetic models in contrast to the kinematic ones known especially from Ptolemy. There are a few procedure texts for making calculations; among the preserved ones in Egyptian, there is a calculation for Jupiter and the moon (Neugebauer and Parker 1969,

Astronomy in Egypt   67 250–​52), as well as a recently discovered still unpublished text from Tebtunis that gives indications about the calculation for Venus. The more important tables are epoch tables (indicating successive occurrences of a specific event of a planet), templates (giving day-​by-​day progress), ephemerides (giving day-​by-​day positions), sign-​entry almanacs (providing dates when a planet moved to a new zodiacal sign), monthly almanacs (giving the positions and significant events of the planets) and five-​day almanacs (giving planetary positions). Most of them are by now also documented in Egyptian. It should be stressed that all these tables used for calculating the positions of the planets were not intended as exercises in themselves but served for practical use in astrological forecasts. A substantial number of astrological treatises (many of them still unpublished) are preserved, most of them in demotic Egyptian (Ross 2007; Winkler 2009; 2016). Those discussing individual destinies are normally based on the position of the planets in the houses of the dodecatropos (see Astrology, C09, sec. IX.A.1) or of the decan at the time of birth. Also actual horoscopes on papyri and ostraca are attested in substantial numbers both in Egyptian and Greek. The importance of astrological conceptions can also be seen in the fact that astronomical ceilings of public monuments (temples) tend to depict the planets in positions that correspond to theories about the planetary positions at the moment of the birth of the cosmos. Private monuments (tombs and coffins), if they depict astronomical positions, tend to show the planets at the moment of the birth of the owner. Little is known about the social position of astronomers (Fissolo 2001; Dieleman 2003; Evans 2004; Winkler 2016). We can suppose that they were normally part of the temple staff.

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70    Ancient Scientific Traditions Beyond Greece and Rome Winkler, A. “On the Astrological Papyri from the Tebtunis Temple Library.” In Devauchelle and Widmer 2009, 361–​375. —​—​—​. “Some Astrologers and Their Handbooks in Demotic Egyptian.” In The Circulation of Astronomical Knowledge in the Ancient World, ed. J. Steele, 245–​ 286. Leiden/​ Boston: Brill, 2016.

chapter A2c

E gy p tian Me di c i ne Rosalie David

Modern scholarship has generally maintained that a new, distinctive and rational approach to medical treatment was introduced to Egypt when Greek immigrants settled there in the Ptolemaic period (322 bce‒31 bce). This influx included medical practitioners who, in many instances, came from the Hippocratic School at Cos (Longrigg 1992). With the establishment of a renowned medical school at Alexandria in the 3rd century bce, it is argued (Saunders 1963; von Staden 1989, 1–​31) that the Greek approach and methods marked a distinct transition from the earlier medical traditions that had prevailed in Egypt, virtually unchanged since at least the Old Kingdom (ca 2600 bce). This assumption, and the belief that “irrationality” and “rationality” can be clearly distinguished and attributed respectively to the Egyptian and Greek systems, has been questioned (David 2004). On the basis of extant Egyptian documents, it can be argued that for nearly two thousand years, Egyptian medicine had combined both rational and irrational procedures: rationality was not a new concept introduced by the Greek physicians of Ptolemaic Egypt. However, development of this argument has been hampered by the limitations of extant textual and archaeological evidence; it has been acknowledged that any progress would largely depend on the availability of new information. Since then, re-​evaluation of some literary sources together with palaeopathological studies undertaken on human remains (Aufderheide 2003; David 2008) have contributed new insights. An assessment of this evidence is now timely; first, to identify any further support it may lend to the hypothesis that Egyptian medicine was predominantly pragmatic in its approach, and second, to demonstrate that rationality was not a concept that can be attributed exclusively to the Greek physicians. It has long been recognized that the Egyptian medical system employed a combination of what we identify as “rational” and “irrational” (magical) treatments. Although the Egyptians’ choice of remedy would not have recognized this distinction, it is possible to determine two distinct influences in their medical procedures—​one based on magico-​religious beliefs and the other on scientific observations. According to Egyptian belief, magic was a supernatural force that, together with the creative word, could turn

72    Ancient Scientific Traditions Beyond Greece and Rome concepts into reality. It had made creation possible and enabled the universe to be maintained. This source of energy, believed to have precedence and influence over other forces of nature and all created forms, sprang from the utterance of the creator god. Magic was available only to the gods, but they delegated this power to the king, from whom practitioners of medicine in turn derived their healing abilities (Ritner 1993). Physical conditions were generally treated according to the perceived cause. For example, in cases such as trauma, where the cause was evident, rational methods that included bone setting or simple surgery were employed; however, for a condition such as fever, where the cause remained hidden but could possibly be attributed to some supernatural power, magic was used. Thus, an objective, scientific system, based on observation of the patient and knowledge of anatomy, existed alongside magical procedures performed for conditions attributed to the vengeance of the dead, punishment by the gods, or malevolence of enemies. However, the choice of treatment was not exclusively cause based: for example, it is not evident why magic was sometimes used for minor burns or scorpion bites when rational methods could have been employed. In the 3rd century bce, Greek physicians began to differentiate between rational treatments and those based on superstition (Pinch 2006, 133), and notable advances were introduced by, for example, Herophilus (active ca 300 bce‒ca 250 bce), who started to practice medicine in Alexandria (von Staden 1989), and his contemporary Erasistratus (active ca 300 bce‒ca 250 bce). Citations from Herophilus’ writings that survive in the works of later physicians, especially Galen (Nutton 1993), preserve fragmentary information about his achievements. Sources of evidence for Egyptian medicine include medical documents, tomb scenes, physicians’ stelae, and preserved human remains; additionally, from the Greco-​Roman period there are surgical instruments and the unique wall relief in the Temple of Kom Ombo with its debatable representation of surgical instruments. This wealth of literary, archaeological, and physical remains has survived because of Egypt’s unique environmental conditions: heat and dryness have preserved the tombs and their contents, and most evidence about Egyptian civilization survives from this funerary context. However, when considering disease and medicine, the evidence has its own limitations. Tomb wall reliefs follow the convention of depicting the elite in perfect, idealized form—​youthful and in perfect health—​and indications of physical deformity or dis­ ease only occur occasionally in portrayals of servants and menials. Archaeological evidence, as exemplified by the sanatoria at Denderah (Daumas 1957) and Deir el-​Bahri (Milne 1914), is also limited, and only 12 extant major medical papyri are available for study—​surely representing only a fraction of the original archive of such documents in use throughout the millennia. Skeletal and mummified human remains provide a major source of direct evidence about disease and diet: the continuous history of Egypt’s population in one location presents a special opportunity for epidemiological and pathological studies over a 7,000 year period; both skeletal and mummified remains are preserved, enabling researchers to employ a wide range of investigative techniques; and because both intentional and natural mummies have survived that span the social spectrum, it is feasible to study associations between health and wealth. However, although

Egyptian Medicine   73 modern studies have produced extensive evidence about disease processes, they provide far less information about medical treatment. Recent and earlier studies provide some insight into the status of Egyptian medicine. The most important extant medical papyri (translated and studied in the Grundriss der Medizin der alten Ägypter 1954–​73) present fragmentary information about the Egyptian concept of physiology and describe a variety of case studies that include recommended surgical, pharmaceutical, or magical treatments (Leitz 2000). Inscribed on papyrus, the documents date from the Middle Kingdom through to the Roman period, although some may be copies of much earlier works. Since most were acquired through private sales, little is known of their provenance, but the group evidently includes several different types of documents. The Hearst Papyrus, for example, discovered in an ancient town house, may represent a handbook of instruction used regularly by a local doctor. Other papyri, although they probably incorporate material drawn from smaller collections, appear to be more structured and systematic, and they may have been compiled by scribes in the House of Life, a building attached to some temples. Again, some documents may preserve outlines of medical lectures, while others are possibly lecture notes or clinical handbooks, recording instruction received during medical training. No document deals with a single subject; each incorporates a variety of subject matter, and there are instances where some elements are repeated in different documents, for example, in Papyrus Ebers (Wreszinski 1913; Ebbell 1937) and Papyrus Berlin (Wreszinski 1909). The proportion of rational to irrational treatments in each papyrus varies considerably, and there is no evidence that rationality replaced magic in the later periods. In his definitive translation and commentary of the Edwin Smith Papyrus, Breasted (1930) demonstrated the unique nature of this large fragment that has survived from a book on the treatment of wounds. According to a more recent assessment (Bynum and Porter 1993, 2: 963), the papyrus “first indicated an empirico-​rational content for ancient Egyptian medicine, which . . . historians had previously considered entirely magic-​ religious in character.” This papyrus, possibly a firsthand account of clinical experience, has been dated to ca 1570 bce; however, its grammar and vocabulary may indicate that it was a copy of an even earlier version that, according to Breasted, could have originated in the Old Kingdom (ca 2650 bce). Others disagree with this opinion, but it is indisputable that this is the earliest extant treatise on surgery, demonstrating that at an early date, surgery was already a distinct specialization. The focus of the document is general surgery and surgery of the bones; it deals with injuries suffered by male patients, rather than disease processes. No other medical papyrus presents the same overall organization:  this is an instruction manual rather than a collection of prescriptions, and for the first time, medical conditions are totally attributed to physical rather than supernatural causes. The main text reflects an entirely rational approach, although a separate, miscellaneous set of spells was added on the recto of the papyrus roll. Progressing downward from head to foot, a series of 48 case studies address various injuries; each case is dealt with under the headings of title, examination with list of

74    Ancient Scientific Traditions Beyond Greece and Rome symptoms, diagnosis, prognosis (recovery, probable recovery, or uncertain outcome), and indicated treatment. Whereas some erroneous physiological concepts, such as the contribution the metu (conduits through which fluids were believed to pass) made to the functionality of the body, are found in other medical papyri, the Edwin Smith Papyrus marks a very significant progression in medical procedure. For example, one advance usually attributed to the Greeks is found here: in each case, the symptoms, instead of being assessed in isolation, are considered in groups (syndromes). Another significant discovery is presented in Case 8 (Breasted 1930, 203–​206). Dealing with a compound comminuted fracture of the skull that displays no visible injury, this case concludes with the observation that injury to the brain and skull can affect the lower limbs, thus confirming an awareness of the localization of functions within the brain. According to Breasted, the papyrus also demonstrated that the Egyptians knew how to count the pulse thousands of years earlier than the Greeks. This, however, remains a debated point: for example, Nunn (1996, 207) claims: “Herophilus was the first to time the pulse using a portable klepsydra (water clock), calibrated for different ages of his patients.” The traditional opinion is that the pharmaceutical prescriptions that formed a key element in many medical papyri were based largely on irrational principles. Some employed spells to drive away the patient’s affliction, while others used ingredients (minerals, and plant and animal products) that included disagreeable substances, such as excrement or urine to expel evil spirits from the patient, or “good” ingredients, such as aromatic oils, to attract gods who could provide impetus to the healing process. Nunn (1996, 136) claims: “The ancient Egyptian pharmacopoeia was weak by modern standards. The basis of treatment was mainly empirical rather than rational and, in most cases, aimed at the relief of symptoms rather than the eradication of the cause of dis­ ease.” Generally, the placebo effect has been credited with a major role in treatment, and medicines have been considered to have very little therapeutic efficacy. In 2006, a three-​year study entitled “The Pharmacy in Ancient Egypt Project” was established at the University of Manchester (UK) to investigate plant-​based medicines in the Egyptian pharmacopoeia (David 2010). Whereas previous research had involved either literary studies of the medical papyri or archaeo-​botanical studies of Egyptian plant remains, this project adopted a multidisciplinary approach. Historical and scientific analytical methods were employed to study the medical texts and to investigate plant and inorganic remains from Egypt. The aims were to provide the first scientifically based assessment of the contribution of Egyptian pharmacy to modern science; determine the therapeutic accuracy of treatments prescribed in the papyri; identify in mummified remains any plant-​based medicines that might have been prescribed for disease found in the mummy; and trace geographical sources and trade routes for some of the ancient Egyptian pharmaceutical ingredients. An initial consideration was the level of accuracy in the existing translations of pharmaceutical ingredients in the papyri, some 30% of which are disputed (Campbell 2007). Most of the documents were translated many decades ago, and early translators made educated guesses at identifications, consulting contemporary pharmacopoeia

Egyptian Medicine   75 to find an ingredient with the same medicinal use that most closely fitted the description. Translators rely heavily on context to infer the meaning of a word, and “educated guesses” in one document can often be validated by comparison with the same word in another text. However, some words for plant and mineral ingredients found in the medical papyri do not occur in any other texts, and thus the accuracy of the translations cannot be confirmed. For this project, a different approach was adopted in an attempt to confirm the identity of the debatable ingredients. Was the translator’s suggested ingredient available to Egyptians at the time of the text’s composition, and could it have worked in the way the prescription indicated? To attempt to answer the first question, archaeological and geological evidence of ancient Egyptian plant material was used to confirm if the indicated plant ingredient grew or was traded in Egypt or surrounding countries. To address the second question, the therapeutic efficacy of a selected drug was assessed by testing samples reproduced from ancient recipes; the texts contained the necessary information for this, including the ingredients, method of preparation, and dosage. An analytical comparison of prescriptions taken from the medical papyri with modern standards and protocols demonstrated that 64% of Egyptian prescriptions had a therapeutic value on a par with drugs in use over the past 50 years. Although the physicians were often ignorant of the causes of disease and concentrated on the symptoms, it is evident that in many cases they were aware of the appropriate drug, dose, and method of delivery to be used. It is true that some drugs only had a placebo effect and magic undoubtedly played a significant role in treatment, as exemplified by the prescription to treat migraines by anointing the head with the skull of a catfish (Papyrus Ebers 250), and the incantation for the common cold (Papyrus Ebers 763). Nevertheless, the project has demonstrated that rational treatments predominated in the prescriptions. Examples identified in the pharmacopoeia include effective laxatives, antacids, and treatments for diarrhea, flatulence, musculoskeletal disorders, and wounds. Some ingredients prescribed in the papyri have particularly interesting modern parallels: for example, the ancient use of celery for pain relief is reflected in contemporary exploration of its antirheumatic properties; the recommended use of saffron for back pain recurs in a similar prescription of Crocus sativa and safflower in modern traditional medicine; and pomegranate, a powerful antihelminthic prescribed in the papyri to treat parasites, was used until about 50 years ago to expel tapeworms. These studies have provided new identifications of some plants used in the ancient Egyptian pharmacy and have confirmed existing translations of ingredients in the papyri or enabled them to be revised. It has been possible to determine the accuracy and therapeutic efficacy of these treatments, and although no evidence of an Egyptian pharmacopoeia has been found, a plausible identification can now be made of 284 ingredients from 134 plant species, and 24 animal and 28 mineral sources. Perhaps most significantly, the results contradict the long-​held assumption that ancient Egyptian treatment was largely based on superstition and demonstrate that the Egyptians were practicing effective pharmacy many hundreds of years before Galen (Campbell and David 2010).

76    Ancient Scientific Traditions Beyond Greece and Rome Based on the theory that rationality and irrationality were distinct concepts in Egyptian medicine, a perception has developed that each group of medical practitioners was restricted in its ability to provide from a defined range of treatments—​ either pragmatic or magical—​and that generally their roles as healers were not interchangeable: the sau (magicians) offered spells and incantations, while the swnw and wa’ab-​priests of Sekhmet adopted more rational methods of treatment (Gardiner 1917; von Kanel 1984). The medical papyri, however, actually present a different perspective. They indicate that rational and irrational methods were closely associated; that the roles of practitioners, at least to some extent, were interchangeable; and that an individual practitioner could choose from a selection of treatments. Two passages (Edwin Smith Papyrus, Case 1, Gloss A, and Papyrus Ebers 854a), for example, confirm that the swnw, wa’ab-​priests of Sekhmet and the sau could play interchangeable roles when treating patients. Another papyrus has provided conclusive evidence that the kherep Serqet (Controller of Serqet) was not exclusively a practitioner of magic (Sauneron 1989). His prime duty was to prevent and cure all kinds of stings and bites, and some holders of this title also had links to magic and medicine. The Brooklyn Papyrus (47,218.48 and 47,218.85), a doctor’s manual used by the kherep Serqet when treating patients for snakebites, includes both magical incantations and a series of conventional treatments based on observation of the patient. It clearly states that the kherep Serqet was in charge of the management of snakebites and possessed the appropriate remedies. The significance of this document is that it confirms the kherep Serqet employed conventional methods and incantations, and that their functions and duties could be interchangeable with those of other healers. Thus, the literary sources indicate that an individual practitioner could hold several titles and fulfil different functions, and in terms of practitioners and prescribed treatments, it is clear that no rigid distinctions were recognized or drawn between rationality and irrationality. Over the past 40 years, scientific studies of mummified and skeletal remains have made a major contribution to our understanding of disease incidence. Recent studies range from radiological investigations of major collections (Raven and Taconis 2005) to investigations of specific diseases such as atherosclerosis (David et al. 2010; Allan et al. 2009) and cancer (David and Zimmerman 2010). However, until now, this type of research has revealed relatively little information about treatment methods. Some rare examples provide evidence of medical procedures. One notable instance are the two sets of splints, attached to two bodies discovered in tombs dating to Dynasty 5 (ca 2400 bce), which were uncovered by the Hearst expedition of the University of California to Naga ed-​Deir. These had been applied to a comminuted fracture of the middle of a femur and to a compound fracture of the radius and ulna (Smith 1908). Although these examples provide no evidence of healing before death, other surgical interventions were more successful. During the archaeological survey of Nubia, the researchers noted, amongst the many examples recovered, the perfect alignment in the healed fractures of six long bones of the limbs, and they commented on the outstanding skills of the medical practitioners who had set them (Jones 1908).

Egyptian Medicine   77 To search for further evidence of pharmaceutical treatments, an innovative study has applied ancient DNA analysis to detect if any traces of plant-​based medicines can be detected in mummified remains. A further development would entail the use of ancient DNA techniques to investigate some plant-​based therapies administered to treat conditions found in mummies. Unfortunately, the investigation has shown that the possibility of finding identifiable DNA residues from a topical remedy on an Egyptian mummy is unlikely because the larger deposits that would offer the best chance of success would probably have been removed during the washing stages of mummification (Metcalfe 2010). More positive results have been obtained from a biomechanical assessment of two artificial big-​toe restorations from ancient Egypt (Finch 2011). Before it was realized how significant these examples are to the history of prosthetics, the earliest artificial limb to be identified was a bronze and wooden leg discovered at Capua in the burial of a wealthy man who lived ca 300 bce. The Egyptian toe replicas, although of an earlier date, were generally regarded as funerary in purpose—​intended to restore the completeness of the body before burial, rather than designed for use in life. However, the new studies undertaken on the Greville Chester toe in the British Museum and the other example in the Egyptian Museum, Cairo, have challenged that assumption. Research has involved the application of gait-​analysis techniques to replica artificial big toes at the Centre for Rehabilitation and Human Performance Research Gait Laboratory at the University of Salford (UK). This has concluded that both devices could have afforded at least limited ambulation, and evidence of wear indicates that they were probably used while the owner was still alive. Since the Cairo toe, discovered in the Theban tomb of a priest’s daughter, Tabaketenmut, can be dated between 950 bce and 710 bce, it should now be regarded as probably the earliest known prosthetic device. This conclusion suggests that prosthetic medicine was already emerging in Egypt at least as early as this period and provides further support for recognizing the Egyptians as the pioneers and developers of an essentially pragmatic medical system.

Bibliography Allan, A. H., R. C. Thompson, L. S. Wann, M. I. Miyamoto, and G. S. Thomas. “Computed Tomographic Assessment of Atherosclerosis in Ancient Egyptian Mummies.” Journal of the American Medical Association 302 (2009): 2091–​2094. Aufderheide, A. C. The Scientific Study of Mummies. Cambridge:  Cambridge University Press, 2003. Breasted, J. H. The Edwin Smith Surgical Papyrus. 2 vols. Chicago: University of Chicago Press, 1930. Bynum, W. F., and R. Porter, eds. Companion Encyclopaedia of the History of Medicine. 2 vols. London and New York: Routledge, 1993. Campbell, J. M. “Pharaohs and the First Prescriptions.” Pharmaceutical Journal 279 (Dec. 2007): 735–​737. Campbell, J. M., and A. R. David. “The Application of Archaeobotany, Phytogeography and Pharmacognosy to Confirm the Pharmacopoeia of Ancient Egypt 1850‒1200 BC.” In

78    Ancient Scientific Traditions Beyond Greece and Rome Pharmacy and Medicine in Ancient Egypt: Proceedings of the Conferences Held in Cairo (2007) and Manchester (2008), ed. J. Cockitt and R. David, 20–​23. Oxford: Archaeopress, 2010. David, A. R. “Rationality Versus Irrationality in Egyptian Medicine in the Pharaonic and Graeco-​Roman Periods.” In Magic and Rationality in Ancient Near Eastern and Graeco-​Roman Medicine, ed. H. F.  J. Horstmanshoff and M. Stol, 133–​151. Leiden and Boston: Brill, 2004. —​—​—​, ed. Egyptian Mummies and Modern Science. Cambridge:  Cambridge University Press, 2008. —​ —​ —. “The ‘Pharmacy in Ancient Egypt Project’ at the KNH Centre for Biomedical Egyptology.” In Pharmacy and Medicine in Ancient Egypt:  Proceedings of the Conferences Held in Cairo (2007) and Manchester (2008), ed. J. Cockitt and R. David, 1–​5. Oxford: Archaeopress, 2010. David, A. R., A. Kershaw, and A. Heagerty. “The Art of Medicine: Atherosclerosis and Diet in Ancient Egypt.” The Lancet 375 (27 Feb. 2010): 718–​7 19. David, A. R., and M. R. Zimmerman. “Cancer: An Old Disease, a New Disease, or Something in Between?” Nature Cancer Reviews 10 (Oct. 2010): 728–​733. Ebbell, B. The Papyrus Ebers. Copenhagen, London, Oxford: Levin & Munksgaard, 1937. Finch, J. “The Art of Medicine: The Ancient Origins of Prosthetic Medicine.” The Lancet 377 (12 Feb. 2011): 548–​549. Daumas, F. “Le sanatorium de Dendara.” Bulletin de l’Institut Français d’Archéologie Orientale 56 (1957): 35–​58. Gardiner, A. H. “Professional Magicians in Ancient Egypt.” Proceedings of the Society for Biblical Archaeology 24 (1917): 157–​179. Ghalioungui, P. Magic and Medicine in Ancient Egypt. 2nd ed. Amsterdam: B. M. Israel, 1973. Jones, F. W. “Some Lesions from Ancient Fractures.” British Medical Journal 1 (1908): 455–​458. Leitz, C. Magical and Medical Papyri of the New Kingdom. London:  British Museum Press, 2000. Longrigg, J. Greek Rational Medicine:  Philosophy and Medicine from Alcmaeon to the Alexandrians. London: Routledge, 1992. Majno, G. The Healing Hand. Cambridge, MA: Harvard University Press, 1975. Metcalfe, R. J. “Molecular Methods for the Study of Ancient Pharmacy.” In Pharmacy and Medicine in Ancient Egypt:  Proceedings of the Conferences Held in Cairo (2007) and Manchester (2008), ed. J. Cockitt and R. David, 110–​112. Oxford: Archaeopress, 2010. Milne, J. G. “The Sanatorium of Deir el-​Bahri.” Journal of Egyptian Archaeology 1 (1914): 96–​98. Nunn, J. F. Ancient Egyptian Medicine. London: British Museum Press, 2000. Nutton, V. “Galen and Egypt.” In Galen und das Hellenistische Erbe, ed. Jutta Kollesch and Diethard Nickel, 11–​32. Stuttgart: Franz Steiner, 1993. Pinch, G. Magic in Ancient Egypt. London: British Museum Press, 2006. Raven, M. J., and W. K. Taconis, eds. Egyptian Mummies: Radiological Atlas of the Collections in the National Museum of Antiquities at Leiden. Turnhout: Brepols, 2005. Ritner, R. The Mechanics of Ancient Egyptian Magical Practice. Chicago: Oriental Institute of the University of Chicago, 1993. Saunders, J. B.  de C.  M. The Transitions from Ancient Egyptian to Greek Medicine. Lawrence: University of Kansas Press, 1963. Sauneron, S. Un traité Égyptien d’Ophiologie. Cairo:  L’Institut Français d’Archéologie Orientale, 1989. Smith, G. E. “The Most Ancient Splints.” British Medical Journal 1 (1908): 732–​734.

Egyptian Medicine   79 von Deines, H., H. Grapow, and W. Westendorf. Grundriss der medizin der alten Ägypter. 9 vols. in 10 parts. Berlin: Akademie–​Verlag, 1954–​1973. von Känel, F. Les Prêtres-​ouâb de Sekhmet et les Conjurateurs de Serket. Paris:  Presses Universitaires de France, 1984. von Staden, H. Herophilus: The Art of Medicine in Early Alexandria. Cambridge: Cambridge University Press, 1989. Wreszinski, W. Der Grosse Medizinische Papyrus des Berliner Museums. Leipzig: Hinrichs, 1909. —​—​—. Der Papyrus Ebers. Leipzig: Hinrichs, 1913.

A3. India

chapter A3a

M athem atics i n I ndia u ntil 650 ce Toke Lindegaard Knudsen

India is the name of a country in South Asia, presently a rising economic power. In the following, however, the word “India” refers not to the modern country of that name but rather to the entire Indian subcontinent. That is, all of South Asia, including the modern countries of Afghanistan, Bangladesh, Bhutan, India, the Maldives, Nepal, Pakistan, and Sri Lanka. India, in this extended sense, has a long and rich history involving a multitude of cultures, languages, and religions. Advances in all fields of human learning took place there, including important advances in mathematics.

1.  The Earliest Mathematical Knowledge in India The first cultures with urban centers in South Asia arose in the third millennium bce along the great rivers of its northwestern part, in what is now the modern countries of Pakistan and India. Given these cultures’ impressive cities of intricate brick buildings and their involvement in active trade with Mesopotamia and other parts of the ancient world, it is clear that their inhabitants must have possessed some considerable amount of mathematical knowledge. However, no records survive from these cultures that with certainty can be called mathematical (Plofker 2009, vii). Therefore, this survey of Indian mathematics will commence with a later period. In the second millennium bce the northwestern part of the South Asia was controlled by groups of Indo-​European peoples, from whose language Sanskrit is descended. While these cultures originally followed oral traditions, literacy eventually prevailed and texts were written. The earliest extant Sanskrit texts are a group of religious texts known as the Vedas. The Vedas are sacred to Hinduism and have played a major role in the development of

84    Ancient Scientific Traditions Beyond Greece and Rome Buddhism and Jainism. Written in Vedic Sanskrit, an archaic form of the Sanskrit language, the Vedas includes collections of hymns used for ritual, such as the Ṛg-​veda, the oldest of the Vedas and generally dated to the second millennium bce, and the Yajur-​ veda. The corpus also contains later texts, including exegetical literature that interprets Vedic ritual and instructions in its performance (such as the Śata-​patha-​brāhmaṇa) and philosophical texts (such as the Upaniṣads). It is with the Vedas, the literature of these Indo-​European cultures, that we begin this account of mathematics in India.

1.1 Recording of Mathematical Knowledge in India Before discussing the mathematics of ancient India, it is important to discuss the media by which such knowledge was preserved and handed down generation after generation. Various materials were used for recording and preserving knowledge in India: birch bark in the northwest, palm leaves in the south, and, later, locally made paper. In gen­ eral, the subtropical climate of the Indian subcontinent, with its humidity and insects, is not kind to such materials, and as a result it is rare to find manuscripts that are older than two or three hundred years (an exception is the northwest of the subcontinent, where the climate is drier). The indigenous scribal tradition would therefore continuously copy texts deemed worth preserving, sometimes ritually disposing of the old manuscript in a river after copying it. As a result, the Indian manuscripts, including mathematical texts, that have survived until the present are copies of copies of copies, dating to, say, the last three hundred years. Needless to say, the continued copying of texts by scribes inevitably leads to all sorts of unintended and intended consequences: grammatical errors, passages mistakenly left out, intentional deletion of passages for a number of reasons, and insertion of new passages into the text. In addition, individual leaves (not infrequently the first or last leaf) of a manuscript may be damaged, destroyed, or missing, and unbound manuscripts are at risk of having their leaves separated. As a result, many manuscripts contain texts that are incomplete. Around the middle of the 20th century, with the introduction of new ways of copying and preserving texts, the scribal tradition started to die out. At present there is a staggering amount of manuscripts in the Indian subcontinent, mostly held privately, which has not been catalogued or copied, and which are at risk of being lost due to their deterioration on account of neglect and the climate. Among these uncatalogued manuscripts there is a great amount of mathematical texts, some of which are not presently known or have never been examined by researchers.

1.2 Mathematics in the Vedas The Vedic corpus does not present or otherwise contain any systematic presentation of mathematics. However, there are scattered passages in the texts that shed some light

Mathematics in India   85 on the mathematics known at the time (that is, ca 1500–​600 bce). These passages, all dealing with whole numbers, reveal that a decimal system to express numbers was known in early times, as evidenced in passages of the Ṛg-​veda (see, e.g., Ṛg-​veda 2.1.8, 2.18.5‒6, 3.9.9), where the Sanskrit words for the first 10 round numbers 10, 20, 30, 40, 50, 60, 70, 80, 90, and 100, as well as 1,000, are mentioned. Later on, names for powers of 10 up to 10^12 (that is, 1,000,000,000,000, or one trillion in the short scale and one billion in the long scale) are given in the context of ritual. See, for example, Yajur-​veda 7.1.15, 7.2.11, 7.2.20 (the references are to the Taittirīya-​saṃhitā of the Black Yajur-​veda, one of the two schools of that text, the other being the White Yajur-​veda). What we find in the texts is, as is readily seen, an elaborate system of numbers. Its construction is not coincidental; it clearly goes far beyond what would have been necessary in daily life at the time. Why this extensive and sophisticated system was developed is not known. Daily life certainly does not call for names of such large numbers, and in no other ancient cultures were names for numbers this large in ordinary use. It is tempting to seek a rationale in the realm of mystical religion or spirituality, though there is no conclusive explanation (Plofker 2009, 14–​15). An interesting passage regarding numbers is found in the Śata-​patha-​brāhmaṇa (10.4.2). Couched in a mystical story of Prajāpati, the creator god, dividing his body into more bodies, each consisting of a given number of bricks, the total number of bricks being 720, the passage essentially covers how to express 720 as the product of two positive integers. For example, we can split 720 into 2 parts of 360 bricks; into 3 parts of 240 bricks; into 5 parts of 180 bricks; and so on, up to the 24 parts of 30 bricks. We cannot, however, divide 720 bricks into 7 or 8 parts each containing the same number of bricks since neither divides 720 evenly. The passage explicitly notes that Prajāpati did not divide himself seven-​or eightfold, or in other ways that would produce a fraction when the number is divided into 720. As such, the passage is essentially a list of pairs of natural numbers, where each pair multiplied together gives the number 720.

1.3 The Śulba-​sūtras A major focus of the Vedas is ritual. Ritual has a myriad of requirements and instructions, all stated in the sacred texts (the Vedas). These include the recitation of ritual hymns and the singing of ritual songs, purification rituals, specific directions for the priests, and much more. Beyond these instructions of the Vedas, there are the practical steps necessary for actually carrying them out. Of particular interest to us are the practical steps to construct geometrical figures of given areas on the ground, such as for a sacrificial arena or a fire altar, and piling bricks to construct the fire altar. The texts that provide this practical knowledge necessary for the rituals of the Vedas are called the Śulba-​sūtras, or “Rules of the Cord,” referring to the fact that many of the constructions are carried out using cords. The Śulba-​sūtras, generally dated to the period 800–​200 bce, are composed in short, aphoristic statements. A number of commentaries on the Śulba-​sūtras exist, but they postdate the texts themselves by a

86    Ancient Scientific Traditions Beyond Greece and Rome millennium or more. For this reason, the reconstructions of the commentaries may not reflect the mathematical knowledge at the time of the Śulba-​sūtras, but rather that at the time that the commentaries were written. Although one might think that measuring and erecting sacrificial arenas and fire altars are simple procedures, they involve a significant amount of nontrivial mathematics. The main example of the use of advanced mathematics in the rituals of the Vedas is a ritual known as Agnicayana. In the Agnicayana, which is an extensive and elaborate ritual reserved for the elite, a fire altar of a fixed area of 7.5 square puruṣas (a puruṣa being the height of a man with his arms stretched upward; if the ritual is repeated by the same patron, the shape is preserved but the area increased) is constructed in five layers of 200 bricks each; a total of 1,000 bricks. The shape of the fire altar directly determines the outcome of the ritual. For example, a fire altar in the shape of an eagle (the oldest shape used in the Agnicayana ritual) yields flight to heaven for the patron of the sacrifice. The correlation between shape and outcome is shown in table A3a.1. An in-​depth discussion of ritual is beyond the scope of the present essay, but it is necessary to note that in rituals one often sees a construction of a microcosm symbolically representing the macrocosm. Manipulation of this microcosm consequently affects the macrocosm (that is, the world we inhabit), yielding certain desired results. For the microcosm to be an accurate representation of the macrocosm, it is necessary that the microcosm is constructed properly. That is, it must be constructed strictly according to instructions laid out in the ritual texts. In the case of the Agnicayana rituals, that means that the prescribed shapes are constructed correctly. For this reason, the Āpastamba-​śulba-​sūtra (8.6) states that the deformation of the fire altar is disallowed in the sacred texts. The Śatapatha-​brāhmaṇa goes further than that, stating if the fire

Table A3a.1 Shapes and Outcomes for Agnicayana Fire Altars Shape of Fire Altar

Outcome for Patron

Eagle

The heavenly world

Heron

A head in yonder world

Alaja bird

Support from heaven

Isosceles triangle

Destruction of foes

Rhombus

Destruction of foes

Chariot wheel

Destruction of foes

Trough

Food

Circle

A village

Pyre

The world of the ancestors

Tortoise

World of the Supreme Spirit

Mathematics in India   87 altar is deprived of its true proportions, the patron of the ritual will suffer the worst for sacrificing. In other words, correct shapes are needed for a successful outcome of the ritual. Moreover, incorrect shapes lead to disastrous outcomes for the patron of the Agnicayana. The correct shape cannot be achieved without careful analysis and methods. Thus, the construction of a correct shape requires mathematical methods. This is true for the seemingly simple (but deceptively so) tasks of constructing, say, accurate squares, rectangles, and triangles on the ground, and even more so for more complicated tasks, such as constructing two different shapes (say, an isosceles triangle and a circle) with the exact same area. While the former task can be accomplished with a bit of mathematical knowledge (in the Śulba-​sūtras, it is accomplished through the use of the Pythagorean theorem), the latter is decisively nontrivial. Constructing a circle with the same area as an isosceles triangle is impossible to do with the tools employed by the ancient Indians (described below). It boils down to a problem that the ancient Greeks engaged with (and is found in other cultures as well, such Babylonia, Egypt, and China): the quadrature of the circle. For the practical constructions, the Śulba-​sūtras direct that bamboo rods, cords, and pegs be used as tools. Pegs are hammered into the ground, and cords, with loops at either end, can be attached to them. Bamboo rods were used at the earliest times but seem to have been replaced by cords. In fact, the Śulba-​sūtras (Āpastamba-​śulba-​sūtra 9.1) contain only one rule for constructing a square using a bamboo rod and two pegs, but multiple ones using a cord and pegs. To construct a square on the ground, the Śulba-​sūtras make use of Pythagorean triples. That is, three numbers (a,b,c) for which a^2 + b^2 = c^2. The numbers a, b, and c, if interpreted as lengths, form a right triangle. To combine two squares into a third square of an area equal to the sum or the difference of the areas of the two original squares, the texts use the Pythagorean theorem. The Śulba-​sūtras also contain an extremely good approximation to the square root of 2: 1 + 1/​3 + 1/​(3*4)—​1/​(3*4*34), or 577/​408. If we start with a square of side 1 meter, a square of side 577/​408 meters will differ in area from 2 square meters by approximately 6 square millimeters. The difference is clearly negligible in a practical context. It must be noted here that while writing the approximation as a sum of fractions in this way is useful for the contemporary reader to immediately get a feeling for its size, it misrepresents the ancient mathematics involved. The authors of the Śulba-​ sūtras did not employ fractions the way we do. For a rationale of these numbers, see Kichenassamy 2006. Overall, the Śulba-​sūtras presents a system of mathematics in which the full application of the Pythagorean theorem was understood; several Pythagorean triples were known, many of which were used practically for constructions; there was a highly developed ability to construct geometrical figures and to find areas and draw similar figures. They had a remarkable approximation to the square root of 2, and they had approximate methods for the squaring the circle and circling the square (in the best case, corresponding to a value of π of 3.088).

88    Ancient Scientific Traditions Beyond Greece and Rome

2.  The Classical Period The Vedic period is generally considered to have ended in the middle of the first millennium bce. The 6th and 7th centuries bce saw growing urbanization in India, which brought with it changes to society. Furthermore, Sanskrit underwent a development from being a primary, spoken language to being a language used for religious and learned discourses (much like Latin in medieval Europe). Here we will focus on the period from the end of the Vedic period up to 650 ce. Note, though, that while 650 ce fits the end of the time frame of the present volume, it is an artificial cutoff in the specific context of India. India has no break in tradition at this point in time; in fact, such a break does not occur until the early modern period many centuries later. However, in keeping with the time frame of this volume, we will limit ourselves to the period before 650 ce. Along with the urbanization of the early classical period, there arose a growing bureaucracy concerned, unsurprisingly, with the keeping of records. Such record-​keeping included taxes and interest rates, all of which depend on the use of numbers; that is, on mathematics.

2.1 The Decimal Place-​Value System It is in the classical period that one of the most celebrated mathematical achievements in India took place: the creation of the place-​value decimal system. In this system, 10 different digits (the numbers 1 through 9, as well as 0) are used to express any given number. The system is so familiar that it needs no further explanation here. Its origins, however, remain unknown (Plofker 2009, 44, 47–​48). Neither the Brāhmī script (the ancestor of all later scripts in the Indian subcontinent), which was used in inscriptions on the monuments of the Mauryan emperor Aśoka (reigned from about 269 bce to 232 bce), nor Kharoṣṭhī, another script used on Aśoka’s monuments, make use of place-​value numerals (see Plofker 2009, 44–​45, for more details on numerals in these scripts). The earliest inscriptions involving the decimal place-​value system date to the middle of the first millennium ce. These early examples of the decimal place-​value numerals are written in later Indian scripts and often give the number of a year according to one of the different eras used in the Indian subcontinent. However, beyond actual inscriptions, descriptions of the system are found in Sanskrit texts dating to earlier times (Plofker 2009, 45–​46). Authors of Sanskrit treatises, traditionally written in verse (see ‘Prosody,” sec. 2.2), used a different method of representing numbers (still according to the decimal place-​ value system). This system, called bhūta-​saṃkhyā, allowed numbers to be represented using words. For example, moon/​ocean/​eyes yield the number 241 after the two eyes of human beings, the four oceans of the Indian tradition, and the one moon (notice that

Mathematics in India   89 the word-​string is interpreted from right to left, whereas Sanskrit is read from left to right). In order to fit the meter, this system requires that we have a number of words (or synonyms of the same word) available for each number. The advantage of this system is that it aids memorization and helps better preserve the text. It is easier for a scribe to make an error in a digit of a number than it is to get a whole word wrong.

2.2 Prosody Much of the literature written in Sanskrit is written in verse form (commentaries, however, are traditionally composed in prose), using various meters described in the system of Sanskrit prosody. In this system, a metrical verse is divided into four quarters, each consisting of a fixed number of syllables. A syllable can be either light (that is, the time to pronounce the syllable is short) or heavy (that is, the time to pronounce it is longer). Generally, each quarter has the same fixed pattern of light and heavy syllables, though there are exceptions to this rule. Each of the eight different syllabic patterns of three syllables is given a name (rather, a particular syllable) in this system. As such, each group of syllables can be divided into groups of three (the last group potentially having only one or two syllables in it) and given a name by stringing together the syllable-​names for each of the groups. An early Sanskrit treatise on prosody is the Chandaḥ-​sūtra, attributed by the tradition to Piṅgala. Almost nothing is known about this Piṅgala; his date is uncertain, but he likely lived around 200 bce. The Chandaḥ-​sūtra gives the earliest known systematic enumeration of meters based on the fixed pattern of light and heavy syllables in a quarter. If we denote a light syllable by “0” and a heavy syllable by “1,” a verse with five syllables per quarter could have each quarter look like 00110, 10101, or 01110. In this case, where a quarter of a verse consists of five syllables, the Chandaḥ-​sūtra correctly finds that there are 2^5, or 32, distinct syllabic patterns, of which we explicitly listed three. In general, if there are n syllables per quarter, there will be 2^n distinct syllabic patterns. The rule given in the Chandaḥ-​sūtra correctly arrives at this result. Seen in the context of mathematics, the analysis of meters in the Chandaḥ-​sūtra is really an application of combinatorics. The Chandaḥ-​sūtra also asks the question, if there are n syllables per quarter, how many of the 2^n possible syllabic patterns contain exactly m heavy (or, equivalently, light) syllables? To answer this question, the Chandaḥ-​ sūtra describes and makes use of what it terms a Meru-​figure. Since Meru is the name of a mythological mountain, the figure has the form of a mountain; that is, broad at the base and becoming thinner with height, culminating in a peak. This “mountain shape” is identical to what we now call Pascal’s triangle. Indeed, the correct number of syllabic patterns with m heavy syllables can be found using Pascal’s triangle. A representation of the Meru-​figure is shown in figureA3a.1. It has 1’s along its top edges; any other element is the sum of the two elements to the left and the right above it. Detailed studies of the combinatorial analysis of syllabic patters in ancient India can be found in Van Nooten (1993), Sarma (2003), and Sridharan (2005).

90    Ancient Scientific Traditions Beyond Greece and Rome 1 1 1 1 1 1

3 4

5

1 2

1 3

6 10

1 4

10

1 5

1

Figure A3a.1  Meru-​figure from the Chandaḥ-​sūtra. Drawing by author.

It is important to note here that the Chandaḥ-​sūtra mentions the Sanskrit word for “empty” (śūnya), which later came to designate “zero” in Indian mathematics (Plofker 2009, 56).

2.3 Mathematics in the Buddhist and Jain Traditions The mathematics examined so far all comes from the Sanskrit tradition of Hinduism. Other traditions, however, also studied and contributed to mathematics in ancient India. Notable among these are the Buddhist and Jain traditions. The Jain tradition is rife with speculations on size and on both the finite and the infinite, including postulating different types of infinities (Plofker 2009, 57–​59). The kinds of infinities postulated by the Jains include infinity in two directions (that is, in area) and infinity all over. A striking feature of Jain mathematics is its classification of various types of computations. The list, which has 10 items, includes operations (as in the operations of arithmetic); squares, or products in general; cubes; and fourth powers (Hayashi 2003, 120).

2.4 Mathematical Astronomy The earliest known text on astronomy in India is the Jyotiṣa-​vedāṅga, a text accompanying the Vedas, which is concerned with calendrics and the timing of rituals. The text exists in two recensions. The text works with a year of 366 days and provides astronomical parameters for the motion of the sun and the moon across the sky. From around 400 ce, astronomy in India became dominated by what we may refer to as the classical tradition of Indian astronomy. The theory and models of astronomy became codified in treatises known as siddhāntas; that is, comprehensive treatises that not only provide the mathematical formulae necessary for computing planetary positions, predicting lunar eclipses, and so on, but also expound the model and theory behind these formulae. While divided between a number of different astronomical schools, the texts share a general, common model: The spherical earth is the center of the universe.

Mathematics in India   91 Around it orbits the sun, the moon, and the planets. To account for the observed motions of these heavenly bodies, an epicyclic model is employed. That is, the sun, the moon, and the planets do not orbit the earth on perfect circles, but on smaller circles centered on a perfect circle with the earth as its center. The earliest known example of a siddhānta is the so-​called Paitāmaha-​siddhānta. The name of the treatise derives from the Sanskrit word pitāmaha, “grandfather,” a common name of the god Brahmā, called thus because he is the creator of our universe. The Paitāmaha-​siddhānta is presented as a dialogue between Brahmā and the sage Bhṛgu, the former instructing the latter in the science of astronomy. The Paitāmaha-​siddhānta, as it has been handed down to us through the centuries, is an incomplete and corrupt text that at some point in time was incorporated into a purāṇa (literally, Old Tales; the purāṇas are religious texts of an encyclopedic nature, covering, among many other topics, cosmology and astronomy). The topics dealt with in the text include computation of mean and true planetary positions (the former via parameters supplied in the text, the latter via trigonometry) and computation of lunar and solar eclipses. Later siddhāntas followed a general structure that addressed these same topics. Astronomical parameters play a crucial role here. For example, mean celestial motion and positions are found via given parameters and proportions of them. The texts will provide parameters for how many times a planet orbits the earth in a set period of time (generally a kalpa of 4,320,000,000 years), the mean velocities of the sun, the moon, and the planets known at the time (Mercury, Venus, Mars, Jupiter, and Saturn). The trigonometry discussed in the texts allows for the computation of the true position of a planet at a given time. The texts also provide approximate formulas, including iterative ones, for carrying out computations. More than on actual observations, the classical astronomical schools of India rest on ingenious mathematical innovations and manipulations of the existing model. Such innovations can be of two kinds: simplifications to aid computation, or expansion of complexity in an effort to be more accurate.

2.5 Mathematics in the Classical Period During the part of the classical period under discussion here (that is, until 650 ce), the Indian tradition did not produce independent mathematical works. Rather, mathematical expositions were found as chapters of larger astronomical works. Later on, mathematical works were written as independent treatises, though some subfields of mathematics, notably trigonometry, continued to be included under astronomy. Techniques, such as the so-​called pulverizer (that is, the solution in integers to the equation ax + by = c, where a, b, and c are integers; see Plofker 2009, 149–​150) are found in these chapters. Such techniques often have applications in astronomy. At this point, we will turn our attention to three noteworthy Indian mathematicians before 650 ce.

92    Ancient Scientific Traditions Beyond Greece and Rome

2.6 Āryabhaṭa With a crater on the moon and a satellite of the modern country of India named after him, one of the towering figures in the history of astronomy and mathematics in Indian mathematics is Āryabhaṭa. His most famous work is the Āryabhaṭīya, an astronomical work with mathematical chapters. According to his testimony, he was born in 476 ce. Āryabhaṭa used his own alternative to the bhūta-​saṃkhyā system. His system, however, was less effective. It produces random strings of syllables, which are easy for a scribe to copy incorrectly. The Āryabhaṭīya gives an excellent approximation to the value of π, namely 62832/​20000 = 3.1416. Other topics engaged are trigonometry, the pulverizer, and geometry.

2.7 Brahmagupta The astronomer and mathematician Brahmagupta was born in 598 ce. His main work is the Brāhma-​sphuṭa-​siddhānta, an astronomical siddhānta with mathematical chapters. In the treatise, Brahmagupta is critical of Āryabhaṭa and the model he employed in the Āryabhaṭīya. In the Brāhma-​sphuṭa-​siddhānta, Brahmagupta gives algebraic rules for the number 0. In other words, 0 is in this system a number in its own right. It can be added to another number or multiplied by a given number. In other words, rather than just indicating an empty place in a number representing as a string of digits, 0 is here an actual algebraic entity. Brahmagupta went further still in his investigation of the number 0, formulating an unsuccessful attempt at a definition of division by 0. Other impressive mathematical results given by Brahmagupta include Brahmagupta’s formula, which gives a rule for computing the area of quadrilaterals inscribed in a circle, the so-​called cyclic quadrilaterals. Brahmagupta also studied a difficult second-​order equation, now referred to as the Pell equation: given a positive integer N which is not a square, find positive integers x and y such that Nx^2 + 1 = y^2. Brahmagupta showed that if a solution in positive integers can be found to Nx^2 + k = y^2, where k is one of -​1, 2, -​2, 4, or -​4, we can construct a solution to Nx^2 + 1 = y^2 (Plofker 2009, 195).

2.8 Bhāskara I Bhāskara I, so called to distinguish him from a later and more famous mathematician of the same name (Bhāskara II, born 1114 ce), wrote a commentary on the Āryabhaṭīya in 629 ce. In that commentary, he presented a remarkable and accurate approximation to the sine function for angles between 0 and 90 degrees, which is expressed as a ratio of two second-​degree polynomials (Plofker 2009, 81–​82). In other words, a sine value can be found without using a table of sines and interpolation, but by direct computation.

Mathematics in India   93

2.9 A Long History Covering a period of more than a millennium and a half, this brief essay only touches the tip of the iceberg that is the history of mathematics in India before 650 ce. In the interest of space, many episodes have been described briefly and others omitted entirely. It is hoped that the bibliography will lead the interested reader to more comprehensive sources. In particular, (Plofker 2009) is a recent and reliable account of the history of mathematics in India.

Bibliography Primary Sources in Translation Ṛg-​veda. Jamison, Stephanie W., and Joel P. Brereton, trans. The Rigveda: The Earliest Religious Poetry of India. New York: Oxford University Press, 2014. Śata-​patha-​brāhmaṇa. Eggeling, J. Satapatha-​ Brahmana According to the Text of the Madhyandina School. 5 vols. Oxford: Oxford University Press, 1897. Śulbasūtras. Sen, S. N., and A. K. Bag. The Śulbasūtras of Baudhāyana, Āpastamba, Kātyāyana and Mānava with text, English translation and commentary. New Delhi:  Indian National Science Academy, 1983. Vedāṅga-​jyotiṣa. Sarma, K. V., and T. S. Kuppanna Sastri. “Vedāṅga-​jyotiṣa of Lagadha (in its Ṛk and Yajus recensions) with the Translation and Notes of T. S. Kuppanna Sastry.” Indian Journal of History of Science 19 (1984), supplement. Yajur-​veda. Griffith, Ralph T. H. The Texts of the White Yajurveda. New Delhi: Munshiram Manoharlal, 1987.

Secondary Literature Bag, A. K., and S. R. Sarma, eds. The Concept of Śūnya. New Delhi: Indian National Science Academy, 2003. Brummelen, Glen Van. The Mathematics of the Heavens and the Earth: The Early History of Trigonometry. Princeton, NJ: Princeton University Press, 2009. Datta, B., and A. N. Singh. History of Hindu Mathematics. Delhi: Bhartiya Kala Prakashan, 2001. Dunmore, Helen, and Ivor Grattan-​Guinness, eds. Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences. Baltimore, MD:  Johns Hopkins University Press, 2003. Emch, Gerard, et  al., eds. Contributions to the History of Indian Mathematics. New Delhi: Hindustan Book Agency, 2005. Gillispie, Charles Coulston, ed. Dictionary of Scientific Biography. Vol. 2. New  York: Scribner, 1970. Hayashi, Takao, “Indian Mathematics.” In Dunmore and Grattan-​Guinness 2003, 118–​130. Keyser, Paul T. and Georgia L. Irby-​Massie, eds., Encyclopedia of Ancient Natural Scientists: The Greek Tradition and Its Many Heirs. New York: Routledge, 2008. Kichenassamy, Satyanad. “Baudhāyana’s Rule for the Quadrature of the Circle.” Historia Mathematica 33.2 (2006): 149–​183.

94    Ancient Scientific Traditions Beyond Greece and Rome Pingree, David. “Bhāskara I.” In Gillispie 1970, 114–​115. —​—​—​. “Brahmagupta.” In Gillispie 1970, 416–​418. Plofker, Kim, and Toke Knudsen. “Āryabhaṭa.” In Keyser and Irby-​Massie 2008, 167–​168. —​—​—​. “The Paitāmahasiddhānta.” In Keyser and Irby-​Massie 2008, 604–​605. Plofker, Kim. Mathematics in India. Princeton, NJ: Princeton University Press, 2009. Sarma, Sreeramula Rajeswara. “Śūnya in Piṅgala’s Chandaḥsūtra.” In Bag and Sarma 2003, 126–​136. Sridharan, R. “Piṅgala and Binary Arithmetic.” In Gerard et al. 2005, 34–​62. Van Nooten, B. “Binary Numbers in Indian Antiquity.” Journal of Indian Philosophy 21 (1993): 31–​50.

chapter A3b

Sanskrit Me di c a l Literatu re Tsutomu Yamashita

On the Indian subcontinent, the oldest evidence of medicine is found in the Indus Valley civilization dating roughly 2600–​1900 bce. However, based on archeological evidence, a direct connection between the medicine of this era and that of the later historical era still remains indistinct in a strict sense. In the written records of the later historical era in India, evidence of medicine can be broadly broken into two categories. The first category: the medically related lore and activities found in fragments of religious texts and other literary works. The second category: the systematic medicine known as Āyurveda presented in specific medical texts written in Sanskrit.

1.  Medicine in the Veda The earliest textual evidence of medicine in India is found in the Veda (Vedic literature) dating roughly 1500–​500 bce, which is included in the above mentioned first category. The Veda is a collective term for the texts of revelation, or śruti, which literally means “hearing” or “what is heard” from the gods. The word veda is a general noun that means “knowledge” in Sanskrit. The main body of the Veda consists of four kinds of corpora (saṃhitā) written in Vedic Sanskrit: the Ṛgvedasaṃhitā; the Yajurvedasaṃhitās, which contain the Kṛṣṇa Yajurveda and the Śukla Yajurveda; the Sāmavedasaṃhitā; and the Atharvavedasaṃhitā. Of the four kinds of Vedic corpora, medically related lore is randomly recorded mainly in the Atharvavedasaṃhitā, and partly in the Ṛgvedasaṃhitā. Auxiliary Vedic texts from later periods also contain medical accounts in the descriptions of ritual practices and mythological stories (Zysk 1985; Meulenbeld 2003–​2004).

96    Ancient Scientific Traditions Beyond Greece and Rome The medical knowledge found in the Veda, which are primarily religious texts, inevitably lacks unity, and it is difficult to recognize it as a systematic and rational medicine. Some of the medical ideas within the Veda can be roughly summarized as follows: The causal factors of diseases are mostly attributed to supernatural forces that come from outside the human body. Therapeutics is primarily associated with magical procedures in which chanting mantras plays an essential role. A wide range of anatomical vocabulary, likely gained through observation of ritual animal sacrifice, is found in places of the texts. Several kinds of breath (prāṇa) are believed to circulate in the human body in order to maintain it (Filliozat 1975). The physiological and pathological theories of later systematic medicine are clearly not found in the Veda.

2.  Āyurveda as a Systematic Medicine After a long temporal gap from the era of the Veda, treatises and corpora specialized in medicine began to appear in India beginning centuries following the Christian era. These medical texts written in mainly Sanskrit are generically known as Āyurveda [a‫׃‬juruve‫׃‬də] (the knowledge of life). It must be noted that Āyurveda developed far later than the Veda, and that the texts of Āyurveda, despite the similarity in name Āyur-​ “veda,” are not formally included in the orthodox Veda. The extant texts of Āyurveda, even those from the early stage, illustrate an almost completed knowledge of systematic medicine that likely developed through medical experiences and speculations garnered over the course of centuries. However, because few textual sources exist showing the gradual development of medicine from its rudimentary stages in the period between the Veda and the Āyurveda texts, it is difficult to trace the historical development of Āyurveda in the texts. It is nevertheless clear that the intricate structures contained within each voluminous corpus of Āyurveda suggest a complicated process of textual development in which not one but several authors revised the texts over a long time. This may reflect the complexity of historical development of Āyurveda as a systematic medicine. (For the medical treatises of an early date found in the Bower manuscript, see Hoernle [1893‒1912] 2011 and Wujastyk 2001, 198‒209. For the relationship between the Buddhist canons and the Āyurveda texts, see Mitra 1985 and Zysk 1991.)

3.  Relationships between Vedic Medicine and Āyurveda Specialized medical texts written in Sanskrit reveal that Āyurveda had been developing as a systematic medicine within particular theoretical frameworks of which an essential part was diverted from philosophical concepts (Dasgupta 1975, 2:273‒436). In this

Sanskrit Medical Literature    97 regard, there is a distinct difference between medicine described in the Veda and that in the Āyurveda texts. However, besides religious faith and the basic worldview, some vestiges of medical notions and terms from the Veda remain in the Āyurveda texts. For instance, physiological speculation regarding circulation of the several kinds of breaths (prāṇas) and other specific physiological terms (for example, rasa and ojas) are commonly found in the Āyurveda texts. Some anatomical vocabulary found in the Vedic literature was also adopted in Āyurveda often with slight changes in meanings. The causal factors of several intractable diseases are attributed to supernatural forces. Religious rituals, especially the chanting of mantras that are limited to particular treatments, are also recommended in some Āyurveda texts (Filliozat 1975, 117‒160; Zysk 1985, 10‒11). In addition to these vestiges, we can find other remnants of the Veda, which might have been intentionally left, in the Āyurveda texts. For example, the word Āyur-​“veda” was modeled after the orthodox Veda, and the word saṃhitā (corpus), which appears in the titles of the corpora of Āyurveda, as we see later, were apparently named after the Vedic saṃhitās. In some medical texts (for example, the Suśrutasaṃhitā, Sūtrasthāna 1.6), Āyurveda itself is defined as an auxiliary division (upāṅga) of the Atharvaveda. The origin of Āyurveda is related to the Vedic gods in the mythical story found in some Āyurveda texts. The likely explanation of these textual situations of Āyurveda at an early stage is that Āyurveda has been developed by contemporary physicians (bhiṣaj) as an empirical and systematic new medicine in Hindu society. During the long term of historical development of Āyurveda, specialized medical texts were being prepared within newly invented theoretical frameworks. However, to establish a position as a reliable medical system in Hindu society, it would need to develop under the authority of the Veda. Therefore, physicians would have had to intentionally write the texts of Āyurveda in a similar format to the Veda (Chattopadhyaya 1979). The corpora of Āyurveda from the early period consists of the Carakasaṃhitā [tʃæraka-​sanhita:] (the corpus of Caraka), the Suśrutasaṃhitā [suʃruta-​sanhita:] (the corpus of Suśruta), and the Aṣṭāṅgahṛdayasaṃhitā [aʃta:ŋga-​fridaya-​sanhita:] (the corpus of the eight branches’ essences). These corpora are known as the three major works (Bṛhattrayī) of Āyurveda. The three minor works (Laghutrayī) of Āyurveda, which belong to the later period, consist of the Mādhavanidāna or Rogaviniścaya (the pathological treatise of Mādhavakara) (Meulenbeld 1974), the Śārṅgadharasaṃhitā (the corpus of Śārṅgadhara), and the Bhāvaprakāśa (the treatise of Bhāvamiśra).

4.  The Two Schools of Āyurveda and the Textual Formations A mythical story of the origin of Āyurveda can be found in the beginning part of the Carakasaṃhitā (Sūtrasthāna 1.3‒40). This story states that knowledge of Āyurveda,

98    Ancient Scientific Traditions Beyond Greece and Rome which had originally been created by the Lord Brahmā, was handed down by the gods Prajāpati and Aśvin and from them to the god Indra. Sage Bharadvāja, on behalf of humans, visited the god Indra to learn about Āyurveda and brought Āyurveda to the human world. Sage Bharadvāja then introduced Āyurveda to another sage, Punarvas Ātreya. Sage Ātreya in turn taught Āyurveda to his six disciples:  Agniveśa, Bheḍa, Jatūkarṇa, Parāśara, Hārīta, and Kṣārapāṇi. It was the six disciples of Punarvas Ātreya who recorded their master’s teachings and compiled each corpus of Āyurveda. Within the six disciples’ corpora, Agniveśa’s work, the Agniveśatantra is supposed to be the original form of the Carakasaṃhitā. The original Agniveśatantra no longer exists, but, after the original text was altered and compiled by revisers in different periods, it came down to us as the Carakasaṃhitā. Two revisers of the Carakasaṃhitā are known:  Caraka and Dṛḍhabala. The Carakasaṃhitā (Cikitsāsthāna 30.289‒290) reveals that Caraka could not complete his revision of the whole text. Another reviser, Dṛḍhabala, completed the work instead, adding the 17 chapters of the sixth section, and the last two sections. The medical corpus, the Carakasaṃhitā, was thus named for one of its revisers. The school of Āyurveda, as represented by the Carakasaṃhitā, is known as the Ātreya school. In addition to the Carakasaṃhitā, of the six disciples’ corpora of this school, Bheḍa’s corpus, the Bheḍasaṃhitā (or Bhelasaṃhitā) still exists, though it is incomplete. Another school of Āyurveda is represented by the Suśrutasaṃhitā. Like the Carakasaṃhitā, the Suśrutasaṃhitā (Sūtrasthāna 1.3‒21) contains a mythical story on the origin of Āyurveda. In this story, Dhanvantari, king of Kāṣī, who is an avatar of Lord Brahmā, imparts Āyurveda to his seven disciples. One of these disciples, Suśruta records this knowledge as a corpus called the Suśrutasaṃhitā. In the Suśrutasaṃhitā, the position of Ātreya in the Ātreya school is changed to Dhanvantari. The school is thus known as the Dhanvantari school of Āyurveda. This school specializes mainly in surgical treatments (Śalya). The extant text of the Suśrutasaṃhitā also seems to have been created by authors and revisers from different historical periods. Ḍalhaṇa, who is one of the commentators on the Suśrutasaṃhitā, mentions one reviser’s name as Nāgārjuna (the Nibandhasaṃgraha on the Suśrutasaṃhitā, Sūtrasthāna 1.1‒2), but Ḍalhaṇa does not provide other details about this reviser.

5. The Carakasaṃhitā The eight branches (aṅgas) of Āyurveda are enumerated in the Carakasaṃhitā (Sūtrasthāna 30.28), namely, (1) Kāyacikitsā: internal medicine; (2) Śālākya: treatments of diseases in the region from the neck up; (3) Śalyāpahartṛka: surgical treatments; (4) Vi ṣagaravairodhikapraśamana: treatments for toxins by animal and vegetative poisons; (5) Bhūtavidyā: demonology and mental disorders; (6) Kaumārabhṛtya: obstetrics, gynecology, and pediatrics; (7) Rasāyana: methods of longevity; (8) Vājīkaraṇa: methods

Sanskrit Medical Literature    99 concerned with aphrodisiacs. Of the eight branches, the Carakasaṃhitā primarily deals with (1) Kāyacikitsā: internal medicine, which is at the top of the list. The textual structure of the Carakasaṃhitā does not follow the order of the eight branches. The eight sections (sthānas) are not branches but are ordered in this corpus from the perspective of educational effect. That is, if a student of Āyurveda learns it in order from the first to the final section, that student can reasonably gain an understanding of the whole picture of Āyurveda of the Ātreya school. The eight sections of the Carakasaṃhitā are made up of 120 chapters. The outlines of the eight sections are as follows: The first section, Sūtrasthāna (30 chapters): general information and theories of the Ātreya school; foods, drinks, and drugs. The second section, Nidānasthāna (8 chapters):  etiology and pathology of intractable diseases and mental disorders. The third section, Vimānasthāna (8 chapters): theories of diets; life circumstances; pathology; physiology; the study method and logics of Āyurveda. The fourth section, Śārīrasthāna (8 chapters): philosophical, anatomical, and embryological expositions on the human beings; obstetrics. The fifth section, Indriyasthāna (12 chapters): death of the human beings; signs of foretelling death. The sixth section, Cikitsāsthāna (30 chapters):  methods of longevity (Rasāyana); methods concerned with aphrodisiacs (Vājīkaraṇa); pathologies and treatments of each disease. The seventh section, Kalpasthāna (12 chapters):  preparations of emetic and purgative drugs; the systems of weights and measures. The eighth section, Siddhisthāna (12 chapters): applications of the various therapeutic measures. Internal medicine (Kāyacikitsā) and its related subjects are dealt with throughout all the sections, and other branches are also partly illustrated. Approximately 1,100 medicinal plants’ names, including their synonyms, are found in the Carakasaṃhitā (Singh and Chunekar 1999, ix). These medicinal plants are mainly used as compound drugs. The authors and revisers of the Carakasaṃhitā did not explicitly mention the dates of the text. According to G. Jan Meulenbeld, judging from the anteroposterior relationships of the related texts and facts found within these texts, Dṛḍhabala, who seems to have compiled the extant text of the Carakasaṃhitā, might belong to the period ca 300 to 500 ce (Meulenbeld 1999‒2002, IA:9‒200).

6. The Suśrutasaṃhitā The eight branches (aṅgas) of Āyurveda are also enumerated in the Suśrutasaṃhitā (Sūtrasthāna 1.7). The contents of the eight branches are almost identical to those of the Carakasaṃhitā’s, but the order is different. The branch of Śalya (surgical treatments) is at the top in the Suśrutasaṃhitā’s list and is dealt with primarily in this corpus. The Suśrutasaṃhitā consists of five main sections (sthānas) (120 chapters) and one supplemental section (Uttaratantra) (66 chapters). The five main sections cover the major subjects of the Dhanvantari school relating to surgery, and the supplemental section deals with other subjects. The outlines of the main and supplemental sections

100    Ancient Scientific Traditions Beyond Greece and Rome are as follows:  The first section, Sūtrasthāna (46 chapters):  general information and theories of the Dhanvantari school; foods, drinks, and drugs. The second section, Nidānasthāna (16 chapters): etiology and pathology of intractable diseases, and bone fractures. The third section, Śārīrasthāna (10 chapters):  philosophical, anatomical, and embryological expositions on the human beings; obstetrics. The fourth section, Cikitsāsthāna (40 chapters):  pathologies, treatments, and drugs related to diseases and wounds; methods of longevity (Rasāyana); methods concerned with aphrodisiacs (Vājīkaraṇa). The fifth section, Kalpasthāna (8 chapters): hygiene of foods and drinks; detoxification treatments (Agadatantra). The supplemental section, Uttaratantra (66 chapters): treatments of diseases of the region from the neck up (Śālākya); pediatrics (Kaumārabhṛtya); internal medicine (Kāyacikitsā); demonology and mental disorders (Bhūtavidyā); theory of tastes; the maintenance of health; the logic for academic work (tantrayukti); medical theories. The third section (Śārīrasthāna 5.47‒49) contains a noteworthy description of the methods of human dissection, written in a manner suggesting it was intended to educate surgeons (Zysk 1986). This description is quoted in a later medical text, the Aṣṭāṅgasaṃgraha (Sūtrasthāna 34.38). Although the date the Suśrutasaṃhitā was completed is unknown, judging from its contents, writing style, and relation to other texts, it is likely it was completed slightly later than the Carakasaṃhitā revised by Dṛḍhabala (Meulenbeld 1999‒2002, IA:203‒389).

7. The Aṣṭāṅgahṛ̣dayasaṃhitā The Aṣṭāṅgahṛdayasaṃhitā consists of six sections (sthānas) (120 chapters in total). The outlines of the sections are as follows: The first section, Sūtrasthāna (30 chapters): introductory topics to Āyurveda; regimens for a healthy life; foods, drinks, and drugs; the basic theories of Āyurveda regarding tastes; physiology; various therapies and surgical treatments. The second section, Śārīrasthāna (6 chapters):  embryology, anatomy, and prognosis. The third section, Nidānasthāna (16 chapters):  diagnosis, etiology, and pathology of intractable diseases. The fourth section, Cikitsāsthāna (22 chapters):  treatments and drugs of diseases. The fifth section, Kalpasthāna (6 chapters): preparation of emetic and purgative drugs; pharmaceutics. The sixth section, Uttarasthāna (40 chapters): pediatrics (Bāla); demonology and mental disorders (Graha or Bhūtavidyā); treatments of diseases in the region from the neck up (Ūrdhvabhāga); surgical treatments (Śalyā); detoxification treatments (Daṃṣṭrā); methods of longevity (Ajara); methods concerned with aphrodisiacs (Vṛṣan). The five main sections of the Aṣṭāṅgahṛdayasaṃhitā, like the Suśrutasaṃhitā, cover the major subjects; the last section deals with other minor subjects. While direct and indirect quotations from the Carakasaṃhitā and the Suśrutasaṃhitā often appear in the Aṣṭāṅgahṛdayasaṃhitā, the originalities and new position of this work are also

Sanskrit Medical Literature    101 distinguished in places. Although the Carakasaṃhitā and the Suśrutasaṃhitā are written in a combination of prose and verse, the Aṣṭāṅgahṛdayasaṃhitā is written solely in concise verses. The text seems to have been compiled, with some interpolations, to combine the teachings of the Ātreya and Dhanvantari schools of Āyurveda with the new knowledge of medicine. Thus, the Aṣṭāṅgahṛdayasaṃhitā is recognized as one of the three great works (Bṛhattrayī) of Āyurveda along with the Carakasaṃhitā and the Suśrutasaṃhitā. Judging from the anteroposterior relationships of the texts, the extant version of the Aṣṭāṅgahṛdayasaṃhitā attributed to Vāgbhaṭa was likely completed after the Dṛḍhabala’s revision of the Carakasaṃhitā, and also slightly after the Suśrutasaṃhitā (Meulenbeld 1999‒2002, IA 393‒473). In addition to the Aṣṭāṅgahṛdayasaṃhitā, a similar medical compendium known as the Aṣṭāṅgasaṃgraha [aʃta:ŋga-​sangraha] (the compendium of the eight branches) is also attributed to Vāgbhaṭa. Whether the author of these two texts is the same Vāgbhaṭa or two persons with the same name is a matter of controversy among scholars, as is the textual relationship between the two medical works (Meulenbeld 1999‒2002, IA 477‒685).

8.  The Physiological and Pathological Theories of Āyurveda A notable characteristic of traditional Indian thought is its affinity for enumeration and hierarchical classification of various objects and phenomena in the universe. This tendency is commonly found in religious and secular texts as well, including the medical texts of India. In the Sanskrit texts of Āyurveda, the physical constitutions and temperaments of human beings; diseases and their causal factors; foods, drinks, and drugs; life environments; and almost all things relating to human life are arranged topically, enumerated item by item, and classified according to hierarchy. The numbers and orders of these items have important implications when applying the results of classifications. The three doṣas (morbific entities or morbific agents considered to have analogical functions of wind, fire, and water in the human body) and the six rasas (tastes and qualities of foods, drinks, and drugs; rasa literally means “essence”) are mainly applied as the primary criteria of these classifications in Āyurveda. The features and mutual reactions of each item and factor therefore become visible and are simplified in the analogical correlations of the doṣas and the rasas. In the therapeutics of Āyurveda, the physician makes a diagnosis and decides the treatment method based on an analysis of the mutual reactions of each factor through classification of the patient’s original constitution, causal factors of disease, remedial measures,

102    Ancient Scientific Traditions Beyond Greece and Rome and drugs. The principle of treatment behind the Āyurveda is not unlike the Hippocratic formula: contraria contrariis curantur (the opposite is cured with the opposite). The word doṣa literally means “defect” in Sanskrit, but in Āyurveda, doṣa becomes one of the bodily entities. The doṣas are classified into three categories (tridoṣa): vāta, pitta, and kapha (or śleṣman) often misleadingly translated as “wind,” “bile,” and “phlegm.” The three doṣas have their own functions and original places associated with the elemental images of wind, fire, and water in the human body. They might be, more realistically, identified as the gaseous matter, digestive fluid, and viscid fluid respectively in the human body. In the contexts of traditional medicine, doṣa is often translated as “humor” by a careless association of the humoral theory of Greek medicine. However, in Āyurveda, at least, one of the doṣas, vāta denotes a gaseous matter in the body, not a bodily fluid like a humor in Greek medicine. When doṣas maintain equilibrium in their quantities and qualities, the human body is considered healthy in the physiology of Āyurveda. Any disruption of balance in the doṣas leads to disorders or diseases of the body and mind. The types and conditions associated with these disorders or diseases are mainly determined by which doṣa or doṣas are involved, and how the doṣa or doṣas are involved. In this regard, the three doṣas act not only as fictional criteria of classification but also as actual entities or morbific agents in the body (Meulenbeld 2009; 2011). Other bodily elements, besides the doṣas, also play important parts in the physiology of Āyurveda. There are the seven bodily elements (dhātu) and waste products (mala or kiṭṭa). The seven bodily elements are nutrient fluid or essence of food and drink (rasa), blood (rakta), muscular tissue (māṃsa), fatty tissue (medas), bone (asthi), bone marrow (majjā), and generative element or semen (śukra). These seven bodily elements have their own functions and are linked together in this order. At first, digested foods and drinks are transformed into nutrient fluid (rasa) in the body. Then, a part of the nutrient fluid changes into the next element, blood (rakta). Thus, through linkage, a part of each dhātu continuously transforms into the next element. The serial order of the seven elements is significant in this process. When this transformative process runs in its normal order and state, the human body is in good condition. Waste products (mala or kiṭṭa) are produced during this process. When the seven bodily elements and the waste products maintain their normal quantities and qualities, they are assumed to contribute to keeping the human body in good condition. In the physiology of Āyurveda, the concept of several channels (mainly, srotas, dhamanī, sirā, and nāḍī) in the human body is also significant when it concerns the transfer and circulation of entities and breaths (prāṇas) in the human body. These channels are not directly envisaged as anatomical structures, but their existence running in every direction throughout the human body is envisaged. These channels are supposed to provide passages to the doṣas, dhātus, malas, and prāṇas. Thus, their interactions proceed dynamically through the network of channels in the human body. Furthermore, agni (fire) of the human body is considered to play a central role in the process of digestion and other bodily functions (Jolly 1901; Kutumbiah 1969).

Sanskrit Medical Literature    103 In this manner, the predominant theory of the physiology of Āyurveda can be construed as a kind of dynamic theory of fluids, gaseous matters, and fire in the human body depending on their mutual interactions.

9.  Sanskrit Texts and Translations Aṣṭāṅgahṛdayasaṃhitā: Aṣṭāṅgahṛdayam composed by Vāgbhaṭa . . . collated by Aṇṇā Moreśwara Kuṇṭe and Kṛṣṇa Rāmchandra Śāstrī Navare. Bhiṣagāchārya Hariśāstrī Parāḍakara Vaidya ed. 1939. 7th ed. Varanasi and Delhi:  Chaukhambha Orientalia, 1982. English Translation: Vāgbhaṭa’s Aṣṭāñga Hṛdayam. Trans. K. R. Srikantha Murthy. 3 vols. Varanasi: Krishnadas Academy, 1991‒1995. Aṣṭāṅgasaṃgraha: Śrīmad Vṛddhavāgbhaṭaviracitaḥ, Aṣṭāṅgasaṅgrahaḥ Induvyākhyāsahitaḥ. Anaṃta Dāmodara Āṭhavale ed. Puṇe: Maheśa Anaṃta Āṭhavale, 1980. English Translation: Aṣṭāñga Samgraha of Vāgbhaṭa. Trans. K.  R. Srikantha Murthy. 3 vols. Varanasi: Chaukhambha Orientalia, 1995‒1997. Bhelasaṃhitā: Bhela Saṁhitā. V. S. Venkatasubramania Sastri and C. Rajeswara Sarma eds. New Delhi:  Central Council for Research in Indian Medicine & Homoeopathy, 1977. English Translation:  Bhela-​Saṃhitā  .  .  .  Trans. K.  H. Krishnamurthy. Varanasi: Chaukhambha Visvabharati, 2000. Carakasaṃhitā: The Charakasaṃhitā of Agniveśa revised by Charaka and Dṛiḍhabala . . . Vaidya Jādavaji Trikamji Āchārya ed. 1941. 4th ed. New Dehli: Munshiram Manoharlal, 1981. English Translation:  Caraka-​Saṃhitā, Agniveśa’s treatise refined and annotated by Caraka and redacted by Dṛḍhabala. Trans. Priyavrat Sharma. 4 vols. Varanasi and Delhi: Chaukhambha Orientalia, 1981‒1994. Suśrutasaṃhitā: Suśrutasaṃhitā of Suśruta . . . Vaidya Jādavji Trikamji Āchārya and Nārāyaṇ Rām Āchārya, eds. 1938. 5th ed. Varanasi, Delhi: Chaukhambha Orientalia, 1992. English Translation: Suśruta-​Saṃhitā  .  .  .  Trans. Priya Vrat Sharma. 3  vols. Varanasi: Chaukhambha Visvabharati, 1999‒2001.

Bibliography Chattopadhyaya, Debiprasad. Science and Society in Ancient India. Calcutta: Research India Publication, 1979. Dasgupta, Surendranath. A History of Indian Philosophy. 4 vols. 1922. Indian ed. Delhi,: Motilal Banarsidass, 1975. Filliozat, Jean. La doctrine classique de la médecine Indienne, ses origines et ses parallèles grecs. 2nd ed. Paris: École française d’Extrême-​Orient, 1975. Hoernle, A. F.  Rudolf, ed. The Bower Manuscript, Facsimile Leaves, Nagari Transcript, Romanised Transliteration and English Translation with Notes. 1893‒1912. Reprint, New Delhi: Aditya Prakashan, 2011.

104    Ancient Scientific Traditions Beyond Greece and Rome Jolly, Julius. Medicin. Grundriss der Indo-​Arischen Philologie und Altertumskunde. III.10. Strassburg: Verlag von Karl J. Trübner, 1901. Kutumbiah, P. Ancient Indian Medicine. Rev. ed. Bombay: Orient Longmans, 1969. Meulenbeld, G. Jan. The Mādhavanidāna and Its Chief Commentary Chapters 1‒10. Leiden: E. J. Brill, 1974. —​—​—​. A History of Indian Medical Literature. 5 vols. Groningen: Egbert Forsten, 1999‒2002. —​—​—​. “Āyurveda and Atharvaveda:  Their Interrelationship in the Commentaries on the Kauśikasūtra.” Studia Asiatica, International Journal for Asian Studies 4‒5 (2003‒2004): 289‒312. —​—​—​. “Some Neglected Aspects of Ayurveda or the Illusion of a Consistent Theory.” In Mathematics and Medicine in Sanskrit, ed. Dominik Wujastyk, 105–​117. Delhi:  Motilal Banarsidass, 2009. —​—​—​. “The Relationships between Doṣas and Dūṣyas: A Study on the Meaning(s) of the Root murch-​/​mūrch*.” Electronic Journal of Indian Medicine 4 (2011): 35–​135. Mitra, Jyotir. 1985. A Critical Appraisal of Āyurvedic Material in Buddhist Literature, with Special Reference to Tripiṭaka. Varanasi: Jyotiralok Prakashan, 1985. Singh, Thakur Balwant, and K. C. Chunekar. Glossary of Vegetable Drugs in Brhattrayī. 2nd ed. Varanasi: Chaukhamba Amarabharati Prakashan, 1999. Wujastyk, Dominik. The Roots of Āyurveda, Selections from Sanskrit Medical Writings. Rev. ed. New Delhi: Penguin, 2001. Zysk, Kenneth G. Religious Healing in the Veda, with Translations and Annotations of Medical Hymns from the Ṛgveda and the Atharvaveda and Renderings from the Corresponding Ritual Texts. Transactions of the American Philosophical Society Held at Philadelphia for Promoting Useful Knowledge. Vol. 75, Part  7. Philadelphia:  the American Philosophical Society, 1985. —​—​—​. “The Evolution of Anatomical Knowledge in Ancient India, with Special Reference to Cross-​cultural Influences.” Journal of the American Oriental Society 106.4 (1986): 687‒705. —​—​—​. Asceticism and Healing in Ancient India, Medicine in the Buddhist Monastery. New York and Oxford: Oxford University Press, 1991.

A4. China

chapter A4a

A ncient C h i ne se M athem at i c s Alexei Volkov

It would be impossible to identify the moment in time when mathematical activities were conducted on Chinese soil for the first time; there exist mentions of institutions established for elementary mathematics instruction as early as the late second millennium bce. These mentions are found in texts compiled in the late mid-​first millennium bce and therefore may contain later reconstructions whose reliability can be questioned; however, the earliest extant mathematical texts are dated to the last centuries of the first millennium bce, and it would be reasonable to conjecture that the state of the discipline they represent resulted from a relatively long period of development. This chapter is devoted to the earliest period in the history of traditional Chinese mathematics, in particular, it will focus on the mathematical treatises compiled prior to the beginning of the Sui 隋 dynasty (581–​618 ce); this chronological boundary corresponds to the time when China was united again after a long period of disunity that started with the fall of the Han 漢 dynasty (206 bce‒220 ce).1

1.  Mathematical Treatises The mathematical treatises compiled during the period under investigation can be subdivided into two groups. The first group includes the mathematical texts that survived most likely due to their use for educational purposes during the Sui, Tang 唐 (618–​907 ce), and Song 宋 (960–​1279 ce) dynasties. (Some mathematical texts preserved in manuscript 1  In this chapter I use the transliteration system pinyin adopted in Mainland China and in European sinology. The titles of texts and names of authors are provided in traditional versions of Chinese characters supplemented, in the case of publications of modern Mainland Chinese authors, by their simplified versions.

108    Ancient Scientific Traditions Beyond Greece and Rome form in the library of the Dunhuang monastery have connections with this group; for a description and preliminary analysis of those, see Libbrecht 1982.) The received versions of these texts were physically produced (printed) much later than the time when they were compiled; they, therefore, may contain alterations made during the second half of the first millennium ce or even later. The second group of mathematical treatises, less numerous but extremely important for our understanding of the earliest period of the development of Chinese mathematics, consists of three recently excavated manuscript texts presumably compiled in the late first millennium bce. Only one of them has been published and translated, while two others are currently under investigation.

1.1 Mathematical Texts Listed in Bibliographies of Standard Histories Bibliographic sections of the standard histories Sui shu 隋書 (Documents of the Sui [dynasty]), Jiu Tang shu 舊唐書 (Documents of the Tang [dynasty], Old [version]), [Xin] Tang shu 新唐書 (Documents of the Tang [dynasty], New [version]), and Song shi 宋史 (History of the Song [dynasty]) contain lists of titles of mathematical treatises presumably preserved in the imperial library at the moment when the histories were compiled; a considerable number of these treatises were written prior to the beginning of the Sui dynasty (i.e., 581 ce). Unfortunately, only some of them—​in particular, those used for mathematics instruction in the state university of these three dynasties—​are still extant. It remains unknown whether the titles of certain lost treatises and information about their compilers and commentators may guarantee that these treatises were close enough to the extant texts with identical or similar titles. For instance, all the extant editions of the treatise Jiu zhang suan shu 九章算術 (Computational Procedures of the Nine Categories) contain nine juan 卷 (chapters, lit. scrolls) and are commented on by Liu Hui 劉徽 (fl. 263 ce) and Li Chunfeng 李淳風 (602–​670 ce). It was often suggested that they stemmed from the treatise titled Jiu zhang suan jing 九章筭經,2 which is listed in the bibliographic chapter of the official history of the Song dynasty, Song shi, that also contained nine juan and was commented on by Liu Hui and Li Chunfeng (Song shi, juan 207: 4a). Meanwhile, the bibliographic chapters of the histories of the Sui and Tang dynasties contain mentions of the nine texts titled Jiu zhang suan shu 九章筭術 or Jiu zhang suan jing 九章筭經 (see table A4a.1).3 One can see that the listed bibliographic chapters do not contain any mentions of a treatise titled Jiu zhang suan shu or Jiu zhang suan jing that contained nine chapters (juan) and was commented on by Liu Hui and Li Chunfeng. Moreover, Liu Hui is not 2 

In the titles of mathematical treatises two versions of the character suan (筭 and 算) were used; their meanings were slightly different: according to the etymological dictionary Shuo wen jie zi 說文解字 by Xu Shen 許慎 (55?—​149? ce), the character suan 筭 meant “counting rods,” while suan 算 meant the operations performed with them. In this chapter, I use the character suan 筭 instead of the character suan 算 in the title of a treatise if in at least one source the former character was used instead of the second. 3  Table A4a.1 suggests that the Western translations of the title of the treatise rendering the term “jiu zhang” 九章 as “nine chapters” (or even “Nine books,” as Berezkina and Vogel suggested) are due to a

Ancient Chinese Mathematics    109 Table A4a.1 Treatises titled Jiu zhang suan shu and Jiu zhang suan jing listed in the Sui shu, Jiu Tang shu, and [Xin] Tang shu Number of juan 卷 Author

No.

Title

Commentator(s)

Reference

1

Jiu zhang suan shu 九章筭術

10

Liu Hui 劉徽

Not specified

Sui shu, ch. 34, p. 24a

2

Jiu zhang suan shu 九章筭術

2

Not specified

Xu Yue 徐岳 and Zhen Luan 甄鸞

Sui shu, ch. 34, p. 24a

3

Jiu zhang suan shu 九章筭術

9

Xu Yue 徐岳

Not specified

Tang shu, ch. 59, p. 27b

4

Jiu zhang suan shu 九章筭術

1

Not specified

Li Zunyi 李遵義

Sui shu, ch. 34, p. 24a

5

Jiu zhang suan shu 九章算術

9

Not specified

Li Chunfeng 李淳風

Tang shu, ch. 59, p. 28b

6

Jiu zhang suan jing 九章筭經

29

Xu Yue 徐岳, Zhen Luan 甄鸞 et al.

Not specified

Sui shu, ch. 34, p. 24a

7

Jiu zhang suan jing 九章筭經

2

Not specified

Xu Yue 徐岳

Sui shu, ch. 34, p. 24a

8

Jiu zhang suan jing 九章算經

1

Xu Yue 徐岳

Not specified

Jiu Tang shu, ch. 47, p. 15b

9

Jiu zhang suan jing 九章算經

9

Zhen Luan 甄鸞

Not specified

Jiu Tang shu, ch. 47, p.15b; Tang shu, ch. 59, p. 27b

mentioned as a commentator even once but is instead credited with the authorship of a treatise titled Jiu zhang suan shu in 10 juan; Li Chunfeng is mentioned as the only commentator of a treatise with the same title in 9 juan. It appears impossible to know how much the contents of the treatises listed in table A4b.1 had in common with those of the extant treatise Jiu zhang suan shu.

1.2 Formation of the Corpus of Mathematical Treatises in the Early First Millennium ce It can be argued that modern historians of Chinese mathematics systematically downplayed the social context in which the Chinese mathematical treatises were used and, at least in some cases, designed, namely, the context of mathematics instruction. The misunderstanding, given that the number of chapters (lit. scrolls, juan) of the treatise may have varied from 1 to 29. As the principal commentator of the treatise, Liu Hui, suggested in his preface, the jiu zhang 九章 in the title refers to the ancient term “jiu shu” 九數, “nine types of computations”; for more details see Volkov 2010, 281, n. 1.

110    Ancient Scientific Traditions Beyond Greece and Rome received descriptions of the state educational institutions of the first and early second millennium ce suggest that all the mathematical treatises compiled prior to the late first millennium ce and extant nowadays were used as textbooks since the 7th century onward; moreover, it can be argued that versions of these texts (or at least texts having the same or slightly different titles) were used for mathematics instruction even earlier. The latter claim is based on the available descriptions of an educational institution established during the Northern Zhou 北周 dynasty (557–​581 ce) whose capital was located in Chang’an 長安 (modern Xi’an 西安), that is, in the same city where the mathematics educational institution of the Tang dynasty was reopened later (Volkov 2014, 58–​63). The abovementioned bibliographies allow identifying a set of mathematical treatises compiled or commented upon by Zhen Luan 甄鸞 (b. ca 500, d. after 573 ce), a prominent scholar active at the courts of the Liang 梁 (502–​587 ce) and Northern Zhou dynasties (on whom, see Li 1997, 257–​258; Volkov 1994c). These treatises were to be used as mathematics textbooks and are as follows (see also Li 1955, 70–​72): 1. Zhou bi 周髀 (Gnomon of the Zhou [dynasty]), in 1 juan, with commentaries of Zhen Luan (Sui shu, juan 34, p. 18b; Jiu Tang shu, juan 47, p. 13b; [Xin] Tang shu, juan 59, p. 26a). 2. Jiu zhang suan shu 九章筭術 (or Jiu zhang suan jing 九章筭經) listed in table A.4.b.1 under numbers 2, 6, and 9. 3. Wu cao suan jing 五曹算經 (Computational Treatise of Five Departments), in 2, 3, or 5 juans, compiled by Zhen Luan (Jiu Tang shu, juan 47, pp. 15b‒16a; Song shi, juan 207, pp. 1a, 3b). 4. Sun zi suan jing (Computational Treatise of Master Sun), in 3 juans, compiled and commented by Zhen Luan (Jiu Tang shu, juan 47, p. 15b). 5. Xiahou Yang suan jing 夏侯陽算經 (Computational Treatise of Xiahou Yang), in 1 or 3 juan(s), compiled by, or with commentaries of, Zhen Luan (Jiu Tang shu, juan 47, p. 16a; [Xin] Tang shu, juan 59, p. 27b). 6. Zhang Qiujian suan jing 張丘建算經 (Computational Treatise of Zhang Qiujian), in 1 juan, compiled by, or with commentaries of, Zhen Luan (Jiu Tang shu, juan 47, p. 16a; [Xin] Tang shu, juan 59, p. 27b). 7. Zhui shu 綴術 ([Computational] Procedures of “Mending” (the exact meaning of the term zhui remains unknown), in 5 juans, compiled by Zu Chongzhi 祖沖之, with explanations (shi 釋) by Zhen Luan ([Xin] Tang shu, juan 59, p. 29a; the Sui shu, juan 34, p. 24b, contains a record of a book in 6 juans with this title, but neither author nor commentator is specified). 8. Shu shu ji yi 數術記遺 (Procedures of “Numbering” Recorded to Be Preserved [for Posterity]), in 1 juan, compiled by Xu Yue 徐岳 (b. ca 185, d. ca 227 ce), with commentaries of Zhen Luan (Jiu Tang shu, juan 47, p. 16a; [Xin] Tang shu, juan 59, p. 27b).4 4  It is possible that the same treatise was listed in the Song shi, juan 207, p. 3b as Da yan suan shu fa 大 衍算術法 (Computational Procedures and Methods of “Great Expansion”), 1 juan, compiled by Xu Yue, with the commentaries of Zhen Luan.

Ancient Chinese Mathematics    111 9. San deng shu 三等數 ([Large] Numbers of Three Ranks), in 1 juan, compiled by Dong Quan 董泉, with commentaries of Mr. Zhen [Luan?] (Jiu Tang shu, juan 47, p. 16a). 10. Wu jing suan shu 五經算術, in 2 juans, compiled by Zhen Luan.5 The role played by Zhen Luan in the history of mathematics in China has often been considered insignificant (see, for instance, Qian 1981, 94). Berezkina (1980, 55–​56), however, stressed the importance of his contribution; Li Di also acknowledged Zhen Luan’s impact and devoted a section of his monograph to him (1997, 257–​269).

1.3 Extant Mathematical Treatises 1.3.1 The Jiu zhang suan shu 九章算術 (Computational Procedures of Nine Categories) This treatise has been often considered the most influential ancient Chinese mathematical writing. The precise time of compilation is unknown; the preface of Liu Hui suggests that the treatise was compiled by the state officers Zhang Cang 張蒼 (ca 253‒152 bce) and Geng Shouchang 耿壽昌 (fl. 75 bce‒49 bce) on the basis of earlier (damaged) version(s) of an ancient mathematical text used for mathematics instruction that started from the beginning of the Zhou 周 dynasty (1046–​256 bce). Modern Western scholarship suggests that the compilation of the received version indeed took place during the Former Han 前 漢 dynasty (206 bce‒9 ce) on the basis of earlier materials (Cullen 1993a; see also Chemla and Guo 2004, 43–​46, 54–​56; Guo, Dauben and Xu 2013, 44–​55). The recent discovery of the mathematical text Suan shu shu 算數書 of the late first millennium bce seems to support this claim (Chemla and Guo 2004, 3–​8). All the received versions of the treatise are based on the Song dynasty edition of 1213 ce. The treatise is a collection of 246 mathematical problems with solutions and answers devoted to geometrical, arithmetical, and algebraic matters that can be identified as calculations of areas of rectilinear and curvilinear figures, operations with common fractions (­chapter 1), the “Rule of Three” (­chapters 2 and 3), problems on “proportional distribution” (­chapter 3), calculation of common denominators, extraction of square and cube roots (­chapter 4), calculation of volumes (­chapter 5), simple, compound, and inverse proportions (­chapter 6), “Rule of False Position” (­chapter 7), solution of simultaneous linear equations (­chapter 8), and various problems related to right-​angle triangles including Pythagoras’ theorem (­chapter 9). Several translations of the Jiu zhang suan shu into European languages exist. Éľvira I. Berezkina (Эльвира И. Березкина) published the earliest translation in 1957, into Russian; this translation did not include translations of the commentaries written by Liu Hui and Li Chunfeng that traditionally accompanied all the extant editions of the 5  There is a record of a book with this title in the Sui shu (juan 34, p. 24b), in 1 juan, but neither its author or commentator is specified. The [Xin] Tang shu, juan 59, p. 28b contains a mention of a book with this title in 2 juans; there is no mention of its author and its only commentator is Li Chunfeng.

112    Ancient Scientific Traditions Beyond Greece and Rome treatise. There are also translations into German (Vogel 1968; without commentaries of Liu and Li), French (Chemla and Guo 2004), Czech (Hudeček 2008), and English (Shen, Crossley, and Lun 1999; Guo, Dauben, and Xu 2013); the French and two English publications provided complete translations and analysis of Liu Hui’s and Li Chunfeng’s commentaries.

1.3.2 The Zhou bi suan jing 周髀算經 (Computational Treatise on the Gnomon of the Zhou [Dynasty]) This anonymous compilation, presumably of the late first millennium bce (Cullen 1993b; 1995), includes elements of an archaic cosmological system often identified as “Hemispherical Dome Heaven” (gai tian 蓋天, literally “Canopy-​shaped Heaven”); it opens with a mention of Pythagoras’ theorem for the triangle with the sides (3, 4, 5) and contains a voluminous commentary attributed to an otherwise unknown commentator Zhao Junqing 趙君卿, conventionally dated from the 3rd century ce and often identified with Zhao Ying 趙嬰 whose commentaries are mentioned in the earliest bibliographical records of the treatise. Zhao’s commentary contains an interesting collection of (verbal) formulas describing relationships between the sides of an arbitrary right-​ angled triangle; Gillon (1977) published the first translation and detailed discussion of this part of Zhao’s commentary, and Cullen (1996) translated the treatise into English.

1.3.3 The Hai dao suan jing 海島算經 (Computational Treatise [Beginning with a Problem Concerning] a Sea Island) This relatively short (nine problems) treatise was compiled by Liu Hui as an addendum to the Jiu zhang suan shu; the Tang dynasty editor Li Chunfeng published the problems of Liu Hui as an independent treatise. The treatise was translated several times (Berezkina 1974; Ang and Swetz 1986; Swetz 1992); however, the original proofs of Liu Hui’s correctly devised algorithms remained unknown. Several authors suggested reconstructions based on application of similar triangles; however, Wu Wenjun (1982a; 1982b) argued against such reconstructions. Instead Wu provided reconstructions based on manipulations with areas of figures that resembled approaches found in Liu Hui’s commentaries on some problems of the Jiu zhang suan shu and in Zhao Junqing’s commentaries on the Zhou bi suan jing.

1.3.4 The Sun zi suan jing 孫子算經 (Computational Treatise of Master Sun) This anonymous (despite its title) treatise was most likely compiled between the late third and the early 5th century ce (Lam and Ang 2004, 28; cf. Volkov 2012a, 517, n. a). The earliest extant version of the received version of the treatise in 3 juans is a block-​print of 1213. The handwritten collection of texts Yong le da dian 永樂大典 (Great [Compendium] of Models [of Scholarship Produced in the Reign Period] “Eternal Happiness” [i.e., 1403–​1407 ce]) contained unidentified portions of the treatise; they still existed in the late 18th century and were used by Dai Zhen 戴震 (1724–​1777) to produce his edition of 1773, but, unfortunately, are lost now. Modern editions (SJSS 1963; SJSS 2001) are based on the block-​print of the

Ancient Chinese Mathematics    113 13th century and on Dai Zhen’s edition (see Lam and Ang 2004, 28–​32). Berezkina (1963) translated the treatise into Russian, and Lam and Ang (2004) into English. The treatise contains three chapters (juans); the first chapter provides basic information concerning metrological systems (measures of length, weight, etc.), the system of “large numbers,” that is, terms used to refer to powers of 10 larger than 104, that runs from 108 up to 1080 (this is one of three systems mentioned in the Shu shu ji yi, see below), approximate values of π (= 3) and √2 (= 7/​5), and descriptions of procedures of multiplication and division performed with counting rods. The rest of this chapter contains two lists of operations the purpose of which remains unknown; they may have been used for instruction since their structure may have provided the instructor and/​or learners an easy way to check the correctness of the operations performed with a counting device (counting rods). Chapters 2 and 3 of the treatise contain 28 and 36 problems, respectively. The structure of the treatise differs considerably from that of the Jiu zhang suan shu, where the problems to be solved with one and the same method are grouped together (Berezkina 1963, 7). The methods of ­chapters  2 and 3 include, among others, operations with common fractions, the “rule of three,” computation of areas and volumes of rectilinear and curvilinear figures, proportional distribution/​ partnership and sharing, progressions, simultaneous linear equations, the rule of false position. One of the most famous problems traditionally associated with the name of Sun zi, the so-​called Sun zi remainder problem (pb. 26 of juan 3) is as follows: one is asked to find an unknown integer number N such that {N≡r1 (mod m1), N≡r2 (mod m2), N≡r3 (mod m3)} for a particular case r1=2, r2=3, r3=2, m1=3, m2=5, m3=7 (SJSS 2001, 282; cf. Berezkina 1963, 37; Martzloff 1997, 310; and Lam and Ang 2004, 139, 220). Modern historians usually relate it to the “remainder problem” solved by the mathematicians L. Euler (1740, 65–​66) and C. F. Gauss (1801, 25–​26); see Libbrecht 1973, 214–​266, 370–​ 371, Sandifer 2007, 356, and Plofker 2007.6 The actual origin of the Chinese method remains unknown; Martzloff (1997, 322) and Bréard (2014, 172) connect it to calendrical computations.

1.3.5 Zhang Qiujian suan jing 張丘建算經 (Computational Treatise of Zhang Qiujian) The treatise was used for mathematics instruction during the Tang dynasty and was reprinted (possibly with editorial alterations) in the early 13th century. The received version contains three chapters (juans) with 32, 22, and 38 problems, respectively (Ho 1965 attempts to reconstruct the lacuna of about two problems). On the basis of the information about taxation system mentioned in the treatise, Qian (1981, 90–​91) suggested that the treatise was completed between 466 and 485 ce (compare Ho 1965, 6  The “remainder theorem” found in modern textbooks states that if in a system of congruencies {x≡r 1 (mod m1), . . . , x≡rn (mod mn)} all mi, mj are co-​prime, then for each i = 1, . . . , n a unique ki < mi can be found such that (M/​mi)·ki ≡ 1 (mod mi) for M = m1· . . . ·mn, and the unique solution (modulo M) of the problem can be found as x = (M/​m1)·k1·r1 + . . . + (M/​mn)·kn·rn, since (M/​mi)·ki ≡ 0 (mod mj) if i≠j.

114    Ancient Scientific Traditions Beyond Greece and Rome and SJSS 2001, 293, 297); the preface of the treatise mentions the Sun zi suan jing, which suggests that the treatise is later than the Sun zi suan jing. There is no information about the presumed author of the treatise, Zhang Qiujian 張丘建. Berezkina (1969a) published an annotated Russian translation of the treatise. Lam Lay Yong 1997 translated and discussed 48 of the 92 problems. For detailed analyses of the mathematical methods found in the treatise, see Berezkina (1969a, 18–​27; 1980, 41–​ 47) and Lam (1997, 208–​236). In her translation Berezkina included the part called cao 草 “record of computations” (following Berezkina 1969a; Ho 1965 and Lam 1997 render this part as “workings”). This was presumably authored by the astronomer Liu Xiaosun 劉孝孫 (fl. 6th c. ce: see SJSS 1963, 326 and SJSS 2001, 297, 343, n. 1; compare with Ho 1965, 37 and Lam 1997, 212), which Lam omitted while keeping the “procedures” shu 術, that is, the algorithms to be used to solve the problems. The problems of the treatise are related to operations with common fractions (juan 1, pbs. 1–​6), progressions and proportional distribution (juan 1, pbs. 17, 22–​23, 32; juan 2, pbs. 1, 13; juan 3, pbs. 1, 20–​21, 36), simultaneous linear equations (juan 1, pb. 21; juan 3, pbs. 12–​15), extraction of square and cube roots (juan 2, pbs. 19–​21; juan 3, pbs. 30–​31), solution of quadratic equations (juan 2, pb. 22; juan 3, pb. 9), computation of areas and volumes of rectilinear and curvilinear figures (juan 2, pbs. 7–​11, juan 3, pbs. 4–​11). The last problem of the treatise is the famous problem of indeterminate analysis known as “the problem of one hundred fowls” (Berezkina 1969a, 59–​60, 81; Lam 1997, 235–​236): one must find positive integer solutions of the simultaneous equations {5x+3y+z/​3=100; x+y+z=100}. Qian’s treatise correctly provides all three solutions of this problem, even though the method he used remains unknown (Volkov 2002, 395–​400).

1.3.6 Xiahou Yang suan jing 夏侯陽算經 (Computational Treatise of Xiahou Yang) The preface of the Zhang Qiujian suanjing mentions a treatise authored by Xiahou Yang, which should mean that Xiahou’s text was produced prior to the compilation of Zhang’s. However, modern historians argue that the extant treatise with the same title is a later compilation produced by Han Yan 韓延 in the late 8th century ce (Qian 1963, 551–​553; Martzloff 1997, 141; see also Kogelschatz 1981, 16–​17, 47). Thus, we will not discuss it (Berezkina 1985 provides an annotated Russian translation).

1.3.7 Wu cao suan jing 五曹算經 (Computational Treatise of Five [Government] Departments) The name of the author and the time of compilation of this relatively short treatise (67 problems) remain unknown; Berezkina who studied it and translated it into Russian (1969b) conjectured that it may have been compiled “approximately in the 4th century ad” (Berezkina 1980, 47). This hypothesis contradicts the opinions of Qian (SJSS 1963, 409) and Guo and Liu (SJSS 2001, 349), who credited it to the authorship of Zhen Luan. All the bibliographic entries concerning this treatise found in dynastic histories Jiu Tang shu, Xin Tang shu and Song shi mention Zhen Luan as its compiler (discussed above in

Ancient Chinese Mathematics    115 section 1.2). For a description of its contents see Berezkina 1969b, and 1980, 47–​52 and Martzloff 1997, 139. The contents of this treatise were often considered “easy” compared with those of other contemporaneous or even earlier treatises:  its problems focus on the calculation of areas and volumes of rectilinear and curvilinear figures (often rather “rough” approximations are used for curvilinear figures), multiplication and division of integers and metrological decimal fractions (the common fractions are not used at all in this treatise, as Berezkina 1969b, 83 noticed), and the “rule of three.”

1.3.8  Wu jing suan shu 五經算術 (Computational Procedures [Needed for Understanding] of the Five Classics) Guo and Liu (2001, 373) attribute the extant version of this treatise to Zhen Luan; they apparently followed Qian (1963, 437). In turn, Martzloff (1997, 124)  considers Zhen Luan as one of the commentators and claims the compiler is “unknown”; indeed, as has been mentioned above, no record of Zhen Luan’s authorship can be found in bibliographic chapters of official histories. Martzloff, however, suggests “ca. 566” as the date of its compilation, which may be consistent with the hypothesis of Zhen Luan’s authorship. All modern editions of the treatise, including those found in SJSS 1963 and SJSS 2001, stem from the edition produced by Dai Zhen in 1774 on the basis of fragments of the treatise copied in the aforementioned collection Yong le da dian; the volume of the latter collection containing these fragments is no longer extant. The edition of Dai Zhen contains explanations of Zhen Luan and Li Chunfeng. The treatise contains a number of quotations from “classical” Confucian books, such as The Book of Documents (Shu jing 書經), The Book of Poems (Shi jing 詩經), The Book of Changes (Yi jing 易經), among others, related to mathematical matters (in particular, mathematical theory of music, metrology, numerological cosmography, etc.) and describes the “system of large numbers” identical with the one discussed in the Shu shu ji yi (discussed later). The treatise has never been translated into any modern language.

1.3.9 The Shu shu ji yi 數術記遺 (Procedures of “Numbering” Recorded to Be Preserved [for Posterity]) The treatise Shu shu ji yi was one of the treatises lost by the late 12th century; the government officer and bibliophile Bao Huanzhi 鮑澣之 (fl. 1200–​1213 ce) found a copy of it in the library of the Daoist monastery Ningshou guan 寧壽觀, copied it by hand, and printed it together with other mathematical treatises presumably used in the state university during the Tang and the Northern Song (960–​1127 ce) dynasties; however, the format of the text found by Bao differs from that of other texts of the collection (in particular, it does not contain the colophon mentioning the editorship of Li Chunfeng as do other extant texts of the collection). The treatise is basically a record authored by Xu Yue 徐岳 of a very short dialog between Liu Hong 劉洪 (b. ca 130, d. ca 210 ce) and an unidentified hermit referred to as “Master [from the mountain] Tianmu” 天目先生; Volkov 1994c argued that this “Master” was Chunyu Shutong 淳于叔 通 (fl. ca 167 ce), a government officer versed in the “Art of Numbers,” shu shu 數術.

116    Ancient Scientific Traditions Beyond Greece and Rome The dialog contains two parts. The first part is devoted to the problem of “finiteness of numbers,” probably related to the Buddhist concept of reincarnation, and contains a description of “[large] numbers of three ranks” san deng shu 三等數, that is, of a set of 10 terms to which numerical values (powers of 10) can be assigned in three different ways (Brenier 1994; Volkov 1994c). The second part contains descriptions of 13 methods of representation of numbers with counting devices; one of them, the “computations with pearls” (zhu suan 珠算), refers to a form of abacus similar to the Roman abacus. There is an additional part of the treatise containing a dialog between Zhen Luan (the commentator) and “somebody” concerning some particularities of operations with counting rods. Zinin (1985; 1986) translated the treatise and the part of Zhen Luan’s commentary related to counting devices into Russian. The question of the “finiteness of numbers,” the central topic of the opening part of the treatise, was discussed in Volkov 1994c; see also Volkov 1997, 23–​28 on Zhen’s scientific and religious activities.

1.4 Recently Unearthed Treatises 1.4.1 Suan shu shu 筭數書 (Scripture on Computations [to Be Performed] with Counting Rods) In 1983 a mathematical treatise written on bamboo strips and titled Suan shu shu 筭數 書 was found in China in a tomb sealed circa 186 bce. The treatise was published for the first time in 2000 (SSS 2000a; 2000b) and later reproduced photographically (SSS 2001, 2006); it was translated into modern Chinese (Peng 2001; Horng et al. 2006) and English (Cullen 2004; Dauben 2008). A large number of publications on the Suan shu shu was produced in Mainland China, in Taiwan, in Japan, and in the West (Dauben 2008, 172–​177, and Zou 2008, 95–​98), and several international conferences devoted to it were held recently (see, for instance, HPM 2006). One of the most intriguing questions is the possible connection between the Suan shu shu and Jiu zhang suan shu (Chemla and Guo 2004, 3–​8).

1.4.2 Suan shu 算術 ([Computational] Procedures [to Be Performed with] Counting Rods) A mathematical text titled Suan shu 算術 was found during excavations at Shuihudi 睡 虎地 (Hubei Province, P. R. of China) in 2008. This text remains unpublished; a short excerpt from it was published (SS 2008) and studied by Chemla and Ma (2011).

1.4.3 Shu 數 (Numerical [Procedures (?)]) This text, dated to the Qin dynasty (221–​206 bce), was found in China during illegal excavations, purchased in Hong Kong in 2007, and is currently preserved in the Yuelu Academy 嶽麓書院/​岳麓书院 (Hunan University, Changsha, Hunan Province, P. R. of China). The book was the topic of several publications (Xiao and Zhu 2009a-​c; Zhu and Xiao 2009) and of an international conference held in Changsha in 2010 (Zou 2011). The

Ancient Chinese Mathematics    117 text remains unpublished but is circulating within a small international community of scholars working on the history of Chinese mathematics.

2.  Mathematical Methods of Commentators The commentaries of Zhao Junqing on the Zhou bi suan jing have been mentioned above; they contained statements equivalent to algebraic identities proved through manipulations with geometrical figures (Gillon 1977). Similar techniques were used by Liu Hui in his commentaries on ­chapter 9 of the Jiu zhang suan shu (Swetz and Kao 1977) and most likely in his Hai dao suan jing (Wu 1982a; 1982b); in his commentary on ­chapter 4 of the same treatise, Liu Hui used (no longer extant) diagrams to explain the procedure of square and cube roots extraction. Other parts of Liu Hui’s commentary contain descriptions of infinitesimal methods used to justify the formulas of the area of a circle and the volumes of a pyramid and a sphere. The commentary on the volume of a sphere found in the Jiu zhang suan shu contained an additional part authored by Zu Gengzhi 祖暅之 or Zu Geng 祖暅 (b.?, d. after 525 ce; transliterated as “Zu Xuan” by Martzloff 1997), in which the calculation of the volume of a sphere started by Liu Hui was completed.

2.1 Area of a Circle and Approximate Values of π There is only one text written prior to the mid-​first millennium AD describing in detail a procedure designed for calculation of an approximate value of π; it was authored by Liu Hui and is found in his commentary on problems 31–​32 of the first chapter of the Jiu zhang suan shu. (For translations of Liu Hui’s commentary, see Berezkina 1974, 253‒258; Chemla and Guo 2004, 144–​148, 177–​189; and Guo, Dauben, and Xu 2013, 99–​145.) Liu started with a hexagon (a1  =  R) and doubled its sides. In figure A4a.1, AB  = ak-​1, AO = CO = BO = R, CD = hk-​1, DO = Hk-​1, AC = BC = ak. Liu Hui performed the following steps for k = 2, . . ., n (the value n he adopted for his computations was equal to 5, and the level of accuracy p he used was equal to 6):7 1. Calculate an approximate value of AD2: ak2−1 / 4  ; 2p

2. Calculate an approximate value of OD2 = AO2 − AD2: R2−​ ak2−1 / 4  ; 2p

7 Here ⎣⎦ is the generalized floor function, ⎣x⎦  = (⎣10px⎦)/​10p, where ⎣x⎦ is the floor function, that is, p p

⎣x⎦ is the integer part of the number x.

118    Ancient Scientific Traditions Beyond Greece and Rome  3. Calculate an approximate value of OD: Hk-​1 =  

(R − a 2

2 k −1

/ 4 

2p

) 

; p +1

4. Calculate an approximate value of CD = OC–OD: hk-​1 = R–Hk-​1; 5. Calculate an approximate value of CD2: (R–Hk-​1)2; 6. Calculate an approximate value of AC2 = CD2 + AD2: ak2 = hk2−1 + ak2−1 / 4    ; 2 p 2 p  7. Calculate an approximate value of AC: ak =  ak2   ; p  8. Calculate an approximate value of the area of the 3·2k+1—​sided polygon: Sk+1 = 3·2k·[ak·R/​2] = 3·2k-​1·ak·R. The operations (7) and (8) were performed only for calculation of the sides an-​1, an, and the areas Sn, Sn+1. At the last steps of his procedure, Liu Hui evaluated the area of the circle as belonging to the interval (Sn+1, Sn+1), where Sn+1 was the area of the polygon Pn+1 with 3·2n+1 sides and Sn+1 was the area of the rectilinear figure including the circle and composed of the triangles AOB and the rectangles AEFB: a Sn+1 = Sn + 3 ⋅ 2n ⋅ SAEFB = Sn+1 + 3 ⋅ 2n ⋅ hn ⋅ n = Sn+1 + ( Sn+1 − Sn ). The approximation he 2 obtained for π was 157/​50 (equivalent to 3.14—​Chinese mathematicians often expressed approximate values as common fractions). It is possible that Zu Chongzhi (429–​500 ce) used this or a similar method to obtain for π his approximate values 22/​7, 335/​113, and the evaluation 3.1415926 < π < 3.1415927 (Volkov [1994b] analyses Liu’s method and discusses Zu’s results). Received sources contain mentions of several approximate values of π used in China prior to the mid-​first millennium ce, such as Zhang Heng’s 張衡 (78–​139 ce) value √10 and Wang Fan’s 王蕃 (219–​257 ce) value 142/​45. Some values can be reconstructed E A

C ak

hk–1

ak–1

D

F B

Hk–1

O

Figure A4a.1  Liu’s method for calculating an approximate value of π. Drawing by author.

Ancient Chinese Mathematics    119 on the basis of analyses of the so-​called standard measuring vessels of the first half of the first millennium CE whose design involved calculation of the volume of a cylinder, among them there are such approximate values as 41/​13, 3927/​1250 (= 3.1416; this value was also mentioned in the commentary on the Jiu zhang suan shu), 160/​51, 47/​15, and 69/​22 (Volkov 1994d; 1995).

4.2 Volume of a Pyramid The algorithm provided in the Jiu zhang suan shu (chap. 5, pb. 15) for the volume of a pyramid having one edge of length h perpendicular to a rectangular base with sides a abh and b is equivalent to the formula V = . To prove the validity of this formula, Liu 3 Hui designed an infinitesimal procedure in which the ratio of volumes of the pyramid and its complement to a triangular prism was found to be equal 2:1; since the volume of abh the prism was equal to , it provided a justification of the suggested formula (Wagner 2 1979; Chemla and Guo 2004, 396–​398, 429–​433; Guo, Dauben, and Xu 2013, 543–​559). The method was discussed by a number of historians, yet there is no consensus concerning the underlying concepts of infinitesimals used by Liu Hui.

4.3 Volume of a Sphere In his commentary on problem 24 of juan 4 of the Jiu zhang suan shu, Liu Hui criticizes the algorithm found in the treatise (according to which the volume of a sphere with diameter D equals 9/​16D3) and suggests that this algorithm was based on the wrong assumption that the volumes of a cylinder and of the inscribed sphere have the ratio 4:3 (actually, 4: π). Liu Hui does not provide the exact ratio of the volumes but suggests that the ratio 4:3 (i.e., 4: π) holds for another solid, namely, an intersection of two cylinders (referred to as hegai 合蓋, “joined together square-​shaped box-​lids,” figure A4a.2), and a sphere inscribed into it. The ratio of the two volumes was obtained with the application of the method of comparison of the areas of cross-​sections equivalent to the Cavalieri principle. To calculate the volume of the hegai described by Liu Hui, Zu Gengzhi suggested considering a supplement of this solid to the circumscribed cube. It was shown that the cross-​section of the 1/​8th of the supplement made at height H would have the area H2; since it equals the area of a cross-​section of the pyramid with square base and all three dimensions equal to R = D/​2 made at the same height, Zu Gengzhi concluded that the volumes of the two solid bodies are equal (figure A4a.3).

(

) (

)

The volume of the hegai therefore equals 8 Vcube − Vpyramid = 8 R 3 − 1 3 R 3 = 16 R 3 = 2 D3 ; since the ratio of volumes of the hegai and the inscribed sphere equals 3 3 4: π, the volume of the sphere is (π / 4 )(2 /3 D3 ) = π /6 D3.

120    Ancient Scientific Traditions Beyond Greece and Rome

Figure A4a.2  Liu’s description of a hegai. Drawings by author.

R

R

R

R

R

H

R

Figure A4a.3  Zu Gengzhi’s method for calculating the volume of a hegai. Drawing by author.

This method was discussed in 1930s by Mikami Yoshio 三上義夫 (1875－1950) and Li Yan 李儼 (1892－1963); in the West it remained unmentioned in (Needham and Wang 1959) and was described by Kiang (1972) and Wagner (1978a). Yushkevich (1982b) noticed that the body used in the Chinese derivation of the computational formula, the intersection of two cylinders, looked similar to that mentioned by Archimedes in his letter to Eratosthenes discovered by Heiberg in 1906 (Heiberg and Zeuthen 1907; Heiberg 1909; Veselovskii and Rozenfeľd 1962; Dijksterhuis 1987) and posed a question of the possible connections between these methods. In the aforementioned publications of modern historians, Zu Gengzhi’s statement about the equality of volumes of two solid figures composed as agglomerations of infinitely thin cross-​sections with equal areas was interpreted as a form of the Cavalieri principle. However, it remains unknown whether the method suggested by Zu Gengzhi was not based on more technical considerations not provided in his commentary (Volkov 1994a).

Ancient Chinese Mathematics    121

5. Conclusions To conclude this brief and thus necessarily incomplete account, two salient features of Chinese mathematical tradition of the period under consideration should be stressed. First, the extant mathematical texts show a certain connection with the context in which they were compiled, studied, and transmitted, namely, the context of mathematics instruction. The role of this particular context was often underplayed by the modern historians of Chinese mathematics; however, without taking into consideration this particular didactical function of the texts briefly presented here, it would be impossible to conduct their adequate evaluation and interpretation. Second, it should be noted that the sophisticated methods partially preserved in the commentaries of Liu Hui, Zhao Junqing, and Zu Gengzhi represented a dimension of this mathematical tradition that remained otherwise invisible in the treatises written in conventional textbooks format; it can be argued that it was this dimension that shaped the interpretative strategies of the learners.

Bibliography Primary Materials Suan jing shi shu 算經十書 (SJSS) Qian Baocong 錢寶琮, ed. Suan jing shi shu 算經十書 (Ten mathematical treatises). Beijing: Zhonghua shuju, 1963. Suan jing shi shu 算經十書 (SJSS). Guo Shuchun 郭書春 and Liu Dun 劉鈍, eds. Suan jing shi shu 算經十書 (Ten mathematical treatises). Taibei: Jiuzhang, 2001. Suan shu 算術 (SS). Hubei sheng wenwu kaogu yanjiusuo 湖北省文物考古研究所 (Research institute for material culture and archeology of Yunmentg province) and Yunmeng xian bowuguan 雲夢縣博物館 (Museum of Yunmeng province). “Hubei Yunmeng Shuihudi M77 fajue jianbao 湖北雲夢睡虎地 M77 發掘簡報 (Short report on the excavations of the tomb M77 at Shuihudi in Yunmeng, Hubei Province).” Jiang Han kaogu 江漢考古, 109: 31–​ 37, plates 11–​16, 2008. Suan shu shu 算數書 (SSS). Jiangling Zhangjiashan Hanjian zhengli xiao zu 江陵張家山漢簡 整理小組 (Team of restoration of the Han [dynasty] bamboo strips [found at] Zhangjiashan in Jiangling). “Jiangling Zhangjiashan Hanjian ‘Suan shu shu’ shiwen”《江陵張家山漢簡 〈算數書〉釋文》 (Transcription of the Suan shu shu of the Han [dynasty written on] bamboo strips [found at] Zhangjiashan in Jiangling). Wenwu 文物 (Sept. 2000a): 78–​84. Suan shu shu算數書 (SSS). Su Yi-​Wen 蘇意雯, et al. “Suan shu shu jiaokan《算數書》校勘” (Collation of the Suan shu shu). In HPM Tongxun 通訊 (HPM Newsletter) 11.3 (2000b): 2–​ 20. http://​math.ntnu.edu.tw/​~horng/​letter/​hpmletter.htm. Suan shu shu 算數書 (SSS). Zhangjiashan Han mu zhujian (erbai sishi qi hao mu) 張家山漢 墓竹簡〔二四七號墓〕 (Bamboo strips from the Han [Dynasty] tomb number 247 in Zhangjiashan). Beijing: Wenwu Chubanshe, 2001.

122    Ancient Scientific Traditions Beyond Greece and Rome Translations in Western Languages (listed chronologically for each treatise) Jiu zhang suan shu 九章算術 Berezkina, Éľvira I. “Matematika v devyati knigakh” (Mathematics in Nine books [= Jiuzhang suanshu]). Istoriko-​matematicheskie issledovaniya. Studies in the History of Mathematics, Moscow. 10 (1957): 427–​584. Vogel, Kurt, trans. Chiu chang suan shu: Neun Bücher arithmetischer Technik, Ein Chinesisches Rechenbuch für den praktischen Gebrauch aus den Frühen Hanzeit. Braunschweig: Friedrich Vieweg Verlag (Ostwalds Klassiker), 1968. Swetz, Frank J. and T. I. Kao. Was Pythagoras Chinese? An Examination of Right Triangle Theory in Ancient China. University Park and London: Pennsylvania State University Press, 1977. [Annotated translation of ­chapter 9 of the treatise.] Shen Kangsheng, John N. Crossley, and Anthony W.-​C. Lun. The Nine Chapters on the Mathematical Art: Companion and Commentary. Oxford and Beijing: Oxford University Press, 1999. Chemla, Karine, and Guo Shuchun. 九章算術. Les Neuf Chapitres: Le classique mathématique de la Chine ancienne et ses commentaires. Édition critique bilingue traduite, présentée et annotée par Karine Chemla et Guo Shuchun. Glossaire des termes mathématiques chinois anciens par Karine Chemla. Paris: Dunod, 2004. Hudeček, Jiří. Překlad, vysvětlivky a úvod [Translation, explanations, and introduction]. Matematika v Devíti Kapitolách (Mathematics in nine chapters [= Jiu zhang suan shu 九章算 術]). Praha: Matfyzpress, 2008. Guo Shuchun, Joseph Dauben, and Xu Yibao. 九章筭术 [= 九章算術]. Nine Chapters on the Art of Mathematics. A Critical Edition and English Translation Based upon a New Collation of the Ancient Text and Modern Chinese Translation by Guo Shuchun; English Critical Edition and Translation, with Notes, by Joseph W. Dauben and Xu Yibao. 3 vols. Shenyang: Liaoning Education Press, 2013.

Zhou bi suan jing 周髀算經 Cullen, Christopher. Astronomy and Mathematics in Ancient China: The Zhou bi suan jing. Cambridge: Needham Research Institute and Cambridge University Press, 1996.

Hai dao suan jing 海島算經 Berezkina, Éľvira I. “Dva teksta Lyu Hueya po geometrii” (Two texts of Liu Hui on geometry). Istoriko-​matematicheskie issledovaniya 19 (1974):  231–​273. [This paper contains annotated translations of two texts: (233–​248) the Hai dao suan jing with Berezkina’s commentaries and reconstructions, as well as her discussion of Liu Hui’s methods; and (253–​258) Berezkina’s translation of Liu Hui’s commentary on problems 31–​32 of juan 1 of the Jiu zhang suan shu containing a detailed description of his method of calculation of the approximate value of π.] Ang Tian-​Se and Frank J. Swetz. “A Chinese Mathematical Classic of the Third Century: The Sea Island Mathematical Manual of Liu Hui.” Historia Mathematica 13 (1986): 99–​177. Swetz, Frank J. The Sea Island Mathematical Manual: Surveying and Mathematics in Ancient China. University Park: Pennsylvania State University Press, 1992.

Sun zi suan jing 孫子算經 (Computational Treatise of Master Sun) Berezkina, Éľvira I. “O matematicheskom trude Sun’-​tzy. Sun’-​tzy:  Matematicheskiï traktat. Primechaniya k traktatu Sun’-​tzy” (On the mathematical work of Sun zi. Sun zi: Mathematical treatise. Annotations for Sun zi’s Treatise). Iz istorii nauki i tekhniki v stranakh Vostoka (On the History of Science and Technology in the Countries of the East), 3 (1963): 5–​70.

Ancient Chinese Mathematics    123 Lam Lay Yong, and Ang Tian Se. Fleeting Footsteps: Tracing the Conception of Arithmetic and Algebra in Ancient China. Singapore: World Scientific, 2004.

Zhang Qiujian suan jing 張丘建算經 (Computational Treatise of Zhang Qiujian). Berezkina, Éľvira I. “O traktate Zhan Tsyu-​Tszyanya po matematike” (On Zhang Qiujian mathematical treatise). Fiziko-​matematicheskie nauki v stranakh Vostoka 2 (1969a): 18–​81.

Xiahou Yang suan jing 夏侯陽算經 (Computational Treatise of Xiahou Yang) Berezkina, Éľvira I. 1985. “Matematicheskii traktat Syakhou Yana” (Mathematical treatise of Xiahou Yang). Istoriko-​matematicheskie issledovaniya 28 (1985): 293–​337.

Wu cao suan jing五曹算經 (Computational Treatise of Five [Government] Departments) Berezkina, Éľvira I. “O matematicheskom traktate pyati vedomstv” (On mathematical treatise of five [government] departments). Fiziko-​matematicheskie nauki v stranakh Vostoka 2 (1969b): 82–​97.

Wu jing suan shu 五經算術 (Computational Procedures [Needed for Understanding] of the Five Classics) [Description of contents and discussion of several problems/​methods in Berezkina 1980, 56–​62.]

Shu shu ji yi 數術記遺 (Procedures of “Numbering” Recorded to Be Preserved [For Posterity]) Zinin, Sergei V. “Nekotorye problemy kitaiskoi aritmologii” (Some problems of Chinese arithmology). In The 16th Soviet Sinological Conference “State and Society in China”: Proceedings, pt. 1, 151–​155. Moscow: Nauka, 1985. —​—​—​. “Pozdnehan’skaia kosmologicheskaia skhematika” (Cosmological schemata of the Later Han dynasty). In Istoriia i kuľtura Vostochnoi i Yugo-​vostochnoi Azii (History and Culture of East and Southeast Asia), ed. Sergei Volkov, pt. 1, 84–​93. Moscow: Nauka, 1986. [See also a partial translation in Volkov 1994c, 71–​72, 76–​77.]

Suan shu shu 算數書 (Scripture on Computations with Counting Rods) Cullen, Christopher. The Suan shu shu 算數書 “Writing on Reckoning”:  A Translation of a Chinese Mathematical Collection of the Second Century bc, with Explanatory Commentary. Cambridge: Needham Research Institute, 2004. Dauben, Joseph W. “算數書 Suan shu shu: A Book on Numbers and Computations.” Archive for History of Exact Sciences 62 (2008): 91–​178. [See Peng 2001, and Horng et al. 2006 for translations into modern Chinese].

Suan shu 算術 ([Computational] Procedures [to Be Performed with] Counting Rods) Chemla, Karine, and Ma Biao. “Interpreting a Newly Discovered Mathematical Document Written at the Beginning of the Han Dynasty in China (Before 157 B.C.E.) and Excavated from Tomb M77 at Shuihudi (睡虎地).” Sciamvs 12 (2011): 159–​191.

Shu 數 (Numerical [Procedures (?)]) [See Xiao and Zhu 2009a-​c; Zhu and Xiao 2009.]

124    Ancient Scientific Traditions Beyond Greece and Rome

Other Works Publications in Oriental Languages Horng Wann-​Sheng 洪萬生, Lin Cang-​Yi 林倉億, Su Hui-​Yu 蘇惠玉, Su Jun-​Hong 蘇俊鴻. Shu zhi qiyuan: Zhongguo shuxue shi kaizhang ‘Suan shu shu’ 數之起源﹕中國數學史開章 “筭數書” (The origin of the numbers: Suan shu shu, the opening chapter of the history of mathematics in China). Taibei: Taibei shangwu yinshuguan, 2006. [Contains an edition of the text Suan shu shu, on pp. 239–​263.] HPM. “International Symposium on the Suan shu shu:  Appraisals and Appreciations.” [In Chinese] Materials of the Symposium held at National Taiwan Normal University, Taipei, Taiwan, August 23‒25, 2006. In HPM通訊 (History and Pedagogy of Mathematics Newsletter), 9 (9). http://​math.ntnu.edu.tw/​~horng/​letter/​909.pdf). Li Yan 李儼. (Zhongguo suanxue shi 中國算學史 (History of Chinese mathematics). Shanghai: Yinshuguan, 1954. —​—​—​. Zhongguo gudai shuxue shiliao 中國古代數學史料 (Historical materials for [study of] ancient Chinese mathematics). Shanghai: Zhongguo kexue tushu yiqi gongsi, 1955. Li Di 李迪.Zhongguo shuxue tongshi: Shanggu dao Wu Dai juan 中國數學通史。上古到五 代卷。(Comprehensive history of Chinese mathematics. Volume [on the period] from antiquity to the [time of] Five Dynasties). Nanjing: Jiangsu jiaoyu chubanshe, 1997. Mikami Yoshio 三上義夫. “Seki Takakazu-​no gyōseki to Keihan-​no sanka narabi-​ni Sina-​ no sampō to no kankei oyobi hikaku 關孝和の業績と京坂の算家並に支那の算法 との關係及び比較” (The works of Seki Takakazu, viewed in their relations with the mathematicians of Kyoto and Osaka, and with the Chinese mathematical theories). Tōyō gakuhō 東洋學報 22.1 (1934): 54–​99. Peng Hao 彭浩, ed. Zhangjiashan Han jian ‘Suanshu shu’ zhushi 張家山漢簡算數書注釋 (Commentary and interpretation of the Han [dynasty treatise from] Zhangjiashan Suan shu shu [written] on bamboo strips). Beijing: Kexue, 2001. Qian Baocong 錢寶琮, ed. Zhongguo shuxue shi 中國數學史 (A history of Chinese mathematics). Beijing: Kexue, 1981. Wu Wenjun 吴文俊. “Woguo gudai cewangzhixue chongcha lilun pingjia jian ping shuxueshi yanjiu zhong mouxie fangfa wenti 我国古代测望之学重差理论评介兼评数学史研究中 的某些方法问题” (On evaluating the chong cha theory used in the ancient Chinese discipline of surveying, and critical notes on some methodological problems in the history of mathematics). Kejishi wenji 8 (1982a): 10–​30. —​—​—. “Hai dao suan jing gu zheng tan yuan海岛算经古证探源” (Research on the origins of the ancient demonstrations in the Hai dao suan jing). In Jiu zhang suan shu yu Liu Hui 《九 章算术》与刘徽, ed. Wu Wenjun 吴文俊, 162–​180. Beijing: Shifan daxue, 1982b. Xiao Can 肖灿, and Zhu Hanmin 朱汉民. “Yuelu shuyuan cang Qin jian Shu shu zhongde tudi mianji jisuan 岳麓书院藏秦简《数书》中的土地面积计算 “(Computation of areas of terrains in the Book on Numerical [Procedures] of the Qin [dynasty on bamboo] strips held in Yuelu Academy). Hunan Daxue Xuebao (Shehui kexue ban) 湖南大学学报（社会科学 版） 23.2 (2009a): 11–​14. —​—​—. “Yuelu shuyuan cang Qin jian Shu de zhuyao neirong ji lishi jiazhi 岳麓书院藏 秦简《数》的主要内容及历史价值” (Historical value and main contents of the [book]  ‘Numerical [Procedures]’ of the Qin [dynasty on bamboo] strips held in Yuelu Academy). Zhongguo shi yanjiu 中国史研究 3 (2009b): 39–​50.

Ancient Chinese Mathematics    125 —​—​—​. “Zhou Qin shiqi guwu cesuanfa ji bizhong guannian—​Yuelu shuyuan cang Qin jian Shu de xiangguan yanjiu 周秦时期谷物测算法及比重观念—​—岳 ​ 麓书院藏秦简《数》的相 关研究 (Methods of measuring cereals and the concept of proportion in the periods Zhou and Qin: A study of the [book] ‘Numerical [Procedures]’ of the Qin [dynasty on bamboo] strips held in Yuelu Academy). Ziran kexue shi yanjiu 自然科学史研究 28.4 (2009c): 422–​425. Zhu Hanmin 朱汉民, Xiao Can 肖灿. “从岳麓书院藏秦简《数》看周秦之际的几何学成 就” (Acheivements of the science of geometry of the [late] Zhou[early] Qin, considered [on the basis of] the [book] ‘Numerical [Procedures]’ of the Qin [dynasty on bamboo] strips held in Yuelu Academy). Zhongguo shi yanjiu 中国史研究 3 (2009): 51–​58. Zou Dahai 鄒大海. “Chutu jiandu yu Zhongguo zaoqi shuxueshi 出土簡牘與中國早期數 學史” (Unearthed texts on bamboo strips and history of ancient Chinese mathematics). Renwen yu shehui xuebao 人文與社會學報 2.2 (2008): 71–​98. —​—​—​. “Guanyu Qin jian shuxue zhuzuo Shu de guoji huiyi zai Yuelu shuyuan juxing—​‘Yuelu shuyuan cang Qin jian (di er juan) guoji yanjiuhui’ jianjie 关于秦简数学著作《数》的 国际会议在岳麓书院举行—​《岳麓书院藏秦简》(第二卷)国际研读会”简介 (On the international meeting in Yuelu Academy devoted to the mathematical work  ‘Numerical [Procedures]’ on [bamboo] strips [dated to] the Qin [dynasty]—​a brief introduction of the Second International Workshop on Qin dynasty bamboo strips held in Yuelu Academy). Ziran kexue shi yanjiu 自然科学史研究 1 (2011): 131–​132.

Publications in Western Languages Berezkina, Éľvira I. Matematika Drevnego Kitaya (Mathematics of Ancient China). Moscow: Nauka, 1980. Bréard, Andrea. “On the Transmission of Mathematical Knowledge in Versified Form in China.” In Scientific Sources and Teaching Contexts Throughout History:  Problems and Perspectives, ed. Alain Bernard and Christine Proust, 155–​185. Dordrecht: Springer, 2014. Brenier, Joël. “Notation et optimisation du calcul des grands nombres en Chine. Le cas de l’échiquier de go dans le Mengqi bitan de Shen Gua (1086).” In Nombres, Astres, Plantes et Viscères: Sept essais sur l’histoire des sciences et des techniques en Asie Orientale, ed. Isabelle Ang and Pierre-​Étienne Will, 89–​111. Paris: Collège de France, 1994. Cullen, Christopher. “Chiu chang suan shu [= Jiu zhang suan shu]. 九章算術.” In Loewe 1993, 16–​23 (Cullen 1993a). —​—​—​. 1993b. “Chou pi suan ching [= Zhou bi suan jing]. 周髀算經.” In Loewe 1993, 33–​38, (Cullen 1993b). —​—​—. “The Zhou Bi revisited.” In East Asian Science: Tradition and Beyond, ed. Hashimoto Keizo, Catherine Jami and Lowell Sskar, 429–​434. Osaka: Kansai University Press, 1995. —​—​—​. “The Suàn shù shū 算數書, ‘Writings on Reckoning’: Rewriting the History of Early Chinese Mathematics in the Light of an Excavated Manuscript.” Historia Mathematica 34.1 (2007): 10–​44. Dauben, Joseph W., and Xu Yibao. “Nine Chapters on the Art of Mathematics. Introduction.” In Guo, Dauben, and Xu 2013, 39–​89. Dijksterhuis, Eduard Jan. Archimedes. Princeton, NJ: Princeton University Press, 1987. Euler, Leonhard. “Solutio Problematis Arithmetici de inveniendo numero, qui per datos numeros divisus, relinquat data residua.” Commentarii Academiae Scientiarum Imperialis Petropolitanae 7 (1735): 46–​66. Gauss, Carl Friedrich. Disquisitiones arithmeticae. Leipzig: Fleischer, 1801.

126    Ancient Scientific Traditions Beyond Greece and Rome Gillon, Brendan S. “Introduction, Translation, and Discussion of Chao Chun-​ Ch’ing’s ‘Notes to the Diagrams of Short Legs and Long Legs and of Squares and Circles.’” Historia Mathematica 4 (1977): 253–​293. Heiberg, Johan Ludvig, trans. [Archimedes’] Geometrical Solutions Derived from Mechanics. Chicago: Open Court, 1909. Heiberg, Johan Ludvig, and Hieronymus Georg Zeuthen. “Eine neue Schrift des Archimedes.” Bibliotheca Mathematica 7 (1907): 321–​363. Ho Peng Yoke. “The Lost Problems of the Chang Ch’iu-​chien Suan Ching, a Fifth-​Century Chinese Mathematical Manual.” Oriens Extremus 2 (1965): 37–​53. Kiang, Tao. “An Old Chinese Way of Finding the Volume of a Sphere.” Mathematical Gazette, May 1972, 88–​91. Kogelschatz, Hermann. Bibliographische Daten zum frühen mathematischen Schrifttum Chinas im Umfeld der “Zehn mathematischen Klassiker” (1. Jh. v.  Chr. Bis 7.  Jh. n.  Chr.). München:  Veröffentlichungen des Forschungsinstitut des Deutschen Museums für die Geschichte der Naturwissenschaften und der Technik, Reihe B, 1981. —​—​—. “Mathematics.” In Brill’s Encyclopedia of China, ed. Daniel Leese, 630–​632. Leiden and Boston: Brill, 2009. Lam Lay Yong. “Jiu Zhang Suanshu (Nine Chapters on the Mathematical Art): An Overview.” Archive for History of Exact Sciences 47 (1994): 1–​51. —​—​—. “Zhang Qiujian Suanjing (The Mathematical Classic of Zhang Qiujian): An Overview.” Archive for History of Exact Sciences 50 (1997): 201–​240. Libbrecht, Ulrich. Chinese Mathematics in the Thirteen Century: The Shu-​shu chiu-​chang of Ch’in Chiu-​shao. Cambridge, MA, and London: MIT Press, 1973. —​—​—. Mathematical Manuscripts from the Tunhuang [= Dunhuang] Caves. In Explorations in the History of Science and Technology in China, ed. Li Guohao et  al., 203–​ 229. Shanghai: Chinese Classics, 1982. Loewe, Michael. Early Chinese Texts: A Bibliographical Guide. The Society for the Study of Early China and the Institute of East Asian Studies, University of California, Berkeley, 1993. Martzloff, Jean-​Claude. A History of Chinese Mathematics. Berlin: Springer, 1997. Plofker, Kim. “Euler and Indian Astronomy.” In Leonhard Euler: Life, Work and Legacy, ed. Robert E. Bradley and Edward Sandifer, 147–​166. Amsterdam: Elsevier, 2007. Sandifer, C. Edward. The Early Mathematics of Leonhard Euler. Washington, DC:  The Mathematical Association of America, 2007. Siu Man-​ Keung, and Alexei Volkov. “Official Curriculum in Traditional Chinese Mathematics:  How Did Candidates Pass the Examinations?” Historia Scientiarum 9.1 (1999): 85–​99. Veselovskii, Ivan Nikolaevich, and Boris Abramovich Rozenfeľd, trans. Arkhimed. Sochineniya (Archimedes. Works, Russian translation from Greek and Arabic). Moscow: GIFML, 1962. Volkov, Alexei. “Transformation of Objects in Ancient Chinese Mathematics and Their Evolution.” In Notions et perceptions du changement en Chine, ed. Viviane Alleton and Alexei Volkov, 133–​148. Paris: Collège de France, 1994a. —​—​—. “Calculation of Pi in Ancient China:  from Liu Hui to Zu Chongzhi.” Historia Scientiarum 4.2 (1994b): 139–​157. —​ —​ —. “Large Numbers and Counting Rods.” Extrême-​Orient Extrême-​Occident 16 (1994c): 71–​92. —​—​—​. “Supplementary Data on the Values of Pi in the History of Chinese Mathematics.” Philosophy and the History of Science: A Taiwanese Journal 3.2 (1994d): 95–​110.

Ancient Chinese Mathematics    127 —​—​—​. “Quantitative Analysis of Liu Xin’s Standard Measuring Vessels.” In East Asian Science: Tradition and Beyond, ed. Hashimoto Keizō, Catherine JamI, and Lowell Skar, 377–​ 384. Osaka: Kansai University Press, 1995. —​—​—​. “Science and Daoism: An Introduction.” Taiwanese Journal for Philosophy and History of Science 5.1 (1997): 1–​58. —​—​—. “On the Origins of the Toan phap dai thanh (Great Compendium of Mathematical Methods).” In From China to Paris:  2000 Years Transmission of Mathematical Ideas, ed. Yvonne Dold-​Samplonius, Joseph W. Dauben, Menso FolkertS, and Benno van Dalen, 369–​ 410. Stuttgart: Franz Steiner Verlag, 2002. —​—​—. “Geometrical Diagrams in Liu Hui’s Commentary on the Jiuzhang suanshu.” In Graphics and Text in the Production of Technical Knowledge in China, ed. Francesca Bray, Vera Dorofeeva-​Lichtmann, and Georges Métailié, 425–​459. Leiden: Brill, 2007. —​—​—​. “Commentaries upon Commentaries:  The Translation of the Jiu zhang suan shu 九 章算術 by Karine Chemla and Guo Shuchun (Essay Review).” Historia Mathematica 37 (2010): 281–​301. —​—​—​. “Argumentation for State Examinations: Demonstration in Traditional Chinese and Vietnamese Mathematics.” In The History of Mathematical Proof in Ancient Traditions, ed. Karine Chemla, 509–​551. Cambridge: Cambridge University Press, 2012a. —​—​—​. “Recent Publications on the Early History of Chinese Mathematics (Essay Review).” Educação Matemática Pesquisa 14.3 (2012b): 348–​362. —​—​—​. “History of Mathematics Education in Oriental Antiquity and Middle Ages.” In Handbook on the History of Mathematics Education, ed. Alexander Karp and Gert Schubring, 55–​70, 79–​82. New York: Springer, 2014. Wagner, Donald B. “Liu Hui and Zu Gengzhi on the Volume of a Sphere.” Chinese Science 3 (1978a): 59–​79. —​—​—. “Doubts Concerning the Attribution of Liu Hui’s Commentary on the Chiu-​chang suan-​shu.” Acta Orientalia 39 (1978b): 199–​212. —​—​—​. “An Ancient Chinese Derivation of the Volume of a Pyramid: Liu Hui, Third Century a.d.” Historia Mathematica 6 (1979): 164–​188. Youschkevitch, Adolf P. “Nouvelles recherches sur l’histoire des mathématiques chinoises.” Revue d’histoire des sciences 35.2 (1982a): 97–​110. Yushkevich, Adoľf P. “Issledovaniya po istorii matematiki v drevnem Kitae” (Research on the history of mathematics in ancient China). Voprosy istorii estestvoznaniya i tekhniki 3(1982b): 125–​136.

chapter A4b

Astral Scie nc e s i n Ancient C h i na XU FENGXIAN

1.  General Introduction The counterpart of the word “astronomy” in Chinese is 天文 tian wen. Tian means heaven, and wen means writing, character, or pattern. Thus on the one hand the word tian wen means writings in the heavens, or patterns of the heavens, while on the other hand it means the lore of the heavens. In ancient Chinese culture, there wasn’t a supreme religious god, but heaven itself was regarded as the supreme being. Tian wen was thought to reveal the 道 Dao, or way, of heaven. Astral sciences began very early in ancient China. As pointed out by 司马迁 Sima Qian (145–​90 bce), the great historian and astronomer of Western Han: Ever since the people have existed, when have successive rulers not systematically calendared the movements of the Sun, Moon, stars and asterisms? (Pankenier 2013, 218)

“To calendar the movements of the sun, moon, stars and asterisms” was the duty of the rulers, so observation of celestial phenomena and making the calendar were officially organized, and only the highest rulers had the authority to promulgate calendars. In the 尧典 Yao dian (Canon of Yao) chapter of 尚书 Shang shu (Book of Documents), the earliest document of China, much of the content was devoted to describing Emperor Yao’s work on astronomy. In 2003 an ancient observatory was found in the late Neolithic Taosi site in Xiangfen County, Shanxi Province, China. This 4,000-​year-​old observatory was designed to observe the rising sun in different seasons, including at the summer and winter solstices (Xu and He, 2011; Pankenier, Liu, and de Meis 2008). All discoveries from the Taosi site pointed to it as the capital of Emperor Yao, and the observatory conforms to the records in Yao dian.

130    Ancient Scientific Traditions Beyond Greece and Rome As described by Yao dian, the purpose of the earliest astronomy was “in reverent accordance with august heaven, to compute and delineate the sun, moon and the stars, and the celestial markers (chen), and so to deliver respectfully the seasons to be observed by the people” (trans. Needham 1959, 188). Determining the seasons was not only necessary in an agricultural society but was also commanded by heaven. The ancient Chinese astral sciences system was found in the Spring and Autumn period (770–​476 bce) and the Warring States period (475–​221 bce). Astrology was the main force driving the development of astronomy. In this period astronomers and astrologers were active in feudal states and diligently observed the sky. The 28 宿 xiu system was established, which was 28 groups of stars roughly along the equator or the ecliptic and used as markings on the sky. The idea of field allocation, 分野 fen ye, arose, which allocated celestial areas, different stars or different planets to different terrestrial areas. Three main allocation patterns were formed:  the 28 xiu were allocated to the 12 terrestrial areas 州 zhou of that time, the five planets were allocated to different states, and the seven stars of the Big Dipper were allocated to different states, too. During the Warring States period, there were two well-​known astrologers, 甘德 Gan De and 石申夫 Shi Shenfu: the former wrote an eight-​volume book entitled 天文星 占 Tianwen xingzhan, Astronomy and Astrology, and the latter wrote an eight-​volume book entitled 天文 Tianwen, Astronomy. These two books are lost now, but many of their contents were retained in 开元占经 Kaiyuan zhanjing, an astrological book composed by 瞿昙悉达 Qutan Xida (Gautama Siddha) in the 8th century ce. Besides Gan De and Shi Shenfu, there was another famous astrologer 巫咸 Wu Xian, whose dates are unknown; he seems more like a legendary figure. Gan De, Shi Shenfu, and Wu Xian’s observations and naming of stars established the first star catalogues in Chinese history, and they also observed the five planets carefully. Calendar making developed from the Spring and Autumn period to the Warring States period. In the book 春秋Chun qiu, Spring and Autumn, the chronological history of the State of 鲁Lu from 722 to 479 bce, hundreds of calendrical dates were recorded. Studies on these records showed that different feudal states may have used different calendars, but they were all luni-​solar calendars, and their intercalary months were set more and more regularly. In the Warring States period, a rule of taking 365¼ days as a year, and setting seven intercalary months in 19 years became conventional, and six different calendars based on this rule were implemented by different feudal states. Special celestial phenomena were recorded in the histories, for example, the Spring and Autumn chronicle Chun qiu recording 37 solar eclipses, three comets, and also meteorites. The 秦 Qin dynasty (221–​207 bce) set up the first united empire in Chinese history, but it was too short for astral sciences to develop. The 汉 Han dynasty (202 bce—​220 ce) experienced two quite long stable and prosperous periods: 西汉 Western Han or 前汉 Former Han, 202 bce—​8 ce, 东汉 Eastern Han or 后汉 Later Han, 25–​220 ce. Astral sciences developed quickly in every respect, and the traditional Chinese astronomical frame of reference was improved and

Astral Sciences in Ancient China    131 perfected. The Han dynasty initiated the tradition of compiling an official history of the preceding dynasty. The first official history 史记 Shi ji, The Grand Scribe’s Records, by Sima Qian of Western Han, established a precedent with the 天官书 Tian guan shu, the Chapter on the Heavenly Offices, and the 历书 Li shu, the Chapter on the Calendar. Thus began the tradition of including the chapters of astronomy and the calendar in official histories. But in fact, the chapter Tian Guan Shu in Shi ji was much more a chapter on astrology than on astronomy. In the 汉书 Han shu, the History of the Former Han, the corresponding chapters were entitled 天文志 Tian wen zhi, Treatise on Astronomy, and 律历志 Lü li zhi, Treatise on Harmonics and the Calendar, and versions of these two treatises often appeared in later official histories. Owing to these treatises the progress of astral sciences after the Han dynasty became well documented. Usually the Treatise on Astronomy recorded not only important astronomical affairs, discussions, and arguments of astronomers, but also chronological records of special celestial phenomenon from the view of astrology, including eclipses, comets, “guest stars” (novas and supernovas), sunspots, special positions of the moon and the five planets, and so on. These kinds of records came to form a uniquely continuous astronomical rec­ ord, quite valuable in modern astronomical researches. From the Han dynasty to the Sui dynasty (589–​618 ce), the calendar was regarded as having a special relation with harmonics and metrology, so the chapters on the calendars in the official histories were combined with those on harmonics, and were entitled the Treatise on Harmonics and the Calendar. From the Tang (618–​907 ce) onward, this practice was discontinued, so the chapters on the calendar were often simply entitled Treatise on Calendar. The Treatises on Harmonics and the Calendar often recorded the history of calendrical reform during the preceding dynasty and included the main contents of important calendars. The Western Han launched a large-​scale calendar reform in the 2nd century bce. The court recruited astronomers and calendar experts from all over the country, designed and made several astronomical instruments, measured the positions of the stars, designed calendar calculating methods, and promulgated the new 太初 Tai chu calendar in 104 bce. The text of the Tai chu calendar no longer exists, but it was revised into the 三统 San tong calendar for which there is a complete account in the Treatise on Harmonics and the Calendar in the History of the Former Han Dynasty. The San tong calendar incorporates most features of traditional Chinese calendars. The subsequent 四 分 Si fen (quarter-​day) calendar of Eastern Han revised some of the astronomical data of the San tong calendar, and added some new astronomical tables. Thus the main features of the Chinese calendar had roughly taken shape. Discussions on the origin and structure of the heaven and the earth were very frequent in both the Western Han and the Eastern Han. The 盖天 gai tian theory (celestial dome theory), the 浑天 hun tian theory (celestial sphere theory) and the 宣夜 xuan ye theory (infinite empty space theory) formed the three most prominent theories on the structure of the heaven and the earth. In the Eastern Han, the famous astronomer 张衡 Zhang Heng (78–​139 ce) designed many astronomical instruments and elaborated the Hun tian theory.

132    Ancient Scientific Traditions Beyond Greece and Rome During the 魏 Wei, the晋 Jin, and the Southern and the Northern dynasties (220–​589 ce), the country was not united most of the time, and wars were frequent, but the development of astral sciences did not stop. In the 3rd century ce, an astronomer named 陈 卓 Chen Zhuo collected and organized the stars identified by Gan De, Shi Shenfu, and Wu Xian into 283 官 guan (“officials,” in fact, constellations), totaling 1,464 or 1,465 stars. This became the definitive version of traditional Chinese constellations and individual stars. During Eastern Jin (317–​420 ce), 虞喜 Yu Xi (281–​356 ce) discovered precession, and this was first adopted by 祖冲之 Zu Chongzhi (429–500) in his 大明 Da ming calendar. During the 6th century ce, 张子信 Zhang Zixin, after about 30 years’ observation while evading warfare on an island, discovered the uneven motions of the sun and the five planets, and also the effects of parallax on lunar eclipses. Discussions on the cosmos were quite active in this period, but most of them were revisions of the Han conceptions. In the 隋 Sui dynasty (581–​618 ce), the country was reunited again. The astronomical discoveries of Zhang Zixin were adopted as corrections to the calendars. Among these, the 皇极 Huang ji calendar by 刘焯 Liu Zhuo (544–​610 ce) was most prominent. In order to implement the corrections, more complicated mathematical methods and tables were introduced into calendar calculations. The whole sky was divided into three 垣 yuan and 28 xiu, a total of 31 areas, which became the established pattern until recent times.

2.  Mapping the Sky and Observation of Celestial Phenomena Ancient Chinese astronomy used an equatorial coordinate system, with the 28 xiu and the North Pole acting as the frame of the system. The 28 xiu were 28 groups of stars along the celestial equator or the ecliptic counted from west to east. In fact they are Chinese constellations. The 28 xiu evolved from the earlier four 象 xiang, four big constellations grouped near the equator. The 4 xiang referred to the 青龙 qing long (azure dragon) in the east—​roughly from Virgo to Sagittarius, the 白虎 bai hu (white tiger) in the west—​roughly from Andromeda to Orion, the 朱雀 zhu que (vermillion bird) in the south—​roughly from Gemini to Corvus, and the 玄武 xuan wu (a tortoise and a snake) in the north—​roughly from Sagittarius to Pegasus. Archaeological discoveries show that the idea of the four xiang had already formed in the mid-​Neolithic period more than 5,000 years ago (Chen 2003, 1–​3, and the first color photograph on the flyleaf; Pankenier 2013, 38–​39). The 28 xiu were completed in the Spring and Autumn period at the latest. A lacquer hamper lid from the tomb of Marquis乙 Yi of 曾Z eng in Hubei Province dated to ca 433 bce was painted with the 28 xiu roughly in a circle, with the dragon and the tiger outside the circle on the right and left respectively, and the Big Dipper inside the circle. The names of the 28 xiu were shown instead of sketches in the form of dots and lines.

Astral Sciences in Ancient China    133 The concept of the North Pole originated very early, and from that concept certain important philosophical concepts evolved after the Warring States period. The Big Dipper revolving around the North Pole was a very important constellation in ancient China. The direction of the handle of the Big Dipper, which was regarded as having special cosmic meaning, was used to determine the seasons from the Warring States period. In the Han dynasty the Big Dipper was regarded as the carriage of 帝 Di, the Supernal Lord, as depicted by 司马迁 Sima Qian in Shi ji (The Grand Scribe’s Records): The Dipper is the Supernal Lord’s carriage. It revolves about the centre, visiting and regulating each of the four regions. It divides yin from yang, establishes the four seasons, equilibrates the Five Elemental Forces, deploys the seasonal junctures and angular measures, and determines the various periodicities—​all are tied to the Dipper. (Pankenier 2013, 93–​94)

Measurement of the widths of the 28 xiu must have begun in the Spring and Autumn period. In the Warring States period 甘德 Gan De and 石申夫 Shi Shenfu measured them independently, and for several xiu they choose different groups of stars. In early Han there survived two sets of widths of the 28 xiu, both of which were measured along the equator, using the North Pole as the pole. The differences between the two were caused by choosing different “determinative stars.” One of them was called 古度 gu du “ancient degrees” by 刘向 Liu Xiang (ca 77–​6 bce) in his 洪范传 Hong fan zhuan; the widths of the 28 xiu on a round plate from a Western Han tomb dated to ca 170 bce belong to this system. This system was inclined to choose bright stars as determinative stars, but in certain cases this resulted in the defect of assigning the stars west of the determinative star to the field of the neighboring western xiu. The other system of 28 xiu extensions was recorded in 淮南子 Huainanzi (The Book of Huainan), 天文训 Tian wen xun (the Chapter on Astronomy), which was composed in early Han. This system was inclined to use the most western star in each xiu as the determinative star, thus ensuring that all the stars in a certain xiu were located within the range of the same xiu. This set of data was believed to have been measured by Shi Shenfu in the Warring States period. This system was adopted by the San tong calendar by the end of the Western Han and became the official system in later dynasties. Table A4b.1 shows the common names of the 28 xiu, the determinative stars and widths of the 28 xiu in this system. In ancient China, the celestial circle was divided into 365¼ 度 du, not 360 degrees, because in early calendars before the Tai chu calendar reform, the length of a tropical year was 365¼ days, and one du was defined as the distance of the sun’s motion in one day. To describe the position of a given star using the 28 xiu and North Pole, one parameter is 去 极度 qu ji du, means the du to the North Pole, the other is 入宿度 ru xiu du, means the equatorial du from the determinative star of the xiu concerned. Systematic naming of the stars was first carried out by the astrologers Gan De and Shi Shenfu in the Warring States period. In addition, there was also a legendary figure named 巫咸 Wu Xian. They named many stars and described magnitudes, colors, and

134    Ancient Scientific Traditions Beyond Greece and Rome Table A4b.1 The 28 xiu, Their Determinative Stars and Widths (度 du) Name

Determinative Star

Width

Name

Determinative Star

Width

1

角Jiao

α Vir

12

2

亢Kang

κ Vir

9

15

奎Kui

ζ And

16

16

娄Lou

β Ari

12

3

氐Di

α Lib

4

房Fang

π Sco

15

17

胃Wei

35 Ari

14

5

18

昴Mao

17 Tau

11

5

心Xin

6

尾Wei

σ Sco

5

19

毕Bi

εTau

16

μ1 Sco

18

20

觜Zi

φ1 Ori

7

箕Ji

8

斗Dou

γ Sgr

11¼

21

参Shen

δ Ori

φ Sgr

26

22

井Jing

μ Gem

2 9 33

9

牛Niu

β Cap

8

23

鬼Gui

θ Cnc

4

10

女Nü

ε Aqr

12

24

柳Liu

δ Hya

15

11

虚Xu

β Aqr

10

25

星Xing

α Hya

7

12

危Wei

α Aqr

17

26

张Zhang

υ1 Hya

18

13

室Shi

α Peg

16

27

翼Yi

α Crt

18

14

壁Bi

γ Peg

9

28

轸Zhen

γ Crv

17

relative positions of certain stars, mainly for astrological purposes. Kai yuan zhan jing, an astrological book written by  瞿昙悉达  Qutan Xida (Gautama Siddha) in the 8th century ce in the Tang dynasty, contains an ancient star catalogue of 120 stars, including their ru xiu du, their qu ji du, and their du from the ecliptic. Kai yuan zhan jing claimed those were data measured by Shi Shenfu. But modern scholars have different opinions. Maybe Shi Shenfu measured some of them in the Warring States period, and others were measured in Western Han before the Tai chu calendar reform. Sima Qian gave a complete description of all the stars, including 89 星官 xing guan (constellations), and more than 400 individual stars in his Chapter on the Heavenly Offices in The Grand Scribe’s Records. He gave their astrological meanings and described the positions, colors, and magnitudes of some stars in detail. This is the earliest extant Chinese work on the whole sky. The instruments used in measuring the widths of the 28 xiu in the Warring States period were not recorded. In the late 2nd century bce, before the Tai chu calendar reform, several instruments were made, among them maybe an armillary sphere, which at a minimum had a horizontal ring, an equatorial ring, a meridian ring, and a sighting tube. A bronze ecliptic sphere was built in the Eastern Han, and the widths of the 28 xiu along the ecliptic were measured with this instrument and recorded in the Treatise on Harmonics and the Calendar, in the History of the Later Han. Ancient Chinese did not have the concept of the ecliptic pole, instead the widths of the 28 xiu on the ecliptic were measured using the North Pole as the pole along the ecliptic ring on the instrument. In Eastern Han the famous astronomer Zhang Heng not only built an armillary sphere but

Astral Sciences in Ancient China    135 also a celestial globe that could show the heavens revolving. On the globe were the circle of perpetual visibility, the circle of perpetual invisibility, the North Pole and the South Pole, the equator and the ecliptic, with the 24 节气 jie qi (solar terms) inscribed along the ecliptic, the 28 xiu and other stars, and the sun, the moon, and the five planets. Half of the globe was above the horizontal circle and half below it. This rotating sphere was water powered, moving in accordance with the sky. This instrument has been lost, but it was described in the Treatise on Astronomy in the History of the Jin Dynasty. The number of stars on the globe was not mentioned. According to various texts, stars of Gan De, Shi Shenfu, and Wu Xian were represented in different colors on star chats during the Han dynasty. In the 3rd century ce, astronomical official 陈卓 Chen Zhuo merged the constellations and stars of Gan De, Shi Shenfu, and Wu Xian into 283 官 guan (constellations) and 1,464 or 1,465 individual stars. The ancient Chinese constellation system was then settled, and did not change until the Jesuits came to China in the 17th century. In the Sui dynasty several poems delineating the constellations came out, and the three 垣yuan (enclosures) called 紫微垣 ziwei yuan (the purple forbidden enclosure), 太微垣 taiwei yuan (supreme palace enclosure), and 天市垣 tianshi yuan (heavenly market enclosure) were mapped out around the North Pole. In 步天歌 Bu tian ge, a poem by 丹元子 Dan Yuan Zi of the Sui, the sky was divided into three yuan and 28 xiu, a total of 31 areas. This work first described the constellations and stars in the 28 xiu, then those in the three yuan. Thereafter, this became the conventional sky division scheme. Observation of culminating stars began very early in China and persisted through many centuries, leading to the discovery of precession. The Yao dian chapter in Shang shu (Book of Documents) recorded the culminating stars at dusk at the two solstices and the two equinoxes in the time of Emperor Yao in about 2000 bce. From the Warring States period not only the culminating stars at dusk and dawn but also the sun’s positions against the background of the 28 xiu during the 12 months were recorded. The sun’s position rendered the stars invisible, so their positions were calculated using the culminating stars at dusk and at dawn, timed with a clepsydra. Records from the Warring States claimed that at winter solstice the sun was at the beginning of 牵牛 Qian niu, that is, 牛 Niu, the ninth of the 28 xiu. In Western Han, before the Tai chu calendar reform, astronomers were aware that the sun’s position at winter solstice was different from the Warring States record, and they recorded the new position in Tai chu calendar. In the Eastern Han, in preparation for the Si fen calendar, astronomers found that the sun’s position at winter solstice was at 21 du in 斗 Dou, the eighth of the 28 xiu, five to six du from the Warring States position. This new value was adopted by the Si fen calendar. But during the Han dynasty no correct explanation was given for this change, some even thinking that it was because the Warring States value had been measured with the “ancient degree” system. It was Yu Xi (281–​356 ce) of the Eastern Jin (317–​420 ce) who first clearly set forth the explanation for precession. Yu Xi’s discussion on precession doesn’t survive, but from later astronomers’ narrations we can determine that he discovered precession from the changing of

136    Ancient Scientific Traditions Beyond Greece and Rome culminating stars at winter solstice. He compared the record of the culminating star at winter solstice recorded in Yao dian with his own observation, and found the difference. He claimed that the seasons did not cling to stars, but that “the heaven is heaven, the year is the year.” He gave the value of precession as one du every 50 years. After Yu Xi, 何承 天 He Chengtian (370–​447 ce) also discussed precession and arrived at the value of one du every 100 years (equivalent to ca 59′ per century). 祖冲之 Zu Chongzhi (429–​500 ce) was the first to introduce precession into calendar. In around 570 ce, after about 30 years’ observation with an armillary sphere, 张子信 Zhang Zixin found that the sun and the five planets all had uneven motions. He found the sun’s uneven motion by observing that the time of real eclipses was different from that predicted by calendar, and he summarized that “the sun moves slower after the spring equinox, and faster after the autumn equinox.” For the uneven motions of the five planets, he found this was connected with the seasons and their positions among the stars. He explained the reason: In moving among every xiu, each of the five planets has their own likes and dislikes. When they stay where they like, they stay longer and move slower, thus can be seen early; when they stay where they dislike, they stay shorter and move faster, thus can be seen late.

Observation of the five planets may have begun at the beginning of the second millennium bce (Pankenier 2013, 193–​219). According to the literature, in early times the five planets were regarded as having no retrograde motion, until Gan De and Shi Shenfu (of the Warring States period) found that Venus and Mars had retrograde motions. In the Han it was realized that all the five planets had retrograde motions. The silk manuscripts unearthed from 马王堆 Mawangdui, in Changsha, buried in 168 bce, contained an astrological text concerning the five planets (Xi 1989a). Besides a long paragraph of astrological contents, the text provided three tables giving the motions of Jupiter, Saturn, and Venus for the 70 years between 246–​177 bce. Table A4b.2 shows the synodic periods and sidereal periods of Jupiter, Saturn, and Venus in the Mawangdui silk manuscript. The five planets were combined with the five phases theory, which was one of the basic philosophical theories of ancient China, or it may be that the five phases theory was originally based on observation of the five planets in early times.

Table A4b.2 The Data for Jupiter, Saturn, and Venus in the Mawangdui Astrological Text on the Five Planets Jupiter

Saturn

Venus

Synodic Period

395.44 days

377 days

548.40 days

Sidereal Period

12 years

30 years

8 years

Astral Sciences in Ancient China    137 The ancient Chinese were very diligent in observing and recording abnormal celestial phenomena. Solar eclipses, comets, “guest stars” (novas and supernovas), and sunspots were the main phenomena of interest. The Mawangdui silk manuscripts contained 29 figures of comets in various shapes, with 18 different names for them (Xi 1989b). Most abnormal celestial phenomena were bad omens, solar eclipses and comets being the worst. After the Han, with the improvement in calculation of solar eclipses, comets became the worst omens. In the Warring States period astrologers made predictions of the fate of feudal states based on abnormal celestial phenomena. In the unified empire from the Han dynasty on, prediction of the country’s fate was not permitted and astrology was strictly forbidden to anyone besides the responsible officials. Abnormal celestial phenomena were understood to be caused by inappropriate human behavior or as heaven’s warning to his “son,” that is, the emperor. Sometimes emperors took special virtuous steps to ward off the ill effects of the omens. For example, the emperor may have avoided the central hall, reduced his food intake, or cancelled musical performances. In another vein, he might show closer to attention to the people, for instance, sending imperial envoys to inspect local governments and to hear ordinary people’s opinions, or promulgate imperial edicts reducing penalties, and so on.

3. Calendar Making The ancient Chinese calendar was a luni-​solar calendar. From the Han dynasty on, a standard calendar usually included calculations of the sun, the moon, the five planets, the daylight and nighttime, eclipses, and so forth. As the ancient Chinese used a luni-​ solar calendar, a “month” referred to a lunar month, that is, from one new moon day to the next, and a year had to begin on a new moon day, that is, at a syzygy. After having been used for a long time, a calendar would become inaccurate, and syzygies and eclipses predicted by the calendar would not conform to the actual observation and it became clear that a new calendar was needed. The ancient Chinese calendar paid particular attention to seeking various cycles. The tropical year, the cycle of intercalary months, the synodic and sidereal periods of the five planets, and the eclipse cycle were the most important ones. In addition, there was a special 60 干支 ganzhi cycle that was formed by the combination of 10 干 gan or 天 干 tiangan (heavenly stems) and 12 支 zhi or 地支 dizhi (earthly branches). This ganzhi cycle was first used in naming the days, and lunar eclipse records verified by modern calculations show that the continuous sequence has not been interrupted since the Shang dynasty in the 13th century bce (Zhang 1999). From the 2nd century bce on, this cycle also began to be used in labeling the years. From the Han through the Sui, calendrical systems always strove to find a common date for the beginning of all the cycles. In a luni-​solar calendar the basic cycles are the lengths of the tropical year and of the month, and their common multiples, that is, the cycle of intercalary months. At the latest, from the Warring States period on, the tropical year was determined by observing

138    Ancient Scientific Traditions Beyond Greece and Rome the length of the gnomon’s shadow at noon. When the length of the shadow was longest this was the winter solstice, while the shortest shadow marked the summer solstice. A shadow 1.5 尺 chi long for an eight 尺 chi tall gnomon at summer solstice was recorded in the Chinese classic 周礼 Zhou li, or the Rites of Zhou, which was explained by a commentator as having been determined by 周公 Zhou Gong (Duke of Zhou) in the 11th century bce. From the Han dynasty on, observing the gnomon’s shadow was the first step in calendar making, and observation of the winter solstice was used to determine the tropical year. At the beginning of the Han, a kind of 四分 Si fen (quarter-​day) calendar passed down from the Qin was adopted. It took 365¼ days as the tropical year, and prescribed seven intercalary months every 19 years. This meant there were 235 months in every 19 years, thus the length of a month being 29 499/​940 days. In the middle of the Western Han, a great calendar reform was implemented, and the new 太初 Tai chu calendar was promulgated in 104 bce. The original text of Tai chu calendar has not survived. By the end of the Western Han, 刘歆 Liu Xin (ca 50 bce‒23 ce) revised the Tai chu calendar into his 三统 San tong calendar, which was preserved in the Treatise on Hharmonics and the Calendar, in the History of the Former Han. The San Tong calendar adopted 29 43/​81 days as the length of a month, and prescribed seven intercalary months every 19 years, thus the length of a tropical year became 365 385/​ 1539 days. At least at the beginning of the Han, the complete system of 24 节气 jie qi, or solar terms, appeared. In this system a tropical year was divided equally into 24 parts, the first days of each of the 24 parts were called 节气 jie qi, and every second jie qi, among which were the two solstices and the two equinoxes, were called 中气 zhong qi (middle qi). In the Spring and Autumn period and in the Warring States period, the beginning of a year varied among the feudal states: the month containing the winter solstice was used, as well as each of the two following months. From the Tai chu calendar on, the month containing the zhong qi named 雨水 Yu shui (i.e., when the sun’s longitude is 330º in modern terms) was used as the first month of the year. In the Warring States period, intercalary months were usually put at the end of a year and counted as the 13th month. The San tong calendar set up the rule of defining the months that did not contain a zhong qi as intercalary months, and this rule was preserved in later calendars. The San tong calendar gave the synodic periods and sidereal periods of the five planets, and divided the synodic periods into several steps, describing the planets’ motions in each steps. The synodic periods of Jupiter, Mars, and Saturn were divided into six steps, while those of Venus and Mercury were divided into 10 steps. Before the Han, it had been thought that the sidereal year of the Jupiter was 12 years, and the belt along the equator or ecliptic was divided into 12 parts, called 12 次 ci, each of the 12 ci having their own names. The 12 ci may have been established in early Zhou in the 11th century bce, and they played a very important role in astrology during the Spring and Autumn period. Liu Xin realized that the sidereal year of Jupiter was not precisely 12 years, and so he provided for a “leap ci” every 144 years. The San tong calendar also provided a cycle

Astral Sciences in Ancient China    139 of 135 months for eclipses and gave the table of the sun’s positions for each of the 24 solar terms, as well as the widths of the 28 xiu in the equatorial system. The San tong calendar had a strong numerological flavor, endeavoring to explain every datum as the combination of certain mysterious numbers. For example, with regard to the denominator 81 in the length of the month, it was explained as the “self-​multiplication” of 9, the length of the standard tuning pipe note called 黄钟 huang zhong, which explains the preoccupation with harmonics at the time. The Si fen calendar promulgated in 85 ce and used in Eastern Han corrected the lengths of the tropical year and of the month, and added a table of extensions of the 28 xiu along the ecliptic. Another table was added, which listed seven observable quantities (the sun’s position; the ecliptic distance to the pole, which in fact was the sun’s declination; the length of the gnomon’s shadow; length of day by the clepsydra; length of the night by the clepsydra; the culminating stars at dusk; and the culminating stars at dawn) at each of the 24 jie qi. From the Han dynasty on, there were two methods of dividing the day-​and-​night times (i.e., one solar day), one being to divide it into 12 parts, called 12 时辰 shi chen, and the other to divide it into 100 parts, called 100 刻 ke (one ke is thus a little less than 15 minutes). The clepsydra adopted the 100 ke system. The boundary between the daytime and night was defined as 2.5 ke before the sun’s rising in the morning and 2.5 ke after the sun’s setting in the evening. Thus dusk and dawn became two exact times instead of simply two broad time periods. The Si fen calendar of Eastern Han gave 65 ke for daytime and 35 ke for nighttime at the summer solstice. The culminating stars at dusk and dawn were not real stars, but the actual du in the 28 xiu, which is equal to the right ascension. In the early Eastern Han, astronomers found that the moon did not display uniform motion and that the “fastest” position advanced three du every cycle. In fact, this is the anomalistic month. By the end of the Eastern Han, in the 乾象 Qian xiang calendar of 刘洪 Liu Hong in 206 ce a table was added dividing an anomalistic month into four phases and giving the corrections for this motion. After the Eastern Han, from the 3rd to the 5th centuries ce, the length of the tropical year and the cycle of intercalary months were improved, more tables were introduced into calendars, and the magnitude and beginning direction of an eclipse began to be calculated. More than one century after the discovery of precession by Yu Xi, Zu Chongzhi (429–​500 ce) studied the relative texts again and concluded that the winter solstice moved one du to the west along the equator every 45 years and 9 months. He introduced this value into his Da ming calendar, which was completed in 462 ce. Around 570 ce Zhang Zixin made three great discoveries: the uneven motions of the sun and the five planets, and the effects of parallax on lunar eclipses. In the beginning of the Sui, there was a violent dispute over the calendar that lasted for more than 20 years. The three discoveries by Zhang Zixin were all applied in the two calendars presented to the Sui court, the 大业 Da ye calendar and the 皇极Huang ji calendar. The most prominent of these was the Huang ji calendar, composed by 刘焯 Liu Zhuo (544–​610 ce), but it was never promulgated. In order to correct the uneven motions of the sun and the moon, Liu Zhuo invented the quadratic interpolation method in calculating the positions of the

140    Ancient Scientific Traditions Beyond Greece and Rome sun and the moon, thus calculating the real syzygies and eclipses. The uneven motion of the sun also resulted in corrections to the day and night expressed in ke with the clepsydra. Liu Zhuo also made great improvements in calculating the five planets. Before Liu Zhuo’s calculations a synodic period was often divided into several steps, and the motion in each was treated as uniform motion. In introducing the uneven motions of the five planets, Liu Zhuo corrected the motions of the five planets day by day according to their positions among the stars. All these complicated mathematical methods and tables advanced the ancient Chinese calendar to a higher stage of development.

4.  Cosmology and Cosmogony As recorded in Treatise on Astronomy, in the History of the Jin Dynasty, 蔡邕 Cai Yong (133–​192 ce) of the Eastern Han had said: “Formerly those who discussed the heaven formed three schools: the Gai tian, the Hun tian, and the Xuan ye.” The 盖天 gai tian (celestial dome) theory, the 浑天 Hun tian (celestial sphere) theory, and the 宣夜 xuan ye (infinite empty space) theory represented the most important cosmological theories in ancient China. The origins of these three schools are difficult to determine, but their theories were all well explained in the Han dynasty. The gai tian school had the 周髀算经 Zhou bi suan jing (Zhou-​era Method for Gnomon Calculation) as its classic. Zhou bi suan jing is a 经jing (classic) on astronomy and mathematics that was listed as the first among the 10 official mathematical classics in the Tang dynasty (618–​907 ce). The extant version of Zhou bi suan jing may have taken shape in the 1st century bce, but the theories it contains would be much earlier. The Zhou bi suan jing consists of two volumes. The first volume gives a set of data of the heaven and the earth. Most were obtained using measurements of the gnomon shadow, the 勾股 gou gu theorem (same as the Pythagorean theorem), and the presumption that the shadow of an 8-​chi-​tall gnomon varies 1 cun for every 1000 li. (The 尺 chi and the 寸 cun are length units, that varied over time. 1 chi = 10 cun, and in the Zhou dynasty 8 chi was about an ordinary person’s height. The 里 li is a unit of length on the earth. The length of the li and its relation with chi varied over time too: in the Han dynasty, 1 chi ≈ 0.231 meters, and 1 li = 1800 chi, about 416 meters.) When the gnomon’s shadow was 6 chi long at noon, observing the sun with a bamboo tube 8 chi long and 1 cun in diameter, the sun’s surface just covered the hole. Using the gou gu theorem, the distance between the heaven and the earth was found to be 80,000 li. Since the shadow of the North Pole was 103 cun, the place beneath the North Pole was 103,000 li north of the place of the observer, that is, the location of Zhou. The sun rotated around the North Pole. Since at summer solstice the sun’s shadow at noon was 16 cun, the place beneath the sun at this time was 16,000 li south of Zhou. So at summer solstice the sun’s radius of rotation was 119,000 li. At the winter solstice at noon, the sun’s shadow was 135 cun, thus the place beneath the sun was 135,000 li south of Zhou

Astral Sciences in Ancient China    141 and the sun’s radius of rotation was 238,000 li. Seven concentric equidistant circles were drawn around the North Pole, the inner one being the sun’s orbit at summer solstice while the outermost one was the sun’s orbit at winter solstice, thus forming six rings between them. These were called seven 衡 heng and six 间 jian, and used to account for the sun’s different orbits in different seasons. Sunlight could only reach a distance of 167,000 li, and where the sunlight could not reach it was night. This explained why daytime is longer in summer than in winter. In this model, heaven and the earth should be two parallel flat planes, but Zhou bi suan jing did not state this. In the second volume, it said that heaven was like a pointed hat, and the earth was like an upside-​down plate, the North Pole being the center of heaven. Both heaven and earth were elevated at the center in the north, and tilted down toward the outside. In this view the heaven and the earth were not two parallel flat planes. So in fact Zhou bi suan jing’s system was internally not self-​consistent. According to various texts, the earliest star charts were gai charts drawn on the gai tian theory. These kinds of charts did not survive. But from the medieval period, one of the typical ways of drawing star charts was to show all the stars in the sky on a round map, the center of the map being the North Pole and the boundary circle being the circle of the perpetual invisibility. The circles of the perpetual visibility and the equator took the North Pole as their center, but the circle of the ecliptic deviated from that. The 28 xiu and other constellations were all drawn on the map. This kind of drawing was developed from the earlier gai charts. The hun tian school, or the celestial sphere school, grew up in the Han dynasty. In fact, since the widths of the 28 xiu were measured in the Warring States period, and there should have been an instrument like an armillary sphere to measure them, astrologers of the Warring States must have been aware of a global heaven. Hun tian theory rejected the gai tian theory and became widely accepted in the Han. 扬雄 Yang Xiong (53 bce—​ 18 ce) was the most prominent figure in this controversy. He originally was an advocate of the gai tian theory, but after long discussion and debate, he became an advocate of the hun tian theory. He proposed eight questions that he thought the gai tian theory could not explain but the hun tian could explain well. Zhang Heng of Eastern Han was the representative figure of the hun tian school. He designed and fabricated an armillary sphere and a celestial globe, and wrote 浑仪注 Hun yi zhu, Commentary on the Armillary Sphere. In it he wrote: The heavens are like a hen’s egg and as round as a crossbow pellet; the earth is like the yolk of an egg, and lies alone in the center. Heaven is large, the earth is small. Inside the lower part of the heavens there is water. The heavens are supported by qi, the earth floats on the water. (trans. Needham 1959, 217)

He then provided detailed explanations of the degrees of the heaven, the altitude of the North Pole, and why only half the stars could be seen, and so forth. The textual basis for the xuan ye theory was already lost by the Han, and only an official named 郗萌 Xi Meng remembered the teaching from his former masters. The

142    Ancient Scientific Traditions Beyond Greece and Rome basic idea was that heaven had no shape, no body, it was high and distant and without bounds:  “The sun, the moon, and the stars float in empty space, their moving and stopping all rely on qi.” The sun, the moon, and the five planets moved in their own way because they were not rooted or attached to anything. These three theories were the most representative theories in the Han. Many discussions and arguments were presented in detail concerning them throughout the Han and up to the Southern and the Northern Dynasties, with several modified forms of the gai tian and the hun tian making their appearance. Since the hun tian theory could explain the motions of the sun, the moon, and the stars well, and the armillary sphere and celestial globe based on the hun tian theory demonstrated the motion of the heavens well, it gradually replaced the gai tian theory. The xuan ye theory explained heaven was not a physical shell and the motions of the sun, moon, and the five planets, and it conformed well to ancient Chinese philosophy and concept of 气 qi; it also evolved to more refined versions in later times. After the Jin dynasty (265–​420 ce), Buddhism expanded in China, and sometimes Buddhist theories influenced cosmological theory. Cosmogony was an important problem in the Han dynasty, and speculations about the origin and evolution of the universe can be found in many texts, such as Huainanzi (Book of Huainan), Tian wen xun (Chapter on Astronomy), in the early Western Han, and Zhang Heng’s commentary in the middle period of the Eastern Han. There were some common features in various accounts of the formation of the cosmos. In the beginning there was void or nothingness, which was silent and gloomy. Then came the 混 沌 Hun dun, or chaos, and everything was in a homogenous state. Then 气 qi emerged. Gradually the clearer and thinner qi rose up and formed heaven, while the heavier and turbid qi condensed to form the earth. The condensation and spread of qi formed the sun, the moon, the stars, and the five planets in heaven, and formed the mountains, the waters, and everything on the earth. The philosophical concept of 道 Dao, or the Way, was introduced into the process of formation of the cosmos. In the Huainanzi, the Dao emerged from the void, while in Zhang Heng’s theory, the origin and evolution of the cosmos was a process of the growth of the Dao from root to stem to fruits. The physical properties of the sun, moon, and stars were not clearly stated in various cosmogonies but tended to be regarded as a kind of 象 xiang, or image, corresponding to 形 xing, or shape, on the ground. After the Han dynasty discussions about cosmogony continued, but were not so active and almost all were based on the Han theories.

Bibliography 陈久金 Chen Jiujin. 中国古代天文学家 Zhongguo gudai tianwen xue jia. 北京 Beijing: 中 国科学技术出版社 Zhongguo kexue jishu chubanshe (China Science and Technology Press), 2008. Chen provides a biographical and historical account of “Ancient Chinese Astronomers” from the legendary period up to the 19th century. 陈美东 Chen Meidong. 中国科学技术史·天文学卷 Zhong guo ke xue ji shu shi, tian wen xue juan. 北京 Beijing: 科学出版社 Kexue chubanshe (Science Press), 2003. This is the “volume

Astral Sciences in Ancient China    143 of astronomy” in a series of books on History of Science and Technology in China, and in this book Chen studies the history of Chinese astronomy from the Neolithic era to the end of Qing, ca 3000 bce–1911 ce. 陈美东Chen Meidong. 中国古代天文学思想 Zhongguo gudai tianwenxue sixiang. 北京 Beijing:  中国科学技术出版社 Zhongguo kexue jishu chubanshe (China Science and Technology Press), 2008. Chen studies “Astronomical Thought in Ancient China,” covering all three cosmological models discussed here. Lloyd, Geoffrey E.  R. Being, Humanity, and Understanding:  Studies in Ancient and Modern Societies. Oxford and New York: Oxford University Press, 2012. Lloyd, Geoffrey E. R., and Nathan SIVIN. The Way and the Word: Science and Medicine in Early China and Greece. New Haven, CT: Yale University Press, 2002. Needham, Joseph. Science and Civilisation in China. Vol. 3: Mathematics and the Sciences of the Heavens and the Earth. Cambridge: Cambridge University Press, 1959. Pankenier, David W. Astrology and Cosmology in Early China. Cambridge:  Cambridge University Press, 2013. Pankenier, David W., Ciyuan Liu, and Salvo de Meis. “The Xiangfen Taosi Site: A Chinese Neolithic ‘Observatory’?” Archaeologia Baltica 10 (2008): 141–​148. http://​www.lehigh.edu/​ ~dwp0/​Assets/​images/​taosisite.pdf. 吴守贤, 全和钧 Wu Shouxian, and Quan Hejun. 中国古代天体测量学及天文仪器 Zhongguo gudai tianti celiang xue ji tianwen yiqi. 北京 Beijing:  中国科学技术出版社 Zhongguo kexue jishu chubanshe (China Science and Technology Press), 2008. Wu and Quan explore “Ancient Chinese Astrometry and astronomical instruments.” 席泽宗 Xi Zezong (a). “马王堆汉墓帛书中的《五星占》” “Mawangdui hanmu boshu zhong de wuxingzhan” (The text of the ‘five planets account’ in the Mawangdui Silk Manuscripts). In 中国古代天文文物论集 Zhongguo gudai tianwen wenwu lun ji (Collective essays on ancient Chinese astronomical relics), ed. 中国社会科学院考古研究所 Zhongguo shehui kexueyuan kaogu yanjiusuo. Institute of Archaeology, Chinese Academy of Social Sciences, 46–​58. 北京 Beijing: 科学出版社 Kexue chubanshe (Science Press), 1989. 席泽宗Xi Zezong (b). “马王堆汉墓帛书中的彗星图” “Mawangdui hanmu boshu zhong de huixing tu” (The comet figures in the Mawangdui Silk Manuscripts). In 中国古代天文文物 论集 Zhongguo gudai tianwen wenwu lun ji, 1989 29–​34. Xu Fengxian, and He Nu. “Short Description (ICOMOS-​IAU Case Study Format):  Taosi Observatory, China.” In Heritage Sites of Astronomy and Archaeoastronomy, ed. Clive Ruggles and Michel Cotte, 87–​91. Paris: International Council on Monuments and Sites & International Astronomical Union, 2011. http://​www2.astronomicalheritage.net/​index.php/​ show-​entity?identity=16&idsubentity=1. 张培瑜 Zhang Peiyu. “日月食卜辞的证认与殷商年代” “Ri yue shi buci de zhengren yu yinshang niandai” (“The Identification of oracle bone inscriptions related to solar and lunar eclipses and the Shang Dynasty dating”). 中国社会科学 Zhongguo shehui kexue (Social sciences in China) 5 (1999): 172–​198. 张培瑜, 陈美东, 薄树人, 胡铁珠 Zhang Peiyu, Chen Meidong, Bo Shuren, and Hu Tiezhu. 中国古代历法 Zhongguo gudai lifa. 北京 Beijing: 中国科学技术出版社 Zhongguo kexue jishu chubanshe (China Science and Technology Press), 2008. The four authors study “The Ancient Chinese Calendar” from Spring and Autumn period to the end of the Yuan dynasty, i.e., 770 bce–​1368 ce.

B

E A R LY G R E E K SCIENCE

chapter B1

P y t hagoras and  Pl ato Andrew Gregory

Pythagoras, Plato, and their followers are often lumped together in accounts of ancient science. There are reasons why this should be, but there are also reasons why we should be suspicious of this association and be aware of the differences and the similarities between the two schools of thought. Plato was certainly influenced, to some degree, by the Pythagoreans, though to what extent is a matter of debate. In the ancient world after Plato, there was a trend to attribute all of the Pythagoreans’ work to Pythagoras and to assimilate the Platonic and Pythagorean views together, sometimes attributing Plato’s views to Pythagoras. In the modern world, there has been a tendency to group Pythagoras and Plato together on the basis that both were pioneers of the role of mathematics in science and both were allegedly interested in some form of numerology or number mysticism. The nature of mathematization they envisaged, however, has different manifestations and significantly different motives.

1. Pythagoras 1.1 Pythagoras Pythagoras was born in Samos ca 570 bce and died ca 490 bce. Around 530 bce he relocated to Croton, which became a center for the Pythagoreans. Pythagoras himself wrote nothing, and if his contemporaries wrote anything about him, nothing of this has survived; so all we know of Pythagoras comes from significantly later sources. The “Pythagorean question” is how trustworthy these sources are for an attempt to reconstruct Pythagoras’ thought (Huffman 1999). It is possible to generate a picture of Pythagoras as someone who was an expert in mathematics and geometry, who proved Pythagoras’ theorem, who made important discoveries on harmonics and mathematized harmonic theory, who in astronomy believed there was a harmony of the spheres, who believed the world was in some way constituted from numbers, and that mathematics was the key to understanding the cosmos. However, it is clear that from the time of Plato

148   Early Greek Science and Aristotle onward that many sources treated Pythagoras as a semidivine or a divinely inspired figure. These sources glorified Pythagoras, often seeing him as the origin of philosophy and attributing to him many of the ideas of the later Pythagoreans, Plato and Aristotle (Burkert 1972; Huffman 1999; Huffman 2014; Lloyd 2014). Many forged works were generated purporting to be by Pythagoras. Since Walter Burkert’s seminal Lore and Science in Ancient Pythagoreanism (1972), it has been held that to find out about Pythagoras, we must look to the earliest and least corrupt sources on him, which means looking at Plato and Aristotle. The picture that emerges is radically different. It is of someone whose key beliefs were in the immortality of the soul and reincarnation and whose expertise was in the fate of the soul after death and in the nature of religious ritual. Pythagoras’ major achievements are seen as advocacy of and founding a way of life based on stringent dietary regulations, strict self-​discipline, and the keen observance of religious ritual. It is notable though that while both Plato and Aristotle talk of pre-​Socratic natural philosophy, they do not give Pythagoras any significant role in this, nor do they recognize any Pythagorean cosmology prior to Philolaus (Plato, Republic 531a, 600a, Sophist 242c; Aristotle, Metaphysics 1.5, De caelo 2.13). Pythagoras is not credited with a proof of Pythagoras’ theorem nor seen as a significant mathematician or geometer by Plato and Aristotle, which is true of early histories of Greek mathematics as well. Pythagoras is not associated by Plato and Aristotle with any harmonic theory (Plato, Republic 531a, Timaeus 35b; Aristotle, De caelo 2.9). It should be noted that one often-​quoted tale of Pythagoras is that he discovered the mathematical ratios underpinning harmonics (2:1 as the octave, 3:2 as the fifth, 4:3 as the fourth, etc.). He is alleged to have done so by listening to the sounds made by hammers in a smithy and finding the weights of these hammers to be in these integer ratios. However, the weight of a hammer has no such direct relationship to the note it will produce, so this tale must be false. Burkert’s approach, while a significant advance, does not entirely close the Pythagorean question. Plato did not claim to be a historian, and when he mentions previous thinkers or theories he does so in philosophical, polemic, or literary contexts, which makes it difficult to judge how accurate his representation is. Aristotle, though he did give historical surveys, is notorious for interpreting previous thinkers in terms of his own thought, sometimes producing serious distortions. There is evidence that Pythagoras was aware of something related to Pythagoras’ theorem without having himself generated a proof—​perhaps Pythagorean triples (integer side lengths for Pythagorean triangles such as 3, 4, 5), perhaps a significant diagram, perhaps the theorem, but not the proof (Burkert 1972). Pythagoras clearly highly valued such knowl­ edge as he is said to have sacrificed an oxen upon its discovery. Zhmud (1998a) makes the best case for discovery by Pythagoras. There is also evidence that Pythagoras valued mathematics in education. It may well be the case that the notion of the tetraktys can be traced back to Pythagoras. The tetraktys is the first four numbers, and their sum is the Pythagorean perfect number, 10. They are often arranged in the manner depicted in figure B1.1.

Pythagoras and Plato   149

Figure B1.1  Pythagorean tetraktys. Drawing by Paul A. Whyman, based on sketch by author.

There is evidence that the tetraktys was in some way related to the harmony sung by the Sirens, which in turn may be related to the notion of the harmony of the spheres (Aristotle, De caelo 2.9). Recent advances in our understanding of the relations, in ancient Greece, between religion and science and between magic and science have rendered the position where Pythagoras was an important religious thinker but still interested in science more plausible. A parallel here is the scholarship on Empedocles. Historians who believed religion and science to be incompatible sorted Empedocles’ fragments into two different works and assigned them to different parts of his life. More recently, historians who are happy with the compatibility of science and religion have made significant advances in piecing the fragments together in other ways, producing a more coherent picture of Empedocles. A similar historiographical realignment has occurred in thinking about magic and science. We are not then forced to choose between a religious/​magical Pythagoras and a scientific Pythagoras, but may have a Pythagoras who combines all of these elements. The current state of the Pythagorean question then, is that while Pythagoras was not the important mathematician, cosmologist, and harmonic theorist of legend, he did have an interest in mathematical and related issues and that the tradition he fostered facilitated later Pythagoreans such as Philolaus and Archytas, who developed many of the views later attributed to Pythagoras (Huffman 1999). Before we move on to Philolaus and Archytas, Alcmaeon of Croton (dates uncertain but probably a generation younger than Pythagoras) has often been assumed to be a Pythagorean but is now generally reckoned not to have been. The earliest evidence that he was a Pythagorean comes from Diogenes Laërtius in the 3rd century ce. Aristotle wrote on the Pythagoreans, but he wrote separately on Alcmaeon. He also contrasts Pythagorean views on opposites with those of Alcmaeon. The opposites that interest Alcmaeon do not appear in the Pythagorean table of opposites, and the critical limited/​ unlimited Pythagorean pair did not interest Alcmaeon.

1.2 Philolaus Philolaus of Croton lived from ca 470 to ca 385 bce. Philolaus and Archytas were the most significant contributors to the Pythagorean tradition in the pre-​Socratic period.

150   Early Greek Science Philolaus wrote one book, On Nature, which if Pythagoras wrote nothing, is probably the first book of the Pythagorean tradition, of which a few fragments survive. He worked on astronomy, cosmology and cosmogony, on harmonic theory, medical theory, and had an ontology of an unlimited that was determined by limiters (Huffman 1993). With Philolaus we have the first surviving Pythagorean cosmology, depicted in figure B1.2. From the center moving outward, there is a central fire, a counter-​earth, the earth, the moon, the sun, the five naked-​eye planets (Mercury, Venus, Mars, Jupiter, Saturn) and the stars. This cosmology is notable for being one of the very few in antiquity to displace the earth from the center of the cosmos. Instead there is a central fire (not the sun) with the earth and sun orbiting around it. No explicit reason has survived why the earth was placed in motion. How well this model could account for the phenomena of the heavens is still open to debate, as is whether accounting for the phenomena or some form of religious/​eschatological symbolism was its main function. It does seem that Philolaus replied to criticism that his model would not account for the phenomena by elaborating on his system to suggest how the criticisms might be met. In reply to the objection that we do not see the counter-​earth or central fire, Philolaus supposed a rotation of the earth such that we are always looking in the opposite direction. In reply to the objection that if the earth was in motion within his system, we would not see the sun and moon as we do, Philolaus replied that the earth’s orbit was small in relation to the relevant distances so the effect would be negligible. This would suggest that both critics and Philolaus took his system seriously as a model (Huffman 1993). Aristotle is critical of Philolaus on slightly different

Figure B1.2  Cosmology of Philolaus. Drawing by Paul A. Whyman, based on sketch by author.

Pythagoras and Plato   151 lines, saying that the reason Philolaus supposed there to be 10 heavenly bodies was that 10 was the perfect Pythagorean number (Aristotle, Metaphysics 1.5, De caelo 2.13). One explanation of why there is a central fire in Philolaus’ cosmology is his cosmogony. Fragment 7 has a hearth in the center of the sphere as the first thing to be generated as the cosmos is fitted together. The cosmos comes to be from the unlimited and limiters. The outline of Philolaus’ view of unlimited and limiters is clear enough, even if we lack enough information to say much in detail about this view. It would seem that fire is first limited in the center of the cosmos, and then other unlimiteds are drawn in. There is some debate on exactly what these are, but it is likely they include breath, space, and time. The evidence is unclear, leading to debate about whether number is generated with the cosmos and whether the central fire is in some sense the number one, or whether being the first unity, one describes the central fire. In common with other pre-​S ocratic cosmogonies, limit and unlimited are seen as existing prior to the organization of the cosmos, so there is no creation ex nihilo. The idea of the application of limit to the unlimited may be a comment on Anaximander, who had an initial unlimited that separated out into the elements rather than being limited (Huffman 1988, 1999, 2001).

Harmony Philolaus’ theory of music is a form of what is known as just intonation, that is, it is based on ratios of small integers (Barker 1989). Whether Pythagoras, Philolaus, or someone else discovered that the lengths of string required to generate musical notes have simple ratios or not, Philolaus produced the first theoretical account of this. If the length of a string is halved, then the note it sounds is an octave of the first note, and ratio of the string lengths is 2:1. If the ratio is 4:3 we get a musical fourth, and if the ratio is 3:2 we get a musical fifth. Both of these notes sound harmonious when played with the original note. A fourth and a fifth make an octave (4/​3 x 3/​2 = 12/​6 = 2/​1). The difference between a fourth and a fifth is 9/​8 (4/​3 x 9/​8 = 3/​2). 9:8 is the ratio used to generate one whole tone. So if the root note is taken as 1, the first note in the scale will be 9/​8. The second note will be 9/​8 x 9/​8 = 81/​64. The Philolean semitone is generated by 256:243. The third note in the scale is 81/​64 x 256/​243 = 4/​3 (a musical fourth). The following note is 4/​3 x 9/​ 8 = 3/​2 (a musical fifth), then 3/​2 x 9/​8 = 27/​16, then 27/​16 x 9/​8 = 243/​128, and finally 243/​ 128 x 256/​243 = 2, which gives the octave a ratio of 2:1. Modern music uses something called 12-​tone equal temperament (12ET) where there are equal ratios between the 12 semitones making up an octave, that ratio being 12√2 (the 12th root of two). Table B1.1 gives some sense of the differences: The first row is Philolaus’ notes expressed as ratios. The second row gives the modern note names in the key of C major. The third row are notes in 12ET expressed in “cents,” where 1,200 cents = one octave and 100 cents = one semitone. The fourth row is Philolaus’ note position expressed in cents.

152   Early Greek Science Table B1.1 1

9/​8

C 0

D 100 200 203.91

81/​64

4/​3

E

F

300 400

500

407.82 498.04

3/​2 G 600 700 701.96

27/​16 A 800 900 905.87

243/​128

2

B

C

1000 1100 1109.78

1200 1200

The Philolean scale is mathematically very pure, using only powers of 2 and 3. The ratio 256/​243 initially looks obscure, but in fact is 28/​35. Just intonation, like that of Philolaus, gives a purer sound to harmonies based on the fourth and the fifth, but it is rather inflexible and impractical. The advantages of 12ET are that it is easier to modulate (change key within a piece of music), easier to tune a range of different instruments to play together, and that chords (three or more notes sounded together) sound rather better, at the cost of a little purity of some harmonies.

Medical We have some information on Philolaus’ medical views on the embryo and on disease. Philolaus conceived of the embryo as hot, as for him both womb and sperm are hot. On birth, we breathe in cool air. There are clear parallels here with the cosmogony of a central fire drawing in the unlimited, and such parallels between birth and cosmogony are common among the pre-​Socratics. On disease, Philolaus considered blood, bile, and phlegm to be hot, and imbalances of hot, cold, and nutrition to be cause of disease, a possible implication being that the appropriate cooling of the body is critical to health, in a parallel with the first breath cooling the newborn infant.

Archytas Archytas of Tarentum (428‒347 bce) is important for his work in mathematics, cosmology, and harmonic theory and was also active as a political leader. If he wrote anything, it has not survived as a whole. Only four genuine fragments have come down to us, though they are important ones, along with some important testmonia. There were many works forged in Archytas’ name in late antiquity (Huffman 2005).

Cosmology The most famous argument that we have from Archytas is a thought experiment concerning the finite nature of space. Archytas imagines someone standing at the limit of a finite cosmos. Can this person take a staff and thrust it beyond the limit of the cosmos? If he can, and our intuition is that he can, then this is not the limit of space, and we have a new limit. Moreover, this thought experiment is replicable; that is, wherever a new limit is supposed, we can suppose someone thrusting a staff beyond it. Therefore space is unlimited.

Pythagoras and Plato   153 This argument was much discussed in antiquity. The Stoics and Epicureans supported it and argued for an unlimited space, while Plato and Aristotle argued in their own way for a limited space, and the argument was much discussed by later commentators. Two replies to Archytas were (1) it is impossible to stand at the edge of the cosmos, or, more subtly, (2) outside the cosmos there is neither time nor space so there is nowhere to thrust the staff. Archytas’ argument is less discussed nowadays as we have the conception of finite but unlimited space which has no edges (Huffman 2005).

Music Theory Archytas’ work on harmonic theory builds on that of Philolaus, and Archytas also had a theory of pitch (Barker 1989; Huffman 2005). According to Archytas, the pitch of a sound is related to how quickly it travels: a sound traveling more quickly has a higher pitch. Actually the speed of sound is a constant for a given medium, and it is frequency that is critical to pitch—​how rapidly a string vibrates determining the frequency rather than the speed of the sound. Archytas produced a variation on Philolaus’ musical scale, using 9:8, 8:7, and 28:27 to determine the notes up to the fourth (9/​8 x 8/​7 x 28/​27 = 4/​3). This sort of scale is known as a diatonic, and Archytas also worked on two other types of scale, the chromatic and the enharmonic. A chromatic scale includes all 12 semitones (which in 12ET would be equally spaced). The key ratios for Archytas’ chromatic scale are 32:27, 243:224, and 28:27 (32/​27 x 243/​224 x 28/​27 = 4/​3). In the chromatic scale, A# = Bb. In an enharmonic scale this is not so, and what we would call A# differs from Bb. The key ratios for Archytas’ enharmonic scale are 5:4, 36:35, 28:27 (5/​4 x 36/​35 x 28/​27 = 4/​3). In contrast to Philolaus, who seems to be generating in some ways an ideal scale, Archytas seems to have been describing the scales in use during his time (Barker 1989, 50). He may be the target of Plato’s criticism that the Pythagoreans search for audible harmonies when they should be considering which numbers are harmonious and why.

Mathematics Archytas demonstrated one very important property of what are known as superparticular ratios, that is ratios of the type where n + 1:n. If p bears the same proportion to q as q does to r, then q is the mean proportional of p and r (if p:q:: q:r). This is important in music, as a double octave (4:1) can be split into two octaves with a mean proportional as 4:2 is the same proportion as 2:1. Archytas proved that there is no mean proportional for numbers in superparticular ratios. This means that critical musical ratios, such as 3:2, 4:3, and 9:8 (which all have the form n + 1:n) have no mean proportional and cannot be split in to two equal parts. Archytas is famous for having provided a solution to the “Delian problem,” that of doubling the volume of a cube (Heath [1913] 1981; Mueller 1997; Huffman 2005). What length is required for the sides if the volume of a cube is to be doubled? Archytas’ solution built on an insight of Hippocrates of Chios. If L is the length of the original cube, it is possible to set up a series of ratios such that L:a:: a:b:: b:2L (L is in proportion to a, as

154   Early Greek Science a is to b, as b is to 2L). It is then possible to derive the relation L:2L = L3:a3. As L3:a3 is in the ratio of 1:2, a3 is twice L3, and the cube can be built with sides of length a. Archytas’ solution, which is too complex to give in full here, involved constructing four similar triangles in the proportions suggested by Hippocrates by an imaginary rotation of triangles and calculation of their points of intersection. At the beginning of his book on harmonics, Archytas praised the value of four disciplines, astronomy, geometry, “logistic” (calculation), and music (Huffman 2005). He also praised those who have practiced these disciplines before him. Of these disciplines, he takes calculation to be the key subject. It is hard to be precise on exactly what Archytas meant by logistic, though doubtless it is related to the notion that to know something is to know its relation to number, whether that be in terms of musical ratios, geometry or astronomy.

2. Plato We have the great majority of the works of Plato, 428/​427‒328/​327 bce, though the interpretation of them is complex, as Plato wrote dialogues rather than treatises, and it is far from clear how the views given to the characters in these dialogues relate to Plato’s own views. Opinions on the nature and contribution of Plato’s views on science and their subsequent influence have been widely varied and continue to be so (Lloyd 1968, 1991; Anton 1980; Gregory 2000a; Johansen 2004). At least in part this is due to continuing disagreement about the nature of Plato’s metaphysics but also involves the disputation of certain key passages where Plato mentions scientific topics. Plato has been accused of being anti-​science, or at least anti-​physical or empirical science, while others have seen him as an important pioneer of the role of mathematics in science and of an important tradition in ancient astronomy. Recent work on Plato has focused on the context and goals of investigation for Plato. The key metaphysical issue is Plato’s contrast between the particular things in the world about us and the forms. Exactly what Plato took the forms to be and whether he believed in them for his entire career are still hotly contested questions. One way of characterizing the difference between particulars and forms is like this. Particulars are perceptible, changing, material, and we can only have opinions about them. Forms are apprehended intellectually, are entirely unchanging, are immaterial, and we can have knowledge about them. Forms are said to be, while particulars are in a state of becoming. In the middle books of the Republic, Plato develops the allegories of the sun, line, and cave, where he emphasizes the ascent from the perception of particulars to the contemplation of forms as important for philosophy (Plato, Republic 509d ff.). It is here that he also makes the notorious comment that astronomy should be pursued by means of problems as with geometry, and we should set empirical considerations aside. Where does this leave science? Some commentators have taken the view that science for Plato only concerns forms and being, and so excludes observation (Heath [1913]1981, 135; Mueller 1980, 104; Knorr 1993, 399; Hetherington 1993, 85). Others have taken the view that science for Plato deals with

Pythagoras and Plato   155 the physical world of becoming, but as such science can never rise above the level of opinion (Cornford 1937, 29; Lee 1955, 311). In support, they cite that Plato’s Timaeus, his later work on the nature of the cosmos, calls itself an eikos muthos, a likely story. More recent work has challenged these sorts of views on several levels. The characterization of forms and particulars given above has become known as the “two worlds” view and has come under fire for being too rigid and formulaic and insufficiently subtle to capture Plato’s concerns. Rather than viewing science or scientific disciplines as the sole province of one of these worlds, recent commentators have emphasized the notion of ascent such that disciplines begin by perceiving particulars and ascend to considering forms, thus giving an empirical role to each discipline (Gregory 2000a). Commentators have also pointed out that in the middle books of the Republic, Plato also comments that having ascended to the contemplation of forms and learned about justice, it is the duty of the guardians to return to govern the world about us (Lloyd 1991). So too then, knowledge of the relevant forms may help with scientific disciplines. The context of the comments about astronomy and observation in the middle books of the Republic has also been deemed important. Plato is discussing how astronomy should be used in the philosophical education of the guardians of his ideal state. In this context it is not surprising that he calls for them to think about the nature of the heavens rather than carry out observations. Plato is making an educational point, not a point about how we investigate the heavens. If we turn to the Timaeus (47a ff), we find a eulogy about how sight can help with astronomy, and, as Vlastos has commented, the Timaeus is full of the language of observational astronomy (Vlastos 1975). On the nature of the Timaeus’ account, exactly what Plato meant when he described it as an eikos muthos which translates literally as “likely myth” but may be translated in several other ways, is a matter of ongoing debate (Burnyeat 2005; Betegh 2010). Some commentators emphasize that the thoroughgoing teleological account of the cosmos and all it contains show Plato’s treatment of the natural world to be a serious one, especially as the place of humans in the cosmos and how humans should seek to improve themselves are also important themes in the Timaeus (Lloyd 1968). In his early work, the Phaedo, Plato is critical of the physiologoi, the philosophers who have come before him who have carried out historian peri phusis, the investigation of nature. It is clear that he believes their explanations, based solely on material considerations, are inadequate. Does this mean that Plato dismisses the investigation of nature, or, in his later work the Timaeus, does he show how it should be carried out using teleological explanation? Any view of Plato’s science must account for the brute fact that Plato wrote the Timaeus, a work that gives a full teleological account of the origins of the cosmos, the disposition of the cosmos, the nature and origins of the elements, and the nature and origins of human beings. The Timaeus was possibly the most influential work on natural philosophy in the whole of antiquity.

Astronomy The model of the heavens that Plato gives in the Timaeus is sometimes called a two-​ sphere model, though this is slightly misleading. The stars are arranged in a spherical

156   Early Greek Science pattern and rotate once a day on an axis that passes through the earth (see figure B1.3). The sun, moon, and five naked-​eye planets (Mercury, Venus, Mars, Jupiter, and Saturn) have an additional circular motion, again centered on the earth, but with the axis offset from that of the stars. The moon takes a month to complete its extra circular motion; the sun, Mercury, and Venus a year; while the other planets have unspecified periods (Plato, Timaeus 38b ff.). The key innovation here is the notion of regular, circular motions being combined to give an account of the heavenly bodies. This principle will go unchallenged to 1609 and Kepler’s discovery that planetary orbits are ellipses around the sun. If the axes are offset by the angle of the ecliptic (approx. 23.5 degrees), then this model will work well for the sun. Plato does not give any figure here, but says the angle is like that made by the arms of the Greek letter χ. Plato’s model has the sun, moon, and planets all moving in one plane. Viewed from the earth this means that sun, moon, and planets all follow one path across the heavens. As a first approximation this is fine, but the orbits of the moon and planets are all at small inclinations to the plane of the earth’s orbit around the sun. This means that the moon and planets move within a band around that of the motion of the sun, known as the zodiac, which was well-​known at the time. Mercury and Venus, as they have smaller orbits than the earth, are always seen relatively close to the sun, sometimes preceding it, sometimes following it. When Venus precedes the sun, it is seen low on the horizon just before

Figure B1.3  Model of the heavens in Plato, Timaeus. Drawing by Paul A. Whyman, based on sketch by author.

Pythagoras and Plato   157 sunrise; when it follows the sun, it is seen low on the horizon just after sunset. Because in Plato’s model, the sun, Mercury, and Venus all have uniform speeds, this phenomenon cannot be accounted for. Also problematic is planetary retrograde motion. Viewed from the earth, each of the naked-​eye planets appears periodically to reverse its course for a period before resuming its forward motion. We understand this as an effect of the relative motion between the earth and the planets against the background of the stars. However, if the earth is immobile, all the motions of the heavens must be merely apparent. Plato’s combination of two regular circular motions cannot reproduce this phenomenon. A final major defect of Plato’s system is that if sun, moon, and earth are all permanently in the same plane, there will be full eclipses of the sun once a month and full eclipses of the moon every month, with no other type of eclipse. It is clear from a close reading of the Timaeus that Plato is aware of most, if not all, of the problems (Gregory 2000a). There are two ways of addressing these difficulties. Some scholars have argued that for the model to be in accord with the phenomena, we must drop the idea of regular circular motion, however insistent Plato may appear on this principle, and note that Plato says that Mercury and Venus are subject to a “contrary power” in relation to their movements relative to the sun (Cornford 1937; Knorr 1990). More recently it has been argued that it is improper to assume that every ancient theorist believed their model was able to account for all of the phenomena. Simplicius states that Eudoxus was well aware of phenomena that could not be accounted for by his own model. On this view, Plato’s model is a prototype, strong on principle (combinations of regular circular motion), better at explaining some phenomena than previous models but still with significant defects as we might expect from a prototype. As mentioned, Plato would have been aware of at least some of these defects (Gregory 2000a). How influential this model was is again the subject of an ongoing controversy. Simplicius reports Plato as having asked others to work out which combinations of regular circular motions would save the phenomena. Simplicius’ sources have been questioned, and certainly there was a tendency in later antiquity to portray Plato as an architect of the sciences, so we ought to be cautious (Mittlestrass 1962, 154; Vlastos 1975, 110; Zhmud 1999, 220). Some commentators have doubted whether Plato could have made such a remark on the grounds that either he did not believe in regular circular motion or that he was implacably opposed to observational astronomy. If Plato did hold to regular circular motion and considered his model a prototype with flaws, one can see why he would ask others to work out which circular motions would save the phenomena.

Eudoxus Eudoxus of Knidus (ca 410‒ca 347 bce) was an important associate of Plato. We have very little of his original work, but we do have accounts of his astronomy preserved by later writers such as Simplicius (Simplicius, De Caelo Commentary). His work in astronomy can be seen as building on that of Plato (Gregory 2003). Where Plato used models involving two regular circular motions for the sun, moon, and

158   Early Greek Science planets, Eudoxus used three for the sun and moon and four for the planets (see figure B1.4). Plato Two Motions

Eudoxus Three Motions

Eudoxus Four Motions

Figure B1.4  Comparison of the models of Plato and Eudoxus. Drawing by Paul A. Whyman, based on sketch by author.

The third motion for the moon gives in motion in latitude through the zodiac and so provides a much better model. The third and fourth motions for the planets produce a figure known as the hippopede (see figure B1.5). 4

8 7

5

1

3 6

2

Figure B1.5  Diagram of the two motions constituting the hippopede. Drawing by Paul A. Whyman, based on sketch by author.

When this is combined with the other two motions, the result is seen in figure B1.6. 4 5

6

7

8

1

3 2

Figure B1.6  Diagram of the four combined planetary motions. Drawing by Paul A. Whyman, based on sketch by author.

This allows Eudoxus to give some account of the retrograde motion of the planets, though the system is not flexible enough to provide a full account (Mendell 1998; Yavetz 1998). Eudoxus also did important work in mathematics, developing the theory of proportions such that it was able to cope with irrational numbers, integers, and rational fractions. There has been debate about the interaction of Plato and Eudoxus, with the suggestion that the astronomy of the Timaeus was largely inspired by Eudoxus, the motivation for this supposition often being that Plato was not sufficiently interested in the physical world to produce such a sophisticated astronomy. There is, however, no evidence to support this opinion.

Pythagoras and Plato   159

Cosmology Plato’s astronomy is set within a broader cosmological picture. It is important to recognize that the Greeks had no concept of gravity. They of course knew that heavy objects fall to earth and that the heavens have regular motions but generated other ways to explain these phenomena. For Plato the cosmos was a living entity, though of a rather special sort. It has intelligence and self-​motion, though Plato was adamant it did not have limbs, organs of sensation, or organs of ingestion or excretion. It is a purely spherical, rotating entity (Plato, Timaeus 33b ff.). What is he attempting to capture with this model? The motions of the heavens were perceived as orderly and regular with the stars having a certain set pattern (hence the “fixed stars”). The motions of the planets were intricate, due to the Greek belief in a central and stable earth. We understand many of the motions of the heavens as apparent motions, generated by the motion of the earth. If the earth is believed to be entirely motionless though, all the motions of the heavens are real motions. Whereas we would explain the retrograde motion of the planets as an apparent effect generated by the relative motion of earth and planet against the star field, for the Greeks the planets really did reverse their motion. In addition to the cosmos having a soul, the individual planets have souls as well, so they can move relative to the cosmos. For Plato, regular and orderly motion was characteristic of intelligence, while irregularity was characteristic of matter on its own. In contrast, we take mechanism, in particular clockwork, to be a paradigm of regularity and contrast that with human frailty. That is an attitude of the 17th century and the rise of the mechanical philosophy and after though, and was not shared by the ancients (Furley 1987). Another important point in relation to this is that while we think of physical law in terms of equations and exceptionless laws, this has not always been so, and there have been significant alternatives. In particular, in the ancient world, it was possible to conceive of physical law as analogous to civil law. So for Plato there are courses that the planets ought to follow, but no physical or mathematical necessity that forces them to follow those courses. However, for Plato intelligence always chooses what is good, and so the world soul and planetary souls always choose to do what they ought to do. For Plato, the absolute regularity of the heavens is underpinned by the intelligence of the heavens. Plato also incorporates music in his cosmology (Plato, Timaeus 36a ff.). Specifically, he uses the musical ratios in the scale advocated by Philolaus to determine the sizes of the orbits of the sun, moon, and planets. This illustrates an important difference between Plato and modern cosmology. Where we would happily accept that the ratios of the orbits of the planets are an accidental matter, Plato’s demiurge must have criteria for why he has set the orbits up like this as all he does is for the best. Here it is important to understand that this is a very early stage in the mathematization of the world. Although it may be evident to us that we should describe the world in terms of the

160   Early Greek Science equations familiar to modern physics, this has not always been so. If we accept this, it is easier to see why Plato attempts to incorporate not only mathematics but geometry and musical theory into his cosmology as well. Plato was far from being alone in this. As late as the 17th century, Johannes Kepler, famous for his three laws of planetary motion, was attempting to determine the nature of the elliptical orbits of a sun-​centered cosmos in terms of the geometry of the Platonic solids and the ratios of musical theory. In this context, we can see why Plato chooses Philolaus’ scale over Archytas’. Philolaus’ scale is musically the purest in some sense and mathematically the most elegant. As it does not have to be played, but just defines the ratios of the orbits, the practical problems with the scale are unimportant.

Cosmogony Plato’s account of cosmogony was highly influential in the ancient world. In the Timaeus, Plato gives an account of how the cosmos came into being. Before the cosmos, there was chaos. Plato’s craftsman god, the demiurge, then generated a cosmos from this chaos, at all times working with what would be best in mind (Timaeus 29e ff.). By imposing “number and form” on this chaos he generates the basic triangular particles and from these the “elements” of earth, water, air, and fire (Timaeus 53d ff.). From the elements the earth, the solar system, animals, and man are all generated in the best possible manner, and there is also a process by which the heavens and humans are ensouled. Once the cosmos is formed, it can only be dissolved by the demiurge, who, being entirely good, will never have any inclination to do so. The key debate about Plato’s account of cosmogony is whether it is meant to be taken literally. This debate began in antiquity and is unresolved. Some scholars say that we should take the cosmogony as a counterfactual analysis (Baltes 1996). The primordial chaos is what the world would be like if the demiurge was not constantly maintaining the cosmos in its present organized state. There was no point of generation for the cosmos, no point when it came to be, but it is in a permanent state of becoming and dependent on the demiurge. Some scholars note, if taken literally, there are many inconsistences in the cosmogony, but from the allegorical view those inconsistences are unimportant. They also observe that very early interpretations of the Timaeus took the cosmogony as allegorical. The literalists, on the other hand, argue that the inconsistencies are tolerable, especially as Plato warned us that the account is difficult and we should not expect perfect consistency from it. Examining ancient interpretations, they point out that Aristotle argued that either something came into being and then passed away at a later stage or always has and always will exist. This argument was very influential in antiquity, and the motivation for the early literalist view was to save Plato, who seemed to believe in a beginning but not an end for the cosmos, from criticism along these lines. The debate is unlikely to be resolved swiftly or decisively as many

Pythagoras and Plato   161 aspects of the interpretation of the Timaeus are involved. However, the two most recent studies of ancient cosmogony have both come out in favor of a literalist view, citing evidence both in the Timaeus and in Plato’s other works (Gregory 2007, 2009; Sedley 2008). One further important aspect of Plato’s cosmology and cosmogony is that he was adamant that there is only one cosmos that has been well organized by the demiurge. This is in sharp contrast with the ancient atomists, who believed there to be many universes that came about by chance. A key part of the atomist account is that a vortex, which forms spontaneously from atoms moving in an infinite void, will organize matter “like to like” and thus into a cosmos. Plato considers a cosmos to be a fitting and harmonious blend of hot and cold, dry and wet, soft and hard, and so on, that is, blends of opposites. He argued that if we only employ a like-​to-​like principle in cosmogony, it accounts for the grouping of like things but not of unlike things. Plato’s argument for a unique cosmos by design is not merely theological. He attacked explanations of cosmogony that rely on chance by noting the points of implausibility in those accounts (Gregory 2007).

Matter Plato famously offered a new type of matter theory: geometrical atomism. In contrast to the earlier atomist theory of Leucippus and Democritus, which allowed all shapes and sizes of atoms, Plato allowed only two basic shapes, both triangular (Plato, Timaeus 53d ff.). In contrast to the theories of the Milesians, where there was a basic substance such as water or air from which all the other substances were generated, Plato argued that we have no reason to believe earth, water, air, or fire to be basic, because we see each of them turning into the other. Instead, he supposed there to be shapes more basic than the elements that are below the level of perception. The justification for these shapes is that they are the best and most beautiful, which is why they were chosen by the demiurge. The two shapes are shown in figure B1.7.

√3

2

1

√2

1 1

Figure B1.7  The two fundamental cosmic triangles. Drawing by Paul A. Whyman, based on sketch by author.

162   Early Greek Science These two basic shapes are said to coalesce into two complexes, depicted in figure B1.8.

2

1

√3

2 √3

1

1 √2

Figure B1.8  The two complexes into which the triangles coalesce. Drawing by Paul A. Whyman, based on sketch by author.

These more complex shapes in turn form solid bodies, the tetrahedron, the cube, the octahedron, and the icosahedron (twenty-​sided); see figure B1.9.

Figure B1.9  Tetrahedron and cube. Drawing by Paul A. Whyman, based on sketch by author.

These are four of the Platonic solids, that is, solids made up of identical faces. They are also the elements: the tetrahedron being fire, the cube being earth, the octahedron being air, and the icosahedron being water. The cube is reckoned to be earth on the basis of the stability of the cube and of earth; while the tetrahedron is reckoned to be fire because of its sharp angles, and its swift motion is able to cut things as fire does. Fire, air, and water are able to transmute into one another; for example, when a solid breaks apart into triangles, these triangles can re-​form as any of the three solids. Earth is excluded from this, having a different type of triangle as its basis. The theory of geometrical atomism has been seen as the basis for the use of equations in chemistry (Vlastos 1975). However, Plato does not use it this way, and his purpose is to give a theory of matter based on a small number of mathematically well-defined entities. Here again we can see Plato’s predilection for explaining origins in terms of design rather than accident. Where the atomists had an infinite number of particle shapes and sizes, Plato proposes only two basic shapes, both mathematically well-​defined and both chosen by the demiurge because they are good shapes.

Pythagoras and Plato   163

Body and Medicine Plato’s account of the body, disease, and treatment is not much discussed but does occupy a significant part of the Timaeus. The account serves several important functions for Plato and was very influential in some traditions up to the 17th century, the time of the scientific revolution. Like all else in the cosmos, humans are generated by the demiurge with the best in mind. Part of the scheme of their construction is to house the tripartite soul (reason, spirit, appetite), with the intellectual faculties being housed as far as possible from the more base appetites of hunger and sex. The generation of living beings completes the account of the cosmos and makes the cosmos itself a proper whole. It is noteworthy that Plato describes the construction of humans in terms of the geometrical atomism he set out. Another important feature is that humans are a microcosm of the cosmos as a whole. While Plato does not originate the macrocosm/​microcosm language, it is clear that for him, many aspects of the human body take on characteristics of the cosmos. It has the same sort of order, it acts on its contents as the cosmos acts on its contents (e.g., Timaeus 81ab), and our minds, too, have circuits like those of the heavens. This, although not original to Plato, was highly influential in Neoplatonism and various magical traditions up until the 17th century. One important aspect of human construction is that humans are a single, well-​ designed species, not the result of a series of accidents, parallel to Plato’s thinking on cosmogony. Plato may well have had Empedocles in mind when he said that our heads were given means of locomotion, otherwise they would get stuck in ruts in the ground. Empedocles’ account entails a rather nightmarish world where individual, dissociated body parts join together accidentally until viable species are formed. How though, do some of those parts, like heads, move around? Plato also emphasized that human body parts need to be arranged not only in the correct order but also the right way round. So, not only is there a need for there to be heads, necks, chests, and abdomens in the correct order, there is also a need for the correct orientation of faces, throats, breasts, and stomachs to the front. Plato, as with his argument against the atomist cosmogony, adds further layers of implausibility to their account. Plato’s account of the human body also reveals something interesting about the relation of reason and necessity. The account in the Timaeus is set in three stages. First, we are given the works of reason; second, the works of necessity; third, a combination of reason and necessity. It is critical to Plato’s account that, while the demiurge is well intentioned and does everything as best as he can, there are constraints on what he can do. The reason the demiurge imposes cannot be absolute but is tempered in some way by necessity. Exactly what Plato meant by reason and necessity has been the subject of much debate. Some have taken the view that nothing can act with perfect regularity in the physical world because of this compromise of reason with necessity, matter not behaving in a regular manner. What emerges from the description of humans is that the issue here may be more of an engineering consideration. How thick should the human

164   Early Greek Science skull be? For defense and long life, as thick as possible, for the best perception, as thin as possible. The demiurge does his best but cannot instantiate both of these considerations, so human skull thickness is a compromise (Cornford 1937; Morrow [1950] 1965; Gregory 2000a; Johansen 2004). In terms of medicine, Plato is very much in favor of good diet and regimen allied to gentle medical intervention rather than any radical use of drugs, purgatives, emetics, and so forth. Essentially, he sees the body as a self-​regulatory system (as with the cosmos as a whole), which occasionally needs a little maintenance and help rather than vigorous medical intervention. Plato’s account of aging is that the collections of triangles that constitute the elements of our body gradually lose their ability to cohere, leading to a gradual deterioration of the bodies functions. Thus death in old age is seen as a perfectly natural occurrence for Plato.

Plato a Pythagorean? Whether Plato was some form of Pythagorean has been much debated in the literature. In light of recent scholarship on Pythagoras, Philolaus, and Archytas, the key initial question must be: What sort of Pythagoreanism have we in mind? Although there are certain important Pythagorean influences on Plato, it is now generally accepted, since the reliability of later sources has been determined, that it is unwise and misleading to consider Plato to be a Pythagorean (for example, Taylor’s [1928] view that the Timaeus was essentially a Pythagorean work is no longer considered a viable interpretation). Plato and the Pythagoreans have some significant differences regarding scientific issues. First, the cosmology of the Timaeus is geometrical rather than arithmetical in nature. For the Pythagoreans, the cosmos is an arithmetical cosmology, that is, it is constituted, in some sense, of numbers. For Plato in the Timaeus, the demiurge imposes specific geometrical shapes on the primordial chaos to generate a cosmos. These are the (1, 1, √2), and (1, √3, 2) triangles from which the cubes, tetrahedra, octahedra, and icosahedra of earth, fire, air, and water are formed. It is these shapes that form the basis of Plato’s cosmos, not numbers. Aristotle is critical of Plato for what he takes to be the arbitrary way in which Plato allows his analysis of the elements to end at triangles when it could have gone further to lines, numbers, and points. Plato’s geometrical atomism allows him to deal with irrational numbers such as √2 and √3 by treating nature as geometrical and having numbers apply to shapes. That is not so clear for the arithmetical conception of nature where every geometrical length ought to be expressible as the ratio of two natural numbers. If these numbers represent a length, then if we ask how long something is, we count the number of monadic lengths involved. A problem for such a scheme comes with the discovery of the irrationality of the square root of two, for here we have a number/​length that cannot be expressed as a ratio of two natural numbers or as a multiple of a monadic length. Plato’s use of musical theory in cosmology highlights some differences with the Pythagoreans, as well as an evident influence. Philolaus’ scale uses the numbers 1, 2, 3, and 4 in various ratios to generate a musical scale. The rationale for this is 1 + 2 +

Pythagoras and Plato   165 3 + 4 = 10, the Pythagorean perfect number, or, in other words, the justification is numerological. So too Aristotle criticizes the Pythagorean assumption that there are 10 celestial bodies (earth, moon, sun, five naked-​eye planets, counter-​earth, and central fire) on the basis that 10 is the perfect number and so there should be 10 celestial bodies (Aristotle, Metaphysics 1.5). Plato accepts there are seven visible heavenly bodies to (moon, sun, and five naked-​eye planets) and has seven terms that generate his musical scale (1, 2, 3, 4, 8, 9, 27), which are the relative lengths of the soul stuff that the demiurge uses to fashion the orbits for these bodies (Plato, Timaeus 35b). Plato then generates a tone and semitone scale from these terms. The derivation is again geometric (dividing the soul stuff) rather than purely arithmetic as with the Pythagoreans. So while Philolaus has a numerological derivation of cosmology and of music, Plato has a cosmological derivation of music. It may also be important to note that in the Timaeus and subsequent works of Plato, there is no mention of any audible harmony of the heavenly bodies. There is a harmony to the structure of the world soul, but no sound.

Kennedy The most recent development on Plato and Pythagoras has been the work of Jay Kennedy (Kennedy 2010). He claims that Plato organized his work stichometrically; that is, Plato was aware of the number lines in each of his works and in each part of his works. He further claims that Plato divided each of his works into 12 parts and that Plato has means of indicating the transition from one 12th to another. So Plato may make a reference to divine justice, or a speech may begin at a 12th part of a work. Kennedy also claims that there is a harmonic organization to Plato’s works based on a 12-​note division of the octave. Thus, each of the 12 parts represents a semitone. It is claimed that Plato writes predominantly of positive ideas at harmonious parts of the scale and predominantly of negative ideas at dissonant parts. The final claim is that this sort of analysis reveals Pythagorean doctrine and information about Pythagoras encoded in the text. Kennedy supports these theses with statistical analysis that certainly at first sight looks impressive in its breadth and claimed results. If Kennedy’s claims are shown to be true, they will revolutionize our understanding of both Pythagoras and Plato. It would be fair to say that this is a big “if,” and that scholars have so far reacted with some caution to Kennedy’s theses (Gregory 2012). One important issue at stake here is our understanding of how and why Plato wrote his works. Whether Kennedy’s claims about the organization of Plato’s works withstand tight scrutiny will be the critical question. While he claims impressive accuracy for his results, accuracy is not the same as statistical significance. If I claim Plato uses the letter α at each of the 12th points of his works, that will doubtless be very accurate, but given the profusion of α in the rest of his work, it will not be statistically significant. The real test for Kennedy’s work will be running proper tests for statistical significance on the claims he has made.

166   Early Greek Science

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Plato Anton, J. P., ed. Science and the Sciences in Plato. New York: Eidos, 1980. Artmann B. and L. Schäfer. “On Plato’s ‘Fairest Triangles’ Timaeus 54a.” Historia Mathematica 20 (1993): 255–​64. Baltes, M. “Gegonen Platon, Tim. 28 B 7.  Ist die Welt real entstanden oder nicht?” In Polyhistor: Studies in the History and Historiography of Ancient Philosophy Presented to Jaap Mansfeld on His Sixtieth Birthday, ed. K. Algra et al., 76–​96. Leiden: Brill, 1996. Betegh, G. “What Makes a Myth Eikos?” In One Book, the Whole Universe: Plato’s Timaeus Today, edited by R. D. Mohr and B. Sattler, 213–​224. Las Vegas, Zurich, Athens: Parmenides, 2010. Bulmer-​Thomas, I. “Plato’s Astronomy.” Classical Quarterly 34 (1984): 107–​12. Burnet, J. Platonis Opera. 5 vols. Oxford: Clarendon Press, 1903–​1910. Burnyeat, M. B. “Eikos Muthos.” Rhizai 2.2 (2005): 143–​165. Bury, R. G. Plato’s Timaeus. Cambridge, MA: Loeb, 1929. Calvo, T., and L. Brisson, eds. Interpreting the Timaeus and Critias. Sankt Augustin: Academia, 1997. Cavagnaro, E. “The Timaeus of Plato and the Erratic Motion of the Planets.” In Calvo and Brisson 1997, 351–​62. Cornford, F. M. Plato’s Cosmology London: Routledge & Kegan Paul, 1937. Crombie, I. M. “Cosmology and Theory of Nature.” In An Examination of Plato’s Doctrines. Vol. 2: Plato on Knowledge and Reality, 153–​246. London: Routledge & Kegan Paul, 1963. Dicks, D. R. Early Greek Astronomy to Aristotle. Bristol: Thames and Hudson, 1970. Furley, D. J. The Greek Cosmologists. Vol. 1: The Formation of the Atomic Theory and Its Earliest Critics Cambridge: Cambridge University Press, 1987. Gregory, A. D. “Astronomy and Observation in Plato’s Republic.” Studies in History and Philosophy of Science 27 (1996): 451–​471. —​—​—. Plato’s Philosophy of Science London: Duckworth, 2000a. —​ —​ —. “Plato and Aristotle on Eclipses.” Journal for the History of Astronomy 31 (2000b): 245–​259. —​—​—​. “Eudoxus, Callippus and the Astronomy of the Timaeus.” In Ancient Approaches to Plato’s Timaeus. Bulletin of the Institute of Classical Studies, Supplement 78, ed. R. W. Sharples and A. Sheppard, 5–​28. London: Institute of Classical Studies, 2003. —​—​—. Ancient Greek Cosmogony, London: Duckworth, 2007. —​—​—​. “Plato on Order from Chaos.” Proceedings of the Biennial Conference on Greek Studies, ed. E. Close, G. Couvalis, G. Frazis, M. Palakisoglu, and M. Tsianikas, 47–​54. Adelaide: Flinders University Press, 2009. —​—​—​. “Kennedy and Stichometry: Some Methodological Considerations.” Apeiron 45.2: 157–179. Hackforth, R. “Plato’s Cosmogony Timaeus 27d ff.” Classical Quarterly, new series 9 (1959): 17–​22. Heath, T. L. Aristarchos of Samos. 1913. Reprint, New York: Dover, 1981. Heiberg, J. L., ed. Simplicius. Aristotelis in De Caelo Commentaria. Berlin:  Akademie der Wissenschaften, 1894. Hetherington, N. S. Encyclopedia of Cosmology:  Historical, Philosophical and Scientific Foundations of Modern Cosmology. New York: Garland, 1993.

168   Early Greek Science —​—​—. “Plato and Eudoxus: Instrumentalists, Realists or Prisoners of Themata?” Studies in History and Philosophy of Science 27 (1996): 271–​289. Huffman, C. A. A History of Pythagoreanism. Cambridge: Cambridge University Press, 2014. Johansen, T. K. Plato’s Natural Philosophy:  A Study of the Timaeus-​ Critias. Cambridge: Cambridge University Press, 2004. Kennedy, J. B. “Plato’s Forms, Pythagorean Mathematics, and Stichometry.” Apeiron 43(2010): 1–​31. Keyt, D. 1971. “The Mad Craftsman of the Timaeus.” Philosophical Review 80: 230–​35. Knorr, W. “The Interaction of Mathematics and Philosophy in Antiquity.” In Infinity and Continuity in Ancient and Medieval Thought, ed. N. Kretzman. Ithaca, NY: Cornell, 1982. —​—​—​. “Plato and Eudoxus on the Planetary Motions.” Journal for the History of Astronomy 21 (1990): 313–​329. Kraut, R., ed. The Cambridge Companion to Plato. Cambridge:  Cambridge University Press, 1992. Lasserre, F. The Birth of Mathematics in the Age of Plato. London: Hutchinson, 1964. —​—​—​. Die Fragmente des Eudoxus von Knidos. Berlin: de Gruyter, 1966. Lee, H. P. D. The Republic. London: Penguin, 1955. —​—​—. Plato: Timaeus and Critias. London: Penguin, 1965. Lennox, J. G. “Plato’s Unnatural Teleology.” In Platonic Investigations, edited by D. J. O’Meara, 195–​218. Washington, DC: Catholic University of America Press, 1985. Lloyd, D. R. “Symmetry and Asymmetry in the Construction of the ‘Elements’ in the Timaeus.” Classical Quarterly 56 (2006): 459–​474. —​—​—. “The Chemistry of Platonic Triangles:  Problems of Interpretation in the Timaeus.” HYLE—​International Journal for Philosophy of Chemistry 13 (2007): 99–​118. —​—​—​. “Symmetry and Beauty in Plato.” Symmetry 2 (2010): 455–​465. Lloyd, G. E. R. “Plato as a Natural Scientist.” Journal of Hellenic Studies 28 (1968): 78–​92. —​—​—​. Early Greek Science to Aristotle. London: Chatto and Windus, 1970. —​—​—​. “Saving the Appearances.” Classical Quarterly 88: 202–​222., 1978. —​—​—. The Revolutions of Wisdom. Berkeley: California University Press, 1987. —​—​—. “Plato and Archytas in the Seventh Letter.” Phronesis 35 (1990): 159–​174. —​—​—. “Plato on Mathematics and Nature, Myth and Science.” In Methods and Problems in Greek Science: Selected Papers, 333–​351. Cambridge: Cambridge University Press, 1991. —​—​—. “Pythagoras.” In Huffman (2014). Mendell, H. “Reflections on Eudoxus, Callippus and their Curves:  Hippopedes and Callippopedes.” Centaurus 40 (1998): 177–​275. Mittlestrass, J. Die Rettung der Phänomene. Berlin: de Gruyter, 1962. Mohr, R. D. The Platonic Cosmology. Leiden: Brill, 1985. Morrow, G. R. “Necessity and Persuasion in Plato’s Timaeus.” Philosophical Review 59 (1950):  147–​ 160; Reprint. Studies in Plato’s Metaphysics, ed. R.  E. Allen, 421–​ 437. London: Routledge & Kegan Paul, 1965. Mourelatos, A. P. D. “Astronomy and Kinematics in Plato’s Project of Rationalist Explanation.” Studies in the History and Philosophy of Science 12 (1981): 1–​32. Mueller, Ian. “Ascending to Problems: Astronomy and Harmonics in Republic VII.” In Anton 1980, 103–​122. —​—​—​. “Platonism and the Study of Nature.” In Method in Ancient Philosophy, ed. J. Gentzler, 67–​90. Oxford: Oxford University Press, 1998. Patterson, R. “The Unique Worlds of the Timaeus.” Phoenix 35 (1981): 105–​119. Reale, G. “Plato’s Doctrine of the Origin of the World, with Special Reference to the Timaeus.” In Calvo and Brisson 1997, 149–​164.

Pythagoras and Plato   169 Robinson, T. M. “Understanding the Timaeus.” Proceedings of the Boston Area Colloquium on Ancient Philosophy 2 (1986): 103–​119. —​—​—. “Aristotle, the Timaeus and Contemporary Cosmology.” Philosophical Inquiry 15 (1993): 48–​58. De Santillana, G. “Eudoxus and Plato.” Isis 32 (1949): 248–​262. Sedley, D. Creationism and its Critics in Antiquity. Berkeley:  University of California Press, 2008. Shorey, P. “Platonism and the History of Science.” Proceedings of the American Philosophical Association 46 (1927): 159–​182. Skemp, J. B. The Theory of Motion in Plato’s Later Dialogues. Cambridge: Cambridge University Press, 1942. Smith, N. D., ed. Plato: Critical Assessments. 4 vols. London: Routledge, 1998. Sorabji, R. Time, Creation and the Continuum. London: Duckworth, 1983. Tarán, L. “The Creation Myth in Plato’s Timaeus.” In Essays in Ancient Greek Philosophy, ed. J. Anton and G. Kustas, 372–​407. Albany: State University of New York Press, 1971. Taylor, A. E. A Commentary on Plato’s Timaeus. London: Oxford University Press, 1928. Vallejo, A. “No, It’s Not a Fiction.” In Calvo and Brisson 1997, 141–​148. Visentainer, J. “A Potential Infinity of Triangle Types: On the Chemistry of Plato’s Timaeus.” HYLE—​International Journal for Philosophy of Chemistry 4 (1998): 117–​128. Vlastos, G. “Disorderly Motion in Plato’s Timaeus.” Classical Quarterly 33 (1939): 71–​83; repr. in Studies in Greek Philosophy. Vol. 2: Socrates, Plato, and Their Tradition, ed. G. Vlastos, 247–​ 264. Princeton, NJ: Princeton University Press, 1995. —​—​—​. “Creation in the Timaeus: Is It a Fiction?” In Studies in Plato’s Metaphysics, ed. R. E. Allen, 401–​419. London: Routledge & Kegan Paul, 1965; repr. in Studies in Greek Philosophy. Vol. 2: Socrates, Plato, and Their Tradition, ed. G. Vlastos, 265–​279. Princeton, NJ: Princeton University Press, 1995. —​—​—. “Plato’s Supposed Theory of Irregular Atomic Figures.” Isis 58 (1967): 204–​209; repr. in Platonic Studies, 2nd ed., ed. G. Vlastos, 366–​373. Princeton, NJ: Princeton University Press, 1981. —​—​—​. Plato’s Universe. Seattle: University of Washington Press, 1975. —​—​—​. “The Role of Observation in Plato’s Conception of Astronomy.” In Anton 1980, 1–​22. Wright, M. R. Cosmology in Antiquity London: Routledge, 1995. —​—​—, ed. Reason and Necessity: Essays on Plato’s Timaeus. London and Swansea: Duckworth, Classical Press of Wales, 2000. Yavetz, I. “On the Homocentric Spheres of Eudoxus.” Archive for History of the Exact Sciences 52 (1998): 221–​278. Zeyl, D. Plato: Timaeus. Indianapolis: Hackett, 2000. Zhmud, L. “Die Beziehungen Zwischen Philosophie und Wissenschaft in der Antike.” Sudhoffs Archiv 78 (1994): 1–​13. —​—​—. Wissenschaft, Philosophie und Religion im Fruhen Pythagoreismus. Berlin: Akademie Verlag, 1997. —​—​—​. “Plato as ‘Architect of Science.’” Phronesis 43 (1999): 211–​244.

chapter B2

Early M ath e mat i c s and Astronomy Leonid Zhmud

There is no generally agreed starting point for the history of Greek mathematics and astronomy. Those scholars who prefer dealing with the fully preserved works begin with Euclid’s Elements and Autolycus’ of Pitane On the Moving Sphere, written ca 300 bce, when Greek mathemata—​geometry, arithmetic, astronomy. and harmonics—​were already fully formed. An awareness that scientific methods and theories known from the works of Euclid and Autolycus are not exactly their own methods and theories, but very often originate from the 4th, the 5th, and even the 6th centuries, leads other scholars to search for the earliest written text in mathemata. Such a text is represented by a long fragment from the writing of Hippocrates of Chios (ca 440/​30 bce) on the squaring of lunes (moon-​shaped areas between circular arcs). This takes us almost 150 years back, to a period when Greek mathematicians and astronomers systematically started to reveal their theories in writing and arrange previous discoveries. Indeed, Hippocrates was the author of the first Elements (Euclid’s Elements were the fourth such work), where geometrical theorems were systematically expounded in a deductive though not yet entirely axiomatic way. The first systematic work in astronomy was written most probably by Hippocrates’ compatriot Oenopides of Chios (ca 450 bce). Archytas of Tarentum, a generation younger than Hippocrates, was the author of the first writings specifically on arithmetic and harmonics known to us.

1.  Eudemus: The Milesians of the 6th century bce Hippocrates’ fragment came to us as a quotation from the History of Geometry by Eudemus of Rhodes (ca 330 bce), a student of Aristotle and the author of the first

172   Early Greek Science histories of science. As well as the History of Geometry, he wrote the History of Astronomy, beginning these sciences with Thales of Miletus (fl. ca 585 bce)—​the famous Sage, whom Aristotle regarded as the founder of natural philosophy. Thales wrote nothing; the other famous mathematician of the 6th century bce, Pythagoras of Samos, also left nothing in writing. One has to concede that to write the history of pre-​ Euclidean mathematics on the basis of contemporaneous texts is impossible: there are no such texts for the time from Thales to Hippocrates (and almost none for that from Hippocrates to Euclid). What is known about the earliest period of Greek mathemata amounts very often to the fragmentary evidence provided by Eudemus; in some cases it can be augmented by the independent testimonia but never by a preserved though fragmentary text. Nevertheless, if one does not want to overlook the century and a half preceding Oenopides and Hippocrates, a period in which geometry and astronomy came into being and took shape, the best thing to do is to follow Eudemus’ reports, while subjecting them to critical scrutiny (Zhmud 2006; cf. Netz 2004). Most modern histories of Greek science bear some important features inherent in Eudemus’ histories. One of them consists in regarding the ancient Orient as a source of Greek mathematics and astronomy. Geometry, says Eudemus, was discovered by the Egyptians as a result of the practical needs of land surveying, and arithmetic, in turn, was discovered by the Phoenicians, who were employed in trade. Thales, first having traveled to Egypt, brought geometry to Greece; he discovered much himself and instructed his successors in the principles of the other things (fr. 133 W.). The Egyptian origin of geometry is already attested in Herodotus (2.109), and after him in Aristotle (Metaphysics A 1.981b23), meaning that Eudemus simply reflected the widespread egyptophilia of the Greeks, especially in their approach to the past. The prestige of Egyptian geometry was so great that the gifted mathematician Democritus boasted that nobody excelled him in the construction of lines with proofs, even the Egyptian “rope stretchers,” that is, land surveyors (DK 68 B 299). After more than a century’s investigation of Egyptian mathematics, however, there is no basis to assume the presence in it of anything resembling theory or proof. It is more probable that in the Archaic period the Greeks borrowed from Egypt practical knowledge needed for land surveying, building, and the like, the more so as early Greek architecture and sculpture bear obvious traces of Egyptian influence. All available evidence on Egyptian borrowings relates to practical mathematics, moreover to arithmetic rather than geometry. Thus, late scholia to Plato’s Charmides (163e) refer to Egyptian methods of multiplication and division and also to operations with fractions (Heath 1921, 14, 41, 52). As the most conventional histories of science still do, Eudemus focused in his works on specific discoveries in mathemata and their authors, the “first discoverers.” His list of Thales’ discoveries runs as follows. Thales: (1) was the first to prove that the diameter divides the circle into two equal parts (Euclid 1.def.17); (2) was the first to learn and state that the angles at the base of any isosceles triangle are equal (1.5), calling them, in the archaic manner, similar, not equal; (3) was the first to discover that if two straight lines intersect, the vertical angles are equal (1.15); and (4) knew the theorem about the equality of the triangles that have one side and two angles equal (1.26), which he must have used

Mathematics and Astronomy    173 to determine the distances of ships from the shore. Obviously, Thales’ theorems of angles and triangles cannot have originated in Egyptian geometry, since the Egyptians neither engaged in comparing the size of angles nor the similarity of triangles. In Egyptian and Babylonian mathematics there was no notion of the angle as a measurable magnitude. As Kurt von Fritz (1971, 568 n. 79) observed, “All theorems ascribed to Thales are either directly related to the problems of symmetry and can be ‘demonstrated’ by the method of superposition, or such that the first step of the demonstration is evidently based on considerations of symmetry while the second, which brings the argument to conclusion, is simply an addition or subtraction.” Indeed, Thales’ propositions can be reduced to the symmetries of the so-​called Thalesian basic figure (Becker 1966, 37), that is, a rectangle with the diagonals inscribed in a circle, the center of which is on the intersection of the diagonals (see figure B2.1). Thales appealed in his demonstrations to the visualizability of the geometrical drawing but certainly went beyond this. Aristotle (Analytica Priora 41b13–​22) refers to an archaic-​looking proof of a theorem that the angles at the base of any isosceles triangle are equal (Euclid, 1.5), which might well go back to Thales (Heath 1926, 1:252–​253; Becker 1966, 38–​39). It is based on the equality of mixed angles, in particular angles in a semicircle and angles of a segment of a circle, which could be proved by using only the superposition method. The proof in Aristotle can be re-​established in figure B2.2. ABC is an isosceles triangle with its vertex in the center of the circle. Prove that its base angles are equal. ∠ 1 is equal to ∠ 2, since they are angles of a semicircle; ∠ 3 is equal to ∠ 4, since they are angles of a segment of a circle. Taking equal angles from equal angles, we obtain that angles CAB and ACB are equal. Thus, the proof demonstrates the normal procedure of deductive reasoning. The idea of proof is vital for the history of Greek mathematics, for this is what both distinguishes it from the earlier mathematical cultures, like Egypt and Babylon, and makes it akin to modern mathematics. (Recent history of mathematical proof, Chemla 2012, sheds new light on the methods of proving the correctness of algorithms and computations in the East Asian cultures but does not change the traditional view on the Greek origin of deductive proof.) The systematic application of deductive proof was

Figure B2.1  Thalesian basic figure. Drawing by W. Sinelnikow based on O. Becker, Das mathematische Denken in der Antike. Göttingen, 1966.

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B

A

1

3

4

2

C

Figure B2.2  Aristotle’s proof of equality of base angles in isosceles triangle. Drawing by W. Sinelnikow based on O. Becker, Das mathematische Denken in der Antike. Göttingen, 1966.

the most important factor in the formation of theoretical mathematics on an axiomatic basis; this led to the formulation of theorems valid for any numbers, and consequently ousted the empirical, computational methods from mathematical science. Further, it stimulated the search for the axiomatic bases of mathematical theory, since deductive constructions in order to be true and noncontradictory must of necessity rest on initial propositions accepted without proof. Some scholars believe that deductive proof appeared at the very beginning of Greek geometry; others insist that mathematics developed empirically until the early 5th century bce, whereas deductive proof was borrowed from the Eleatic philosophy or was gradually developed in geometry itself. The problem with the extra-​mathematical origin of the deductive proof is that in philosophy it does not possess the logical cogency and irrefutability that it does in mathematics (cf. section 2). Yet the intra-​mathematical origin of the deductive method is also not without problems, insofar as this method is not something inherent in dealing with numbers and figures: for thousands of years mathematics developed without it in the ancient Orient, including India and China. Could mathematics of the practical and computational kind, as it existed in archaic Greece, give rise of itself to a striving for strict proof? Hardly: Thales in geometry and Pythagoras in arithmetic began by proving things of no practical use that were also too simple to be demonstrations of technical virtuosity. (Høyrup [1994] regards the demonstration of technical virtuosity as one of the chief stimuli in the development by Babylonian scribes of increasingly complex types of calculation.) If mathematics did not of itself give rise to deductive proof, or adopt it from outside, then, most probably, it came into being in mathematics under the influence of external impulses. As distinct from Babylonian and Egyptian scribes versed in computation, Thales was not a professional: he was a wealthy and politically influential aristocrat. Why did he decide to prove that the angles at the base of an isosceles triangle are equal? And why did he achieve public recognition in this pursuit? Two centuries after Thales’ birth an Athenian audience knew him as a famous geometer (Aristophanes, Birds, 1009; Clouds, 180), which would be impossible if their attitudes to fame and geometry did not

Mathematics and Astronomy    175 partially overlap. The problem is more general than Thales’ geometry, it relates to how Greek science was born and what distinguishes it from similar pursuits in other ancient cultures. A comparison of Greek and Chinese intellectual traditions, offered by G. E. R.  Lloyd, emphasizes a conspicuous feature of Greek science:  its highly competitive character, which reflects, in turn, an agonistic character of Greek society and culture revealed by Jacob Burckhardt (1898–​1902). “The competitiveness of Greek intellectual life” was the decisive factor in the formation of Greek science and, in particular, axiomatico-​ deductive mathematics (Lloyd 2004, 133, 140, 144). This spirit of pure competition arose in Greek agonistics and then spread to areas of intellectual creativity, multiplying tenfold the force of those striving for truth (Zaicev 1994). A second important factor was that, in the Greece of the 8th to 5th centuries, for the first time in human history, all aspects of productive cultural activity, including those lacking a direct utilitarian purpose, gained public approval. The social climate of the time encouraged any and all creative achievements, independent of the extent of their practical value, thus establishing the most powerful stimuli for new investigations. Once set on the path of free research, unconstrained by narrow practicality and corporative ethos, the mathematicians quickly realized that to apply strict, logical proof makes it possible in this pursuit to achieve irrefutable and hence universally recognized results (Zaicev 1994, 167). “Thales seems by some accounts to have been the first to study astronomy, the first to predict eclipses of the sun, so (says) Eudemus in his History of Astronomy” (fr. 144 W.). The prediction of the solar eclipse was the most famous “discovery” made by Thales, and it was reflected in many early sources, among them in his younger contemporary Xenophanes (DK 21 B 19). Successful prediction captured the imagination of the Greeks and made Thales the “father of astronomy,” but what is meant by “prediction,” and how can it be explained? Thales could not have had a theory offering a correct explanation of solar eclipses—​such a theory only appeared in the mid-​5th century bce. Since Greek tradition before Thales does not know of any predictions of eclipses, the very idea could only have been of Babylonian origin. In the early 6th century bce, Babylonian astronomy was the only one capable of making predictions that concerned all potential lunar and solar eclipses for a given year, without trying to explain them. Until the mid-​ 20th century, the predominant opinion was that Thales’ prediction could have relied on the so-​called Saros, a period of 223 synodic months (≈18 years), used by the Babylonians to predict lunar and solar eclipses. Later it became known that the Babylonians were unable to reliably predict solar eclipses for a given point either in the 6th century or later (Neugebauer 1957, 142–​143). It is quite probable, however, that Thales having known about one of the Babylonian schemes, boldly used it to fix the date of the next solar eclipse and thus by lucky coincidence “predicted” the eclipse of May 25, 585 bce, almost full in Miletus. Thales’ prediction, no matter how famous it was, left no traces in Greek astronomy, which later on was concerned with explanations of the celestial phenomena, including eclipses, not their predictions. Another discovery of Thales, “that the sun’s period with respect to the solstices is not always the same” (Eud. fr. 145 W.), had a more durable effect. It seems that Thales tried to estimate the solstices’ dates and, hence, the length of the solar

176   Early Greek Science year more accurately than known before. Such an activity became a part of the “calendaric astronomy” that tried to find the best ratio between the solar year and the lunar month for the luni-​solar calendar. The results of these investigations, however, were never applied to the civic calendar, remaining a matter for astronomers and philosophers. In the 6th to early 5th centuries among them were the astronomers Cleostratus of Tenedos, Harpalus and Matricetas, and the philosophers Xenophanes and Heraclitus. Cleostratus, in particular, suggested the first intercalation period for a luni-​solar calendar, octaëteris (eight years), which presumed the year to be 365¼ days long; it was further improved by Harpalus and others engaged in astronomical observations (DK 6 A 1, B 4). In contrast to Babylonian astronomy that was in principle ageometric, the most important stream of Greek astronomy was the creation of geometrical models representing and explaining the apparent motion of the heavenly bodies. It started with Anaximander of Miletus (fl. ca 570 bce), the first Greek thinker who revealed his theories in writing; he also created the first geographical map of the earth. The system of Anaximander was a peculiar combination of bold speculations, geometrical and spatial imagination, and astronomical observations (he used the gnomon to determine the solstices and equinoxes and set up a sundial in Sparta: DK 12 B 1). The earth in this system has the shape of a column’s drum, and its depth is a third of its width. The earth is freely suspended, supported by nothing, and is afloat in the center of the cosmos. It is this counterintuitive idea, unprecedented in the preceding astronomy, that became a cornerstone of the specifically Greek conception of the universe (Couprie 2011, 99). Anaximander imagined further that the earth is enclosed by three wheels, which consist of thick air (and thus are invisible) and are full of fire: the sun, the moon, and the stars being the holes in the wheels. The sun is the same size as the earth (another revolutionary insight!), and the wheel of sun is the highest of all, followed by the moon and stars; distances from the earth to the stars, the moon, and the sun are equal to 9, 18, and 27 radii of the earth. Solar and lunar eclipses occur when the openings in the rim of the wheel are stopped, which means the moon shines with its own light. Though Anaximander’s model of the cosmos was not yet purely geometrical, but also physical, with time this physical component receded into the background, whereas geometry became the basis of what Aristotle called “mathematical astronomy.” The other conspicuous features of this system, instrumental in shaping Greek astronomy, are that it is devoid of any divine presence and influence, which are typical, for example, of Babylonian and Chinese astronomy, and that it rests on the assumption of a concealed order of the world that can be revealed both geometrically and numerically. Pythagoras and his school shared this assumption. In a new epistemological situation in the 5th century, the idea of the invisible things and/​or regularities in nature was expressed in the pregnant dictum of Anaxagoras of Clazomenae (ca 500‒ca 428 bce): “appearances are a sight of the unseen” (DK 59 B 21a). Developing this line of thought, Eudoxus of Knidos (ca 390‒ca 337 bce) put forward the principle of “saving (preserving) the appearances” that was to underlie the whole subsequent history of Greek astronomy: to explain the apparently irregular movement of the sun, moon, and planets along the ecliptic by attributing uniform circular movement to them.

Mathematics and Astronomy    177 The circular motion of the sun and moon around the earth, most probably by analogy with the visible circular motion of the stars around the North Pole, was postulated already by Anaximander’s system, though his wheels related rather to the diurnal motion of the two luminaries than to their motion along the ecliptic. Unlike Anaximander, his student Anaximenes of Miletus (fl. ca 550 bce) introduced no new geometrical concepts; he only “moved” the stars beyond the moon, sun, and planets, to the outer place, where they have a fixed position on the celestial vault (DK 13 A 14). As a separate group, distinct from the fixed stars, the planets (“wandering stars”) appeared for the first time in Anaximenes, but he did not say anything specific about them. On the whole, the Greeks learned about planets rather late and slowly. In the 6th century, they had no fixed names for them, with the exception of Venus, which was called the Evening and Morning Star, depending on the time of its appearance. That it is the same planet was first attested, according to Theophrastus, in the learned poem of Parmenides (ca 475 bce). The word “planet” and the fixed number of the planets appear in the late 5th century, and still later, in the mid-​4th century, their names, borrowed from Babylon:  the stars of Hermes, Aphrodite, Ares, Zeus, and Kronos. The sun and moon were also regarded as planets, for they, too, have independent movement along the ecliptic.

2.  The Contributions of the Pythagoreans In the late 6th century the Ionian tradition of geometry and astronomy was transferred to Magna Graecia by Pythagoras, who circa 530 bce left his native Samos because of Polycrates’ tyranny and moved to Croton. Pythagoras taught metempsychosis, and many of his ethical rules were supported by belief in his god-​like nature. The dual nature of this figure was attested by Aristotle: “Pythagoras, the son of Mnesarchus, first dedicated himself to the study of mathemata, especially numbers, but later could not refrain from the wonder-​working of Pherecydes” (Arist. fr. 191). This combination of the rational and the religious is not unique among the pre-​Socratics: the natural philosopher Empedocles pretended to be a wonder-​worker and was a proponent of metempsychosis. However peculiar Pythagoras’ personality was, in mathemata he continued the work of Thales and Anaximander, and none of the Pythagoreans known to us by name are linked with anything remotely supernatural or miraculous. The Pythagorean school existed until the mid-​4th century bce, having in almost every generation significant mathematicians and astronomers: Hippasus of Metapontum (fl. ca 500/​490 bce), Theodorus of Cyrene (active ca 440‒ca 400 bce), Philolaus of Croton (active ca 440‒ca 400 bce), Archytas (active ca 410–ca 360 bce), Ecphantus of Syracuse (first part of the 4th century bce). The names of the other Pythagorean mathematical scientists remain unknown.

178   Early Greek Science Pythagoras’ contributions to astronomy are hard to discern, partly because the late antique tradition ascribes too much to him: discovering the sphericity of the earth, the obliquity of the ecliptic, the planets’ motion along the ecliptic, dividing the celestial and terrestrial spheres into zones, and so on. Early sources are much more reticent. Even if they do connect Pythagoras with astronomy, as with Aristotle’s Protrepticus (fr. 18, 20 Düring), they do not refer to any specific discoveries. Eudemus, in particular, mentions his followers, rather than Pythagoras: “Anaximander was the first to find an account of the sizes and distances (of the planets), as Eudemus says, adding that the Pythagoreans were the first who found the order of their position” (fr. 146 W.). Although Eudemus’ fragment does not indicate the number and order of the heavenly bodies, he clearly had in mind their “correct” arrangement, which was accepted in the astronomy of his time: moon—​sun—​Venus—​Mercury—​Mars—​Jupiter—​Saturn—​celestial sphere. It was established that, relative to the stars, Mercury and Venus moved the fastest (their sidereal period was equated to that of the sun), Mars more slowly, Jupiter more slowly still, and Saturn extremely slowly. These observations, together with data on the relative brightness of some of the planets (Venus being brighter than Mercury), formed the basis of their order. Which Pythagoreans did Eudemus mean? In Philolaus’ system, five planets were located between the moon and the sun on one side and the stars on the other. Philolaus, however, radically transformed the order of the planets by introducing the Central Fire (Hestia), which he situated in the center of the universe, and around which he made the earth, the invisible counter-​earth and all other celestial bodies revolve (DK 47 A 16–​ 17). We should look, then, at the earlier stage of Pythagorean astronomy. Alcmaeon of Croton (ca 500/​490 bce), the Pythagorean natural philosopher, thought, according to the late doxographer Aëtius, that the planets move from west to east in a direction opposite to the movement of the fixed stars (DK 24 A 4). If we believe this evidence, Alcmaeon was aware that the planets, sun and moon, apart from their diurnal movement, also have an annual movement along the ecliptic from west to east, which is to say that they rise each day further to the east in the zodiacal constellations. Though Alcmaeon was not an astronomer (his other astronomical views look rather naive), he might have gained this knowledge from the other Pythagoreans. The evidence of Aëtius implies that the motion of the planets along the ecliptic is circular, as we see later in Oenopides, Hippocrates, and Philolaus. Aristotle says that Alcmaeon taught that the soul was immortal because, like all divine celestial bodies—​the sun, moon, planets, and the whole heaven—​it is in constant motion (DK 24 A 12). This kind of motion also had to be circular. Transferring the circular motion from Anaximander’s model to the motion of the sun, moon, and planets along the ecliptic, the Pythagoreans must have proceeded both from observations and from considerations of symmetry as they attempted to regularize the motion of all the celestial bodies following a single principle. Since a circle was at that time the only possible method of geometrical presentation of planetary motion (only a circular motion is continuous, says Aristotle, Physics 264b9–​28), the planets’ numerous deviations from circular orbits were simply ignored.

Mathematics and Astronomy    179 The revolution of the celestial bodies around the earth is attested in the other early Pythagorean theory (prior to Philolaus), the famous “harmony of the spheres” that was borrowed by Plato in the Republic (616b–​617d) and acknowledged but refuted by Aristotle: The theory that music is produced by their (sc. planets and stars) movement, because the sounds they make are harmonious, although ingeniously and brilliantly formulated by its authors, does not contain the truth. It seems to some thinkers that bodies so great must inevitably produce a sound by their movement: even bodies on earth do so, although they are neither so great in bulk nor moving at so high a speed, and as for the sun and moon, and the stars, it is incredible that they should fail to produce a noise of surpassing loudness. Taking this as their hypothesis, and also that the speeds of the stars, judged by their distances, are in the ratio of the musical consonances, they affirm that the sound of the stars as they revolve is concordant. (De caelo 290b, tr. W. Guthrie)

Like Anaximander’s model, this theory has a physical component, lacking in Philolaus. There is no sound without movement, said Archytas’ Pythagorean predecessors in harmonics (DK 47 B 1); consequently, there can be no movement without sound, even though we do not hear the celestial harmony. The speed of rotation of the celestial bodies in this system is directly proportional to their distances from the earth, which, according to the late commentator Alexander (Aristotle, fr. 13 Ross), make up the arithmetical progression 1, 2, 3, 4. . . (n + 1). Thus, the ratios of the distances correspond to the ratios of the basic concords: the octave (2:1), the fifth (3:2), the fourth (4:3), and so on. The doctrine of heavenly harmony does not lend itself to detailed reconstruction, especially in its musical part. What is important for us is to state that it is based on Pythagoras’ discovery of a link between music and number, which led to the inclusion of harmonics in the mathemata. Late antique tradition about how Pythagoras discovered the ratios of concords, such as Nicomachus’ story about an experiment with the hammers (Harmonics, 6), is unreliable, but the discovery itself is attested by Plato’s student Xenocrates (ca 395–​313 bce), who left behind numerous works on mathematical sciences: “Pythagoras discovered also that the intervals in music do not come into being apart from number, for they are an interrelation of quantity with quantity” (fr. 87 Isnardi Parente). That Pythagoras found the numerical expressions of the octave, the fifth, and the fourth is indirectly confirmed by the evidence of the famous musicologist Aristoxenus (active ca 340—​ca 300 bce), a student of the last Pythagoreans and then of Aristotle. He says that Hippasus fashioned four bronze discs of the same diameter, with thickness in the ratios 2:1, 3:2 and 4:3; when struck they produced harmonic concordance (Aristox. fr. 90 W.). Hippasus of Metapontum was a student of Pythagoras, and his experiment was conducted to confirm what Pythagoras had already discovered, most likely by observations and experiments with a stringed instrument. (Though the Greeks knew no regular practice of experimentation, sporadic experiments were performed.) The ratios of the basic concords are closely bound up with arithmetic b = (a + c ) / 2

180   Early Greek Science and harmonic b = 2ac/(a+c) means, which, according to information that goes back to Eudemus, were known to Pythagoras and Hippasus (Zhmud 2006, 173–​175). Thus, the fifth (3:2) is the arithmetic mean between the terms of the octave (2:1), and the fourth (4:3) is the harmonic mean between them; taken together, they form a “musical” proportion (12:9 = 8:6). The only preserved fragment of Eudemus’ History of Arithmetic deals with the Pythagorean ratios of the three concords (fr. 142 W.). During the 5th century bce, arithmetic and harmonics as related sciences remained a monopoly of the Pythagorean school: whereas the Ionians Oenopides and Hippocrates studied only geometry and astronomy, Hippasus (DK 18 A 12–​15), Theodorus (DK 43 A 4), Philolaus (DK 44 Α 26, B 5–​6), and Archytas (DK 47 A 16–​19, B 1–​2) were engaged also in two other sciences of the quadrivium. “Pythagoras more than anybody else seems to have valued the science (or theory) of numbers and to have advanced it, separating it from the merchants’ business and likening all things to numbers,” says Aristoxenus in his On Arithmetic (fr. 23 W.). This is close to what Aristotle noted about Pythagoras’ study of numbers (fr. 191), but is more specifically related to the origin of arithmetic as a theoretical science, distinct from the art of calculation. The arithmetic known to us from the three books of Euclid’s Elements (books 7–​9) is the theory of arithmoi, which is to say whole numbers greater than one, and their properties. “A unit is a beginning of a number” (and thus not a number), and “a number is a multitude consisting of units”—​these definitions from the same fragment of Aristoxenus are likely to have opened an early Pythagorean arithmetical treatise. The next definitions introduce two basic kinds of number:  even numbers are divisible into equal parts, odd number are divisible into unequal parts and have a middle. (Philolaus, following the arithmetic of his time, also mentions the division of numbers into even, odd, and even-​odd: DK 44 B 5). The latter assertion indicates that the early Pythagoreans represented numbers not by line segments, as Archytas (DK 47 A 19) and later Euclid did, but by psephoi, counting stones. (Hence there is no “middle” in Euclid’s definition of the odd number: 7.def.7). If you add or subtract a psephos to or from an even number, you get an odd number (DK 24 B 4), says a character from the comedy of the Sicilian writer Epicharmus (ca 480 bce), alluding most probably to Pythagorean arithmetic. (Practical arithmetic does not need and, thus, does not know odd and even numbers. It is Epicharmus’ fragment, where “even” and “odd” in their mathematical meaning first occur in Greek literature, whereas the practical and computational mathematics of Mesopotamia and Egypt did not have special terms for odd and even numbers.) The simplest example of this arithmetic is a summation of odd and even numbers, represented by pebbles; such arithmetical series produce the so-​called figurate numbers (figure B2.3). The added number, called the gnomon, preserves the form of that to which it is added. square number 1 + 3 + 5 + ... + (2n − 1) = n2 ;

oblong number 2 + 4 + 6 + ... + 2n = n (n + 1). The presence of definitions in the early Pythagorean arithmetic implies that it contained some deductively proved propositions. The high standard of Archytas’

Mathematics and Astronomy    181

Figure B2.3  Gnomon for square and oblong numbers. Drawing by W. Sinelnikow based on T.L. Heath, A History of Greek Mathematics. Oxford, 1921.

arithmetical proofs (DK 47 A 19) shows that by the late 5th century bce arithmetic was established as a demonstrative science. In Archytas’ opinion, it even surpassed geometry in clarity and exactness, accomplishing proofs where geometry failed (DK 47 B 4). An early specimen of the axiomatic-​deductive method in arithmetic is the theory of even and odd numbers, preserved at the very end of the last arithmetical book of the Elements (Becker 1966, 44–​49). This theory, consisting of propositions 9.21–​34, based only on definitions of even and odd numbers (7.def.6–​11), is of an elementary character and lacks any intrinsic connection with the material of other arithmetical books. Here are its first five propositions in abridged form:

21. 22. 23. 24. 25.

The sum of even numbers is even. The sum of an even number of odd numbers is even. The sum of an odd number of odd numbers is odd. An even number minus an even number is even. An even number minus an odd number is odd.

Becker showed that both the propositions and their proofs retained by Euclid are easily illustrated through the use of psephoi. Meanwhile, four of these propositions (9.30–​31, 33–​34) are proved by reductio ad absurdum, one of the powerful tools of Greek mathematics, which allows the establishment of a proposition by showing that its contradictory involves impossible consequences, for example that the same number is both even and odd. We see again how very simple mathematical problems lead to nontrivial results. It is hard to establish whether indirect proof originated in arithmetic or earlier in geometry (proposition I, 26, attributed by Eudemus to Thales, is proved indirectly). Judging by the preponderance of reductio ad absurdum in the theory of even and odd, one can reasonably infer that deduction, which is to say a formal proof technique, was shaped by the early Pythagorean psephoi-​arithmetic, which appealed not to the (then nonexistent) lettered diagram (cf. Netz 1999) but to pebbles arranged in such a way as to give an ocular demonstration. Further nontrivial results of Pythagorean arithmetic appeared rather quickly. First was the discovery of the irrationality of √2, the classic example of which is the incommensurability of the diagonal of a square with its side. The probable context of the discovery was the search for the ratios of the sides in the right-​angled triangle

182   Early Greek Science that corresponded to Pythagoras’ theorem (see the end of this section). It was found then that the side and diagonal of a square cannot be expressed as a ratio of two numbers. This theorem was one of Aristotle’s favorite mathematical examples: referring to it more than 15 times, he twice alludes to the fact that its indirect proof relies on the theory of odd and even numbers (Analytica priora 1.23, 41а24–​27, and 1.44, 50а37). It might have been that Archytas had this very proof in mind, saying that arithmetic accomplishes proofs where geometry fails (DK 47 A 4). “The analysis of certain classes of problems in geometry, e.g. the construction of irrational lines, can only be completed by means of arithmetical principles” (Knorr 1975, 311). Plato ascribes to Theodorus a proof of irrationality of the magnitudes between √3 to √17 (DK 43 A 4), which means that the proof of the irrationality of √2 was found earlier. Ancient tradition, probably going back to Eudemus, attributes the discovery of irrationality to the Pythagoreans; the name of Hippasus is mentioned or implied in the legendary stories surrounding it (von Fritz 1974, 545–​575; Zhmud 2012, 274–​275). The ancient (though not the original) arithmetical proof of the proposition that the diagonal and side of a square are incommensurable in length is preserved at the end of book 10 of the Elements (app. 27); it makes use of the Pythagoras’ theorem, the theory of even and odd numbers, the method of reductio ad absurdum, and the least numbers in a given ratio. This all points to its Pythagorean origin. As we know from Archytas (DK 47 A 17) and Eudemus (fr. 142 W.), the early Pythagoreans took the ratios of the concords in lowest terms (2:1, 3:2, 4:3), which they called “first numbers,” or pythmenes (base numbers). Archytas’ proof that a superparticular ratio (n + 1): n, and so the concordant intervals represented by it, for example the fifth and the fourth, cannot be divided into equal parts (DK 47 A 19) and have no mean proportional (or geometric mean), also contains reductio ad absurdum and the least numbers in the same ratio. The problems evoked by the discovery of irrationality provided the impulse for the research of Theodorus and his student Theaetetus (discussed later), the author of the general theory of irrational magnitudes (book 10 of Euclid’s Elements) and led to the development of Eudoxus’ theory of proportions, which was applicable to commensurable and incommensurable magnitudes (book 5). In the modern literature, the impact of Hippasus’ discovery has often been overrated. Thus, it was widely believed that it was originally motivated by Pythagoras’ dogma “all is number” and then had dealt a “fatal blow” to this dogma by demonstrating the existence of incommensurable magnitudes in geometry, which in turn led to the “foundation crisis” in Greek mathematics. All three assumptions are not borne out by the reliable sources. The “foundation crisis” of the 5th century bce is a retrospective projection of what happened in mathematics at the turn of the 20th century (Knorr 2001). The motto “all is number” is unattested in ancient Pythagoreanism; it was first ascribed to the unnamed Pythagoreans by Aristotle, who mistakenly regarded them as the predecessors of the Platonic number doctrine (Zhmud 2012, 433–​452). As for general interaction between mathematics and philosophy, Greek mathematics appeared to have been independent of contemporary philosophy, whereas the latter was frequently influenced by mathematical ideas (Knorr 1981). One of the earliest examples of such an influence was systematic deductive reasoning, including

Mathematics and Astronomy    183 indirect proofs, employed by Parmenides (DK 28 B 8) and his student Zeno (DK 29 A 15, B 1–​2) in attempting to prove their bold theses that contradicted all experience, for example, that there is no movement or plurality. “Parmenides’ reasoning is the extension of the Pythagorean proof . . . . Not only in mathematics, where the Pythagoreans had already developed reductio ad absurdum proofs in their exploration of quantities, but throughout nature—​in philosophy, physics, everywhere—​it became possible to show simply by examining their logical consequences that some generalizations cannot be true” (Brumbaugh 1981, 54–​55). The Eleatics put deductive proof in a much wider context, but, in contrast to the Pythagorean mathematicians, they succeeded neither in proving any of their basic theses nor even in formulating their indirect proofs in a rigorous form. Their reductio ad absurdum proofs are formally incomplete. Two pieces of early Greek geometry—​the theorem of Pythagoras and the theory of the application of areas that Eudemus deemed “ancient” and attributed to the “Pythagorean muse” (fr. 137 W.)—​were from the 1930s considered derived from Babylonian mathematics. One of its rediscoverers, O. Neugebauer (1957, 40), believed to find on the tablet Plimpton 322 (18th century bce) “the fundamental formula for the construction of triples of Pythagorean numbers,ˮ that is, positive integers (a, b, c) for which a2 + b2 = c2. The much-​repeated idea that the Babylonians knew the Pythagorean theorem became a cliché, and Pythagoras was regarded as the transmitter of Babylonian knowledge (van der Waerden 1961, 92–​93). Over recent decades, the leading students of Babylonian mathematics have changed this trend. First, the Babylonians knew not the theorem, but the rule for determining the values numerically, which they did not prove or even formulate explicitly (Høyrup 1998). Secondly, a detailed examination of the tablet has shown that it has nothing to do with number-​theoretical problems in general, nor with Pythagorean numbers in particular, but contains a school problem using a list of reciprocal pairs (Robson 2001). As for the Greeks, Proclus (5th century AD) in his commentary on the first book of Euclid (In Euclid, 428.7–​21) ascribes to Pythagoras the method of defining Pythagorean triples, starting from the odd number, which is based on figurate numbers (Heath 1926, 1:356). The first author to claim that Pythagoras proved the theorem named after him was a certain Apollodorus the Arithmetician (Diogenes Laërtius 8.12), who may be identical with the Democritean Apollodorus of Cyzicus (second half of the 4th century bce); he was followed by virtually all the Greek writers who wrote about it. This evidence, though not irrefutable, is confirmed by the fact that the proof of irrationality of √2, associated with Hippasus, is based on Pythagoras’ theorem. Hippocrates already knew the generalized Pythagorean theorem for acute-​and obtuse-​angled triangles (2.12–​13); it comes from book 2 of the Elements, which belongs to the Pythagoreans. The application of areas with excess or defect, “one of the most powerful methods on which Greek geometry reliedˮ (Heath 1926, 1:343), relates to the transformation of areas into equivalent areas of different shape. The propositions of this theory, comprising theorems 1.44–​45, the entire book 2 of the Elements, and theorems 6.27–​29, can be reformulated into algebraic identities and quadratic equations. Thus, the application of areas with defect means the construction on a given line a of the rectangle ax,

184   Early Greek Science so that by subtracting from it the square x2, the given square b2 is obtained (ax –​ x2= b2). Proposition 2.3 can be presented as the identity (a + b)a = ab + a2 and 2.4 as (a + b)2 = a2 + 2ab + b2. Since the late 19th century, these propositions have come to be known as geometric algebra and seen as a geometric reformulation of algebraic problems. When Neugebauer found in Babylonian mathematics corresponding identities and equations, he concluded that the algebra reformulated by the Greeks was Babylonian. That he regarded his interpretation as a working hypothesis, unconfirmed by documentary evidence (Neugebauer 1957, 147), did not prevent it from soon becoming the dominant theory. This theory came under attack from S. Unguru (1975), who claimed that the application of areas was not a reformulation of Babylonian algebra, but arose on Greek soil in the course of solving purely geometric problems. After a lengthy discussion, most historians of Greek mathematics accepted his view. “We have no good reason to believe,ˮ noted Taisbak (2003, 306), “that the Greeks were thinking of quadratic equations in any form when working with the different types of application of areas.ˮ Revealingly, there is no evidence of the practice of mathematics analogous to geometric algebra in Mesopotamia in the 6th‒5th centuries: all extant texts relate to the Old Babylonian period. “Old Babylonian mathematics cannot have influenced early Greek developments: it was a part of a scribal culture that all but died out nearly a millennium before the earliest Greek literate culture, 1200 miles away” (Robson 2005, 13). Real or assumed isomorphism between two mathematical theories, formulas, or methods often gives rise to common-​origin hypotheses, but only the theories placed in a specific historical setting with identifiable ways of transmission survive the tests.

3.  The Milesians, Pythagoreans, and Athenians: Productive Interactions In the mid-​5th century bce, studies of geometry and astronomy were revived in Ionia by two natives of Chios, Oenopides and Hippocrates. Before them we know only Anaxagoras, who taught that the moon received its light from the sun and offered correct explanations for both lunar and solar eclipses (DK 59 B 8, A 76–​77). On the whole, however, his astronomy was physical rather than mathematical. Oenopides, mentioned by Eudemus in both the History of Astronomy and the History of Geometry, attempted to establish closer connections between these two mathemata. According to the late evidence, he “was the first among the Greeks who wrote down the methods of (mathematical) astronomyˮ (Boll 1894, 53–​55), which is essentially confirmed by the early sources. Eudemus attributes to Oenopides two elementary geometrical constructions that later entered Euclid’s book 1: to draw a perpendicular to a given straight line from a point outside it (1.12); at a point on a given straight line, to construct a rectilinear angle equal to a given rectilinear angle (1.23). Oenopides considered problem 1.12 useful for astronomy. Proclus says the same about proposition 4.16 (this is the last proposition of book 4, which

Mathematics and Astronomy    185 the scholia to Euclid 273.3–​13, probably on the authority of Eudemus, ascribe to the Pythagoreans), on a regular pentadecagon inscribed in the circle: its side is equal to the angle between the celestial equator and the zodiacal circle, that is, 24° (In Euclid, 283.7–​10, 269.8–​18). Theon of Smyrna’s excerpt from Eudemus clarifies the way in which it may be related to Oenopides’ astronomy: he “was the first to discover the obliquity of the zodiacal circle” (Eud. fr. 145 W.). This can mean either that Oenopides discovered that the annual path of the sun is inclined to the celestial equator or that he first measured the angle of the obliquity of the ecliptic (Bodnar 2006, 4–​6). The latter variant seems more plausible in view of Aëtius’ evidence about Alcmaeon and the zodiacal motion of the planets (DK 24 A 4). The ecliptical motion of the sun, moon, and planets against the background of the celestial sphere is attested both in Philolaus (DK 44 A 21) and in Hippocrates (DK 42 A 5), which is hard to explain if Oenopides shortly before them discovered that the annual path of the sun is oblique. Von Fritz (1937, 2258–​2259) argued convincingly that the end of Theon’s excerpt from Eudemus was originally related to Oenopides: “And others discovered in addition to this that the fixed stars move round the immobile axis that passes through the poles, whereas the planets move round the axis perpendicular to the zodiac and that the axis of the fixed stars and that of the planets are separated from one another by the side of a (regular) pentadecagon” (fr. 145 W.). Though Oenopides’ astronomical system defies reconstruction, we can surmise that his work, firstly, incorporated geometrical notions of the structure of the universe developed by the Greeks from Anaximander to Anaxagoras, removing them from the cosmological context to which they belonged in the works of natural philosophers, and secondly, expounded them in conformity with the requirements of the deductive geometry of the mid-​5th century. There is reciprocal influence between the Pythagoreans and the Chians: Oenopides held the same theory of the Milky Way, as being the former course of the sun, as did the Pythagoreans (DK 41 A 10); Philolaus borrowed from him the 59-​year luni-​solar cycle (Eudemus fr. 145 W.; DK 44 A 22). Hippocrates shared the view of some Pythagoreans that a comet is one of the planets, visible at long intervals and rising low over the horizon (DK 42 A 5). Hippocrates’ theory as set out by Aristotle is more complex than the Pythagorean, demonstrating advanced concepts of the geometry of the universe: the celestial sphere is divided into zones by a celestial equator and two tropic circles crossed by the oblique circle of the zodiac; the planets move in circular orbits along the ecliptic; the horizon divides these circular orbits into unequal segments; and the earth, to all appearances, is spherical (Wilson 2008). The sphericity of the earth, safely attested for Philolaus, is related in the Greek tradition alternatively to Pythagoras and Parmenides (Diogenes Laërtius 8.48). From what we know about their astronomy, neither appears to be a suitable candidate for this discovery; it is safer to attribute it to the Pythagorean tradition of the 5th century, though certainty is impossible. The discovery of the earth’s spherical shape led to the formation of the main astronomical model of antiquity, which consisted of two concentric spheres, the celestial and the terrestrial, divided into zones. In the generation of Philolaus and Hippocrates, this two-​sphere model of the cosmos was still in the making (Philolaus’ spherical earth was not the center of the cosmos), in a more developed form we find it in Plato’s Republic and later in his Timaeus.

186   Early Greek Science An Athenian astronomer Meton (ca 430 bce) belonged probably to the same generation as Philolaus and Hippocrates. Meton and his colleague Euctemon made systematic observations in different regions of Greece; created the first astronomical calendars, the so-​called parapegmata; suggested a new 19-​year calendar cycle; and determined the inequality of the four astronomical seasons (according to their calculations, the seasons are 90, 90, 92, and 93  days, starting with the summer solstice). Meton and Euctemon were the earliest of the Greek astronomers whose dated observations are cited by Ptolemy. By the time of Hippocrates several geometrical problems, such as squaring the circle and doubling the cube, became famous, attracting the attention of audiences far beyond a narrow circle of specialists. Aristophanes ridicules Meton for promising to square the circle (Birds 1004–​1009); Plutarch describes Anaxagoras as busy in prison squaring the circle (DK 59 A 38); Aristotle and Eudemus record unsuccessful attempts by the Sophists Antiphon of Athens and Bryson of Heraclea to solve the same problem. The agonistic spirit that surrounded the problem of doubling the cube led Greek geometers to continually search for new solutions to the problem long after it had been solved, first by Archytas, and then by his student Eudoxus and by Eudoxus’ student Menaechmus (Knorr 1986). Eratosthenes’ dialogue Platonicus, relying on the Academic legend of Plato as the architect of mathemata, ascribes to the latter an instrumental role in doubling the cube, but this tradition is unreliable (Zhmud 2006: 84–​86; Kouremenos 2011). The way to Archytas’ solution was paved by Hippocrates, who was the first to reduce the problem of doubling the cube to finding two mean proportionals x and y in continuous proportion between two lines, a (side of the cube) and 2a, that is, if a: x = x: y = y: 2a, then x 3 = 2a3, x = a 3 2 . It was suggested long ago that Hippocrates came to this idea by analogy with the planimetric problem, solved by the Pythagoreans, of doubling the square, which is equivalent to the problem of finding the mean proportional x between two lines, a and 2a, x 2 = 2a2, x = a 2 (Heath 1921, 201). In turn, Archytas found a brilliant solution to the problem formulated by Hippocrates, which was reported by Eudemus (fr. 141 W.). Archytas constructed a series of similar right triangles AMI, AIK, AKD and then showed that their sides are in continued proportion, so that AM: AI = AI: AK = AK: AD, where AM was equal to the side of the original cube and AD = 2AM (figure B2.4). To prove this, he employed a remarkable stereometric construction, which for the first time introduced movement into geometry (note that the moving point D appears twice). Point K, the key point for the construction of similar triangles, was determined as the intersection of three surfaces of revolution: the right cone, the torus, and the half-​cylinder (Knorr 1986, 50–​52; Huffman 2005, 342–​346). The problem of squaring the circle arose in the first part of the 5th century, after the Pythagoreans had found how to square a rectangle (Euclid 2.14). Being equivalent to constructing a line segment whose length is √π times the radius of the circle, the problem is unsolvable using compass-​and-​straightedge techniques, or even algebraic equations, as was established in the late 19th century. (It does not seem, however, that in the pre-​ Euclidean period Greek mathematicians consciously restricted the means allowable to

Mathematics and Astronomy    187

L

K

M

M

K

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A

A

D

I

Z

I

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AM : AI :: AI : AK :: AK : AD

D

E

T

O

Figure B2.4  Archytas’ stereometric construction, and the similar triangles whose sides are in continued proportion. Drawing by W. Sinelnikow based on C. Huffman, Archytas of Tarentum. Cambridge, 2005.

P1

P2

P3

Figure B2.5  Squaring the circle by inscribed polygons. Drawing by Paul A. Whyman, based on W. Knorr. The ancient tradition of geometric problems. Boston: Birkhäuser, 1986.

their constructions to compass and straightedge; see Knorr 1986, 40–​41). It is unknown, whether Anaxagoras came up with a solution of the problem. The solutions of Antiphon and Bryson, says Aristotle, were “eristic” (Sophistic Refutations sec. 11, 171b16–​18, 172a2–​ 7; Physics 1.2, 185a14–​17), which is to say unscientific, since they proceeded not from geometrical principles. Eudemus passes over Bryson in silence but specifies Antiphon’s procedure (fr. 140 W.): the latter started by inscribing a regular polygon in a circle; then, by doubling the number of its sides repeatedly, he obtained an inscribed polygon whose sides coincided with the circumference (see figure B2.5). Thus, concludes Eudemus, Antiphon did not admit the basic principles of geometry, in particular, that geometrical magnitudes are infinitely divisible. This criticism, which reflected a position of the mathematicians, applies to Bryson as well. We know from late sources that, squaring the circle, he added circumscribed polygons to the inscribed ones and claimed that by multiplying their sides he could obtain an intermediate polygon equal to the circle. T. L. Heath, the author of the still-​standard history of Greek mathematics, believed that Antiphon’s and Bryson’s procedures anticipated the famous method of exhaustion, discovered by Eudoxus (Heath 1921, 222), but this idea did not find much support.

188   Early Greek Science Whereas Aristotle believed that Hippocrates pretended to have solved the problem of squaring the circle, but had committed a logical mistake (Sophistic Refutations sec. 11, 171b12–​16; Physics 1.2, 185a14–​17), Eudemus disagreed with his teacher: The quadratures of lunes, which were considered to belong to an uncommon class of propositions on account of the close relation (of lunes) to the circle, were first investigated by Hippocrates, and his exposition was thought to be in correct form. (Fr. 140 W., tr. T. Heath)

The opinion of specialists, to which Eudemus refers, implies that though originally squaring the lunes was most probably intended to lead to squaring the circle, Hippocrates did not claim to have solved the last problem, so Aristotle’s interpretation was incorrect (Lloyd 1987). But Hippocrates succeeded in squaring three out of the five lunes that are possible in plane geometry (two others were found in the 18th century), namely, with the outer circumference equal to a semicircle (see figure B2.6a), greater than a semicircle (see figure B2.6b), and smaller than a semicircle, the most elaborate case. He also squared a figure that consisted of a lune and a circle. In his problem-​solving attempts, Hippocrates did not proceed axiomatically. Thus, he started his quadrature of the lunes not from definitions or unproved principles, but by proving two theorems: first, similar segments of circles have the same ratio as the squares on their bases (12.2), which he then reduced to the second theorem, that the squares on the diameters have the same ratio as the circles. But Hippocrates’ Elements, (a)

Γ b

b’ ∆ a

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∆

b A

c’’

c’ a c

Γ

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c’‘’

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Figure B2.6  Two of the lunes of Hippocrates. Drawing by Paul A. Whyman.

Mathematics and Astronomy    189 whose goal was to organize interrelated mathematical propositions in their logical sequence, must have built them on the explicitly formulated definitions and axioms. A papyrus text, most probably dating back to a Platonist of the 4th century bce, asserts that in Plato’s time “the theory of proportions (μετρολογία) and research on definitions reached their peak, as Eudoxus and his students completely revised the old theory of Hippocrates” (Zhmud 2006, 87–​89). Whereas Eudoxus created a new theory of proportions applicable to commensurable and incommensurable magnitudes, Hippocrates, working around 75  years before him, applied Pythagorean theory of proportions to a new field—​solid geometry—​and worked out the axiomatic basis for his Elements. It is generally believed that his compendium contained much of books 1–​4 and 6 of the Euclidean Elements and that most propositions of book 3 belonged to Hippocrates himself. The authorship of arithmetical books 7–​9 is a tricky question. Eudemus’ History of Geometry did not touch on this, and from his History of Arithmetic only one fragment is preserved. Many scholars believed that an arithmetical compendium analogous to Hippocrates’ Elements in geometry existed before Archytas, but what did it comprise? Archytas obviously relied on the basis of book 7, which may have then belonged to Theodorus, a contemporary of Hippocrates, though this is no more than conjecture; Knorr (1979, 244) attributed book 7 to Theaetetus. Book 8 is usually related to Archytas; the end of book 9 to the early Pythagoreans. What is certain is that Theaetetus’ theory of irrational magnitudes is based on these arithmetical books. The first significant geometer who was born in Athens, Theaetetus was, as mentioned, a student of Theodorus and belonged, according to Eudemus (fr. 133 W.), to the generation of Archytas and Plato. This places his birth around 435/​425 bce, but since Plato depicts him in the Theaetetus, whose dramatic date is 399 bce, as an adolescent, his birth date is usually given as 415/​413 bce. It is known, however, that Plato sometimes changed the age of his personages depending on the dramatic situation in the dialogue, so that it may be safer to stick to the dating provided by Eudemus, who was particular about chronology. Theaetetus’ main achievements in mathematics, the theory of irrational lines (book 10), and the theory of the regular solids (book 13) show him as a successor of the Pythagoreans. He proved that there is an infinite number of straight lines, which are incommensurable in length or both in length and in square; and introduced three particular kinds of such lines, medial, binomial, and apotome, associating them with three known means, the geometric, the arithmetic, and the harmonic (Eudeus, fr. 141-​I W.). According to a scholion on book 13 (Scholia in Euclid, 654.3), which very likely derives from Eudemus, the Pythagoreans constructed three regular solids, pyramid, cube, and dodecahedron, to which Theaetetus added the octahedron and icosahedron (see figure B2.7). Though the construction of the octahedron, a combination of two pyramids on a square base, is much simpler than that of the dodecahedron, they are ascribed respectively to Theaetetus and Hippasus, who lived a century before him (von Fritz 1945; Zhmud 2012, 275). To divide the theories of regular polyhedra into

190   Early Greek Science

Figure B2.7  The five regular solids. Drawing by W. Sinelnikow.

two stages—​the investigation of individual polyhedra and their general theory—​ helps clarify why the more complex polyhedron was constructed before the simpler one (Waterhouse 1973). Hippasus studied not the theory of regular solids as such, but the dodecahedron itself. On the other hand, Theaetetus, having posed the question of which regular solids could be constructed, easily discovered the octahedron. He wrote a systematic treatise, in which he set forth methods for constructing the five regular solids and for inscribing them in a sphere; he also described the relations between the edges of the regular solids and the diameter of the sphere. The last book of Euclidean Elements is based on this treatise. The five regular solids became famous outside of mathematics, after Plato used them in his Timaeus to impart a geometric structure to the four physical elements traditional for Greek philosophy. Creating the world, the Platonic demiurge makes fire from pyramids, air from octahedra, water from icosahedra, earth from cubes, and he uses the dodecahedron to decorate the whole universe. In the Hellenistic era, the five regular solids were called “Platonic bodies,” and Proclus even claimed that Euclid belonged to the Platonic school “and this is why he thought the goal of the Elements as a whole to be the construction of the so-​called Platonic figuresˮ (In Euclid, 68.20–​23). Proclus’ teleological view of the history of mathematics is typically Neoplatonic but is akin to Plato’s own “appropriative” approach to mathematics. Since the geometricians and astronomers do not know how to make use of their discoveries, asserts Plato in his early Euthydemus (290c), those of them who are not utter blockheads must hand these discoveries over to the dialecticians, who will find proper use for them—​just as hunters and fishermen give what they catch to cooks!

Mathematics and Astronomy    191

4.  Mathematics: The Beginning of Self-​R eflection The successes of mathemata during the 5th century bce made their methods of attaining true knowledge highly attractive, especially against the background of the endless debates of the natural philosophers about basic principles, as well as doubts and denials that the truth is attainable, expressed by the Sophists. Philolaus became one of the first pre-​Socratics to introduce mathemata into a philosophical work and to make its results and methods an object of discussion and analysis. (Parmenides and Zeno took from mathematics the technique of deductive proof, but in them we find no reflection on the subject of their borrowed methods.) The Pythagoreans, involved in mathemata, were the first to look at mathematics from an epistemological point of view. In his treatise On Nature, Philolaus declares: “And indeed all the things that are known have number. For without it we can neither understand nor know anythingˮ (DK 44 B 4). This fragment of Philolaus often has been taken as evidence of the Pythagorean doctrine that “everything is number.” But “to have number” does not mean “to consist of numbers,” it means “to be countable,” since “number or that which has number is countable” (Nussbaum 1979). Thus, number in Philolaus makes a knowable thing countable, for example, by representing the octave as a ratio 2:1, the fifth as 3:2, and the fourth as 4:3 (fr. 6a Huffman). “Fr. 6a suggests that the whole-​number ratios which govern musical scales served as the model of the kind of mathematical account which should be supplied for all phenomenaˮ (Huffman 2012). Archytas started his Harmonics by praising his Pythagorean predecessors, “those concerned with the mathematical sciences” (hoi peri ta mathemata), for their, one might say, great epistemological successes. They showed true insight, and it is not strange that they have a correct understanding of particular things as they really are: For since they exercised good discrimination about the nature of the universe (peri tas tōn holōn phusios), they were likely also to get a good view of the way things really are taken part by part. They have handed down to us a clear understanding of the speed of the heavenly bodies and their risings and settings, of geometry, of numbers, and not least of music. For these sciences seem to be sisters. (DK 47 B 1, tr. A. D. Barker, slightly modified)

In Archytas, the word mathemata acquires its terminological character and designates a particular group of four mathematical sciences, all of which he regards as related. (This quadrivium soon appears in Plato’s Republic.) It is these sciences, claims Archytas, that give us real understanding of the world and everything in it. This claim is, firstly, very un-​Platonic, for Archytas obviously did not need any intermediary to interpret results of scientific research; and secondly, it is quite unusual, for in antiquity claims to true understanding of reality were usually raised by philosophers rather than by mathematicians.

192   Early Greek Science There were other exceptions, too (Feke 2014). Of all the mathemata, Archytas clearly preferred arithmetic, declaring in particular that it surpassed all other arts, including geometry, in clearness, evidence, and obviousness, which makes it, in comparison, more demonstrative (DK 47 B 4). Apart from the fact that arithmetic is more exact than geometry, it is also socially useful. In the introduction to On Mathematical Sciences, Archytas relates important social changes, such as an increase of concord and an advance toward greater equality, the to the discovery of calculation. Moreover, calculation proves capable of improving people’s moral qualities, keeping them from greed and injustice or, at any rate, exposing these vices (DK 47 B 3). Archytas’ conviction that mathematical knowledge makes a man and, accordingly, the society in which he lives better, was shared by his friend Plato. In the same fragment, Archytas again tackles epistemological issues, presenting different ways of acquiring knowledge: To know what was heretofore unknown, one has either to learn it from another, or to discover oneself. What one has learnt, he has learnt from another and with another’s assistance, what one has found, he has found himself and by his own means. Discovery without research is difficult and rare, by research easy and practicable, but without knowing (how) to research it is impossible to research. (DK 47 B 3)

To make a discovery, conscious research is needed because one cannot conduct research without knowing how to do it. What, then, must the researcher know? To all appearances, he must know what and how to seek—​in other words, he must know the object and method of his research. It follows, then, that the method, which is to say the art of correct research, becomes for Archytas a prerequisite for success in science, although he did not altogether rule out the chance, small as it might appear, of an accidental discovery. Thus, by the beginning of the 4th century bce, Greek exact sciences not only succeeded in creating new powerful methods and in solving many difficult problems but began also to look narrowly at themselves: What did they achieve, and why did this become possible? We can only regret that the results of this self-​analysis are so seldom available to us.

Bibliography Becker, O. Das mathematische Denken der Antike. Göttingen: Vandenhoeck & Ruprecht, 1966. Bodnár, I. Oenopides of Chius. Preprint 327 of the Max Planck Institute for the History of Science, Berlin, 2007. Boll, F. Studien über Claudius Ptolemäus. Leipzig: Teubner, 1894. Brumbaugh, Robert. The Philosophers of Greece. Albany:  State University of New  York Press, 1981. Burckhardt, Jacob. Griechische Kulturgeschichte. Berlin: Spemann, 1898–​1902. Chemla, Karine, ed. The History of Mathematical Proof in Ancient Traditions. Cambridge: Cambridge University Press, 2012.

Mathematics and Astronomy    193 Couprie, Dirk. Heaven and Earth in Ancient Greek Cosmology. Berlin: Springer, 2011. Feke, Jacqueline. “Metamathematical Rhetoric: Hero and Ptolemy Against the Philosophers.” Historia Mathematica 41 (2014): 261–​276. Fritz, K. von. “Oinopides.” RE 17 (1937): 2258–​2272. —​—​—. “The Discovery of Incommensurability by Hippasus of Metapontum.” Annals of Mathematics 46 (1945): 242–​264. —​—​—​. Grundprobleme der Geschichte der antiken Wissenschaft. Berlin: de Gruyter, 1971. Heath, T. L. A History of Greek Mathematics. Vol. 1. Oxford: Clarendon Press, 1922. —​—​—​. Euclid: The Thirteen Books of the Elements. 3 vols. Cambridge: Cambridge University Press, 1926. Høyrup, J. In Measure, Number, and Weight: Studies in Mathematics and Culture. Albany: State University of New York Press, 1994. —​ —​ —. “Pythagorean ‘Rule’ and ‘Theorem.’” In Babylon:  Focus mesopotamischer Geschichte, Wiege früher Gelehrsamkeit, Mythos in der Moderne, ed. J. Renger, 393–​407. Saarbrucken: Saarbrücker Druck und Verlag, 1998. Huffman, C. A. Archytas of Tarentum:  Pythagorean, Philosopher and Mathematician King. Cambridge: Cambridge University Press, 2005. —​—​—. “Philolaus.” In The Stanford Encyclopedia of Philosophy, ed. Edward N. Zalta, Summer 2012 edition, http://​plato.stanford.edu/​entries/​philolaus/​. Knorr, W. R. The Evolution of the Euclidean Elements. Dordrecht and Boston: Reidel, 1975. —​—​—. “On the Early History of Axiomatics: The Interaction of Mathematics and Philosophy in Greek Antiquity.” In Theory Change, Ancient Axiomatics and Galileo’s Methodology, ed. J. Hintikka et al., vol. 1, 145–​186. Dordrecht: Springer, 1981. —​—​—. The Ancient Tradition of Geometric Problems. Boston: Birkhäuser, 1986. —​—​—​. “The Impact of Modern Mathematics on Ancient Mathematics.” Revue d’histoire des mathématiques 7 (2001): 121–​135. Kouremenos, Theokritos, “The Tradition of the Delian Problem and Its Origins in the Platonic Corpus.” Trends in Classics 3 (2011): 341–​364. Lloyd, G. E. R. “The Alleged Fallacy of Hippocrates of Chios.” Apeiron 20 (1987): 103–​128. —​—​—. Ancient Worlds, Modern Reflections. Oxford: Oxford University Press, 2004. Netz, Reviel. The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History. Cambridge: Cambridge University Press, 1999. —​—​—. “Eudemus of Rhodes, Hippocrates of Chios and the Earliest Form of a Greek Mathematical Text.” Centaurus 46 (2004): 243–​286. Neugebauer, O. The Exact Sciences in Antiquity. 2nd ed. Providence, RI:  Brown University Press, 1957. Nussbaum, M. “Eleatic Conventionalism and Philolaus on the Conditions of Thought.” Harvard Studies in Classical Philology 83 (1979): 63–​108. Robson, E. “Neither Sherlock Holmes nor Babylon: A Reassessment of Plimpton 322.” Historia Mathematica 28 (2001): 167–​206. —​ —​ —​ . “Influence, Ignorance, or Indifference? Rethinking the Relationship Between Babylonian and Greek Mathematics.” British Society for the History of Mathematics 4 (2005): 1–​17. Taisbak, C. M. “Exceeding and Falling Short: Elliptical and Hyperbolical Application of Areas.” Science in Context 16 (2003): 299–​318. Unguru, S. “On the Need to Rewrite the History of Greek Mathematics.” Archive for History of Exact Sciences 15 (1975): 67–​114.

194   Early Greek Science Waerden, B. L. van der. Science Awakening. New York: Oxford University Press, 1961. Waterhouse, W. C. “The Discovery of the Regular Solids.” Archive for History of Exact Sciences 9 (1972): 212–​221. Wilson, M. “Hippocrates of Chios’s Theory of Comets.” Journal for the History of Astronomy 39 (2008): 141–​160. Zaicev, A. Das griechische Wunder. Die Entstehung der griechischen Zivilisation. Konstanz: Universitätsverlag, 1993. Zhmud, L. The Origin of the History of Science in Classical Antiquity. Berlin: de Gruyter, 2006. —​—​—​. Pythagoras and the Early Pythagoreans. Oxford: Oxford University Press, 2012.

chapter B3

Early Greek G e o g ra ph y Philip G. Kaplan

Geography, the study of lands, their climates, resources, and peoples, has a complex and tenuous relationship to the physical sciences. Many of its concepts and techniques are part of the scientific tradition, including the formulation and testing of theory, observation, precise measurement, and taxonomy. On the other hand, geography has strong ties to the “softer” disciplines of the social sciences. This is partly due to the breadth and diversity of its concerns; but it is also a function of its origins. As a form of intellectual inquiry, geography can be traced to early Greece, where it was born in the same movement that produced the discipline of history. That the two disciplines were born together is hardly an accident. Geography and history are two ways of organizing an understanding of the world; the former in terms of the first three dimensions of space, and the latter as the fourth of time. A geographical understanding is spatial; discrete elements relate through proximity and orientation. Historical understanding, at least as it developed in the Greco-​Roman world, is linear and sequential; discrete elements are arranged in order, and linked together by causation. In antiquity the two approaches were necessarily complementary. The developments that produced geography and history also engendered the disciplines of ethnography, natural science, astronomy, and medicine, which eventually emerged as distinct fields of study but began as an undifferentiated complex of curiosity about the physical world. Tracing the origins of geography as a field of intellectual endeavor is first and foremost a matter of determining how these various subjects became distinct areas of inquiry. It is also essential to understand how the key elements of geographical inquiry—​the concern for understanding and organizing the world in terms of its spatial relationships—​emerged in the early Greek period.

1.  Geography in the Near East and Egypt In the world of classical scholarship, it was once routine to minimize the contributions of the Near East and Egypt to the development of the discipline of geography. This

196   Early Greek Science perspective has since given way to a broader view. Since the lands of North Africa and the Middle East have not produced early texts that were explicitly geographical in nature, their priority to the Greeks in matters of geography has routinely been doubted (see Thomson 1948). There are good reasons for not doing so. The Greeks themselves, starting with Herodotus, implicitly or explicitly credited the Egyptians with advanced land-​surveying techniques. Furthermore, there is some evidence that the Egyptians and the Babylonians developed fundamental cartographical conceptions that were later borrowed and developed by the Greeks (see the chapters on Babylonian and Egyptian cartography in Harley and Woodward 1987). The Babylonians developed the practice of drawing both larger scale plans of buildings and smaller scale maps of cities, such as the famous map of Nippur from ca 1500 bce. The “Babylonian World Map” from ca 600 bce shows a very schematic view of the world inscribed in a double circle, with Babylon at the center. On a less sophisticated level, the understanding of geospatial relationships in terms of itineraries developed in the context of epics and accounts of travel. The earliest examples—​such as the epic of Gilgamesh—​show little concern for the spatial relationships of the various places the hero travels, but later texts, such as the Assyrian royal annals, generally arrange their narratives of conquest along recognizable routes. In Egypt, descriptions of protracted travel appear as early as the Middle Kingdom, in accounts of voyages to the land of Punt, which are however mostly lacking in specific topographic or toponymic detail. The expansionist kings of the New Kingdom were also prone to presenting their campaigns into Palestine and Syria in the form of itineraries. In addition, a literary tradition developed of stories of travel and misadventure abroad. Two surviving exemplars of this tradition are the Tale of Sinuhe, a popular account from the Middle Kingdom (ca 1950 bce) of the travels, triumphs, and return of an Egyptian court official who fled to Syria; and the Tale of Wenamun, from the Third Intermediate period (ca 1000 bce), about the difficulties faced by a functionary of the Temple of Amun in Thebes in his quest to secure wood from the cities of the Phoenician coast. Neither tale focuses on geographical description per se, but they contain enough toponymy to suggest a presumption of familiarity with the lands where the stories take place and a realistic sense of the geospatial ordering of those lands.

2.  Space and Time in Greek Myth In Greece, both the geographical and the historical understanding have their origins in an earlier mythological cosmology (Hübner 2000). This mythological cosmology is a totalizing conception: it presents a complete picture of the world, albeit one that does not describe or seek to explain all elements of the world in space and time—​although the cosmology becomes more elaborate and detailed over time, as gaps are filled in and inconsistencies are reconciled. The earliest Greek cosmology is preserved in Hesiod’s Theogony, although its origins are far earlier, and may have been inspired by Hittite and

Early Greek Geography    197 Near Eastern cosmologies (West 1997, 276–​305). The Hesiodic cosmology provided a framework for the creation and current state of the kosmos—​including, by implication if not in complete detail, the physical world of the poet and his audience—​by providing a narrative of how the kosmos came into being. It also generated a framework for an understanding of the development of elements in time by explaining the primary elements in the dynamic of human history: the gods are all powerful and control the conditions of human existence; mortals are born to suffer; and conflict plays a key role in divine and human affairs. A key feature of the cosmogonic myth (although it is not explicitly expressed in the narrative, in contrast to, for example, the cosmogony in Genesis 1–​2) is that time and space are unitary, in that the elements of the physical universe are described when they come into being by the (pro)creative acts of the divinities. The world as it is, therefore, is nothing more than a physical record of the events that brought it into being. Furthermore, the linking element of the chronological, and hence physical, relationships is not causality so much as familial descent: places are linked by the ancestry of their eponymous gods and heroes. It is an approach that disregards spatial relationships. In Theogony 338–​345, Hesiod produces a list of the daughters of Okeanos (Ocean), who are the major rivers of the world known to the Greeks; but the list is not given in a spatially coherent order. Their genealogical link to Ocean provides a sufficient understanding of their physical relationship. This totalizing and unitary approach is continued in the latter part of the Theogony, as well as in later genealogical catalogues, starting with the Hesiodic Catalogue of Women. Such works attempt a complete survey of the generations of men, down to the Trojan War. At the same time, the genealogies of heroes also “map” the peoples of the world known to its author, and by extension explain the relationships of the places they inhabit. The heroes are eponyms for the peoples and places of the world; as such, time and place are united. These relationships are genealogical, and therefore might be considered proto-​ethnographical; but they are not proto-​geographical inasmuch as they do not require, or even suggest, spatial relationships between the elements. The later tradition of mythography continued to use genealogies for their basic structure. Anaximander of Miletus is credited with a heroology, and Hecataeus of Miletus (FGrHist 1) wrote a genealogiai that was cited frequently. Hecataeus’ work seems to question the more fantastic claims of divine and heroic ancestry, and to map the traditional legends onto a fuller understanding of the geography of the known world. The genre of genealogical mythography was continued by later writers, such as Asios of Samos, Akousilaos of Argos (ca 525 bce; FGrHist 2), and Pherecydes of Athens (ca 450 bce; FGrHist 333). With the rise of geography as a distinct discipline, such genealogies ceased to play a role in explaining relationships between peoples and places of the world. The Homeric poems, although generally thought to have been composed or written down before the Hesiodic cosmogony, take the universal cosmogony as a background familiar to the poems’ audiences. The poems approach the understanding of the dynamics of time and space differently, however. For one thing, the poems treat the gods as secondary elements in what is at heart a human story. The gods may help or hinder, but they are marginal to the human conflict at the center of the stories: the quarrel

198   Early Greek Science between Agamemnon and Achilles and its consequences, and Odysseus’ attempts to return home, his son’s attempts to learn about his father, and the showdown with the suitors. As a result of this emphasis, the Homeric poems also limit the temporal and physical dimensions of the story they tell, reflecting the human consciousness at the heart of their stories. Temporally, the stories play out on a human scale—​not even a human lifespan, but a shorter time: a few weeks late in the war, or the interval between Odysseus’ arrival in Phaeacia and his triumph over the suitors on Ithaca. Events prior to the narrow bright beam cast by the narrative exist in a penumbra of human memory and storytelling. Physical space exhibits the same foreshortened quality: in the Iliad, the topography of the battlefield outside of Troy, from the ships on the beach to the walls of the city, is described consistently and occasionally vividly. On the central stage of the narrative, physical and topographical relationships are delineated fairly surely, including Troy itself with its walls, towers, and gates; the trees and spring outside the walls; the plain of the Scamander; the beach where the Achaean ships lie; and marking the boundaries of the action, the Hellespont and Mount Ida. Everything else exists in the shadows—​even Mount Olympus, despite being a physical setting for several scenes in the poem. Other regions exist in memory, including the homelands from where the Greeks and the Trojan allies have journeyed to take part in the war, and the towns of the Troad sacked by the Greeks. Their geographical location is immaterial, and so vaguely suggested; Lycia, the home of Glaukos and Sarpedon, is simply “far away” (tēlothen) by the banks of the Xanthos River. The only place in the Iliad where geography far from Troy appears in an organized form is in the Catalogue of Ships, the extensive listing of the contingents of Greeks who participated in the expedition against Troy, and the shorter list of Trojans and allies (Greek catalogue: Iliad 2.495–​759; Trojan catalogue: 816–​877). Whether the lists represent a relic of Bronze Age geographical data, a view of the Aegean contemporary with the composition of the rest of the poem, or a later insertion of material, is a question of extensive and unresolved debate. These lists are rich in certain kinds of geographical information, namely gentilics, names of settlements (described as ptoliethra), occasional topographical details—​mountains, ridges, hollows, rivers, springs—​and the odd mention of climate and agricultural products. These latter may relate actual geographical information about the places with which they are associated, although as always with Homeric epithets, in some cases the use of a descriptive term may be metri causa (Visser 1997, 78–​150). More significantly, the order of the places has been described as a sequence of itineraries (Giovannini 1969, 52–​64; Anderson 1995, 187–​ 188). The Greek list starts in central Greece with the Boeotians and works its way south to the Peloponnese, west to the Ionian islands, then east to the Dodecannese. It then shifts north to the lands between Thermopylae and Olympus. While a strict order is not observed, the grouping of places adjacent to one another does exhibit a rudimentary kind of geospatial awareness that is as essential in geographical thought as chronology is in historical thought. Similarly, the Trojan catalogue arranges the allies of the Trojans along roughly four radial lines, again possibly reflecting itineraries: perhaps trade routes (Leaf 1912, 270), or simply lines along the cardinal directions, slightly

Early Greek Geography    199 distorted (Burr 1961, 149). Understanding geospatial relationships as itineraries has long been recognized as the earliest form of true geographical awareness to develop in Greece: see especially Janni (1984) who distinguishes between the spazio odologico of the itinerary and the later spazio cartografico. Whether any of these sequences represent true routes of travel, they nonetheless reflect an understanding of adjacency and proximity, key features of an emerging geographical consciousness. In the Odyssey the foreshortening of the “here and now” compared to the “there and then” is similarly marked, although the latter plays more of a role in the narrative. The poem’s “action” takes place in a restricted set of locales—​Phaeacia, Ithaca, Pylos, Sparta—​but much of the hero’s adventure took place previously and is recounted by him in a long tale (apologos) told to the Phaeacian court. The places where the story is set are sketched with some physical detail, although uncertainties about the location of the first three have persisted. The latter three places are linked by Telemachus’ journey to find news of his father; although the journey is only briefly sketched out, it anchors these places in a world familiar to the Greeks. Places reported indirectly in the poem, on the other hand—​Troy, Egypt, Crete, and the various stations in Odysseus’ apologos—​ exist in penumbral form in human storytelling and imagination. While the settings of the story exist in a physical relationship to one another, separated by distances that can be traversed by human initiative—​Phaeacia represents a special case that must be considered separately—​the relationships between geographical spaces in the “there and then” are not established, at least in spatial terms. The “Troy” that exists as a real place in the Iliad no longer exists in the Odyssey: it has been destroyed and cannot be returned to except in the recollections of Odysseus, Nestor, Menelaus and Helen, and the bards who sing of it. In the Odyssey only a few select individuals—​Nestor, Menelaus, and Odysseus, all of them storytellers who can travel through the “there and then” in their tales—​can negotiate the passage back to the “here and now.” Nestor’s journey back is unproblematic but only briefly described. Menelaus’ is more problematic and involves a disorienting storm and passage through several strange (but real) lands. Although this might also suggest an itinerary, Menelaus’ description of his wanderings (4.83–​85) presents severe problems in terms of making sense of his route home. The places and peoples he lists—​ Cyprus, Phoenicia, the Egyptians, Ethiopians, Sidonians, and Erembians—​place him in the eastern Mediterranean and North Africa, but the order, at least of the last two, is nonsensical. Odysseus’ lying tales (14.199–​320, 17.424–​444, 19.172–​202) take him from Crete to Troy to Egypt to Phoenicia to Thesprotia, or from Egypt to Cyprus to Ithaca. These are plausible journeys and adventures, far more realistic than his “actual” journey; but being falsehoods, the route he describes shifts with each retelling. They serve to underscore the fantastic nature of Odysseus’ actual route. Odysseus’ journey home is the farthest and most difficult, involving passage through the “fairy-​land” and ultimately to the underworld and back. The hero’s route as narrated by him traces a notional route through space. The places in the apologos however, whose locations were long afterward sought by geographers, exist in the poem only in narrative and temporal relationship to one another; their spatial relationship is indeterminate. To the Odysseus sitting in the Phaeacian court, the places he tells of visiting no longer

200   Early Greek Science exist in any physical sense, as they are located in his past, and like Troy, they cannot be revisited, except in story. The one exception proves the rule: Odysseus and his men return to the Cave of the Winds after they leave it, not as a deliberate act but as a result of a violation of a god’s command. Odysseus does not choose to go back and does not know the way, but is blown there because of his crew’s disobedience while he is asleep. Odysseus is finally able to bridge the gap between the unlocatable other places and the locatable land of home by a two-​stage process in which he surrenders his conscious will and indeed his consciousness. To leave Kalypso’s isle, he first builds a raft, which is wrecked in a storm and is only brought to the liminal space of the Phaeacians’ isle through the intervention of the goddess Ino; when he arrives, he passes out. Later, he must rely on the Phaeacians’ magical ability to cross over into the known world and again is made to sleep through the passage. The gap between the “here and now” and the “there and then” raises the age-​old question of the “reality” of the geography of Odysseus’ route. The Stoic view, articulated extensively in Strabo, is that Homer was the first geographer (see Strabo 1.1.1 and passim). Homer’s knowledge, the Stoics maintained, was perfect and comprehensive, but disguised in places by his use of poetic language. This view informs attempts to place Odysseus’ route home in the “real” world of the Central Mediterranean or elsewhere; but Eratosthenes’ skeptical view of the impossibility of tracing Odysseus’ route (see Strabo 1.2.15) prevails in serious scholarship. At best, the fantastic lands and creatures that Odysseus encounters are “sailors’ tales,” rumors of fantastic places beyond the edge of the known world. Even in the places of the “here and now,” only occasionally can Homer’s topographical details be matched with the modern landscapes of Greece and Anatolia. Ithaca is the most well-​known example of this problem:  the discrepancies between Homer’s seemingly factual description of the island and its environs and the modern landscape of modern Ithaki have frustrated attempts to map the epic convincingly (in spite of Luce 1998). The spatial relationships that are key to a geographical mindset develop further in the surviving fragments of post-​Homeric epic and lyric poetry. Although this material is often hard to date, the increasing use of toponyms, particularly of lands to the east and west of Greece, tells of the expansion of the Greeks’ geographical horizons in the age of colonial expansion and increased contacts with the Phoenicians, Lydians, Carians, Egyptians, and Persians. Through much of the Archaic Age, the main form in which geographical information was organized remained the itinerary. The clearest example of this mode of organization of geographical information is the Homeric Hymn to Apollo, whose sections—​considered by many as separate hymns, although recent studies see them as one (Miller 1986, xi, 111–​117; Richardson 2010, 9–​13)—​describe three routes through Greece. The Delian hymn contains a passage (lines 30–​44) that is framed explicitly as an itinerary, being an account of Leto’s wanderings through the Aegean in search of a place to give birth to her children. The route starts with Crete and moves up to Athens and Euboea; then with some back and forth, it goes through the northern Aegean, over to the Anatolian coast and down to Karpathos, and finally into the Cyclades, ending with Delos. The route is circular rather than linear, arguably an early form of the periplous (sailing around), although the list of places does not make a direct

Early Greek Geography    201 sailing route. Of the sites chosen, some are well-​known, while others are less so, or even obscure; they might all have been associated with the worship of Apollo (Richardson 2010, 87–​90). They are a list of places, not cities: although introducing the route as a series of inhabitants of the lands through which Leto passes, the hymn projects this journey into the mythic past before human settlement, and emphasizes the geophysical features of the places. This makes this list very different from later itineraries, which highlight cities as stopping places on travel routes. The Delphic section also contains an itinerary describing Apollo’s search for an oracle site. The god traces a route from Mount Olympus down through northern Greece to Boeotia, and finally to the site of the future oracle of the god at Delphi. The passage is rich in toponymy, and is especially detailed in describing places in Boeotia, suggesting perhaps a Boeotian origin for the Pythian section of the poem (Crudden 2001, 1090). It is not a true itinerary, however, since the route is distinctly non-​linear—​being the path of a god, it describes a trip no human could make. The god makes a digression to Cape Lekton in the Troad, and the places in Boeotia, to the degree that they can be mapped, suggest a meandering route. As in the route to Delos, the list emphasizes geophysical spaces rather than settlements, although it includes some places that were cities, in myth at any rate, such as Iolcus, and lists peoples, such as the Perrhaebi and the Aenienai. At the same time, the hymn emphasizes its primordial setting by referring to Thebes before humans lived there. The final itinerary of the poem is in the passage describing the voyage of the Cretan ship that is commandeered by Apollo (lines 389–​435). Here the voyage is described very much as a periplous, following the course of a sailing ship rounding the western Peloponnese. The general route from Knossos to Delphi is clear, and the description of sailing into the Corinthian gulf on the approach to Krisa seems based on experience. A  number of the toponyms are obscure—​appearing elsewhere only in Homer—​and those that can be located demonstrate that they are not all in order geographically. The somewhat disordered nature of the lists points to a key aspect of the poetic itineraries that distinguish them from true geographical writing. While they show a familiarity with the toponymy of the regions they describe and presuppose some knowledge of the physical relationships of these places, they are not intended to convey that information in any systematic fashion. The poems may be intended to honor the places named, or simply to establish a general sense of the reality of the god’s journeys and their power to traverse distances impossible for men. They are not meant to provide useful descriptive information about the landscapes through which the poem passes. They express a nascent geographical understanding but do not convey it in any systematic fashion.

3.  The Ionian Pre-​S ocratics and the Periegetic Tradition The origins of systematic geographical thought can be found in the milieu of the Ionian natural philosophers of the 6th century bce, specifically that of Miletus. The Ionian

202   Early Greek Science pre-​Socratics are thought to be the first generation of “rationalists” who dispensed with the older mythological conceptions and attempted an understanding of the nature of the universe divorced from divine action, searching instead for physical principles to account for basic observations about the kosmos. Whether their approach was truly revolutionary or was a development of earlier cosmological thinking is a long-​debated question (so Stokes 1962; 1963). It is undeniable, however, that their cosmological speculations, along with the burgeoning role Miletus played in colonization and trade throughout the Mediterranean, encouraged an interest in describing, cataloguing, and eventually mapping the oikoumenē, the settled world and its peoples. They also laid the groundwork for the development of an understanding of the size and shape of the world and the lands it contained, and the various geophysical processes that created it. The Milesians were remembered in later doxography as being primarily concerned with identifying a physical element that would provide an alternative cosmogonic principle to the mythological cosmogony of Hesiod. These early attempts at a physical cosmogony led the Milesians to provide etiologies for the physical features of the known world. Thales, whose primordial element was water, seems to have been interested in the question of the Nile flood, seeing in the creation of the Delta an ongoing proof of the progenitive power of the element. He was also known in later tradition to have been interested in problems of astronomy, geometry, and hydrology, and so was a pioneer in the elements of mensuration that would later become essential to cartographic geography—​ although the biographical tradition concerning his accomplishments suffered embellishment over the years. Concerns about the fundamental cosmogonic principle, and the resulting cosmology, gave rise to speculations about the shape of the earth, as well as its position in the universe. Thales had the round earth floating on water (DK 11A 12, 14, 15); while Anaximander imagined the earth as a column drum, with the oikoumenē on its upper surface, hanging in space (DK 12A 10). These theories were not radical departures from the earlier mythological cosmologies—​the circular earth surrounded by the river Ocean, which Herodotus attributes to his predecessors, is clearly a direct descendant of the cosmological scheme depicted on Achilles’ shield. But the need to reconcile the theoretical construct with established data concerning places that the Ionians had contact with led to considerations of the disposition of lands on the disk and the formation of the earliest continental theory. Speculations about the number, borders, and extent of the continents are not preserved in the doxographical tradition; but Herodotus (2.15–​17; 4.36.2) dismissively credits these speculations to the Ionian logographers, which may refer to this earlier generation. The division of the lands of the world into two, and later three, continents seems to be the first major innovation of Greek geographical thought, and the first attempt to organize lands in purely spatial, as opposed to linear and narrative terms. This intellectual innovation is credited to Anaximander, who created the first map of the world, initiating a tradition of Greek cartography that was to be passed along to the Romans and later Europeans. Heidel (1921) maintained that there was a descriptive component to Anaximander’s creation, based on the assertion in the Suda entry on him that he wrote a Periodos Ges (Circuit of the Earth); but Herodotus

Early Greek Geography    203 (4.36) and later writers use the term to refer to maps, so it is hardly conclusive. Since later sources never cite Anaximander or the other Milesian pre-​Socratics for specific geographical information, it is very unlikely that their work contained that sort of information. Hecataeus of Miletus, the most important individual of the Ionian tradition in the development of geographical thought, drew on another stream of tradition that developed in this time period. It is the tradition of periploi and periegeseis (or periodoi ges), texts that describe a sea route following coastlines in the former case, or a land route around the known world in the latter. Although this tradition bears some relation to the itineraries found in early Greek poetry, how far back it may be traced as a distinct (sub-​)literary genre is a matter of great uncertainty. The earliest extant example of a periplous is the text preserved among the manuscripts of the Geographi Graeci Minores, an account of the coasts of the Mediterranean and Black Seas wrongly attributed to Scylax of Caryanda. Analysis of toponymy in the text has pointed to a date for the composition of the text in the mid-​4th century bce, although elements of the text may go back to earlier times (Blomqvist 1979). But this type of text, of which later examples survive, may have its origins in an earlier genre of exploration accounts. The Scylax whose name was wrongly attached to the periplous was the explorer who was credited by Herodotus (4.44) with leading an expedition sent by Darius to explore the Indus River and the Ocean route back to Mesopotamia in 512–​509 bce. Some fragments attributed to Skylax indicate that he produced a written text describing his journey (Brill’s New Jacoby 709). The Phoenicians who claimed to have circumnavigated Africa at the order of the Egyptian king Necho II (610–​595 bce; Herodotus 4.42), may have also produced a written account. Another early exploratory text is that of Hanno, king of the Carthaginians perhaps in the 5th century bce, which describes an exploratory expedition down the Moroccan coast, perhaps as far as Cameroon. This account purports to be a Greek translation of a Punic text set up in a temple in Carthage. It is garbled, with possible gaps, and is very hard to map onto the African coast. Some have seen it as a pastiche based on Herodotus and references to Hanno in late sources (Germain 1957). If real, it may only have come into the Greek world late, in Polybius’ day or even Juba’s. These early accounts served to describe new routes and were probably meant to assert the control by Egypt, Persia, or Carthage over the territory circumnavigated (Kaplan 2009). Both the Milesian philosophical tradition and the emerging genre of periegetic literature shaped the work of Hecataeus of Miletus (FGrHist 1), a pioneer in the development of the discipline of geography. Although not counted as one of the pre-​Socratics in the doxographic tradition, Hecataeus had close affinities with the Milesian natural philosophers. He did not share the preoccupations of the other Milesians with the physical stuff of the universe, but he was clearly influenced by their speculations on the shape of the world. Agathemeros (Geog. 1.1.1) claims that Hecataeus improved on the map made by Anaximander, possibly by adding more detail to it. He was also central to the development of exploratory accounts into a fully realized periegesis. Although Agathemeros describes him as a much-​traveled man (aner polyplanes), aside

204   Early Greek Science from Herodotus’ reference (2.143) to Hecataeus’ visit to Egypt, there are no references in the fragments to Hecataeus’ physical presence in the lands he surveyed. Rather than a travel account, his work was a systematic description of the world’s lands and peoples. The periegesis or periodos ges, a pioneering work of descriptive geography, is known only from numerous fragments, the majority of which are preserved in the Ethnica of Stephen of Byzantium. Because of its fragmentary state, there is much that is uncertain about its organization. Many of the citations refer to a Periegesis Europes, or Asias, from which Jacoby inferred that the work was divided into two parts—​occasional references to Periegesis Libyes, Agyptiou, and regions in Greece are probably sections of one of the two parts. This division makes it clear that Hecataeus adopted the division of the world into two continents. How each part was organized internally is hard to determine. The titles and the way places are described in relation to one another suggest a work that was structured as a linear progression around the world, much like the earlier mythological itineraries and the genre of periploi. The route seems to follow the coastline of the lands abutting the Mediterranean. At the same time, there are a number of spatial indicators preserved in the fragments, in which places are described as being to the north, south, east, or west of other places. Hecataeus also covered places he knew of inland from the sea. This tendency is particularly marked in his discussion of Asia, where he had sources of information from Persian informants of areas in the Asian interior. His need to integrate this more complex spatial reality into the previous linear conception led to a truly two-​dimensional cartographic framework. Hecataeus retained the linear practice of measuring distance by day’s travel—​only one surviving fragment, from Ammianus (FGrHist 1 fr. 197), credits Hecataeus with measuring the breadth of the Black Sea in stades, and this is almost certainly a misstatement on Ammianus’ part. On the other hand, the use of days’ travel in a non-​narrative context marks a crucial step in the development of a truly cartographic sensibility, since it suggests a conception of distance that is standardized and universal. The fragments of Hecataeus give hints of his nascent sense of geospatial order, but they preserve mainly his toponymy, along with the names of peoples associated with the places he lists. This may to a large degree be an artifact of his preservation in Stephen, for whom the names of peoples are of paramount importance. Many of the entries in Stephen also discuss the mythological origins of the names; this data might come from Hecataeus, suggesting a close link between his Genealogiai, which mapped Greek mythology onto the known world, and his Periegesis. In addition, some fragments preserve a broader range of interests, particularly in regard to foreign lands: the question of the cause of the Nile flood (fr. 302); wonders such as the floating island of Chemmis (fr. 305), and monstrous creatures such as sciapods and pygmies (fr. 327, 328); local vegetation (fr. 291, 292, 296) and wildlife (fr. 324); the food, dress, and way of life of local inhabitants (e.g., fr. 154, 284, 287, 323, 335, 358). Several fragments refer to information also related by Herodotus, who must have borrowed from Hecataeus without attribution. It has been suggested, by Jacoby and others, that much of Herodotus’ ethnographical and natural history data concerning foreign lands may have come from Hecataeus; although more recent scholarship has minimized the amount that Herodotus borrowed from his

Early Greek Geography    205 predecessor. Herodotus is widely, but wrongly, assumed to be critical of his predecessor’s achievements, but he refers to Hecataeus several times in positive terms.

4.  The Origins of Cartography The intellectual movement that produced the first geographical writing also produced the first maps in the Greek world. Credit for this development goes to Anaximander. Whether he invented the concept of the map himself or copied it from the Babylonians, Egyptians, or others remains uncertain. The map he is credited with is described as a geographikon pinax (Eratosthenes in Strabo 1.1.11). Although no details of it survive, it undoubtedly attempted to represent the shape of the oikoumenē in two dimensions. His map was certainly very schematic, of the circular variety criticized by Herodotus (4.36.2), drawn as if with a compass, with Europe and Asia the same size. Hecataeus’ improved version—​probably the basis of the map Aristagoras carried in his attempt to recruit support for the Ionian Revolt (Herodotus 5.49)—​had not only the outline of the land, the sea, and rivers but also some indications of where the Greeks’ neighbors to the east lived. In Herodotus’ telling, these names are arranged in a linear fashion, from the coast of Anatolia to the Persian heartland; so it is not clear that this map, or Herodotus’ understanding of it, reflected a fully two-​dimensional arrangement of places. The singular accomplishment of the early maps is that they finally divorce space from time. Lands are seen not as points on a line to be moved through in the course of a narrative, but as ever-​existing spaces that maintain fixed relationships with one another in two dimensions: Janni’s (1984) “spazio odologico” is supplanted by a “spazio cartografico.” The cartographic revolution was slow to develop in Greek geographic thought. Herodotus describes Aristagoras’ map as a bronze tablet (pinax) on which was engraved the circuit of all the land (gēs apasēs periodos), along with all the seas and rivers. He then has Aristagoras point out to Cleomenes an itinerary of adjacent lands and peoples, from the Ionians to Susa. He follows this with his own problematic assessment of the route, with distances in parasangs and stades, as well as days’ travel (5.52–​3). His numbers are apparently exact, but contain difficulties and do not add up properly to his totals. Elsewhere, Herodotus gives a more comprehensive cartographic account of the world (4.36–​41), beginning with a dismissive statement about how some people (by whom he means the Ionian philosophers) draw maps of the world that are overly schematic, with a circular Ocean running around the perimeter and Europe and Asia drawn as the same size. He then describes the regions of Asia, using Persia as his starting place and point of reference. Next he gives a much more cursory description of Africa, and then, caught up in several digressions concerning the exploration of the east and the circumnavigation of Africa, he neglects to provide a description of Europe. While not comprehensive, and certainly not accurate, his description does try to translate a visual image of a map into verbal terms, while avoiding the linear periegetic style of previous geographical

206   Early Greek Science description. Herodotus’ description of the world demonstrates the limitation of a cartographical account: it must be totalizing, but, at the same time, if there are parts of the world that are not well-​known, it results in blank spaces on the map. If Herodotus had not deliberately adopted a cartographic framework in this section, he would not have needed to admit how little he knew of Africa, Europe, and the outer edges of the world. The unknown regions could have simply been elided from the itinerary. Maps continued to be used to render comprehensive conceptions of the world  in ever-more detailed fashion, as is clear from scattered references from the 5th century bce and later. None of these maps survive, but the references to the shape of the oikoumenē in the 4th century suggest a shift from a circular world map to a rectangular shape (Heidel 1937). Before the development of the coordinate system in the Hellenistic era, cartography held limited practical interest. The few references to maps in the 5th century suggest that they were unfamiliar to most people and viewed with suspicion, as shown by the reception of Aristagoras’ map in Sparta; so also there is Strepsiades’ comical skepticism at being shown a map of the world (gēs periodos apasēs) in Socrates’ Pondertorium (Aristophanes, Clouds 206–​209; see Dilke 1985, 21–​31). Although the later development of cartographic coordinates and consideration of the problems of projection would allow maps to render spatial relationships more precisely, they never displaced verbal description as the primary means by which the rich matrix of data could be rendered in a geographic account.

5.  Geography in Historiography: Herodotus and His Successors While Hecataeus pioneered the genre of geographical writing and advanced in some way the practice of cartography, to Herodotus of Halikarnassos goes the credit for uniting geographical and ethnographical interests with historical narrative. Jacoby’s view that Herodotus began his writing career as a collector of geographical and ethnographical information before turning to telling the story of the Persian Wars is no longer widely accepted. Herodotus’ geographical and historical concerns are fully complementary. Despite his criticism of the Ionian logographers, the debt he owes to them is evident. In the Egyptian logos he devotes substantial space to critiquing the speculations of the “Ionians” concerning the division of the continents, the place of the Egyptian delta, and the question of the origin of the Nile (2.15–​17, 20–​24; see Thomas 2000, 75–​101). At the same time, he makes use of their ideas: his famous observation that Egypt is a gift of the Nile is taken from Hecataeus, and his observations about fossils found in high places being evidence of ancient seas may have come from Xanthos of Lydia. Elsewhere (4.36) he attacks prior mapmakers—​presumably the same Ionians—​for their overly schematic rendering of the earth. He implies in several places—​the “map of Asia” (4.36–​40; see above), the description of the Royal Road (5.52–​54), the Satrapy list (3.89–​97), and

Early Greek Geography    207 Xerxes’ army list (7.61–​100)—​that he has access to sources of geographical information on the Persian Empire, although whether his sources are Persian or Greek has long been debated. It is not possible to correlate his descriptions of the Persian Empire exactly with the lists of subject peoples found in Persian royal monuments. Herodotus’ grasp of geographical theory is rudimentary: he is aware of maps and uses cardinal direction indicators, but he does not always render these accurately. He has only a vague idea of meridians and lines of latitude, expressed in the opinion that one place is “opposite” another (e.g., the mouths of the Ister and the Nile, 2.34). His conception of the relationships of places is mostly fully realized in two dimensions; although this is combined uneasily with the older itinerary conception, as in his description of Aristagoras’ map, the Persian Royal Road, Darius’ Scythian expedition, and Xerxes’ expedition to Greece. His one true innovation in geographical thought is his attempt to render distances in objective units of measurements (stades, schoinoi, and parasangs), rather than in itinerary measurements (days’ walk or sail), which had been used by Hecataeus. He calculated distances from itinerary measurements, as he explains in his rendering of the dimensions of the Black Sea (4.85‒6), so his figures are unreliable. Nevertheless, he can be credited with first applying the concept of objective measurements of distance; much in the same way that his chronological calculations, while often wildly inaccurate and based on generational calculations, inaugurated the interest in accurate chronology in Greek history writing. To Herodotus, geography is never an isolated set of concerns, but is tied closely to ethnography and natural history. His description of foreign lands encompasses not only their physical layout but also the nomoi¸ or customs, way of life, and religious practices of their inhabitants. He inherits an  interest in non-​Greek peoples  along with his geographical interest, from Hecataeus. Herodotus tends to emphasize the antithetical aspects of other peoples’ customs—​their contrasts with Greek customs—​ and the marvels (thaumata) of other peoples, including their particularly striking constructions. He also tends to make a link between the lands and the peoples: he is inclined to define regions by the peoples who inhabit them. In a famous statement he defines Egypt as the land inhabited by the Egyptians, and even in his purely geographical passages he also tends to describe places by the peoples who inhabit them. In addition, he expresses an idea, found also in the contemporary Hippocratic Airs, Waters, Places, that the different environments and climates found in different lands shape the characters of the peoples who inhabit them; but those characters can change if the people change lands (Thomas 2000, 86–​100; Isaac 2004, 56–​69). He suggests that the Persians were originally strong because they came from a harsh land. When they came to rule all of Asia, which he and the Hippocratic text associate with luxuriousness and effeminacy, they became weaker. This is part of Herodotus’ explanation for the triumph of the Greeks over the barbarians: Greece, like all of Europe, is a rugged, impoverished land, and so bred tougher men who could withstand the invasion of the weaker Asiatics. At the same time, Herodotus is not enslaved to the concept of geographical determinism: he famously emphasizes the role of nomos, or custom, in shaping human behavior; and so acknowledges that customs can change independently

208   Early Greek Science of geographical influences, as when he tells of Croesus advising Cyrus to forbid the Lydians from wearing weapons, and rather to wear fine clothes, play music, and engage in trade in order to make them docile (1.156). In his relation of details of natural history, he also emphasizes marvels: generally the more fantastic descriptions of exotic creatures are relegated to the remote regions of the earth, although he manages to relate incredible details even when describing phenomena he claims to have witnessed, such as the winged snakes of Arabia (2.75). Because of the heterogeneity of Herodotus’ narrative, his presentation of world geography is far from systematic. He mentions toponymy, physical relationships and features, along with ethnographical and natural history data, in the context of the various logoi that make up much of the first half of his work, as well as in parts of his narrative of the Persian Wars, such as his description of Xerxes’ invasion route. But the information he provides is not always clear, accurate, or relevant to the context in which it is presented. Because of the thematic focus of his narrative, Herodotus has the most to say about the geography of Asia. His account of Anatolia is detailed in the west, unsurprising given the eastern Greek perspective he represents; but it is scantier in the east. He famously underrepresents the distance from the Black Sea to the sea opposite Cyprus, and is unclear regarding the course of the Halys River. He is knowledgeable of the Greek and native settlements around the Black Sea, but in introducing his new system for measuring distances by objective units, badly miscalculates the size of the sea. His account of Skythia and its peoples is both detailed and rigidly schematic (so Hartog 1988); as it shades off into the far north, it becomes increasingly implausible, involving one-​ eyed Arimaspeans and gold-​ guarding griffins (Romm 1992). He possesses some knowledge of the Syria-​Palestine littoral, and he claims to have visited Tyre, but his knowledge of inner Asia, including Mesopotamia, Arabia, and the Persian heartland is somewhat vague, except for a detailed but questionable description of Babylon. He is aware, surprisingly, that the Caspian is an inland sea and knows that the Red Sea connects to the Arabian Sea, but he seems unaware of the Persian Gulf, and he expresses doubt whether this is all part of an encircling Ocean. His knowledge of the eastern Persian Empire, perhaps gleaned from a perusal of the explorer Scylax’s account of his journey down the Indus river, goes only as far as a mistaken notion of the course of the Indus River and a vague conception of a vast desert beyond it. When discussing Africa, Herodotus is most detailed and reliable in reference to Egypt, which he claims to have visited as far as Elephantine (although this has been doubted: see Armayor 1985). To the west, he has some knowledge of Cyrenaica, and of Carthage; beyond that he has scraps of information about the Atlas Mountains, the Moroccan coast beyond the Pillars of Heracles, and the great desert and its tribes. Of sub-​Saharan Africa he can merely report on second-​or third-​hand stories of men of Pygmy stature and a large river in the west, which he supposes a continuation of the Nile (but is, if anything, the Niger). He has heard of the Phoenician circumnavigation of the continent but reserves judgment; although in reporting the detail about the sun being

Early Greek Geography    209 on the right-​hand side, he shows a glimmer of understanding of the relationship of latitude to the apparent position of heavenly bodies. Of Europe he has even less to say. He knows the Mediterranean out to Sicily and has heard Phocaean stories of the kingdom of Tartessus in Spain, but he can’t relate this to his vague understanding of the Celts, the town of Pyrene, or the source of the Eridanus (Po) River. As he turns to the tale of the Persian Wars, Herodotus uses geographical information in the service of his historical narrative and, in some cases, as an explanatory mechanism. He is generally quite familiar with the geography of the Greek world. His battlefield topography can be confused, but he is knowledgeable about Xerxes’ route into Greece, except for some occasional uncertainties. In pointing to the reasons for the failure of the Persian expeditions, he portrays the hubris of the Persian kings as manifesting in the form of transgressions of fundamental geographical boundaries: Cyrus’ crossing of the Araxes River leads to his death; Cambyses’ invasion of Egypt leads to his madness and downfall; Darius’ crossing of the Danube in pursuit of the Scythians ends in failure. These instances presage the great failures of Darius’ and Xerxes’ expeditions, brought on by their transgression of the fundamental boundary between Europe and Asia, made explicit by Xerxes’ hubristic punishment of the Hellespont for destroying his bridge (7.35). In more particular terms, Herodotus displays an understanding of the ways in which insufficient knowledge of topography, leads to the defeat of the Persians. He refers repeatedly to the logistical failures caused by the long march of the Persians, and demonstrates how the Persian ignorance of the topography of Greek locales at Thermopylae, Salamis, and Plataea lead to the delay and defeat of the Persian forces. Descriptive geography continued to be closely associated with historical narrative in the centuries after Herodotus, although it did not always receive the focused attention that it had in the first historian’s work. Thucydides does not demonstrate an interest in geography in and of itself. Most of the events he describes take place in lands familiar to his Greek audience, and his concern is not to introduce a broader view of the world. Only occasionally, when he describes a locale less familiar to mainland Greeks, does he attempt geographical description. In his introduction to the Sicilian expedition (6.1), for example, he notes the general ignorance among Athenians about the size and population of the island; but he only briefly alludes to the island’s size and proximity to the mainland, before discussing in greater detail its early history of settlement. Nevertheless, his narratives of military events in the war incorporate topographical and toponymic details that are generally reliable. While there are notorious problems—​such as the layout of the situation at Pylos—​Thucydides clearly understood the importance of topography in military conflicts. Xenophon, too, assumes a general understanding of Greek geography in the Hellenika, although his approach to the topography of the conflicts he describes is more casual. In the Anabasis, Xenophon purports to render an accurate account of the route of the Cyreans into and out of the heart of the Persian Empire. He follows Herodotus’ lead in giving measures, in both days’ march and parasangs,

210   Early Greek Science of the intervals between various stations on the journey. Xenophon also describes the lands through which the Greeks pass, noting distinctive local features, in particular connections with myth in the outward journey through the familiar lands of Anatolia, and similarly with the return stages from Trapezus along the Black Sea coast. The description of the portion of the journey from Cunaxa to the Black Sea, on the other hand, reads more like an exploratory account, describing various places that Greeks had not previously seen—​although it is written not from the perspective of an explorer but of a military commander with a keen eye for terrain. Xenophon also had an eye—​military rather than ethnographical—​for the details of dress and weapons borne by the various groups the Greeks faced. This is not to say that Xenophon’s description is entirely lucid and accurate: witness the unresolved debate about the exact route of the Ten Thousand, and various disagreements about places mentioned along the way (e.g., the Phasis River, and the site of the trophy erected on first seeing the sea near the Pontic shore). Indeed, Xenophon’s descriptions of landscape, climate, and the ethnography of the peoples the Cyreans encounter are selective and exemplary rather than thorough. Another successor to Herodotus who claimed to use eyewitness testimony to increase the store of geographical knowledge of the larger world was Ctesias of Knidos, a physician who spent time in the Persian heartland as the personal physician of Artaxerxes II. In his work the Persika (Persian Matters) he claimed to “correct” Herodotus on Persian history and customs, but the stories he gathered at the Persian court are more fanciful than those of his predecessor. Although he wrote a work, the Indika, on India, there is little evidence he traveled there; at best, he gathered stories of the lands to the east in the Persian court. Ctesias’ claim to superior knowledge was further undermined by his credulity: he notoriously accepted such fabulous creatures as the martichore, the unicorn, and the sciapod (shadefoot). Ephorus of Cyme (ca 405–​340; Brill’s New Jacoby 70), the first historian to attempt to write a universal history, followed Herodotus in presenting a geographical synthesis as part of a historical narrative. His work was written kata genos, meaning he covered the different regions and peoples of the world separately. He devoted two books of his now lost work to a descriptive geography of the world, arranged periegetically as a tour of lands around the Mediterranean and Black Seas. Ephorus’ cartographical conception was different from, if not necessarily an improvement on, the older Ionian circular map of the world. He was influenced by Democritus of Abdera’s idea that the inhabited world was oblong (Agathemeros 1.1.2, DK B 15). Ephorus portrayed the oikoumenē as a rectangle, bounded by the Celts in the west, the Scythians in the north, the Indians in the east, and the Aithiopians in the south. His rectangular view of the oikoumenē did not take into account the newly conceived idea of a spherical earth (see below). Ephorus continued the traditions of Ionian speculation: he proposed a theory as to the origins of the Nile flood (pointing to the monsoons) and wrote about earthquakes, although he is not recorded as advancing his theory why they occur. His geography was tied closely to ethnography, and like Herodotus, he favored antitheses and wonders.

Early Greek Geography    211

6.  Geography in Scientific Thought: Eudoxus and Aristotle From the time of the Ionian pre-​Socratics, speculation about the shape and size of the earth; the number and disposition of the continents; and geophysical phenomena, such as the creation of deltas, flooding, the appearance of fossils at high altitudes, earthquakes, and later the tides, were of concern to natural philosophers. Herodotus, while dismissing the overly schematic speculations of the Ionians, avidly collected the theories known to him and, in some cases, added his own far-​fetched speculations. Others continued to build the theoretical framework for a better understanding of the structure and layout of the earth. The notion that the world is a sphere is attributed by later sources to the Samian Pythagoras or to Parmenides of Elea in the 5th century bce; the two are also credited with dividing the earth into climatic zones (although Dicks [1970, 51 and 64] is skeptical). Eudoxus of Knidos, of the mid-​4th century bce, applied geometry and astronomy to a better understanding of the earth. He pioneered the creation of the celestial sphere and may have been the first to divide the globe into zones based on the celestial lines, although he did not accurately place the arctic and tropic circles. He supported the oblong oikoumenē of Democritus and Ephorus, making it twice as long as it was wide. He also wrote a seven-​volume Circuit of the Earth (Periodos Ges), which was probably a compilation of data concerning the lands and peoples of the world, not a travel account. In this sense it was not unlike the roughly contemporary Periplous, later wrongly attributed to the early explorer Scylax, which compiled information about the cities and peoples on the coasts of the Mediterranean and Black Seas, as well as the Moroccan coast. In all areas of natural philosophy, Aristotle represents a watershed in the development of Greek thought, not so much for his innovations as for the systematic exposition of theories developed by his predecessors. Aristotle did not write specifically on descriptive geography. Instead, he incorporated his theories about the size and shape of the earth in De caelo (On the Heavens), and included extensive speculations on the causes of geophysical phenomena in the Meteorologica, a work that makes no distinction between astronomical, meteorological, and geophysical questions. He accepted the sphericity of the earth on the basis of his assertion that it must be at rest at the center of the universe, although he also adduces the evidence of the curved shadow seen on the moon during eclipses, and the changing stars viewed as one moves north to south (de Caelo 2.14 [297a9–​298a9]). He gives an excessive figure of 400,000 stades (ca 74,000 km) for the earth’s circumference (de Caelo 2.14 [298a15–​17]); the actual figure is 40,075 km at the equator. He follows Eudoxus in dividing his globe into zones; but he, and several after him, continued to use a celestial arctic circle of ever-​visible stars that shifted with one’s latitude (Meteorologica 2.5 [362a33–​b30]). Aristotle repeats Herodotus’ complaint about people who draw circular maps. Instead, based on his belief that the moderate zone was the only habitable one, he posits an elongated oikoumenē with a proportion

212   Early Greek Science of 5:3; although he notes that the habitable zone could extend all the way around the earth, were it not limited by the Ocean. He also posits the existence of a southern habitable zone, entirely out of contact with the northern one. Elsewhere in the Meteorologica, Aristotle has lengthy discussions of several geophysical phenomena, such as the cause of rivers—​in which he lists the major rivers of the world—​the seas and the creation of land, flooding, and the cause of earthquakes. While his theories are often mistaken—​ particularly in regards to earthquakes, which he credits to escaping gasses—​his attempts to come up with generalized explanations reflect the growing body of knowledge about geography and geophysical phenomena on which he drew. His influence, although baleful on certain points (such as the central place of the earth in the universe), at least inspired his followers to further speculation on the design of the earth. Along with the widened horizons of Alexander’s expedition east and the exploratory journeys in the northern seas of Pytheas of Massilia, these speculations laid the groundwork for the revolution in geographical thought heralded by Eratosthenes, Posidonius, and other pathfinders of Hellenistic science.

Bibliography Anderson, John K. “The Geometric Catalogue of Ships.” In The Ages of Homer: A Tribute to Emily Townsend Vermeule, ed. Jane B. Carter and Sarah P. Morris, 181–​191. Austin: University of Texas Press, 1995. Armayor, O. Kimball. Herodotos’ Autopsy of the Fayoum: Lake Moeris and the Labyrinth of Egypt. Amsterdam: J. C. Gieben, 1985. Blomqvist, Jerker. The Date and Origin of the Greek Version of Hanno’s Periplus. With an Edition of the Text and a Translation. Lund: Liber Läromedel & Gleerup, 1979. Burr, Viktor. ΝΕΩΝ ΚΑΤΑΛΟΓΟΣ. Untersuchungen zum homerischen Schiffskatalog. Aalen: Scientia Verlag, 1961. Crudden, Michael. The Homeric Hymns: Translated with an Introduction, Notes, and Glossary of Names. Oxford: Oxford University Press, 2001. Dicks, D. R. Early Greek Astronomy to Aristotle. Ithaca, NY: Cornell University Press, 1970. Dilke, Oswald A. W. Greek and Roman Maps. Ithaca, NY: Cornell University Press, 1985. Germain, Gabriel. “Qu’est-​ce que le Périple d’Hannon? Document, amplification littéraire ou faux intégral?,” Hespéris 44 (1957): 205–​248. Giovannini, Adalberto. Étude historique sur les origines du catalogue des vaisseaux. Berne: Francke, 1969. Harley, John B. and David Woodward, ed. The History of Cartography I:  Cartography in Prehistoric, Ancient and Medieval Europe and the Mediterranean. Chicago and London: University of Chicago Press, 1987. Hartog, François. The Mirror of Herodotus: The Representation of the Other in the Writing of History. Translated by Janet Lloyd. Berkeley and Los Angeles: University of California Press, 1988. Heidel, William Arthur. “Anaximander’s Book, the Earliest Known Geographical Treatise.” Proceedings of the American Academy of Arts and Sciences 56 (1921): 239–​288. —​—​—​. The Frame of the Ancient Greek Maps. With a Discussion of the Discovery of the Sphericity of the Earth. American Geographical Society Research Series no. 20. New York: American Geographical Society, 1937.

Early Greek Geography    213 Hübner, Wolfgang. “Mythische Geographie.” In Geschichte der Mathematik und der Naturwissenschaften in der Antike. 2, Geographie und verwandte Wissenschaften, ed. Wolfgang Hübner, 19–​32. Stuttgart: Steiner, 2000. Isaac, Benjamin. The Invention of Racism in Classical Antiquity. Princeton, NJ:  Princeton University Press, 2004. Janni, Pietro. La mappa e il periplo:  Cartografia antica e spazio odologico. Rome:  Bretschneider, 1984. Kaplan, Philip. “The Function of the Early Periploi.” The Classical Bulletin 84 (2009): 27–​46. Leaf, Walter. Troy: A Study in Homeric Geography. London: Macmillan, 1912. Luce, John V. Celebrating Homer’s Landscapes: Troy and Ithaca Revisited. New Haven, CT: Yale University Press, 1998. Richardson, Nicholas, Three Homeric Hymns: To Apollo, Hermes, and Aphrodite. Hymns 3, 4, and 5. Cambridge: Cambridge University Press, 2010. Romm, James S. The Edges of the Earth in Ancient Thought: Geography, Exploration, and Fiction. Princeton, NJ: Princeton University Press, 1992. Stokes, Michael C. “Hesiodic and Milesian Cosmogonies-​I.” Phronesis 7 (1962): 1–​37. —​—​—. “Hesiodic and Milesian Cosmogonies-​II.” Phronesis 8 (1963): 1–​34. Thomas, Rosalind. Herodotus in Context:  Ethnography, Science, and the Art of Persuasion. Cambridge and New York: Cambridge University Press, 2000. Thomson, J. Oliver. The History of Ancient Geography. Cambridge:  Cambridge University Press, 1948. Visser, Edzard. Homers Katalog der Schiffe. Stuttgart & Leipzig: B.G. Teubner, 1997. West, Martin L. The East Face of Helicon: West Asiatic Elements in Greek Poetry and Myth. Oxford, New York: Clarendon Press, 1997.

chapter B4

Hipp o crates a nd E a rly Greek M e di c i ne Elizabeth Craik

1.  Primary Sources. The Hippocratic Corpus and Other Evidence The principal primary sources for early Greek medicine are contained in the treatises of the Hippocratic Corpus; although the association of its contents with the historical Hippocrates, celebrated doctor and medical writer of the 5th century bce, is tenuous: the writing styles and medical knowledge are too diverse to belong to one author or even to one region or one century (see Craik 2015, and the Bibliographic Survey at the end of this article). The nature of this large and disparate body of texts, some 70 in number, and collectively comprising the largest extant body of Greek prose, is fully discussed in section 3. The works of the Corpus are all anonymous; there are no dedicatees and very few references to contemporaries (only to Empedocles in On Ancient Medicine, and to Melissus in On the Nature of Man). However, from other sources we know the names of many early Greek doctors, to add to the name of Hippocrates. Important information on medical ideas that were current in the 5th and 4th centuries bce is found in a papyrus dating from the 2nd century ad, conventionally known as Anonymus Londinensis. Despite this late date, the ideas seem derived, at least to some extent, from a history of medicine compiled by Aristotle’s pupil Menon. The clumsy name arises from its location in London and its anonymous character. The discovery of the papyrus was announced at the end of the 19th century; it was edited soon afterward, and there is an accessible commentary (Kenyon 1892; Diels 1893; Jones 1947). In this compilation, devoted in large part to a summary of different views of the aetiology of disease, 24 doctors are named. Those named include Hippocrates, and many figures previously unknown and several—​including Plato—​known to us not as medical but as philosophical writers. Among the latter are many Pythagorean thinkers, such as

216   Early Greek Science Philolaus. This brings us to another important collection of primary source material, the fragments of the so-​called pre-​Socratic philosophers, whose investigations of physis (nature) embraced the nature of the body and the nature of the universe (Diels and Kranz 1952; Huffman 1993). These thinkers are further discussed in section 2. The word “fragments” is sadly recurrent in accounts of early Greek medicine. Diocles of Carystus in Euboia and Praxagoras of Kos, for instance, are important figures, much cited in antiquity, but we can only guess at the detail of their thought from the chance content of scanty surviving material, which is hard to reconstruct and contextualize. Much painstaking and challenging work is demanded of scholarly editors, first to determine which references and citations are to be regarded as genuine, and then to interpret their content (van der Eijk 2000–​2001; Steckerl 1958). By contrast, we can see that Plato and Aristotle both had extensive medical interests:  here, the problem is to extract the medical material from a large body of nonmedical work and to explain its significance. As noted, Plato is described as a doctor in the Anonymus Londinensis. There the dialogue Timaeus is summarized: that work does indeed contain—​embedded in much mystical content—​an account of human bodily development and of human physiology in health and sickness. Similarly, Plato’s depiction of the doctor Eryximachus in Symposium is realistic and knowledgeable, though not entirely sympathetic. Relations between doctors, sophists, and the philosophical schools were evidently complex, and these categories overlapped. The brother of the celebrated rhetorician Gorgias was a doctor. Aristotle was the son of a distinguished doctor, and much in his biological writing meshes with contemporary medical research on embryology, respiration, and other topics; even his writing on rhetoric and literature is imbued with medical imagery and allegory. More specifically, medical questions are addressed in question-​and-​answer format in the Aristotelian Problemata (Craik 2001, 2006a; Oser-​Grote 2004 is a useful collection of testimonies). Literary sources can be supplemented by epigraphical evidence. Many inscriptions recorded on stone stelai (columns) praise doctors and promulgate thanks for their assistance to local communities, especially in circumstances where they were disinterested enough to waive the usual fees. Further, there is a large body of inscriptions recording miracle cures occurring in temples of Asclepius. As a corollary, there are extensive collections of votive offerings expressing gratitude for such divine intervention (Edelstein and Edelstein 1945 is still the standard work on the cult of Asclepius). The archaeological evidence afforded by instruments used by ancient doctors is an important adjunct to written materials. There is copious evidence in such finds, most notably for the specialized practice of ophthalmology (Majno 1991 is a very accessible survey). That there was some interaction between secular and sacred medicine is suggested by the presence in the same places—​Kos, Epidaurus, and, later, Pergamum—​of healing shrines and medical traditions. Hippocratic medicine has been viewed by some scholars as a rational and scientific movement; by others as an amalgam of elements, not excluding religion and superstition. Divine and human ways of healing were less distinct than might appear at first sight: the medical (professedly rational) and mantic (apparently irrational) traditions continued to coexist. Apollo, god of prophecy, was also god

Hippocrates and Early Greek Medicine    217 of healing before this became the special province of his son Asclepius, who was born of a mortal woman but later regarded as a divinity. Medical prognosis—​foretelling the outcome of illnesses—​shares some characteristics—​including some fundamental elements of terminology—​with the activities of oracular shrines—​foretelling the outcome of mundane activities (Lloyd 1979; Langholf 1990; Longrigg 1993; Laskaris 2002).

2.  Secondary Sources: Intellectual Ambience, Origins, and Development of Greek Medicine We may begin with Homer (c. 800 bce), the fons et origo for so many aspects of Greek thought. According to Homer, the first teacher of medicine was Cheiron the centaur, who is represented as a just and wise culture-​hero, originator not only of medicine but also of many other technai (crafts). It was Cheiron who gave instruction on medicinal plants to Asclepius, who in turn conveyed this knowledge to his sons Machaon and Podalirius. According to the Catalogue of Ships (Iliad 2.729–​733), Cheiron and the sons of Asclepius, doctors of the Greek troops at Troy, came from the region later known as Thessaly. And according to early mythical traditions, King Eurypylus of Kos originated from Thessaly. Already we see that it is on the fringes of the Hellenic world that medicine appears to be most flourishing. Thessaly (where Hippocrates died), and Kos (his birthplace) were regions of enduring importance in the history of Greek medicine. The origins of Greek anatomy and physiology lie in the Iliad, where an extensive knowledge of the effects of battle wounds on the form and function of different bodily parts is evident. Much terminology later regarded as technical is found already in epic verse. In the ensuing literary tradition (for instance, in Attic drama), a similar easy familiarity with such terms is apparent; conversely, in the ensuing scientific tradition (notably, for instance, in anatomical description), poetic expression and modes of thought, such as descriptive use of simile and analogy, persist. The 5th century saw the development of medicine into a self-​conscious technē (craft or science), and with it the origin of the enduring reputation of Hippocrates. Galen has been influential in shaping our view of the Hippocratic phenomenon and of early Greek medicine generally, despite the centuries that distance him from the classical period. Galen’s slanted presentation of Hippocrates as his paradigmatic predecessor in the medical profession influenced the entire later tradition (Smith 1979 is a seminal study). In a passing comment, Galen famously declared, “In the old days, there was great rivalry between the doctors of Kos and of Knidos. . . . They were joined by the doctors from Italy: Philistion, Empedocles, Pausanias and their followers. There were these three bands of doctors competing with one another. The Koan group had most and best, but the Cnidian came close and the Italian too was of considerable account” (de methodo medendi 1.1, 10.5–​6 K.).

218   Early Greek Science Galen’s view that there were choroi (bands or schools) of doctors in different regions was taken seriously, and much 20th-​century scholarship was devoted to attempts to isolate differences between Koan and Cnidian medicine in particular. However, although there seem to be traces in the Hippocratic Corpus of works emanating from these two regions (the extant work Koan Prognoses, an extensive and important aphoristic collection, and the lost Cnidian Opinions, mentioned only in allusive polemic in Diseases 2), the differences once postulated—​such as that Kos was concerned primarily with treatment of the sick and that Knidos was concerned with tabulation and description of disease—​have proved hard to substantiate (Jouanna 1974 and Grensemann 1975 were pioneering works; Thivel 1981 provides a skeptical view). The Roman writers Celsus and Pliny, who like Galen had access to many texts now lost to us, stressed rather the western element in medical traditions, as represented by Pythagoras and Empedocles. Herodotus, who was a contemporary of Hippocrates, is completely silent on the subject of Coan and Cnidian medicine, but he was emphatic that the best medical practitioner was Democedes of Croton (in south Italy); and that Croton, enhanced by him, was the foremost medical center; Cyrene (on the Libyan coast) came second (Herodotus 3.125, 131–​132). It was undoubtedly at Croton and in other regions of the west Greek world, such as Sicilian Syracuse, that attempts at systematic description of the organization and working of the body began in the early 5th century. On the fringes of the intellectual movement associated with Pythagoreanism, Alcmaeon of Croton examined and described the internal structure of the eye and the ear, making deductions about sensory perception through links to the brain, and Empedocles of Acragas in Sicily wrote in a visionary fashion of digestion (regarding blood as an agent of nutrition) and of respiration (arguing that breath served to cool innate heat). In the east, at around the same time, Diogenes of Apollonia essayed an account of the vascular system, detailed and reasoned in content; while in Thrace, to the northeast of the Greek mainland, Democritus of Abdera formulated a wide range of scientific and medical theories on topics including conception and embryology. Though little of his output has survived, and that only in fragmentary or derivative tradition, Democritus was a prolific writer. It is remarkable that many of his works seem to have had titles the same as, or similar to, several transmitted in the Hippocratic Corpus:  works on the nature of man, on flesh, on humors, and on dietetics. Democritus drew primarily on scrutiny of animals such as dogs, pigs, goats, and sheep for his findings. The anatomical views of Democritus may have been particularly influential on Hippocratic writers, who similarly depended on information from animal sources. The concept of comparative anatomy scarcely surfaced; for the most part it was assumed—​as it was by early modern medical writers—​that the anatomy of humans could be illustrated from that of other animals. Aristophanes in the comedy Clouds (the first version was produced in 423 bce) parodies intellectual doctor-​scientists. In the 5th century, writers who might now be classified as scientists, philosophers, or sophists were not clearly differentiated from medical theorists and practitioners: all were concerned with a quest for “beginnings”

Hippocrates and Early Greek Medicine    219 and with an exploration of “nature.” Often these words are nearly synonymous: many treatises are entitled simply On Beginnings or On Nature. Alcmaeon’s book on nature was said to embrace both medicine and natural philosophy, and Protagoras’ book on origins probably considered the human condition. The nature of man might be regarded as the theoretical (elemental) composition of the body or its practical (anatomical and physiological) constitution or even its social function. Concern with such topics exercised the intelligentsia generally: Prodicus, famous as a pedantic philologist, wrote a work on the nature of man, and Epicharmus, a comic dramatist, wrote also on veterinary medicine. The relationship between the work of these scientists, glimpsed in the surviving fragments of the pre-​Socratics and the works surviving intact in the Hippocratic Corpus, is complex. However, certain shared ideas are recurrent. There is, for example, a predilection for opposing principles, for parallel pairs such as hot and cold, wet and dry, thick and thin, rare and dense, rest and motion; and there is a concern for the relation of microcosm to macrocosm, of human life to the universe. In medical terms, health is commonly seen as a balance of opposing principles; thus, excessive cold or excessive heat may upset the balance of the body. Theories explaining physical function and malfunction are based on the same premises as conjectures on cosmological phenomena and expressed in similar language (Lloyd 1966). It has become conventional to look to the east for influence on early Greek civilization. The debt of Homer to the east is now generally acknowledged. In material culture too, influences are readily traceable. Medicine, too, may have drawn ideas from other regions—​both to the south and to the east of the Greek mainland. The existence of similarities between different medical systems is suggestive but not necessarily significant. There are obvious methodological problems, especially where material from different eras is compared. Caution is required. Egyptian medicine surely exerted an influence on early Greek medicine; indeed, there are traces of this in Homer. Homer mentions Egypt as a source of pharmaka (drugs) (Odyssey 4.227–​228). In the Hippocratic Corpus there is reference to Egyptian, Libyan, and Ethiopian specifics. Egypt was familiar to the Greeks in the 7th century, when mercenaries served under the pharaohs, and there were Greek and Carian settlers. There was a flourishing trade in grain and other goods between Greece and Egypt. Cyrene, named by Herodotus as a significant medical center, may have played a part in the dissemination of knowledge from Egypt to Greek lands:  to Italy through Sicily and to Kos and Knidos through its mother city Thera. The importance of Cyrene as a medical center is corroborated by its place as the center of trade in the rare healing plant silphion, depicted on coins of the region (Theophrastus, Historia Plantarum 4.3.1, and also 9.1, 9.4, 9.7). Like Kos and Epidaurus, it was a center, too, of Asclepius worship (Craik 2005). That many intellectuals knew Cyrene well can be seen from the patronage enjoyed by the lyric poet Pindar (Pythians 4 and 5). Surviving papyri from Egypt indicate specialist interests in ophthalmology (Ebers Papyrus, ca 1500 bce) and gynecology (Kahun Papyrus, ca 1820 bce). There is much stress also on remedies for the gastrointestinal tract, especially the use of purgatives. In

220   Early Greek Science Places in Man, which is probably one of the earliest Hippocratic works, all these aspects are paralleled, both in general approach and in points of detail; and other treatises too show markedly similar elements in gynecological and ophthalmological content (Craik 1998). In the Ayurvedic medicine of India, as in early Greek speculation on physis (nature), microcosm and macrocosm are viewed as parallel. A central Ayurvedic doctrine is that of three doṣas: these are physiological substances that course through the body in a functional equilibrium dependent on a dynamic fluctuating interplay; disease results when their balance is disturbed. In some schemes, there is a fourth dosa, blood. The Ayurvedic dosas (vata, pitta, and kapha) have Greek analogues and similarities to the humors of Greek medicine. Or rather two evidently do; the third is more elusive. Pitta has the characteristics of Greek bile (hot, fluid, acrid); kapha has the characteristics of Greek phlegm (cold, stable, oily). Vata, usually translated “wind” (clear, dry, moving), might be aligned with Greek pneuma or psyche (breath or vapor) drawn into the lungs. In some Greek medical works, wind plays an important part. The first part of the work usually translated as Airs, Waters and Places treats the importance of environmental factors in health and disease. The second part sets out to discuss characteristics of the inhabitants of “Asia.” The two parts are generally viewed as disparate; but perhaps oriental ideas may be viewed as a unifying factor. The conjunction may be explained if the treatise is drawing on oriental source material: obliquely in the first part where climate and air (~ vata) feature and more directly in the second, on the subject of comparative anthropology. In the work usually translated as On Winds or On Breaths (physai) wind or breath (variously physa, aer, or pneuma) is a fundamental principle with a pervasive place both as an indicator of health and as a morbific factor. On Winds is a treatise of unusual content in its affirmation that all diseases are caused by “winds” or “breaths,” affecting the body or the atmosphere. As this view resembles that apparently attributed to the historical Hippocrates in the Anonymus Londinensis, the work has some claim to be considered truly Hippocratic. There is similar stress on wind in Plato’s Timaeus, already noted above (Filliozat 1949 is an original voice; Valiathan 2003, 2007, and 2009 contain much valuable information, clearly presented; Horstmanshoff and Stol 2004 is a useful collection). Perhaps we may look still further to the east: beyond India to China. A central similarity between traditional Chinese medicine and early Greek medicine can be seen in the application of cutting (phlebotomy or acupuncture) and cautery (heat applied by instruments or by moxibustion) to particular parts of the body, viewed as channels or ducts, the purpose being to rid the body of noxious matter and thus disease. Both the Hippocratic physicians and Chinese practitioners viewed anatomical structures and orifices in terms of the vessels or channels supposedly linking them to one another and to other areas of the body. Greek phlebes and Chinese mo are significant in physiology (normal—​carrying blood and pneuma analogous to qi) and pathology (abnormal—​ carrying noxious matter). More specifically, the Chinese du channel (governor vessel) from the spine to the back of the head, carrying the life force, is similar to that of the Greek vessel carrying vital myelos, or cerebro-​spinal fluids (Lloyd 1996 offers magisterial coverage; Craik 2009a presents in-​depth treatment of a particular parallel).

Hippocrates and Early Greek Medicine    221 Such similarities may be put down to coincidence or to the common result of shared medical concerns. But there were considerable contacts and opportunities for transmission of ideas. It is known from the case histories detailed in the Epidemics that Hippocratic physicians practised on the fringes of the Greek peninsula:  in regions to the north such as Thessaly, Thrace, and the island of Thasos; and also in regions to the east, including such cities as Cyzicus on the Asiatic side of the Propontis (Sea of Marmara). The most far-​flung case recorded is at Odessa on the western shore of the Black Sea (modern Bulgaria). Many of the cities mentioned in the Epidemics had a flourishing trade, exporting timber, grain, dried fish, and various luxury goods to the Greek mainland. It is reasonable to suppose that ideas traveled these trade routes along with merchants and their goods. The Black Sea region is contiguous to the regions inhabited by the Scythians, a nomadic people with a wide-​ranging habitat. Contact between the continents and the cultures, with such nomadic peoples as intermediaries, is surely a possibility. It is certain that Hippocratic doctors had access to medical specifics unavailable in Europe, sourced not only from Egypt (noted above) but also from the Far East. Cinnamon and other spices are mentioned quite casually. Although some scholars have assumed that Greek knowledge of India began with Alexander’s expeditions, it may be that he opened routes already partially known. It is possible to name individuals who moved freely between the continents, among them the medical man Democedes, so celebrated according to Herodotus. Democedes’ career can be reconstructed: powerful patronage took him to the court of Darius in Persia and to Polycrates in Samos. That there were routes from east to west—​which might be covered by contiguous stages, rather than encompassed in a single journey—​is evident from the presence of scraps of silk in Egypt and Europe long before our first written sources allude to it. We may wonder if it is a coincidence that Kos, home of Hippocrates and center of Greek medicine, became a center also of sericulture.

3.  Hippocrates and the Hippocratic Corpus Hippocrates, doctor and medical writer, was born on the island of Kos in or around 460 bce and spent part of his life in Thessaly, where he died in Larissa at an advanced age. Only these facts are certain—​and even these not completely so. And yet this shadowy figure came to be regarded as the “father of medicine.” In part this is because of a Greek tendency to identify and idealize a protos heuretes (first finder, or inventor) for all human activities and achievements, especially for all arts and crafts; in part it is a matter of timing, as the life of Hippocrates spanned the 5th century when Greek civilization flourished; in part doubtless a certain truth underlies the myth of Hippocratic achievements and distinction.

222   Early Greek Science The evidence for the life of Hippocrates is like the evidence for the lives of many other important figures of Greek antiquity: firstly, scanty scattered references in contemporary or near-​contemporary writers (in this case, in the comic poet Aristophanes and the philosopher Plato); secondly, biography of a sketchy and unreliable sort, from a much later period; thirdly, a collection of letters, allegedly written by or to him but apparently invented by adherents and admirers, also much later (Pinault 1992 presents and discusses the biographical evidence; Smith 1990 presents and discusses the letters and related texts). From the first category we can see that already in his lifetime Hippocrates was celebrated as an outstanding teacher and an authoritative writer, paradigmatic of the medical profession. This is evident from exchanges in Plato’s Protagoras, which has a dramatic date of 440–​430 bce and in Phaedrus, similarly dateable to before 415 (Protagoras 311b; Phaedrus 270c). In addition, parody of the Hippocratic Oath in Aristophanes’ Thesmophoriazousae (270–​274), produced in 411 bce, suggests a general familiarity in Athens with Hippocratic ideas and practices. Some 50 years later, an incidental reference to Hippocrates made by Aristotle confirms that he was viewed as a highly prestigious figure (Aristotle, Politics 7.4, 1326a15–​16). The second and third categories contain much anecdotal information; some of this may be accepted with due caution, but some is not believable. For example: Hippocrates was taught medicine by his father (very plausible); Hippocrates was a pupil or follower of the rhetorician Gorgias and/​or of the scientist-​philosopher Democritus (plausible); Hippocrates was called in to treat Democritus when people thought Democritus had gone mad (implausible); Hippocrates burned down the temple of Asclepius on Kos after making records of the temple cures there (very implausible). There are four short vitae extant—​three in Greek (one attributed to Soranus of Ephesos, a medical writer specializing in gynecology; one in the Suda; and one by Tzetzes) and one in Latin (in a 12th-​century anonymous treatise entitled Yppocratis genus, vita, dogma). The material of the spurious letters, which are colorful and elaborate in slant, overlaps with that of the vitae. The text of an Attic decree, preserved among the letters, honors Hippocrates for a visit to Athens, allegedly made at the time of the great plague (early in the decade 430‒420); both decree and visit are usually judged apocryphal. A salient common feature of the biographical tradition is that Hippocrates is designated “Asclepiad,” literally “descendant of Asclepius.” In old established usage, this term meant simply “doctor” and indeed, as we have seen, the Homeric doctors Machaon and Podalirius were presented as sons of Asclepius. The 6th-​century poet Theognis makes incidental use of the term “Asclepiad” in a general sense (Theognis 432). However, persistently repeated genealogies in the biographical tradition make Hippocrates a literal descendant of the god, variously 17th or 19th in a direct line. The fabricated chronology is evidently based on a calculation of the time between the fall of Troy (typical ancient estimate, 1140 bce) and the birth of Hippocrates (typical estimate, ca 460 bce):  by allocating the date 1140 to Podalirius and 460 to Hippocrates, and by allowing the duration of a generation to be (as was conventional) 40 years, we find that Hippocrates is, on inclusive reckoning, 19th in line from his putative divine ancestor. The names given in the genealogies for Hippocrates’ immediate family are father Heraclides, grandfather

Hippocrates and Early Greek Medicine    223 Hippocrates, sons Thessalus and Dracon, and an unnamed daughter who married a doctor, Polybus. This nomenclature is plausible enough:  the names Thessalus and Dracon are attested in use at Kos as early as the 4th century. Polybus was regarded as the author of certain Hippocratic works, the treatise On the Nature of Man being attributed to Polybus by Aristotle (Historia animalium 3.3, 512b12–​24). Hippocrates came to be imbued with the divine aura of his supposed progenitor Asclepius. Soon after his death, Hippocrates was elevated to heroic, or semidivine, status and honored by the performance of sacrifices. The honor of heroization was accorded to very few 5th-​century figures. Among those few was the tragic poet Sophocles, who had a peculiar association with Asclepius. According to a well-​established ancient tradition, Sophocles was heroized after his death and given the title Dexion (cognate with a common Greek verb connoting “receive”) because, when Asclepius’ cult was introduced to Athens, he “received” the god in his house; he “took over the priesthood of a deity who was associated with Asclepius and with Cheiron” (Radt 1999 treats the testimonia: Vita Sophoclis 11 and 17; Etymologicum Magnum s.v. Dexion). An associative aura seems to have extended to physicians in general: a Hellenistic inscription from Kos records that doctors, evidently a cohesive group with its core in kinship, continued to receive particular honors and were entitled, along with priests and other dignitaries, to receive special cuts of meat at state sacrifices (SIG 1026). As mentioned, the Hippocratic Corpus comprises some 70 treatises, heterogeneous in character. All are written in the Ionic dialect. How are we to classify this vast and multifarious body of material? The first to attempt classification was the lexicographer Erotian, who lived in the age of Nero—​or, rather, the classification of Erotian is the first we can see clearly: the extent of his debt to certain predecessors (such as Bacchius 3rd century bce, whom he cites frequently) is debatable. The Hippocratic Corpus as recognized and addressed by Erotian is almost, though not entirely, coincident with that recognized today (Nachmanson 1917, 1918). Erotian’s classification is subject to the same constraints as all later attempts at classification: since many of the works are very mixed in character and resist neat pigeonholing, their multifarious content militates against their being placed squarely in a single division. Yet Erotian’s organization is intelligent. It prefigures both the modern physician’s classification of subjects in medical textbooks and the modern philologist’s classification of works on a generic basis. Erotian begins with works on signs, that is prognostic signs, a subject of fundamental importance in ancient theories of pathology (Prognostic; Prorrhetic 1 and 2; On Humors); then continues with works on aetiology and nature, equally fundamental to ancient views of physiology and anatomy (On Winds; On the Nature of Man; On the Sacred Disease; On the Nature of the Child; Airs, Waters and Places). These first two categories make up an overarching approach to the basic theories of medical practice and correspond broadly to the modern doctor’s divisions of knowledge under the heads of anatomy, physiology, and pathology. At the same time, the content of these categories corresponds broadly to the content of “handbooks” in modern generic terms. But these works are not merely handbooks; simply, among other things, they fulfill a purpose similar to that of the modern handbook. Thus, no work is devoted

224   Early Greek Science exclusively to anatomy, but anatomy is introduced where appropriate to topics addressed. Thirdly, Erotian goes on from the theory that underpins medical practice to the practice itself; that is, to the therapy which is based on the theory. This he subdivides as on the one hand “surgical” (On Fractures; On Articulations; On Sores; On Head Wounds; On the Surgery; Mochlicon; On Haemorrhoids; On Fistulae) and on the other hand “dietary” (On Diseases 1, 2; On Regimen in Acute Diseases; On Places in Man; On Diseases of Women 1, 2; On Nutriment; On Infertile Women; On Use of Liquids). Once again, his classification corresponds to modern generic designations. These works are, in modern terms, “instruction manuals.” In many cases a set of instructions is clearly given, steps in a procedure being prefaced by words signifying “then,” “next.” Fourthly, Erotian allows for a small group of works mixed in character (Aphorisms; Epidemics). Erotian’s fifth and final category comprises works on the technē (craft) of medicine (The Oath, The Law, On the Art, On Ancient Medicine). The works of this final category might be viewed in generic terms as “manifestos.” This early attempt at classification might be refined and revamped in various ways. But major topics such as anatomy, physiology, pathology, therapy, and ideology are recurrent in modern attempts to isolate and categorize the main types of material addressed. An important topic not separately recognized by Erotian is gynecology, although a large fraction of the Hippocratic Corpus is devoted to gynecological topics—​primarily to pregnancy and fertility treatment (Dean-​Jones 1994 and King 1998 are valuable works on Hippocratic gynecology; Totelin 2009 discusses the evidence for and nature of recipe cures). Erotian subsumes those gynecological works that he does include in his lexicon under the heading of dietary treatment, doubtless because recipe cures feature so prominently in the gynecological texts. But it may be reiterated that many works might be placed in more than one category. In particular, Erotian’s “mixed” category might be considerably extended. In his major edition produced in the 19th century, Littré classified the treatises according to his own, at times subjective, view of Hippocratic authenticity and relative dating. Littré’s important categorization was justly influential but unfortunately resulted in protracted neglect, complete or comparative, of several of the many works he had regarded as unimportant and accordingly had relegated. In the long Hippocratic tradition, particular works—​and indeed particular passages or even phrases of particular works—​have tended to be privileged. On Ancient Medicine has come to be regarded, without particular reason, as quintessentially Hippocratic. Similarly, the statement in On the Sacred Disease that epilepsy is no more “sacred” than any other disease has been unjustifiably regarded as a radical blanket rejection of all irrational medical method; on the contrary, rational and irrational methods continued to exist in the time, and in the writings, of Galen. Littré accorded a preeminent place to On Ancient Medicine, the only work printed, following a long and judicious general introduction, in the first of his nine volumes. Littré’s “first class,” devoted to supposed “writings of Hippocrates” included also Prognostic; Aphorisms; Epidemics 1 and 3; On Regimen in Acute Diseases; Airs, Waters

Hippocrates and Early Greek Medicine    225 and Places; On Articulations; On Fractures; Mochlicon; The Oath; and The Law. The second class comprised works attributed to Polybus, son-​in-​law of Hippocrates (On the Nature of Man; On Regimen in Health). The third comprised works regarded as pre-​ Hippocratic (Koan Prognoses; Prorrhetic 1). The fourth comprised works attributed to the “school” of Kos and to supposed Hippocratic contemporaries or pupils (On Sores, On Fistulae, and On Haemorrhoids; On Winds; On Places in Man; On the Art; On Regimen 1‒4; On Affections; On Internal Affections; On Diseases 1‒3; On Seven Month Birth and On Eight Month Birth). The fifth comprised works Littré regarded as mere extracts or notes (Epidemics 2, 4, 5, 6, and 7; On the Surgery; On Humors; On Use of Liquids). The sixth comprised treatises he viewed as the work of a single author and forming a particular group in the Corpus (On Generation; On the Nature of the Child; On Diseases 4; On Diseases of Women; On Diseases of Girls; On Infertile Women). The seventh a treatise perhaps by Leophanes (On Superfetation). The eighth comprised treatises that for various reasons—​mainly relating to advanced anatomical knowledge—​were to be regarded as late (On the Heart; On Nutriment; On Flesh; On Sevens; Prorrhetic 2; On Glands). The ninth comprised a mixed bag of fragments or compilations (including On Anatomy; On Dentition; On the Nature of Woman; On Excision of the Fetus). The tenth comprised works mentioned in antiquity but are now lost. The eleventh comprised apocryphal pieces such as the Letters. Littré’s analysis differs completely from that of Erotian in its stress on estimates of authenticity and chronology. Erotian made only one such judgment: on the dubious authenticity of Prorrhetics; the reference may be to both or to only one of the works with this title. However, like the classification of Erotian, it too is visionary in many ways. A few aspects may be singled out. Of the first class, Aphorisms had long been a key element in the view of Hippocratic wisdom held by practising physicians:  edited, translated, and cited more than other texts, it had acquired a canonical status. Littré correctly distinguishes between Aphorisms and Koan Prognoses, although the two compilations are alike in form, both comprising lengthy collections of disjointed sayings, conveying useful information for the doctor. The content of the latter is somewhat more restricted, dealing primarily with prognostic guidance, though this relates to a wide range of diseases and conditions; it is also more clearly organized by subject matter. There is some overlap in content, but differences in vocabulary and modes of expression suggest that the collections had different origins; Koan Prognoses is, as Littré clearly saw, closely related to Prorrhetic 1. There is an obvious distinction to be made between the collections of disjointed observations, such as those found in the various aphoristic collections, and the coherent and reasoned compositions such as those presented in On Ancient Medicine and On Winds; and again there is an evident distinction between a short work such as The Oath, which can be described as a professional manifesto, and a short work such as Mochlicon, which is a derivative compilation, summarizing the content of On Fractures and On Articulations. Yet Littré regarded all of these works as Hippocratic. A recurrent problem in addressing the question of authorship (now somewhat unfashionable in Hippocratic scholarship) is the complex intertextuality that marks the tradition. Passages are

226   Early Greek Science repeated, sometimes with minor variations, in different works. Modern study of orality and literacy has focused on such aspects. At the same time, the modern tools of lexicon and concordance have facilitated identification of repeated passages. The aphoristic texts, in particular, mesh with other Hippocratic material, especially material in the Epidemics. For instance, On Humors, a collection of miscellaneous aphorisms on signs and symptoms to be observed by the physician, with particular attention paid to the nature of body fluids and evacuations, and to signs which indicate medical crisis, records case notes overlapping in content with Epidemics 6. And two short aphoristic works unequivocally regarded as “late” by Littré, but containing some material replicated elsewhere in supposedly “early” works, are On Dentition and On Nutriment. These collections differ greatly. The former is a set of 32 aphorisms, concise in expression and condensed in content, relating to feverish illnesses besetting infants at the time of teething. The second is a collection dealing with the importance of nourishment to all parts of the body in a style that is contorted, with much riddling antithesis in the manner of the pre-​Socratic thinker Heraclitus. There are a few extreme cases of intermingling material. Perhaps significantly, two of these relate to anatomy, a fundamental and probably much rehearsed topic. On Bones, which despite its title—​probably drawn from the first words, bones being the subject of the first section—​deals with the blood vessels and presents various views of the vascular system. Different parts of the treatise can be traced to different sources (Harris 1973; Duminil 1998). On Anatomy, a very short piece, comprising a single page in the modern printed text, is an account, with some reference to comparative anatomy, of the internal configuration of the human trunk. It seems to be a late pastiche, incorporating material both from Hippocratic sources and from the work of Democritus (Craik 2006b). By far the most celebrated text in the Corpus is The Oath (all aspects of The Oath, with emphasis on reception, are discussed in Jackson 1996). The Oath articulates medical concerns and medical ethics in a way generally regarded as timeless: it is much cited for its treatment of the perennial problem of medical confidentiality and perennial concern of respect for patients, and for its firm stance in opposition to abortion and euthanasia. It is no surprise to find The Oath elevated to the first class by Littré; it is perhaps more surprising that The Law, which has attracted much less general attention, goes up with it. The Law, however, is properly linked with The Oath, both for its content and for its character—​and probably also its date. Debate on the technē of medicine centers on the qualities required for medical expertise and understanding: innate ability, proper instruction, and diligence. There is an allusion to the peripatetic nature of the profession and to the “sacred” character of its knowledge. Other deontological works Decorum and Precepts are now generally treated as “late,” probably rightly; but, at the same time, they seem to incorporate “early” material and to echo debates of the 5th century on the relative value of nature and nurture. Thus the author of Decorum argues that personal “nature” is necessary for progress in “crafts,” as “the needful in skill and craft cannot be taught.” Overall, the passage seems to be a diatribe against would-​be educators who place their reliance on words alone—​it is a sign of ignorance and lack of professionalism to think and not to act; speech that arises from

Hippocrates and Early Greek Medicine    227 taught action is good; clever speaking without action is bad. A series of oppositions is implicit: nature ~ education; practice ~ theory; action ~ reflection; doing ~ speaking. Similar oppositions can be seen in Precepts: nature can be stirred and “taught” by multitudinous multifarious things. The description in Decorum of men motivated by “base, venal and disreputable concerns,” “working the agora,” and “traversing cities” might be applied verbatim to the 5th-​century sophists; further, the description of the reactions of the populace to such people—​a progress from youthful enthusiasm to adult embarrassment and finally, in old age, to such bitterness that they legislate for their expulsion from the city—​is very apt to their followers. Similarly, the disparaging remarks in Precepts attacking display in flowery lectures recall Plato’s strictures against such sophists as Prodicus; “experience” is more useful than “opinions.” The writer of On Fractures and On Articulations, deeply imbued with the same ideas and debates as those traced in the deontological works, cleverly situates medical writing in the context of contemporary controversy and seems to capitalize on popular prejudices to enhance his reputation. On Fractures begins with polemical criticism of over-​contrived or know-​all doctors who go wrong through their preconceived theories: they fail to observe the natural correct position of the limbs, and, despite their reputation as “wise,” they should be considered “ignorant.” In the ensuing content, there is frequent use of such derogatory terms. In both On Fractures and On Articulations the term “just” is used for “natural” or “proper” with regard to the position of the bone or limb prior to accident, and treatment is described by the same adjective, “just,” “in the right way.” There is a suggestion of moral superiority; it is notable that some two-​thirds of the occurrences of the adjective in the Corpus appear in On Fractures, On Articulations, and Mochlicon. Our writer knows what is “just,” while inferior practitioners, despite their claims, are “sophistic” and ignorant. In the era of sophistic teaching, clever speech came to be regarded as incompatible with just action. On Fractures and On Articulations (and with them Mochlicon, which comprises a summary of these related works) are highly technical in content and so little read today by philologists, few of whom have had any medical training. But no one would dispute the claim of these treatises to a place in the top rank. Galen devoted the first of his many Hippocratic commentaries to these works. Littré’s admiration was endorsed by the acclamation of other 19th-​century doctors (Adams 1849; Petrequin 1877–​1878). On Fractures and On Articulations have been much praised for their clinical excellence. The excellence of the Greek prose style has been less remarked on, but it is indeed remarkable. Despite the technicality of the content, the style is both clear and elegant throughout, beautifully organized in sentences marked but never marred by such rhetorical devices as (especially prevalent) antithesis, with precise and delicate use of particles. On Fractures and On Articulations are very sophisticated in both presentation and content, and were surely consciously intended for posterity. These works seem to have been known in Athens and to have had a seminal influence on writers in other genres: Euripides and Plato apparently knew On Articulations. This is a very important writer, with a prolific output, as he refers to his own treatises, completed or projected, on

228   Early Greek Science a wide range of subjects. Perhaps indeed we have here the words of Hippocrates, as was believed, according to Galen, already at the beginning of the 4th century by Ctesias of Knidos (Hippocratis de articulis liber et Galeni in eum commentarius 18A.731K.). The author of On Articulations promises a work on glands, a work of precepts about massage, a work on lung diseases, a work on the subject of the intercommunications of vessels (phlebes and arteriai), and a work on the various ways different parts of the body interact. Other Hippocratic authors, too, claim to have written, or state their intent to write, about a similar range of subjects. The author of On Affections says he will write on diseases of the eye; also on cases of suppuration, of phthisis (consumption), and of gynecological ailments. Debate has centered on such claims of authorship: on whether the extant treatise On Glands may be attributable to the same writer as On Articulations; and whether the extant treatise On Sight may be attributable to the same writer as On Affections. In both cases, the answer seems to be negative (Craik 2006b; 2009). One of Littré’s great insights is the attribution to a single writer of a large group of interrelated works (On Generation; On the Nature of the Child; On Diseases 4; On Diseases of Women; On Diseases of Girls; On Infertile Women). In these treatises, there is a degree of cross-​reference and common content, as well as shared vocabulary and idiom. On grounds of similar features in both language and content, the short treatise On Glands can be regarded as of common authorship with this group of works on human reproduction and embryology (Craik 2009b). This finding has implications for our appreciation of the mixed character of the gynecological texts, which, at least in part, and in some cases, emanate from an author with a sophisticated knowledge of the body. Littré’s second class comprises the works (On the Nature of Man; On Regimen in Health) attributed to Polybus. Aristotle quotes, with that ascription, a passage from On the Nature of Man in which the vascular system is described (Aristotle, Historia animalium 3.3, 512b12–​24). In all ancient manuscripts, On the Nature of Man and On Regimen in Health are transcribed as a single work; the two contain similar provisions for attaining and maintaining a state of health. On the Nature of Man is written in an agonistic debating style and is most celebrated for its exposition of the nature of the four humors—​blood, phlegm, yellow bile, and black bile—​that must be in proper balance to ensure bodily health. It is the only work of the Corpus that explicitly takes this stance. These two works, transmitted as one, have been immensely influential because of this clear statement of humoral theory, often mistakenly regarded as present throughout the Corpus. Although it became dominant in later medical thought—​ and in literary works, where the humors were viewed as elements conditioning personality—​it was not fully developed in the Corpus. The work On Humors has a misleading title, based on a passing reference to humors in the first sentence; as noted above, it is aphoristic in character. Littré evidently expended most thought on his earlier categories. That attributed to the “school” of Kos is a very mixed bag: among important works so relegated are On the Art, which arguably has an equal and parallel place to On Ancient Medicine and

Hippocrates and Early Greek Medicine    229 resembles it in language and content. On the Art is a carefully worked treatise that sets out to demonstrate that there really is an art (i.e., a craft, or science) to medicine. Various arguments to the contrary are set out and rebutted, for instance, the contention that medical cures arise not from the art but from luck. Other treatises placed in this catch-​all category are On Affections (discussed above) and On Places in Man, which seems to be early and may have a west Greek origin (Craik 1998). This long work may have served as a medical vademecum, as it deals with a large number of subjects in anatomy, physiology, and pathology, as well as enunciating various medical precepts and doctrines. Throughout, there is much stress on bodily balance as a factor in health and on flux of excess or noxious matter from the head to other parts of the body (eyes, chest, etc.) as a causative agent in disease; there is an excursus on gynecology. The purpose of the works may be debated. It is apparent that the purpose, format, and intended readership alike varied. Some works seem to be composed for internal circulation to a group of practitioners (for instance, the case notes of Epidemics); some are—​or profess to be—​written for laymen (for instance, On Affections). It is sometimes suggested that the deontological treatises are written as recruitment brochures. Rather, it appears that they are criticisms of others who advertise, and of formal teaching, seen as meretricious. And if they seek to recruit, it is to an informal associative method of learning. The suspicion of word-​based education is in line with suspicion of the type of education purveyed by the sophists. Right thinking is compromised by formal education and cleverness in expression is mistrusted. Through popular nervousness about the dangers of unscrupulous teaching, the verb “teach” itself carried a risk of pejorative overtones; thus, overstudied or contrived self-​presentation is deprecated. In the short tract On the Surgery, the regular practice of the doctor’s office can be seen: it is merely a suitable room in the home where father and son(s) worked with their assistants. The value of their medical content may be debated also. The authors’ understanding of the functions and workings of the body is highly precarious. Although some authors regard the heart as central to the working of the (blood) vessels, others view the head as central. Although some authors show an understanding of the lymphatic system, this is not common to all. The reproductive system is poorly understood. The existence of differences between the anatomy of humans and the anatomy of other animals is unappreciated. The theory of noxious flux from the head to the lower body persists, in default of evidence. Humoral theory, too (though in a less exaggerated form than commonly supposed), is a triumph of belief over evidence. Some authors adhered inflexibly to the view that diseases were resolved through crisis and by “coction.” And yet—​even after the early modern discoveries of Harvey, Aselli, and others brought major advances in understanding the human body—​Hippocratic works were still used as guides by doctors in medical theory and practice. Although to some extent physicians relied on excerpts made by others, rather than reading and interpreting the texts for themselves, the Hippocratic Corpus had an enduring importance in the medical history of modern Europe (Burnet 1685 is a typical specimen of this genre).

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Bibliographic Survey The standard edition of the Hippocratic Corpus is that of E.  Littré (10  vols., Paris, 1839–​1861). F.  Z. Ermerins (3  vols., Utrecht, 1859–​1864) contains much of philological importance. A Latin translation by F. M. Calvus (Rome, 1525) preceded the Greek editio princeps of F.  Asulanus (Venice, 1526). Early editions that still repay study include those of J. Cornarius (Basle, 1538), A. Foesius (Frankfurt, 1595) and J. A. van der Linden (Leiden, 1665). Modern editions devoted to individual works have appeared in the ongoing series Corpus Medicorum Graecorum and (with French translations) Budé, Collection des Universités de France. The most accessible English translation, extending to most though not yet all works of the Corpus, is in the Loeb Classical Library (10 vols. by different translators, London, Cambridge, MA, 1923–​2012). Indispensable works of reference are the Index Hippocraticus, ed. J.  H. Kühn and U.  Fleischer. Göttingen, 1986–​ 1999; Concordantia in Corpus Hippocraticum, ed. G.  Maloney and W.  Frohn, Hildesheim, Zürich, New  York, 1986–​ 1989; also A. Anastassiou and D. Irmer, Testimonien zum corpus Hippocraticum. Göttingen, 1997–​ 2006. Two important modern works are Vivian Nutton, Ancient Medicine. London, New York, 2004, with c­ hapters 4–​6 on Hippocrates; and Jacques Jouanna, Hippocrates. English translation Baltimore, 1999; French edition Paris, 1992. Adams (1849) is dated in approach but sound in judgment. There are useful articles on “Hippocrates” in The Complete Dictionary of Scientific Biography by R. Joly. Vol. 6:418–​443; and, a substantial revision, H. King. Vol. 2:322–​326; also in L. Edelstein, “Hippokrates,” Nachträge, RE S.6 (1935): 1290–​1345. See now the comprehensive treatment of Craik, London, 2015. Papers published in proceedings of the triennial Colloques Internationaux Hippocratiques, beginning 1972, collectively cover much ground. See:  I Strasbourg, 1972, ed. L. Bourgey and J. Jouanna; II Mons, 1975, ed. R. Joly; III Paris, 1978, ed. M. D. Grmek and F. Robert; IV Lausanne, 1981, ed. F. Lasserre and Ph. Mudry; V Berlin, 1984, ed. G. Baader and R. Winau; VI Quebec, 1987, ed. P. Potter, G. Maloney and J. Desautels; VII Madrid, 1990, ed. J. A. López-​Férez; VIII Leiden, 1993, ed. Ph. van der Eijk, H. F. Horstmanshoff and P. H. Schrijvers; IX Pisa, 1996, ed. I. Garofalo, A. Lami, D. Manetti and A. Roselli; X Nice, 1999, ed. A. Thivel and A. Zucker; XI Newcastle, 2002, ed. Ph. Van der Eijk; XII Leiden, 2005, ed. M. Horstmanshoff; XIII Austin, TX, 2008, ed. L. Dean-​ Jones and R. M. Rosen; and XIV Paris, 2012, ed. J. Jouanna and M. Zink.

Bibliography Adams, F. The Genuine Works of Hippocrates. London: Sydenham Society, 1849. Burnet, T. Hippocrates contractus. Edinburgh: J. Reid, 1685. Craik, E. M. Hippocrates Places in Man. Oxford, New York: Oxford University Press, 1998. —​—​—​. “Plato and Medical Texts: Symposium 185c‒193d.” Classical Quarterly 51 (2001): 109–​114. —​—​—​. “The Hippocratic Treatise Peri opsios (de videndi acie, on the Organ of Sight).” In Hippocrates in Context, ed. P. J. van der Eijk, 191–​207. Leiden: Brill, 2005.

Hippocrates and Early Greek Medicine    231 —​ —​ —​ . “Tragedy as Treatment:  Medical Analogies in Aristotle’s Poetics.” In Dionysalexandros: Essays on Aeschylus and His Fellow Tragedians in Honour of Alexander F. Garvie, ed. D. L. Cairns and V. J. Liapis, 283–​299. Swansea: Classical Press of Wales, 2006a. —​—​—​. Two Hippocratic Treatises On Sight and On Anatomy. Leiden: Brill, 2006b. —​ —​ —​ . “Hippocratic Bodily ‘Channels’ and Oriental Parallels.” Medical History 53 (2009a): 105–​116. —​—​—​. The Hippocratic Treatise On Glands. Leiden: Brill, 2009b. —​—​—. The “Hippocratic” Corpus: Content and Context. London: Routledge, 2015. Dean-​Jones, L. A. Women’s Bodies in Classical Greek Science. Oxford:  Oxford University Press, 1994. Diels, H. Anonymi Londinensis ex Aristotelis Iatricis Menoniis et  aliis Medicis Eclogae, Supplementum Aristotelicum 3.1. Berlin: G. Reimer, 1893. Diels, H., and W. Kranz, Die Fragmente der Vorsokratiker. Berlin and Zurich: Weidmann, 1952. Duminil, M.-​P. Hippocrate. Vol. 8. Paris: Collection des Universités de France, 1998. Edelstein, E. J., and L. Edelstein. Asclepius. Collection and Interpretation of the Testimonies. Baltimore, MD: Johns Hopkins University Press, 1945, repr. 1998. Filliozat, J. La doctrine classique de la médecine indienne. Ses origines et ses parallèles grecs. Paris: Imprimerie Nationale, 1949. Grensemann, H. Knidische Medizin, Ars Medica, Abt. 2, Gr.-​Lat. Med. Bd. 4.  Berlin and New York: de Gruyter, 1975. Harris, C. R. S. The Heart and the Vascular System in Ancient Greek Medicine. Oxford: Oxford University Press, 1973. Horstmanshoff, H. F. J., and M. Stol, eds. Magic and Rationality in Ancient Near Eastern and Graeco-​Roman Medicine. Leiden: Brill, 2004. Huffman, C. A. Philolaus of Croton:  Pythagorean and Presocratic. Cambridge:  Cambridge University Press, 1993. Jackson, Stanley W., ed. The Journal of the History of Medicine and Allied Sciences 51.4 (1996). Jones, W. H.  S. The Medical Writings of Anonymus Londinensis. Cambridge:  Cambridge University Press, 1947. Jouanna, Jacques. Hippocrate: Pour une archéologie de l’école de Cnide. Paris: Collection des Universités de France, 1974. Kenyon, F. “On a Medical Papyrus in the British Museum.” Classical Review 6 (1892): 237–​240. King, H. Hippocrates’ Woman. London, New York: Routledge, 1998. Langholf, V. Medical Theories in Hippocrates:  Early Texts and the Epidemics. Berlin and New York: de Gruyter, 1990. Laskaris, J. The Art Is Long: On the Sacred Disease and the Scientific Tradition. Leiden: Brill, 2002. Lloyd, G. E. R. Polarity and Analogy. Cambridge: Cambridge University Press, 1966. —​—​—​. Magic, Reason and Experience: Studies in the Origin and Development of Greek Science. Cambridge: Cambridge University Press, 1979. —​—​—. Adversaries and Authorities:  Investigations into Ancient Greek and Chinese Science. Cambridge: Cambridge University Press, 1996. Longrigg, J. Greek Rational Medicine. London, New York: Routledge, 1993. Majno, G. The Healing Hand. Cambridge, MA: Harvard University Press, 1991. Nachmanson, E. Erotianstudien. Uppsala: Akademiska, 1917. —​—​—. Erotiani vocum hippocraticum collectio cum fragmentis. Uppsala: Appelbergs, 1918. Oser-​Grote, C.M. Aristoteles und das Corpus Hippocraticum: die Anatomie und Physiologie des Menschen. Stuttgart: Steiner, 2004.

232   Early Greek Science Petrequin, J. E. Chirurgie d’Hippocrate. Paris: Imprimerie nationale, 1877–​1878. Pinault, J. R. Hippocratic Lives and Legends. Leiden: Brill, 1992. Radt, S. L. Tragicorum Graecorum fragmenta. Vol. 4: Sophocles. Göttingen: Vandenhoeck & Ruprecht, 1999. Smith, W. D. The Hippocratic Tradition. Ithaca, NY, London: Cornell University Press, 1979. —​—​—​. Hippocrates: Pseudepigraphic Writings. Leiden: Brill, 1990. Steckerl, F. The Fragments of Praxagoras of Cos and His School. Leiden: Brill, 1958. Thivel, A. Cnide et Cos? Essai sur les doctrines médicales dans la collection Hippocratique. Paris: Collection des Universités de France, 1981. Totelin, L. M.  V. Hippocratic Recipes:  Oral and Written Transmission of Pharmacological Knowledge in Fifth-​and Fourth-​Century Greece. Leiden: Brill, 2009. Valiathan, M. S. The Legacy of Caraka. Chennai: Orient Longman, 2003. —​—​—. The Legacy of Suśruta. Chennai: Orient Longman, 2007. —​—​—​. The Legacy of Vāgbhaṭa. Hyderabad: Universities Press India, 2009. van der Eijk, P. J. Diocles of Carystus:  A Collection of the Fragments with Translation and Commentary. Leiden: Brill, 2000–​2001.

C

H E L L E N I ST IC G R E E K SCIENCE

chapter C1

Aristotle, the I nv e ntor of Natu ral S c i e nc e Jochen Althoff

1. Life Aristotle from the small village Stageira in the easternmost part of the Chalcidice was born in 384 bce as the son of the doctor Nicomachus, who served as the physician of King Amyntas III, the grandfather of Alexander the Great (Flashar 2011, 2004; Düring [1957] 1987). Having lost his father at an early age, Aristotle went to Athens when he was 17, joining Plato’s Academy and studying there until Plato’s death, 347 bce; Aristotle is certainly the most important student of Plato. Aristotle left Athens after Plato’s death, most probably because of the difficult political situation for a man with close connections to the Macedonian court in a time when Philip II of Macedonia more and more threatened the Athenian Empire. These difficulties will become a kind of leitmotiv during his life, which is somewhat typical of the transition from the classical to the Hellenistic era. Aristotle is very much an intellectual link between these two historical periods. From Athens he went to Assos in Asia Minor, just opposite the island of Lesbos, where King Hermeias offered him the opportunity to work (and the king’s sister or niece Pythias as a wife). Two years later he moved to Mytilene on Lesbos, where he met the young Theophrastus who later became Aristotle’s successor as head of the Peripatos school. At the same time, he started his zoological studies, as shown by the many fishes from the area of Lesbos that he describes in his biological works (Lee 1948; Leroi 2014). In 343/​342 bce Aristotle was called by Philip II to be the teacher of his son Alexander, who was 13 at the time. This episode lasted just three years but gave rise to a fantastic but mostly fictitious tradition about the great king and the great philosopher—although neither of them was that great during these years. Aristotle is said to have produced a copy of Homer’s Iliad for Alexander. The future great king became convinced that he was a direct descendant of Achilles, and Aristotle showed his early interest in poetics.

236   Hellenistic Greek Science In 335/​334 Aristotle returned to Athens. Xenocrates was head of the Platonic Academy at that time, but Aristotle does not seem to have been interested in joining the school. He preferred to found his own school in the precinct of Apollo Lykeios in the northeastern part of Athens, which needed the help of Demetrius of Phaleron, because neither Aristotle nor Theophrastus (who accompanied him) could buy land in Athens, not being Athenian citizens. Later the Athenian fiscal officer Lycurgus (ca 390–​324 bce, who built the still famous theater of Dionysus) seems to have built a library and school for Aristotle in Athens (Flashar 2004, 218). The common modern name peripatos for the Aristotelian Lykeion (still alive in the French lycée) became common only after his death, under his successor Theophrastus (Flashar 2004, 496–​505). (The meaning of peripatos has been disputed since antiquity: most probably it refers to a type of building with columns, a colonnade or peristyle, in which teaching took place.) As in 347 bce, Aristotle again had to flee from Athens in 322 bce because of political difficulties. Once again anti-​Macedonian resentments took over after the death of Alexander the Great in 323 bce, and Aristotle went to the island Euboea not far from Athens, where he owned a house from his mother’s side. In this last resort he died of an unknown disease in October 322 bce at the age of 62. Although his death nearly coincides with that of Alexander (June 323 bce), which marks the beginning of Hellenism, in many ways Aristotle’s work continued to influence science and philosophy of the Hellenistic era and many centuries after. Seeing that his life was not too long, and was troubled by difficult political constellations and many changes of place, it is most remarkable in how many different fields of learning Aristotle achieved groundbreaking results. Quite often he even founded the disciplines themselves. He was the first to lay the foundations of logic and philosophy of language (especially interesting for scientific research are his Posterior Analytics), developed out of the Platonic practice of dialectic reasoning. He worked on ethics and politics, which he considered to be closely related (Nicomachean Ethics and Politics). He was the first to write a concise treatise on poetics, in which he related the existence of poetry to basic anthropological facts (the inborn tendency to learn by imitation, mimesis, and the pleasure in enjoying imitations by others). He also wrote about rhetoric, developing a specific understanding of rhetoric as a kind of theory of communication. He has been famous ever since for his philosophical writings, which came to be known under the title of Metaphysics (ta meta ta physika, things/​problems/​ writings that come after the natural things/​problems/​writings), which, if nothing else, introduced the term “metaphysics” into philosophical language. Aristotle probably never used that term, rather he called the topics dealt with “first philosophy” or “theology.” The theological aspect can primarily be found in the first unmoved mover of Metaphysics, book Lambda (book 12), and quite obviously this concept of god is closely connected to natural science. Even his treatment of the term ousia (being, i.e. substance) in the Metaphysics shows close parallels to his biological writings (Cho 2003). All these observations fit well Wolfgang Kullmann’s thesis that Aristotle is much more a scientist than a philosopher in the modern sense of these words (Kullmann 2014) because most of his work in other fields is clearly related to scientific research.

Aristotle   237 Whereas Plato did not show much interest in natural science, because he focused on his philosophy of ideas (compared to which natural things are only deficient copies of a lesser degree of reality), Aristotle spent most of his life and work on natural science. Nevertheless he kept some of the basic tenets of his teacher. Like Plato he was not ready to accept the variable and unstable character of most natural things by just describing their outlook and the changes they undergo. He was looking for the stable element, the reliable truth within all these changes. Aristotle would not go as far as Plato, who finally said goodbye to all natural research and concentrated on unchanging objects only grasped by the intellect, his famous “ideas” that truly exist in their own realm somewhere above and behind nature. Plato, however, is more favorable to observation and natural explanation in his late Timaios (Kullmann 1998, 137–​160). But after all, Aristotle sought the reliable, and that means true, features of natural objects. In the field of biology, he finds these in the plant and animal “species.” (This word is a Latin translation by Cicero of the Greek eidos, “visible form,” which Plato used as a synonym for his ideai, “ideas,” and Aristotle for the species.)

2.  The System of Sciences In book Epsilon (book 6) of his Metaphysics, Aristotle develops a system of scientific disciplines (1025b25–​26). Basically they are threefold: there are practical, productive, and theoretic disciplines (praktikē, poietikē, theoretikē dianoia). The practical disciplines are ethics and politics, which consider men acting within society. The productive disciplines enable craftsmen to produce artifacts (houses, ships, tools, pictures, statues, etc.). Aristotle has not left any writings on productive disciplines, with the possible exception of the Poetics and of Historia animalium, book 10, a treatise on sterility, which has been claimed as a medical treatise of Aristotle (van der Eijk 2005). Most important are the theoretical disciplines, because pure thinking, understood as theoretical observation and investigation (theoria), is the most human practice (as described in the Nicomachean Ethics 10 with its praise of the bios theorētikos). Aristotle in Metaphysics Epsilon, sec. 1, names three theoretical “philosophies,” as he calls them: mathematics, natural sciences, and theology (1026a18–​19), of which the first and foremost is theology. This teaching is developed in Metaphysics Lambda. It is centrally concerned with the first unmoved mover, which serves as a transcendent primary moving cause for the whole cosmos. Though in Metaphysics Lambda the theological perspective prevails (the unmoved mover is given godlike attributes: unchanging, eternal, etc.), this principle is closely connected to natural processes of movement and change (in the wide sense of the word that Aristotle gives to his term kinēsis). This is stressed in Physics 8, a work that in general deals with the basic features of natural phenomena. Once again, therefore, even the most abstract discipline of Aristotle’s system of sciences, that is,

238   Hellenistic Greek Science theology, is closely linked with natural science. Natural science (physikē) in Metaphysics Epsilon, sec. 1 is named the second important theoretical discipline after theology.

3. Physics, Part I Let us now turn to the Physics (or “lecture on physics” as the complete title says), which forms a general introduction to the basic conceptions of natural sciences. Like many other Aristotelian works that have come down to us as distinct treatises with separate titles (e.g., Metaphysics, Meteorologica, De partibus animalium), the Physics is not a coherent single work but was later compiled by an editor from different smaller treatises. Books 1 and 2 may have been separate treatises covering the principles of natural sciences. Books 3–​6 form a second block dealing with the central concept of movement (kinēsis) in the widest sense, which to Aristotle is not just locomotion but also a change of quantity (becoming bigger or smaller, growth and decay) or quality (becoming harder or softer, changing colors, and what we would call its state of aggregation, etc.). Book 7 is problematic and some parts of it do not seem to be Aristotelian at all and is left out here (Flashar 2004, 245). Book 8, as mentioned, contains Aristotle’s reflections about the first unmoved mover and is parallel to Metaphysics Lambda (book 12). After book 1, which mainly contains a critical discussion of what Aristotle’s predecessors thought about the principles of nature (a typical feature of most of Aristotle’s works, the so called doxography; cf. Althoff 1999), book 2 starts with a definition of natural objects (2.1 [192b8–​23]): Aristotle takes it for granted that there exist natural objects like animals and their parts, plants and the so-​called simple (i.e., not compound) bodies, that is, the classical four elements fire, air, water, and earth, which he takes over from Empedocles. These natural objects are opposed to artifacts, technically produced objects like beds and clothes, which always need some technician or craftsman as external producers. The defining characteristic is obviously the kind of movement these two classes of objects possess. Whereas natural objects move or change by themselves, that is, by some inner force, artifacts cannot move or change by themselves. When wooden beds (as artifacts) fall apart and the wood disappears in the long process of rotting, this is due to the natural material used for its construction. Regarding the generation of both classes of objects, things become more complicated: physical objects and artifacts need an exterior force to be generated. The individual animal needs parents to be produced, whereas artifacts need technicians or craftsmen. But procreation within a species is a natural process that is a basic feature of life. In that respect, it is an internally generated process without any external force. In Aristotle’s view, the species of plants and animals are eternal; they do not develop in a process of evolution. This eternity does not extend to the individual members of the species, but the continued series of

Aristotle   239 individuals constitutes the eternity of the species (De generatione animalium 2.1). Technical production, however, of beds or clothes is by no means natural or necessary and always needs an external human actor; never has a bed been seen to grow naturally in the woods.

4.  Elementary Physics Even we moderns agree that the ability to move oneself is one of the central characteristics of animal life. Therefore, we have few problems with Aristotle’s basic separation of living beings and artifacts. What appears strange to us is his example of the elements, which he also claims have an interior moving force. The underlying theory is developed in De caelo 4: each element has its natural place in the universe, to which it tends to move unless otherwise hindered. So in the end (seen from a supposed state of disorder and mixture) there will be a layered universe with fire on top, air second, water third, and earth as the fourth and last layer below. The elements, accordingly, possess an internal moving force that drives them toward their natural place, where the movement stops. These forces work in a centrifugal direction (away from the center of the earth, i.e., the light elements fire and air) or in a centripetal one (toward the center of the earth, i.e., the heavy elements earth and water). As an aside, I mention the invention (or better, taking over) by Aristotle of a fifth element, the famous “ether” (aithēr, De caelo 1.2). This is the material of the sphere above the course of the moon, the superlunary world of the stars, and it moves in an eternal circular motion. The purely hypothetical ether enjoyed a long life and was not abandoned until Einstein’s special theory of relativity, published in 1905. Aristotle claimed it because he needed an element with circular motion (to complete the rectilinear movement of the other elements), and it shows once again the significance of motion for Aristotle’s natural science. By including the elements among those objects that move because of an internal agent, Aristotle succeeded in defining a very broad field of physical objects. Nature not only covers every living being (humans, animals, plants) but also every inanimate thing in the world (stones, metals, waters, all kinds of natural resources), because everything in the sublunary world is composed of these four elements (Solmsen 1960; Seeck 1964; Bos 1973). The difference between nonliving and living beings is defined in De anima 2.2 (cf. King 2001; Föllinger 2010). Abstractly speaking, the defining feature is possessing soul or not. All bodies with souls are distinguished from bodies without soul by being alive (2.2 [413a21–​22]). Soul is not a material entity, but it always belongs to material bodies and enables (or rather, is) the correct function of the body and its parts. Soul can be divided into different functions: the most basic are (1) nutrition and reproduction (specific movements of the organism), (2) sense perception and locomotion and, finally,

240   Hellenistic Greek Science (3) reason (nous). If only the first of these functions is present, the body is alive. The progression of these capacities (the more complex always including the less complex) results in Aristotle’s famous scala naturae: plants only have the ability of nutrition and reproduction, animals in addition can perceive and move, humans have the additional capacity of reasoning (but also the two lower functions). Reason is the only function of which Aristotle is not quite sure if it is linked to certain organs. In his work De generatione et corruptione, book 2, Aristotle goes one step further in his elementary theory. He analyzes the four elements as combinations of opposite qualities that adhere to some postulated first matter, which in reality never exists in a pure state without any qualities. These opposite qualities he divides into two pairs: one active, warm (thermon) and cold (psychron), one passive, wet/​liquid (hygron) and dry (sklēron). Combining one active with one passive quality, he defines the four elements: fire is warm and dry, air warm+wet, water cold+​wet, and earth cold+dry. This new theory reduces the classical Empedoclean elements to four qualities. Because each two of the classic elements share one common quality (e.g., fire and air are both warm, air and water are both wet, etc.), Aristotle assumes that such close neighbors can most easily change into one another; they only have to exchange one of their qualities. Elements, therefore, can change into each other. And that eternal change is exactly what happens in the sublunary sphere, the world of our immediate experience. This new theory at first looks somewhat artificial. But it also accounts for certain aspects of everyday experience. Water in rivers and the sea quite normally appears to us as cold and wet (because it normally has a temperature lower than our body temperature), fire certainly seems to have the opposite qualities, not at least because fire can dry up water and moistness. It is not as easy to determine earth as cold and dry, because at least fertile soil always seems to contain some humidity. But Aristotle decided to take such humidity as secondarily added water, probably led by the observation of the burning of pottery clay. Most controversial is the definition of air as warm and wet. Winds in the Mediterranean mostly have a cooling effect—​but perhaps Aristotle ascribed this rather to the movement, not to the air itself. The assumed humidity is probably derived from meteorological phenomena like clouds, rain, snow, dew, and so forth. The truth is that antiquity never developed the concept of a “gas,” as we nowadays call it (a 17th-​century coinage by Jan Baptista van Helmont, from the Greek chaos). The only “gas” known was air, and all the ancient scientists had great problems describing it adequately. In the specific form of pneuma (which originally means just “wind”), it served (already at the end of Aristotle’s life, cf. De motu animalium 10) as a quasi-​mystic philosophical matter to perform specific functions of the soul or even as the material representation of the world soul conceived by the Stoics (Solmsen 1961; Althoff 1992, 283–​291). It is in book 4 of the Meteorologica that Aristotle discusses the details of the combination of the four elements into more complex substances (once again the book, aptly called Aristotle’s “chemical treatise” by Düring 1944, does not belong to the first three books that deal with real meteorological phenomena; cf. Viano 2002). Aristotle calls these more complex substances homoiomerē (an adjective to be applied to “parts”), that

Aristotle   241 is, homogeneous substances, which, being mechanically divided, always produce parts of a completely identical nature compared with the whole (defined in De generatione et corruptione 1.1 [314a18–​24]; 1.10 [328a10–​18]). This in his view holds for inorganic materials like stones or metals, but also for organic body tissues like flesh, bone, sinew, skin, intestine, hair, fiber, and veins (Meteorologica 4.10 [388a13–​18]). The next more complex structures are the anhomoiomerē (inhomogeneous parts), which are composed of different homogeneous parts. Examples are face, hand, foot; as well as wood, bark, leaf, and root: Meteorologica 4.10 (388a18–​20). A hand consists of bones, skin, sinews, veins, “flesh” (which we prefer to call muscles), and so forth; and a leaf consists of a leaf stalk, a leaf blade, and so on. The same holds for the even more complex structure of the individual organism as a whole (a human, a dog, a horse, a tree, a bush, etc.). The two active qualities warm and cold, working on the two passive qualities wet and dry, form all of these complex substances (from homogeneous to the complete organism). These procedures result in new chemical combinations—​the homoiomerē and different physical features of the new substances (hardening/​drying, softening/​ liquefying, ripening, cooking—​a most central concept, cf. Lloyd 1996—​are explicitly mentioned as effects of warm and cold). Although Aristotle in Meteorologica, book 4 is basically concerned with inorganic materials, organic substances are never far away. They are explicitly mentioned in the last chapter of the book (Meteorologica 4.12). Aristotle contends that the physical features of flesh, bones, and so on (i.e., hardness, softness, flexibility, strength, etc.) are produced in the same way as the inorganic substances, by the effects of warm and cold on wet and dry. But this chemical explanation is not sufficient. What is missing is the most important explanatory tool that Aristotle invented for natural science: the final cause. The final cause describes the function of everything, the reason expressed in a final form, stating the end for which something exists, that is, why an organism or an artificial object comes into being. Aristotle is very proud of his final cause, and he criticizes all his predecessors for not having recognized the importance of this factor in scientific explanation. Because the Physics books lay the theoretical framework for Aristotle’s natural sciences, it is small wonder that this final cause is also proudly presented there within the theory of the four causes (2.3 and 2.8). Aristotle’s basic assumption is that scientific explanation is concerned with the causes of natural phenomena. We only “know” things when we know the reasons (the “because of,” to dioti, as he quite peculiarly says), why those things happen and/​or exist. There are four types of causes (or factors that are at work), which are always involved and have to be taken into account: first, the material cause; second, the formal cause; third, the moving cause; fourth, the final cause. Aristotle exemplifies this by the process of building a house: bricks, wood, nails, and so on serve as material of the house (material cause). The form of the house is outlined in the plan, which the architect draws and which represents the outlook of the building when completed (formal cause; in biology formal and final cause are practically the same: De generatione animalium 1.1). The construction workers are the ones that move the material to the designated place, after they have cut the beams and boards into the right sizes, and put them together according to the plan (moving cause). The whole

242   Hellenistic Greek Science building has a certain end, for which it is being erected, namely to protect its inhabitants from bad weather, to give them room to work and to live in, to demonstrate their social status, and so on. This is the final cause for its existence. This final cause is most important and determines all the other causes or factors that lead to producing an artifact. If the weather in the region where you plan to build a house is mostly snowy and frosty, you will build another form of house than in the desert of New Mexico (and you will use different materials). Aristotle would have fully subscribed to the modern saying that “form follows function.” Each of these solutions requires certain materials and certain movements or phases of building, and each step leads to new preconditions in terms of material and movement. Obviously all four factors or causes are closely connected, but the most important are the first decisions (1) to build a house at all, and (2) what purpose this house is to serve. If we return to the Meteorologica 4, it will become clear that the effects of warm and cold on wet and dry substances can be understood in terms of material (wet/​dry) and moving cause (warm/​cold). Like a potter burning his pottery and thus producing the intended form and features for the aim that his pot is supposed to serve (storing liquids, serving food), so heat and cold work together to form homogeneous substances. The problem is: What is the final cause in the production of such substances (and who is the technician or craftsman coordinating all the movements)? In Meteorologica 4.12 Aristotle first states that the final cause can be more clearly detected in the more complex organic composites like the anhomoiomerē (i.e., organs or complex structures of the body) because there the function (ergon, much the same as telos or purpose) of each part can be more clearly recognized. The more basic the parts are (the more they can be described as material of something else: this holds of tissues, metals, elements, and other homoiomerē), the less clear their final cause. The element fire, for example, can hardly be associated with a final cause. To flesh (a homoiomeres or tissue), however, a certain function and therefore a final cause can be ascribed: it is the sense organ of touch, forms the outline of the body, and protects the bones and inner organs (De partibus animalium 2.9). Most clear is the function of a complex part like the tongue (an organ or anhomoiomeres), which in Aristotle’s understanding is the sense organ of taste and (in humans) an organ for the pronunciation of words and letters (De partibus animalium 2.16 [660a1–​2]). But when he turns to the question of who or which provides the final causes of the more complex structures, Aristotle in Meteorologica 4.12 is a little less than clear: he says that the more complex structures in artifacts are not due to heat or cold and their movements (these are responsible for creating the homoiomerē), but to the technician or craftsman. In the field of natural substances of higher complexity (anhomoiomerē), it is “nature or some other cause” (390b14). At first sight this looks like Aristotle postulates some kind of creator like the Platonic dēmiourgos in the Timaeos. This impression is reinforced by phrases like “nature does this and that,” which Aristotle often employs. But it is most important to stress that this is only a metaphorical way of speaking. And the metaphor is definitely not taken from religious ideas of a creator god (which Aristotle rejects), but from the analogy of producing

Aristotle   243 artifacts. Aristotle always sees close connections between nature and art (comprising all kinds of crafts and trades, technai; cf. Fiedler 1978). Accordingly he says in Physics 2.8 (199a12–​15) that if a house were not an artifact but a natural organism, it would still come into existence in the same way. The same conviction is expressed in Aristotle’s famous saying that “art/​craft imitates nature:” Physics 2.2 (194a21–​23), 2.8 (199a15–​17), and Meteorologica 4.3 (381b6–​7). For Aristotle, all natural things, including those in the sublunary sphere (i.e., our earth), are eternal. This is why he does not need a creator god like Plato does. In the sublunary sphere eternity is only present in a restricted form: individual lives of humans, animals, and plants (but also metals and stones) are, of course, mortal or subject to decay. But the species of animals and plants exist forever; there is no such thing as evolution, at least generally speaking (but cf. Zierlein 2007; Lennox 2001a). Their eternity is supplied by a steady stream of individuals that all die individually but secure the ongoing existence of the species as a whole. This is a major presupposition for nature’s working:  in Physics 2.8 (199b26–​30), Aristotle claims that not even a technician always reflects on the single steps he has to undertake to finish his product. If he is experienced, most of his acts follow automatically without much reasoning. Nature works like such an experienced professional because it always produces single organisms as individual members of an eternal species. And moreover, nature not only provides the moving cause (working with the qualities warm and cold as tools), but also the material (i.e., the basic qualities wet and dry, the elements, the homoiomerē) on which the movements are exerted. In terms of modern computer science one could speak of a program that nature follows (cf. on De generatione animalium below). We have again reached the point where Aristotle’s ideas about the structure of the world lead to thoughts about biology. Basically the mechanisms in inorganic and organic chemistry (to use modern terms) are the same. It will not have become completely clear yet how these mechanisms work in the field of biology, but we will return to that later. Within the sphere of elements and simple substances (homoiomerē), however, there is an ongoing cycle of basic material being formed by the four basic qualities, and the continuous generation and destruction of inorganic substances. And the moving cause for all these changes lies within the natural substances themselves. In De generatione et corruptione 2.10, Aristotle explains why the process of generation and dying is circular and eternal. It needs some circular eternal movement, constantly giving a new impulse. And it is the heavenly spheres, to which the stars and—​of special importance—​the sun are fixed, that revolve in such a circular movement. According to Aristotle’s view, it is not so much the ongoing change from day to night that brings about new impulses for change in the world. Much more important is the changing position of the sun within the ecliptic, which brings about the circular change of seasons. The resulting differences in temperature are the necessary impulses for change within the cycle of elements (and, furthermore, of the organic world). Within the cosmos as a whole there is another cause for the circular movement of the spheres of the planets and stars:  this is the unmoved mover, as Aristotle

244   Hellenistic Greek Science argues in Physics 8.5. Whereas at the beginning of Physics book 2, Aristotle claimed there are natural things that move by themselves (living beings), he now states not even these self-​movers are such in the strict sense of the word. Even they need an external impulse for their movement (and one has to keep in mind that Aristotle’s term “movement,” kinēsis, has a broad sense; it covers all kinds of natural processes:  growing, decay, changing one’s features, locomotion, etc.). As we have seen, the immediate cause is the circular movement of the sun in the ecliptic, but behind that lies still another cause, namely the unmoved mover. Aristotle argues that the chain of moving forces, where always one thing is moved by the next, must have an end. At some point one has to arrive at a mover that is not moved by another cause. This last source of movement has to be unmoved but nevertheless moves everything else in the cosmos. So we find a threefold system of moving causes in the cosmos: first and foremost, there is the unmoved mover; it effects, secondly, the circular motion of the spheres of the planets and stars, especially the sun; and the movement of the sun, thirdly, moves all processes of coming to be and passing away in the organic and inorganic world. The borderline is the sphere to which the moon is attached, so that we have the superlunary sphere of the planets and stars and the sublunary sphere of the world as we can experience it most immediately. With a view to this borderline, one can as well speak of a twofold division of the cosmos, and Aristotle changes his perspective quite freely.

5. Cosmology It may at this point be apt to take a closer look at Aristotle’s cosmology as it is treated in his work De caelo (in 4 books; cf. Jori 2009), which is one of his earliest writings on natural science (an astronomical date given in 2.12 [292a3–​6] results in an age of 27, that is 357 bce, for the time of writing that sentence at least). In books 1–​2, Aristotle deals with the heavenly bodies (aithēr, fixed stars, spheres, planets), and, in book 3, with the sublunary elements fire, air, water, and earth. Book 4 explains the problems of the natural tendency of the elements in relation to their weight. As remarked above, Aristotle in book 1 for the first time mentions the new element aithēr, which he characterizes by the circular motion that is typical of the heavenly bodies. It is eternal and godlike, and therefore the cosmos as a whole is eternal. The cosmos has the form of a sphere that turns clockwise because that is the more perfect movement (one of the many axiological statements). The stars and planets, being globes, are made of aithēr just like the global spheres, to which they are fixed. They can only move together with their spheres. Whereas the spheres cannot be perceived, because the aithēr is transparent, the stars and planets can be seen as little globes of fire. This is due to their movement in the air that surrounds the spheres of aithēr and that leads to frictional heat so intense that they catch fire. The earth itself does not move and also has the

Aristotle   245 shape of a globe. It is relatively small and lies in the middle of the cosmos, which revolves around it. Book 3 gives an earlier version of the theory of the elements as mentioned above. We have also already summarized Aristotle’s ideas about the natural tendency of each element toward a certain place in the sublunary sphere. In book 4 these tendencies are explicitly linked to the weight of the elements.

6.  Physics, Part II Since we have started our overview with the Physics and the most basic tenets of Aristotle’s natural science presented there, we should now complete the picture with the other topics dealt with in Physics. Aristotle starts with a few remarks about scientific method. We generally understand an object or process when we know the more basic elements or principles of which they consist or exist. The same holds for natural science (hē peri physeōs epistēmē, 184a14–​15), which aims to explore the principles (archai) of natural things and processes. The process of recognition starts with the observation of concrete things we know well (i.e., the objects of the empirical world that surround us), and the process ends with real understanding of their reasons and causes. Having turned to the principles of natural phenomena, Aristotle feels obliged to discuss the many different views his predecessors have maintained: the material principles of the early pre-​Socratics and the monistic thesis of Parmenides and Melissos about the unchangeable unity of being. The latter in his view excludes the possibility of any change or movement within nature, and therefore does not allow natural science at all. After all, nature is characterized by the existence of change and movement (first statement of this fundamental thesis 185a12–​13). Besides the discussion of his predecessors Aristotle in book 1 tries to solve the problem of how many principles one has to assume (1.7). Movement happens between two opposites (the cold becomes warm, the small big, the uneducated educated; this is much less obvious in local movement), so that pairs of opposites are necessary for movement. In addition, an underlying matter is needed, in which these opposites can occur (cold metal, for instance, becomes warm; an uneducated human becomes educated). So it is in sum three factors that form the principles of nature: two opposites and one underlying matter. The content of book 2 has mostly been summarized above (natural things generating their movement from within; the four types of causation). An important claim in 2.2 is that the natural scientist (unlike the mathematician, e.g.) always takes account of the form together with the material. This is directed against the Platonic ideas, which are most real without any material admixture. Another topic is chance and automatic processes. Because everything in nature is organized toward an end, for Aristotle both concepts are difficult to explain. He nevertheless tries to give an explanation because

246   Hellenistic Greek Science these factors have played major roles in earlier models of natural explanation (chance with the atomists, automatic processes with materialistic pre-​Socratics like Empedocles, for whom the material has certain built-​in mechanisms of producing things). For Aristotle these two factors are aberrations from teleologically organized processes that sometimes appear as simple defects of the end product or sometimes constitute secondary aims by changing or being added to some primarily intended end (2.4–​6). In book 3 Aristotle deals with the problem of infinity and states that it only has a potential character, and this especially in mathematics. Series of numbers can potentially be infinitely continued, but no real thing is ever infinite (neither elements, nor substances, nor organisms, not even the cosmos as a whole). Book 4 considers space (topos, 4.1–​5), then empty space (4.6–​9), and finally time (4.10–​14). Aristotle defines space in a very concrete way: space is always filled with concrete things; in this respect he talks about place, rather than space in an abstract sense. He denies the existence of an abstract space without anything in it. This place of a thing does not move with that thing; the moving object changes its place continuously. We have already heard that the four elements tend toward their natural places, which is just a specific subcategory of object-​related space as developed in 4.1–​5. Aristotle, therefore, denies the existence of empty space. Wherever there are no things present, there cannot be space. This assumption is primarily directed against the atomists, for whom empty space is a necessary correlate to full-​bodied atoms; this denial, however, is one of the weaker parts of his natural science. Aristotle in Physics 6 also argues against the atomistic theory of matter as being composed of invisibly small particles that cannot be further divided. Against this position he states the continuity (to syneches) of matter, which is primarily derived from the nonatomistic continuity of time. And both the continuity of time and matter in the end follow from the existence of movement in nature. If time would consist of minute atomic particles of “nows,” movement could only proceed in little jerks, and during these atomic stretches of time no movement would take place at all (because no time would elapse). All these statements are refutations of atomistic theories of time and matter and Eleatic paradoxes of movement. Once again the central role of movement becomes obvious, whose existence Aristotle in his typical down-​to-​earth attitude simply takes for granted. Just as space, in Aristotle’s mind, does not have any abstract existence apart from objects in it, time does not have an abstract existence without anything moving. It is with the help of moving objects that we can observe time passing by (cf. Leiß 2004). Books 7–​8 of the Physics deal with the causation of movement, ultimately relating it to an unmoved mover. The most important details of these books have already been sketched. To sum up the contents of the Physics as a whole, I  quote Flashar (2004, 351): “Space, time and continuum have been shown to be functional concepts” (sc. always related to natural objects, Althoff) “which are interrelated in order to enable experience and explanation of events, i.e. movement and change, in the physical world.”

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7.  Meteorology/​Geology Before we discuss Aristotle’s central biological works, we turn our attention to another discipline of natural science that Aristotle seems to have founded:  this is “meteorology,” on which a treatise in four books has come down to us. We have already seen that Meteorologica book 4 has a different topic (Aristotle’s “chemical treatise”). Books 1–​3, however, consider much of what we nowadays call meteorological phenomena, though the concept of meteorology is broader: oceans and earthquakes are dealt with (2.1–​3 and 2.7–​8), as well as minerals and metals (3.6), topics we might subsume under the heading of “geology.” Furthermore Aristotle deals with comets and the Milky Way, which we would rather attribute to astronomy. These differences from modern disciplines are mostly due to (false) locations of celestial phenomena by Aristotle. At the beginning of Meteorologica he defines his topic as the phenomena appearing between the aithēr above and the earth below, that is, within the sublunary sphere. They are closely connected with the four elements, which form the matter within this sphere. Astronomical phenomena like comets and shooting stars are explained (1.4–​7) by the fiery nature of the uppermost layer of material just underneath the sphere of the moon. This fiery matter does not really burn (because then it would be bright all the time) but is a kind of potential fire (hypekkauma, tinder, 1.4 [341b19]). It stems from one of two exhalations (anathumiaseis, 1.4 [341b5–​12]) that Aristotle postulates as the material causes for almost all the meteorological phenomena. When the earth is heated by the sun, two exhalations arise: one humid (atmidōdēs anathymiasis), which stays nearer to the earth and becomes air (this is what we call the “atmosphere,” a word unknown to Aristotle and coined only in the 17th century), and one dry and smoky (kapnōdēs anathymiasis), which rises to the outermost region just underneath the sphere of the moon. This last one is the so-​called fire. It is this outermost layer that the circular motion of the sphere of the moon affects (we have already seen that there is a continuous chain of impulses from the unmoved mover down to the earth), and so the potential fire material every now and then becomes actual fire by friction. This then can be observed on the earth as shooting stars and comets. The Milky Way is explained in basically the same way (1.8). Meteorologica 1.9–​13 deal with what we would call meteorological phenomena in the narrower sense: rain, fog, clouds, dew, hoar frost, snow, and so on. All these features of the weather are explained by the hydrological cycle: water evaporates from the sea and rivers by the heat of the sun, rises up, cools, condenses, and falls back to the earth. In a more specific sense the moist exhalation as mentioned in 1.4 is the material cause. Quite naturally Aristotle in Meteorologica 1.13 treats the rivers on earth and states that they are not fed by big subterranean reservoirs in the earth (as some of his predecessors claimed). They gain their water from condensed humid air (condensing also within the earth) and precipitation that slowly trickles down underneath mountains to the source(s) of the

248   Hellenistic Greek Science rivers. In this context, Aristotle gives a short catalogue of rivers, which demonstrates his geographical knowledge (1.13 [350a15–​b30], cf. the maps in Lee 1987, 102–​104). In Meteorologica 1.14 Aristotle develops the interesting idea that within a very broad range of time the distribution of dry land and sea on earth changes continuously: what used to be land gets flooded and becomes sea, and what is sea will become land by drying up (Verlinsky 2007). The earth works like a living organism growing and decaying under the changing influence of the sun. His main example is Egypt and the delta of the Nile, which—​as he correctly observes (following Herodotus 2.10–​14)—​is a piece of land that has developed in historical times. In Meteorologica 2.1–​3, the nature of the sea is explored. It does not have sources but is refilled by the rivers. Its salt stems from the continuous evaporation of fresh water, which leaves the salt water in the sea. This happens much like food being digested in an organism: the sweet parts of it go up, become concocted to blood and nurture every part of the body, whereas the residues are salty and bitter. Once again, the earth is compared to an organism. The winds are explained in 2.4–​6 as results of the dry exhalation mentioned in 1.4. Earthquakes (2.7–​8) happen when the two exhalations do not leave the earth but remain in hollow spaces under the surface. When this subterranean wind-​like pneuma is checked or enclosed in some cave, a trembling and shaking of the earth’s surface results. Again this phenomenon is compared to tremors and throbbing of living bodies, which in the same way are caused by enclosed pneuma (2.8 [366b15–​17]). Thunder and lightning come next (2.9) and are similarly explained by the enclosure and explosive disruption of the dry exhalation in the clouds. Hot air expelled downward catches fire and is seen as a lightning bolt. (Aristotle did not know about electricity, which was not adequately described before the 18th century.) From 3.2 to 3.6 Aristotle explains phenomena like halos and rainbows as reflections of the light of sun and moon in mist or tiny drops of water. Because he does not know the exact working of the refraction of light, he has to resort to very complicated theories to explain the colors of the rainbow. His basic claims are that small mirrors only reflect colors, not shapes, and that reflection weakens our sight. Therefore the rainbow does not reflect the sun as a whole, but only its colors, and the weakening of sight produces the three colors Aristotle claims for the rainbow: red, green, and blue. At the very end of the “real” Meteorologica (3.6 [378a15–​b6]), Aristotle briefly returns to the effects of the two exhalations enclosed in the earth, which he had already used for explaining earthquakes. The dry or “smoky” (kapnōdēs) exhalation produces minerals, which Aristotle here calls “substances dug or quarried” (orykta, 378a20), that cannot be melted. He names for example realgar, ochre, ruddle, sulfur, and cinnabar. The moist or “vaporous” (atmidōdēs) exhalation produces the metals. The moist nature still shows in their fusibility. These remarks appear to be an appendix and pose some special problems.

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8. Biology Biology, or more exactly zoology, forms the core of Aristotle’s natural science. The topic is developed in the three big works Historia animalium (in 10 books, some of which are of doubtful authorship, the largest Aristotelian writing by far), De partibus animalium (4 books), and De generatione animalium (5 books), to which must be added the smaller works De incessu animalium, De motu animalium, and the “Parva naturalia” (seven writings that were not gathered before the 13th century). Even the work De anima (3 books) shows a strong tendency towards biology, though combined with philosophical discussions.

8.1  Historia animalium The history of the compilation of the Historia animalium is complicated (cf. Flashar 2004, 253–​254; Balme and Gotthelf 1991, 1–​21; Balme and Gotthelf 2002, 1–​6). That leads to different book numbers in different editions (especially difficult are books 7, 8, and 9). The two books at the end (9 and 10 in Balme’s numbering) deal with generation and development of humans, and with human sterility, topics that do not fit well with the rest of the books; book 10, therefore, is often supposed to be non-​Aristotelian (cf. Balme and Gotthelf 1991, 26–​30). In the first six chapters of book 1, Aristotle states the aim of his work. He refers back to what he has said about homoiomerē (i.e., homogeneous or uniform parts) and anhomoiomerē (limbs or organs) and declares the differences in these parts between the species as most relevant. Besides differences in parts there are differences in (1) the kinds of life certain species live and (2) their mental dispositions (ēthē, 487a12). Whereas the first aspect coincides with what we call animal behavior, the second point tends toward a human interpretation of animal behavior. Aristotle gives some examples (488b12–​ 28): the ox is gentle, sluggish, and not aggressive; the wild boar is ferocious, aggressive, and stubborn; deer and hare are intelligent and timid; the lion is “liberal,” brave, and high-​bred. Because there are certain basic functions all animals share, they also have in common the parts necessary to perform these functions. Aristotle explicitly mentions organs to take in food and to discharge the residue (1.2), because nutrition is the most basic function. The same holds for reproduction (1.3; 1.5), although this function shows a much greater variety, which implies a greater variation of parts concerned. The most fundamental sense all animals share is touch, and Aristotle understands flesh (or its analogue) to be the sense organ of touch (489a17–​29). And though some sessile species (sponges, etc.) exist, most animals (in contrast to plants) have locomotion. Accordingly, they need locomotive organs (1.5 [489b19–​490b6]).

250   Hellenistic Greek Science At the beginning of 1.6 (490b7–​15), Aristotle gives an overview of the main groups of animals (megista genē) he distinguishes, and by that shows some taxonomic interest, although this is not foremost (Kullmann 2007, 196–​210). He names (1) birds, (2) fishes, (3) cetaceans (like whales)—​all these are blooded (roughly congruent with what we call vertebrates, cf. Hirschberger 2001). Opposed are four groups that do not have blood, but some analogous fluid (corresponding to our invertebrates): (4) hard-​shelled animals (ostrakoderma, often translated testaceans), (5)  soft-​shelled animals (malakostraka, often translated crustaceans) like lobsters and crabs, (6)  “softies” (malakia, often translated as cephalopods), (7) insects (entoma). Humans stand as a separate species with no superposed main group. The following anatomical description of the parts of animals starts from the parts of the human body, because that is known best and can thus be taken as a kind of standard. By the same basis of immediate knowledge, the organs and limbs (anhomoiomerē) will be treated first and then follow the uniform parts (homoiomerē, what we would call the tissues). It is impossible to give a short account of the manifold differences of parts Aristotle describes in the following books (1.6–​4.7). Scholars have counted 581 different species (Flashar 2004, 359). These are followed by descriptions of sense organs and more gen­ eral physiological features like voice, sleep, and differences of sex (4.8–​11). Books 5–​6 deal with generation and embryonic development, and book 8 (book 9 in Balme’s order) deals with the reproduction of humans, a topic that had been announced in 5.1. All these books contain observable facts (how do animals mount each other, breeding seasons, ages of maturity, development of the eggs, the embryo, etc.), not so much causal explanations, and this is very important. As Aristotle remarks in 1.6 (491a7–​11), the gen­ eral aim of Historia animalium is to describe the differences and the features (diaphorai kai symbebēkota) of all animals: “Having done this, we must attempt to discover the causes” (Peck 1965, 35). The twofold method expressed here sounds very familiar to us:  first, one has to collect the facts of a certain field (in this case, zoology); and second, one has to explore the causes behind these facts. Historia animalium offers the first part of this operation, whereas other writings (especially De partibus animalium and De generatione animalium) present the second part (cf. Kullmann 1998, 55–​81). Because differences also occur in the behavior of animals (as stated 1.1 [487a10–​b32]), books 7–​8 (Balme) treat these differences. In book 7 these are nutrition, drinking, diseases, and habitat; and, in book 8, character and intelligence (including nesting habits). Most of the unbelievably many noted facts certainly go back to Aristotle’s systematic observations, which started on a large scale during his stay on Lesbos. Besides that he used literature (e.g., Homer and Herodotus) and reports of specialists (fishermen, craftsmen, breeders, beekeeper, etc.). Against a few mistakes and wrong conclusions stand thousands of correct and very acute observations about animals and their behav­ ior, which even today are difficult to observe. A lot of these observations have only recently been reaffirmed. One has to admit that reading the Historia animalium is not always thrilling (but it was not supposed to be a thriller). Yet one can admire the monumental, and mostly successful, effort Aristotle undertook. One of the problems with

Aristotle   251 the biological works is to understand them well, for which the cooperation of philological with biological expertise is needed, as it has been so amazingly achieved by Aubert (a biologist) and Wimmer (a philologist) and D’Arcy Thompson in their editions in the 19th century. Only recently has a new German translation with commentary been started under the supervision of Wolfgang Kullmann (cf. Kullmann 2007, for De partibus animalium), of which the first volume has appeared (Zierlein 2014; in process are Schnieders 2015; Epstein 2017). These volumes compare Aristotle’s observations with modern biological research throughout. There is much to be expected for a correct assessment of Aristotle’s efforts by this new edition.

8.2  De partibus animalium The work De partibus animalium in 4 books consists of two parts (cf. Kullmann 2007; Lennox 2001b). Book 1, which is a general introduction to biology from Aristotle’s early Academic years, was only later prefixed to the other three books. Books 2–​4 deal with the parts of animals in the way stated at the beginning of Historia animalium: after the collection of observed facts, the investigation of the causes for the different facts follows in De partibus animalium (1.5 [645a36–​b6]; and 2.1 [646a8–​12], with a direct reference). Aristotle reconfirms the priority of the final cause over the material cause, but he reminds his readers that the natural scientist has to look at both aspects. In 1.5 (645b14–​ 19) he points out that, like artificial tools, each limb and organ exists for a certain function; this function can be described as the purpose or end of each organ. And like a craftsman styling his product according to the function it is to perform, nature styles the single organs according to their function. Therefore the main purpose of De partibus animalium is to describe and explain the different functions of the organs and how they are styled to fulfill these functions. Aristotle confirms, against Plato, the great value and pleasure of an exploration of animals and plants. After all, biology starts from objects well-​known to us (as opposed to the stars and skies and their movements, which are much more regular and divine but more difficult to observe), and “in all natural things there is somewhat of the marvelous” (1.5 [645a16–​17], translation by Peck 1961, 99, and 101). We remember that, according to Metaphyiscs E.1, natural philosophy obtains the second rank after theology and that the bios theorētikos, according to the Nicomachean Ethics book 10, is the ideal way of living. Book 2 starts with a recapitulation of the different types of matter, out of which living organisms consist: first qualities (here called dynameis), elements, homoiomerē (i.e. homogeneous or uniform parts: tissues), and anhomoiomerē (organs and limbs). Aristotle begins with the explanation of the homogeneous parts of animals (blood, serum, lard, suet, marrow, bile, and flesh, 2.2–​9; semen and milk are reserved for De generatione animalium). Blood is the most important “tissue” (cf. Kullmann 2007, 366) because it is formed out of concocted food and is itself the nutriment for all other parts of the body. Consequently, then, all the other uniform parts are explained as products from blood and the factors effecting concoction are the heat and the cold of the single organism. We

252   Hellenistic Greek Science therefore find the same distribution of active and passive qualities as in the inorganic world (see above, cf. Althoff 1992). Brain (2.6) and flesh (2.7) belong to the tissues of the body. The brain is in Aristotle’s view a cooling tissue of marginal importance. It balances the heat of the warmer and higher developed animals, which is primarily located in the heart. Behind this lies a peculiar version of Aristotle’s theory of the mean: heat has a tendency to grow beyond limits, unless it is cooled to some middle intensity. Aristotle has not yet discovered the nerves (that was achieved by Herophilus and Erasistratus in Alexandria in the 3rd century bce): the word neuron, which later became the term for “nerves,” here denotes sinews. For Aristotle it is the blood vessels that transfer impulses from the sense organs to his central organ, the heart, and voluntary impulses back to the extremities. Moreover, Aristotle did not know the circulation of the blood. He compares the system of blood vessels to an irrigation system with the heart as a pool or source, from which the blood vessels lead the blood to the extremities, where it becomes flesh and continuously nurtures the body (3.10 [668a13–​21]). The flesh is a kind of modeling clay that sticks to the bones as the firm underlying structure, and both form the body of the animal. In De partibus animalium 2.10–​4.14, Aristotle explains a long series of inner organs and outer limbs of all kinds of animals with regard to their function and the material structure that results from this. Again the human species is the norm (because the most highly developed species), but all kinds of “lower” animals are discussed as well. For details see Kullmann 2007. The short work De incessu animalium continues the topic of De partibus animalium, insofar as it is concerned with the limbs that produce locomotion, but specifically asks for the reasons of the differences in limbs and ways of moving (cf. Kollesch 1985). This work is supplemented by De motu animalium (cf. Nussbaum 1978; Labarrière 2004), which may have been the latest work written by Aristotle. It develops the psychophysical background of locomotion, and to the irritation of many scholars presents the inborn pneuma (air) in ­chapter 10 as a substantial new substance within the body. This could be a later addition, perhaps by Aristotle himself (Althoff 1992, 285).

8.3: De generatione animalium Maybe the most interesting work of Aristotle’s zoology is De Generatione animalium in five books. It starts once again with the presentation of the four basic causes, of which now the moving cause will be foremost. Books 1–​3 deal with the generation of animals, and book 4 contains details about the different sexes and the theory of heredity. Book 5 seems to be a later addition, treating the secondary features as they are transmitted in generation (forms of hair, color of the eyes, changing of teeth; cf. Liatsi 2000); we will not consider it here. Aristotle takes sexual generation as the norm, because this is the way higher animals procreate. The male is in his view the animal with a higher degree of heat, which enables it to concoct the blood further, so that it becomes semen. The female is colder

Aristotle   253 and cannot reach such a high degree of concoction; instead it produces the menstrual blood. The latter is the material of procreation, the semen—​or, more exactly, the heat in it—​delivers the moving cause. In the act of copulation the tool, so to speak (that is, the moving heat), is brought onto the material and gradually shapes it into a new animal. This mechanism works like the constitution of inorganic homoiomerē out of the passive qualities under the influence of the active heat. Aristotle quite often speaks of some movements (kinēseis) of heat within semen, which are activated according to a kind of program successively to form the new embryo. The process is ingenuously compared to the production of cheese from milk with the help of rennet (2.4 [739b20–​26]). After that first act of fermentation, the heart comes into existence (the famous punctum saliens, pulsating point), because the new embryo needs an internal principle for its further development. And the heart is the organ of the final concoction of food into blood and the source from which the blood via the blood vessels is distributed to the body and lets it grow (Althoff 1997; and 2006). Therefore the blood vessels develop next and form a kind of blueprint of the future body (2.6 [743a1–​11]), and then the other parts of the body are formed step by step out of concocted blood. It is very important to recognize that Aristotle proposes an epigenetic development of the embryo (which continues even after birth: growing of hair and teeth, puberty, etc.). Aristotle can therefore be seen as the first to develop the concept of a genetic program, which nowadays is so familiar to us. The whole process of generation has the aim of producing a continuous series of individuals of one and the same species (because parents always generate offspring of the same species as their own: 2.1 [731b24–​31]). The individuals are subject to death, but the species through this process remains eternal. A second very important topic of De generatione animalium is the theory of inheritance (4.3). From what we have learned so far, it is hard to explain the fact that, sometimes, female features are transmitted to the newborn child. The female only provides the material on which the male movements in the semen work. But Aristotle reminds us that the menstrual blood is, like the semen, a concoction of normal blood that nourishes the body. Therefore it also contains some heat, and this can function in the same way as the heat of the male semen. Every once in a while the male heat fails to form the female material, and then the female impulses become effective instead. There are even movements (in the male semen and in the female menstrual blood), which stem from grandfathers and grandmothers of father or mother. Sometimes even these very faint movements are activated and form parts of the embryo. It will then have inherited features of the grandparents. According to this very refined theory, then, the forming of a male offspring is normal, but because females are indispensable for generating offspring, quite often a female offspring is formed as the second best. The whole theory of generation and inheritance is developed in close connection to the observed facts and in an ongoing discussion of the positions of other scholars before Aristotle. The physiological mechanisms presented in De partibus animalium and De generatione animalium are also the basis of the processes explained in the Parva naturalia (Althoff 2018). They deal with functions common to soul and body (De sensu sec. 1 [436a6–​17], cf. King 2006), of which the most important are waking and sleeping (De

254   Hellenistic Greek Science somno et vigilia), youth and age, breathing, life and death (De iuventute); sense perception (De sensu) is not mentioned there, neither is memory (De memoria et reminiscentia, cf. King 2004), dreams and prophecy in sleep (De insomniis/​De divinatione per somnum, cf. van der Eijk 1994), nor length and shortness of life (De longaevitate), which are the other topics of this collection. The explanation of dreams is strikingly modern: they are remainders of sense perceptions during the day, which are still present in the blood in the form of movements of heat and come to the surface, when at night no new sense perceptions are possible.

9. Conclusion The most important aspect of Aristotle’s natural science is that he was the first to consider it worthwhile to gather all the information he could get about natural phenomena, be it inorganic or organic processes. In a second step, he worked them into an orderly structure and developed all kinds of explanations, using only a restricted set of explanatory models. His main efforts lie in zoology, where he never tired of tackling even the most difficult problems like generation and inheritance. Naturally some of his observations and a lot of his explanatory models are obsolete from a modern point of view. But he has nevertheless initiated many impulses that nowadays are still present in many fields of scientific research. This concerns the basic method of field research and secondary explanation, the fundamental definitions of causes and the special role of the teleological (i.e., functional) principle in biology. His epigenetic model of generation is strictly developed from observed facts and comes close to modern ideas of genetic programs. We therefore observe not a radical change of paradigm but rather a continuity of concepts in biological research over the centuries. There is no anthropological necessity in the development toward a natural science. Aristotle of Stageira can with full right claim to have invented a way of scientific research that is still of the utmost importance today.

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chapter C2

Epicuru s and H i s C i rc l e Philosophy, Medicine, and the Sciences Teun Tieleman

1.  Epicurus: Life and Work Epicurus was born of Athenian parents on the island of Samos, at the time an Athenian colony (klērouchia), in 341 bce. As an Athenian citizen, Epicurus came to Athens at the age of 18 to fulfill his military service (ephēbeia) (323–​322). Our sources indicate an early interest in philosophy, so it seems highly likely he took the opportunity to acquaint himself with the philosophies taught in Athens, most notably Platonism and Aristotelianism (to which he developed a predominantly polemical relation later in his career). As part of the political and military events following the death of Alexander the Great (323 bce), the Athenian colonists, including Epicurus’ parents, were expelled from Samos (Diogenes Laërtius 10.1–​2). Epicurus rejoined them in Colophon, on the western coast of Asia Minor. In nearby Teos he studied with Nausiphanes, an atomist and follower of Democritus. Later he moved to Mytilene on Lesbos, where he taught philosophy for several years and became the central figure of a group of fellow-​philosophers (sumphilosophountes) including Hermarchus (who was to succeed him as head of the Epicurean school). Next he set himself up as a teacher of philosophy in Lampsacus on the Hellespont, where he converted others, who would remain loyal friends throughout his life, to philosophy (Diogenes Laërtius 10.12–​15). During this period he took note of, and responded critically to, research carried out by the mathematicians in nearby Cyzicus (Sedley 1976). When he lived and taught in Lampsacus, Epicurus still called himself a follower of Democritus (Plutarch, Adversus Coloten 1108E). What we know about Epicurus’ philosophy suggests that Democritus was a primary influence on his physics and

258   Hellenistic Greek Science ethics (even if he and his followers later tried to minimize this influence). In 307/​6 bce Epicurus returned to Athens, this time for good. He bought a house with a spacious garden (kēpos) enclosed with walls; hence ‘the Garden’ became a common way of referring to his school. Here he taught and lived amidst his followers, who formed a close-​knit community of philoi, that is, friends and relatives. Epicurus died there in 271/​0 bce, having made dispositions for the survival of his writings and the philosophical community he had gathered around him (Diogenes Laërtius 10.17–​21; cf. Clay 2009, 11–​12). To a degree, Epicurus’ Garden shared some of its characteristics with other philosophy schools founded in early Hellenistic Athens: a succession of heads, who taught, wrote, and set a personal example of what their teaching meant in practice. Like the Stoics, Epicurus promulgated the ideal of philosophy as a life-​transforming activity aimed at attaining happiness (eudaimonia). But our sources indicate in Epicurus’ case a far greater emphasis on a shared life of like-​minded friends who avoided political involvement. His community was marked by the ideals of friendship, kindliness, and goodwill. Common celebrations and holidays were held in honor of Epicurus and in commemoration of friends and relatives who had died prematurely (Dorandi 1999, 56–​ 57; Clay 2009, 26–​27). The Garden included some of his relatives, as well as slaves and women. The presence of the two latter categories was no doubt frowned upon. This may be reflected by the characterization by hostile sources of the women as prostitutes, a jibe encouraged by the hedonist ethics preached by Epicurus. Even so, his closest associates about whom we are informed, the so-​called leaders (kathēgemones)—​ Metrodorus, Hermarchus, and Polyaenus—​were all male. Epicurus’ welcoming of slaves and women in his circle should not be taken to imply a political agenda let alone activism. He believed in keeping the private and public domains separate as much as possible. For all his insistence upon the life shared among friends, Epicurus wrote a great deal. Indeed, Diogenes Laërtius reports that Epicurus was so prolific that he eclipsed all before him in the number of his writings (10.26) and presents a list of forty-​one titles, which is incomplete, yet provides “the best.” Of these, the first title, On Nature (Peri phuseōs), stands out because of its length: 37 (!) books (i.e., papyrus scrolls), which in itself may stand as a witness to the importance lent by Epicurus to physics in spite of its subordinate status (on which see sec. 2). This main work has not been preserved, but fragments have been found in the Epicurean library of the so-​called Villa of Piso (or Villa of the Papyri), which was covered under lava and ashes when mount Vesuvius erupted in 79 ce. Since its discovery some 200 years ago, the library has yielded to scholarship the badly damaged and charred remains of works by Epicurus, his followers, and commentators, as well as the founder of the library, the Epicurean Philodemus of Gadara (active first half of the 1st century bce). Work on their restoration (insofar as possible) continues (see also Gordon, chap. D02). Another main source is book 10 of Diogenes Laërtius’ Lives and Doctrines of Distinguished

Epicurus and His Circle    259 Philosophers, probably from the earlier parts of the 3rd century ce. Diogenes includes three letters by Epicurus to intimates that are designed as summaries (epitomai) of his philosophy:  the long and often densely written Letter to Herodotus (10.35–​83), presenting principles of natural philosophy derived, it seems, from On Nature; the shorter Letter to Pythocles (a follower who had chosen to remain in Lampsacus), dealing with astronomy and meteorology (10.84–​116), and the Letter to Menoikeus (10.122–​134), discussing morality. In addition, Diogenes includes the Kuriai Doxai, that is, Authentic (or Main) Doctrines, a collection of statements and considerations summarizing Epicurean wisdom and, like the letters, meant to be memorized by followers as guidance in certain circumstances (cf. Cicero, On Ends 1.20; Diogenes Laërtius 10.116). (There is a similar collection of moral and social maxims known by the Latin title Gnomologium Vaticanum or, alternatively, Sententiae Vaticanae, discovered in a 14th-​century manuscript in the Vatican library and first published in 1888.) These letters and collections of maxims are the only authentic works by Epicurus to survive; even so, they are together far more extensive than what is left of other philosophers of the same period, for example, the founders of Stoicism.

2.  Philosophy of Nature: Scope and Aim Epicurus was driven by a mission:  liberate humankind from irrational emotions, in particular the fear of death and the gods. His ethics is geared to this highest good or goal, which coincides with happiness and peace of mind or tranquility (ataraxia). This determines the status and rationale of the inquiry into the natural world. Physics (or natural philosophy) is not pursued for its own sake but subservient to his moral and spiritual mission. People should know the truth about the cosmos because it shows that the gods do not intervene in their lives and that its structure and processes can be explained without appeal to them. Further, death is “nothing to us” and so not to be feared: we are simply no longer there to experience pain or anything else; there is no afterlife in which punishments are meted out (or for that matter rewards bestowed) as suggested by traditional mythology. But then, clearly, much (if not everything) depends on achieving a firm foundation for the physical theories if these are to support the moral mission. This is why Epicurus develops a theory of knowledge involving unquestionable criteria of truth. For dialectic and logic he has little time: these are useless (as are other arts, see below). In addition, he is critical of those scientific inquiries that, despite their claims, fail to satisfy his epistemological requirements, such as mathematics and astronomy. But then, their uncertain results are not needed to lead the good life as conceived by Epicurus. His sensitivity to the limits of knowledge therefore comes with an insistence on what is useful for attaining happiness.

260   Hellenistic Greek Science

3.  The Relation of Philosophy to the Arts and Sciences Epicurus was notorious for his opposition to cultural education (paideia in Greek). There is an anecdote preserved by Diogenes Laërtius, in a fuller version by Sextus Empiricus (a Pyrrhonist skeptic, probably 3rd century ce) according to which Epicurus turned to philosophy when his grammar teacher was unable to answer his question where Chaos at the beginning of Hesiod’s Theogony came from (Diogenes Laërtius 10.6; Sextus Empiricus, Against the Professors 10.18–​19). Other testimonies attest to his view that training in the traditional arts may distract us from happiness and indeed be positively harmful (Diogenes Laërtius 10.6; Plutarch, Epicurus actually makes a pleasant life impossible 1094D; Athenaeus, Deipnosophists 13.588A). Epicurus’ targets were the so-​called liberal arts, in particular: grammar (including literature), rhetoric, dialectic, arithmetic, geometry, astronomy, and music. In targeting them, Epicurus questioned nothing less than what most of his contemporaries were used to regard as the source of elite culture and prestige. Behind this attitude lies his conviction that philosophy alone offers a road toward happiness and so deserves our full attention; the arts do not meet this high standard of necessity and are criticized for it (Blank 2009, 216). In practice, this means that Epicurus rejected claims that he felt only philosophy is entitled to make, for example, the claim made by grammarians that literature offers nudges toward happiness or wisdom or that made by astronomers that their computations offer certain knowl­ edge about the heavenly bodies and their rotations. Philodemus continued Epicurus’ criticism in separate treatises devoted to rhetoric, music, poetics, as well as household management. In criticizing the arts in the six books of his Against the Professors, Sextus Empiricus derives arguments from Epicurean sources from the 2nd to 1st centuries bce, including, probably, Philodemus, as well as his master Zeno of Sidon (ca 150 bce‒ca 79/​ 8, or later?). These arguments typically contest the usefulness of the arts for the good life, but it is also made clear that they are especially directed against the pretensions of the higher or theoretically orientated forms among them. Practically oriented ones such as “lower grammar,” understood as the art of reading and writing, are to be pursued as very useful for life (Sextus, Against the Professors 1.44–​56). A similar attitude is found in what remains of the relevant treatises by Philodemus: there are nontechnical ways of properly running one’s household, that is, without becoming, or posing as, an expert. Music may bring pleasure and is appropriate for an Epicurean, provided he or she avoids the toils inevitably entailed by a complete musical education. Likewise, the Epicurean should avoid an active political or military career as it disturbs his peace of mind, but other occupations are acceptable and wholesome insofar as they do not distract us from philosophy. Apparently, Philodemus’ activity as a poet—​at least in his own mind—​satisfied this condition (see Blank 2009). Clearly, the attitude found in Philodemus and the relevant passages in Sextus goes back to the founder himself. One may in particular note Epicurus’ polemics against the

Epicurus and His Circle    261 astronomers as reflected in what remains of books 11 and 12 of his On Nature as well as the summary in the Letter to Pythocles (Sedley 1976). This quarrel includes Epicurus’ notorious contention that the sun is about the size it appears to us (Letter to Pythocles 91; later hostile sources choose to specify this as “the size of a foot”). This position has earned Epicurus rebuke and ridicule ever since antiquity. But this is justified only to a degree. According to Epicurus’ empiricist epistemology knowledge should be based on a certain and clear foundations such as were not available for deciding issues such as the size of the planets. If any pronouncement had to be made, he relied rather on an analogy from things that could be perceived such as fires seen and felt on earth. Many of the theoretical models of contemporary astronomy testify to a tendency towards premature or excessive mathematization (cf. Algra et al. 2001). This does not make Epicurus a great (but sadly neglected) astronomer. But his position deserves to be considered in its own proper context. Epicurean epistemology, it may be recalled, comes with a keen sensitivity to the limits of knowledge. The principle of infinite divisibility lay at the heart of geometrical theory as developed by the famous mathematician Eudoxus in the first half of the 4th century bce. Epicurus and his followers, however, believed in a minimal unit (Greek elachiston) out of which atoms and hence everything else is composed, taking this not merely as a physical minimum contingent upon the nature of matter but as a theoretical minimum than which nothing smaller is conceivable (Letter to Herodotus 56–​59; Sedley 1976, 23, and 1999, 374–​379; Verde 2013). This led them to reject geometry as a science. Thus Cicero writes: Not even the belief in a minimal unit is worthy of the natural scientist and indeed Epicurus would never have held it, if he had preferred to learn geometry from his associate Polyaenus instead of making Polyaenus himself unlearn geometry. (On Ends [De finibus bonorum et malorum] 1.20)

Polyaenus of Lampsacus, formerly a prominent mathematician himself, was one of Epicurus’ earliest (and leading) converts, from the time when the latter taught in Lampsacus (311/​10–​307/​6 bce), and came to believe that “all geometry is false” (Cic. Prior Academics 2.106; cf. Sedley 1976, 24). Later the important Epicurean Zeno of Sidon, whom we already encountered as Philodemus’ teacher, was to continue the campaign against geometry, eliciting a rebuttal from the Stoic Posidonius (Proclus, On Euclid’s elements, pp. 199.3–​200.6, 214.15–​218.11 Friedlein = Posidonius, fr. 46, 47 EK; on Posidonius’ use of geometry see Tieleman, this volume, chapter D5, sec. 5; on the Epicureans’ rejection of geometry as a science see also Cambiano 1999). But what about Epicurus’ attitude to the claims and status of medicine? The list of treatises by Epicurus presented by Diogenes Laërtius 10.28 includes the title “Opinions about Diseases [nosōn] to Mithrēs” (a title which according to some has to be supplemented with “and on Death,” cf. Papyri Herculanenses 1012, col. 37, 3–​5 Puglia = fr. 18 Arrighetti , where however the title is On Diseases and Death). It is however highly doubtful whether this title betrays an interest in the art of medicine. Conceivably, it dealt with the correct opinion on, and attitude to be taken toward, disease (cf. Diogenes

262   Hellenistic Greek Science Laërtius 10.22; Epicurus, Authentic Doctrines 2 and 4). However this may be, Epicurus also looked to medicine as providing a model for the role played by the philosopher. Plato and Aristotle had already compared philosophy with medicine. Epicurus proceeded to thematize this idea: the philosopher is the doctor of the soul, dispensing therapeutic arguments aimed at curing us of wrong assumptions and the attendant affections, or passions (pathē), of the soul, most notably fear of the gods and of death (Epicurus fr. 221 Usener = 247 Arrighetti; cf. Gnomologium Vaticanum 64; Diogenes Laërtius 10.138 = fr. 504 Usener, first text; cf. Nussbaum 1986, and 1994): Empty is that philosopher’s argument, by which no affection (pathos) of a human being is therapeutically treated. For just as there is no use in a medical art that does not cast out the affections (pathē) of bodies, so there is no use in philosophy if it does not expel affection (pathos) from the soul.

The so-​called fourfold medicine (tetrapharmakos) consists of four tenets summarizing the core of his teaching: (1) the gods do not harm us; (2) death means nothing to us; (3) pleasure is easy to attain; (4) pain is easy to disregard or avoid. But in drawing this analogy between philosophy and medicine, Epicurus did not consider them of equal status. Like the other arts, medicine was subordinate to philosophy; in fact, philosophy enjoyed unique status, just as the soul does in relation to the body. This is at any rate what one might glean from the following fragment preserved by Marcus Aurelius: Epicurus says: “In my illness I did not lecture on the affections of this poor body, nor did I chatter about any such things with those who came to visit me; but I kept discussing the important issues of natural philosophy. In particular, I dwelled on this point, how the intellect, while partaking in such processes in this bit of flesh, attains tranquility, safeguarding its own good. In so doing I did not permit the doctors to put on airs as if they did something really important. No: my life went on well and nobly.” (Meditations IX.41; Epicurus fr. 191 Usener = 259 Arrighetti)

When suffering physical pain and discomfort one should be concerned with one’s mental condition. Thus Epicurus does not lecture on physical disease, as he might have done on other occasions, even if this, apparently, does not count as one of the more “important issues of natural philosophy.” The ones on which he does concentrate (death? the gods?) enable him to achieve peace of mind, that is, ataraxia, the Epicurean goal in life (Diogenes Laërtius 10.128). In such circumstances, then, one should turn to philosophy not medicine. In doing so, Epicurus puts the doctors in their place. Our Stoic source, Marcus Aurelius, approves of the attitude recommended by Epicurus, pointing out that this passage is about maintaining one’s identity—​and dignity—​as a philosopher in the face of illness and death. As such, the passage—​which may have been derived from one of Epicurus’ letters—​recalls another, more famous passage from the letter written by Epicurus from his deathbed to his pupil and friend Idomeneus (cited by Diogenes Laërtius, 10.22 = fr. 138 Usener = 259 Arrighetti).

Epicurus and His Circle    263 Here Epicurus writes that he suffers intense pains caused by strangury and dysentery, but he counteracts them through the mental joy of remembering his discussions with Idomeneus. When medicine cannot help anymore, philosophy remains effective:  it empowers one to laugh at the physical pains suffered in illness (cf. Plutarch, Against the Blessedness of Epicurus 3, 1086B = fr. 600 Usener, not in Arrighetti but cf. 197 Arrighetti). So in the case of medicine, too, Epicurus accepts its usefulness within limits and debunks undue pretensions on the part of the doctors. His use of the “medical model” in defining the philosopher’s role should not be allowed to obfuscate that Epicurus was concerned to defend and justify the status of philosophy in relation to such a culturally and socially central art as medicine. In addition, the 4th century bce saw the emergence of other sciences as pursuits independent of philosophy, the main example being mathematics and, in particular, applied mathematics, in which geometrical models were used to explain the physical world, as in optics and astronomy (cf. the work of Eudoxus of Knidus). Like some Stoics (see Stoicism, chap. D5, this volume), Epicurus responded critically, at least insofar as the new sciences seemed to threaten the status of philosophy. But where the Stoic policy allowed for the discriminating acceptance of scientific insights, Epicurus launched a more radical counterattack, contesting their theoretical foundations. In the case of the geometrical sciences, obviously, this is not just motivated by the struggle for cultural primacy, but follows from theoretical considerations, most notably Epicurus’ insistence on perception as the main criterion with which to judge dubitable pronouncements. Astronomy deals with distant objects that are not or only to a limited degree perceptible. In such cases the philosopher or scientist will have to refrain from presenting one particular explanation as true and be satisfied with a series of alternative explanations, all of which are possible (cf. Bakker 2016). Of large domains of physical reality, then, no certain knowledge is available—​a position which one might characterize as a form of “regionalized skepticism.” Given this epistemological outlook, Epicurus contested the claims made by mathematical astronomers that their theories corresponded to reality and offered a purely physical astronomy-​cum-​meteorology in their stead. Among the extant remains of his work, this is represented by his Letter to Pythocles (which is also preserved by Diogenes Laërtius, 10.84–​116) in particular. In regard to certain tenets fundamental to his natural philosophy and so, indirectly, to his whole enterprise of offering humankind the road toward happiness, Epicurus did lay claim to certainty, even though they could not be based on direct perception either, in particular that of atoms and void as the two basic constituents of reality. To these and the natural philosophy based upon them we now turn.

4.  Natural Philosophy: Atoms and the Void Epicurus brought a robustly empiricist approach to the study of the nature of things (cf. Giovacchini 2012). It is sensation that teaches us that there are two basic constituents

264   Hellenistic Greek Science of reality, or “complete natures” as he calls them in the Letter to Herodotus: bodies, the existence of which is directly attested by sense-​perception, and the void, which necessarily exists as that in which the bodies are and through which they move, that is, space. The void is not evident to sense-​perception, but reason infers its existence from what is directly observed to be the case, viz. bodies being in their place and moving about (Letter to Herodotus 39–​40). From a historical point of view, Epicurus’ void as three-​ dimensional space independent of body (cf. Plato and Aristotle) represents what may be the first concept of physical space. Given this starting point, Epicurus inferred from the coming into being and passing away of bodies the existence of indivisible (lit. “uncuttable,” atomoi) particles forming clusters and falling apart, an idea he took, with some modifications, from Democritus of Abdera (see sec. 11). The underlying assumption is that the total mass of body must remain constant. These basic constituents or atoms have to be indivisible, because otherwise they would themselves fall apart and disappear—​which is perceived not to be the case. Epicurus assumes that an atom has shape, size, and weight; other qualities, such as color, are secondary in the sense of belonging to the visible compounds of atoms. Among themselves the atoms may vary considerably in size, though in each case remaining invisible (Letter to Herodotus 54–​55). In this connection, Epicurus posits the theory we have already encountered in connection with Epicurus’ rejection of geometry:  the theory of theoretically indivisible minima, that is, the smallest conceivable parts of atoms (which are physically indivisible). This concept in many ways represents Epicurus’ answer to the puzzles raised by some of Zeno of Elea’s paradoxes concerning movement, viz. that there is indeed a smallest unit. In a way typical of his methodology he argued for this concept by drawing an analogy with the smallest perceptible unit: so, too, we have to assume a theoretical minimum (Letter to Herodotus 56–​59; Sedley 1999, 374–​379, with further references). The universe (Gr. to pan, “the whole of things,” i.e., not just the cosmos or world) is infinite. What is finite has an ultimate limit, of which we can only think in relation to something outside it. But there is nothing to limit it, so the universe is infinite. But it is infinite in terms not only of its sheer extent but also of the number of bodies, that is, atoms: if the void would be infinite but the atoms finite in number, they would simply disperse without making contact and forming compound bodies—​which is observed not to be the case (Letter to Herodotus. 41–​42). Here Epicurus assumes that atoms are in constant motion, since the void offers no resistance. Given their weight, they have a natural tendency to move perpendicularly downward, but if this were always the case no compounds would be formed. Epicurus therefore introduces his notorious “swerve” (parenklisis, Lat. clinamen), the occasional (and presumably minimal) deviation of an atom from its perpendicular downward movement (Lucretius 2.216–​250, with Long and Sedley 1987, 50–​52). The swerve triggers a concatenation of collisions: the solid, hard atoms collide and bounce in all directions. Often atoms are caught in a space enveloped by a shell of atoms clustering together. Compound bodies are formed, but the atoms locked inside keep moving, that is, vibrating. From the surface of bodies thin films of atoms are separated off, that is, images (eidōla), which form the basis of Epicurus’ theory

Epicurus and His Circle    265 of perception since it is these images that may be picked up by our sense organs (Letter to Herodotus 43–​44, 46–​53, 61–​62). The biggest compound to be formed is a world or cosmos (Greek kosmos, whose range of meaning also includes “order” and “ornament”; hence perhaps “world–​order”):  a giant system, which, also, is the result of a cascade of interactions between colliding and clustering atoms (cf. Letter to Pythocles 88). It appears that Epicurus explained the origin of the world by reference to various factors. There is the more traditional idea of a primordial vortex whereby the main elementary masses are sifted: from earth at the center via water and air to fire near the periphery of the system, that is, the heavenly regions. This process, then, is triggered by the collision of atoms and the product of the resulting movements. But the resulting order cannot be explained without giving due weight to the shape, size, and weight of the atoms (Letter to Pythocles 88–​90, with Furley 1999, 424–​431). These features explain why certain compounds can occur and others do not, at least not regularly or successfully (in which case they do not last) (Letter to Herodotus 73–​74). Again Epicurus draws an inference from the perceptible order of things: the invisible atoms, too, do not possess an infinite variety of sizes and shapes but display certain patterns producing particular patterns at the visible level and often familiar from common experience (Letter to Herodotus 54). Here one may think of the genesis of species of animal and the regularity of their procreation. Interestingly, Epicurus developed an evolutionary account according to which the fitness of existing species is the outcome of a process of elimination of unviable organs and organisms (Lucretius 4.823–​877; cf. Simplicius, On Aristotle’s ‘Physics’ pp. 371.33–​372.14 = Long and Sedley 13J). Contrast the teleological accounts of Plato and the Stoics in particular (in which appeal is made to divine agency also). Given the infinitude of the universe and the inexhaustibility of material (i.e., atoms), Epicurus proceeds to posit an infinite number of kosmoi, or worlds. Ours, then, is not the only one, let alone that it has been created for our sake. Some of these other worlds may resemble ours, but they will on the whole be different to varying degrees: it is by no means the case that the colliding and clustering atoms produce the same orderings every time. Moreover, the worlds, including the one we inhabit, will sooner or later meet the fate of all bodies, that it is to say, they will be dissolved while others will be generated. The human race, then, is also bound to disappear, contrary to Aristotle’s view that all species are perpetual. There is no individual afterlife either: the human soul is a fine blend of a few different kinds of atoms (viz. breath, air, heat, and a fine stuff lacking a proper name), enabling it to move the body and fulfill its other functions, including rational thought (Aëtius 4.3.11 = fr. 315 Usener = 159 Arrighetti; cf. Letter to Herodotus 63–​67). But the soul cannot function and exist without the body and does not survive it. After death, then, there is no sensation either. Being dead is therefore not something to be frightened of: “death is nothing to us,” it is not our concern—​ an argument that may insufficiently obviate the aspect of our clinging to life as distinguished from being afraid of what might await us when we die (Lucretius 3.417–​462, 624–​633, 806–​829 = Long and Sedley 1987, 14F‒H; cf. Letter to Herodotus 63–​68; death nothing to us: Letter to Menoikeus 124; and Lucretius 3.830–​831).

266   Hellenistic Greek Science The rule that every body will eventually dissolve has a possible exception: the gods. Contrary to what one might expect, Epicurus was not an atheist, although he was fervently opposed to the ways the gods were portrayed in myths, viz. as intervening in human affairs, especially in ways that inspire unnecessary concerns and fears threatening human happiness. Think, for instance, of the punishments meted out by gods in this life and the next according to Homer and other mythological poets. But Epicurus took the images we receive of gods, notably in dreams, as requiring the existence of an object explaining them (on the eidōla see above). But how we have accustomed ourselves to think of gods represents a distortion, which has found support in the cultural authority of Homer. Epicurus takes the correct core notion to be that of the gods’ blissful state, their happiness. From there we can perhaps correctly infer a few other features, such as their immortality. However, Epicurus took meddling in human affairs as something that goes against their blessedness, entailing as it does effort and concern. Rather, the gods enjoy themselves in their holy abodes between different worlds from which the images we sometimes receive of them are separated. Here too there is a moral point, however. These images offer us an idea of the good life to emulate in our world and in the time granted to us (Letter to Herodotus 76–​77, Letter to Menoikeus 123–​124, Cicero, On the Nature of the Gods 1.43–​49; Sextus, Against The Professors 9.43–​47; Lucretius 5.1161–​ 1125; cf. Long and Sedley 1987, sec. 23). Again, there is a clear and wide gap separating Epicurus from his philosophical opponents. According to the Stoics, divine providence rules our unique world in such a way as to involve provisions for the survival and benefit of humans, who are the crowning glory of all creation. Plato in his Timaeus had influentially expounded a similar worldview, and moreover repeated his conviction that the human soul is immortal. The overarching message is that the world has been made for us in order to lead morally meaningful lives and flourish. The only element shared by Epicurus is that he, too, thinks it is all important to know what kind of world we have been born into, so that we may draw from this knowledge certain conclusions about our attitude toward life (Lucretius 5.156–​234; Cicero, On the Nature of the Gods 1.18–​23, 52–​53). But Epicurus holds we should know that the world has not been designed for our welfare and is a pretty inhospitable place, a point exemplified by the following passage from Lucretius: A child, when nature has first spilt him forth with throes from his mother’s womb into the realm of light, lies like a sailor cast ashore from the cruel waves—​naked on the ground, without speech, helpless for life’s tasks. And he fills the place with his miserable wailing, not without justification, in view of the quantity of troubles that lie ahead for him in life! (5.222–​227 = Long and Sedley 1987, sec. 13F; their translation)

There is no god (or gods) who created an order providing a context of justification for leading a moral life and flourishing as human beings. It is then up to us to create an order of our own—​and this is exactly what Epicurus intended his philosophy to make possible, and what he tried to put into practice by founding a community of co–​philosophers and friends.

Epicurus and His Circle    267

5. Conclusion The preceding account of Epicurus’ natural philosophy has been necessarily selective (just as what we have said about its epistemological and methodological foundations). But a few salient points have emerged. Epicurus’ study of the natural world reflects the importance he attached to knowledge of the main facts of nature, leading him, for instance, to compose his On Nature in 37 books. At the same time it was not primarily driven by scientific curiosity but by a moral mission, viz. to liberate human kind of fears harmful to our welfare, viz. that of death and that of gods. Epicurus often considers a series of naturalistic explanations of, say, astronomical phenomena enough just to achieve that aim—​a procedure that was further justified in terms of the theory of knowledge and demonstration he developed. Despite these limitations, the philosophy of nature Epicurus developed is extremely interesting because of its sustained insistence upon natural causes (as opposed to geometrical models), its identification of atoms and the void as the basic constituents of physical reality, its consistent materialism, and its mechanistic (and so antiteleological) approach.

Bibliography Note:  The standard edition of Epicurean material is still Usener (1887; repr. 1966). That by Arrighetti (1960; new ed. 1973) is, however, more comprehensive, including much papyrological evidence omitted by Usener. I have therefore cited both collections. Articles in EANS:  375 (Hermarkhos), 555 (Metrodoros), 650 (Philodemos), 176–​ 680 (Poluainos), 739–​740 (Sextus Empiricus). Algra, Keimpe. Epicurus en de zon:  Wiskunde en fysica bij een Hellenistisch filosoof. Amsterdam: Koninklijke Nederlandse Academie van Wetenschappen, 2001. Algra, Keimpe, Jonathan Barnes, Jaap Mansfeld, and Malcolm Schofield, eds. The Cambridge History of Hellenistic Philosophy. Cambridge: Cambridge University Press, 1999. Arrighetti, Graziano, ed. Epicuro. Opere. Nuova edizione riveduta e ampliata. Torino: Einaudi, 1960, 1970; revised and augmented ed. 1973. Asmis, Elizabeth. Epicurus’ Scientific Method. Ithaca, NY, London:  Cornell University Press, 1984. Bakker, Frederik. Epicurean Meteorology:  sources, methods, scope and organization. Leiden: Brill, 2016. Blank, David. “Philosophia and Technē: Epicureans on the Arts.” In Warren 2009, 216–​233. Cambiano, Giuseppe. “Philosophy, Science and Medicine.” In Algra et  al. 1999, 585–​613, esp. 587–​590. Clay, Diskin. “Deep Therapy.” Philosophy and Literature 20 (1996):  501–​505. (Review of Nussbaum 1994.) Dorandi, Tizano. “The Schools: Organization and Structure.” In Algra et al. 1999, 55–​62. Furley, David. Two Studies in the Greek Atomists. Princeton, NJ:  Princeton University Press, 1967. —​—​—​. “Cosmology.” In Algra et al. 1999, 412–​451.

268   Hellenistic Greek Science Giovacchini, Julie. L’empirisme d’Épicure. Paris: Classiques Garnier, 2012. Long, Anthony A., and D. N. Sedley. 1987. The Hellenistic Philosophers. 2  vols. Cambridge: Cambridge University Press. Morel, Pierre-​ Marie. “Epicurean Atomism.” In Warren 2009, 65–​83. Nussbaum, Martha. “Therapeutic Arguments:  Epicurus and Aristotle.” In:  The Norms of Nature: Studies in Hellenistic Ethics, ed. M. Schofield and G. Striker, 31–​74. Cambridge and Paris: Cambridge University Press, 1986. —​—​—​. The Therapy of Desire. Princeton, NJ: Princeton University Press, 1994. Romeo, C. “Demetrio Lacone sulla grandezza del sole (PHerc. 1013).” Cronache Ercolanesi 9 (1979): 11–​35. Sedley, David. “The Structure of Epicurus’ On Nature.” Cronache Ercolanesi 4 (1974): 89–​92. —​—​—​. “Epicurus and the Mathematicians of Cyzicus.” Cronache Ercolanesi 6 (1976): 23–​54. —​—​—​. “The Character of Epicurus’ On Nature.” In Atti del XVII congresso internazionale di papirologia, vol. 1, 381–​387. Napoli:  Centro Internazionale per lo Studio dei Papiri Ercolanesi, 1984. —​—​—​. “Hellenistic Physics and Metaphysics.” In Algra et al. 1999, 355–​411. Taub, Liba. “Cosmology and Meteorology.” In Warren 2009, 105–​124. Usener, Hermann. Epicurea. Stuttgart: Teubner, 1966; repr. of first ed. 1887. Verde, Francesco. Elachista: la dottrina dei mini nell’epicureismo. Leuven: Leuven University Press, 2013. Warren, James, ed. The Cambridge Companion to Epicureanism. Cambridge:  Cambridge University Press, 2009.

chapter C3

H e l l enistic M at h e mat i c s Fabio Acerbi

1.  The Styles of Hellenistic Mathematics Hellenistic mathematics is identified by a certain style of writing:  lexical, syntactical, and expositive choices that are adhered to with remarkable rigidity by the authors sharing them (for the works and their contents see sec. 4 and sec. 8). Actually, three stylistic codes were employed, each related to a specific mathematical content: these are the demonstrative, the procedural, and the algorithmic codes (Acerbi 2012). The language of the demonstrative code, in which all geometric texts are written, is formulaic and generative, meaningful syntactical units being repeated exactly; context sensitivity is delegated to the denotative letters. Stylistic rigidity gives prominence to the extraordinary logico-​algorithmic potentialities of Greek language: mathematical discourse is interspersed with lexical pointers having well-​defined logical functions. A mathematical proposition can be divided in the following specific parts: (1) enunciation (protasis), where the property to be established is stated (a theorem) or the object to be constructed is proposed (a problem); (2) setting out (ekthesis), where denotative letters are assigned to the objects of the initial configuration; (3) determination (diorismos), where what is sought is stated in lettered form; (4) construction (kataskeuē), where auxiliary objects are introduced or the operations required to solve a problem are performed; (5) proof proper (apodeixis), the only part where deductive chains are worked out; this is usually introduced by a “paraconditional” announced by epei “since” and recently baptized “anaphora” (Federspiel 1995), where states of fact posited in parts 2 and 4 are used to draw the first conclusions; (6) conclusion (sumperasma), which normally repeats the enunciation and is attested in the Elements only. The subdivision coincides with an ancient one, first surfacing in Proclus (iE, 203–​207). This scheme reflects a series of well-​defined linguistic facts, identified by three markers: verbal modes and tenses, denotative letters, and particles.

270   Hellenistic Greek Science 1) Verbal modes and tenses. In the enunciation and within the proof one finds indicative and subjunctive, present or aorist. The ekthesis and the kataskeuē are in the suppositive mode: this is characterized by the imperative, present or perfect. The ekthesis is frequently, and typically, further marked by the presence of a present imperative of “to be,” in initial position and with “presential” value (“to be present”; Ruijgh 1979): it is a stylistic trait, initializing the list of assigned objects. Operations performed in the protasis are normally qualified by an aorist subjunctive; the same operations performed in the kataskeuē are invariably expressed by a perfect imperative. In both cases the verbal form is in the passive: the mathematical object is, as it were, “acted upon” in the kataskeuē. The perfect is employed, in modes other than the indicative, for its aspectual value of enestōs suntelikos “completed present,” without temporal connotation. The protasis of a problem has the verb at the (directive) infinitive; this is invariably replaced, in all citations of constructions and in the lettered reprise of the protasis at the end of the problem (not a sumperasma!), by a perfect indicative conveying result. Sometimes the perfect appears purely connoting state: bebēkenai “to stand upon,” said of an angle on an arc of circumference (Elements 3.def.9), antipeponthenai “to stand in inverse relation,” said of magnitudes (6.15); tetmēsthai “to stand cut,” said of a straight line cut in extreme and mean ratio (6.def.3); gegonetō “let it have come to be,” the opening formula of an analysis; keklisthai “to stand inclined,” said of a plane on a plane. (11.def.7) All this makes the author and temporality disappear from a proof. Some scattered markers of authorial intentionality remain, but they are restricted to conventional clauses: the formula legō hoti “I claim that” introducing the diorismos, verbal adjectives of a metamathematical character like deikteon “it is to be proved,” the formula homoiōs dē deixomen “very similarly we shall prove” introducing a potential proof, the definitions containing personal forms of kalein “to call,” some occurrences of middle verbal forms, where the mathematician “does for himself,” for instance, porisasthai “provide” in the very first definitions of the Data. 2) Denotative letters. They are absent from the protasis and sumperasma, first appearing in the ekthesis. 3) Particles. The extensive use of particles is a general characteristic of Greek; mathematical style charges them with logical connotations. There are three levels; in the first level, the particle functions as a Satzadverbium: a) Particles identifying the specific parts of a proposition or marking an argumentative reprise after a deductive hiatus: gar, oun, dē (in fact, then, thus). In particular, any transition between ekthesis and kataskeuē that cannot be distinguished through other markers, is always made conspicuous by a suitable particle. b) Particles with inferential value, that make the chain assumption-​ coassumption-​conclusion typical of every single deductive unit explicit: de, alla, dē, ara, gar (and, but, thus, therefore, for). The first two levels may overlap,

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the associated particles being coupled: for instance, an “anaphora” is seldom introduced by a simple epei: that a transition has occurred to a new specific part must be further marked by a particle with maximal scope; accordingly, one usually finds epei oun, epei gar (since then, in fact since). c) Connective particles that form compound statements from simple ones: kai, ē(toi), men . . . de, ei /​ ean (and, or, whereas . . . but . . . , if).

2.  Production and Diffusion of Hellenistic Mathematics Greek mathematical works were not diffused through official channels. They were usually sent to some addressee and were frequently preceded by a prefatory epistle. The latter inform us how mathematical works were “edited” and diffused (see van Groningen 1963, Dorandi 2007 for ancient “editions”). Apollonius sends the books of his Conics one by one: 1–​3 to Eudemus of Pergamum, 4–​7 to Attalus: therefore, each book was originally diffused in a single exemplar, sent to its addressee. In the preface to book 2, Eudemus is asked to “communicate it to those who are worthy to take part in such things; and Philonides the geometer, whom I introduced to you in Ephesus, should he ever visit Pergamum, communicate it to him” (AGE 1, 192). In the preface to book 1, we learn more (AGE 1, 2): Apollonius affirms that he redacted two versions of the Conics. The first he had communicated, “in a hurry” and “putting down all that occurred to [him], with the intention of returning to it later” to Naucrates the geometer, at the request of whom he undertook the investigation, when the latter was on the point of sailing from Alexandria. The first two books, still uncorrected, circulated also among Apollonius’ acquaintances. The second redaction is the one he is about to send, after correction, to Eudemus. In the preface of book 4, the prehistory of some research themes is reduced to: (i) a writing by Conon on the first of them, addressed to some Thrasydaeus; (ii) the reaction of Nicoteles, who deems Conon’s treatment as utterly unsatisfying; (iii) Apollonius himself claiming that, in Nicoteles’ polemical writing, the solution of problems connected with the second theme was only announced. Apollonius points out that he has not yet found this solution “demonstrated, either by [Nicoteles] himself or by anyone else” (AGE 2, 2–​4); the same holds for the remaining themes of book 4. Apollonius was accustomed to return to the same subject, either to correct what he had already published or to work it out from another perspective. Hypsicles corroborates this view in the preface of the so-​called book 14 of the Elements, where he says that an Apollonian tract on the comparison between the dodecahedron and the icosahedron inscribed in the same sphere was redacted twice, and qualifies the “other book” by Apollonius as a “second edition,” “made to circulate after being redacted with care, or so it seems” (EE 5.1, 1 and 4).

272   Hellenistic Greek Science The prefatory letters of Archimedes’ works show that he regularly circulated lists of open problems and conjectures and then their solutions. In case a conjecture revealed itself false, he shows why, but he complains that none of his addressees had ever been engaged in solving the proposed problems (AOO 2, 2). Similarly, Archimedes sends his works to individuals, in each case urging them to communicate them to “those who are acquainted with mathematics” (AOO 1, 4). Such an “edition” was sent out in a single exemplar, as we gather for instance from the fact that Heracleides physically carried to Dositheus the proofs now collected in On the Sphere and the Cylinder 1 and 2. In the preface to On Spirals, Archimedes expressly says that Dositheus, the addressee, comes last, after a number of colleagues had examined the proofs (AOO 2, 2). This is the well-​known phenomenon of the first diffusion, preceding the true “edition,” of a writing within a restricted circle, as probably was the case with books 1–​2 of Apollonius’ Conics. The prefatory letters later became a literary subgenre. Real introductions, doctrinally and rhetorically accomplished, filled with topoi and aiming at giving the reader a doctrinal frame justifying the composition and the main assumptions of the work, can be found in post-​Hellenistic authors, like Hero, Ptolemy and Pappus (Vitrac 2008). The presence of an addressee in these prefaces is nothing but a stylistic trait. On the other hand, some works are preceded by spurious introductions, redacted during Late Antiquity and sometimes mere transcriptions of class lectures, concerned with justifying assumptions or with lexical questions (such as those attached to Euclid’s Phenomena and Optics, redaction B).

3.  The Evolution of Hellenistic Mathematics In order to appreciate the evolution of Hellenistic mathematics, we cannot assess the later products on the criterion of originality. The correct parameter is the variety of scholarly activities operating in the tradition, erected on a canon that was already closed when Ptolemy wrote. That approach was caused by the predominance of a rhetorico-​ grammatical curriculum in higher education, entailing a rigid adherence to a canon of texts, and includes among its tools a wide-​ranging intellectual syncretism (philosophical, lexical, logico-​mathematical), a concern with structure and a liking for variation. The main steps of an evolution dictated by such parameters, eventually resulting in the works of the late commentators, were the following: 1) Apollonius explores mathematical domains of great originality but, at the same time, of a marked metamathematical and scholarly connotation (Acerbi 2010b). He is the key character of the subsequent evolution. Proclus informs us of the following Apollonian interventions on basic items in the Elements: clarification of

Hellenistic Mathematics   273 the notions of line and of surface (iE, 100 and 114), a general definition of angle (123–​125); proof of common notion “items equal to the same are also equal to one another” by using the notion of “superposition” (183, 194–​195); alternative constructions: displacement of a segment (227), mean point of a segment (279–​ 280), perpendicular to a straight line through a point on it (282), displacement of an angle (335–​336); alternative proof that the base-​angles of an isosceles triangle are equal (249–​250). Apollonius is probably the author of a subtle attempt at proving the fifth postulate of the Elements, a tract extant in Arabic under the name of Thābit ibn Qurra (Sabra 1968). More generally, Apollonius apparently pursued the idea that an already full-​fledged mathematical theory gains when inserted in a larger system. This can be done by introducing classifications of loci (Elements and maybe Plane Loci) and of lines (About the Helix), by discussing and coordinating assumptions, by reforming the terminology of the Data and making it fit that of the Elements, by rewriting portions of the Elements (General Treatise) and by reducing certain constructions to others (Neuseis). Apollonius’ general characterizations of the main property of conic sections in Conics 1.11–​13 can also be read in this perspective. There already existed similar characterizations, which he generalized by showing that they hold with respect to any diameter of a conic section (the so-​called oblique conjugation), not only with respect to the axis (orthogonal conjugation). Apollonius systematized not only the theory of conic sections but also the domain of loci, most notably the plane ones (see sec. 6.5). He classified them rather abstractly and possibly reformed their format, according to Pappus: they can be “occupation” (ephektikoi) loci, as a point is locus of a point; “path” (diexodikoi) loci, as a line of a point or a surface of a line; “conversion” (anastrophikoi) loci, as a surface of a point (Collection 7.21). He also systematized the variegated panorama of neusis-​techniques, by reducing many of them to plane constructions (Collection 7.27–​28). This is the first sustained attempt in Greek mathematics at solving problems by requiring that minimal mathematical techniques be employed. 2) Hero was the first to offer texts provided with a commentary aiming at making explicit and amplifying the network of their mathematical connections. He wrote a commentary on the Elements that we know only indirectly. He probably set the canon of the genre: addition of missing cases, of lemmas and corollaries, of mathematical complements; proposal of alternative proofs, aiming at strengthening the deductive structure or at simplifying it; replacement of direct proofs by indirect ones and vice versa; elaboration of counterexamples (apparently a Porphyrean speciality: Proclus, iE, 297–​298, 347–​352); structural adjustments such as changing the order of certain propositions, suppressing or adding definitions or common notions. He was concerned with logical consistency and deductive structure, adapting demonstrative techniques from other fields, as for instance in the rewriting of the proofs of the sequence Elements 2.2–​10 (Tummers 1994, 74–​86). The new proofs are framed in the format of analysis and synthesis, do not involve

274   Hellenistic Greek Science









any auxiliary constructions, and present the sequence as a connected chain of results, Elements 2.1 working as a “principle” (in the Elements they are mutually independent). 3) Hero again pursues a mathematical syncretism mixing geometrical and arithmetical, analytical and algorithmic practices (Metrics, for which see Acerbi and Vitrac 2014), pure and mixed style (the mechanical treatises). 4) Menelaus wrote Geometric Elements, no longer extant. Presumably from this work is extracted the alternative proof of Elements 1.25 transcribed by Proclus (iE, 345–​ 346). Other fragments from the Geometric Elements are found in Arabic sources (Hogendijk 2000). The initial string of prepositions of the Spherics can be read as a rewriting, in a different deductive order and without resorting to indirect proofs, of the corresponding theorems of Elements 1. 5) Diophantus disintegrates the stylistic canon described in sec. 1, most notably by interspersing the proof with authorial markers (mainly verbal forms in the first person) that fit his approach “by reduction” to the arithmetical problems he sets out to solve (cf. Acerbi 2011b, sec. 7). 6) Serenus brings the scholarly Apollonian tradition to an extreme: he claims to have commented the Conics (Heiberg 1896, 52); he writes two treatises in “traditional” form, that extend or amplify Apollonian elaborations. In the Section of a Cone he studies exclusively the triangular sections generated by a plane passing through the apex of a cone, an argument only hinted at in the beginning of Conics 1. In the Section of a Cylinder he shows that the generic cylindrical section coincides with the ellipse. He sets out the definitions and the first 20 propositions of his work in strict parallel with the corresponding ones in Conics 1 (defs. 4–​7 are an explicit quotation), to recover in succession the main properties of the ellipse. 7) Pappus, the last Hellenistic mathematician and a “mathematical Atticist,” as it were, explodes the corpus in a galaxy of lemmas, corrections, complements, and monothematic expositions totally disconnected the one from the other; he was the first to present antiquarian digressions. He assembled and organized the exegetical tradition on the Conics (Collection 7.233–​311). He discussed the opportunity of adding common notions to those of the Elements (Proclus, iE, 197–​198).

4.  Ontological Commitment and the Rules of the Game Lines are the real objects Hellenistic mathematics deals with: the way in which lines are defined demonstrates its appreciation of the mode of existence of mathematical entities. The Greek geometrical corpus does not contain a general, independent characterization of a geometric line as a mathematical genus on which to impose some ordering

Hellenistic Mathematics   275 principle; even the designation “curved line” (kampulē grammē) fell out of usage after Apollonius. Each single curve was defined or identified as a mathematical object on the basis of a variety of techniques (cf. Acerbi 2010b): 1) Generative constructions. These normally amount to cutting a surface with a plane. In this way were defined the conic (Conics 1.11–​13) and toric sections (iE, 112). 2) Pointwise geometrical constructions: a procedure is given to find isolated points that lie on the curve; the latter is then approximated by joining such points by line segments or arcs of other known lines. Pointwise constructions are, for instance, employed by Diocles to generate the curve (that in modern times came quite improperly to be called “cissoid”) by means of which he solves the problem of duplication of the cube (Eutocius at AOO 3, 66–​70, Arabic translation at Diocles 1976, 97–​113 = CG, 131–​141), and to identify the parabola as the curve enjoying the focus-​ directrix property (Diocles 1976, 63–​7 1 = CG, 112–​116). As only a finite number of points can be generated in this way, one might well wonder what is the ontological status of Diocles’ first curve. 3) Intersections of surfaces, in their turn obtained by rotation of plane figures (conic, cylindrical, toric surfaces). This is the case of the curves implicit in Archytas’ method for solving the problem of doubling the cube (Eutocius, on the authority of Eudemus, in AOO 3, 84–​88). 4) “Mechanical” constructions, in which some geometrical objects, for instance straight lines, are allowed to move, the curve being generated by the motion of some suitable point on them. Of such a kind are the definitions of most higher curves, such as: (i) all kinds of spirals and helices (the plane spiral is defined and studied—​after a suggestion by Conon, if we are to believe Pappus, Collection 4.30—​in Archimedes’ On Spirals; a very abridged exposition is in Pappus, Collection 4.31–​38; the spherical helix is described ibid., 4.53–​55); (ii) Nicomedes’ conchoid (generation and application of the curve to solve the problem of duplication of the cube in Eutocius, AOO 3, 98–​106, and in Pappus, Collection 4.39–​44); (iii) the quadratrix (generation, criticisms thereon by Sporus, and application of the curve to solve the problem of squaring the circle in Pappus, Collection 4.45–​50; at 4.45 he claims that the curve was used by Dinostratus, Nicomedes, and “some other moderns”); and (iv) very likely other special curves of which we only have the name (see for instance Pappus, Collection 4.58, and Simplicius, On Aristotle’s ‘Physics’, 60 = On Aristotle’s ‘Categories’, 192). Some sources suggest that attempts were made to replace the “mechanical” generations with other methods perceived as more geometrical. Pappus, Collection 4.51–​52, mentions such attempts with approval, showing that the quadratrix can be obtained from the plectoid surface (a screw) generated by the cylindrical helix, after intersection with a suitable plane and subsequent orthogonal projection on the base plane. 5) Setting forward a property that univocally identifies the curve (cf. the definition of a circle at Elements 1.def.15); in ancient technical jargon, this is a “characteristic

276   Hellenistic Greek Science property” (sumptōma). A “principal” characteristic property was usually provided together with the definition of a curve, but the former was carefully differentiated from the latter, that was normally set out in generative or “mechanical” terms. The best known example of such an approach is Conics 1.11–​13, where the definitions of the single conic sections are given at the very beginning of the enunciation, the associated principal sumptōma at the end of it. This approach is described as a matter of course by Pappus at Collection 3.20, and, accordingly, endorsed in his survey of special lines at Collection 4.30–​59. A special kind of mathematical proposition, with peculiar stylistic features, was conceived to store characteristic properties of known lines: these are the locus theorems. Their enunciation sets out exactly a univocal relation between a set of geometrical constraints (summarized in the sumptōma) imposed upon a point, and a curve that the point is said “to touch,” that is, to lie on. The peculiar demonstrative format in terms of analysis and synthesis of locus theorems guarantees that the condition set out in their enunciation is in fact a necessary and sufficient one. 6) There is only one example of a sumptōma identifying a whole class of lines that did not receive, as a class, a generative definition: these are homeomeric lines (Acerbi 2010a). Imposing an order on the variegated population of lines entails classifying the corpus of problems in which these lines enter as necessary mathematical tools. In its turn, this entails fixing the rules of the game, namely, setting limitations on the very techniques of solution of the problems. According to the standard scheme we find in ancient sources, in fact, problems were classified as “plane” if their solution involved only straight line and circle, “solid” if their solution involved conic sections, “linear” if any other curve was needed (see Pappus, Collection 3.20–​21 and 4.57–​59; a similar classification of loci is expounded at Collection 7.22, of neuseis at 7.27). It was obvious to ancient geometers that any plane problem could also be solved by solid methods, and so forth, and quite clear to them that any single problem falls essentially into a single category, if employing a minimal set of mathematical tools is required—​even if no proof is offered of this (cf. Collection 3.21 and 4.59; the normative character of Pappus’ prescription is likely to originate with Apollonius).

5.  The Force of the Tradition: Three Research Themes It is a classical thesis, that can be traced back to Menaechmus (iE, 78) and has been recently reaffirmed with force (Knorr 1986), that the construction problems are the internal engine of Greek mathematics. The three canonical problems (duplication of a cube, trisection of an angle, and squaring the circle) would of course be such, but also

Hellenistic Mathematics   277 the constructions of the regular polygons in Elements 4 and of the regular polyhedra in Elements 13, closing whole sections of the Euclidean treatise. This historiographical position is questionable. i) Many accounts about the constructive efforts of Greek geometers are biased by passage through two filters typical of Late Antiquity. The first is the ideology of the heuristic value of analysis. We find an explicit expression of it at Pappus, Collection 7.1; to him, the entire analytical corpus was composed to train one in solving problems of construction. The second filter is the compilatory attitude of the late commentators, our sole sources on the three classical problems. Compiling many solutions to the same problem creates a false impression of a mass effort. ii) The three classical problems did not receive equal attention; we know many solutions of the duplication problem, but far less are transmitted of the trisection problem, and only two for the quadrature of the circle: Archimedes’ and the one via quadratrix. The latter is fallacious, the former does not solve the problem on Greek standards (the circumference rectified using the spiral is not “given”). iii) In Greek mathematics prominence is accorded to the systematic, for instance in the Elements, the Conics and the Arithmetics, and methodological aims, for instance in the entire Heronian corpus or in the “full immersions in analysis,” as it were, constituted by the Apollonian analytical works. All of this is irreducible to a constructive endeavor. iv) Nonconstructive assumptions are frequently made in Greek geometry. An interesting example comes from the tract On Isoperimetric Figures. The main theorem, namely, that a regular polygon is greater than a nonregular polygon isoperimetric to it and having the same number of sides, is proved by a sort of “local symmetrization.” One assumes that the maximal polygon is neither equilateral nor equiangular and drives this assumption to contradiction by showing how to construct, by making two adjacent sides or two angles equal, a greater isoperimetric polygon. The problem lies in the fact that the existence of a maximal polygon is posited without proof. Moreover, the process of “local symmetrization” is not effective: it cannot produce, starting from a given polygon, the maximal (regular) one in a finite number of steps. The approach, then, is eminently non-​constructive. I give three examples of research themes constituted as traditional and in which constructive issues are only one facet of many:  the study of regular polyhedra, the quadratures made using the method of exhaustion, and the application of conic sections to the theory of burning mirrors. The section closes with the description of a combinatorial achievement by Hipparchus, showing that Greek mathematics was not so geometrically oriented as is usually assumed. Regular polyhedra. The tradition assigns to Theaetetus the invention of the notion of regular polyhedron (initial scholium to Elements 13, in EE 5.2, 291), even if single

278   Hellenistic Greek Science such polyhedra were certainly known before him. He probably set out a precise definition, thereby establishing that only five of them exist (a proof is attested as a corollary to Elements 13.18). The Elements do not define them as a class; they are defined singularly, the tetrahedron excepted (Elements 11.def.25–​28). Book 13 deals exclusively with them: after some preliminary results, each of them is inscribed in a sphere equal to a given one (quite roundabout a procedure, see below), and the value of the edge is established taking as a standard the diameter of the sphere (Elements 13.13–​17). Finally, the edges are compared with one another. The edges of the icosahedron and of the dodecahedron are identified with two of the irrational lines introduced in book 10, the minor and the apotome, respectively. The theme originated a series of variations, involving almost all subsequent mathematicians. The testimony of the so-​called book 14 of the Elements is crucial: Aristaeus wrote a treatise about the Comparison of the Five Figures, proving among other things that the triangular face of the icosahedron and the pentagonal face of the dodecahedron inscribed in the same sphere are inscribed in the same circle (EE 5.1, 4). Apollonius wrote a Comparison of the Dodecahedron and the Icosahedron and spurred Hypsicles to take up anew the issue in what eventually became book 14 of the Elements. It is not easy to disentangle Hypsicles’ contributions from those of his predecessors. The ratio of the two solids when they are inscribed in the same sphere is first proved to be the same as the one between their surfaces, then to one between two line segments, namely, the edges of the icosahedron and of the cube inscribed in the same sphere. The final reduction is a step into abstraction: the ratio is the same as suitable combinations of the parts of a segment cut in extreme and mean ratio. Dropping the condition that the faces must be similar, Archimedes identified and classified the 13 semi-​regular solids, as we know from Pappus (Collection 5.33–​36). Pappus again offers other constructions of the five solids, alternative to those in the Elements and framed in the format of analysis and synthesis; he presents also a comparison of the volumes of regular polyhedra that are isoepiphanic (have equal surface area), within a wider section about isoperimetric theorems (Collection 3.86–​95 and 5.72–​105). The so-​called book 15 of the Elements is a late compilation (probably early 6th century ce). The book solves a few cases of the problem of inscribing one regular polyhedron in another, providing also a procedure to calculate the number of their edges and vertices, and constructions suited to determine the value of the dihedral angles. The constructions in Elements 13.13–​17 are not perspicuous. Those presented by Pappus in Collection 3.86–​95, that he almost surely draws from an earlier source, are preceded by some preparatory material and owe their greater clarity to two factors: they proceed by analysis and synthesis and they directly inscribe the polyhedra in a given sphere, starting from two plane sections of the sphere containing opposite and parallel faces of the solids (an edge for the tetrahedron). The constructions of icosahedron and dodecahedron also require the production of the two circular sections containing the residual vertices, 3 and 5 each, respectively. As a bonus, Pappus shows that the edge of the tetrahedron and the faces of the cube and of the octahedron inscribed in the same sphere are inscribed in the same circle, and the ratio of the squares on the diameters of

Hellenistic Mathematics   279 this circle and of the sphere is 2/​3. In their turn, the faces of the icosahedron and of the dodecahedron are inscribed in the circle the square on whose radius is 1/​3 of the square on the straight line that has the same ratio to the diameter of the sphere as does the side of a decagon to the side of a pentagon, when the decagon and pentagon are inscribed in the same circle. Quadratures by exhaustion. In the prefaces to Sph. cyl. 1 and Method (AOO 1, 4; 2, 430), Archimedes expressly ascribes to Eudoxus the proof of results that we read as the corollary to Elements 12.7 and as 12.10. In Quadrature of the Parabola he asserts that what we now read in Elements 12.2 was proved by resorting to the lemma that “the excess by which the greater of two unequal regions exceed the lesser, if added to itself, can exceed any given bounded region,” and what we now read in Elements 12.18, the corollary to 12.7, and 12.10, by resorting to a “similar” lemma (AOO 2, 264). Archimedes does not mention Eudoxus about Elements 12.2 and 18: this suggests these results were proved by other geometers. Book 12 of the Elements is the first sustained application of the so-​called method of exhaustion. The following results are proved, always in the form A:B::a:b: circles are to one another as the squares on the diameters (2); pyramids which are under the same height and have triangular bases are to one another as the bases (5), and, consequently, any pyramid is a third part of the prism which has the same base with it and equal height (corollary to 7). Any cone is a third part of the cylinder having the same base and equal height (10); cones and cylinders of the same height are to one another as their bases (11); similar cones and similar cylinders are to one another in the triplicate ratio of (that is, as the cubes on) the diameters of their bases (12); spheres are to one another in the triplicate ratio of their respective diameters (18); propositions 12.1, 3–​4, 6–​8 and 16–​17 are lemmas. A typical proof applying the method is framed as a reductio, showing that the proportion stated in the enunciation cannot be realized by a figure Z greater or lesser than the assigned one (always the second term in the proportion A:B::a:b). In rough outline, the method employed in book 12 is the following. Assume first that there exists a Z < B and satisfying the proportion. The difference of Z and B will be a region homogeneous to both. The idea is to find a region S contained in B and such that Z < S < B and that, together with a region S´ similar to it and contained in A, gives rise to the proportion S´:S::a:b. From this and from A:Z::a:b it follows (Elements 5.11) A:Z::S´:S. But Z < S, therefore (Elements 5.14) A < S´, which is impossible since S´ is contained in A. The case Z > B is treated by a trick of no interest here. How to find figure S is the real problem, and this is the core of the method, which works through successive “approximations” of B by a sequence of figures. How to select such a sequence depends, in a crucial way, on the initial configuration. This is the reason why the demonstrative scheme of exhaustion is general but cannot be applied in an automatic way to any assigned figure. In the rest of the mathematical corpus, most notably in Archimedes, the technique admits subtle variations. The many results he established in this way are summarized in the table C3.1.

280   Hellenistic Greek Science Table C3.1  Theorems proved by exhaustion in Archimedes Sph. cyl. I.13–​14

The surface of any right cylinder (or isosceles cone) without the base is equal to a circle whose radius is mean proportional between the side of the cylinder (or cone) and the diameter (radius) of the base of the cylinder (cone).

Sph. cyl. I.33

The surface of any sphere is four times the greatest circle in it.

Sph. cyl. I.34

Any sphere is four times the cone that has its base equal to the greatest circle in the sphere, and its height equal to the radius of the sphere.

Sph. cyl. I.42

The surface of any segment of a sphere less than a hemisphere is equal to a circle whose radius is equal to the straight line drawn from the vertex of the segment to the circumference of the circle that is the base of the segment of the sphere.

Sph. cyl. I.44

To any sector of a sphere is equal the cone that has its base equal to the surface of the segment of the sphere identified by the sector, and height equal to the radius of the sphere.

Circ. 1

Any circle is equal to the right triangle, of which the radius is equal to one of the sides about the right angle, and the circumference is equal to the base.

Con. sph. 4

Any region contained by a section of an ellipse has, to the circle that has the diameter equal to the major diameter of the ellipse, the same ratio as its minor diameter to the major diameter or to the diameter of the circle.

Con. sph. 21–​22

Any segment of an obtuse-angled conoid, cut by a plane (non-​) perpendicular to the axis, is 3/​2 of the cone that has the same base and the same axis as the segment.

Con. sph. 25–​26

Any segment of a right-​angled conoid, cut by a plane (non-​) perpendicular to the axis has, to the cone that has the same base as the segment and equal height, the ratio that the straight line equal to the axis of the segment and three times the line adjoined to the axis, combined, has to the straight line equal to the axis of the segment and twice the line adjoined to the axis, combined.

Con. sph. 27–​28

If any spheroid is cut by a plane through the center and (non-​) perpendicular to the axis, half the spheroid is twice the cone that has the same base and the same axis as the segment.

Con. sph. 29–​30

If any spheroid is cut by a plane not through the center and (non-​) perpendicular to the axis, the lesser segment has, to the cone that has the same base and the same axis as the segment, the ratio that half the axis of the spheroid and the axis of the greater segment, combined, has to the axis of the greater segment.

Spir. 24

The region contained by the spiral traced in the first turn and the first straight line among those at the origin of the revolution is a third part of the first circle.

Spir. 25

The region contained by the spiral traced in the second turn and the second straight line among those at the origin of the revolution has, to the second circle, a ratio of 7 to 12.

Quadr. 24

Any segment contained by a straight line and a parabola is 4/​3 of the triangle that has the same base as it and equal height.

Add to this Quadrature of the Parabola 16–​17 and Method 15; the former proves the same result as Quadrature of the Parabola 24 with a mechanical method, the latter measures the “cylindrical nail,” obtained by cutting off from a cylinder inscribed in a parallelepiped the portion delimited by half the base circle of the cylinder and by a plane passing through a diameter and a suitable edge of the prism (see figure C3.1).

Hellenistic Mathematics   281

Figure C3.1 Cylindrical nail. Drawing by K. Saito.

Burning mirrors (cf. Acerbi 2011c). The geometrical behaviors of the visual rays (emitted by the eye) and of the solar rays were studied by different sciences, though grounded on the same hypotheses (cf. Geminus in [Hero], Definitions 135.12, HOO 4, 104–​106). However, the first work dealing, albeit marginally, with burning mirrors, Euclid’s Catoptrics, treats both domains, which later are separate. In it, after prop. 28 had emphasized the strategic role of the middle point of the radius of the sphere when objects are seen in concave spherical mirrors, prop. 30 studies, passing from the visual to the solar rays, the burning properties of the same mirrors. In Diocles’ On Burning Mirrors, the separation between the research domains is completed, remaining a distinguishing feature of all subsequent elaborations. The domain was a long-​lasting one. Diocles is a contemporary of Apollonius, while Anthemius of Tralles, the last author involved, lived in the 6th century. At about the same period we must assign the anonymous of the Fragmentum mathematicum bobiense (MGM, 87–​92). Only five propositions of Diocles’ treatise deal with burning properties of mirrors (Toomer 1976, 44–​7 1 = CG, 102–​116): 1, focal properties of parabolic mirrors; 2 and 3, focal properties of spherical mirrors; 4 and 5, pointwise construction of a parabola using the focus-​directrix property. To these one must add a short tract, again in Arabic only, of a certain Dtrūms (CG, 180–​213), if we accept that it is a corruption of a Greek name. The study of burning mirrors was framed in a strictly geometrical format, quite unusual in works of applied mathematics. The proof of the focal properties of the parabola underwent successive refinements by Diocles, Dtrūms, and the Anonymus Bobiensis; the proof of the latter is a few-​line argument. To construct a parabola with given focal distance requires an altogether different approach. Diocles, Dtrūms, and Anthemius (who simply proposed a nonrigorous version of Diocles’ construction), singled out a sumptōma of the parabola allowing a pointwise construction. Diocles’ sumptōma coincides with the property of equidistance from a given point and a given straight line: the focus-​directrix property, which will surface again in Collection 7.313–​318. The crucial result in the proof that any point to which this property applies satisfies also the “principal” sumptōma of the parabola with given axis, vertex, and latus rectum is a well-​ known four-​point lemma: Elements 2.8 (the four points, in order: projection on the axis

282   Hellenistic Greek Science of a point on the parabola, focus, vertex, and intersection with the axis of the tangent to the parabola drawn from the point on it). Dtrūms’ pointwise construction of the parabola follows the Dioclean scheme but does not resort to the focus-​directrix property. Three points are given: two of them are the opposite extremes of the same ordinate, the third is the vertex; it is required to draw the parabola through them. As in Diocles’ proof, the special location of the points gives also in position the tangents to the parabola through them, and it would be easy to determine the curve by means of the proportionality relations established in Conics 3.41. Dtrūms follows a different route: his proof is a replica of the argument given in Archimedes, Quadrature of the Parabola 4–​5. Another peculiar feature of Dtrūms’ approach is to isolate a four-​point technical lemma, whose role is analogous to the one of Elements 2.8 in Diocles’ proof. The lemma must have been a widespread tool, since we find it in Pappus, Collection 7.89–​90, 220–​221, and 277, who offers five slightly different proofs. Diocles and Dtrūms display a feeling for what we nowadays would call “structure”: the linear lemmas become the real core of a proof, beyond the contingent geometrical embellishments; the fact that they can be applied in disparate configurations testifies that they belong to an order of mathematical reflection that somehow extracts the “essential geometrical content,” as it were—​sequences of points on a straight line—​from a particular geometrical configuration. The linear lemmas dictated the directions of research:  as basic demonstrative tools, they imposed their own presence in the proofs, thereby conditioning the kind of results available. Pappus’ Collection is the place where this tendency comes to its extreme and induces a disintegration of the corpus. Hipparchus’ numbers. They are mentioned by Plutarch in Stoic Self-​Contradictions 1047c–​e and Table-​Talk 8.9, 732f–​733a:  Hipparchus showed that “affirmation gives 103049 conjoined propositions and negation 310952.” He did the calculation to refute the leading Stoic philosopher Chrysippus, who claimed that “the number of conjunctions produced by means of ten propositions exceeds a million.” It happens that 103049 is the 10th Schröder number. Such numbers were first (re-​)introduced in 1870 to solve a series of “bracketing problems.” Suppose that a string of n letters is given: it is requested to find all possible ways to put the letters between brackets. The bracketing of a single letter is always omitted, as well as overall brackets enclosing the whole string of letters and brackets. One bracketing of a string of ten letters is: (x(xx)x)xx(xx)(xx). If s(n) denotes the number of possible bracketings of a string of n letters, then we have s(1), s(2), . . . , s(11), . . .  =  1, 1, 3, 11, 45, 197, 903, 4279, 20793, 103049, 518859, . . . Hipparchus’ first number coincides thus with the 10th Schröder number s(10). One remarks also that (s(10) + s(11))/​2 = 310954.

Hellenistic Mathematics   283 It is possible to explain Hipparchus’ numbers in terms of some peculiar features of Stoic logic; this has also led to a reappraisal of ancient Greek combinatorics (Acerbi 2003). The connectives of Stoic logic are subjected to rigid syntactical rules. Among them the rule of prefixing the connective particle assumes a prominent position: in the case of a conjunction a kai “and” was prefixed, as in kai hēmera esti kai nux esti “both it is day and it is night.” If we represent the propositions referred to by Plutarch as a string of 10 letters, counting conjunctions in an affirmative sentence coincides with counting bracketings of strings of letters since the Stoic prescription distinguishes between syntactically different conjunctions. The explanation of Hipparchus’ second number requires a little more argument, since an additional negation is involved (and one must also amend the 310952 transmitted by Plutarch). To compute the number of bracketings of a string of n letters, an effective algorithm, which was probably within Hipparchus’ reach, takes into account the recursive character of the process: s(n) with n ≥ 2 is the sum of s(i1) . . . s(ik) over all ordered partitions of n into k ≥ 2 positive addenda such that i1 + . . . + ik = n. In words, one starts by fixing the first level of brackets, that is, the most external one (here the representation in terms of trees is useful). The building blocks at this level are single letters or brackets. To calculate the total number of possible bracketings given a specific configuration of first-​level brackets one has to take the product of the numbers of possible bracketings associated with each building block. The only nontrivial contributions to the product arise when the building block is a bracketed string made of i (2 < i < n) letters and possibly further brackets, so that its contribution amounts to s(i). As an example, take the bracketing of 10 letters above. There are five first-​level building-​blocks: (x(xx)x), x, x, (xx), (xx), which can be associated with the following string of digits, each corresponding to the number of x’s in the relative building block: 4, 1, 1, 2, 2. With this partition of 10 fixed, the corresponding contribution to the sum is s(4)s(1)s(1)s(2)s(2) = s(4) since s(1) = 1 = s(2). Fixing the first level of brackets corresponds to picking up one specific ordered partition of n, that is, one specific addend in the above sum. Summing over all possible partitions (i.e., all ways of fixing the first level of brackets) we get the result. One is thus enabled to determine the numbers s(n) in succession starting from the obvious s(2) = 1.

6.  Hellenistic Mathematics: A Manuscript-​Based Map Hellenistic mathematics has come to us through a manuscript tradition reflecting, to a large extent, editorial choices made in the imperial age or in Late Antiquity. As a consequence, our knowledge of it is distorted by the formation of privileged lines of transmission or of canons, although the selection did not normally operate within the corpus of writings of a single author. Listing the Greek mathematical works with respect to the

284   Hellenistic Greek Science complexity of their tradition also provides us with some useful insights about their reception and their placement within literary subgenres (sec. 8 lists critical editions and other material). For completeness’ sake, I include some late authors. 1) The whole tradition depends on a single manuscript: Pappus’ Collection (Vaticanus graecus 218), books 1–​4 of Apollonius’ Conics (Vaticanus graecus 206), Hero’s Metrics (Seragliensis G.İ.1). 2) There are two ancient recensions, with minor variants: Euclid’s Elements and Data (main testimony of one of the recensions:  Vaticanus graecus 190), Theodosius’ Spherics (the same applied to Vaticanus graecus 204). 3) There are two ancient recensions, with conspicuous variants: Euclid’s Optics and Phenomena (main testimony of one of the recensions: Vaticanus graecus 204). 4) There is an ancient and a Byzantine recension, differing in style:  commentaries of Pappus and Theon on Ptolemy’s Almagest (both are incomplete; best manuscript Laurentianus Pluteus 28.18), Theon’s commentaries to Ptolemy’s Handy Tables (Greater Commentary:  best manuscript Vaticanus graecus 190; Little Commentary: the ancient tradition is finely branched), the anonymous Prolegomena to the Almagest (best manuscripts Marcianus graecus 313 and Vaticanus graecus 1594), whose tradition only partly coincides with that of Ptolemy’s treatise. 5) The tradition is ancient and has several branches; sometimes it is possible to reconstruct a (partial) stemma, sometimes it is not. In the case of the Archimedean corpus the first subarchetype can be reconstructed with certainty from its many apographs, the second has left traces only in the Latin translation by William of Moerbeke (Ottobonianus latinus 1850), the third is the much celebrated palimpsest (formerly Hierosolymitanus Sancti Sepulchri 355). The contents of the three subarchetypes do not overlap exactly. Ptolemy’s Almagest is transmitted by a manuscript in uncial (Parisinus graecus 2389) and by several manuscripts in minuscule (Marcianus graecus 313; Vaticanus graecus 1594, 180 and 184); the number of independent testimonies allows us to go back with certainty to a 6th-​century recension, made in the Neoplatonic school of Alexandria, and very likely to an earlier scholarly recension. 6) The tradition is late and complex, but it is possible to reconstruct a stemma of all manuscripts:  books 1–​4 of Diophantus’ Arithmetics (Marcianus graecus 308; Vaticanus graecus 191 and 304; Matritensis 4678). 7) Philological monsters: Geometry and Stereometry included in the Heronian corpus; they are an editorial patchwork of extracts from several manuscripts (Seragliensis G.İ.1; Parisinus graecus 1670; Parisinus suppl. graecus 387; Vaticanus graecus 215). The evolution of book production techniques and scholarly or pedagogical aims have determined, to a large extent, the textual tradition of writings of different authors but of related subject. This is the phenomenon of the formation of corpora composed of works perceived as falling in the same research domain. Two major collections of this kind are known, one surviving and the other lost. The former is the so-​called little astronomy,

Hellenistic Mathematics   285 whose earliest accessible form is in Vaticanus graecus 204, written in the first half of 9th century. It is worthwhile to give its contents in detail: (1) Theodosius, Spherics (f. 1r); (2) Autolycus, On the Moving Sphere (f. 38r); (3) Euclid, Optics redaction B (f. 43v); (4)  Euclid, Phenomena redaction b (f. 59r); (5)  Theodosius, On Habitations (f. 77v); (6) Theodosius, On Days and Nights (f. 84r); (7) Aristarchus, On the Sizes and Distances of the Sun and Moon (f. 109v); (8) Autolycus, On Risings and Settings (f. 119r); (9) Hypsicles, On Rising Times (f. 133v); (10) Euclid, Catoptrics (f. 136r); 145r only the final diagrams of the Catoptrics, 145v blank; (11) Eutocius, commentary on Conics (f. 146r); (12) Euclid, Data (f. 173v); (13) Marinus, Prolegomena to Data (f. 196r); (14) Scholia to Elements (f. 199r). The Vaticanus graecus 204 is the result of the assemblage of (a) an homogeneous corpus of writings not later than the 1st century bce (items 1–​10, all pertaining to astronomy), probably already contained in a single codex, of (b) commentaries of 6th-​ century authors (Eutocius, Marinus) to which a commented-​on work happened to be attached (the Data), and of (c) later scholarly material (the scholia). The so-​called analytical corpus is described by Pappus in Collection 7. It included in this order Euclid’s Data, Apollonius’ Cutting off of a Ratio in two books, Cutting off of an Area in two books, Determinate Section in two books, Contacts in two books, Euclid’s Porisms in three books, Apollonius’ Vergings in two books, Plane loci in two books, Conics in eight books, Aristaeus’ Solid Loci in five books, Euclid’s Loci on a Surface in two books, Eratosthenes’ On Means. In book 7 of the Collection, Pappus gives first a description of the treatises up to the Conics (Collection 7.4–​42), presenting then a long series of lemmas, corrections, additions to them (Collection 7.43–​321). Of this corpus, made up of writings of Hellenistic authors, only Data and Conics 1–​4 survive in Greek; Apollonius’ Conics 5–​7 and Cutting off of a Ratio exist only in Arabic translation, Conics 8 and all the rest being lost. Other treatises have been transmitted only in Arabic, usually in a restricted number of manuscripts:  Diocles’ On Burning Mirrors, Menelaus’ Spherics, four books of Diophantus’ Arithmetics, probably coinciding with books 4–​7 of the original treatise.

7.  The Texts We Read When We Read Hellenistic Mathematics A further question is the status of the texts we have access to. The mathematical works were exposed to the manifold manipulations all ancient literary products have been subjected to:  editions and recensions, commentaries, local rewritings and epitomes. Add to this that Greek mathematical style produces texts that are typically “unsaturated,” as it were, both from the linguistic and from the logico-​deductive point of view, yet they can be completed in an univocal way as for their content. Finally, the mathematical works were not simply read, but used and reworked by other mathematicians. As a consequence, in the tradition of mathematical writings the phenomenon of multiple recensions assumes an extent without parallels in other areas of literary production

286   Hellenistic Greek Science (for a complete survey of Byzantine recensions of Greek mathematical works see Acerbi 2016). A paradigmatic example is Apollonius’ Conics, of which we know: i) The original double edition by Apollonius (see sec. 2). ii) Eutocius’ edition, prepared by collating several divergent recensions; this is the text we now read. The commentary Eutocius wrote in the margins of his edition is extant, but it has followed a line of transmission different from that of the Conics. iii) An anonymous Byzantine recension, within a larger project of a mathematico-​ astronomical corpus (Decorps-​Foulquier 1987). iv) Several independent recensions during the Renaissance. They were at the basis of Latin translations such as Memmus’ (1537) or of editions like the masterly 1710 princeps of Halley, or were employed as working exemplars of noted scientists (the anonymous recension from which derives Norimbergensis Cent. V, App. 6, owned by Regiomontanus). The interventions on the text can be arranged into three levels, depending on the size of the linguistic units involved. 1) Local adjustments of disparate kinds: insertion of nouns like “angle” or “straight line,” of particles and articles (for instance in the expressions designating angles); fine-​tuning between the specific parts of a proposition; modification of the denotative letters and reshaping of the diagram; normalization of the syntax and of the formulaic expressions. Such variants, that tend to cumulate, are at once forms of hypercorrection and of “hypercharacterizing,” and correspond precisely to the dialectal hypercorrections to which the texts of archaic poetry were exposed. In Heiberg’s and Menge’s prolegomena to their own editions of the Elements and the Data one finds a complete inventory of this kind of modifications (EE 5.1, xxxix–​lviii; EOO 6, xxxii–​xlviii). 2) Insertion of deductive steps, of expressions aiming at making generality explicit; correction of faulty arguments or filling up of lacunae; addition of metamathematical clauses:  postponed explanations, quotations of enunciations (sometimes made context sensitive by using local letters) or of definitions, references to suppositions, appeals to the evidence or to the diagram, analogical or potential proofs, identifications of objects (syntagmata preceded by “that is”). 3) Redaction of alternative proofs (Vitrac 2004), addition and displacement of definitions, changes in the order of principles or propositions, functional changes (for instance from corollary to proposition), combining or splitting propositions, substitution of proofs, addition or elimination of cases within one and the same proposition, insertion of lemmas to prove assertions left unproved in a proof.

Hellenistic Mathematics   287 Such variants could be directly inserted in the text, if they were conceived in view of a new recension, or simply annotated in the margins, eagerly included in the text at some stage of copy (a striking example is studied in Acerbi 2009).

8. Onomasticon The list contains name, certain or presumed date, and mathematical works of the main authors mentioned in this chapter. After the name, references to the corresponding biographical entries in some standard reference works are provided. The bibliographical references are to the critical editions of the surviving texts, to important mentions of the lost works in ancient writings, or to fundamental secondary literature. Anthemius of Tralles (DSB 1.169–​170, RE 1.2 [1894] 2368–​2369, EANS 90–​91): d. 534 ce. On Surprising Mechanisms: theory of conic sections applied to optics (MGM, 78–​87, CG, 349–​359). Apollonius of Perga (DSB 1.179–​193, RE 2.1 [1895] 151–​ 160, EANS 114–​115): ca 200 bce. Conics: Eight books (seven extant), from 5 to 7 in Arabic only (AGE 1 and 2, 2–​96; Decorps-​Foulquier et al. 2008–​2010; Toomer 1990). Cutting off of a Ratio in two books, only in Arabic translation (Rashed and Bellosta 2010). Lost works, traces of which can be found in Arabic authors (Hogendijk 1986): Cutting off of an Area in two books, Determinate Section in two books, Contacts in two books, Vergings in two books, Plane Loci in two books. A treatise on the comparison of the dodecahedron and the icosahedron (EE 5.1, 1–​4). Researches in astronomy (Almagest 12.1), on unordered irrational (Pappus, commentary on Book X of the Elements 1.1, 2.1; Proclus, iE, 74; EE 5.2, 83), on the ratio between a circumference and its diameter, on numeric systems able to express large numbers (Collection 2), on the cylindrical helix, on foundational themes (AGE 2, 101–​139; Acerbi 2010a, 2010b). Archimedes of Syracuse (DSB 1.213–​231, RE 2.1 [1895] 507–​539, EANS 125–​128): d. 212 bce. On the Sphere and the Cylinder 1 and 2 (in origin two treatises), Measurement of the Circle, On Conoids and Spheroids (AOO 1), On Spirals, On the Equilibrium of Planes in two books, The Sand-​reckoner, Quadrature of the Parabola, On Floating Bodies in two books, Stomachion, Method (AOO 2). On Mutually Tangent Circles, in Arabic only (AOO 4). Relative chronology in Knorr 1978. Aristaeus (DSB 1.245–​246, RE S.3 [1918] 157–​158, EANS 130–​131): ca 300 bce. Solid Loci in five books, lost (Collection 3.21, 7.3, 29–​31, 33–​35; Jones 1986, 574–​587). A treatise On the Comparison of the Five Figures, cited by Hypsicles (EE 5.1, 4).

288   Hellenistic Greek Science Conon of Samos (DSB 3.391, RE 11.2 [1922] 1338–​1340, EANS 486): ca 250 bce. Researches on the plane spiral (Collection 4.30) and on the mutual intersections of conics (AGE 2, 2). A treatise in seven books On Astrology (Probus, ad Ecl. 3.40). Diocles (DSB 4.105, RE 5.1 [1903] 813–​814, EANS 255): ca 150 bce. On Burning Mirrors, a rearranged epitome in Arabic translation, partly attested in Greek as extracts by Eutocius: focal properties of parabola and circumference (Toomer 1976, CG, 98–​141; AOO 3, 66–​70, 160–​176). Diophantus of Alexandria (DSB 4.110–​119, RE 5.1 [1903] 1051–​1073, EANS 267–​ 268): ca 250 ce. Arithmetics in 13 books, six of which transmitted in Greek (DOO 1, 2–​448), four in Arabic version only (Sesiano 1982, DA). On Polygonal Numbers, incomplete (DOO 1, 450–​480; Acerbi 2011b, 191–​199). Lost works: Porisms (DOO 1, 316, 320, 358), Moriastica (scholium to Iamblichus, on Nicomachus’ Arithmetics, 127; and DOO 2, 72). Eratosthenes of Cyrene (DSB 4.388–​393, RE 6.1 [1907] 358–​389, DPhA 3.188–​236, EANS 297–​300): active ca 240–​195 bce. A lost treatise On Means included in the analytic corpus (Collection 7.3, 22, 29). Contributions to the theory of numeric means (Theon of Smyrna, Exposition, 106–​111 and 113–​119). Design of a device to find arbitrarily many mean proportionals between two given lines (Eutocius in AOO 3, 88–​96). Euclid (DSB 4.414–​459, RE 6.1 [1907] 1003–​1052, DPhA 3.252–​272, EANS 304–​ 307): ca 250 bce. Elements in 13 books (EE 1–​4), Data (EOO 6), Optics, Catoptrics (EOO 7), Phenomena, Sectio canonis, on the location of notes on the string of a monochord (EOO 8). An elementary treatise of mechanics, only in Arabic version (Woepcke 1851; Acerbi 2007, 2455–​2484). Lost writings:  Porisms in three books (Collection 7.13–​20 and 193–​232; Simson 1776; Hogendijk 1987), Pseudaria, on fallacious proofs (Acerbi 2008), On the Division of Figures (Archibald 1915, Acerbi 2007, 2383–​2454), Loci on a Surface in two books (Collection 7.312–​318), Conics in four books (Collection 7.30). Hero of Alexandria (DSB 6.310–​315, RE 8.1 [1912] 992–​1080, DPhA Suppl. 87–​103, EANS 384–​387): ca 50 ce. Pneumatics in two books, Automaton Construction (HOO 1), Mechanics (only in Arabic) and Catoptrics (HOO 2 and Jones 2001), Metrics in three books, Dioptra (HOO 3, the first also Acerbi and Vitrac 2014). Artillery Construction and Cheiroballistra: artillery manuals (Wescher 1867, Marsden 1971). Surely spurious but traditionally included in the Heronian corpus: Definitions, Geometry (HOO 4), Geodesy, Stereometry 1 and 2, On measurements (HOO 5), Handbook of Agriculture. Hypsicles (DSB 6.616–​617, RE 9.1 [1914] 427–​433, EANS 425): ca. 150 bce. The so-​called 14th book of the Elements (EE 5.1, 1–​22). On Rising Times of the zodiacal signs (De Falco and Krause 1966). Lost works on number theory (DOO 1, 470–​472; Acerbi 2011b, 196–​197). Menelaus of Alexandria (DSB 9.296–​302, RE 15.1 [1931] 834–​835, DPhA 4.456–​464, EANS 546): ca 100 ce.

Hellenistic Mathematics   289 Spherics in three books, only in a number of Arabic revisions: geometry of the surface of the sphere, with explicit astronomical applications (Halley 1758; Krause 1936; Acerbi 2015). Geometric Elements, only a few fragments in Arabic authors (Hogendijk 2000), Method for the Determination of the Magnitude of Each of the Mixed Bodies, only in Arabic version (Würschmidt 1925). Maybe a work on planetary theory (Jones 1999, 69–​80). Nicomedes (DSB 10.114–​116, RE 17.1 [1936] 500–​504, EANS 580): ca 150 bce. Invention of the conchoids and their application to doubling the cube (Eutocius in AOO 3, 98–​106; Collection 4.39–​44; Simplicius, On Aristotle’s ‘Physics’, 60 = On Aristotle’s ‘Categories’, 192). Use of the quadratrix to square the circle (Collection 4.45–​50). Pappus of Alexandria (DSB 10.293–​304, RE 18.3 [1949] 1084–​1106, EANS 611–​612): ca 320 ce. Collection in eight books, the first being lost, the last also in Arabic (Hultsch 1876–​ 1878; Jackson 1972; Jones 1986). A commentary on Ptolemy’s Almagest, of which only two books of 13 survive (iA 1). A commentary on Elements X, only in Arabic (Junge and Thomson 1930). Serenus of Antinoe (DSB 12.313–​315, RE 2A.2 [1923] 1677–​1678, EANS 734–​735): ca 250 ce. On the Section of a Cylinder, aiming at recovering the main properties of the ellipse. On the Section of a Cone, by a plane passing through its apex (Heiberg 1896). A commentary on Apollonius’ Conics, lost (ibid., 52). Theodosius of Bithynia (DSB 13.319–​321, RE 5A.2 [1934] 1930–​1935, EANS 789–​ 790): ca 150 bce. Spherics in three books:  geometry of the sphere, with implicit astronomical applications (Heiberg 1927; Czinczenheim 2000). On Habitations:  on phenomena pertaining to the rotation of the celestial sphere, in function of the observer’s latitude; On Days and Nights in two books: on the relative lengths of day and night in function of the sun’s position on the ecliptic (Fecht 1927). A commentary on Archimedes’ Method, works in astronomy and gnomonics (Suda Θ 142, Vitruvius, Arch. 9.8.1). Zenodorus (DSB 14.603–​605, RE 10A [1972] 18, EANS 845): ca 150 bce. On Isoperimetric Figures, extracts survive in book 1 of Theon’s commentary on the Almagest (iA, 355–​379), in Pappus’ Collection (5.3–​19, 38–​40) and in the anonymous Prolegomena to the Almagest (Acerbi, Vinel, and Vitrac 2010).

Bibliography Abbreviations AGE: Apollonii Pergaei quae Graece exstant cum commentariis antiquis. 2 vols. J. L. Heiberg, ed. Leipzig: Teubner, 1891–​1893. AOO:  Archimedis opera omnia cum commentariis Eutocii. 3  vols. J. L. Heiberg, ed. Leipzig: Teubner, 1910–​1915. CG: Les catoptriciens grecs I. Les miroirs ardents. R. Rashed, ed. Paris: Les Belles Letters, 2000.

290   Hellenistic Greek Science DA: Diophante. Les arithmétiques. 2 vols. R. Rashed, ed. Paris: Les Belles Letters, 1984. DOO: Diophanti Alexandrini opera omnia cum Graeciis commentariis. 2 vols. P. Tannery, ed. Leipzig: Teubner, 1893–​1895. EE: Euclidis Elementa. 5 vols. J. L. Heiberg, ed. Leipzig: Teubner, 1969–​1977. EOO: Euclidis opera omnia. Vols. 6–​8. J. L. Heiberg and H. L. Menge, eds. Leipzig: Teubner, 1898–​1916. HOO:  Heronis Alexandrini opera quae supersunt omnia. 5  vols. W. Schmidt et  al., eds. Leipzig: Teubner, 1899–​1914. iA: Commentaires de Pappus et de Théon d’Alexandrie sur l’Almageste. 3 vols. A. Rome, ed. Città del Vaticano: Biblioteca Apostolica Vaticana, 1931–​1943. iE:  Procli Diadochi in primum Euclidis Elementorum librum commentarii. G. Friedlein, ed. Leipzig: Teubner, 1873. MGM: Mathematici Graeci Minores. J. L. Heiberg, ed. København, 1927. Acerbi, F. “On the Shoulders of Hipparchus: A Reappraisal of Ancient Greek Combinatorics.” Archive for History of Exact Sciences 57 (2003): 465–​502. —​—​—​. Euclide, Tutte le Opere. Milano: Bompiani, 2007. —​—​—​. “Euclid’s Pseudaria.” Archive for History of Exact Sciences 62 (2008): 511–​551. —​—​—​. “The Meaning of πλασματικόν in Diophantus’ Arithmetica.” Archive for History of Exact Sciences 63 (2009): 5–​31. —​—​—​. “Homeomeric Lines in Greek Mathematics.” Science in Context 23 (2010a): 1–​37. —​—​—​. “Two Approaches to Foundations in Greek Mathematics: Apollonius and Geminus.” Science in Context 23 (2010b): 151–​186. —​—​—​. “Pappus, Aristote et le ΤΟΠΟΣ ΑΝΑΛΥΟΜΕΝΟΣ.” Revue des Études Grecques 124 (2011a): 93–​113. —​—​—​, ed. Diofanto, De polygonis numeris. Pisa and Roma: Fabrizio Serra Editore, 2011b. —​—​—​. “The Geometry of Burning Mirrors in Greek Antiquity. Analysis, Heuristic, Projections, Lemmatic Fragmentation.” Archive for History of Exact Sciences 65 (2011): 471–​497. —​ —​ —​ . “I codici stilistici della matematica greca:  dimostrazioni, procedure, algoritmi.” Quaderni Urbinati di Cultura Classica, new series, 101 (2012): 167–​214. —​—​—​. “Traces of Menelaus’ Sphaerica in Greek Scholia to the Almagest.” SCIAMVS 16 (2015): 91–​124. —​—​—​. “Byzantine Recensions of Greek Mathematical and Astronomical Texts:  A Survey.” Estudios Bizantinos 4 (2016): 133–​213. Acerbi, F., N. Vinel, and B. Vitrac. “Les Prolégomènes à l’Almageste. Une édition à partir des manuscrits les plus anciens:  II. Le traité des figures isopérimétriques.” SCIAMVS 11 (2010): 92–​196. Acerbi, F., and B. Vitrac, eds. Héron, Metrica. Pisa and Roma: Fabrizio Serra Editore, 2014. Archibald, R. C. Euclid’s Book on Division of Figures. With a Restoration Based on Woepcke’s Text and on the Practica Geometriae of Leonardo Pisano. Cambridge: Cambridge University Press  1915. Czinczenheim, C. Édition, traduction et commentaire des Sphériques de Théodose. Thèse, Université de Paris IV, Sorbonne. Lille: Atelier National de Reproduction des Thèses, 2000. Decorps-​Foulquier, M. “Un corpus astronomico-​mathématique au temps des Paléologues. Essai de reconstitution d’une recension.” Revue d’Histoire des Textes 17 (1987): 15–​54. Decorps-​Foulquier, M., M. Federspiel, and R. Rashed, eds. Apollonius de Perge, Coniques. 4 vols. in 7. Berlin and New York: de Gruyter: 2008–​2010. Dorandi, T. Nell’officina dei classici. Roma: Carocci, 2007.

Hellenistic Mathematics   291 De Falco, V., and M. Krause, eds. Hypsikles, Die Aufgangszeiten der Gestirne. Göttingen: Vandenhoeck und Ruprecht, 1966. Fecht, R., ed. Theodosii De Habitationibus Liber De Diebus et Noctibus Libri duo. Berlin: Weidmann, 1927. Federspiel, M. “Sur l’opposition défini/​indéfini dans la langue des mathématiques grecques.” Les Études Classiques 63 (1995): 249–​293. Halley, E., ed. Menelai Spæricorum libri III. Oxford, 1758. Heiberg, J. L., ed. Sereni Antinoensis opuscula. Leipzig: Teubner, 1896. —​—​—​, ed. Theodosius Tripolites Sphaerica. Berlin: Weidmann, 1927. Hogendijk, J. P. “Arabic Traces of Lost Works of Apollonius.” Archive for History of Exact Sciences 35 (1986): 187–​253. —​—​—​. “On Euclid’s Lost Porisms and Its Arabic Traces.” Bollettino di Storia delle Scienze Matematiche 7.1 (1987): 93–​115. —​—​—​. “Traces of the Lost Geometrical Elements of Menelaus in Two Texts of al-​Sijzî.” Zeitschrift für Geschichte der arabisch-​islamischen Wissenschaften 13 (2000): 129–​164. Hultsch, F., ed. Pappi Alexandrini Collectionis quae supersunt. 3  vols. Berlin:  Weidmann, 1876–​1878. Jackson, D. E. P. “The Arabic Translation of a Greek Manual of Mechanics.” Islamic Quarterly 16 (1972): 96–​103. Jones, A., ed. Pappus of Alexandria, Book 7 of the Collection. 2 vols. New York: Springer, 1986. —​—​—​. Astronomical Papyri from Oxyrhynchus. Philadelphia:  American Philosophical Society, 1999. —​—​—​. “Pseudo-​Ptolemy De Speculis.” SCIAMVS 2 (2001): 145–​186. Junge, G. and W. Thomson. Pappus, Commentary on Book X of Euclid’s Elements. Cambridge, MA: Harvard University Press, 1930. Knorr, W. R. “Archimedes and the Elements: Proposal for a Revised Chronological Ordering of the Archimedean Corpus.” Archive for History of Exact Sciences 19 (1978): 211–​290. —​—​—​. The Ancient Tradition of Geometric Problems. Boston: Birkhäuser, 1986. Krause, M., ed. Die Sphärik von Menelaos aus Alexandrien in der Verbesserung von Abû Nasr Mansûr B. ‘Alî B. ‘Irâq. Berlin: Weidmann, 1936. Marsden, E. W. Greek and Roman Artillery:  Technical Treatises. Oxford:  Oxford University Press, 1971. Rashed, R. and H. Bellosta, eds. Apollonius de Perge: La section des droites selon des rapports. Berlin and New York: de Gruyter, 2010. Ruijgh, C. J. “Review of: Ch. H. Kahn, The Verb ‘Be’ in Ancient Greek.” Lingua 48 (1979): 43–​83. Sabra, A. I. “Thâbit ibn Qurra on Euclid’s Parallels Postulate.” Journal of the Warburg and Courtauld Institutes 31 (1968): 12–​32. Sesiano, J., ed. Books IV to VII of Diophantus’ Arithmetica, in the Arabic Translation Attributed to Qusṭā ibn Lūqā. New York and Heidelberg: Springer, 1982. Simson, R. Opera quaedam reliqua. Glasgow, 1776. Toomer, G. J., ed. Diocles, On Burning Mirrors. Berlin and New York: Springer, 1976. —​—​—​, ed. Apollonius, Conics, Books V to VII. The Arabic Translation of the Lost Greek Original in the Version of the Banū Mūsā. 2 vols. Berlin and New York: Springer, 1990. Tummers, P.M.J.E., ed. Anaritius’ Commentary on Euclid:  The Latin Translation, I–​ IV. Nijmegen: Ingenium, 1994. van Groningen, B. A. “ΕΚΔΟΣΙΣ.” Mnemosyne 16 (1963): 1–​17.

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chapter C4

He l lenistic Ast ronomy Alan C. Bowen

1. Introduction In the interval from Aratus and Aristarchus of Samos (3rd century bce) to Claudius Ptolemy (2nd century ce), there was a dramatic restructuring and reorientation in what was called astrologia—​a term typically rendered “astronomy,” though “celestial science” or “science of the heavens” would be more accurate. The primary cause of this change was doubtless the transmission of Mesopotamian astrology to the Greco-​Roman world and its subsequent, creative reception. Yet, the details of how this change occurred remain elusive (see Bowen 2009). There are from the 3rd century on clear instances in which we see Hellenistic Greeks adapting Babylonian theory—​P. Hibeh 27 (3rd century), for example, adapts an arithmetic, linear zigzag scheme for the increase/​decrease of the length of daytime throughout a year of 360 days in order to structure an Egyptian festival calendar of 365 days (see Bowen 2008b). But, while there is evidence of Greek interest in astrology in the late 2nd century, the earliest horoscopes in Greek date only from the late 1st century bce (see Neugebauer and Van Hoesen 1959). The problem, however, is not just a lack of documentary remains; it is also one of how historians have read the texts surviving from this period. This problem of reading is the result of blindness induced by two wrong-​headed assumptions and one questionable mode of argumentation. The first assumption begins with the undeniable truth that astronomy is an exact or mathematical science and then adds that historians should, therefore, isolate and focus on the development and transmission of numerical parameters, mathematical models, and techniques of calculation. Thus, Otto Neugebauer, after remarking on the great variety of the notions of astronomy in antiquity, proposes (1983, 35–​36; emphasis mine): We shall here call “astronomy” only those parts of human interest in celestial phenomena which are amenable to mathematical treatment. Cosmogony, mythology, and applications to astrology must be distinguished as clearly separate

294   Hellenistic Greek Science problems—​ not in order to be disregarded but to make possible the study of the mutual influence of essentially different streams of development. On the other hand, it is necessary to co-​ordinate intimately the study of ancient mathematics and astronomy because the progress of astronomy depends entirely on the mathematical tools available.

The second is the thesis that historians are duty bound to produce narratives, stories that “make sense” of the extant texts and artifacts. Both assumptions miss the mark. The first is a false reduction. Granted, it is true that Hellenistic astrologia embarked on a process of increasing technical sophistication which was greatly enriched in the 2nd century ce, notably, in Ptolemy’s writings, although Tihon (2010) provides indications that Ptolemy’s immediate context was more complex than hitherto suspected. The reasons for this development, however, were never purely technical but lay also, for example, in considerations of the relations of this science to other intellectual disciplines and to broader philosophical and cultural concerns about how one should make decisions in the course of living one’s life. Indeed, such considerations put into question the very idea of what astrologia is and who its practitioners are. Thus, the assumption that historians should isolate and concentrate on the mathematical apparatus of this science is no more compelling than the contention that historians of the automobile today should bracket political questions raised by global warming, financial questions raised by an emergent global economy, and cultural aesthetics in favor of accounts of the automobile restricted narrowly to matters of its engineering. To the contrary, in both instances, the technical and the nontechnical interpenetrate one another to such an extent that their separation in principle is not an act of clarity but of folly. As for the second assumption, even if one holds that historians are to produce narratives and is comfortable with the narcissism that this usually entails, the problem is that the documents extant in Hellenistic astrologia either come to us without indication of their authors and provenance or they are typically works by authors who are otherwise unknown and difficult to contextualize. In other words, what survives to this day does not permit a credible narrative. Moreover, the persistent effort to impose on this period Simplicius’ narrative of the development of astronomical theory from the time of Plato to Autolycus of Pitane is predicated on misreadings of what Simplicius writes and are thus nugatory as well (see Bowen 2013b). Allied with both these assumptions is a curious kind of argumentation in which late citations (quotations, paraphrases, reports) of earlier works are taken to convey historical fact. Plainly, there is no problem when such citations are used to understand the source making the citation and his times. Otherwise, however, these citations have probative value only when there is direct, supporting evidence from what is cited and its historical context. Regrettably, most citations bearing on Hellenistic astrologia are about matters for which there is no such supporting evidence. Yet, rather than refrain from using these citations in reconstructing Hellenistic astrologia, scholars defend their readings of them by claiming that they are not just possible but probable. Yet, our

Hellenistic Astronomy   295 sense of what is probable is largely determined by our culture and the history it tells itself and is hardly a reliable guide to the history of other cultures, especially when so much historical fact is wanting. Indeed, to rely on such a sense in reconstructing Hellenistic astrologia is to project one’s expectations onto the past and thus to impede an account that honestly seeks to interpret, on its own terms, what has survived from Hellenistic times. This kind of argumentation, then, is a method of blindness, a way of failing to perceive the extant documents in favor of what others say about them. The situation is hardly improved when interpreting citations involves mathematical analysis, since the certainty of mathematics still cannot bridge the gap to historical truth. As for the idea that citations by scientific writers should be trusted because they are part of an activity that is by nature objective and free from corrupting passions, this may have passed as solemn truth in the time of Hermann Diels, but today it is derisible. Accordingly, in what follows, I shall put aside readings of Ptolemy which, in spite of what he says, infer that Apollonius discovered the equivalence of the epicyclic and eccentric hypotheses of planetary motion and the existence of stationary points in epicyclic motion—​ almost 100  years before these matters were demonstrably relevant in astrologia—​ and supports them fallaciously by drawing mathematical consequences from theorems in Apollonius’ treatises (see Bowen 2013b, 244–​246). Moreover, I shall not construct a narrative situating the mathematical details of astrologia during the period from Aratus to Ptolemy. Instead, I shall examine several texts from this period to determine what they tell us of the broader intellectual issues and ideas that constrained and inspired the technical development evident in theorizing about the heavens during this time. Since the impact of Babylonian astrology is first recorded in texts written in the latter parts of the 2nd century bce and later, I shall attend primarily to treatises written in the following two centuries. Each of the core texts to be discussed is well known. The problem lies in understanding and connecting what they say about astrologia. To date, the scholarly response has been limited to generally negative comments about the worth of the particular claims made. It should come as no surprise, then, that these texts have been relegated to the margins in modern accounts of ancient astrologia. Yet, one of their striking features is that the author typically undertakes to demonstrate the great importance and value of what he writes and contends that he is best qualified to convey this information to the reader. Thus, in the texts considered, what is written is interpreted not in some artificially imposed (narrative) context or in a vacuum: these texts have a purpose, and the meaning of the sections in which they present astrologia must be grasped by reflecting on these assertions of personal authority and any claims of benefit to the reader. As I will explain, these texts, when read accordingly, show a fundamental disagreement about astrologia and why it should be studied. But it would be wrong to suppose that the fundamental question was simply What is astrologia?, because there was already in place a loose collection of activities and theoretical writings apparently constituting

296   Hellenistic Greek Science this discipline.1 It is more useful to say that the question “What is astrologia?” was taken up in two closely interrelated and ultimately inseparable questions: (1) What precisely is to be included in astrologia? (2) How does astrologia stand in relation to philosophia?2 These concerns for the articulation and demarcation of astrologia, respectively, constitute the framework in which the writers considered staked out their positions and advocated their views.

2.  Diodorus Siculus and His Bibliotheca historica It is in the proem to the Bibliotheca historica (ca 30 bce) that Diodorus defines himself in relation to his reader. The first step in his assertion of authority (1.1.1–​1.2.8) consists in praise of historical writing and historians. The basic thesis is that, since we all learn from experience, we should be grateful to those who write universal histories because they offer instruction that extends our experience without the attendant danger. Granted, the utility of a universal history, that is, of a history rooted in the kinship of all mankind, is primarily political: as Diodorus makes clear, such histories enable us to learn from the successes and failures of others, especially in matters concerning the polis. Still, he does include cultural and intellectual matters that are to be of use to his readers as well. In any event, for Diodorus, the basic value of universal history lies in its enabling decisions about the future. Thus, he concludes, “one must, therefore, acknowledge that the acquisition of this (subject) is in fact most useful for all the circumstances of life” (1.1.4). The second step is an argument that he is the first to undertake writing a proper, universal history (1.3.1–​1.4.5). As he says, previous writers have failed because they have focused on single, self-​contained wars fought by a single people or polis. Indeed, he continues, few have tried to write a history running from the earliest times to their own day; and, of those that have, some have done so without dating the events, others have ignored mythic times or the barbarians, some again have not been able to complete their

1 

Regarding these earlier writings, one should note that, although Hipparchus’ commentary presents itself and its target texts—​Eudoxus’ Phenomena and the poem based on it by Aratus—​as works in celestial science, many surviving treatises such as P. Hibeh 27, Aristarchus’ De magnitudinibus, Hypsicles’ Anaphoricus, do not; and, thus, that inclusion of such treatises in astrologia is a matter of inference from earlier work and later reports. 2 

Philosophia is here understood as that great body of reflection traditionally focused on the explanation of what there is and of how we should act or, at least, of how we should make decisions.

Hellenistic Astronomy   297 work, and no one has carried his account beyond the mid-​2nd century bce. Thus, in spite of the fact that a universal history would be of the highest benefit to mankind, no one before Diodorus has tried to encompass all events and times in a single systematic treatise (1.3.2–​3). After reiterating the shortcomings of contemporaneous historical writing and emphasizing both the great difficulty of writing a universal history and the promise of its supreme utility (1.3.4–​8), Diodorus takes the third and final step in his claim to authority by asserting his special qualifications. First is that he has been working on his account for 30 years, much of it spent traveling throughout Asia and Europe (at no small risk to himself, so he says) in order to familiarize himself with important sites and thus to avoid error.3 Next, he cites his great passion for this project and that he has had access to documentary materials assembled in Rome from around the world. Finally, he notes, he has a good working knowledge of Latin (1.4.1–​5). Thus, Diodorus would have his readers understand that he is the leading authority and guide to a subject of vital importance to them, and that they may rest supremely confident in the truth of what he has to say and its benefit in their decision-​making. It is worth noting that, for Diodorus, astrologia is an ethnic undertaking: rather than present a single or universal account of astrologia, he describes this science as it is found in Egyptian and Chaldean (Babylonian) culture. Thus, in book 1, after accounting for the Egyptian rulers prior to the Trojan War, he eventually comes to the Egyptian claims of priority in the discovery of writing, the observation of the stars, the theorems of geometry, most of the arts, and the best laws (1.69.1–​7); and then to the related matters of priestly education and astrologia. As he tells the story, the sons of priests were trained in the techniques of land measurement (geometria) and arithmetic reckoning (1.81.1–​4). The latter, he says, was very useful for work in astrologia, given that the position and motions of the celestial bodies have received careful observation among the Egyptians (if anywhere else) and they have preserved records concerning each for an incredible number of years, since the study of these matters has been valued from ancient times. (1.81.4)

Moreover, he adds, they have observed most avidly the motions of the wandering stars, that is, their circuits and stations, and, further, the powers of each relative to the births of animals, of which good effects and which bad effects they are productive. And while they are often successful in predicting to men what is going to befall them in life, frequently they announce upcoming destructions of crops or the opposite, bumper crops, and further, plagues for men and cattle; and from observation over a long time they have

3 

Although Diodorus does mention travels to Egypt and Rome, there is no evidence in the Bibliotheca to support the claim that he traveled to Europe and Asia: Sacks 1990, 161 and notes 1–​2.

298   Hellenistic Greek Science foreknowledge of earthquakes, floods, the risings of comets, and all the things which to the many seem impossible to know. (1.81.4–​5)

In sum, Diodorus affirms that the Egyptians have expertise in astrologia deriving from long study and observation of the heavens, and that the main thrust of their astrologia lies in the prediction of harm and benefit on the basis of the positions of the celestial bodies. In book 2, after describing the Assyrian kings and the destruction of their empire by the Medes (2.1.3–​28.8), Diodorus turns to the Babylonians, that is, to those whom he calls Chaldeans, a priestly caste, known, so he says, for their expertise in astrologia, the mantic arts, and the rituals for warding off evils and securing benefits (2.29.1–​3).4 After discussing how Chaldean children were educated, a process arguably superior to education in Greece (2.29.4–​6), Diodorus outlines Chaldean astrologia. He specifically states that the Chaldeans’ long-​term interest in observing the motions and powers of the heavenly bodies and in predicting the future is underwritten by their convictions that the cosmos is by nature both uncreated and indestructible, and that its order is governed by Providence (2.30.1–​2). He next mentions their doctrines regarding the planets or Interpreters (2.30.3–​5); the 30 zodiacal stars or Counseling Gods (2.30.6–​7); how the planets are ominous (2.31.1–​3); the 24 nonzodiacal stars (2.30.4); the Moon (2.30.5–​6); eclipses (2.30.6), and the Earth (2.31.7). As he indicates, there is much more to tell, but since it would be alien to his history—​he presumably does not deem it as useful to the reader—​he concludes by noting (2.31.8–​9) that the Chaldeans have the highest standing in astrologia of all men and have pursued it most diligently, though he finds incredible their claim to have observed the heavens for 473,000 years prior to Alexander’s crossing into Asia (334 bce).

2.1. Diodorus and His Readers For Diodorus, Egyptian, Chaldean (Babylonian), and Greek astrologiae are but varieties of a concern with the heavens. What draws his attention in the Egyptian and Chaldean versions is their utility in predicting the future—​he has no reservations about this (see 1.1.3, 1.81.5, 2.31.1–​3, 17.112, 19.55). The lesson to be learned by his Greek readers is, apparently, that the Greeks would do well to appropriate this science as a means of making decisions about the best course of action. But how this is to be done, he does not say. So far as Greek astrologia is concerned, what survives of the Bibliotheca indicates that it is limited to matters of timekeeping (see 1.98.3–​4) and geography. The Bibliotheca thus leaves open whether astrology is to be yet another subject within Greek astrologia or whether it is to replace it.

4 

On the Chaldeans of history and who Greek writers thought they were, see Eck 2003, 153, n. 3.

Hellenistic Astronomy   299

3.  Vitruvius and De architectura 9 Within a decade of the publication of the Bibliotheca, Vitruvius wrote a treatise on architecture in which he presents his own ideas about astrologia. The rhetorical setup is, however, different and points to a new conception of this science. Unlike Diodorus, who promises benefit to any and all readers, Vitruvius offers to but one reader, Caesar Augustus, the great employer of architects, a book explaining the technical terms and principles of architecture in a way that will allow Caesar to teach himself how to evaluate works built for him (1.pref.1–​3). Granted, Vitruvius does expect others to read his book (see 1.1.18), and it is clear that they are to include other architects (see 7.praef., and 1.1.18). Indeed, by prescribing to the authority the details needed for judgment in matters architectural, Vitruvius makes his book compulsory reading for anyone else in the field. What is new in Vitruvius’ account is the idea that architecture is not just a matter of building walls, it also one of determining that a wall is well built. So, the question becomes, How is the architect to acquire this capacity for judgment? (1.1.1–​2). As Vitruvius sees it, to be educated, [the architect] must be skilled in drawing and learned in geometry; he should know many histories, pay careful attention to the philosophers, understand [the science of] music, and not be ignorant of medicine; he should know the responses of legal experts and comprehend astrologia and the recognized principles of the heavens. (1.1.3)

In the course of explaining why such subjects are necessary (1.1.4–​10), he remarks that, from astrologia are ascertained east, west, south and north, and, further, the theory of the heavens (the equinox, solstice, and the courses of the stars). If one is not acquainted with these matters, he will not in any way be able to understand the theory of sundials. (1.1.10)

Further, he insists that, since [architecture] is such a great discipline adorned and abounding in diverse and numerous branches of learning, I think that only those can rightly declare themselves without qualification to be architects who, by making their ascent by way of the steps of these disciplines from childhood, have been nourished in the knowledge of a great many literary works and arts, and who have arrived at the very lofty temple of architecture. (1.1.11)

Of course, the architect is not to be expert in all these disciplines; as Vitruvius quickly points out, a general education in them will suffice (1.1.12–​16). Thus far, Vitruvius has included astrologia as part of an educational program needed for judging architects and architecture because it is necessary for the design and

300   Hellenistic Greek Science construction of sundials (1.1.10). However, book 9, which is intended to explain this in detail, shows that there is much more to Vitruvius’ appreciation of astrologia than its theory of sundials. The first clue is that, before reiterating in book 9 that he will give an account of the principles of sundials, that is, of how [these principles] are found in the world from the Sun’s rays through the shadows of a gnomon, and for what reasons [these shadows] are lengthened and contracted (9.praef.18),

he inserts an encomium of intellectuals—​he mentions Pythagoras, Democritus, Plato, and Aristotle—​since they benefit mankind with the everlasting utility of their works and are thus so much more to be prized and honored than mere athletes (9.praef.1–​4, 15–​ 17). Curiously, he does not mention any astrologi in particular: still the encomium does frame what follows with the question of its everlasting utilitas. The second clue lies in the subjects that Vitruvius includes in his account of astrologia. Vitruvius begins by asserting that the divine intelligence has arranged the behavior of shadows in such a way that equinoctial shadows cast by gnomons vary in length depending on the terrestrial location of the gnomon, and that the lengths of these equinoctial shadows indicate the shapes of the analemmata on the basis of which the hour lines are constructed (taking due account of the locations and the shadow of the gnomons). He next defines the analemma as the configuration searched out in the course of the Sun and discovered by observation of its shadow as [this shadow] lengthens towards winter solstice. By means of this configuration, through architectural principles and drawings by compass, (the Sun’s) work in the world is discovered. (9.1.1)

Then, he describes the continuously rotating celestial sphere with its axis and pivots (9.1.2), introduces the zodiacal belt with its 12 signs (scil. the dodecatemoria) of equal size (9.1.3), and adds a fundamental principle of celestial timekeeping—​that, while exactly which of these signs are visible will vary with the season, at any point in time there will be six above the horizon and six below (9.1.3). All this is tolerably relevant to the theory of sundials. What follows, however, is not. For Vitruvius now turns to the motions of the seven planets through the zodiacal signs (9.1.5–​10), an account generously supplemented with a demonstration that Venus and Mercury do indeed make stations and retrogradations (9.1.6–​7), and with an explanation of the stations and retrogradations of Mars, Jupiter, and Saturn (9.1.11–​13). Even more unexpected is that the chapter ends with a statement of the order of the planets (9.1.14–​15) and of how this ordering explains their differences in temperature (9.1.16). Granted, there follow chapters on the lunar phases (9.2) and on the correlation of the Sun’s position in the zodiacal signs with the seasons and the length of daytime (9.3) that are arguably relevant. But the next chapters on nonzodiacal constellations to the north (9.4) and south (9.5) are not. Vitruvius does try to pull everything together in ­chapter 9.6:

Hellenistic Astronomy   301 I have given instruction so that there is an overview concerning the revolution of the world about the Earth and the arrangement of the 12 zodiacal signs and of the arrangement of the stars in the northern and in the southern part. For the tracings of the analemmata are found from this turning of the world, the contrary course of the Sun through the zodiacal signs, and the equinoctial shadows of gnomons. (9.6.1)

But he immediately interrupts himself again by remarking on the effects that the 12 signs, the five planets, the Sun, and the Moon have on human life. He then concedes to the Chaldeans their prowess in casting nativities, a discipline which, he says, Berosus first brought to Kos and taught to Antipater and Achinapolus (who reportedly cast nativities based on the moment of conception and not on the moment of birth) (9.6.2). At this point, it begins to become clear that this “digression” which introduces Chaldean astrology by explaining some of the underlying concepts of planetary motion is really a preliminary to a reinterpretation of Hellenistic astrologia that emphasizes the mastery of time. For, in contrast to the Chaldeans, Vitruvius maintains, certain Greek theorists (Thales, Anaxagoras, Xenophanes, and Democritus) have well thought-​out theories explaining “on the basis of what things the nature of things is governed and how [this nature] has its effects” (9.6.3). And, he continues, others who have followed their findings—​he mentions Eudoxus, Euctemon, Callippus, Meton, Philippus, Hipparchus, and Aratus—​have discovered the risings and settings of the stars, and the signs of changes in the weather, on the basis of astrologia through their teachings of the parapegma (9.6.3). Such men, Vitruvius says, merit our admiration and deference “because they were of such great dedication that they seem with divine intelligence to declare in advance the upcoming signs of changes in the weather” (9.6.3), thus putting them among the intellectuals praised in the preface to book 9. The upshot is that, for Vitruvius, there are two types of astrologia, both concerned with divination or the interpretation of celestial signs: the Chaldean, or Babylonian, and the Greek (cf. 9.6.1–​3)—​“Greek” in that Vitruvius does not name any Latin astrologi. Both make predictions on the basis of the configuration of the heavens at a given time. But, whereas Chaldean astrologia looks to the day of someone’s birth in order to determine his life and so forth, Greek astrologia looks to any given day of the year to determine the weather. What is worth noting, however, is that Vitruvius unifies both types of astrologia by construing them causally—​not only does he supply his own causal explanation of the retrogradation of planets above the Sun (9.6.11–​13), he casts the parapegmatists as students of the theorists who propound causal explanations of natural phenomena. By interpreting the configurations of the heavens mentioned in either instance as causes of what is signified, Vitruvius provides a foundational unification of the two types of astrologia that subsumes them under the general rubric of Greek physical theory (physica). But he goes no further in this: his subsuming astrologia under physica seems not to entail, as it did for others, that astrologia is part of philosophia. Thus, for Vitruvius, astrologia is neither propaedeutic to philosophia nor are its starting points established only by philosophical argument. For him, the relation between astrologia and philosophia is very different. As he makes clear, astrologia is a science of divination

302   Hellenistic Greek Science enabling decisions about what one should do; whereas philosophia, with its ruminations on the good and so forth, is not the (sole) arbiter of correct action. Indeed, the job of the philosopher in some instances at least is simply to warrant the claim that decisions about what to do reached through astrologia are in accord with Nature.5 Vitruvius’ presentation in 9.7–​8 of the analemma, the species of sundial, their inventors, and the water clock drives home that the special contribution of astrologia is the ability to make decisions at any moment throughout the year that are in accord with a proper philosophical account of the world. At the same time, Vitruvius envisages a class of astrologi who can actually make a living by casting horoscopes, developing parapegmata for given locales, and designing (if not making) sundials. Thus, like Diodorus, he conceptualizes a profession of astrologia as opposed to a mere intellectual discipline.

4.  New Definitions of Astrologia The idea that “traditional” Greco-​Roman astrologia should include or even adapt Chaldean (Babylonian) astrologia certainly found favor with Manilius. His didactic poem, written in the last years of Augustus’ reign (9–​14 CE), offers to Caesar a detailed account of celestial science that elaborates astrology and its conceptual apparatus in accordance with what Diodorus and Vitruvius would have viewed as Greek astrologia and physical theory. Yet, though the Astronomica is the earliest extant text that actually develops a unified astrologia, it does not follow Vitruvius’ plan: there is no mention of parapegmata, sundials, and water clocks. Others, Geminus and Pliny the Elder among them, held that astrologia should not include astrology at all but for different reasons. So let us turn to them.

4.1. Geminus and his Introductio astronomiae Unlike Diodorus and Vitruvius, Geminus, who was writing at roughly the same time, does not present himself to his reader as an authority in something that will be of use. Instead, he stands before the reader as a teacher whose lessons are, for the most part, cast impersonally and so, presumably, meant to be taken as objective and true. Geminus does, of course, address his reader to introduce the solution to the problem of how the Sun, moving smoothly as it must in a circle, still travels equal arcs in unequal times 5 

Though Vitruvius does emphasize that philosophia explains the nature of things (1.1.7: cf. 1.1.17), he does not explicitly deny that philosophia has no independent contribution to moral discourse: see 7.pref.1 for his acknowledgement of the distinction between natural and moral philosophy. In general, he seems more concerned to emphasize that any art or science succeeds when it is in accord with Nature (something to be shown by philosophia) than to explain what philosophia is.

Hellenistic Astronomy   303 (1.22) and to report on lexical matters (6.5, 16.19–​20).6 He also interjects himself to assist the reader in the course of an arithmetic (8.29–​30, 8.38–​39, 8.47, 18.7) and a geometrical argument (1.40); and he further enhances his standing as teacher and authority when distinguishing what belongs in more advanced studies and what belongs in a first introduction to astrologia such as the present treatise evidently is (5.14–​15, 5.17). But, overall, the authority of the Introductio derives not from its author but from its context and content. As for his reader, there is reason to think that Geminus’ “lessons” are directed in good measure at (would-​be) philosophers or those with philosophical interests. In the first place, we learn from Simplicius that, as Posidonius asserts and Geminus would apparently agree given his Introductio, concern with causation and causal explanation are characteristic of philosophia qua physical theory, not astrologia: It is for physical theory to inquire into the substance of the heavens and of the celestial bodies, into their power and quality, and into their coming into existence and destruction. Through these [investigations], it can certainly offer demonstrations concerning size, shape, and ordering. Astrologia, on the other hand, does not attempt to speak about anything of that sort. Instead, it demonstrates the order of the celestial bodies after declaring that the heavens really are a cosmos, and speaks about the shapes, sizes, and distances of the Earth, the Sun, and the Moon, about the eclipses and conjunctions of celestial bodies, and about quality and quantity in their movements. It follows that since astrologia deals with the theory of quantity, duration, and type of shape, it is reasonable for it to need arithmetic and geometry for this. And concerning these matters, which are the only ones about which it undertakes to supply an account, it has the authority to make inferences through arithmetic and geometry. Now, astrologi and physical theorists will in many cases propose to demonstrate essentially the same [thesis] (e.g., that the Sun is large, that the Earth is spherical), yet they will not follow the same procedures. For, whereas [physical theorists] will make each of their demonstrations on the basis of substance, or power, or “that it is better that it be thus,” or [the processes] of coming into existence and change, astrologi [will do so] on the basis of the [properties] incidental to shapes or to sizes, or on the basis of the quantity of motion and of the time interval appropriate to it. And physical theorists will in many cases deal with the cause by focusing on the causative power; whereas astrologi, since they make their demonstrations on the basis of extrinsic properties, are not adequate observers of the cause in explaining that the Earth or the celestial bodies are spherical, for example. Sometimes they do not even aim to comprehend the cause, as when they discourse on an eclipse. At other times, [astrologi] make determinations in accordance with a hypothesis by setting out some modes [of accounting for the phenomena]; and, if these are the case, the phenomena will be saved. (Kidd 1988–​1999, F18.5–​32)7 6  Geminus speaks in the first person plural: such usage is plainly a fiction (cf. 1.22) and a mark of urbanity that at the least means “I” (cf. 17.5, 17.17). 7  Cf. Bowen 2013b, 38–​51. In general, Simplicius’ quotations are reliable and typically constitute valuable indirect testimony to the early history of the text quoted. In this instance, Simplicius takes

304   Hellenistic Greek Science Second, not only does Geminus mention causation in presenting the theory of aspects and their influence (chap. 2), he attacks the view that the celestial phenomena listed as signs in parapegmata are causes of the correlated changes in the weather, as well as the even more prevalent belief that Sirius’ rising with the Sun is the cause of the intensification of summer heat (chap. 17). Further, that Geminus includes students of philosophy among his readers is certainly consistent with his criticizing philosophers on several occasions (12.14–​19, 16.21.–​23, 17.32–​35). And it does make sense of the fact that, while he mentions numerous instruments, he does not include their design or construction in his articulation of astrologia: such inclusion would have been inappropriate given that philosophia is, for him, the contemplative activity indicated in Simplicius’ report and presupposed in his own reference to the celestial bodies as constituted of either fire or aithēr (17.15, 17.33), a point of debate in his time among Peripatetics, as well as between Stoics and Peripatetics. Indeed, there is reason to hold that Geminus was a Peripatetic philosopher, with the proviso that, in his time, such allegiance did not indicate acceptance of Aristotelian doctrine so much as the practice of taking Aristotle’s works as a starting point in the critical development of one’s own responses to contemporary issues. But let us put that aside and turn to what Geminus conveys to his readers. To begin, Geminus’ Introductio, viewed against the background of Hellenistic astrologia, clearly defines and articulates the subject in a way that no earlier or contemporary (extant) text does. That is, even if one sees Geminus as responding to Diodorus and Vitruvius, it is important to keep in mind that he does not respond with an outline or an agenda but with a worked-​out solution to the problems of the demarcation and the articulation of astrologia. Next, in marshaling the technical detail—​a process of selection and omission that effectively defines this discipline—​it is noteworthy that Geminus marginalizes the Chaldeans. For, though he mentions them twice (2.5, 18.9), only the first reference is astrological in that it concerns the theory of planetary aspects. Moreover, unlike Diodorus and Vitruvius, Geminus does not acknowledge Chaldean expertise. Instead, he simply describes the aspect of opposition, states that the Chaldeans allowed its significance in casting nativities, and supplies a reason that has authority not because it derives from the Chaldeans but, as he says, because it is based on traditionally recognized powers of the celestial bodies (2.4–​6). At the same time, Geminus’ Introductio plays down the role of prediction in astrologia in general and, as one might expect given Simplicius’ report, brings to the fore instead the idea that astrologi should be concerned with making sure that their accounts are in accord with proper causal explanations. Thus, although he does allow that the

pains to assure the reader that Alexander’s citation of Posidonius’ citation of Geminus is also reliable (see Kidd 1988–​1999, F18.1–​4). Whether Posidonius is equally reliable is an open question: the most one may say is that what he attributes to Geminus is consistent with what one finds in Geminus’ Introductio astronomiae.

Hellenistic Astronomy   305 configurations of the planets may serve as the basis for predictions, not only are his examples meteorological rather than genethlialogical—​e.g., For if the North Wind blows when the Moon is in some one of the three zodiacal signs [scil. of the first trigon], the same condition will persist for many days. Wherefore, the astrologi, starting from this observation, predict northerly conditions (2.8: cf. 2.9–​11)

—​what he emphasizes is their underlying causal mechanism (2.13–​14). In the same vein, though Geminus does allow that stellar risings and settings may serve in making predictions about the weather (17.6, 17.23), his concern is likewise with what warrants these predictions. Thus, he criticizes the “peculiar apprehension among the uninformed” that the significations in the parapegmata, that is, the connections of sign (the stellar event) and signified (change in the weather) are causal, and maintains instead that they are just generalizations from experience or rules of thumb. The parapegma thus turns out for him to be a “pretty unscientific part of astrologia” (17.26–​45). Indeed, in his view, it would be far better to use signs given by Nature—​solar and lunar risings and settings, lunar halos, and so forth—​to predict the weather, thereby following, so he says, Boethus of Sidon, Aristotle, Eudoxus, and many other astrologi (17.46–​49). The inescapable conclusion is that, for Geminus, astrologia is not a science of divination but a discipline dependent on philosophia in the guise of physical theory: its value lies in its promoting contemplation and not because it warrants decision-​making. (This is actually quite reasonable: knowing that there will be a change in the weather because there is a lunar halo, for example, does not predispose to any particular course of action.) Thus, while astrologia may include in its conceptual apparatus astrological notions rooted in a causal account, it does not include astrology per se. In short, where Vitruvius uses causal theory to include astrology in astrologia and to deny effectively its subjugation to philosophia, Geminus uses it to exclude astrology from astrologia and ratify its one-​sided dependence. The only form of prediction that Geminus’ astrologia admits is meteorological. One will not find in the Introductio any claim that astrologia is useful in the sense that Diodorus and Vitruvius maintain. A caveat:  the preceding analysis is predicated strictly on what we have in the Introductio. As for the works promised in the Introductio, the most one is entitled to expect is a causal account of why the planets (other than the Sun) appear to have a unsmooth motion in longitude, given that their real motions are all circular and uniform, and a more detailed description of the celestial sphere and how a globe should be marked out.

4.2. Pliny and His Naturalis historia Pliny’s great treatise on Nature was completed in 77 ce and is dedicated to Titus Flavius Vespasianus, elder son of the Emperor Vespasian, some two years before Titus’ accession

306   Hellenistic Greek Science in 79 ce and Pliny’s death a few months later. It is a massive work in 37 books, which his nephew and adoptive son, Pliny (the Younger), describes as “diffuse, learned, and no less diverse than Nature itself ” (Epistulae 3.5.6). This is fair enough, if one does not then treat the Naturalis historia as a mere encyclopedia. In his prefatory letter, Pliny presents his treatise as a lighter work—​lighter in literary values—​about a subject that is barren from a literary standpoint, to wit, the nature of things or, as he glosses it, life (praef.12–​13). Pliny’s focus, then, is not on Nature in isolation but on man’s mundane interaction with it. In fact, were his treatise not dedicated to Titus, it would, he writes, be offered to the lowly crowd of farmers and artisans, as well as to the leisure moments of students (praef.6). After pointing out that Naturalis historia is the first ever of its kind among the Romans and Greeks (praef.14), he admits that writing it was difficult; so, if the result fails in giving novelty to what is ancient, authority to what is new, brilliance to what is old, light to what is dark, charm to what is disdained, credibility to what is doubtful—​indeed, Nature to all things and all her due to Nature (praef.15),

the attempt is still fully honorable and splendid. But, he adds, such concern with literary niceties is beside the point: the value of the Naturalis historia lies in its utility (praef.16). This work, then, is neither a literary text nor one in philosophia qua physical theory. Pliny concludes the letter by making two points. The first addresses the question of authority. He claims (and this is an underestimate) that the Naturalis historia comprises 20,000 noteworthy facts drawn from roughly 2,000 volumes (typically unread because of their abstruseness) written by 100 authors, with many things added which were unknown before or discovered subsequently (praef.17). This claim to authority by virtue of the sheer quantity of factual detail is supplemented by Pliny’s rooting it largely in tradition. As he notes, the most trustworthy (iuratissimi) of modern authors transcribe the ancients word for word, albeit typically without acknowledgment and for unacceptable reasons; and so he advises Titus that rather than steal credibility he will list (in what is now book 1) all the authors whom he has consulted (praef.21–​23). (We should observe, however, that the massive factual detail putatively drawn from past authorities that warrants Pliny’s claim to authority does not always sit well with his assertion that what he writes is also to be useful: there are occasions when the utility of the facts related seems nonexistent or, at least, highly attenuated.) The second point concerns the nature of Pliny’s project. He remarks at some length that the Naturalis historia is in many respects incomplete. This recognition of incompleteness is not, I think, just an admission of personal limitation in accord with literary convention, though there is much of that in his flattery of Titus. It derives, I suggest, from Pliny’s awareness that the human engagement with Nature changes over time; and so, to be useful, his work will require updating every now and then. Again, it is clear that the utility in question is mundane: Pliny advises Titus that he includes a table of contents that will enable others to look for particular topics without reading the treatise through.

Hellenistic Astronomy   307 Book 2, that is, book 1 by Pliny’s reckoning (see praef.17), starts by describing the mundus (world:  cosmos in Greek), that unique, bounded, and eternal divinity that is both a work of nature and the very nature of things (2.1–​2). As one might expect, given Pliny’s explication of “the nature of things” by “life” (praef.13), he is not about to embark on an account of the mundus simplex in what was called natural philosophy at the time. In the first place, he indicates that he will pay no heed to the traditional concerns of philosophia. Thus, he peremptorily dismisses debates about the size of the mundus, its uniqueness, and whether there is anything outside it (2.3–​4). Moreover, in arguing that the mundus is spherical, he adduces only considerations of language and of our common experience of rotating shapes and the sky’s curvature (2.5): he makes no mention of the arguments found in Aristotle’s De caelo, for example; and he shrugs off the “Pythagorean” question of whether the rotating mundus makes a noise and, if so, why we do not hear it (2.6). Likewise, he flatly affirms that there are four elements in the mundus (fire, air, water, and earth), and that the Earth lies at its center in a system defined by the dynamic opposition of light and heavy (2.10–​11), thus overlooking the debate about Aristotle’s fifth element (aithēr)—​which Geminus noticed—​and the whole theory of natural place. But, if the Naturalis historia is not a philosophical work on the mundus, what is it? The answer comes in a digression on god (deus) that is occasioned by Pliny’s mention of the planets situated between the Earth and the constellations engraved on the surface of the mundus. For, after maintaining that in assessing the Sun’s works, we should accept as true that it is the soul or, more clearly, the mind of the entire mundus, that it is the primary governor of Nature and a divinity. It supplies its light to things and takes away shadows; it conceals the remaining stars and fills them with light; it governs the changes of the seasons and the year which is always reborn in accord with Nature’s custom; it disperses the sadness of the heavens and even calms the clouds of the human soul; it also lends its own light to the other stars; [it is] splendid, exceptional, all seeing, and all hearing too, as I see that Homer, the foremost of writers, held in the case of [the Sun] alone (2.12),

he pauses to consider the nature of divinity and its role in Roman life. In his view, there is but one god and it is either the mundus as a whole or some part of it. He rejects as imbecilic any attempt to represent the likeness of god and as an unseemly projection from our fears and frailty, the view that there are many gods (2.14–​16). For the oft-​told stories of divine marriages, adulteries, and so forth, he has nothing but contempt (2.17). To him, the fundamental truth is that “God it is for a mortal to help a mortal; this is the way to eternal glory.” Such, he says, was the course that the Roman princes took and that Titus’ father now takes (2.18). This truth, which goes to the heart of Pliny’s idea of proper Roman life, is supplemented when he asks whether one should accept or doubt the idea that god (whatever it might be) is concerned with human affairs and is not defiled by such involvement (2.20). As he

308   Hellenistic Greek Science says, it is hard to decide which alternative is more advantageous to the human race given what people actually do. Moreover, the question is complicated by the almost universal practice of postulating Fortune as an intermediate deity responsible for the good and bad in human life (2.22). True, he says, another group also banishes her and attributes events to its own star and to the laws of birth, I mean, [the law that,] for all future men, once and at any time there is ever a verdict from god, it is given for the time remaining. This view has begun to take hold; and both learned and unlearned people go to it equally at the run. (2.23)

These adherents of astrology are just like those who rely on any other form of divination (2.24); and together the consequence of their beliefs and practices is that for man, lacking foresight as he does, “the only certainty is that nothing is certain and that nothing is more wretched than man or more arrogant” (2.25). And so, it would follow, belief in divine solicitude is harmful and debilitating. Yet, Pliny will still allow that there is some advantage in accepting it, if only as a political ploy to curb evildoers (2.26). However, as Pliny reflects further, a solicitous god is himself limited. He points out that such a god cannot commit suicide, make mortals immortal, recall the dead, or make one who has lived not to have lived. Indeed, such a god has no power over the past except forgetfulness—​and he certainly cannot change the truths of arithmetic, and so on. Indeed, for Pliny, these very limitations of a solicitous divinity testify indubitably to the power of Nature and that this is ultimately what we mean when we speak of god (2.27). The Naturalis historia will plainly not accommodate astrology or any activity predicated on the belief that there is a god mindful of and concerned with human affairs. Next, it is also clear that this massive work instantiates the dictum that divine being consists in helping others. This is, after all, the principle underlying Pliny’s writing in the first place and his excusing its literary infelicities: as he explains to Titus, so, for my part, I think that there is in learning a special place belonging to those who in overcoming difficulties have preferred the value of helping (utilitatem iuvandi) to the prestige of giving pleasure. (praef.16: cf. 17–​18)

Yet there is more to this instantiation. Like Diodorus and Vitruvius, Pliny presents his work as useful. But, for Pliny, this utilitas is coupled with, and constrained by, the idea of service. And this service is understood, above all, to be a service to the Roman people (2.18: cf. 2.19–​20). This means that the selection of what is recounted in the Naturalis historia is guided by consideration of whether it will help the Roman people and their emperor. This is what motivates, for example, the books on geography, ethnography, human biology, zoology, agriculture, botany, and pharmacology. At the same time, the idea of service is a means by which heroes are identified. Pliny’s praise of Hipparchus is an instructive case in point, as I will explain. When Pliny resumes (2.28), he returns to the account of the mundus in 2.7–​9 and begins a “journey” which proceeds from the outermost reaches of Nature to its

Hellenistic Astronomy   309 innermost core, Earth, and ultimately to man. But, again, at the outset, he affirms that his account will contain nothing to support the various beliefs underlying astrology or divination (2.28–​31). This does not mean, of course, that his description of what lies between the celestial sphere and the Earth (the planets, comets, and meteors) excludes the idea that they have power (vis) and influence events and living things on earth. Pliny holds, for example, that the planets contribute to the weather (2.105–​106, but see 18.352) and that the Moon influences the growth of shellfish (2.109). Still, as he says in his account of meteors, I think that these (like all other natural phenomena) occur at fixed times, not, as the many think by virtue of the diverse causes which the ingenuity of clever men contrives. True, they have been omens of great evils. But I  do not think that the [evils] happened because these [omens] took place; rather, [I think] that [the omens] therefore took place because those [evils] were going to happen, and that the explanation of [the omens] is obscured by their rarity and, therefore, not known in the way that the [stellar] risings mentioned above, eclipses, and many other things [are known]. (2.97)

Likewise it does not mean that Pliny will avoid astrological concepts in explicating the celestial motions (cf., e.g., 2.65). Nevertheless, Pliny’s “itinerary” will not address astrologia and the abstract issues that exercised his sources, Diodorus and Vitruvius, for example, directly. His aim is to provide rules (leges) that are useful (18.321: cf. 18.207–​210) in such very practical matters as locating, sowing, raising, and gathering crops (see 18.321–​365). Moreover, these rules are intended in part for ignorant rustics (18.206). So, it is hardly surprising that he focuses on the subject matter of astrologia and says next to nothing of the science itself. Indeed, his reluctance to engage more abstract questions of the demarcation and articulation of astrologia is suggested by his avoiding the term almost entirely in favor of paraphrases such as the “theory of the stars” (ratio siderum). When he does mention astrologia, it is either the name of a book (18.213) or simply a science that someone has established (7.123, 7.203, 35.199). With that in mind, I will conclude with Pliny’s discussion of eclipses (2.41–​57). As he says, solar eclipses are “a wonder of the first rank in our entire viewing of Nature and like an omen” (2.46). After explaining how lunar and solar eclipses occur (2.47–​48), Pliny remarks on what eclipses tell us about the relative sizes of the Sun, Moon, and Earth (2.49–​52). Then, with this wholly naturalizing account of eclipses in hand, Pliny turns to the history behind this explanation. He starts with Sulpicius Gallus, thereby placing himself firmly in the tradition of a literary topos that emphasizes the great value, especially in time of war, of knowing that eclipses are not omens but naturally recurrent events, a topos taken up before him by Polybius, Diodorus, Cicero, and Livy. In Pliny’s variant of the story, Sulpicius Gallus delivered the Roman army from fear by foretelling an eclipse on the day before the Romans defeated the Greeks at Pydna in 168 BCE (2.53), thus bringing to an end the Third Macedonian War and solidifying Roman hegemony

310   Hellenistic Greek Science in the Mediterranean. The emphasis on prediction is noteworthy: for Pliny, Gallus did not calm the Roman forces by an explanation but by a prediction. And so, in his “history,” Pliny lists Thales’ prediction of a single eclipse—​thus choosing one of the two interpretations of Herodotus, Historiae 1.74 available in his time (see Bowen 2002a, 79–​ 81; Bowen and Goldstein 1994)—​and then Hipparchus’ prediction of eclipses in a cycle of 600 years (2.53: see Bowen and Goldstein 1995). But notice: Pliny is so impressed with Hipparchus that he later describes him as “a partner in the plans of Nature” (cf. 2.95). What this means he has already clarified when he rhapsodizes: O mighty heroes, beyond things mortal, who ascertained the law of such great divinities and freed the wretched mind of man from fear as it shivers in terror of calamities or some death of the stars in eclipses―it is well known that the lofty words of the poets, Stesichorus and Pindar, were [uttered] in this fear of an eclipse of the Sun―or as mankind infers sorcery in the case of the Moon and on account of this offers assistance with jarring, clashing sound―owing to this terror [of lunar eclipses] Nicias, the commander of the Athenians, who was unaware of their cause, destroyed their resources because he was afraid to bring the fleet out of port―glory to your genius, you interpreters of the heavens able to grasp the nature of things, and discoverers of a theory by which you have vanquished the gods and men! For, who, after discerning these things and the fixed labors―for so it has pleased [mankind] to call [them]―of the stars does not accept that mortals are born to their own destiny? (2.54–​55)

In sum, for Pliny, astrologia, the study of the region from the outermost mundus to the Moon is useful because it enables ordinary people to know in advance the changes in the weather and the occurrence of eclipses. Knowing when the weather will change is, of course, a great benefit. Knowing when eclipses are to occur is also a benefit but one that is different and, to Pliny, more important. For, as he would have it, such knowledge enables release from the superstitious fear that at critical moments can bring down armies and empires. This is what underlies the inclusion of astrologia, specifically, prediction, in the Naturalis historia and Pliny’s apotheosis of Hipparchus.

5. Conclusion Hellenistic astrologia is very much a work in progress during the two centuries around the millennium. It was not a settled discipline. Different writers making diverse claims to authority urged in quite different contexts divergent views of what astrologia should be and why it is important. In this way, they helped to define the framework in which the technical apparatus of this science developed. Thus, the fundamental or precipitating cause of change did not lie within the astrologia that goes back to Plato and Aristotle (a study itself in transformation). Indeed, this cause was not intellectual at all: it was instead the embrace of Babylonian astrology at all levels of Greco-​Roman society. That

Hellenistic Astronomy   311 this cause lay outside astrologia licensed intellectuals of diverse backgrounds, not just experts in astrologia, to stand forth and to offer their own solutions to the social and intellectual problems of appropriating astrology. Curiously, however each viewed the astrologers’ predictions of events on Earth given the configurations of the heavens, they all accepted that astrologia should incorporate predictions of the positions of the celestial bodies that are derivable from a theory of their motions. And so, collectively they envisaged a new astrologia that was no longer content just to describe the celestial motions as Aristotle and others had. Thus emerged a new desideratum: a predictive astrologia rooted in a mathematical description of the celestial motions that was also a profession and not merely a discipline.

6. Prospectus In observing that several texts from the 1st centuries bce and bc present themselves as introductions to astrologia, we were able to assess them together in a way which reveals that what they include is dependent on the readers addressed and how their authors seek to persuade or inform these readers. Much more, of course, can be done in pursuing this type of contextualization, since it affords entry, for example, into questions of daily life, education, and social standing. But for now, the question is Is this sort of inquiry still feasible when the documents at issue do not present themselves as introductions and may not show a guiding concern to articulate and demarcate the science of the heavens? To begin, it is important to note that prior to, and concurrent with, these introductions, there were documents in astrologia that served to constrain and channel the development of this science from the 1st century on. To judge from what has survived, however, they did not do this because they constituted a fixed body of learning; rather, they seem to have made their impact by imposing not their results so much as their own questions and demands. Let me indicate briefly how one might pursue this. There are numerous Hellenistic works that describe the celestial sphere. Their progenitor seems to have been Eudoxus’ Phaenomena, an account in prose of the constellations lying on, or in relation to, circles on the celestial sphere that are defined in relation to an observer and his horizon. Eudoxus’ description was subsequently set to verse in another Phaenomena by Aratus, who includes a list of signs of changes in the weather. Both of these works were together the subject of a commentary in prose by Hipparchus (2nd century bce) that presents itself as the substance of a letter addressed to Aischrion (otherwise unknown). This mishmash of literary forms is remarkable and raises the question of why they were chosen, a question to be resolved in good measure by study of how Aratus and Hipparchus position themselves and their work in relation to their readers. But such issues of expository form also had historical significance in that they were taken up in debate about the form of writing appropriate for astrologia. That is, for Hipparchus at least, this question of form was inseparable from the question of expertise in matters celestial. To use his linguistic markers, the critical question was Is the

312   Hellenistic Greek Science celestial scientist an astrologus (like Aratus) or a mathematicus (like Eudoxus)?8 Thus, questions of expository form went directly to the question of the authority of the discipline and its practitioners; and they did not pass away after Hipparchus, as the subsequent tradition of Aratea bears witness. (Aratus’ Phaenomena, sometimes said to be the most widely read work in antiquity after Homer’s Iliad and Odyssey, was the subject of numerous commentaries and Latin translations.) At the same time, this debate over authority is a struggle to define the reader. After all, if poets are false claimants to authority in astrologia and their poetry is misleading, then the readers of poetical works in astrologia lack credibility as well. Related to this nexus of expository form, authority, and suitability is the use of mathematical demonstration in Hellenistic treatises devoted broadly to the rotating celestial sphere—​the De sphaera quae movetur and De ortibus et occasibus by Autolycus (dates uncertain:  see Bowen 2013a); the Phaenomena by Euclid (dates also uncertain:  see Bowen and Goldstein 1991, 246, nn. 29–​30); Theodosius’ Sphaerica, De habitationibus, and De diebus et noctibus (2nd/​1st century bce); and Hypsicles’ Anaphoricus (2nd century bce: see Bowen 2008a). Whether any of these works was regarded as one in astrologia at its time of writing is a nice question. But for now, we should note that, however each was classified, they severally displayed successfully the power of mathematical argumentation in establishing knowledge of the heavens, though at the same time each plainly raises a problem in demarcation—​after all, astrologia is not mathematics. The same is true as well of Aristarchus’ De magnitudinibus, a determination of the relative sizes and distances of the Sun, Moon, and Earth that is cast in an axiomatic, demonstrative style (see Bowen 2013c). In sum, there is, I contend, much to be gained by looking on documents in Hellenistic astrologia as species of literary production and by interpreting their content in relation to their form and their intended readers. The promise in this is an understanding of the place of Hellenistic astrologia in its intellectual and social contexts that has hitherto been lacking. So far as one can tell, none of the issues driving this kind of literary production was settled in antiquity. Thus, it follows that historians today go astray by focusing solely on the positive claims made about the heavens in Hellenistic texts. Such “content” is largely the outcome of the choice of an expository style by a writer who, if he does not seek explicitly to present himself as an authority, still aims to make what he writes authoritative to a select, or even self-​selecting, group of readers.

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chapter C5

Hel lenistic G e o g ra ph y from Eph oru s Throu gh St ra b o Duane W. Roller

1. Introduction By the middle of the 4th century bce, Greeks were aware of the wide extent of the inhabited world. Reports of sailors and traders had determined the outlines of the Mediterranean, and travelers had passed beyond the Pillars of Heracles into the Atlantic. Greeks had gone as far south as Senegal (Carthaginians had gone farther) and perhaps as far north as the nearest portions of the British Isles (Roller 2006, 1–​43). Africa allegedly had been circumnavigated—​although the reports were often disputed—​and trade routes were known across the Sahara to the West African rivers. To the east, the broad expanses of the Persian Empire provided information beyond the Caspian Sea and as far as India, although the routes to and from these distant places were not well-​known (Herodotos 4.42–​45). The north remained obscure: although Baltic amber had come to the Mediterranean since prehistoric times, its place of origin and route were uncertain. There were jumbled reports of great northern rivers, forests, and mountains, but little geographical coherence (Cary and Warmington 1963, 137–​139, 146–​148, 153–​156). It was generally agreed that the earth was a sphere (an idea attributed to Parmenides by Diogenes Laërtius 9.21), and there were attempts—​more intuitive than scientific—​to determine its circumference and to understand the different climate zones. Although the formal discipline of geography was yet to be invented, this vast amount of data led to the first literary attempts to isolate geography as a part of scholarship. Shortly after 340 bce Ephorus of Cyme published the first universal history (Ephorus F223 = Diodorus 15.76.5), which included extensive attention to geographical matters. He divided the world into four parts based on the winds (Ephorus F30a = Strabo 1.2.28). Each was occupied by a specific ethnic group:  the Indians, Ethiopians, Celts, and

316   Hellenistic Greek Science Scythians. An attempt was made to determine the size of these four ethnic regions and to provide data about remote peoples such as the Cimbrians and Cimmerians (Ephorus F131a, F134a = Strabo 4.4.6, 5.4.5). This extensive geographical reach of Ephorus—​from the external Iberian coast to India—​was accompanied by ethnographic data and scientific information about matters that impacted people’s livelihood, such as the tides (Ephorus F132 = Strabo 7.2.1). Ephorus moved closer than anyone previously to a discipline of geography.

2.  Pytheas of Massalia A slightly younger contemporary of Ephorus was the remarkable Pytheas of Massalia, whose published treatise, On the Ocean, records the unusual nature of his explorations. A rare example of a Greek who seems to have traveled largely for scientific reasons, he went farther than anyone previously. Yet reconstruction of the extent of his travels remains difficult, because his treatise is rarely cited, mostly by Strabo (often quoting Polybius), both of whom were hostile toward the Massalian, an early example of rejecting as fantasy the reports of travelers to remote places who observed unusual phenomena (Strabo 2.4.1; Roseman 1994; Roller 2006, 57–​91). Pytheas’ travels do not seem to have been mentioned by Ephorus, so they were probably after 340 bce. Aristotle also failed to cite them, but his student Dicaearchus of Messana knew about them (Dicaearchus F124 = Strabo 2.4.2). This suggests Pytheas was active in the last 3rd of the 4th century bce. The best reconstruction of his voyage is from Massalia north, following existing trade routes either to the mouth of the Garumna (modern Garonne), near the site of Bordeaux, or to the mouth of the Liger (modern Loire), near modern Nantes. He may, in part, have been motivated by reports of tin sources (Strabo 3.2.9). He then crossed to Prettanike (Britain), where he spent an extensive period of time, perhaps over a year. Everywhere he went he recorded distances, the local ethnography, and, importantly, latitudes (based on the height of the sun on the shortest day of the year). He also began to theorize about the tides, perhaps the first to do so. In addition, as he went farther north, he recorded the changing celestial phenomena. Eventually he reached the northern tip of Scotland (where he recorded the latitude) and continued to head north, probably taking passage on fishing boats. He reached the  Faerøe Islands (where he again took the latitude), and soon came to his most famous discovery, Thule (Thoulē), a place where the sea was frozen but also boiling, seemingly a description of the contiguous glacial and volcanic phenomena of Iceland. Although the location of Thule was henceforth disputed and even disbelieved, Iceland seems the best possibility. Reconstruction of Pytheas’ subsequent itinerary is even more difficult. He probably touched the Norwegian coast (Bergos) and eventually entered the Baltic (Balcia), perhaps going as far as the mouth of the Vistula. There is a hint that he used the riverine

Hellenistic Geography from Ephorus Through Strabo    317 systems of eastern Europe to reach the Black Sea (Strabo 2.4.1; Pomponius Mela 3.33), although it is also suggested that he returned to Massalia along the exterior coast (Pliny 4.94–​95). Regardless, it was a remarkable journey that established Greek knowledge about the far north, as well as recording arctic terrestrial and celestial phenomena. The report of Pytheas, although often disputed, provided insights and data that influenced Greek geography. Pytheas’ observations of the tides introduced a difficult problem into geographical theory. As long as Greeks were limited to the Mediterranean with its minimal tides, tidal theory was hardly an issue, but as soon as they ventured beyond the Pillars of Heracles, significant tides were encountered, often with little comprehension. There were early reports of ships becoming stuck, probably having encountered an adverse tide (Roller 2006, 17–​21). Pytheas was exposed to the extremely large tides around the British Isles and brilliantly connected them to lunar activity (Aëtius 3.17.3; Pliny 2.217). The first treatise specifically on the tides was written by Seleucus of Seleuceia (who lived at the head of the Persian Gulf and thus had easy access to the external ocean). Although both Hipparchus and Posidonius attempted to refute Seleucus’ theories, they were unable to do so, and tidal theory remained obscure. Seleucus’ treatise was generally forgotten (Roller 2005, 111–​118).

3.  The Later 4th century bce and the Effect of Alexander Pytheas’ contemporary Aristotle had surprisingly little to contribute to geographical scholarship. No specifically geographical title appears in the list of his works (Diogenes Laërtius 5.22–​27), although there are some geographical comments in his On the Rising of the Nile (perhaps actually a work by Theophrastus), and there were probably some in his lost Governments of 158 Cities. His On the Heavens (2.14) also includes some geographical material: the circumference of the earth is 400,000 stadia (the first recorded figure), and one could reach India across the Ocean from the Pillars of Heracles. In fact, the existence of elephants in both India and West Africa was interpreted to mean some connection between the two regions. Aristotle made it clear that these were not his own ideas but those of his predecessors: Eudoxus of Knidos is a possible source (Roller 2010a, 6–​7). Aristotle also made a number of geographical comments in his Meteorology. Book 2 of the work is devoted to the surface of the earth and its nature, especially the characteristics of the Ocean and the seas. Although Aristotle’s interest was scientific rather than geographical, there is a wide range of topographic knowledge, including the erroneous assumption that the Hyrcanian and Caspian Seas are different (2.1), and the first Greek discussion of the properties of the Dead Sea (2.3).

318   Hellenistic Greek Science Yet there is no evidence that Aristotle considered geography a distinct discipline. But it is a matter of interest that one of his few students known by name, Dicaearchus of Messana, made significant contributions to the emergent discipline, as he began to lay out the overall plan of the inhabited world. In a treatise probably titled Circuit of the Earth, he established a basic latitude line (Dicaearchus F123 = Agathemerus, pr. 5; cf. Kuelzer 2008), which became the standard for future measurement. The line ran from Sardinia through Sicily, the Peloponnesos, southern Anatolia, and the Tauros Mountains, to Mt. Imaios. Clearly it was less than perfectly drawn, with its assumption that Sardinia and Sicily were on the same latitude. He may also have suggested that the circumference of the earth was 300,000 stadia (Keyser 2001, 363–​365), continuing the debate about this calculation. Dicaearchus was able to use information gathered by those who accompanied Alexander the Great on his journey to India, although the fragments of his Circuit of the Earth are too few to determine any specifics. Inclusion of Mt. Imaios, the mountains north and west of India (the name is reflected in the modern “Himalaya”) in his latitude line reflects data from those with Alexander. The accounts of Alexander’s journey were not in themselves primarily geographically oriented, although by necessity they included much topographical material, some of which had been deliberately manipulated to enhance the extent and importance of the king’s journey (as if this were necessary), especially in the Caspian Sea region (Strabo 11.7.4), creating a problem for geographers that lasted until early modern times. Alexander did send forth some explorers, most notably after his return to Babylon in connection with a planned expedition to the Arabian Peninsula. Of particular interest is Androsthenes of Thasos (FGrHist 711) who wrote Sailing Along the Indian [Ocean] Coast, which may have included a report of the sea journey from the mouth of the Indos to the Persian Gulf. The few fragments that survive all relate to the Arabian coast of the gulf itself, especially its ethnography and flora (particularly the mangrove).

4.  The 3rd Century bce and Eratosthenes In the generations after Alexander, the Seleucids gained control of the territory between the Mediterranean and India and stationed a number of envoys in the far eastern portions of the kingdom, including India. Most important of these was Megasthenes (FGrHist 715), who was at the court of Chandragupta at Pataliputra on the Ganges. He seems to have been an intimate of the king and wrote an Indika, largely an ethnography but with much valuable geographical information. He was probably the first Greek to travel along the Ganges, and he also reported on southern India and Taprobane (modern Sri Lanka) (Megasthenes, F6c, 7a, 26 = Strabo 15.1.11–​12, 2.1.19–​20, Pliny 6.81). Another Seleucid official was Patrocles (FGrHist 712), who in the 280s bce traveled in

Hellenistic Geography from Ephorus Through Strabo    319 the vicinity of the Caspian Sea, recording the river system of central Asia. He believed it was possible to make a sea voyage from the Caspian to India (F4a = Strabo 2.1.17), since it was believed that the Caspian actually connected with the External Ocean, due to the geographical manipulations of those with Alexander. Thus, by the middle of the 3rd century bce, there was a large amount of scattered geographical data. Greek knowledge had expanded to include the routes to India, south-​ central Asia, the coast of some of the Arabian Peninsula, coastal West Africa, the British Isles and North Atlantic, the Baltic, and parts of interior Europe. The reception of these data was often uncorrelated with reliability: sometimes accurate data were dismissed or errors accepted. In addition, there was a certain amount of theoretical speculation about the size of the earth, as well as parts of it as yet unexplored. Moreover, there were the rudimentary beginnings of an attempt to connect the various portions of the earth, through Pytheas’ latitude calculations and Dicaearchus’ base line. Yet until the middle of the century both topographical and theoretical data remained uncoordinated. All this changed with the work of Eratosthenes of Kyrene, who wrote the first treatise specifically devoted to geography (Roller 2010a, 15–​30). After an education in Athens, he was summoned to Alexandria by Ptolemy III to be librarian and tutor to the future Ptolemy IV. Eratosthenes’ reputation at this time was largely based on poetry and, to some extent, mathematics, in which his expertise later won the praise of Archimedes. Yet, before long Eratosthenes turned to geographical speculation. The topography of Egypt, where the Nile stretches almost due south 5,000 stadia from Alexandria to Syene (Syēnē) at the First Cataract and beyond, and the location of Syene at the summer tropic, may have given Eratosthenes the idea of determining mathematically the circumference of the earth, a topic that had been a source of speculation for over a century but which had never been calculated with any accuracy. Using Euclidean geometry, Eratosthenes was able to relate the solar angles at Syene and Alexandria at the time of the summer solstice and calculate the circumference at 252,000 stadia. The calculations and conclusions were published in his On the Measurement of the Earth, which survives in only a few fragments cited by astronomical and mathematical authors of the Roman period (Roller 2010a, 263–​267). Eratosthenes then turned to his most important work, Geographica. This word, and related words such as the noun geographia and the verb geographeo, seems to have been first devised by him, using as analogy words such as geometreo, “to measure land” (Roller 2010a, 111). The Geographica was started after 246 bce (the accession of Ptolemy III) and probably completed by 218 bce, since Eratosthenes seems to have no knowledge of the Roman expansion onto the Greek mainland that began in that year. The treatise was only three books long, yet it set forth the complete contemporary knowledge of the new discipline, both theoretical and topographical. Eratosthenes did little fieldwork, and his data were generally collected in the library at Alexandria or through oral information from seamen and merchants. Most of his cited sources are from the era of Alexander or later, indicative of the large amount of material that had recently become available. Despite its significance, the work was probably not widely disseminated and may have vanished by the Roman Imperial period. Knowledge of it is largely due to the

320   Hellenistic Greek Science extensive synthesis made by Strabo of Amaseia, who is responsible for 105 of the 155 certain fragments, thus making it possible to reconstruct the work with a certain amount of thoroughness. Whether a map was included remains uncertain. Eratosthenes began the Geographica with a history of his newly founded discipline, starting with Homer. He was aware of the limitations of the geographical information in the Homeric poems, due to the great expansion of geographical knowledge, especially during and after the time of Alexander. The historical section concludes with the exploration up the Nile by officers of Ptolemy II in the early 3rd century bce. It seems likely that Strabo presents only a filtered and partial view of what Eratosthenes wrote. The treatise then turns to an examination of the physical earth itself and the changes that had occurred to its form. It was obvious that the earth was not static, since marine phenomena could be found far inland. The book closes with a discussion of geographical fantasies. Book 2 is about the shape of the earth. It is the most problematic for a modern reader to interpret, because inevitably material from On the Measurement of the Earth (which may even have been summarized in book 2)  is tangled into Strabo’s recension. It seems that the book centered on the inhabited landmass of the earth—​the so-​ called oikoumenē—​essentially an island surrounded by water (so that in theory one could sail west from the Pillars of Heracles to India). Using imaginative terminology, Eratosthenes set forth his view of the earth, based on the circumference of 252,000 stadia that he had already calculated. He said that the oikoumenē was set into a zone, a portion of the earth shaped like a vertebra or spindle whorl (spondylos), and the oikoumenē itself was shaped like a chlamys. The inhabited world was divided latitudinally into five zones and was over twice as long east-​west as north-​south. Some of these concepts built on previous scholarship: the oikoumenē seems an Aristotelian concept (Meteorology 2.5) and the terrestrial zones were probably first proposed by Parmenides (Strabo 2.2.2). Book 3 is the actual description of the inhabited world, with an emphasis on topography (rather than the ethnic divisions proposed a century earlier by Ephorus). Building on Dicaearchus’ base parallel, Eratosthenes created a number of subsidiary parallels located along a prime meridian that ran through Syene, Alexandria, and Rhodes (figure C5.1). Rhodes was where the base meridian and base parallel crossed. To the north there were parallels as far as the latitude of Thule; to the south there were ones through Meroë and the land of the Cinnamon Bearers (the Horn of Africa). Meridians were a little more problematic but crossed the base parallel at various points from the Pillars of Heracles to India. The system was both brilliant and flawed: although the length of the longest day could be used to calculate latitudes (as Pytheas had done with the shortest day), many of Eratosthenes’ latitude and meridian points relied on more casual local data. It is clear that he had corrected Dicaearchus’ errors with the base latitude in the west, yet most of Eratosthenes’ lines wobbled as they attempted to connect known points. For example, his base meridian runs almost due north from Rhodes to Lysimacheia, but then swings well east to touch Olbia at the north edge of the Black Sea. In the east, especially, data for the meridians are lacking. Nevertheless the system is a remarkable achievement because

Figure C5.1  Eratosthenes’ map of the oikoumene (inhabited world). Drawing by author.

322   Hellenistic Greek Science for the first time it created a grid system for the inhabited earth and allowed places far from one another to be related geographically: Pytheas’ calculations in the northwest could be fitted to those of the Alexander companions in the far east. The remainder of book 3 examines topographically the inhabited world, from east to west. Continuing his use of inventive terminology, Eratosthenes divided the world into “sealstones,” of which there are four (India, Ariana, Mesopotamia, and Arabia). Yet the attempt to force geometric shapes onto the topography of the earth became less and less viable as Eratosthenes moved west, and by Mesopotamia it had broken down entirely. The fourth sealstone, a peculiar combination of Arabia, Egypt, and Aithiopia Ethiopia, is mentioned but generally ignored. The sealstone concept represents Eratosthenes’ attempt to apply Euclidean geometry to the surface of the earth, a good beginning to breaking up and comprehending its component parts, but in the long run untenable, and west of Egypt there are no sealstones. Nevertheless as late as the time of Strabo there was still a tendency to see the parts of the earth as composed of geometric or natural forms (Strabo 8.2.1). The Geographica mentions over 400 places, which could now be related to one another by Eratosthenes’ grid system. Ethnographic comments are rare in the surviving fragments and may not have been preserved by Strabo. The extant quotations become briefer and vaguer in the Mediterranean region, especially in the west, probably because here the Geographica was conspicuously out of date by the time of Strabo, although it is clear that it went as far as the outer coast of Iberia, the British Isles, and the Atlantic coast of Africa. The treatise closed with a discussion of how Alexander had rejected traditional divisions between Greeks and barbarians and had viewed the human race in a more inclusive way. By emphasizing this, Eratosthenes fit the Geographica, with its citation of numerous peoples and places, into the new Hellenistic world of diverse ethnic groups.

5.  Hipparchus and Polybius Eratosthenes’ Geographica defined the state of geographic knowledge in the second half of the 3rd century bce. Yet, within a century, the work was attacked for its methodology, particularly by Hipparchus of Nicaea. As a mathematician and astronomer, he believed that Eratosthenes’ use of overland and maritime measurements received from travelers and sailors was a dangerously flawed technique (especially overland, as travel routes were not in straight lines); and, moreover, only mathematics and astronomy could determine the location of places, two disciplines that were necessary tools for a geographer. His critique was published in his Against the Geography of Eratosthenes, probably around the middle of the 2nd century bce (Dicks 1960, 1–​18). Since most of its fragments are, inevitably, only available through Strabo’s citation of them, who generally took the side of Eratosthenes against Hipparchus, exact interpretation of the latter’s arguments can be difficult.

Hellenistic Geography from Ephorus Through Strabo    323 Hipparchus’ interest in geography was slight, and his work has the characteristics of a polemic. To be sure, mathematics and astronomy could offer greater accuracy than the complex combinations of overland measurements that were the basis of Eratosthenes’ data, yet Hipparchus seemed to ignore that Eratosthenes was quite aware of the limitations of his technique and knew that his measurements were often approximate (Eratosthenes F52, 131 = Strabo 2.1.39, 41). Hipparchus seems to have had no objections to the methodology used to calculate the circumference of the earth, but he also stressed Eratosthenes’ failure to use this technique in locating other places beyond the Syene-​ Alexandria axis. He also criticized Eratosthenes’ attempt to force the surface of the earth into a series of geometric forms. The extant fragments of Hipparchus’ treatise often appear to be a series of picky complaints about errors found in Eratosthenes’ work, but Strabo probably overemphasized Hipparchus’ seeming pedantry. Nevertheless Hipparchus did make some important contributions. Realizing that the calculation of the circumference of the earth at 252,000 stadia now made it possible to determine the number of stadia in a degree (700), he was able to create a much more detailed grid for the surface of the earth (Hipparchus F39 = Strabo 2.5.34), and thus in theory could locate places with much higher accuracy. But the necessary astronomical data were simply lacking for many of the places Eratosthenes had cited, and Hipparchus gave an illusion of accuracy by providing degrees and minutes for locations that had been determined by the traditional method of overland measurements (Dicks 1960, 37). Nonetheless, he was able to calculate some latitudes and straighten some of Eratosthenes’ wobbly parallels. Although Hipparchus’ basic idea was valid—​that mathematics and astronomy could, in theory, determine locations more accurately than land distances—​he was not in the mainstream of geographical theory, since the trend was toward ethnographic rather than mathematical geography, as came to be exemplified by Polybius, Artemidorus, and, above all Strabo. It was only in the Roman Imperial period that scholars such as Marinos of Tyre and the geographer Ptolemy stressed mathematical geography, but without total success, since data were still lacking. Early in 146 bce Carthage fell to the Romans. Access to its archives and libraries on the part of Greeks and Romans meant that the wide range of Carthaginian exploration came to be known. To be sure, a summary of the voyage of Hanno had been available in Greek perhaps since the 5th century bce, but this was only a small portion of the Carthaginian ventures. Hanno’s voyage along the Atlantic coast of Africa around 500 bce had reached the tropics, near Mt. Cameroon, and shortly thereafter the Massalian Euthymenes attempted to replicate the voyage but did not go beyond the Senegal River. Then the Carthaginians actively excluded Greeks from their spheres of influence, jealously guarding the results of their explorations as state secrets (Polybius 3.22; Roller 2006, 57–​58), and there was essentially no further information on the west available to the Greek world until 146 bce. Polybius, who may have been present at the fall of Carthage, was probably the one responsible for examining the Carthaginian archives (Roller 1960, 99–​100). He was also commissioned by the conquerer P. Cornelius Scipio Aemilianus to take a fleet and explore

324   Hellenistic Greek Science the Carthaginian territories on the West African coast (Polybius bk. 34, fr.15.7 = Pliny 5.9–​ 10). He went as far as the tropics and wrote On the Inhabited Parts of the Earth Under the [Celestial] Equator (Polybius bk. 34, fr.1.7–​14 = Geminos 16.33), in which he concluded, contrary to accepted opinion, that the equator was at high altitude (Polybius bk. 34, fr.1.16 = Strabo 2.3.2). How he came to this idea is not certain, but he had Hanno’s report available, which had documented Mt. Cameroon, lying on the coast just north of the equator at an elevation of 4,069 m. He may well have seen the mountain himself. He further believed that the equatorial regions were not hot, as had been supposed, but more temperate than the hot regions on either side. Again this may have been based on the existence of mountains near the equator: not only Mt. Cameroon but also from information the explorers of Ptolemy II, who had gone up the Nile a century previously and had learned of the mountains near the source of the river. Polybius suggested that the temperateness was because the sun did not remain as long over the equator as over the tropics. Remembered today as an historian, Polybius saw himself primarily as an explorer, a new Odysseus (Polybius bk. 12, fr.28.1): a monument in his home town of Megalopolis made no mention of him as an historian but noted his expertise as an explorer (Pausanias 8.30.8). He also attempted to gather evidence for Pytheas’ journey, perhaps traveling to the mouth of the Liger (Loire) River, and questioning Massalians (Polybius bk. 34, fr.10.6–​7 = Strabo 4.2.1). However he allegedly learned nothing: the Massalians, like the Carthaginians, were reluctant to talk about what they considered trade secrets, and Polybius came to believe that Pytheas had made it all up, a point of view reinforced by Strabo. Thus began the collapse of Pytheas’ reputation. Although Polybius did not write any specifically geographical work beyond his brief treatise on the equator, he did include a book on geography within his history (Walbank 1970–​1979, 3:563–​569). This section, book 34, is lost, so it is difficult to determine Polybius’ plan for it, and the fragments now printed as if from book 34 are a collation of geographical citations from later authors, especially Strabo and Pliny. Book 34 was placed after events of 153/​2 bce, perhaps to mark the point at which Polybius began to play a role in events. Although reconstruction of book 34 remains hypothetical, it seems to have begun with a theoretical section, largely concerned with the terrestrial zones and the relation of the earth as a whole to its inhabited part. This was followed by a description of Europe, including an examination of the wanderings of Odysseus and polemics against Pytheas and Eratosthenes. The remainder of the fragments assigned to this book are about Africa: there is no extant material about Asia except a single vague reference to India (bk. 34, fr.13 = Strabo 14.2.29). Polybius’ section on Africa (bk. 34, fr.15.6–​16) is also limited and is mostly distances, although there is the crucial fragment about the exploration of the African coast (bk. 34, fr.15.7 = Pliny 5.9).

6.  Periploi and Fantasies Polybius’ journey down the West African coast to the tropics connects with another feature of geographical scholarship and literature: the periplous. The word originally meant

Hellenistic Geography from Ephorus Through Strabo    325 “circumnavigation” (e.g., Herodotos 6.95) but eventually came to describe both a coastal sailing voyage and the written report of it. As a literary form it is known from the 6th century bce: the earliest preserved (at least derivatively) is that by an unknown Massalian who went from his native city around the Iberian Peninsula and perhaps as far as the British Isles (Keyser 2008). It survives in the geographical poem by Avienus known as the Ora maritima, of the 4th century CE. The earliest periplous actually extant (in part) is the Greek translation and summary of Hanno’s voyage down the African coast. Since essentially all sailing was coastal, it is inevitable that any report of a sailing voyage could be considered a periplous: this is even apparent to some extent in the Odyssey. The lost reports of Alexander’s commanders Nearchos, Onesicritus, and Androsthenes fit into this category. Data from periploi pervaded the writings of many, such as Pytheas and Patrocles, and Strabo used them extensively without actual citation (e.g., 14.3.1–​8, 16.4.4–​14). Despite their pervasiveness in Greek geographical literature, only a few survive. The fragmentary On the Erythraean Sea of Agatharchides of Knidos (ed. Burstein), written in the middle of the 2nd century bce, despite its title and its inclusion of coastal descriptions, is more an ethnography and history of the Ptolemaic interest in the Red Sea region and adjacent Africa. One extant periplous is dedicated to a King Nicomedes (presumably one of the kings of Bithynia in the latter 2nd century bce) by an anonymous author, identified erroneously as Scymnus of Chios (Marcotte 2002, 1–​102; Dueck 2008a). Preserved in about 1,000 lines of iambic verse, it describes the European coast and that of the Black Sea and is the best surviving example of an actual periplous from the Hellenistic period, containing much valuable information about Greek settlements on the Black Sea. The most thorough extant periploi is the Periplous of the Erythraean Sea (not to be confused with the work of Agatharchides), which dates from the mid-​1st century ce and thus lies outside the scope of this chapter (Dueck 2008b). Despite the existence of only a few surviving examples, the periplous was an important part of geographical literature from Herodotos on. In fact, given that so much geographical information in the Greek world was obtained by coastal sailing, it can be difficult to isolate what might be called a “true” periplous since all geographical treatises have an element of the genre. A peculiar by-​product of geographical scholarship was the creation of fantasy tales about remote places that implied a certain geographical knowledge or reality. Although it may be easy to dismiss such accounts as merely a literary genre, often they contained elements of actual geographical knowledge. Since the time of the Odyssey there has been a fine line between accounts of voyages to real places and those to mythical ones, and the real can turn to fantasy in a way that the reader may not immediately comprehend. One can easily see this even in Odysseus’ narrative, which begins with a realistic account of his departure from Troy and the sacking of cities on the way home (Odyssey 9.39–​61). Yet eventually weather makes him and his companions unable to go around the end of the Peloponnesos, and a ferocious storm of nine days’ duration leads him from the known world of the Greek peninsula to the unknown land of the Lotus Eaters (Odyssey 9.80–​84). Regardless of how one believes in the different levels of reality in the narrative, it is clear that Odysseus has left his familiar world and has embarked on

326   Hellenistic Greek Science an adventure in unknown areas. Fantastic geographical tales were constructed in such a way, locating unusual people and places outside the known world. Such a construct could be used for discussing political or sociological theory, as Plato did with Atlantis. Atlantis seems to be the first solid example of the genre; others include the continent beyond the Ocean described by Theopompus (FGrHist 115, F75c = Aelian, Diverse History 3.18), the Hyperborean land of Hecataeus of Abdera (FGrHist 264, F7–​14) and the Indian Ocean fantasy of Euhemeros of Messene (FGrHist 63, F1–​11). Obviously the location of these fantasy worlds had to move as knowledge expanded: the Isles of the Blessed were originally in the Mediterranean but eventually came to be in the Atlantic (Roller 2006, 44–​45). Yet the fantasy worlds often held an element of factual geographical knowledge and thus can be relevant as source material: once the size of the earth became known and was compared with the limited extent of its inhabited portion, it was easy to locate fantasies in or beyond the Atlantic, where early yet vague knowledge of existing islands such as the Azores, Madeira, or the Canaries could provide the basis for locating a new world. After Pytheas went to the Arctic, those regions were fertile locales for fantasies, such as that by Antiphanes of Berga (Plutarch, How One Might Become Aware of His Progress in Virtue 7 [79a]). Complicating the understanding of such writings was a tendency to dismiss some legitimate reports of real places, such as that of Pytheas. Yet this has been a factor of exploration in all eras: where the known world ends, one enters a different world where nature itself differs. The idea continues in modern science fiction.

7.  The 1st Century bce Around 100 bce, Artemidorus of Ephesus wrote a geographical treatise that seems to have been 11 books long, the longest work on the topic to date (Stiehle 1856). It survives, as usual, in citations mostly by Strabo and Pliny, with many toponyms in the Ethnica of the Byzantine grammarian Stephanos of Byzantion. There is also a brief epitome by the late Roman author Marcianus of Heracleia. Artemidorus’ work seems largely to have been remembered for its numerous distances, which are the subject of most of the extant fragments. After an introductory book, the circuit of the inhabited earth begins at the Iberian Peninsula and continues across Europe, and then jumps to Libya and east to India, ending up in Anatolia. Somewhat over 100 fragments survive, and it is admittedly difficult, given this scanty material, to imagine how 11 books could have been filled, but occasional ethnographic and scientific glimpses have been preserved, such as a discussion of natural hydrology at Gadeira (F14 = Strabo 3.5.7) or the climate of West Africa (F77 = Strabo 17.3.8). As presented by Strabo, Artemidorus often saw himself in opposition to Eratosthenes, and one purpose of his treatise may have been to update the earlier scholar. Artemidorus’ treatise was far more detailed than that of Eratosthenes, and it was an important influence on the Geographica of Strabo a century later.

Hellenistic Geography from Ephorus Through Strabo    327 A contemporary of Artemidorus was Posidonius of Apameia, head of a Stoic school on Rhodes and Rhodian ambassador to Rome in the 80s bce. A polymath whose bibliography is enormous and varied, he was an important factor in the transmission of Greek knowledge to Rome. He traveled widely: in addition to moving from his home in Syria to Rhodes and then Rome, he undertook, probably in the 90s bce, an extensive journey to the far west, including the Iberian Peninsula (spending a month in Gadeira) and the Celtic regions (Posidonius, T14–​26). His geographical work, On the Ocean (its title mirroring that of Pytheas) is known from a lengthy yet somewhat confusing summary by Strabo (F49 = Strabo 2.2.1–​2.3.8). The synthesis leaves many gaps, and, in some cases, emphasizes seemingly minor points in the original treatise (such as the career of Eudoxus of Knidos) at the expense of more substantive discussions (such as about the tides). Although Strabo took Posidonius to task for being too philosophical, nevertheless, he realized that On the Ocean was a significant work on geography. Much of Strabo’s summary emphasizes the matter of the terrestrial zones, the division of the earth into bands determined by latitude and climate. Parmenides had originally suggested that there were five zones: two cold, two temperate, and a torrid zone of double width (Strabo 2.2.2). Posidonius generally agreed with this, but he also believed human geography should be brought into play and the ethnic characteristics of those living in particular zones reflected the climate of the zone. Polybius’ six-​zone theory was rejected, as well as his idea that the equatorial region had a high altitude. At this point in Strabo’s summary, the story of Eudoxus of Cyzikos intervenes. As intriguing as this tale is, it seems unlikely that it made up nearly one-​third of On the Ocean, which is the relative scope given to it by Strabo. More than likely it was an anecdote in Posidonius’ discussion about the nature of the External Ocean and whether it was continuous, as Posidonius believed. This issue had been much argued since the time of Eratosthenes, who may have been the first to propose the idea (F16 = Strabo 1.3.13). After recounting the tale of Eudoxus, Strabo seems to have lost interest in Posidonius’ treatise, and only brief comments follow, about the changes in the levels of the earth, the continents, and human ethnography. Again it is difficult to imagine that Posidonius’ treatment of these topics was as limited as Strabo implied. Nevertheless, despite the imbalance of Strabo’s summary, it is possible to see the broad outline of Posidonius’ work. The story of Eudoxus of Cyzikos is known from no other source and is worthy of comment (Roller 2010b, 95–​99). An adventurer rather than geographer, he was responsible for opening the route from Ptolemaic Egypt to India in the later 2nd century bce: previous to that time, there had been no direct trade. But the discovery of the monsoon route made a round-​trip from the lower Red Sea possible and had an important impact on the Ptolemaic economy. Eudoxus, however, after making the first such voyage, ran into difficulty with the Ptolemaic government and abandoned Egypt to position himself in Gadeira, where he made several attempts to reach India by circumnavigating Africa, and eventually was lost at sea. It is unlikely he would be remembered as a personality had not Posidonius learned about him while in Gadeira, presumably shortly after Eudoxus departed on his last voyage and when his return was still possible. There

328   Hellenistic Greek Science is no evidence that he published any account of his travels: the material recorded by Posidonius has all the elements of oral history, with the role of Eudoxus enhanced at the expense of his opponents. Nevertheless, the tale, probably true in general outline, indicates the role of seamen and adventurers in the advance of geographical knowledge. Whether Eudoxus ever completed a cruise around Africa, he made others aware of the possibility and seems to have confirmed the idea of a continuous External Ocean. His attempts to circumnavigate the continent were an inspiration to Portuguese explorers of the later 15th century.

8. The Romans By the 2nd century bce, the Romans had begun to develop their own interest in geographical research. After the fall of Carthage, Scipio Aemilianus had been the patron of the explorations of Polybius, since mastery of Carthaginian knowledge was important to the Romans. The Romans also moved into the Iberian Peninsula and the Celtic territories to the north:  local field commanders included ethnographic data in their reports. In Iberia, Greeks had been limited to the coastal region, so the Roman advance into the interior provided valuable new information, even if in a military rather than academic context. For example, D.  Iunius Brutus led an expedition against the little known Callaicians in northwest Iberia in 137 bce (for which he received the surname Callaicus). Well educated (Cicero, Brutus 107), he wrote a report on his campaign that provided some of the first data on the region, including ethnographic information about the indigenous people (Strabo 3.3.1–​7). Other Romans had Greek scholars in their entourage while in the field. Theophanes of Mytilene (FGrHist 188) accompanied Cn. Pompeius Magnus on his eastern campaign in the 60s bce. Although primarily recording Pompeius’ deeds, when he traveled in remote areas Theophanes was able to report much valuable geographical data. Pompeius reached the Albanians on the west coast of the Caspian Sea (Theophanes F4 = Strabo 11.5.1), a little known region in one of the areas that Alexander’s chroniclers had manipulated geographically, so the available information was suspect. Theophanes provided a new report about the territory between the Black and Caspian Seas. He examined the course of the lower Tanais (modern Don), the accepted boundary between Europe and Asia (F3 = Strabo 11.2.2), and provided local ethnographies (F4–​6 = Strabo 11.5.1, 11.14.4, 11). He remains one of the best examples of how the Romans relied on Greek scholars to record their expanding geographical knowledge. Roman geographical literacy was also enhanced by Greek scholars resident in Rome. In addition to Theophanes, Posidonius was in the city at least sporadically from the 80s bce until around 50 bce (Posidonius, T1–​13). Tyrannion of Amisos was also there during these years. Although essentially a grammarian—​known as the cataloguer of the libraries of Aristotle and Theophrastus (Strabo 13.1.54)—​he was also a geographer (Cicero, Letters to Atticus, 26: Shackleton-​Bailey 1999) and one of the teachers of Strabo

Hellenistic Geography from Ephorus Through Strabo    329 (Strabo 12.3.16). Thus by the middle of the 1st century bce, Greek geographical concepts were firmly established among the Roman elite, even if their interest was primarily to support their military and political needs. Moreover, traditional Greek geographical literature was available in Rome by this time: the Geographica of Eratosthenes, in particular, was well-​known. Cicero planned to model his own geographical work after it, and Julius Caesar, noting the wide extent of the Greek scholar’s knowledge, consulted it when writing about Gaul (Gallic War 6.24) Both Varro (de re rustica 1.2.3–​4) and Vitruvius (1.1.17, 1.6.9, 11) also made use of the treatise. The blending of Greek geographical scholarship and Roman needs is best seen in the career of Juba II, the allied king of Mauretania from 25 bce to 23 ce (Roller 2003). Son of King Juba I of Numidia (whose kingdom had been provincialized), the younger Juba was raised in Rome in the household of Augustus’s sister Octavia and received an excellent education. After he was placed on the throne of Mauretania—​having married Cleopatra Selene, the daughter of Cleopatra VII and Antonius—​he set out to learn as much as possible about his kingdom. He or his surrogates made expeditions to the High Atlas and the Canary Islands (which he named) and sought the source of the Nile in the great river systems of Mauretania. The result of his research was compiled in a treatise titled Libyka, a geographic and ethnographic study of all of North Africa west of Egypt. In 2 bce he accompanied Augustus’ grandson C. Caesar on his Arabian expedition, and then wrote a second treatise, On Arabia, which topographically joined Libyka on the east and examined the course of the Nile, the Arabian Peninsula, and the routes to India, using both existing information from as early as the days of Alexander and contemporary data gathered orally from traders and merchants. Together the two treatises covered the entire southern reach of the inhabited world, from the Atlantic islands to India. They represented a broad range of knowledge possible only in the Roman period and were also an implementation of Augustan policy, which was desirous of learning in detail about the southern extremities of the world. Yet the treatises were written in Greek, demonstrating it was the proper language of geography even among the Romans. Neither treatise survives today: there are over 50 fragments of the two works, largely preserved by Pliny the Elder (Roller 2004, 48–​166).

9.  Homeric Topography A common feature of Hellenistic geographical scholarship is Homeric topography. The obvious topographical content of the Homeric poems, especially the Odyssey, had long been realized. Eratosthenes began his Geographica (F1–​11) by noting that Homer was the first to consider geographical matters, but then he emphasized that Homer was essentially a poet, not a scholar, and stressed that his geographical knowledge was limited. Eratosthenes was fully aware that Greek geographical knowledge by the 3rd century bce had expanded far beyond what Homer had known (F8 = Strabo 7.3.6–​7).

330   Hellenistic Greek Science This portion of Eratosthenes’ treatise is preserved in greater detail than much of the rest, because his point of view incurred the wrath of Strabo, who had been trained as a Homeric scholar and felt it necessary to refute Eratosthenes’ view in detail (Strabo 1.2.3–​24). Nevertheless, Eratosthenes’ Geographica marks the beginning of attempts to relate Homeric topography to the contemporary discipline of geography. By the 2nd century bce, works were being produced that were solely on this topic. Most notably, Demetrius of Scepsis (BNJ 2013) wrote an astounding 30 books on the 62 lines of the Trojan Catalogue (Iliad 2.816–​877); the treatise is lost today but was quoted extensively by Strabo. Demetrius was well placed to do his research since his hometown was only 30 km from Troy. He was perhaps the earliest example of a true topographer, although it is difficult to imagine how he could have provided sufficient detail for a work of such length. Nevertheless, he may have been the first to question the actual location of ancient Troy and the relationship of the contemporary village to the city where the war took place, an issue that has lasted into modern times. Demetrius’ contemporary Apollodorus of Athens (FGrHist 244) wrote 12 books on the Greek Catalogue, replete with ethnographic data. He also produced a commentary on the Trojan Catalogue (F170–​171 = Strabo 14.5.22, 12.3.24), perhaps a separate work written in response to that of Demetrius. One of the more intriguing writers on Homeric topography is Hestiaia of Alexandria, who seems to have traveled in the Troad. In her work on the Iliad she noted that the topography around Troy had changed since antiquity and that one could not be certain where the fighting had taken place. She was also interested in the topic of river deposition (Strabo 13.1.36; Pomeroy 1984, 61, 67, 72). She was quoted by Demetrius, so was active before he published, but perhaps not much earlier. Nothing else is known about her, but she may be the only example of a woman topographical scholar from antiquity. Interest in Homer meant interest in geography. As an example, Crates of Mallos, the librarian at Pergamon who lived in Rome after being sent there as ambassador in the 160s bce, and who came to be called “Homericus” because of the intensity of his scholarship, wrote an analysis of the Homeric poems (Broggiato 2001). Essentially a philologist and grammarian rather than a geographer, he was inevitably drawn into geographical issues and, in order to illustrate the wanderings of Odysseus, constructed the first globe of the earth, which was 10 feet in diameter (F134 = Strabo 2.5.10). He may also have written a treatise on globes. The earth had been assumed to be spherical since the 5th century bce, but Crates seems to have been the first to concern himself with the limitations of representing of a sphere on a flat surface. The globe made it apparent that the inhabited portion of the world was a very small part: something known mathematically for some time, but perhaps not conceived visually until Crates. In fact, with the extent of the inhabited portion generally suggested to be 70,000 stadia east-​west by 30,000 north-​south, and the circumference of the earth at 252,000 stadia, three-​fourths of the globe would be water. Therefore Crates suggested that there must be another inhabited portion, in the south (F37  =  Strabo 1.2.24, 2.3.7). This idea continued to develop to the point

Hellenistic Geography from Ephorus Through Strabo    331 that two centuries later Seneca the Younger (Medea 375–​379) could presume that new worlds would someday be revealed across the Ocean, which became one basis of Renaissance exploration.

10. Strabo The culmination of Hellenistic geographical scholarship is the 17-​book Geographica of Strabo of Amaseia (Roller 2014, 1–​29). It is not an exaggeration to say that practically everything known today about Hellenistic geography appears in this work: were it not for Strabo, there would be very little evidence for the explorations of Pytheas or the geographical scholarship of Eratosthenes, Hipparchus, Polybius, Posidonius, or many others. The Geographica is the only extant work of its genre in Greek and one of the lengthiest surviving pieces of Greek literature. Strabo was born into a well-​connected family of the Pontic aristocracy, probably in the 60s bce, and lived until the 20s CE, a span that saw immense changes in the Greco-​ Roman world. He was broadly educated in Nysa, Alexandria, and Rome, coming into contact with many of the major scholars of the day. His first interest seems to have been not as a geographer but as a Homeric scholar and historian. He served on the staff of Aelius Gallus in Egypt during the 20s bce, and otherwise traveled extensively in Italy, the eastern Mediterranean, and western Asia as far as Armenia. What he did for a living is unknown, but the astonishing number of references to mining and quarrying in the Geographica (over 100) suggests some connection with those industries. He seems to have been working on the Geographica for much of his life, although the final drafting of vast sections of the treatise took place after the accession of Tiberius in 14 CE. The Geographica of Strabo is a complex and diverse work that is difficult for the modern reader to understand (Engels 1998; Lasserre 1982/​3). It includes many topics—​ some of which can only marginally be considered geographical—​including Homeric criticism, cultic history, linguistics, autobiography, Jewish religion, and the nature of Roman power. Unique and unusual words are used throughout the treatise. The text can be so digressive and ambiguous that the reader can easily lose the thread of the discussion. Its long gestation period and its immense length contribute to its difficulty of comprehension. It seems that Strabo was not interested in a concise summary of world geography: although he used the Geographica of Eratosthenes as his model, his own treatise is more than five times as long. Its core nevertheless remains basic geography, yet there are such lengthy digressions that it can be difficult to imagine that the same person wrote the entire treatise. The history of geography and the formative processes of the earth, as well as technical data from Eratosthenes and Hipparchus about how to measure the inhabited earth, occupy the first two books. Beginning with the third book, Strabo progressed through a survey of the inhabited world, starting at the southwestern corner of the Iberian Peninsula. Books 3 and 4 discuss Iberia and the Celtic world; books 5 and 6

332   Hellenistic Greek Science the Italian peninsula and Sicily. Books 7–​10 examine the Greek peninsula and the islands. Books 11–​14 are about Anatolia and the Black Sea littoral:  as both Strabo’s homeland and the site of the Trojan War, this formed the core of the work and was nearly one-​quarter of its bulk. Books 15 and 16 are about India, the Iranian plateau, and Mesopotamia. The concluding book, 17, discusses Egypt, and then jumps to the Atlantic coast of North Africa and returns east across Mauretania, the Carthaginian territory, and the Cyrenaia. It is no accident that the Geographica ends at Cyrene, the hometown of Eratosthenes. Yet other topics are always present. Strabo, like Eratosthenes, believed that Homer was the first geographer, yet unlike the earlier scholar he always believed in the indisputable truthfulness of Homeric topography. Indeed, he felt that contemporary topographical research validated Homeric geography, even when the data seemed to demonstrate the opposite, such as the location of Pharos in Egypt (1.2.30). To be sure, Strabo’s arguments are often precise and sharp, with a strong critical sense, as in the matter of Odysseus and Scylla (1.2.15–​16). Yet his obsession with Homer and the belief in his eternal validity sometimes drove him in peculiar directions, and he often resorted to the excuse of faulty transmission of the text to explain what seems today an obvious error or geographical limitation on the part of Homer (1.1.7, 1.2.16). With a work that is highly diverse, often frustratingly so, the modern reader can be left wondering what Strabo’s purpose was in writing the Geographica. He stressed that geography was important (1.1.1), yet then failed to develop this idea, plunging into the history of geography and other issues such as the formation of the earth and how to measure the inhabited world, followed by actual geographical discussion. Unlike Eratosthenes, Strabo moved from west to east, from Iberia to India, and then back west to Egypt, a format that may have been designed to place Rome at the center of the inhabited world (Clarke 1999, 210–​228), but it also had the precedent of Hecataeus’ Circuit of the Earth. The treatise ends with a eulogistic summary of the Roman contribution (“since they have surpassed all former rulers of which we have a record”), and the final lines of the Geographica (17.3.25) lay out the division of the world into provinces and allied kingdoms, based on the Augustan settlements of the 20s bce but updated half a century to the situation after the accession of Ptolemaeus of Mauretania in 24 ce. This ending suggests the Geographica was in part designed to outline the present state of the inhabited world under Roman control. Yet its long compositional history diffused this motivation somewhat, as things changed greatly over those 50 years, a period spanned in the last section of the Geographica with its simultaneous positioning in the early years of Augustus and the middle years of Tiberius. Strabo wrote that geography was useful for those engaged in political and military activity (1.1.1), a theory he had previously followed in writing his lost Historical Commentaries (cited in Geographica 1.1.22–​23) and that reflects the realities of the Roman Imperial period. Yet he also suggested that his works would be useful to the general public. The Roman Empire was varied and diverse, and its educated population would itself be diverse. The changes in tone in the Geographika reflect this.

Hellenistic Geography from Ephorus Through Strabo    333 Like his contemporary Dionysius of Halicarnassus, who often covered similar topics, Strabo could create a Greek work of broad appeal to a Roman audience anxious to enjoy the newly elevated status of Greek literature in Rome. In the west (books 3–​4, 7), where Strabo had never traveled (2.5.11), he had to rely on published material, especially that of Pytheas, Polybius, Posidonius, Julius Caesar, and the reports of other Roman field commanders. This part of the treatise is a synthesis of previous scholarly reports rather than new topographical research, yet it brought together all the known evidence for Iberia, the Celtic regions, the Alps, and the north. It reached its final form after Germanicus’ victory over the Cherouskians in 16 ce (7.1.4) and would have been written for both a Greek and Roman audience that wanted to know the history and current state of the region. Intruding into the midst of this account of the north and west are the two books (5–​6) on the Italian peninsula and Sicily, designed for an exclusively Greek audience. Strabo, like Diodorus of Sicily and Dionysius of Halicarnassus, was willing to illuminate Roman history and culture for Greeks. The different tone of these two books suggests they may originally have been independent of the Geographica as a whole: a brief ethnography and geography of Italy and Sicily for Greeks. The eulogistic summary of Roman power and Augustan peace that ends book six (6.4.1–​2) reads like the end of a separate work. The rest of the Geographica (books 8–​17) would appeal to an educated general public of either Greeks or Romans. Yet the detailed discussion of Anatolia was probably designed more for Romans, providing a local report of the changes that had occurred in that part of the world since the later 2nd century bce. Strabo stressed the superiority of products from his homeland (e.g., 3.4.15) and thus was not a disinterested observer. Indeed, he was very much involved since his family had played a prominent role in the last years of the Pontic dynasty and the circumstances of the Roman acquisition of the region. He also provided a listing of the luminaries from each major city in Anatolia, a subtle reminder to the Romans of the cultural significance of his home region. The naming of over 200 famous Anatolian men and women, many from Strabo’s era, as well as inclusion of his family history, provides a biographic and Hellenocentric element to the Geographica. Thus Strabo’s Geographica merged geography and politics. Like his contemporary and colleague Juba II, Strabo used geography to assist in the implementation of Roman policy, yet he stressed that there would be no Roman policy to implement without a Greek foundation on which to build it, which was best manifested in the intellectual output of Anatolia. Although Strabo’s obsession with Homer can be frustrating and his wandering digressive style difficult to follow, he took essentially everything that was known about geography (from Homer as he saw him to his own era of Julius Caesar and Juba II) and put it into a single treatise. Strabo was, perhaps immodestly, well aware of the monumental quality of his work (1.1.23). Although there were later treatises on geography, such as that in Latin by Pomponius Mela and the largely catalogic work of Ptolemy, it is significant that after Strabo no other geographical work of such extent or usefulness was produced in Greco-​Roman antiquity.

334   Hellenistic Greek Science

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chapter C6

M echanic s a nd Pneum atics i n t h e Cl assical Worl d T. E. Rihll

1. Introduction Mechanics is the study and movement of masses. In theory, it can extend from the atom to the stars, and key thinkers like Aristotle, and later Newton, endeavored to understand and explain the motion of bodies, such as missiles, ships, and planets. The flight of the javelin provided ancient thinkers with a paradigmatic phenomenon in need of theoretical explanation. What force propelled it in flight? What supported it in flight? In practice, mechanics usually concerned moving dead loads such as stones, water, or wood on building sites, at harbor quays, or in sieges, but simple machines that made life easier were ubiquitous in ancient societies. Pneumatics was the study and exploitation of pneuma, or “breath,” meaning air or steam, including water or other liquids, often involving the use or movement of water to drive motion or maintain air pressure. Air was harnessed to delight, to perplex, and to entertain audiences; and more adventurously, but probably not successfully, to propel missiles in Ctesibius’ compressed air catapult. Classical cities were physically constructed with mechanical devices such as cranes, hoists, and levers. Their inhabitants were supplied with grain ground by machines, water lifted by machines, and wine and olives pressed by machines. They were entertained with stage machinery, such as lifts and trapdoors, and by self-​contained mechanical devices. They fought with machines to raise, demolish, and overlook walls; to shoot and to deflect missiles; to send signals; and to celebrate victory. Some of the greatest ancient thinkers studied these topics to understand what was going on in terms of masses and forces, and the mechanics of the human frame was recognized early (Aristotle, Movement of Animals 7). Some of these efforts were misdirected although rational; for example, the notion of “the immovable mover” seems

338   Hellenistic Greek Science to have been driven by the recognition that forces must be opposed to have any effect, for instance, in Aristotle, Movement of Animals 2–​4: “for there would not be any walking were not the ground to remain still, nor any flying or swimming were not the air and the sea to resist” (668b17–​18). A few ancient propositions in mechanics, for example, those in Archimedes’ Equilibrium of Planes, are as fundamental to this field as Euclid’s are to geometry.

2.  The Two Faces of Mechanics Since Athenaeus Mechanikos in the 1st century bce, if not before, mechanics has two aspects:  theoretical-​ mathematical, and practical-​ functional (On Machines 4.7–​5.9; Whitehead and Blyth 2004). For Pappos (in the 4th century ce or thereabouts), mechanics comprised geometry, arithmetic, astronomy, physics, metalworking, construction, woodworking, and painting (Mathematical Collection 8.1–​2). It is easy to assume a division between theory and practice occurred in antiquity as today, and scholars mainly have done so. We perceive a significant difference in the connotation of the word “mechanics,” in the plural, meaning a branch of mathematics, and “mechanic,” in the singular, as a problem-​solving practitioner, between the academic and the vocational, but these were parts of what Pappos understood as one subject. However, Price long ago (1964) and Berryman recently (2009) argued in favor of a much closer relationship between and interpenetration of theory and practice in antiquity, of philosophical and practical endeavor. Price argued that mechanistic thinking led to the creation of automata, and Berryman that mechanics stimulated ancient philosophical thinking and explanation. Both emphasized the ancient evidence for a mechanical hypothesis to explain natural phenomena. It is easy for a scholar to miss the significance of unfamiliar things, and mechanics is as challenging for the scholar as it was for Pappos and his prospective student. So Drachmann came to recognize that Heron had practical knowledge, in addition to his well-​known theoretical expertise, only through Drachmann’s experience of building a screw cutter following Heron’s instructions: some of Heron’s words conveyed the easiest way to perform a particular operation, which was neither apparent nor appreciated when the text was only read and not materialized (1963, 76). Didactic mechanical literature is imperfectly understood through reading; proper comprehension requires it be performed. Pappos’ list of required skills is idealist rather than realist. However, the demands of mechanics may not have seemed as daunting to others as they did to him. Certainly, mechanics was classified as a branch of mathematics, though mathematically it was then very different from today’s version. Certainly, most known ancient machines could have been invented, constructed, and used by people who were neither literate nor numerate. And certainly, some authors from earlier centuries do sometimes

Mechanics and Pneumatics in the Classical World    339 exhibit disdain for anything involving manual labor, be it in the domain of agriculture, construction, or the mechanical arts. But equally certainly, practical problems that would be challenging in any time and place, such as bringing fresh, clean water to cities, bridging major rivers, and building venues to hold tens or even hundreds of thousands of people, were set and solved by ancient engineers. Academic subjects and the world of work were less separated in antiquity than they are today. Many people were polymaths academically, and they undertook political, military, or economic activities besides (see e.g., Vitruvius 7.pref.14). In the Laterculi Alexandrini (Diels 1904), which appears to be a sort of Hall of Natural and Human Fame for children in an ancient school, a list of then-​and-​there-​famous Mechanikoi appears alongside a few lawgivers like Solon, painters like Zeuxis, sculptors like Pheidias, and architects like Cheirisophus, who is not necessarily the same as the well-​known Chersiphron. Interestingly, one of the people on the relatively long list of famous mechanics, someone called “Abdaraxos who worked in Alexandria” is now otherwise unknown, while Ctesibius, who also worked in Alexandria, is missing (and the lacuna in this part of the text is small). It reminds us that our knowledge is contingent on a variety of factors and is based on personal views. In the classical world the practical-​functional aspect of mechanics did not depend on its users having a correct understanding of the theoretical principles involved. Natural forces were harnessed, channeled, and resisted to create the material culture of the classical Greek and Roman worlds more successfully than those same forces were analyzed and understood. For example, the facts of buoyancy were known to seafarers long before anyone really understood the theory. Aristotle’s remarkable powers of observation had noted that the salinity of water affects buoyancy—​a fact reflected in the Plimsoll line inscribed on modern ships—​but it took Archimedes’ genius to frame and express the mathematical principles of buoyancy in his treatise On Floating Bodies. Apollonios of Perge, known to mathematicians as author of a fundamental work on conic sections, also wrote a treatise, which partially survived (in Arabic), on the construction of a mechanical flute-​player (Lewis 1997, 49–​57). Carpos of Antioch, who recorded that Archimedes wrote a now lost treatise on mechanical sphere-​making, argued that theoretical understanding could positively assist the practical-​functional domain, so this cannot have been the norm or he would not have had to argue for it. Carpos developed geometrical methods to serve engine builders, architects, surveyors, clock makers, mechanics, and scene painters; but he had to fight against the sort of academic snobbery that prefers its mathematics to be useless (Pappos, Mathematical Collection 8.3–​4). Mathematically, mechanics is the study of masses and forces, with a first step that consists in the identification of the forces acting on things. Thereafter the understanding of those forces was deepened and refined through mathematical analysis. Some of the identifications made in classical antiquity were sound (e.g., the simple mechanical powers), and theories based on them developed fruitfully. Some of the identifications were unsound. Of these, the spurious concepts of “natural motion” and “natural place”

340   Hellenistic Greek Science that flowed relatively straightforwardly from an Aristotelian understanding of matter and its qualities (see e.g., Aristotle, On Heaven 1.2) were sterile and actually inhibited a correct understanding of motion. Thus the ancient definition of mechanics as a discipline that examines “bodies at rest, their natural motion, and their motion in general, not only assigning causes of natural motion but also devising methods to force bodies to change their position, contrary to their natures, in a direction away from their natural places” (Pappos, Mathematical Collection 8.1; emphasis added) doomed students to a dead-​end in dynamics that was not clearly identified as such until the 17th century ce (though one can overstate Aristotle’s influence, Sorabji 1988, 201). Where motion was not involved, the ancients made great strides in understanding the forces at work on a body; where motion was involved, false theory hobbled them. It did not prevent practitioners moving vast dead weights such as huge granite obelisks from inland Egypt to the top of a pedestal in the center of Rome or Constantinople (Pliny, Natural History 36.64–​74), nor did it stop them constructing things that moved, including two wooden theaters that rotated to form an amphitheater (Pliny, Natural History 36.116–​120), but ultimately it did handicap those who wished to understand why and how they were able to move anything.

3.  The Reality or Idealization of Described Devices Machines and instruments appear in ancient texts and in the archaeology (Schürmann 1991 collects a large sample). Logically, machines described in texts could be real, unreal, or a combination of the two. What emerges from the ground is obviously real, but it is usually incomplete or decayed, and its purpose is rarely self-​evident. So the best place to start the investigation of devices is with the literary sources of information, which vary in style and substance. At one end of the spectrum are texts that were written apparently to tell the reader how to make specific objects. Examples of such literature are Heron’s and Philon’s books on Pneumatics, which give instructions for the construction of one device after another. These devices vary from the very simple, such as a hinged flap valve (Heron, Pneumatics 1.11) or a cup with integral straw (Philon, Pneumatics 50), to the very complex, such as a wind-​powered hydraulic organ (Heron, Pneumatics 1.43). At the other end of the spectrum are texts that include descriptions of mechanisms only incidentally, because the author’s main aim was to communicate something else, not to describe or tell readers how to construct whatever it is. For example, during a discussion of a particular military campaign, Polybius offers a critique of a military signaling device that involves a detailed description both of an existing system and of a purportedly improved version. In between those literary poles, we have texts that seem to describe types of machine.

Mechanics and Pneumatics in the Classical World    341 Consider the case of catapults. It is clear that the reader was supposed to scale, adopt, and adapt the types described to suit his particular needs and circumstances. We are told explicitly that specific quantities begin with the length or weight of the intended ammunition, which was then plugged into a given formula to set the diameter of a particular component, the washer, and this diameter then served as the module for the other critical components, which were sized as ratios of it. In modern shorthand, the diameter d equals 1/​9 of the length of bolt for a sharp caster, and for a stone thrower d in dactyls = 1.1 times the cubic root of the weight of the stone in drachmai; the frame length for a certain type should then = 6 ½ d, and the width of side stanchions = 1 ½ d, for example (Philon, Belopoiika 55). A template was supplied for use when cutting the most important component from a block of wood (the washer: Philon, Belopoiika 52.20–​53.7), and again the sizing was derived from the ammunition the catapult was intended to launch. Sites found throughout the classical world have preserved scores of washers, a few frames, and depictions which demonstrate unequivocally that machines that correspond to the types described in these texts were actually made in a host of different sizes. Cranes are another class of machine where the texts describe types with variant designs and guidance on their respective strengths and weaknesses, and the user was expected to select the appropriate one for their needs (Vitruvius 10.2). Three-​legged cranes are described as the most stable, for example, but were only good for raising loads placed between the legs, and had to be repositioned frequently on a construction site. Two-​legged A-​frame cranes were good for lifting straight up or dropping down (making an excellent pile driver for a bridge pier for example) but could not rotate. A single beam set upright can rotate in any direction and lean to a useful degree, so it was good for most lifting needs and essential for some tasks, such as loading and unloading ships at the quayside, and they are described as the quickest and easiest type of crane. However, since these cranes needed four control teams at the end of ropes and pulleys to direct and support the beam, as well as the lifting crew handling the load directly, they were relatively difficult to manipulate and were used by specialists, according to Vitruvius (10.2.8). There has been significant debate about the reality of Heron’s Baroulkos. This text, as preserved, provides a single, worked example of how to move a weight of 1,000 talents with a power of five talents, and it does not reduce the relationship between the components to abstract formulae beyond indicating that the ratio of the diameter of the wheel to the diameter of the axle serves as a multiplier (the mechanical advantage). Friction and imperfection is ignored or overlooked. Pappos interpreted this text as Heron’s demonstration of a general theory about lifting a given weight with a given power that was discovered by Archimedes (Mathematical Collection 8.20, part of which probably appears in Heron, Mechanics 1.34 and 2.7), and as a result Drachmann took this text to be “just a theoretical solution of the given problem” (1963, 32). In terms of its components, some are unproblematic—​cables and pulleys persist in construction today—​but some scholars find the gear wheels troublesome. The earliest certain evidence for gear wheels is usually said to be Archimedes’ hodometer, and Archimedes

342   Hellenistic Greek Science died in 212 bce, but the rack and pinion appears in Ctesibius’ water clock, ca 270 bce, and the pinion is a robust type of small gear, while the rack is a linear one. Gears appear at the small scale in • precision instruments such as Heron’s dioptra, where half a toothed wheel engages an endless screw (a physical example of such a half-​wheel has been found in Spain), and clocks such as Ctesibius’; • handy gadgets such as the self-​trimming lamp (where it engages a rack); • trick automata such as the mechanical animal that drinks immediately after a knife has apparently passed right through its neck (Heron, Pneumatics 2.36); • the brass gear from Olbia, Sardinia, found in 2006 and provisionally dated to the 2nd century bce (as yet only published in Pastore 2010); and • the Antikythera mechanism, whose 30 surviving gears are justly famous. At the large scale gears appear in • water mills; and • sakia gear, which is usually part of a water-​lifting apparatus. Gears have not yet been found in ancient weight-​lifting or load-​hauling applications (baroulkos excluded), for which they are not ideal, unlike the windlass or capstan, which continued to be the mainstay in such applications until modern times, for example, in European navies in the age of sail. In high-​power applications, such as mechanized milling, a small gear wheel is often replaced by the more robust lantern pinion (e.g., Moritz 1958, plate 14), and some would argue that the lantern gear preceded the spur gear (Lawton 2004, 59, 65). Typically in large water-​or wind-​powered applications, one gear has metal and the other wooden teeth, so that if too much force is applied, as can happen suddenly and potentially catastrophically with wind and water, the wooden teeth will break: they can be replaced much more easily and cheaply than the whole wheel or the whole mechanism. This raises a more general point about the evidence. Working machine parts wear out more or less quickly. Ancient machines were made mostly of organic materials that have long since decayed, and metal parts were liable to be recycled via a furnace. Wood formed the principal constituent of most kinds and instances of ancient machines, and wood is liable to burn, rot, and be eaten over time. Iron, too, rots easily in the air and on the ground. The hazards of time act unevenly on ancient artifacts, favoring some materials, such as marble, bronze, and gold, and disfavoring others, such as wood and iron, and most tools and machines were made of wood and iron. The physical evidence for the lathe’s existence and use is tooling marks on stone, metal, and even glass artifacts that were shaped on it, not the machine itself. Dependence on texts is therefore heavy, and here appearances may deceive: a text may look like a set of instructions for the construction of a machine, yet the device may be unrealizable for a variety of reasons. These reasons include social and economic factors such as the time or funds

Mechanics and Pneumatics in the Classical World    343 available for completion, as well as technical factors such as an inability to make a particular component or to get it functioning properly. Any ambitious project, ancient or modern, is liable to fall short of its promise on paper (many ambitious projects in modern times fall into this category, and the same is surely true of antiquity). So our recognition that something would not work is not a demonstration that it was a figment of someone’s imagination. The variance between the literary and the material remains of antiquity is quite striking in mechanics. For example, water wheels are hardly mentioned in the surviving literature, yet archaeologically it is now appears that practically every imperial Roman villa had one, in Gaul at least; they are normally some distance from the house and so have not been found and excavated with the rest of the buildings, but when they are sought in an appropriate place in the vicinity, they are usually discovered (Brun 2006). Scholars once dismissed machines described in ancient sources as purely theoretical constructs on the grounds that they thought they would not work at all, as described, or efficiently enough (assuming efficiency was a valid criterion for an ancient patron), as Thompson treated most of the war machines described in de rebus bellicis (Thompson 1952, 77–​79). But such sweeping dismissals are often unfounded (Rihll 2007, 235–​244 for this particular case). In other instances, textual lacunae and corruptions compound the problems of comprehension. For example, in 1963 the hodometer looked like an armchair invention even to Drachmann, a scholar who was a practitioner and who built a reconstruction of Heron’s screw cutter. But the textual difficulties here were solved progressively by Sleeswyk in 1979, 1981, and 1990; and finally Lewis concluded that the marine version, despite its obvious shortcoming of measuring only the movement of the ship relative to the water, would still work better than dead reckoning, and that its results may appear in surviving periploi (Lewis 2001, 139). The fragmentary Olbia wheel’s teeth are even cycloidal, that is, the same shape as modern gear teeth, although the common profile of ancient gear teeth is the equilateral triangle, as in the Antikythera mechanism, an analogue computer from the 1st century bce or earlier. That extraordinary machine, found in 1900 but not published about until the 1970s (and work on it is ongoing), demonstrated that ancient artisans were quite capable of making intricate mechanical models of highly theoretical constructs, in this case of the visible cosmos and several different calendars. Gears embodied then-​current theories on the motion of the heavenly bodies, and the Antikythera mechanism’s maker was able to model physically the solar and lunar anomalies, by means of a nonuniformly divided scale or differential gears (Evans, Carman, and Thorndike 2010). The Antikythera mechanism is significantly more complicated than anything described in the surviving texts and seems to presuppose the existence of other sophisticated machines as part of its own lost heritage. The texts inscribed on the mechanism itself have been published in a special issue of the journal Almagest (March 2016). The Antikythera mechanism is not marred by mistakes or redundancies and can hardly have sprung sufficient and complete from its maker’s imagination. It is, however, still liable to be sidelined by skeptics as highly unusual and of little, if any, relevance to ordinary people’s lives.

344   Hellenistic Greek Science That cannot be said of other ancient machines. For example, the variety of devices developed by and for doctors to extend the limbs and facilitate reduction of dislocations and fractures that are described in surviving medical treatises point toward the pragmatic deployment of mechanical aids in ordinary life. Orthopedics is a relatively transparent branch of medicine, insofar as it is not normally hard to identify a dislocated joint or a fractured limb, and kind words and placebos will not repair the damage. Brute force is temporarily required to overcome the patient’s muscles and pull the joint or ends of broken bone apart to be able to put them back in their rightful place. Since Hippocrates’ time in the 5th century bce, that force was typically supplied either by a couple of strong assistants or by machines that could stretch the human frame to allow the doctor to manipulate bones back into place. The Hippocratic bench was joined by other mechanisms large and small, often bearing the name of their developer, such as Andreas’ engine, Pasikrates’ spanner, and Aristion’s chest (Oreibasios 49.6, 8, 21 respectively). Nymphodoros’ chest (described in EANS 584–​585, illustrated in Drachmann 1963, 176) was an endless screw mechanism in a tidy little box that enabled doctors to exert and control significant force with little fuss and even less display. Vitruvius mentions a Nymphodoros as an author on mechanics (7.pref.14), which would explain how the device acquired its name. The speculum (Figure C6.1) that forced open rectal or vaginal orifices (for treatment of fistulas, for example, Hippocrates, Fistulas 3) gave the doctor precise control over soft tissues,

Figure C6.1  Two kinds of speculum: screw and lever. Drawing by author.

Mechanics and Pneumatics in the Classical World    345 and, in at least some cases, incorporated a female screw (or nut) in bronze; a simpler lever version existed too (e.g., Naples AM 116436). Other mechanisms designed for medical applications include a syringe to draw and inject fluids (Heron, Pneumatics 2.18) and a cupping glass whose low pressure was created by sucking out the air from a communicating chamber, rather than by cooling previously heated air in the glass itself (Heron, Pneumatics 2.17).

4.  Mechanics as Augmented Physics Greek science is underpinned by the belief that the natural world behaves in regular ways. There were disagreements about precisely how and why phenomena in and of the world come into existence, change, and pass away again, but there was common agreement that natural phenomena were not haphazard or arbitrary; they followed patterns of some sort. Civilized people interfered with those natural processes deliberately and precisely in order not to have to live naturally as other animals did. (By choosing to live like dogs, the Cynics aimed to minimize that interference.) To control their environment, their diet, their security, and so on, people built shelters and granaries, made ploughs, clothes, weapons, and suchlike. Grim pragmatism did not claim all their attention, however, and daily life was leavened with devices to increase comfort and joy, and to provide necessities; for example, strung beds replaced straw on the floor; presses were used to extract oils for perfumes, food, and fuel; and lathes turned bronze bells and wooden bowls (e.g., the bronze bell from Castell Collen Roman fort in Wales, diameter 98 mm, ca 4 inches, about the size of a small ship bell). Mechanics was the means by which some of this manipulation of nature was executed; mechanical devices were employed to create what nature would not deliver if left alone. What could be realized by mechanics was in that sense unnatural, and it could sometimes even appear super-​ natural—​that is, contrary to and better than expectations based on normal experience of the world—​a facet of mechanics that was explored and exploited by numerous devices designed specifically to leave audiences awestruck, or at least bemused, by their performances. The identification of the simple mechanical powers and the establishment of the principles of mechanical advantage that could be obtained by the employment of a given machine was a fundamental achievement of ancient thinkers. It enabled those with a little training to work out how to move a given load with the given resources: how many men, using which machines in which ratios, would be necessary to achieve the task. Of course monuments could be built without such knowledge, as the pyramids were, but mechanics permitted a relatively small number of people to move mountains, both to cut them down and to build them up, by amplifying the power applied to the task. Ironically, given that it was a poor understanding of motion that hobbled ancient work on dynamics, a parallelogram of velocities appears in the late 4th century bce in the

346   Hellenistic Greek Science Aristotelian Mechanics (sec. 23) and again in the 1st century ce in Heron’s Mechanics (1.8). But the parallelogram of forces as we know it had to await Stevin (1548–​1620) and Newton (who formulated the principle in 1687: Dugas 1955, 123, 207). The two main branches of ancient theoretical work that had lasting consequences were in statics, concerning bodies and fluids at rest, and pneumatics, concerning fluids and air at rest and in motion. Archimedes’ legacy in statics, rather like Aristotle’s in biology or Galen’s in medicine, was so overwhelming that few apparently undertook further work in the field: after their deaths little progress was made on the topics each had made his own. Statics did not make significant progress from Archimedes’ death until the late 16th century, when Stevin’s De beghinselen der weeghconst appeared. Great trees can cast great shadows that inhibit the growth of other plants in the vicinity. As for pneumatics, the corporality of air was understood early, and the ability of air to create force was recognized in various machines, some of which worked well, such as the organ (see figure C6.2) and some of which probably did not, such as the compressed air catapult. The “water-​thief ” (klepsydra) came in a variety of designs but was essentially a hollow metal or ceramic pot with one hole at the top (usually on a hollow handle, at a convenient spot to place a thumb) and multiple holes at the bottom, which allowed a modest quantity of water to be collected from a source by immersion (see e.g., Kilinski 1986 for surviving specimens). When the user opened the hole at the top, water could flow in or out, and when the user covered it, the water was retained inside or outside

Figure C6.2  Pieces of a pneumatic organ found at Aquincum. Photo by author.

Mechanics and Pneumatics in the Classical World    347 (Philon, Pneumatics 11; Heron, Pneumatics 1.7). This simple domestic vessel harnessed air pressure to perform useful work and led to speculation from the mid-​5th century bce on precisely how it did this: Empedocles’ poem On Nature explained it in terms of air pressure (fr. 100, in Aristotle On Youth, Old Age, Life, Death and Respiration 7), an explanation that was only certainly understood again (and then only by some) from the 17th century (Prager 1974, 5–​6), though Heron seems to have glimpsed the notion of atmospheric pressure (Lewis 2000, 346). Written works on pneumatics by Straton and Ctesibius are largely lost. The siphon principle was discovered early and used to make a considerable range of “delightful” devices (e.g., Philon, Pneumatics chap. 17–​25). So-​called inverted siphon sections on aqueducts, such as the Pergamon siphon (built in the 3rd century bce) or the Aspendos siphon (built in the 2nd century ce) did not involve suction in their operation; they were merely closed pipe sections that contained the water so it could find its own level on the other side of a deep valley (arched bridges were preferred for valleys less than 50m deep). Archimedes’ discovery of specific gravity is one of the most well-​known stories about the ancient world. (One result was that the Greek word eureka has passed into many modern languages as a special term to celebrate a discovery.) Specific gravity expresses density in terms of the relation between a body’s weight and its volume. Archimedes realized that different materials have different densities, and therefore that materials can be distinguished by their density. An easy way to measure an arbitrary volume, whether a human body or an ornate wreath for example, is to measure how much fluid it displaces when immersed. Often this can be done simply in water. Archimedes studied the forces operating in his treatise On Floating Bodies. In Quadrature of the Parabola he explored the center of gravity of ship-​hull-​shaped bodies floating in a fluid to find out at what point they would capsize. Whether this mathematical tour de force was actually used to guide the construction or loading of a ship is not known, but independent legends aver that Archimedes oversaw the building of the world’s then-​largest freighter, the Syrakosia, so the circumstantial evidence is strong if not compelling (Russo 2004, 73–​75; see also Wikander 2008, 796 on Archimedes’ Dimension of the Circle and his hodometer). The wonder-​making branch of mechanics (thaumatopoiike) flourished to astonish, perplex, and entertain audiences in the classical world from Ctesibius’ time onward, if not before, and was revived in the Renaissance to amaze and amuse another generation of patrons. Of course, novelty is a key criterion here, and one that is fundamentally short-​lived; coin-​operated dispensers presumably did amaze when they first appeared (Heron, Pneumatics 1.21), but how many such experiences did an ancient need before she took them for granted, as we do? Gadgets’ adoption is often a matter of taste and fashion rather than utility, efficiency or other rational decision; the spirit optic, for example, which dispenses a measured quantity of liquid, is the norm in British bars though publicans can use thimbles if they prefer, while in other countries free-​flow pourers are normal and the barman is trusted to give fair measures. Philon’s and Heron’s optics are hidden within the container (Pneumatics 28 and 2.1 respectively), but their service to equity is just the same as the modern British version’s.

348   Hellenistic Greek Science

5.  The Utilization of Mechanical Powers The Greeks and Romans developed and deployed a number of fundamental tools and machines. For example, the compound pulley, which is not attested before the Greeks and is still found in modern daily life, allowed huge stones weighing several tons to be lifted and placed carefully and precisely many meters above the ground, atop slender supports; it allowed pile-​drivers to create cofferdams for bridge and harbor works; it allowed sails to be hoisted to the top of masts and across booms to shade the audience at mass public spectacles. The cylinder and piston, which was invented by Ctesibius around 270 bce, was developed to pump air or water in various applications. It formed the essence of the syringe, to draw out and inject fluids; deployed as a pair in the force pump, it created a new type of water-​lifting device, and with the addition of a nozzle and a universal joint, that water could be directed in a jet to put out fires, or water gardens, or power-​wash ceilings. These and similar systems became bread-​and-​butter technologies at the heart of ancient societies. For example, machines for moving and lifting loads took priority over machines for war and entertainment in Philon’s Mechanical Compendium of ca 200 bce. This synthesis opened with Levers and followed with Harbor Works (which was probably more concerned with machines than with structures if surviving works in the corpus are a reliable guide). The three books on military matters, the Belopoiika, Parangelmata, and Poliorketika, the book on Pneumatics, and the book on Automata, all came later in the treatise. Harnessing and using forces and building machines that worked was much easier than understanding what those forces were and how exactly the machine transformed and transmitted them. Accordingly, the ancients utilized falling water pragmatically, through tacit rather than formal knowledge, for example to drive millstones, to stamp and cut rock, and to pound textiles and grains (evidence is collected and discussed in Lewis 1997; Wikander 2000; and Wilson 2002). Less productively, falling masses were used to drive automata for example, sand or lead in both theaters in Heron’s Automaton-​ Construction and water in Philon, Pneumatics 59–​60. Steam was harnessed to make objects levitate; (e.g., Heron, Pneumatics 2.6); rotate (e.g., Heron, Pneumatics 2.11; the device commonly but inappropriately called Heron’s steam engine); or emit noises, e.g., Philon, Pneumatics 58, and Heron, Pneumatics 2.35, which offers a birdsong, a horn, or a blast. Similarly, wind was harnessed as an alternative to muscle power to pump air into the chamber of mechanized pan pipes, aka the hydraulis, or water organ (Heron, Pneumatics 1.43 and 1.42 respectively). Such wizardry was not confined to the small scale: a rotating ceiling to amuse visitors at Nero’s Golden House is attested (Suetonius, Nero 31.2); and, in one celebrated case, an entire theater revolved, not merely the stage or some part of it—​two theaters actually, so that after they had each rotated 180º they formed a single amphitheater (Pliny, Natural History 36.116–​120).

Mechanics and Pneumatics in the Classical World    349 Heron supplies instructions for the manufacture of a device closely resembling one on sale in a modern hardware store to deliver weed killer or provide a power wash: this is an air-​tight reservoir fitted with a mechanical hand pump to create pressure to deliver the liquid contents together with a directional nozzle to steer the jet (Heron, Pneumatics 1.10; a similar but more delicate device appears in Philon, Pneumatics 35). The fire-​ engine pump in Heron, Pneumatics 1.28, achieves much the same result via different means; muscle power is used to lift water that enters a chamber immersed in a tank or reservoir, and unlike the compressed-​air powered jet, which periodically needs to stop spraying while it is refilled with air, this one functions continuously. Precision-​ engineered cast and turned bronze cylinders and plungers that were near air-​tight are documented as early as Ctesibius’ time, around 270 bce. We know he recognized the phenomenal power of compressed air because he tried to harness it to project missiles (Philon, Belopoiika 77.9–​25). There is no reason to suppose that this type of catapult ever got beyond the prototype stage, and one can easily imagine why: it would have been extremely difficult to balance a pair of the cylinders he proposed; and if they were not exactly the same, they would pull the bowstring variably, rendering the catapult inaccurate. Philon’s Pneumatics preserves a host of less ambitious devices to exploit air pressure:  his more-​or-​less scientific investigations are of the same era. For example, Philon lit a “candle” on a stand sitting in a bowl of water, and placed a cupping glass over the top so that its mouth was below the level of the water but above the bottom of the bowl. He observed the water level inside the glass rise after a short while (Philon, Pneumatics 8). He interpreted the phenomena as showing that the flame consumed the air within the vessel and that the water was lifted “in such quantity as air has perished” because it “filled the space which had been emptied.” Such observations are challenging on a number of levels, to ancient and modern readers alike. The Greek is lost, but the original Greek kandēlē (first attested in Athenaeus 15, 701b), if not also the Latin candela, may be mistranslated “candle” in English because it is not clear that candles existed in Philon’s time and place. An ancient lamp would probably work better than a candle in this experiment. Heron chose not to describe “many kinds of presses that have been in use in great numbers for a long time among the common people” because they were less “effective” than the lever and screw presses that he did discuss and analyze (Mechanics 3.20); clearly there was more variety on the ground than is recorded in his work, as we would expect of any technology. His rhetoric may be misleading, of course, but it is important to register that effectiveness was his declared priority, because a common modern presumption is that authors on topics like mechanics focused attention on what were theoretically the most complicated or novel devices; in this instance that is explicitly not the case. Drachmann argued that Heron invented the mechanical screw cutter that is described in the last chapter of his Mechanics, and that this machine tool thereby rendered screw presses much easier to manufacture from the mid-​1st century ce, which in turn lead to the more widespread adoption and use to which Pliny refers (Drachmann 1963, 140). Still, some did not adopt this technology, and it is interesting to consider why. Besides

350   Hellenistic Greek Science various social and economic reasons that may have affected an individual decision, there are mechanical ones. The screw press is more complex and difficult to make than the lever press, but it is not intrinsically better in all regards. Ancient screws of the kind found in presses were probably only about 30% efficient, meaning a lot of the energy that went into operating them was wasted. Pulleys were practical alternatives in most circumstances and were normally at least twice as efficient as screws, so potential users’ rejection of the screw press would have been rational from a mechanical standpoint (Cotterell and Kamminga 1990: 96). The difference in performance would have been apparent to anyone watching such devices carefully, even if it were not computable on papyrus at the time. A villa owner or bailiff, who was familiar with the old lever press, and who somehow learned about the new-​to-​him screw press, and who, for whatever reason, was contemplating investing in a new plant, could perceive how much time and physical effort a device demanded in operation, relative to its output, even if the work was done by others. In other words, those with capital did not need to perform the labor themselves to appreciate something about a machine’s performance. They may have cared less about wasting their slaves’ time and energy than the slaves perhaps cared, but it is abundantly clear from the surviving agricultural treatises that villa owners wasted nothing knowingly. The ancient development of the theory of mechanics followed practice, as is especially obvious when the thinkers got the theory wholly or crucially wrong. Achievements on construction sites led pseudo-​Aristotle, or his source, to reflect on the pulley, for example, and his vague discussion in Mechanics 18 allows much latitude in interpretation. By Heron’s time, comprehension had improved (Mechanics 1.1, better preserved text in Dioptra 37): “the ratio of the weight to the power that lifts it is as the ratio of the taut ropes that carry the burden to the rope that the moving power moves” (Heron, Mechanics 2.12); and of the endless screw engaging a gear, “as many teeth as there are on the wheel, the screw has to make so many turns for the wheel to turn once” (Mechanics 2.18). Heron did not really understand the power of the screw, as is shown by Mechanics 2.29, where his desired outcome could have been achieved by the screw alone and the pulleys and lever would have been redundant. This led Drachmann to suppose that this particular item was a purely theoretical example (Drachmann 1963, 91), but if so, it is an example of a bad lesson, as well as an imperfectly grasped theory, because Heron intended this chapter as a demonstration. Surely it is the better historical method to suppose the ancients made mistakes rather than such errors indicate fantasies? Ancient temples had redundant or oversized columns, too, and early steam ships carried sail and rigging and boiler and coke. It takes time and experience for users of new technologies to develop confidence in them—​if they warrant it (some do not, and are in due course forsaken and forgotten). Practical experience and pragmatism is apparent in many places in ancient texts on mechanics. Let us consider, for example, Heron’s Mechanics. In 2.32 he cites the contrast between imperfect real levers, pulleys, and screws on the one hand and perfect theoretical levers, pulleys, and screws on the other. In 3.15 he mentions that stiff ropes will not work in unloaded pulleys. In 3.2 he says that rope wound round a crane’s mast serves

Mechanics and Pneumatics in the Classical World    351 both to strengthen the pole and—​as long as the gap between each winding is four spans or less—​to provide footholds for anyone needing to climb it. In 3.8 he warns of the need to avoid using too brittle, too soft, folded, or cracked iron for a Lewis bolt, lest it break or bend in operation and consequently drop the load or hit the workers. And in 3.9 he says people harnessed carts that brought stone down from a quarry in tied pairs, so that they acted as counterweights to each other: in this way, as explained in the text, the weight of the ascending cart served to slow the fall of the descending cart, and the fall of the descending cart reduced the force necessary to raise the ascending cart. Imperfect theory combined with pragmatic tweaks demonstrates the author’s struggle to understand and explain mechanical phenomena in action; this is not the work of someone speculating in splendid isolation in an ivory tower. Entertainment provided a major motivation for the development of sophisticated machines and these sometimes involved new simple components that would in time become fundamental (Hill 1984, 199). For example, the cam is first certainly attested in an automatic puppet theater designed by Philon ca 200 bce, though it may have been incorporated in an earlier entertaining automaton, ca 275 bce (Lewis 1997, 84–​86). The famous strategy of keeping the plebeians genial via bread and circuses was accomplished partly by machines to mill grain and mix dough for the bread, and by all sorts of contraptions for the latter: stage scenery and animals were raised through trapdoors and holes from a basement to the arena by means of lifts; runners and riders began races at the same time thanks to mechanized starting gates. Mechanism was not confined to infrastructure, in some cases a machine itself was the entertainment. Philon’s and Heron’s treatises on Pneumatics are replete with such gadgets, many of which aim to surprise and delight guests, on an individual basis, when the person uses the device to, say, wash his hands, pour a drink, or indeed drink. Others are designed to be observed as they go through automated motions, like clockwork toys and town-​clock automated puppets of later ages, and their sizes suggest audiences in the tens or possibly scores, gathered around or in front to watch the performance. What began as entertainment could evolve into something useful, for example, a sound emitted when a cycle was completed. Added to a clock cycle, an entertaining noise became a functional improvement on the design because sound usually reaches more people in more places than does vision. This technological trajectory led to cuckoo clocks and Big Ben. Ancient automata were usually driven by cables rather than cogwheels and were moved by falling weights, water, or by steam generated by fire somewhere on or under the device. They can be apparently, though not actually, very complex. For example, Philon’s collection includes one (Pneumatics 40, reconstruction in Hill 1984, 214 and Lewis 2000, 355) that features a bird on a nest which rises and lifts its wings when a snake, having climbed the tree from the base, nears the chicks; when the snake recedes the bird refolds its wings and returns to sit on the chicks. All the movement depends on just two floats, two hinges, and a single siphon. (The bird from a late antique manifestation of these constructions may have survived: the Attarouthi bird, ca 600 ce, Metropolitan Museum 1986.3.15. The wings are separate, and there was something attached underneath, behind the feet, both of which features would be appropriate for this mechanism.)

352   Hellenistic Greek Science Philon’s treatise supplied only about 25% of the 78 items in Heron’s Pneumatics, written some 250 years later, and there were many other collections of instructions on how to build such devices that Heron could have utilized but are now lost. Writing in a time between Philon and Heron, Vitruvius knew of books on machinery written by Agesistratus, Archimedes, Archytas, Democles, Diphilus, Diades, Ctesibius, Charias, Nymphodorus, Philon of Byzantium, Polyidus, and Pyrrhus (7.1.14).

6. Theory The ancients regularly utilized little wooden wedges to separate massive blocks from the bed stone in a quarry, and some asked how the wedge worked to achieve such a feat (e.g., pseudo-​Aristotle, Mechanics 17, 19; Heron, Mechanics 2.4). In this case the answer eluded everyone until the 17th century, largely because it involves time and motion (on which more below). Although the wedge is an incredibly simple machine (in the technical sense of that word), this demonstrates how difficult it can be to unravel how a device actually operates. In the pseudo-​Aristotelian Mechanics, the principles of the lever, the wheel, the balance, and the wedge are explained and illustrated with simple, everyday examples, such as using the lever to lift a dead load and the wedge to split great masses of stone. The examples are quite extensive: oar, rudder, superstructures, and sails of a ship (these four dissecting a ship into its component simple machines), potter’s wheel, pulley, windlass, shadoof or swape, sling, steelyard (a much more complicated device than the simple balance), dental forceps, nutcracker, and an entertaining object that consisted of multiple friction wheels so that “as a result of a single movement, a number of them move simultaneously in contrary directions, like the wheels of brass and iron which they make and dedicate in the temples” (848a20–​25; Heron refers to something similar centuries later, Pneumatics 2.32). These examples are drawn from all walks of life, including manufacturing and the service sector. In a still widely cited paper, Finley misrepresented this text in a number of ways, of which one is particularly germane to the present argument. He alleged that pseudo-​ Aristotle “deliberately avoided any reference to instruments or machines used in industrial processes, and that when he could not do so altogether—​in the cases of the windlass and the pulley—​he made his references as abstract as possible.” (Finley 1965, 32–​33) But pseudo-​Aristotle’s references to the windlass and pulley are no more in industrial contexts than are his references to levers, wheels, or other mechanical powers at work. Given that the second-​largest manufacturing establishment known in classical Athens was a couch maker, the most obviously industrial example in the Aristotelian treatise on Mechanics is not about windlasses or pulleys at all but about stringing couches (in sec. 25), where the mechanical discussion concerns the differing stresses and tensions on the ropes and the frame depending on whether it is strung diagonally or crosswise; economics enters the discussion too—​crosswise allegedly uses less rope.

Mechanics and Pneumatics in the Classical World    353 Pseudo-​Aristotle and other thinkers were reasoning about the world they observed, including its manufacturing or industrial sector. Their science includes attempts to explain existing, functioning technology. Pseudo-​Aristotle’s analysis of the lever follows by millennia its use in balances and scales in trade. Great blocks of stone had been excavated from quarries by wedges and moved in construction by the use of levers, pulleys, and winches long before he started trying to understand how. When pseudo-​ Aristotle and his colleagues worked on the subject of mechanics and simple machines, they were trying to understand what they saw happening around them. Simple machines are defined as those that cannot be reduced to anything else, and pseudo-​Aristotle attempted to explain them fully. For example he explained the lever in terms of a circle (when it rotates, the ends describe arcs), that is, he tried to reduce it to the mathematical fundament of straight or curved lines. Mathematical proofs for mechanical propositions arrived with Archimedes. The postulates in his surviving Equilibrium of Planes are as fundamental to mechanics as Euclid’s are to geometry, and they make the loss of his Elements of Mechanics (Στοιχεῖα τῶν μηχανικῶν) particularly regrettable. The law of the lever makes its appearance here, but the basic problem of the relationship between power and weight was apparently treated comprehensively in a lost work On Levers. Archimedes wrote for people like himself, and he shared his results with the rest of the world through letters to those who were interested and capable of understanding. As a result, relatively few people knew of his written work, and we may guess that only a small portion of them wanted to expend resources to make copies of available parts of his corpus. That, and the sacking of his hometown by the Roman army after a long and painful siege, explains the loss of fundamental works, despite his fame even in antiquity. Archimedes’ surviving treatises are concerned with mechanical propositions and their proofs, but his fame has always rested on stories about the machines that he designed and built. The various military devices that kept the Romans out of Syracuse for two years usually receive the most attention, but the water screw and the compound pulley are fundamental devices of profound importance to the real world of work, and in the history of the world they had huge impact—​and still do. His contribution to those devices was surely informed by his theoretical analysis and understanding of the relationship between weight and force, which made it possible for him to calculate the mechanical advantage of a given arrangement and therefore design a machine to suit the need (as catapults were built to deliver a given type and weight of ammunition), even if that is not demonstrable from the texts that survived all the hazards they encountered through 22 centuries of European history. The phenomena of friction, acceleration, and inertia were noted in writing by the Hellenistic period. The reduction of friction was a real asset in hauling and lifting, and was evidently achieved through practice, even if analysis was not performed or the understanding achieved was mistaken. For example, on the Nemi imperial barges, floating palaces built for Caligula, were found two different types of bearing, one composed of a sphere with an axle, the other of a cone with an axle (Ucelli 1950, figs. 210, 214). They were each set with seven others of their own type in circular platforms. Either would facilitate the rotation of anything mounted on them. They are the right sort of scale for

354   Hellenistic Greek Science the end of a gangplank for example: it could be stored along the deck and swung out to whatever angle was required to meet a jetty or to allow secure and easy access to the floating palace. Theoretical analysis was less successful. Heron noted in Mechanics 1.21–​23 that unsmooth surfaces are tooth-​like, and he thought this hindered their movement. He recorded that people obtained understanding through experiment: when people placed, under a sledge, rollers that touched only a small part of the ground, “only very little roughness met it,” so that when the haulers used poles they moved the burdens easily, even though the total weight to be shifted was increased as a result; he added, with perceptive awareness of variation in practice, that other people used grease-​smeared planks (tracks) instead. (Guillaume Amontons, 1663–​1705, overturned this understanding, relating friction instead to the force pressing bodies together.) Heron observed that friction is what holds bodies stationary on slopes and suggested what he (mistakenly) thought was needed to overcome the downward tendency of a smooth cylinder on a smooth slope to hold it in place; there is no hint of measurement or numerical quantities. The concepts of acceleration, impetus, and inertia received less attention than did friction in our surviving sources. Straton used the familiar phenomenon of water falling from the roof beginning as a constant stream but arriving as discontinuous dollops of water at the bottom (fr. 40 Sharples) to argue that bodies in free fall accelerated (conveniently in translation in Irby-​Massie and Keyser 2002, sec. 6.3). Aristotle had related velocity to distance and time in the 4th century bce (in On Heaven 1.6, 273b30–​31), but neither he nor anyone else in antiquity is known to have tried to give the relationship a precise mathematical definition, so discussions about acceleration remained in the realm of observed phenomena. The absence of small, regular, equal units of time was a serious factor here that is easily overlooked in modernity because we take their presence for granted. Aristotle simply could not think of time in terms of minutes and seconds (Holford-​Strevens 2007, 7–​10). We use an equinoctial hour clock, which applies universally a specific temporal unit and thereby simplifies the act of measuring time by ignoring nature and observable phenomena, or nature’s clocks. Before Hipparchus, the “hour” varied cyclically in duration from the longest “hour” on the summer solstice (longest day) to the shortest “hour” on the winter solstice (shortest day), as well as from place to place if one changed latitude. Actually, it was even worse than that, because in any given place the length of the hour during the night was the inverse of the length of the hour through the day, because if 1/​ 12th of the daytime is a long hour then 1/​12th of the following night is a short hour. Only on the equinox was the day/​night length equal everywhere (hence the name), to wit, 12 hours daylight and 12 hours darkness. No one is going to think about the movement of masses in terms of, say, cubits per hour in these circumstances. Thus, even though ancient scientists could recognize time as an independent variable (Russo 2004, 104–​105), they could not easily think about that variable in uniform, divisible, measurable units. Philon’s thermoscope (Pneumatics 7) suffered from a similar constraint: it could show changes in temperature, but not measure them in any meaningful and generally recognized way. Likewise, the water clock could measure small units of

Mechanics and Pneumatics in the Classical World    355 time that were, of course, parts of the day but were not standardized subunits of it. Thus although a prostitute nicknamed “Water-​clock” worked in Athens in the 4th century bce (Athenaeus, Dons at Dinner 567c–​d), the story does not reveal the beginnings of the influence of the clock on people’s everyday behavior (pace Russo). Her services ceased when all the water had flowed out, so she worked with the single unit capacity of her water clock, and that is no different intrinsically from the unit of a whole day, or for that matter a whole year (so Lewis 2000, 362). Since prostitutes in her historical context were normally hired for the night, what the story shows is that someone started offering fast sex, or quickies. Plutarch is the only classical author surviving to preserve the speculation that other heavenly bodies might draw things to themselves, as earth demonstrably did of things on it (On the Face in the Orb of the Moon 924e–​f ). The 2nd century bce astronomer Hipparchus, who was familiar with equinoctial hours, that is, with the time period we call an “hour,” and who used them in his astronomical computations, tackled the gen­ eral problem in a treatise On Bodies Carried Down by Their Own Weight. However, it is lost, and Simplicius’ summary of his views as they were known in the 6th century ce (in his Commentary on Aristotle’s ‘On Heaven’, 264–​267) is brief and unmathematical. Such intimations of gravity are intriguing, and, in his most penetrating modern study of related matters, Sorabji (1988, 282) concluded that the notion of inertia was just glimpsed by the Epicureans, though there are analogous ideas in Aristotle. The importance of quantification and accuracy when dealing with the forced movement of masses had been clear to Philon in the 3rd century bce, but it was not to most of his contemporaries or successors. He tried to explain to the “many people” who were perplexed by the variability in the performance of catapults that looked the same, in size and design, and were made of the same sort of materials, wood and metal, that it was essential to be precise and accurate in the construction. Philon quoted Polycleitus, a sculptor, on perfection being achieved through many calculations and emphasized that multiple small errors can result in a large total error (Belopoiika 49.12–​50.13). One imagines that Archimedes’ catapults suffered no such deficiencies in theory or practice, but sadly we know very little about them beyond their existence, for his surviving treatises do not explicitly address the subject. The most detailed description we have of his catapults is that of a lay witness, and it concerns just those built to defend the world’s first three-​masted ship, whose construction he oversaw, the Syrakosia, which, as mentioned, was also then the largest freighter. Aristotle conceived of tools as falling into two gross divisions:  the living and the lifeless. As an example he cited the look-​out as a living instrument and the rudder as a lifeless instrument to help the helmsman in the accomplishment of his work (Politics 1.4). Aristotle even fantasized about a situation in which lifeless instruments anticipated and accomplished what was required of them, observing that no one would need slaves and subordinates “if the shuttle would weave and the plectrum play the lyre itself.” It did not apparently occur to him, or to anyone else for the next 2,000 years or so, that by means of many smaller lifeless components, powered by other than muscular means, looms could accomplish their work not quite unaided, but with little attention by a living

356   Hellenistic Greek Science instrument. Industrialization and technological inventiveness meant that by the mid-​ 19th century, in some parts of the most technologically advanced economy in the world, one person could service as many as six looms simultaneously. We do well to remember that living instruments are still required to service the machines, albeit in ever smaller numbers. Thus far accomplishment; modern automated expert systems that can anticipate, as Aristotle imagined, are being developed as we speak. Aristotle’s analysis still holds and his imagination is yet to be realized.

7. Conclusion Recent scholarship on texts and artifacts that relate to mechanics and pneumatics in the classical world have begun to transform our understanding of the place of machines in it and of the ancients’ comprehension of the principles that such machines embodied in their operation. Human artifice, which enabled people to achieve feats that were unnatural, was investigated with the same sort of enthusiasm and rigor as were natural phenomena. These investigations began about the same time too, with pre-​Socratic philosophers such as Empedocles of Acragas, and they continued at least into the 1st century ce, in the work of people like Heron of Alexandria, and the 2nd century ce, in the work of people like Carpos of Antioch or Apollodoros of Damascus. Machines powered by human or animal muscle, by water, by air, by steam, and by falling weights were employed in agriculture, in quarries and mines, in manufacturing establishments, in service businesses and in the home, either to make tasks easier to perform or allow them to be performed at all.

Bibliography Older editions of Greek texts are available online at the Thesaurus Linguae Graecae, http://​ www.tlg.uci.edu/​ (subscription necessary, though the Canon of authors and Aristotle’s Problems are available to all). Key works in the history of mechanics in the original languages and in translation are steadily coming online; they are collected at the Archimedes Project, http://​archimedes2.mpiwg-​ berlin.mpg.de. Argoud G. and J.-​ Y. Guillaumin. Les pneumatiques d’Héron d’Alexandrie. St. Étienne: l’Université de Saint-​Étienne, 1997. Argoud, G., and J.-​Y. Guillaumin, eds. Sciences exactes et sciences appliquées a Alexandrie. St. Étienne: l’Université de Saint-​Étienne, 1998. Berryman, S. “Ancient Automata and Mechanical Explanation.” Phronesis 48 (2003): 344–​369. —​—​—​. The Mechanical Hypothesis in Ancient Greek Natural Philosophy. Cambridge: Cambridge University Press, 2010. Brun, J.-​ P. “L’énergie hydraulique durant l’Empire romain:  quel impact sur l’économie agricole?” In Innovazione Tecnica e Progresso Economico nel Mondo Romano, ed. E. Lo Cascio, 101–​130. Bari: Edipuglia, 2006.

Mechanics and Pneumatics in the Classical World    357 Cherniss, H., and W. Helmbold. Plutarch: On the Face in the Orb of the Moon. Cambridge, MA: Loeb, 1957. Cohen, M. R., and I. E. Drabkin. A Sourcebook in Greek Science. Cambridge, MA: Harvard University Press, 1966. Cotterell, B., and J. Kamminga. The Mechanics of Pre-​Industrial Technology. Cambridge: Cambridge University Press, 1990. Daremberg, C. and U. C. Bussemaker. Oribase. Œuvres complètes. Paris: Imprimerie Nationale, 1851–​1876. Diels, H. Laterculi Alexandrini. Berlin:  Königliche Preussische Akademie der Wissenschaften, 1904. Drachmann, A. G. Mechanical Technology of the Greeks and Romans. Copenhagen: Munksgaard, 1963. Dugas, R. A History of Mechanics. Trans. J. R. Maddox. Neuchâtel: Griffon, 1955. Evans, J., C. C. Carman, and A. S. Thorndike. “Solar Anomaly and Planetary Displays in the Antikythera Mechanism.” Journal for the History of Astronomy 41 (2010): 1–​39. Finley, M. I. “Technical Innovation and Economic Progress in the Ancient World.” Economic History Review 18 (1965): 29–​45. Gilles, B. Les mécaniciens grecs. Paris: de Seuil, 1980. Heiberg, J. L. Archimedis Opera Omnia. Leipzig: Teubner, 1880–​1881. http://​www.math.nyu. edu/​~crorres/​Archimedes/​Books/​ArchimedesInternet.html. —​—​—​. Simplicius. Commentaria in Aristotelem Graeca. Vol. 7. Berlin: Reimer, 1894. —​—​—​. Heronis Alexandrini Opera quae supersunt omnia. Leipzig: Teubner, 1912. Hett, W. S. Aristotle:  Mechanical Problems. In Minor Works. Loeb Classical Library, 307. Cambridge, MA: Harvard University Press, 1936. Hill, D. A History of Engineering in Classical and Medieval Times. London: Croom Helm, 1984. Holford-​Strevens, L. A Short History of Time. London: Folio, 2007. Originally published as The History of Time: A Very Short Introduction. Oxford: Oxford University Press, 2005. Hultsch, F. O. Pappi Alexandrini collectionis quae supersunt. Berlin:  Weidmann, 1876–​1878. http://​echo.mpiwgberlin.mpg.de/​home/​search?searchSimple=Pappus%20Alexandrinus. Humphrey, J., J. P. Oleson, and A. N. Sherwood. Greek and Roman Technology: A Sourcebook. London, New York: Routledge, 1998. Irby-​Massie, G. and P. T. Keyser. Greek Science of the Hellenistic Era: A Sourcebook. London, New York: Routledge, 2002. Kilinski, K. “Boeotian Trick Vases.” American Journal of Archaeology 90 (1986): 153–​158. Lawton, B. Various and Ingenious Machines:  The Early History of Mechanical Engineering. Leiden: Brill, 2004. Lewis, M. J.  T. Millstone and Hammer:  The Origins of Water Power. Hull:  Hull University Press, 1997. —​—​—​. “Theoretical Hydraulics, Automata and Water Clocks.” In Handbook of Ancient Surveying Instruments of Greece and Rome. Cambridge: Cambridge University Press, 2001. Marsden, E. W. Greek and Roman Artillery:  Technical Treatises. Oxford:  Oxford University Press, 1971. Moritz, L. A. Grain Mills and Flour in Classical Antiquity. Oxford:  Cambridge University Press, 1958. Pastore, G. Il Planetario di Archimede ritrovato. Rome:  Private publication, ISBN 978-​88-​9047152-​0, 2010. Paton, W. R. Polybios Histories. Cambridge, MA: Harvard University Press, 1922–​1927.

358   Hellenistic Greek Science Potter, P. Hippokrates 8:  Fistulas. Loeb Classical Library 482. Cambridge, MA:  Harvard University Press, 1995. Prager, F. D. Philo of Byzantium Pneumatica. Wiesbaden: Ludwig Reichert, 1974. Price, D. de Solla. “Automata and the Origins of Mechanism and Mechanistic Philosophy.” Technology and Culture 5 (1964): 9–​23. Rackham, H. Pliny the Elder, Natural History. Cambridge, MA: Loeb, 1938–​1962. Rihll, T. E. The Catapult: A History. Yardley: Westholme, 2007. Rolfe J. C. Rev. D.W. Hurley. Suetonius Life of Nero. Cambridge, MA: Loeb, 1997. Rowland I. D. and T. N. Howe. Vitruvius Ten Books on Architecture. Cambridge: Cambridge University Press, 1999. Russo, L. The Forgotten Revolution. Trans. S. Levy, Berlin: Springer, 2004. First published as La rivolum mechanik und antike gesellschaft. Stuttgart: Steiner, 1991. Sharples, R. W. “Strato of Lampsacus: Sources, Texts and Translations.” In Strato of Lampsacus, ed. M.-​L. Desclos and W. W. Fortenbaugh, 5–​229. New Brunswick, NJ: Rutgers University Studies in Classical Humanitis 16, 2011. Sleeswyk, A. W. “Archimedes’ Odometer and Water Clock.” In Ancient Technology (no named editor), 23–​37. Athens: Finnish Institute, 1990. Sorabji, R. Matter, Space and Motion:  Theories in Antiquity and Their Sequel. London: Duckworth, 1988. Thompson, E. A. A Roman Reformer and Inventor. Oxford: Clarendon, 1952. Ucelli, G. Le navi di Nemi. Roma: La Libreria dello Stato, 1950. Whitehead, D. Apollodoros Mechanicus, Siege Matters. Stuttgart: Franz Steiner, 2010. Whitehead, D., and Blyth P. H. Athenaios Mechanicus, On Machines. Stuttgart:  Historia Einzelschriften, 2004. Wikander, Ö. “The Water Mill” and “Industrial Applications of Water Power.” In Handbook of Ancient Water Technology, ed. Wikander, 371–​410. Leiden: Brill, 2000. —​ —​ —​ . “Gadgets and Scientific Instruments.” In Oxford Handbook of Engineering and Technology in the Classical World, ed. J. P. Oleson, 785–​799. Oxford:  Oxford University Press, 2008. Wilson, A. “Machines, Power and the Ancient Economy.” Journal of Roman Studies 92 (2002): 1–​32.

Artifacts The Attarouthi bird: http://​www.metmuseum.org/​Collections/​search-​the-​collections/​170006046. Lathe-​ turned bronze bell:  GTJ08424 http://​www.peoplescollectionwales.co.uk/​Item/​ 9058-​bronze-​bell-​from-​castell-​collen-​roman-​fort-​ll.

chapter C7

M edical Se c ts Herophilus, Erasistratus, Empiricists Fabio Stok

1. Introduction Medicine played an important role in the cultural milieu created in Alexandria by Ptolemy I  Soter (323–​283 bce). Interest in the sciences was reinforced by Ptolemy’s connection with the Peripatetic school:  he failed to get the head of the Aristotelian school, Theophrastus, transferred to Alexandria, but he availed himself of the collaboration of another eminent Aristotelian, Demetrius of Phaleron, in founding the Museum (“seat of the Muses”), the institution which later included also the famous Library. Another Aristotelian, Straton of Lampsacus, before becoming head of the Lyceum (287 bce), had been the tutor of Soter’s son, Ptolemy II Philadelphus (283–​246 bce), and the teacher of the astronomer Aristarchus of Samos. The medical interests of the Aristotelian school were flanked by the Alexandrian cultural environment and by the influence of the Hippocratic tradition of Kos, with which Ptolemy had a special relationship: on that isle, Queen Berenice bore Philadelphus, and from it came one of the first intellectuals who settled in the Ptolemaic court, Philetas of Kos. One of the two most eminent personalities of Alexandrian medicine, Herophilus of Chalcedon, had been a student of Praxagoras of Kos. The other, Erasistratus of Ceos, was summoned to Alexandria either by Straton of Lampsacus or by the physician Chrysippus of Knidos. Direct relationships with the Ptolemies and the Museum are not documented either for Herophilus or for Erasistratus. The only testimony is that of Celsus, who says that both physicians “cut open men who were alive, criminals out of prison, received from kings” (On Medicine pref.23 = fr. 7 von Staden), where the kings would obviously be the Ptolemies. But the historical truth of this practice of vivisection is debated, and Celsus’ statement does not seem wholly credible (Scarborough 1976): first, there is the silence of

360   Hellenistic Greek Science Galen, who never speaks of vivisection; and second, Celsus used an Empiricist source, opposed to anatomical research and dissection tout court and which could therefore be suspected of gossip and lies. Leaving aside the doubts on vivisection, surely Herophilus and Erasistratus dissected dead men, and this was an exceptional practice throughout antiquity. Only in Alexandria and only at the time of the first Ptolemies was this practice permitted or tolerated, in the context of the innovation and experimentation that characterized the new city founded by Alexander. The dissection of cadavers was previously precluded by religious and cultural taboos, as it would be for a few decades later in Alexandria itself. Aristotle’s anatomical knowledge had been obtained through dissections of apes and other animals. Also Galen, in the 2nd century ce, would only dissect animals. The anatomical research of Herophilus and Erasistratus remained an exceptional case throughout antiquity because of the use they made of dissection. Apart from dissections, medical research was also stimulated in Alexandria by another exceptional condition: the interdisciplinary exchange permitted by the presence, in the Museum, of scientists and specialists from different disciplines. The interaction between medicine and mechanics is revealed by the instrument constructed by Andreas, a scholar of Herophilus, to reduce dislocations of the larger joints by exploiting the new mechanical technology developed by Archimedes, Ctesibius, and others (von Staden 1998). Herophilus had already used mechanical technology for medical goals, for example, inventing a water clock for measuring pulsations: “by as much as the movements of the pulse exceeded the number that is natural for fill­ ing up the water-​clock, by that much he declared the pulse too frequent—​that is, that the patient had either more or less of a fever” (fr. 182 von Staden 1998). Influences of Alexandrian pneumatics have been revealed in the physiology of Erasistratus, for his principle of the impossibility of a void and also for the functions he attributed to the valves of the heart (Longrigg 1993, 207–​209). Other fields of the Museum’s activities were philology and lexicography, strictly connected with the development of the Library. The works of Hippocrates and other physicians were very soon collected by the Library and permitted the development of Hippocratic exegesis, practiced both by the Herophileans and by the Empiricists. The Herophilean Bacchius, as Galen states, interpreted the rare words of Hippocrates with the help of Aristophanes of Byzantium, librarian and philologist, who “had collected a large number of examples for him” (Kühn 19.64–​65 = fr. 270 von Staden). The formation of medical sects was also favored by some peculiarities of the Alexandrian cultural context: the presence of the Library, the growing production and circulation of books, the rising importance assumed by written communication, and the debates and the controversies caused by the presence of a high number of scientists and practitioners in the same city. These factors paved the way for groups of physicians and aspiring physicians united by a doctrine and by confidence in a teacher. The formation of the sects was paralleled by the development of doxographical literature, in which authors and theories are catalogued and classified in terms that often highlight the variety and disagreements among the authorities.

Medical Sects: Herophilus, Erasistratus, Empiricists    361 Medical Alexandrian sects originated from the schools opened by Herophilus and by Erasistratus, in their own houses, and were based on the transmission and reception of the works of the masters, albeit not without revisions, dissentions, and controversies. The third sect, the Empiricists, was founded by a defector from the Herophilean school and was similarly characterized by an increasingly bookish heritage and by subsequent revisions and fluctuations of the doctrine. In the 1st century bce, all three sects spread throughout Alexandria and remained vital and active until the 1st (Herophileans) and the 2nd century ce (Erasistrateans and Empiricists), arguing among themselves and with the new medical sects that arose in the late Hellenistic and Roman world.

2. Herophilus Herophilus was born in Chalcedon around 330/​320 bce. He was a student of Praxagoras of Kos and moved to Alexandria perhaps through the connection between Kos and the Ptolemies (but Chalcedon also had direct links with Ptolemaic Egypt). He is most renowned for the treatise On Anatomy, in at least four books, of which there remains over 70 fragments. If we compare Herophilus’ anatomical knowledge with that of Aristotle, Diocles of Carystos or even his teacher Praxagoras of Kos, the new acquisitions of knowledge appear spectacular. This great development was due largely to the human dissections practiced in these years in Alexandria. On account of its descriptions, Herophilus’ anatomy remained the most accurate for 1800  years, until the times of Falloppio and Vesalio (mid-​16th century). One of the most important of Herophilus’ contributions was the discovery of the nerves. Galen (Affected Places 3, Kühn 8.212 = fr. 80 von Staden) attributes this discovery to Herophilus and to another Alexandrian anatomist, Eudemus. Herophilus located the origin of the nerves in the brain and in the spine and had a detailed knowledge of several cranial nerves. He described in particular the optic nerve and was especially interested in the structure of the eye, distinguishing between cornea, retina, iris, and choroid coat. With regard to vascular anatomy Praxagoras of Kos had already drawn a distinction between arteries and veins. Herophilus developed this distinction anatomically by observing that the coats of the arteries are thicker than those of the veins. He also described the confluence of the four great cranial venous sinuses, today called the torcular Herophili (torcular, “wine press,” is the Latin translation of the name given to this part by Herophilus). This is an example of his taxonomical approach, common in the Peripatetic tradition and in the Alexandrian culture; many other names given by Herophilus survive in today’s anatomy. Another chapter of Herophilus’ discoveries is that of the anatomy of the reproductive organs. He was the first to describe the ovaries and the tubes and gave detailed descriptions of the male seminal vesicles. There is less information about Herophilus’ anatomy of the abdominal cavity:  the only ample fragment, provided by Oribasius (Corpus Medicorum Graecorum 6.2.1, pp. 36–​37 = fr. 60b von Staden), has been called

362   Hellenistic Greek Science “the first classic description of the liver” (Mani 1959, 45). In another fragment (fr. 98a von Staden), there is the identification and naming of the intestine duodenum, “twelve fingers long.” In physiology and pathology Herophilus, as Galen and other sources state, maintained the humoralism of the Hippocratic tradition, according to which health and diseases are due to balance and imbalance, respectively, in the four humors. There are only scant references to humors in the fragments, denoting perhaps a certain skepticism with the humoral theory (Kudlien [1964] 1971) (references to humoralism, moreover, are almost totally absent in the fragments of the scholars and followers of Herophilus). But Galen clearly attests that Herophilus “tried to emulate Hippocrates’ account of the humors” (Corpus Medicorum Graecorum 5.4.1.2, p. 510 = fr. 132 von Staden). Important physiological acquisitions are ascribed to Herophilus, deriving from his anatomical findings. The discovery of the nerves led him to attribute to the brain the control of the body, as in the Hippocratic On Sacred Disease and at variance with Aristotle’s (and Praxagoras’) preference for the heart. His interest in cerebral functions is also revealed by his dream theory: those dreams not inspired by the gods, he wrote, “are natural and arise then the soul forms an image of what is to its own advantage and of what will happen next” (fr. 226b von Staden). Herophilus differentiated between “motor” (or voluntary) and “sensory” nerves and perhaps tried to explain their functioning by means of the pneuma (breath, but also vital energy or soul): certainly he described the optic nerves as “paths for the pneuma.” Pneuma, ultimately derived from the air through respiration, is attracted from the heart by the arteries, which, however, also contain blood (whereas veins contain only blood). A prominent part of Herophilus’ physiology is his sphygmology, that is, his theory and evidence about the pulse (already considered by his teacher Praxagoras). In his treatise On Pulses Herophilus defined pulsation as an involuntary motion of the arteries, whose function is to attract pneuma and blood from the heart. He distinguished two phases of pulse, contraction and dilation, and defined the modalities of pulse during the stages of life. He also indicated the analogy between human pulsations and the poetic meters (pyrrhic, trochaic, etc.). For the diagnostic use of pulsation he constructed a water clock, adjustable according to the patient’s age, to measure the frequency of the pulse (as mentioned). Sphygmology soon became a distinctive feature of the Herophilean school. In pathology, Herophilus was very interested in semiotics and also used dissection to discover the causes of diseases: Vindicianus (Gynaecology pref. = fr. 64a von Staden) says that physicians who practiced in Alexandria “found it proper to examine the bodies of the dead in order to know for what reason and in what manner they died.” Fragments reveal attempts to find the proximate causes of several diseases. But in other cases, Herophilus seems more cautious and sometimes adopts a skeptical attitude, which takes account of the uncertainty inherent in causal explanations in medicine (von Staden 1989, 116). In his Therapeutics, Herophilus offers several recipes for drugs and medicaments, which he called “the hands of the gods” (fr. 248 von Staden). He endorsed a somewhat

Medical Sects: Herophilus, Erasistratus, Empiricists    363 liberal use of drugs (excessive for Celsus On Medicine 5 pref.  =  fr. 251 von Staden) and adopted an allopathic principle according to which illness is treated by contrary remedies. Like his teacher Praxagoras, he recommended the therapeutic use of phlebotomy, that is, opening a vein to draw blood from the patient. Besides the abovementioned works, Herophilus also wrote a treatise on Dietetics. There are no relevant references to his activity in the field of surgery. The assertion of Tertullian (On Soul 25.5 = fr. 247 von Staden), who accuses Herophilus of having used an instrument known as a “fetus-​slayer,” implying he performed abortions, must be viewed with great caution. In his gynecological treatise Midwifery, Herophilus denied the existence of diseases peculiar to women and also treated gynecological topics in the surviving fragments of Against Common Opinions, a doxographic work concerned with refuting mistaken conceptions. Herophilus initiated the Alexandrian tradition of Hippocratic exegesis, though it remains uncertain whether he wrote a commentary of Aphorisms (Ihm 2002, 134–​135). Perhaps he lived too early to benefit from the collection of Hippocratic works acquired by Ptolemy’s Library, but several interpretations of Hippocratic words are present in the fragments, as criticisms and corrections of Hippocratic statements. Hippocratic exegesis became thereafter an important field of activity for the Herophilean school.

3. Erasistratus Erasistratus was born in Ioulis on Ceos about 320/​315 bce. His father, Cleombrotus, was a physician. Erasistratus had links with the Peripatetic school in Athens, probably with Straton of Lampsacus, but was not a student of Theophrastus, as stated by Diogenes Laërtius (5.57, see Scarborough 1985). He was instead a student, like his brother Cleophantus, of Chrysippus of Knidos, a physician perhaps practicing in Alexandria (another physician Chrysippus, probably the son of Chrysippus of Knidos, was involved in the conspiracy of Arsinoë I against Philadelphus: see Fraser 1972, 1.389). According to a well-​known anecdote, he healed the Seleucid King Antiochos I  Soter from the love sickness for Stratonice, the wife of his father Seleucus I Nicator (293 bce). Fraser (1969) argued that the career of Erasistratus took place in Antioch, but Lloyd (1975) and later scholars maintain that he worked in Alexandria, as a younger contemporary of Herophilus. Obviously, if he was working in Alexandria, it was for a Ptolemy, probably Philadelphus, that he offered the remedy (fr. 267 Garofalo). Like Herophilus, Erasistratus practiced dissections and realized important anatomical acquisitions: he gave the first description of the heart valves and distinguished between nerves and tendons. But his main interest was physiology, on which he wrote a work entitled General Principles. Unlike Herophilus, he totally abandoned Hippocratic humoralism and used mechanistic principles to explain bodily processes, using a corpuscular theory clearly influenced by Straton of Lampsacus. In the fragments of his works, a teleological perspective suggested by Aristotle’s philosophy can also be detected.

364   Hellenistic Greek Science Erasistratus’ basic idea was that matter naturally moves “following toward that which is being emptied” (fr. 74 Garofalo). The assumption is that a natural massed void is impossible: if matter is removed from a contained space, other matter will enter this place. On the basis of this theory, influenced by contemporary pneumatics, Erasistratus constructed a coherent physiological model that includes respiration, the vascular system, muscular activity, and digestion. Expansion of the thorax puts external air in the lungs. Part of the breath is exhaled as the thorax contracts, part goes through the “vein-​like artery” (our pulmonary vein) to the left ventricle of the heart, where it is refined and becomes “vital pneuma.” This vital pneuma is pushed by the heart’s contraction into the arteries, effecting pulsation. Part of the vital pneuma is pushed through the arteries from the left ventricle of the heart to the meninges and the brain, where it is refined and becomes “psychic pneuma” and is distributed in the body by the two kinds of nerves, sensory and motor. Vital pneuma also causes a peristaltic action in the stomach, that is, digestion (like the pestle in the mortar:  fr. 144 Garofalo). Digestion provides liquid nutriment to the liver, which turns it into blood. The veins distribute the blood as nutriment to the body. Muscles, organs, and other parts of the body are all connected by “triple-​plaited” (triplokiai) strands of veins, arteries, and nerves, invisible to human eyes but indispensable for life and growth. Erasistratus’ mechanical model of digestion differs considerably from that of Hippocrates and Aristotle, for whom digestion is realized by heat, through a sort of cooking. The model of respiration is also different from that of Aristotle (and Diocles), who said that the function of the air inspired by the lungs was the cooling of the heart. For Erasistratus heat is irrelevant and the pneuma has a vital function, as it had had for Praxagoras. Unlike Herophilus, Erasistratus maintained that arteries contain only pneuma, not pneuma and blood. This belief was influenced by Aristotle’s teleologism taken up by Erasistratus: nature cannot have created two vessels for the same content (Galen, Blood in the Arteries, Kühn 4.722). To explain the presence of blood when an artery is cut, Erasistratus applied the abovementioned principle that “an empty space fills up”: the leaking of pneuma is immediately followed by the flow of blood from the veins, through invisible blood vessels (sunastomoseis), a sort of “capillary” connecting the veins with the arteries. Erasistratus also tried to demonstrate his assumption experimentally, by cutting the arteries of goats (fr. 47 Garofalo). He used another experiment to demonstrate another axiom of his physiology, the passage of pneuma through invisible pores of the skin. In the experiment an animal was weighed, set down in a cauldron for some period of time without giving it food; at the end his weight, and that of his visible excreta, had decreased because “a considerable emanation has taken place, perceptible only by reason” (fr. 76 Garofalo; see von Staden 1975, 180). Pathology was treated by Erasistratus in several works: On Fevers, On Expectoration of Blood, On Paralysis, On Dropsy, On Podagra, and others. At variance with Hippocratic humoralism, he stated that health is not due to the balance of the humors, but to the

Medical Sects: Herophilus, Erasistratus, Empiricists    365 separation of the different forms of matter (blood, pneuma, and others); diseases are caused by their commixture. Several diseases (inflammation, fever, epilepsy and others) are attributed to the plethora, that is, the excessive blood-​nutriment in the veins. Like Herophilus, Erasistratus argued that there were no diseases particular to women. In Therapeutics Erasistratus criticized phlebotomy and harsh remedies. He preferred to prevent plethora by means of regimen or to prescribe only mild measures. He also wrote a work on cookery (there remains a recipe for a pesto to flavor boiled meat: fr. 291 Garofalo).

4.  The First Empiricists One of the pupils of Herophilus, Philinus of Kos, abandoned the school of the master and founded a new medical school, which was called Empiricist. We know from Marcellinus (On Pulsation 1 = fr. 77 Deichgräber) that Philinus found fault with the theory of pulse, but he certainly also disagreed with the master’s anatomical research: Empiricists stated that dissection is useless because dissected corpses are different from what they were before dissection (fr. 14 Deichgräber). There was also disagreement regarding etiology: the Empiricists denied the possibility of knowing the causes of diseases from theoretical assumptions regarding physiology, and they called this type of cause “hidden,” assuming the possibility of considering only “evident” causes. Philinus argued about this topic with Erasistratus: the latter, according to the pseudo-​Dioscorides On Venomous Animals (= fr. 35 Garofalo), contested the Empiricist opinion that comprehension of “hidden” things and casual explanations are impossible. Erasistratus’ statement can only refer to Philinus, who therefore founded his school when Erasistratus was still alive. Philinus, a native of Kos, was perhaps a senior student, who came to Alexandria through the links between Herophilus and the school of Praxagoras. Arguing not only with Herophilus but also with Erasistratus, he outlined an opposition between Empiricist and “rational” physicians that was accepted by later historiography, even though there never actually was a “rational sect,” but several sects opposed by the Empiricists. The opposition to all the other sects is also demonstrated by the choice of the name “Empiricists,” while Herophileans and Erasistrateans took the name of their sects from those of their masters. Through this choice the Empiricists perhaps considered themselves more a movement (agoge) than a sect (airesis) (Deichgräber 1930, 257). The polemic against the “sects” is revealed by the title of the work by the Empiricist Serapion of Alexandria Against the Sects, in which the Empiricists were not meant to be regarded as a sect. This characteristic of Empiricism led to later uncertainty about the history of the movement and its founder. The source used by Pliny the Elder (29.5 = fr. 5 Deichgräber) identified the founder of the school as Acron of Acragas (5th century bce), a backdating whose purpose was to make the sect older, as was already known by the “Galen” of Introduction (Kühn 14.683 = fr. 6 Deichgräber).

366   Hellenistic Greek Science Another tradition, used by Celsus (On Medicine pref. 10  =  fr. 4 Deichgräber), considered the founder of Empiricism to be the abovementioned Serapion, active shortly after Philinus, about 240–​200 bce. It is likely that this opinion goes back to the same Serapion, who considered himself “the first undogmatic doctor” (which is why Galen An Outline of Empiricism 11 presents him ironically as “the new Asclepius”). Serapion’s claim is confirmed by his antidogmatic polemic, perhaps stronger than that of Philinus: in the Against the Sects, he criticized not only the Alexandrian sects but also Hippocrates (and it is significant that he did not write on Hippocratic exegesis, unlike Philinus and the later Empiricists). In a work entitled Through Three, Serapion considered the three basic concepts of Empiricism: experience (empeiria), physicians’ reports (historia), and analogical reasoning (tou homoiou metabasis:  transition by way of the similar). The empeiria was conceived as the cumulative personal experience of the visible, based on an experiential state named peira, which can be involuntary, voluntary, or imitative. Ancient Empiricism was sometimes compared with the modern experimental method, but its general emphasis on experiential passivity, as von Staden (1975, 192) observed, “smothered any active interest in experimentation.” The second element, the historia, justified the reception of previous experiences. More controversial was the third element, which allowed transitions from one medicament to another or from one disease to another, on the basis of as many observed, visible similarities as possible. In the history of Empiricism this principle was sometimes expanded to introduce rational elements in the empiricist doctrine, sometimes contested from radical perspectives. Criticizing anatomy and physiology, the Empiricists dedicated themselves primarily to pharmaceutics, a field also practiced successfully by the Herophileans. The greater part of the few surviving fragments of Philinus and Serapion concern single remedies, related to specific pathologies. Competition with Herophileans did not prevent convergence: Serapion praised a drug remedy of the Herophilean Andreas (fr. 151 Deichgräber). Another area of dispute with the Herophileans was that of Hippocratic exegesis. Philinus wrote a work in six books against the Hippocratic Lexicon of Bacchius, who had been with him in the school of Herophilus. But Philinus’ three remaining glosses, conserved by Erotianus (fr. 322, 327–​328 Deichgräber), do not differ from those given by Bacchius. In the 2nd century bce a long-​ lasting controversy began about the symbols (charakteres) written in a copy of Hippocrates’ Epidemics book 3, which seems to have been brought to Alexandria by Mnemon of Sidē, a student of Cleophantus, the brother of Erasistratus. The symbols were perhaps written in the epichoric script of Sidē (Nollé 1983), but the Herophilean Zeno, in a work entitled On the Marks, attributed them to Hippocrates himself. His opinion was disputed by the Empiricist Apollonius of Antioch and then by his son Apollonius Biblas (the Bookworm). Apollonius the Elder also wrote a Hippocratic Lexicon and polemicized with the Epicureans on the foundations of sensible experience.

Medical Sects: Herophilus, Erasistratus, Empiricists    367 Empiricist doctrine was revised, after Serapion, by Glaucias of Taras, who treated the three principles of the school in the Tripod, whose title was suggested to him by a work by the Democritean Nausiphanes, pupil of the Skeptic Pyrrho. He also wrote a Hippocratic Lexicon in alphabetical order and commentaries on several Hippocratic treatises. Other fragments concern pharmaceutical, therapeutic, and dietetic matters. Zeuxis, an Empiricist who lived in the late 2nd century bce, was the first to comment on all the Hippocratic works he considered authentic. He criticizes previous commentators, not only Herophileans but also the Empiricist Glaukias. His commentary was superseded by those that Heraclides of Taras composed. Galen (Corpus Medicorum Graecorum 5.10.2, p. 1 = fr. 343 Deichgräber), who knew his commentaries on Epidemics 3 and 6, complained that the others were difficult to find.

5.  The Herophileans Galen (Differences of Pulses 4, Kühn 8.715 = fr. 278 von Staden) states that Herophilean and Erasistratean sects “flourished after Herophilus’ death,” that is, from 255–​250 bce. The first generation of scholars gathered in the house of Herophilus, as suggested by the title of Bacchius’ work Memoirs on Herophilus and the Members of His House, where “house” highlights the close relationship between master and pupils (Fraser 1972, 357). While Herophilus, as it seems, had had no direct relations with the Museum, one of his pupils, Andreas of Carystos, became the personal physician of Ptolemy IV Philopator and was killed during the battle of Raphia (217 bce), as is recounted by the historian Polybius (5.81.6). Besides Andreas and the renegade Philinus, another pupil of Herophilus was the abovementioned Bacchius. More uncertain is the position of Callianax, perhaps a contemporary rather than a successor of Herophilus, and that of Callimachus, mentioned by Polybius (12.25d.3–​4) as head of a “theoretical” school besides that of Herophilus. The autonomy of Callimachus from the sect is confirmed by the Empiricist Zeuxis (fr. 351 Deichgräber), who stated that Callimachus criticized Herophilus’ interpretation of a passage of Hippocrates’ Epidemics. The fragments of almost all the followers of Herophilus show a remarkable silence regarding the field of anatomical research. A consequence, it can be assumed, of a stoppage of the practices of dissection that occurred in Alexandria after the first two Ptolemies, as a result of the reassertion of traditional taboos about cadavers or perhaps also because of the rising popularity of medical Empiricism, adverse to dissection (von Staden 1989, 445–​446). The characteristic topic of the sect remained, in the following centuries, first sphygmology, then Hippocratic exegesis, pharmaceutics, obstetrics, and also surgery, a field supposedly neglected by Herophilus. Another peculiarity of the sect was the high literary culture of its members: Callianax used Homer and the tragedians as reading matter to provide solace for patients fearing death. Bacchius in his Hippocratic Lexicon cited many pieces of evidence from poets. Galen (Diagnosis of Pulses 4, Kühn 8.929 = fr. 276 von Staden) criticizes the Herophileans

368   Hellenistic Greek Science as “loquacious sophists” while Pliny the Elder writes that Herophilus was “descending to mere words and chattering” (26.11 = fr. 13 von Staden) and explains the end of the sect because of the condition that “its members had to have a literary learning” (29.5 = fr. 185 von Staden). Of the works by Bacchius of Tanagra there remain over 60 fragments of his Hippocratic Lexicon, a work criticized by Philinus (see above) and other Empiricists but still used a great deal in the 1st century ce by the grammarian Erotianus. Some fragments deal with sphygmology and pharmaceutics, but his renown seems due, besides the Lexicon, to his commentaries on several Hippocratic treatises. The abovementioned Memoirs contained anecdotes on the school and its members, also used polemically by the adversaries: Galen records the only surviving fragment, on the verbal insensitivity of Callianax (Corpus Medicorum Graecorum 5.10.2.2, p. 203: from the Empiricist Zeuxis). Neither Hippocratic exegesis nor sphygmology seem to have been treated by Andreas, whose fragments (almost 50) reveal, in any case, a very wide range of interests. His role in the Ptolemaic court (see above) assured him renown in the following centuries: the name of the character Andreas in the Letter to Aristeas, the apocryphal work on the translation of the Septuagint made in Alexandria, could have been inspired by the physician of the same name. In the 2nd century bce the poet Nicander (Theriaca 826–​827) seems to allude to Andreas’ attack on the popular view that sea eels go ashore to mate with vipers. In orthopedics Andreas invented an instrument for reducing dislocated limbs (see above). He wrote an epistolary work dedicated to Sosibius, a minister of Ptolemy, dealt with obstetrics, and other topics. Drug remedies and cosmetics were collected in a work entitled Casket, antidotes in On Poisonous Animals. Andreas was not interested (it seems) in Hippocratic exegesis, but in On Medical Genealogy he dealt with the biography of Hippocrates, drawing on the tradition represented by the 5th-​century bce Pherecydes of Athens. A  later source, the Life of Hippocrates According to Soranus, attributes to Andreas, and to his malicious intent, the story that Hippocrates, moving from Kos after his parents had died, “burned the repository of writings in Knidos” (Corpus Medicorum Graecorum 4.175). This is an anti-​Hippocratic tale that von Staden (1999, 155) interprets as “a way of creating greater space for a new, radically innovative Hellenistic authority, Herophilus.” Zeno, who lived in the 2nd century bce, first attributed to Hippocrates the symbols that he read in a copy of book 3 of Epidemics (see above). In addition to Hippocratic exegesis, Zeno was known for his work in pharmacology and for his definition of the pulse, which contains some changes to the previous definitions given by Herophilus and by Bacchius. Demetrius of Apamea, who perhaps lived in the 2nd century bce, was an Herophilean particularly interested in pathology:  in his On Diseases, several times mentioned by Caelius Aurelianus, he dealt with diseases such as mania, phrenitis, hydrophobia, dropsy, pneumonia, priapism, satyriasis, and others. He also wrote a work on semiotics and continued the gynecological tradition initiated by Herophilus. But unlike the latter, he was more interested in pathology than in the anatomy of the reproductive system, and he also rejected Herophilus’ assertion that there are no diseases unique to women.

Medical Sects: Herophilus, Erasistratus, Empiricists    369 Mantias, who lived in the late 2nd century bce, was considered by Galen the first “to have recorded compounds of very many drugs that are worth recommending” (Composition of Medicines by Types 3, Kühn 13.642). His recipe “Attalike,” a compound for upset stomachs, seems to have taken its name from Attalus, one or another of three Kings of Pergamum. The only Herophilean who seems to have been interested in anatomy is Hegetor. He lived in the late 2nd or first half of the 1st century bce, being mentioned by the Empiricist Apollonius of Citius. In On Causes Hegetor censured the Empiricists for their anti-​ etiological stance and their failure to discover the causes of diseases. Specifically for the problem debated by Apollonius, the treatment of dislocated hips, Hegetor said that only an understanding of the hip’s anatomy enables accurate diagnoses of treatable versus incurable dislocations. The only other two surviving fragments of Hegetor regard his definition of pulsation.

6.  The Erasistrateans Erasistratus also had his pupils and among them Straton who, as Galen states, “wrote from the house” of his master (Brain 1986, 43). Straton had also been a student of Chrysippus of Knidos, like Erasistratus himself, and perhaps among the Erasistrateans there was also another student of Chrysippus, Apeimantus. Both Chrysippus and Erasistratus opposed phlebotomy, a therapy recommended instead by Herophilus and his followers, with the proviso that the procedure risked death and that practitioners might err and open an artery. Other pupils of Erasistratus were a Chrysippus mentioned by Diogenes Laërtius (7.186) and perhaps Antigenes, a student of Cleophantus, the brother of Erasistratus, known to Soranus for pediatric therapy (Gynecology 2.83) and mentioned by Galen (Corpus Medicorum Graecorum 5.9.1, 69–​70) as an anatomist. In the following history of the sect there is no detectable research either in anatomy, or in physiology, a field in which the Erasistrateans seem to have limited themselves to preserving and commenting on the writings of the master, sometimes with dissensions and polemics among themselves. The rejection of phlebotomy, the mildness of the therapeutics and the interest in dietetics were probably characteristic of the sect. In fields such as surgery and pharmaceutics their activity seems hardly distinguishable from that of the other sects. Of Straton, the best known of the first Erasistrateans, Soranus gives the recipes of a fumigation to expel the afterbirth (Gynecology 4.14) and of a remedy against uterine prolapse (4.36). Other sources preserve his remedies against dog and snakebites. Rufus of Ephesus (in Oribasius, Corpus Medicorum Graecorum 6.2.1, p. 184) states that Straton was the first to describe elephantiasis, the “new” disease identifiable with leprosy, and that he called it kakochymia (bad-​humor). Erotianus (Α–​108) attributes to Straton the explanation of a Hippocratic word (in an unknown context, considering that Erasistrateans were not usually interested in Hippocratic exegesis).

370   Hellenistic Greek Science A student of Straton was Apollonius of Memphis, active around 250–​200 bce. He refined the names of the parts of body, as is reported in the pseudo-​Galenic Introduction (Kühn 14.699–​700), wrote a treatise On Joints and a work on pathology, in which different kinds of dropsy were classified. Fragments preserve several recipes for specific pathologies (also a remedy against snake bites). He also gave a definition of the pulse, as pneuma from the heart filling the arteries (Galen, Differences of Pulses 4, Kühn 8.759). The unclear relationship of Erasistratus with the Seleucid court (see above) is perhaps connected with the presence of an Erasistratean, Apollophanes of Seleucia Pieria, at the court of Antiochus III (223–​187 bce). He was a physician but also one of the king’s political advisors and wrote a history of contemporary events used by Polybius. He was interested in preparing drugs and antidotes for use at court and gave recipes for flank pains, hemorrhoids, pains in the liver, and other disorders. His opinion on cardiac illness is reported by Caelius Aurelianus (On Chronic Diseases 2.173). Ptolemaeus, who perhaps lived in Alexandria in the 2nd century bce, was an Erasistratean known to Caelius Aurelianus (3.125) for the etiology of dropsy, caused by the hardness of the liver. He can, perhaps, be identified with the surgeon mentioned after Erasistratus by Celsus (On Medicine 6.7.2B–​C) for a recipe against ear ulcers.

7.  Empiricism from Alexandria to Rome At least from the 1st century bce, Empiricists, but also Erasistrateans and Herophileans, expanded their presence outside Alexandria into the Hellenistic and Roman world. This spread of books, doctrines, and practitioners was probably favored by the expulsion of physicians and other intellectuals ordered by Ptolemy VIII Euergetes II in 145/​4 bce. However, the measure did not prevent the subsequent revival of the medical schools, which were flourishing again in Alexandria in the next decades. After Zeuxis the most influential Empiricist was Heracleides of Tarentum, active in Alexandria about 95–​55 bce. Like Philinus two centuries earlier, he was first a Herophilean: a pupil of Mantias, he abandoned this school and joined the Empiricists. Of his works, there remain almost a hundred fragments, revealing his influence in the following centuries. Most of them regard pharmacology, a field in which Heracleides was influenced by the work of Mantias. He also dealt with Hippocratic exegesis: he renewed the polemic against Zeno about the Hippocratic symbols (see above) and wrote three books against Hippocratic interpretations of Bacchius. Other fields of interest also included dietetics and theriatrics, that is, remedies for poisonous bites. His treatise on the therapeutics of internal diseases was largely used by Galen and Caelius Aurelianus (i.e., Soranus). Papyrus Cairo Crawford 1 (EANS 615) reveals his interest in ophthalmic surgery. Continuity with Mantias in pharmaceutics (and in dietetics: Galen, Composition of Medicines by Types 2, Kühn 13.462) suggests a more moderate approach toward rational medicine than that of previous Empiricists such as Serapion. Heracleides’ long fragment

Medical Sects: Herophilus, Erasistratus, Empiricists    371 on the dislocation of the femur quoted by Galen (18A.735 Kühn = fr. 43 Guardasole) reveals a partial acceptance of the position of the Herophilean Hegetor. Galen attributes to Heracleides and to “some other men who called themselves Empiricists” the idea that there is “some power in us which is able to consider and to judge what is compatible and what follows,” a position that seems to differentiate them from the more common Empiricist assertion that “evident perception and memory suffice for the constitution of all arts” (Frede and Walzer 1985, 44). Heracleides was possibly influenced by the contemporary skeptical philosophy, which was revising and moderating the skepticism of Pyrrhon. Skeptical Academism, on the other hand, was certainly influenced by Empiricism’s topics:  Cicero’s above-​ mentioned reference to the polemic on dissection was derived from a philosophical source. Skeptical Platonism was well established in Alexandria in the 1st century (Fraser 1972, 486), and Antiochus of Ascalon, the mentor of Cicero’s Academism, taught in the Egyptian city. However, it seems excessive to consider Heracleides as a skeptical philosopher tout court, as would result from his identification with the “Heracleides” mentioned in the genealogy of skeptical philosophers reproduced by Diogenes Laërtius (9.115–​116). This “Heracleides,” in Diogenes’ report, was a student of Ptolemaeus of Cyrene and teacher of Aenesidemus of Knossos. Deichgräber (1930, 258) argued that Ptolemaeus of Cyrene was the Empiricist teacher of Heracleides after his break with Mantias, but the two fragments he ascribed to him could possibly be by the Ptolemaeus Erasistratean or by some other homonymous physician. There are indeed no grounds to assign to Heracleides such an important role in the history of skeptical philosophy, also considering that the same Diogenes Laërtius mentions our Heracleides in another chapter and presents him as a “physician of Tarentum, Empiricist” (5.94). Heracleides also soon become known in Rome: Varro mentions him in the Menippean satires (fr. 445 Astbury) and published a portrait of him in his Hebdomades (from which derives the image of Heracleides provided by the Vienna codex of Dioscurides). Prior to this, Polybius, who lived from 166 bce in Rome, knew the Empiricist doctrine already. He alludes to the principles of the tripod in his examination of the knowledge required by the military commander (9.14.1). In the next century Cicero refers to the Empiricist polemic against dissection in the philosophical debate of his Academics (2.122). In the first imperial age, Celsus frequently mentions Heracleides, defines him as a “very illustrious author” (On Medicine 8.20.4), and probably uses some his work for the doxographical section of his preface. Besides Heracleides other Empiricists active in the 1st century bce were Diodorus, Lycus, Zopyrus, Apollonius of Citius, and Archibius. This is a presence that makes this the century of the greatest influence of Empiricist medicine. Diodorus is mentioned as an Empiricist by Galen (Method of Healing 2, Kühn 10.142) and by Pliny the Elder (20.119) for a remedy. He perhaps belonged to the school of Heracleides. Lycus of Neapolis is also mentioned for remedies, but he also dealt with Hippocratic exegesis. Zopyrus of Alexandria was a surgeon and pharmacologist: he sent the king of Pontus Mithridates an antidote suggesting he try it on some condemned men.

372   Hellenistic Greek Science That Zopyrus was an Empiricist is suggested by the fact that he was the teacher of Apollonius of Cition, the only Empiricist of whom a whole work survives, the commentary on Hippocrates’ On Joints (Kollesch-​Kudlien 1965). In this work, dedicated to Ptolemy XII Auletes (or to Ptolemy of Cyprus), Apollonius criticizes the Herophileans Bacchius and Hegetor but implicitly also Heracleides, who in part had enhanced, as we have seen, the position of Hegetor. In a lost work of 18 books, Apollonius explicitly opposed Heracleides’ criticisms of Bacchius (whose Lexicon was however Apollonius also criticized). The prevalence of a more radical position under the Empiricists after Heracleides seems confirmed by some other clues. A polemic against dogmatic medicine is pointed out by Archibius in the fragment on the teaching of surgery conserved by the papyrus Berol. 9764, 2 (Marganne 1998, 13–​34) (Archibius’ recipes were known to Asclepiades Pharmacist and Pliny the Elder). From Galen we learn that a certain “Pyrrhonean Cassius,” apparently a skeptical philosopher, not a physician, wrote a book on the “transition to the similar” in which he upheld the thesis “that the Empiricists do not even make use of this kind of transition” (Frede and Walzer 1985, 27). But it remains hazardous (von Staden 1997) to identify the Pyrrhonean with the physician Cassius active in the years of Tiberius and qualified by Celsus as “the most ingenious practitioner of our generation” (On Medicine, pref. 69). The latter was a well-​known physician (his recipe for the relief of colic is given by Celsus, Scribonius Largus, Papyrus Harris 46 [see Andorlini 1981], and others), but he is never defined as an Empiricist, outside his identification with the Pyrrhonean.

8.  The Herophileans Between Alexandria and Men Karou The continuity of the Herophilean sect in Alexandria is pointed out by Chrysermus, active in the 1st century bce. He belonged to an old, high-​born Macedonian family, but despite being a member of the Alexandrian upper class, he does not seem to have been associated with the Ptolemaic court and probably devoted himself to medical activity and the direction of his school. Chrysermus’ main interest seems to have been sphygmology: he amplified and modified the previous definitions of the pulse and included in his own definition that the psychic and vital faculty was the agent of the pulsation. Chrysermus confirms the centrality acquired by sphygmology in the Herophilean tradition, a feature that, after the neglect of anatomy, probably helped differentiate the school from the Empiricists and other schools. Sphygmology provided the Herophileans with a practical diagnostic tool and, furthermore, with a reaffirmation of the relevance of theoretical investigation (von Staden 1989, 448). Contemporary or slightly older than Chrysermus was Dioscurides “Phacas” (nickname suggested by the moles or warts on his face). He was the only Herophilean, after

Medical Sects: Herophilus, Erasistratus, Empiricists    373 Andreas, associated with the Ptolemaic court, at the time of Ptolemy XII Auletes and his sons, Ptolemy XIII and Cleopatra. He is in fact identifiable (von Staden 1989, 520) with the Dioscurides whom Julius Caesar (The Civil War 3.109) presents as an influential advisor of Auletes and ambassador in Rome, killed during the battle that took place in 48 bce in Alexandria. The Suda (Δ–​1206) attributes to him a work on medicine in 24 books. Of his works, there are also some fragments on Hippocratic exegesis. Among Chrysermus’ students there were also Heraclides of Erythrae and Apollonius “Mys” (nickname meaning “mouse,” or “muscle,” or “mussel”). They were active in Alexandria at the end of the 1st century bce, perhaps also in the 1st century ce (both are mentioned by the geographer Strabo 14.1.34 as his contemporaries). Both wrote doxographies of the Herophilean school, Apollonius On the School of Herophilus in at least 29 books, mentioned by Galen and Soranus; Heraclides On the School of Herophilus, in at least seven books. This exploit was realistically suggested by the need to strengthen and revitalize the activity of the sect, which suffered from competition not only with the Empiricists but also with the more recently founded sects, the Pneumatists and the Methodists (von Staden 1989, 456–​458). Apollonius Mys was obviously interested in sphygmology and developed and partially corrected the definition of the pulse given by his teacher Chrysermus. He also wrote two other works: On Perfumes and Unguents (largely used about 200 ce by Athenaeus of Naucratis in his Deipnosophists), and Readily Accessible Remedies (Euporista), a large collection of remedies for common ailments such as headaches, toothaches, skin irritations, and similar things, a work used and sometimes criticized by Galen. Less known is the activity of Heraclides of Erythrae. As well as in sphygmology, he was also interested in another traditional Herophilean topic, Hippocratic exegesis. In his Commentary on Epidemics 3 he closed the old controversy on the letter symbols: he abandoned the position held by Zeno and other Herophilians and agreed with the Empiricists that the letters were not by Hippocrates himself but later interpolations. After Apollonius and Heraclides there is no evidence of the Herophilean sect in Alexandria. It was no longer in existence when, in Alexandria, thanks to the efforts of Marinus (around 70–​120 bce), there was a revival of anatomical studies. The lack of interest, in this field, on the part of the late Herophileans is confirmed by Galen, who states that anatomy was revived, after Eudemus and Herophilus, only by Marinus and Numisianus (Corpus Medicorum Graecorum 5.9.1, pp. 69–​70) The latter, a student of Quintus, in turn, a student of Marinus, was heard by Galen in 152 ce in Corinth. Anatomy is absent also in the activity of the last Herophilean school we know of, the one active from the 1st century bce at the temple of the moon god in Men Karou, near Laodicea. Strabo presents it as a “large Herophilean teaching center of medicine” and identifies a certain Zeuxis (Geography 12.8.20) as the founder of the school. The honorary title Philalethes (Truth-​Lover) adopted by the subsequent heads of the school, Alexander and Demosthenes, suggests that the Zeuxis mentioned by Strabo is to be identified with the “Zeuxis Philalethes” named on the reverse side of two bronze coins from Laodicea, both bearing the head of Augustus (Sebastos) on the obverse (see Benedum 1974). The identification allows the foundation of the school to be dated ca 40/​30 bce.

374   Hellenistic Greek Science The school of Men Karou was strictly structured and had a more institutional character than the Herophilean school of Alexandria. Its association with a cult center suggests some analogies with the Alexandrian Museum, where scientists and scholars were together not only as researchers but also as members of a cult (von Staden 1989, 459–​460). Nothing is known about Zeuxis’ medical activity. Alexander Philalethes succeeded him as head of the school from 7 bce. He had previously been a follower of Asclepiades of Bithynia. Alexander perhaps gave some information on his adherence to the Herophileans in his Opinions, a doxographic work in at least five books. Fragments of other works reveal however a surprising convergence between the atomistic theory of Asclepiades and Herophilean orthodoxy, suggesting that Alexander remained influenced by Asclepiades’ doctrine also after assuming the leadership of the Herophilean school. Anonymous Londinensis refers to the fact that he posited invisible apertures, “apprehensible only by reason,” through which corporeal matter enters and leaves the body (von Staden 1989, 534), a physiology very close to that of Asclepiades. Anonymous Londinensis also attributes the same theory of digestion to Alexander and Asclepiades, and Caelius Aurelianus the same explanation on lethargy (On Acute Diseases 2.1.5–​6). In his Gynaecology Alexander denied the existence of diseases particular to women, a position already held by Herophilus and also by Asclepiades, but denied by the Herophilean Demetrius of Apamea. Alexander’s revisionism is confirmed by his theory of pulse, where he added to the traditional definition, which he called “objective” (“the pulse is an involuntary contraction and distention of the heart and the arteries, such as can become apparent”), a “subjective” definition, for which “the pulse is the beat of the continuous, involuntary motion of the arteries against one’s touch, and the interval occurring after the beat.” This is a definition that perhaps shared the sensualistic epistemology of Asclepiades (von Staden 1989, 535–​536). Alexander had two pupils, Aristoxenus and Demosthenes Philalethes, the latter his successor as the head of the school. A third scholar could have been Gaius, the only Herophilean who was probably Roman (as his name suggests). But we do not know if he studied at Men Karou or in Alexandria. He wrote a treatise On Hydrophobia used by Caelius Aurelianus (On Acute Diseases 3.14.113–​114). Gaius argued that the disease affected the brain and the meninges, where the nerves controlling voluntary actions originate: a somatic explanation consonant with Herophilus’ anatomical theory, but also consistent with Asclepiades’ view that diseases with mental symptoms are centered in the meninges. This is a position similar to that of Alexander Philalethes. Aristoxenus wrote a doxographic work, On the School of Herophilus, in which he criticized many illustrious members of the school, from Bacchius to Chrysermus and Heraclides of Erythrae. If the goal of the work was similar to that of the doxographies written by Heraclides and Apollonius Mys, Aristoxenus’ method seems peculiar in view of his censorious revisionism. He particularly criticized the contemporary Alexandrian school: at variance with Chrysermus’ definition of the pulse, he stated that the “dominance” of the psychic and vital faculty is not peculiar to pulsation but common to all the natural activity of the body.

Medical Sects: Herophilus, Erasistratus, Empiricists    375 The two Herophilean schools active in the last period, those of Alexandria and Men Karou, reveal not only polemics among themselves but also different fields of interest: the Herophileans of Men Karou did not work on Hippocratic philology, a field probably favored in Alexandria by the presence of the Library. Common topics were sphygmology, gynecology, and pharmacology. Both schools seem to have ignored, as we have seen, anatomical research. The internecine quarrels instigated by Aristoxenus contributed to the decline of the Herophilean sect, which seems to have been dissolved about the middle of the century. Pliny the Elder (before 79 ce) affirms that it was “abandoned” (29.5). Perhaps, the end of the school of Men Karou overlapped with the earthquake that struck the area of Laodicea in 60 ce. The last Herophilean we know of is Demosthenes Philaretes, a scholar of Alexander who lived in the middle of the 1st century ce. He wrote on sphygmology, perhaps also on other topics, but his main field of interest was ophthalmology, a branch practiced by Herophilus. In his work On Eyes he dealt with the anatomy and physiology of the eye, then with the pathology and symptomatology of several affections, and finally surgical interventions and eye salves, including the first known description of a cataract operation. In the following centuries, this work was the most authoritative in this field: it was used by Rufus of Ephesus, Oribasius, Aëtius of Amida, Paul of Aegina, and others. A Latin translation entitled Ophtalmicus seems to have survived in the Middle Ages in the library of the monastery of Bobbio. The manuscript was probably brought by Gerbert of Aurillac (Pope Sylvester II) to Rome, where it was later used by Simon of Genoa, the personal physician of Pope Nicholas IV (1288–​1292), when composing his Synonyms. The manuscript was then lost, and with it the only surviving Herophilean work (albeit in Latin translation) that had survived after antiquity.

9.  The Erasistrateans from Smyrna to Rome The Erasistrateans’ presence in Alexandria is not detectable after Ptolemaeus, if he really lived in the Egyptian city (see above). From the 1st century bce, there is evidence of the sect’s activity only outside Alexandria. It was also more long-​lived than the Herophilean sect, though its presence in these centuries is more difficult to reconstruct. The best known is the Erasistratean school at Smyrna directed by Hicesius in the 1st century bce: Strabo (12.8.20) writes that it was active “in the times of our ancestors,” but presently, that is, at the beginning of the 1st century ce, it no longer exists. Hicesius was known by Heraclides of Tarentum and can therefore have founded his school at the beginning of the 1st century bce. His work on dietetics On Materials for Health was largely used by Athenaeus in the Deipnosophists for several recipes of food, especially fish, for

376   Hellenistic Greek Science both the healthy and the sick (Gourevitch 2000). He could possibly be identified with the Hicesius known to Pliny the Elder as the author of a treatise on winemaking (14.120). The same Pliny gives a remedy of Hicesius for wounds and a recipe against toothache and other pains (22.40) and defines him as an “authoritative physician” (27.31). The best known recipe by Hicesius was the Melaina (the black one), already known to Heracleides, a multiple-​use plaster. Another plaster, reported in the 6th century by Paulus of Aegina (Corpus Medicorum Graecorum 9.1, p. 281), was used in the treatment of the external hardening of the uterus. As a surgeon Hicesius is mentioned by Tertullian (On Soul 25.6) in a list of pagan physicians who practiced abortions, but the evidence of this assertion is doubtful. Other members of the school of Smyrna were Menodoros of Smyrna and Heracleides of Ephesus. Menodorus was a friend of Hicesius, as we know from Athenaeus (Deipnosophists 2.59a), who reports his remarks on squashes and their preparation. Oribasius (Corpus Medicorum Graecorum 6.2.1, p. 222) mentions him as a surgeon for a procedure in cases of skull fracture, Papyrus Cairo Crawford 1 for a procedure in eye surgery. Galen (Composition of Medicines by Places 1, Kühn 13.64) preserves the recipe of a cough syrup, for sufferers from phthisis, prepared by a certain Ripalus and named Menodorius, presumably from our Menodorus. Heracleides of Ephesus is mentioned as a “physician of the school of Hicesius” by Diogenes Laërtius (5.94). Like Menodorus he was a surgeon: Oribasius reports that he constructed a variant of the machine by Tekton for reducing dislocations and fractures (Corpus Medicorum Graecorum 6.2.2, p. 9). It seems impossible or very difficult to determine the place and time of the activity of other Erasistrateans mentioned by the sources. Galen (Simples 1, 11.423 Kühn) writes that the pharmacist Hermogenes gave his preference to the Erasistratean sect. One of his recipes for a plaster against infections of the extremities is given by Oribasius (Corpus Medicorum Graecorum 6.2.2, p. 287); another by Aelius Promotus (Dynameron 63.4). Perhaps he is to be identified with the physician and historian Hermogenes celebrated in an inscription of Smyrna of the 1st century ce (CIG 3311): the father of the epigraphic Hermogenes is named Charidemus, like an Erasistratean mentioned by Caelius Aurelianus (On Acute Diseases 3.113 and 118). The identification, it should be noted, implies an Erasistratean activity in Smyrna after the closure of the school of Hicesius. Charidemus, in the fragment preserved by Caelius, denies that hydrophobia specifically was a new disease, rejecting the more radical claim of another Erasistratean, Artemidorus of Sidē, who denied that there could be any new disease. Caelius mentions him before Artorius, a follower of Asclepiades of Bithynia who died in 27 bce. Artemidorus therefore supposedly lived in the 1st century bce. Caelius also gives his definition of cardiac disease as an inflammation in the region of the heart (On Acute Diseases 2.163). Two other names of Erasistrateans seem to belong to Athenians (their names were common in Athens). The first is Athenion, of whom Celsus (On Medicine 5.25.9) gives a remedy against cough. The second is Miltiades, mentioned together with Athenion by Soranus (Gynecology 3.2) for their opinion that some diseases are exclusive to women.

Medical Sects: Herophilus, Erasistratus, Empiricists    377 The last chapter of the history of the Erasistratean sect took place in Rome, at the time of Galen. In On My Books 1, Galen gives a brilliant report of his meeting with the Erasistratean Martialius (or Martianus), during his first stay in Rome (162–​166 ce). Martialius was 70 years old and “enjoyed a great reputation in his time,” being moreover the physician of Eudemos, Galen’s philosophy teacher in those years. Martialius had written on anatomy and “declared the superiority of Erasistratus in all areas of the art, but especially in this,” that is, anatomy. The confrontation with Martialius was quite heated, because Galen says that he wrote his books on Hippocrates’ and Erasistratus’ anatomy “in a rather combative vein” having Martialius in mind. Galen’s polemic regarded several aspects of Erasistratus’ works, primarily phlebotomy vis-​à-​vis the Roman Erasistrateans. The latter criticized it, in accordance with the opinion of their master. On this topic Galen wrote On Venesection Against the Erasistrateans in Rome, besides the homologous On Venesection Against Erasistratus. The several references given by Galen provide an ambivalent picture of the contemporary Erasistrateans, on the one hand, faithful and conservative custodians of the doctrine of the master, on the other hand, inclined to revisions and innovations, which were sometimes radical. A tendency favored by the presence of dissention on specific points of the doctrine, such as the nature of the arteries (Anonymous Londinensis 26–​27) or the physiology of urinary secretion (Galen Natural Faculties 1, Kühn 2.68). An innovation of the Roman Erasistrateans was the function they attributed to parts of the body, such as the spleen and omentum, to which Erasistratus, despite his teleological vision, had not assigned a specific function (Galen, Corpus Medicorum Graecorum 5.4.4.1, p. 85). But the most spectacular episode of revision by the Roman Erasistrateans was their reaction to Galen’s criticism of phlebotomy. After denying the value of this practice, they became too zealous in their support of venesection (Brain 1986, 43–​44). This constitutes a hint of crisis and insecurity that maybe explains the disappearance of the sect after Galen.

9.  The Last Empiricists Galen gives the names of some Empiricist physicians active at Pergamon in his school years. One is the old Aischrion, of whom Galen (Simples 11, Kühn 12.356) praises the pharmacological knowledge and especially a remedy for rabid dog bites based on ash and crayfish (known also from other sources). Another of Galen’s Empiricist teachers was Epicurus of Pergamon, the author of a commentary on Hippocrates’ Epidemics book 6 (Corpus Medicorum Graecorum 5.10.2.2, p. 412). In his juvenile On Medical Experience (150/​151 ce), Galen recounts the quarrel about the principles of medicine that arose between another Empiricist, Philippus, and the Dogmatic Pelops, later Galen’s teacher at Smyrna. The quarrel took place at Pergamon, where Philippus was perhaps also active. In his discourse he expounds the traditional topics of Empiricism; he was also

378   Hellenistic Greek Science interested, like most Empiricists, in Hippocratic exegesis (Galen, Corpus Medicorum Graecorum 5.10.2.2, p. 412). The three Pergamonian Empiricists were probably minor figures (Aischrion perhaps only a practitioner). The most important Empiricists of the 2nd century ce were Menodotus of Nicomedia and Theodas of Laodicea. Both are well-​known to Galen, who wrote lost commentaries on their works. Menodotus dedicated a work to a Severus identifiable with Cn. Claudius Severus Arabianus, consul in 146 ce and a friend of the Emperor Marcus Aurelius. In another work, Menodotus severely criticized Asclepiades of Bithynia, claiming “all of Asclepiades’ views are false” (Frede and Walzer 1985, 43), with a polemical excess that is criticized by Galen. Menodotus (like Theodas) gave importance to the “rational” element in the Empiricist doctrine, perhaps against the Empiricists’ positions that prevailed after Heracleides of Tarentum. It is uncertain if the concept of “epilogism” was introduced by Menodotus or, before him, by the same Heracleides influenced by Epicureanism (Perilli 2004, 143). This concept was considered an inference by means of which it would be possible to discover what is provisionally hidden, but that, under other circumstances, could be observed. The idea of “possibility” is present also in Menodotus’ discussion about the Empiricist tripod: he maintained that the third element of the tripod, the “transition to the similar . . . is not a true criterion but only a criterion of what is possible” (Frede and Walzer 1985, 26). Menodotus distinguished between epilogism and analogism, the latter being the form of reasoning typical of the Dogmatics, which concerns things hidden or nonevident. He presented it as common form of reasoning, beyond the formal logic: “a logos—​reports Galen—​universally known and used . . . which refers to visible things alone” (Frede and Walzer 1985, 91). From Theodas we know the titles of some works: an Introduction to Empiricist medicine, Outlines, and On Parts of Medicine. His emphasis on the rationalistic element of Empiricism is revealed by his definition of the “transition to the similar” (the third element of the tripod) as “reasonable experience” (Frede and Walzer 1985, 27). He discussed also the relation of the tripod with the three constitutive parts of medicine: semiotics, therapeutics, and hygiene. In On Medical Experience 2 Galen mentions, besides Menodotus and Serapion, a certain Theodosius as a “representative of Empiricism.” The name is also present (after Menodotus and Theodas) in the list of Empiricists given by MS Hauniensis Lat. 1653, fol. 73. This Theodosius could probably be identified as the philosopher Theodosius mentioned by Diogenes Laërtius (9.70) who was the author of a work entitled Sceptical Chapters; Diogenes reports that for Theodosius Skepticism cannot be called “Pyrrhonism” because Pyrrhon was not the inventor of Skepticism and had no doctrine. The identification of the physician with the philosopher is suggested by the Suda (Θ–​132), where not only Sceptical Chapters but also a Comment on the Outlines of Theodas are attributed to Theodosius. He lived in the first half of the 2nd century, being known to Galen already at the time of On Medical Experience (Perilli 2004, 198–​200). Galen includes another unknown Empiricist, Callicles, in the nonchronological list of Empiricists he gives in On the Therapeutic Method 2 (Kühn 10.142–​143).

Medical Sects: Herophilus, Erasistratus, Empiricists    379 In the already-​mentioned list of skeptical philosophers given by Diogenes Laërtius we find, as students of Antiochus of Laodicea, Menodotus of Nicomedia qualified as an “Empiricist physician,” and Theodas of Laodicea; as a student of Menodotus, Herodotus of Tarsus, son of Areios; as a student of Herodotos, Sextus Empiricus; as a student of Sextus, “Saturninus called Cythenas, who was also an Empiricist” (9.116). The list is problematic, because Menodotus and Theodas were not, as it seems, philosophers, and Herodotus is hardly identifiable with the pneumaticist physician, generally dated to the 1st century ce. The list seems to be a conflation, in genealogical form, of the names of philosophers and of physicians. Also open to question is the surname “Empiricus” held by Sextus, who is also included in the list of the Empiricists given by pseudo-​Galen’s Introduction (Kühn 14.683). Sextus Empiricus moreover in Outlines of Pyrrhonism 1.236–​241 expresses his preference for the Methodist school over Empiricism. Saturninus is wholly unknown: if really a physician, he could have been the last of the Empiricists.

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chapter C8

Ast rol o gy The Science of Signs in the Heavens Glen M. Cooper

1.  Introduction: Classical Astrology One of the more durable intellectual disciplines from antiquity, the ancients traced the science of astrology to origins in Mesopotamia and Egypt. Originally the concern of rulers and the elite, astrology eventually became democratized, and anyone who could afford some level of the service knew basic features of his natal chart. In connection with the popularity of Stoicism in the Roman Principate, which exalted Fate (equated with the providence of Zeus), astrology flourished. Fully integrated within the accepted natural philosophy, astrology was a science. Several Roman emperors from Augustus on were obsessed with their (and potential rivals’) horoscopes, and some astrologers attained high positions at court. Astrology had its opponents, mainly among the Skeptics and the Christians, whose opposition forced astrologers to refine the principles of their science to create a resilient discipline that not only survived but was also further developed in Arabic and medieval Latin astrology. This chapter is threefold: an introduction; a historical sketch of classical astrology; and finally a discussion of an ancient example of a natal chart, its methods, and an ancient interpretation. Astrology accounts for the effects of the luminaries (sun and moon), planets, fixed stars, and even the lunar nodes, and so forth on our world. It presupposes a geocentric, finite cosmology. In its original Babylonian context, astrology was the interpretation of signs and omens sent by the gods as warnings through celestial events. The Babylonians practiced a kind of astrology (discourse about the stars), but theirs was not the classical horoscopic astrology, which was developed in Hellenistic Egypt. This form added the Ascendant (horoskopos) and the Place system reckoned from it (described later). In its Greek form, astral “effects” were considered to be causes, usually deterministic and ineluctable. A useful distinction was made in medieval times between divinatory (judicial) astrology, with which the present chapter is primarily concerned, and natural astrology,

382   Hellenistic Greek Science which accounted for celestial influences of all kinds, including seismic and meteorological phenomena, though being grounded in the cosmology and physics of the classical Greek natural philosophers, it was skeptical about specific prognostications. As a discipline of natural philosophy, astrology mixed easily with the theory and practice of medicine. Natural astrology was generally accepted until the modern era. By nature eclectic, astrology never had one canonical form. Rather, as a living tradition, it acquired techniques and methods from various eras and peoples, to suit specific needs.

2. Types There were several subdisciplines of judicial astrology in the classical world, each with a distinct relationship to the past, present, or future.

2.1 Universal, or Mundane, Astrology Universal, or mundane, astrology, the oldest form, has its roots in Mesopotamian celestial omens. Omen astrology concerned particular phenomena, as they occasionally occur, from which inferences were made for the future of the kingdom as a whole. These were generalized to determining the effects of the heavens on nations as a whole, and the process often involved weather and seismic forecasting. Some omen astrology appears in Greek literature, which supports a Babylonian origin of astrology. In fact, Ptolemy discusses how to use eclipses to make predictions about nations and peoples (Tetrabiblos 3.4–​8), which was a Babylonian concern.

2.2 Genethlialogy The most familiar form of astrology, genethlialogy, or natal astrology, concerns the past, and involves casting a natal chart for the moment and location of birth (or conception). An outgrowth of genethlialogy was a kind of “continuous horoscopy,” namely, casting a recent chart to compare with the birth chart, to provide up to the moment guidance. Genethlialogy developed in the late Babylonian period: 410 bce is the earliest extant natal chart. Horoscopic astrology contrasts with Babylonian omen astrology, since it adds the Ascendant and connects the configurations of the planets with respect to each other, and with respect to a specific location on the earth.

2.3 Interrogational Astrology Interrogational (or horary) astrology, which concerns the present, attempts to answer a question based on the disposition of the heavens at the moment and place of the

Astrology   383 questioning, and thus is most like pure divination. This technique was used to find a runaway slave, a lost item, and so on. Whereas Dorotheus of Sidon (1st century ce) devoted an entire book to this procedure, Ptolemy (2nd century ce), whose astrology was atypical in his aim to present a strictly scientific astrology in the Tetrabiblos, ignores it.

2.4 Catarchic Astrology Catarchic (or electional) astrology concerns the future and involves casting a chart for an arbitrary future moment to determine the most auspicious moment to begin an enterprise, such as a marriage, a business, a journey, or even the founding of a city. In effect, catarchic astrology reverses genethlialogy: one starts with a desired outcome, finds the time of the astral configuration most conducive to that outcome, and then performs the action in question at that future moment. The legend about Olympias delaying her delivery of baby Alexander (the Great) (r. 336–​323 bce) to ensure him the optimal astral configuration and reports that Seleucus I (r. 321‒281 bce) timed the founding of his city, Seleucia, according to the stars fit this pattern, as do the coronation horoscopes in Byzantium from the reign of Emperor Zeno (r. 474–​491 ce) (Pingree 1976), or the astrological determination of the founding date of Baghdad (Jumādā I, 145 A.H, i.e., July 31, 762 ce. See al-​Biruni [1879], 1984, 262–​263).

3.  The Sources The sources for astrology are varied: example charts are extant in the languages Akkadian, Demotic Egyptian, Greek, and Latin, appearing both in literary texts and handbooks. Much of the Greek material is fragmentary—​ that is, surviving as quotes or excerpts in the works of later authors—​ and has been collected in the CCAG series (Catalogus Codicum Astrologorum Graecorum). Due to the haphazard nature of these sources, reconstructing the history of astrology is tricky, and only an outline is given here. Hadrian’s horoscope (presented and discussed at the end of this chapter) well illustrates the character of these ancient sources: it was originally included by the 2nd century ce physician-​astrologer Antigonus of Nicaea in a collection of horoscopes of historical figures (which has not survived), but Hephaistio of Thebes (4th century ce) excerpted it in his astrological treatise, whence it is known to us. The handbooks, which date from the early 1st century ce to the late 5th century ce, are the quickest way to grasp the concepts and practices of astrology. Bouché-​Leclerc (1899/​1963) surveyed all of the extant handbooks in his useful study: only the most complete handbooks are discussed here. The tendency, as astrology developed, was to multiply parameters, allowing for more options in interpretation. On Hadrian’s chart, the degrees of the planets along the ecliptic are represented, and the Decans (middle outer band on the chart) and the Terms (outer band), as well as the Ascendant, the Places, and the Lot of Fortune. These elements had distinct origins in specific cultures, but horoscopic astrology combined them.

384   Hellenistic Greek Science Furthermore, the astrological handbooks were concerned with “outcomes” (apotelesmata), for example, if configuration X at birth, then outcome Y in life, and they generate a mass of contradictory interpretations. Among many predictions some are bound to hit a target. In practice, the astrologer’s knowledge of the native (i.e., the person whose chart is to be read), as well of psychology, was helpful: he could eliminate many of the predictions that obviously did not apply. The extant interpretations of most of the literary horoscopes are aided by the fact that these are considered after the native’s death.

3.1  Astronomica, Marcus Manilius The Latin Astronomica of Manilius is the earliest astrological treatise to have survived intact. A Stoic for whom Fate is inexorable, Manilius emphasized the orderliness of the political cosmos established by Augustus (r. 27 bce‒14 ce) and continued by Tiberius (r. 14–​37 ce), for which the physical cosmos, operating like a giant mechanism, was a metaphor. Although Manilius presents an extended description of the Signs of the Zodiac, fixed stars, and Places, the planets and their positions are hardly mentioned, which renders his book useless for practical horoscopic astrology. Perhaps the absence of detailed predictive methods reflects the Augustan edict of 11 ce, prohibiting private astrological consultations or inquiries about anyone’s death. Manilius, and later Vettius Valens, describe an alternative Place system, reckoned from the Lot of Fortune rather than from the usual Ascendant, which Manilius calls labores, “labors” (Astron. 3.43–​159; 162c).

3.2 Pentateuch, Dorotheus of Sidon Dorotheus of Sidon (1st century ce) wrote a Greek verse treatise on astrology in five books, which has only survived partly in Greek, and mostly in Arabic, via an 8th–​9th century translation made from a Persian Pahlevi version. On the basis of the horoscopes it contains, the Pentateuch dates to the mid-​1st century ce. It is the earliest comprehensive treatise that includes both horary and natal astrology. Dorotheus may be taken as representative of the typical astrological current, employing lots, house positions, and house rulers. Dorotheus also used the Sign–​Place method of aligning Signs and Places, equating Place 1 with the Sign in which the Ascendant is found, rather than the normal system of reckoning the Places from the actual degree of the Ascendant. The many example nativities provided illustrate his method. One entire book is devoted to the details of determining the length of life, which reflects an obsession of his era.

3.3  Anthologies, Vettius Valens A native of Antioch writing in Greek, Vettius Valens (120‒c.175 ce) wrote the Anthologies in nine books, the most comprehensive extant survey of astrology, containing 123

Astrology   385 horoscopes of actual persons with analyses, most of which are discussed in Neugebauer and van Hoesen. His method was to describe earlier astrological doctrines and then to critique them based on his own experience. The Anthologies was copied more often anciently than any other astrological work. The tradition acquired many accretions, interpolations, and marginalia, which indicates that the work was being used. Valens conducted a quasi-​empirical test of horoscopic astrology: he cast the charts of six men who were victims of a near shipwreck, including possibly himself. He then examined their charts, to see whether the stars indicated that the respective natives would suffer a near-​death experience in the same year. He took the time from birth to a crisis as a function of planetary periods and rising times of the Signs where the planets were situated. Whatever scientific merit this test may have had was abrogated when he selected the values that made the numbers come out the way he wanted! (See Beck, 101–​111.)

3.4 Apotelesmatika (i.e., Tetrabiblos), Ptolemy The Tetrabiblos of Ptolemy (c.100—​c.178 ce) was unusual for its time:  building on Aristotelian ideas and causal explanation, this leading exponent of the exact sciences in antiquity presented the most scientific form of astrology. (See Evans, ch. D10, this volume.) By eliminating the blatantly divinatory aspects but retaining features that were compatible with Greek natural philosophy, Ptolemy physicalized astrology, and he defended it with arguments derived from Posidonius of Rhodes (c.135–​50 bce). Ptolemy’s astrology is thus more systematic than the others, and, although it provides neither worked examples nor procedural instructions, Ptolemy’s Tetrabiblos was most popular among late medieval and Renaissance astrologers and physicians. For Ptolemy, astronomy and astrology are both parts of astronomia (astral science) in the overall scheme of knowledge. What we call “astronomy” is the subject of the Almagest, and astrology is the subject of the Tetrabiblos. The former determines the planetary positions for any time, which the latter uses to generate predictions by considering the changes brought about in our imperfect world by the planetary configurations. Because the recipient matter is imperfect, knowledge of those changes is necessarily conjectural. Ptolemy’s mathematical astronomy first became available to practicing astrologers in simplified form via the Handy Tables by at least the 3rd century ce.

3.5 Mathesis, Iulius Firmicus Maternus The Mathesis of the Sicilian astrologer, Firmicus Maternus (c.280‒c.360 ce), mostly intact, is the lengthiest astrological treatise to have survived from the classical period. Firmicus cautions against inquiring about the state or the emperor’s life, since the emperor, as master of the cosmos, is not subject to the power of the stars. Firmicus answers many objections to astrology and insists that by showing how men are related to the stars, he encourages piety. Much of his astrological material is translated from Greek

386   Hellenistic Greek Science authors, however, he seems to have been unfamiliar with the Tetrabiblos, although he mentions Ptolemy three times. Vettius Valens and Firmicus Maternus treat astrology like a mystery religion, with the author initiating the reader into the mysteries of the Sacred Art. While Vettius requires a solemn oath of those who read his work, enjoining his readers not to divulge the sacred knowledge, Firmicus describes the lifestyle and conduct that the professional astrologer must follow, as an initiate into its sacred mysteries, insisting that one who daily discusses divine things must be pure, avoid greed, and shape his mind to the perfections of the planetary gods (Mathesis 2.30).

4. Origins Classical sources describe either Mesopotamia or Egypt as the original home of astrology. Pliny (7.193), Vitruvius (9.6.2) and Cicero (On Divination 1.18.36; 2.46.97, but with doubts) favored Mesopotamia; but Herodotus (2.82) and Diodorus (1.81) favored Egypt. It seems clear to modern scholarship, however, that, although Mesopotamia was the source of core astrological concepts and the general astrological worldview, horoscopic astrology took its familiar form in Hellenistic Egypt (323–​30 bce). Classical astrology developed from Mesopotamian omen divination. The Enūma Anu Enlil, deriving from the Kassite Period (1595–​1157 bce), records nearly 7,000 astral omens, concerning lunar, solar, meteorological, seismological events, as well as the planets and stars. An epochal shift in thinking about the connection between astral and terrestrial events occurred in the later Assyrian Empire (ca 8th–​5th century bce), due to the demand on royal astrologers for foreknowledge from the stars (Brown 2000). This demand led to competition for better techniques at arriving at predictions, leading to a shift from a qualitative, mythological account, such as in the Enūma Anu Enlil, to a mathematically predictive paradigm, emphasizing precise results. This led to many centuries of meticulous recording of observations and theoretical methods that were useful to Ptolemy and others in constructing the mathematical edifice on which scientific astrology was founded. (See Rochberg, chap. A1b, this volume.) In the latest Babylonian period, near the end of its independence, concern shifted toward individual fate, rather than that of the king and state, perhaps because, with no royal employment, astrologers were cultivating a new market. Or, perhaps because, deprived of their autonomy as a nation, individuals sought empowerment through natal astrology. The extant Babylonian nativities—​32 of which survive (Rochberg 1998)—​ span 410–​69 bce. By determining the positions of sun, moon, planets at the date of birth, noting the conjunctions of any of these to one of the fixed reference stars, predictions could be made about the life of the native. This type of natal astrology, however, has no Ascendant and no Places. The Zodiac, a Babylonian contribution, facilitated the recording of planetary positions, as celestial coordinates. Originally, Babylonians used the actual constellations,

Astrology   387 which are irregularly spaced. However, as mathematical methods for predicting phenomena and generating ephemerides developed, a more precise system was needed, and the 30 degrees per Sign system, counted from a fixed star, was introduced. Precession (discovered by Hipparchus, 2nd century bce) has shifted the Vernal Equinox into the constellation Pisces. Greek astrologers, however, continued to use a Vernal Equinox at Aries 8 or 10 degrees, originally derived from the Babylonian scheme, until Ptolemy set the standard practice of measuring the longitude of a planet from the Vernal Equinox, wherever it happens to be, defined as 0 degrees of the Sign Aries. Although some Babylonian astrology must have been transmitted to Egypt under Persian rule (529–​404 bce), Alexander’s conquests greatly increased the westward flow of ideas. Jones (1991, 1999a, 1999b) showed that some Babylonian predictive astronomy made it to Egypt and was cultivated independently—​in the service of genethlialogy. Hipparchus (2nd century bce), who employed geometrical models to render solar and lunar motions predictable, was one of the first Greek astronomers to use Babylonian planetary records, which he found suitably precise for his needs. (See Zhmud, chap. B2, this volume, for a discussion of Greek geometrical models of the planets’ motions) Josephus (Contra Apionem 1.128) and Vitruvius (9.6.2) report that Berossus (Bēl-​ rē’ušu, Bel is his shepherd) (ca 350–​280 bce) transmitted Babylonian astronomy to the Greeks. Originally a priest, who dedicated a history of Babylon to the Seleucid king, Antiochus I (r. 281–​261 bce), Berossus inexplicably settled on the island of Kos, then under the control of the Ptolemies, who were then Seleucid enemies, where he is said to have founded a school of astrology. Coincidentally, the Hippocratic medical school had already been established at Kos, which invites us to speculate about cross influences between Babylonian astrology and early Greek rational medicine. Because of Berossus’s Egyptian connection, both the Babylonian methods attested in the earlier Egyptian papyri and a Chaldean term system mentioned by Ptolemy (Tetrabiblos 1.21) may have derived from the school of Berossus.

4.1 Ptolemaic Egypt: Birthplace of Horoscopic Astrology The synthesis of Mesopotamian astrological ideas and methods with Egyptian concepts and Greek theoretical and mathematical apparatus, which resulted in horoscopic astrology, occurred in Alexandria during the Hellenistic period. Egyptian contributions have been understated in the past, because, when compared with extant Mesopotamian examples, the very little extant early Egyptian astronomical material has a pictorial rather than mathematical character. However, many examples of Egyptian mathematical astronomy and horoscopes have now come to light, and the surviving Demotic horoscopes, planetary tables, and theoretical treatises are tantalizing clues that more once existed. (See Quack chap. A2b this volume; and Winkler 2009 and 2016) It seems clear that the decans, the Ascendant, and associated Places originated in Egypt. Jones has shown from the papyri that Hellenistic Egyptian astrologers were using computational methods derived from Babylon, which were replaced eventually by Ptolemy’s

388   Hellenistic Greek Science Handy Tables, although both systems coexisted for a time. Some tables were not referred to a specific epoch, and this may be the Perpetual Tables referred to by Ptolemy (Almagest. 9.2). The astrological literature in circulation by the 2nd century bce attributes the origins of astrology to the Egyptians (pharaoh) Nechepso and (priest) Petosiris, considered authorities on astrology, divination, and hermetic magic. These writings contain older, Babylonian-​style omens, and they foreshadow many later issues: time of conception vs. birth; length of life, Lot of Fortune, Lord of the Year, and critical times of the native’s life. Additionally, astro-​botany and astro-​lapidology are discussed, which deal with the stars’ connections with plants and stones, respectively. Greek horoscopic astrology seems to have been originally part of “hermetic” literature, which includes omens, genethlialogy, iatromathematics, and botanical and medical astrology. The references to the priest Petosiris may reflect an authentic temple context for Egyptian astrology, as Jones has shown that most of the astrological papyri belonged to temple libraries. (Jones, 1994, 40) Clement of Alexandria (Stromateis 6.4) describes an Egyptian priestly procession, one of whom is called horoskopos, and another, prophetes. It is generally assumed that these priests were involved with astrological divination.

4.2 Astrology Comes to the Classical World In summary, the elements derived from Babylon consisted of the equal Sign Zodiac coordinate system, arithmetic methods for predictions based on planetary cycles, the importance of eclipses for mundane astrology, the concept of “secret houses” of the planets (which became the exaltations/​depressions), the dodekatemories (dividing each Sign into 12 parts), and the use of triplicities (four groups of three Signs). From Egypt were derived the decans and the Ascendant, which marked the chief difference between Babylonian natal and Egyptian horoscopic astrology. The Ascendant (horoskopos, watcher of the hour), the degree of the Sign rising above the horizon at a given moment, developed from the decans, a division of each Sign into three, 10 degree segments, which were originally markers to tell time at night. The original Egyptian practice was to infer the character of the native, whether lucky or unlucky, from the decan rising at birth. From the Demotic texts derived the sigla for some of the Signs (Neugebauer, 1943).

4.3 The Greek Synthesis Astrology developed into a natural science in the Greco-​Roman world, fully integrated with the prevailing cosmology. Beginning in the early Greek period, ideas flowed from Mesopotamia and Egypt. Some Babylonian astronomical ideas appear in Homer, and Hesiod’s Theogony bears remarkable similarities to the Babylonian creation epic, Enūma Elish (West 1988, 18–​31; Walcot 1966, chaps. 1–​2). Babylonian star names were translated into Greek by the 6th century bce, although the Greeks do not appear to have

Astrology   389 distinguished between fixed stars and planets until the 5th century bce. By the time Oenopides of Chios (mid-​5th century bce) introduced the Zodiac from Babylon, Greek cosmology was ready to incorporate it. Furthermore, by 432 bce, Meton and Euctemon employed Babylonian data and methods in reforming the Athenian calendar. Until Plato and Aristotle, however, there were no cosmology and physics robust enough to accommodate astrology. Plato provided a cosmological framework in the Timaeus, based on divinely ordained numerical and geometrical patterns. In the Epinomis (by his student, Philip of Opus), the planets are named in their canonical order, with Greek names corresponding to Babylonian deities. (See Tarán 1975). Both these works encouraged belief that human souls possess a divinely endowed affinity with the celestial bodies, because we are able to perceive the geometrical harmonies in celestial motions. The surest path to self-​ improvement, therefore, is contemplation of the motions of the planets and stars. Aristotle gave this speculative cosmology a consistent physics, enabling the discussion of planetary influences in terms of natural law (in the Physics; On Heaven; and On Generation and Corruption). The eternally unchanging fixed stars cannot cause changes in our world. Rather, the planets, through their irregular motions—​understood by later Aristotelians as moving closer and farther away from earth—​cause these changes, keeping the four elements of the sublunary world in motion. In the cosmos of the Stoics, the planets move by necessity, fate is inexorable, and the whole system is governed by a Divine Master. (See Tieleman, chap. D5, this volume.) This system formed a parallel to the political realities of the Hellenistic world: many a ruler was flattered by the comparison of himself to Zeus, and fate became an apt metaphor for the new authoritarian rule: since nothing happens by chance, the way to inner peace (ataraxia) is to accept one’s lot. In opposition to fate (heimarmene), there grew a fascination with chance (tyche). The Phaenomena by Aratus of Soli, which was dedicated to king Antigonus Gonatas of Macedon (r. 277–​239 bce), is a product of that Stoicizing milieu, and it eventually became a staple of Roman education under the Principate. It was translated into Latin at least twice, by Cicero and Germanicus, and the physician Galen cites it when he makes an astronomical point. (See section 5 below.)

4.4 Astrology in the Roman World 4.4.1 Republican Period The Romans, an agricultural people, were originally interested in the stars primarily in connection with farming. At first skeptical about astrology, eventually they became avid devotees. In earlier Latin literature, astrologers were associated either with the lower classes, plying their trade in the marketplace or around the Circus Maximus, or grouped with exotic eastern cults. Astrologers were expelled from Rome (139 bce)—​the first of a series of expulsions over the next two centuries—​during a period of unrest because of fear that they would agitate the masses with their prophecies of a new regime or social

390   Hellenistic Greek Science order. The xenophobic Cato (De agricultura 1.5.4, 160 bce) warned farm overseers against consulting astrologers. This fear was well-​founded, for, when an overseer of slaves became leader of the Second Sicilian Slave Revolt (104–​100 bce), he announced that the gods had revealed to him, through astrology, that their revolt would succeed and that he would become king of Sicily. The revolt, however, was crushed. Beginning in the 3rd century bce, aristocratic Romans cultivated Greek thought and literature, which was accelerated via Greek embassies to Rome in the 2nd century bce. Although these Greeks came for political reasons, they lectured on the side to large audiences. Interest in Greek thought grew to such a point that many Greek teachers migrated to Rome to satisfy the demand. The most famous of these embassies occurred in 156 bce, and comprised the Stoic, Diogenes of Babylon; the Academic, Carneades; and the Peripatetic, Critolaus. The Romans thereby learned both of the existence of a kind of astrology that was supported by natural philosophy and about the philosophical debate about fate vs. free will. The Stoic philosophers advanced their views about fate and the effectiveness of astrology, while the Academics, whose greatest representative was Carneades (214/​3–​129/​8 bce), advanced pointed questions and arguments, such as the “twins argument,” to show the vacuity of the astrologers’ claims. Twins born at the same moment and place usually have different destinies. (More of these arguments are discussed later.) Among the most influential of the Stoic proponents of astrology was Posidonius (ca 135–​51 bce) who visited Rome as an ambassador. Cicero (106–​43 bce) attended his lectures while at Rhodes (87 bce). Posidonius was the primary persuasive factor in winning Roman favor for astrology. Cicero, however, later turned against his teacher’s views, presenting arguments derived from the Skeptics in his devastating On Divination (discussed later). The first Roman astrologer about whom we know anything was a friend of Cicero’s, Publius Nigidius Figulus (ca b99–​45 bce). He advanced the doctrine, similar to Plato’s, that the souls of mankind ascend to the stars after death. Looking retrospectively, Figulus was understood as having foretold Octavian’s rise to power, solely on the basis of the planetary configuration and the Ascendant for the day of his birth, derived from his father’s report about the exact moment of birth (Cassius Dio 45.1.3–​5). In spite of the skeptical arguments advanced by Lucretius and Cicero, by the death of Julius Caesar (44 bce), much of the Roman aristocracy had accepted astrology.

4.4.2 Astrology and the Emperors 4.4.2.1 Imperial Uses of Astrology Would-​ be rulers of the Roman state in the 1st century bce—​Pompey, Crassus, and Caesar—​ began to employ astrological predictions about themselves and their regimes—​however, in spite of promises of peaceful and prosperous lives, they all died violently—​as Cicero and other critics of astrology gleefully observed. Curiously, the rise in popularity of astrology corresponds with the decline in the oracles, which Plutarch attempted to explain (De defectu oraculorum). Perhaps that elitist institution gave way

Astrology   391 to more personal, egalitarian astrology. (For Plutarch in his 2nd century context, see Keyser chap. D11, this volume). Octavian (63 bce—​14 ce) was politically more successful with the new interest in astrology. Comets normally portended evil, so his encouraging the belief that the comet of 44 bce was the soul of the divine Julius ascending to the stars was an innovative twist. The stories about Octavian’s predicted greatness convinced later would-​be emperors that they needed such support from the stars. Octavian published his natal chart and employed astrological symbolism on his coins:  Capricorn, probably his Ascendant, became his emblem. This heralded the new era:  the sun (i.e., Sol Invictus) rises in Capricorn after the winter solstice. Manilius supported such views in his Astronomica. In later life, as Augustus, he became anxious about astrology, and, in 11 ce, when he was ill, he issued his anti-​astrology edict, referred to earlier.

4.4.2.2 Thrasyllus’ Family: Astrology as a Means to Political Power Tiberius (r. 14–​37 ce), himself an astrologer, employed a court astrologer, Tiberius Claudius Thrasyllus of Alexandria (d. 36 ce), a famous Alexandrian scholar and polymath. Thrasyllus achieved great renown and power through this position, and, through his son, Balbillus, by a princess of Commagene, founded a “dynasty” of astrologers (Cramer [1954], 1996). Tiberius, who attended his lectures while on self-​imposed exile on Rhodes, ca 6 bce, struck up a friendship with Thrasyllus and made him a Roman citizen (Tiberius Claudius Thrasyllus) after their return to Rome in 2 ce. In his final years, Tiberius, with Thrasyllus’ assistance, reportedly used astrology to scan the horoscopes of men of influence to determine who had imperial destinies and to eliminate them. Vettius Valens later cited Thrasyllus as an astrological authority. Involved in court intrigues, Thrasyllus was probably the brains behind the counter coup against L. Aelius Sejanus (d. 31 ce) (Cramer [1954], 1996, 103–​105). Thrasyllus’ Pinax (table), which contains a description of the natures of the Signs, planets, the nativity of the world, and the cardinal points, and shows how to work problems, survives in summary form in Porphyry and Hephaistio (CCAG 8.3, 99–​101). Thrasyllus’ son, Tiberius Claudius Balbillus (d. ca 81 ce), achieved renown and power though serving as imperial astrologer to Claudius (r. 41–​54 ce), Nero (r. 54–​68 ce), and Vespasian (r. 69–​79 ce), as well as chief military engineer for Claudius on his British campaign (43 ce). Nero made him Prefect of Egypt (54–​59 ce). Excerpts of his treatise Astrologumena survive, which contain a detailed discussion of his famous method for determining length of life (CCAG 8.3, pages 103–​104). Nero’s reign was reportedly ushered in via catarchic astrology, as his mother consulted with astrologers—​one of whom one must have been Balbillus—​regarding the optimal moment to officially commence it. Servius Galba (r. 68–​69 ce), Nero’s successor, as a young man was said to have an imperial destiny, based on his chart. Although Tiberius and Thrasyllus scrutinized Galba’s chart, they spared him, allegedly because his chart indicated that he wouldn’t attain the throne until old age (!)—​he was in fact 72 years old at his accession.

392   Hellenistic Greek Science Domitian (r. 81–​96 ce) was so obsessed with astrology that he was said to have predicted the hour that he was to be assassinated. As he waited for the fateful hour to arrive, the palace conspirators deceived him about the time, and so, thinking that he had survived fate, let his guard down, and they slew him (96 ce). His successor was Nerva (r. 96–​98 ce), who possessed a favorable horoscope. Hadrian (r. 117–​138 ce), whose horoscope will be considered later, was declared to have an imperial nativity—​what that meant will become clear below. Hadrian’s horoscope was analyzed postmortem and functions as a “proof ” that his imperial destiny was foretold him. Hadrian was also said to have selected his successors astrologically, which involved three adoptions: Antoninus Pius (r. 138‒161 ce) by Hadrian, and both Lucius Verus (r. 161‒169 ce) and Marcus Aurelius (r. 161‒180 ce) by Antoninus Pius. Eventually, nearly every emperor from Augustus to Hadrian was said to have had astrological confirmation of their imperial aspirations. After Hadrian, the Stoic emperors, especially Marcus Aurelius, followed a tempered Stoicism, where the power of absolute fate—​and hence astrology also—​was loosened, reconciling belief in fate with belief in a benevolent divine providence. Septimius Severus (r. 193–​211 ce) was obsessed with astrology and inquired about his future, for which he had been indicted for treason under Commodus (r. 180–​192 ce) (cf. Augustus’s 11 ce law), but his case was dismissed since Commodus was so unpopular. In the pattern of Augustus, Septimius published his own horoscope: to strengthen his claim, following the strife after the end of the Antonine dynasty. He depicted his chart in public places but always obscuring the location of the Ascendant to prevent anyone from calculating his death date. Septimius reportedly knew via astrology that he would die on his campaign to Britain, that his son Geta (r. 209–​211 ce) would not long outlive him. Moreover, he chose for a wife a woman whose chart indicated that she would marry a ruler. Following this period of imperial obsession, Roman interest in astrology waned, beginning in the 3rd century ce, due to a general religious mysticism and rational skepticism, both of which opposed astrology. (See Bernard, chap. E2, this volume, for the place of astrology among the mathematical sciences in the later Roman world.)

5.  Astrology and Medicine The close association of medicine and astrology was long and successful. Physicians were expected to give prognoses, and astrology, embedded within the same natural philosophical milieu as medicine, provided additional predictive factors. Both disciplines were conjectural sciences, but their practitioners sought as closely as possible to emulate a mathematical ideal. Casting a chart for the moment the patient fell sick (“hour of decumbiture”) was a special application of genethlialogical astrology that helped the physician know when to intervene and with what type of treatment. (Galen, De diebus Decretoriis, Kühn 9.910.16–​912.16; Cooper 2011a, 338‒341.) There are references to the stars in Hippocrates; however, the emphasis was on meteorological and environmental factors, as in the Airs, Waters, Places. One of the

Astrology   393 founders of medical Methodism, Thessalus of Tralles (ca 20–​70 ce), who was the object of Galen’s vituperation (Therapeutic Method 1, Kühn 10.7–​9; 51–​52, and 2, Kühn 168–​170, inter alia), wrote on astro-​pharmacy, in which he included a brief autobiography in the prefatory letter to an unnamed 1st-​century Roman emperor. He had tried to apply the methods of healing he learned from a text found in a library, purportedly by Nechepso, but the attempt was a complete failure. He then approached the gods to inquire why he failed, and he received a theophany of Asclepius, who informed him that Nechepso had correctly understood that plants and stones have affinities with the stars, but that he had neglected the part about the times and places that these things were to be gathered. Galen (d. ca 216 ce) showed how Aristotelian physics and Hippocratic medicine could be combined in a powerful system that was both rational and empirical, which became a great support for medical astrology (See Johnston, chap. D9, this volume). Due to the influence of his Critical Days, Galen must be considered a founder of medical astrology or iatromathematics. Such was his reputation that the explicitly astrological pseudo-​Galenic Prognostica de decubitu was attributed to him. Recent scholarship, however, has shown that Galen’s interest in judicial astrology was insincere, a mere rhetorical appendage to his natural astrological approach to the problem of medical crises (Cooper 2011b). Consistent with his natural astrology, moreover, Galen urges the physician not to follow the heavenly indicators alone, but to watch the signs in the patient, and to take all evidence into consideration before deciding on a specific course of treatment. It has also been argued that astrological ideas were useful to Galen for his “harmonic” understanding of the patient, nature, and cosmos triad (Cooper, 2011b, 136–​138. See also Hagel, chap. C11, this volume, for a discussion of harmonic theory). Galen’s emphasis on close observation and his sophisticated reasoning were ideals for physicians who followed; some of whom, such as Pietro d’Abano (ca 1257–​1316) and Girolamo Cardano (1501–​1576) sought to replace Galen’s flawed astrology with a more scientific version, which for Cardano was Ptolemy’s. A practice that seems to have combined elements of Babylonian medicine and Egyptian symbolism, namely, melothesia (a forerunner, perhaps, of the medieval “Zodiac Man”), is reminiscent of the Egyptian goddess Nut stretched across the sky. The major parts of the patient’s body were correlated to the Signs, by stretching it out along the Zodiac, beginning with the head at Aries, and ending with the feet at Pisces. No diagrams have survived from antiquity, but this figure appears in texts, for example, Ptolemy, Tetrabiblos 3.12 (See also Bouché-​Leclerc [1899], 1963 319–​325). In medical astrology, the chart taken for a specific moment is used to determine the particular influences on the patient’s body parts.

6.  Opponents of Astrology From the start, astrology had its critics, only some of whom can be discussed here. The critical tradition acquired an arsenal of skeptical questions. Here follows a compilation

394   Hellenistic Greek Science of some of the strongest of these anti-​astrology arguments, compiled from Carneades, Cicero, and Favorinus of Arles (early 2nd century ce). a. People born at the same time, especially twins, have different fates. (Figulus, mentioned earlier, produced a graphic refutation of the twins argument: striking a spinning potter’s wheel twice in quick succession, he indicated that within even a small interval the spinning heavens change significantly.) b. It is impossible to establish the precise moment of birth or conception, either through fallibility of instruments or sight, and even a small difference in time produces a different stellar configuration. c. The astral configuration at conception is necessarily different from the one at birth. Which of the two affects the child, or must both be reconciled? d. Astrology is a recent invention, and its supposed ancient origins are a fabrication of the astrologers. Human history has been far too short to have provided the necessary observations of astral powers upon which a science of astrology could be based. e. Astral influences, which are pervasive, ought to apply to all living things, not just humans. f. People who die at the same time have different fates indicated from their birth charts. g. People are more diverse in races and customs than astrology would indicate. Local traditions and conditions make men different, apart from the stars. h. Other factors than the stars influence a child’s disposition, such as climate, weather, and especially parents’ seed. i. Medicine can alter some physical characteristics supposedly caused by the stars from birth. j. Because one or two astral influences on earth can be established, such as the seasons and the tides, it does not follow that there are others. Yet the whole edifice of astrology is built on the assumption that multiple such correlated influences exist. k. The number of celestial bodies is not known for certain, so how can one predict securely? l. The notion that all our actions, down to the minutest, are ineluctably fated is ridiculous and intolerable. (The visceral argument.) m. The planets are all at different distances from earth, so how can they have the same influence on earth?

7. Skepticism 7.1 Lucretius and Cicero Two influential critics of the 1st century bce, representing two schools of criticism, were Lucretius (ca 155–99 bce) and Cicero (106–​43 bce). Lucretius’ De rerum natura is an

Astrology   395 assault on the Stoics’ ordered, rational universe. Instead, there are only atoms in motion and the void, and no cosmic sympathy, which is the Stoic condition for the possibility of divination and astrology. Cicero, on the other hand, relied on arguments from the Middle Academy in his On Divination, where he presented the first philosophical distinction between astronomy and astrology in the ancient world, in order to refute the latter (see, inter alia, On Divination 2.42). Cicero’s critique of astrology conveyed to the later Latin tradition, for example, Augustine, several standard arguments against astrology. A further argument reveals a fundamental misunderstanding, however, shared with Sextus Empiricus:  they insist astrologers hold that the destinies of everyone born at the same time are the same. However, scientific astrology always took the birth location into account. Cicero’s objections were significant enough, it seems, to provoke Ptolemy to answer them in his Tetrabiblos. (See Evans, chap. D10, this volume.)

7.2 Sextus Empiricus Sextus Empiricus (ca 100–​200 ce) was a physician Skeptic, whose affinities aligned with the Empiricist and Methodist medical schools. Sextus’ extensive writings are the most important Skeptic writings to survive and provide a detailed picture of the Skeptics’ mode of thought. His attack on astrology appears in book 5 of his Adversus mathematicos. Sextus has been criticized for his attacking weaker or incorrect versions of the sciences he refutes. For example, in his account of astrology, he depicts astrologers as constructing a chart by direct observation of the heavens at the moment of birth. This scenario is far from the actual method, which was to calculate the natal chart back in time. Sextus attempts to show, through a trilemma, that astrology is either impossible or useless or both. Events can occur by necessity, by chance, or by human agency. If by necessity, then astrology is useless, because events are unavoidable; if by chance or human agency, then astrology is impossible, since the former occurs randomly, and the latter has no necessary cause, and so neither can be known in advance. An astrologer would counter that Sextus’ trichotomy is misleading, since there may be a predisposing, not necessitating, connection between the stars and events, and even if some events are unavoidable, astrology can help men prepare for them. His other arguments are mainly epistemological, typical of Skepticism, dealing with the uncertainty of critical measurements or human ignorance. For example, the birth time cannot be known precisely: Is it the time when the child first appears or when it has fully emerged? Moreover, the Ascendant, on which the whole natal chart depends, cannot be known precisely, due to the weather or atmospheric refraction, or that the starting and ending points of the constellations cannot precisely be determined (some even overlap). The last again reveals Sextus’ ignorance or misrepresentation, since the equally-​spaced Zodiac Signs had been employed by astrologers for centuries.

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7.3 Tacitus The historian Tacitus (56‒117 ce) questioned the existence of fate in the lives of historical subjects. In an aside, after discussing Tiberius and Thrasyllus, Tacitus wonders whether human lives are governed by fate or chance. Tacitus briefly outlines the two most important rival positions on the issue of stars and fate in human lives, namely, the Epicureans, on the one hand, who denied any concern of the heavens for us at all, moreover, they were opposed to all forms of divination; and the Stoics, on the other hand, who construe everything as bound by threads of fate. He notes that many insist that the heavens are oblivious to earthly affairs, which is why sometimes the good suffer, the evil prosper, and those in dire straits are sometimes happy, while those blessed with abundance are sometimes miserable. Tacitus seems to concur with the majority view that human lives are determined (Annals 6.22).

7.4 Astrology and Christianity At least a dozen imperial decrees expelled astrologers from Rome and Italy, between the deaths of Caesar (44 bce) and Marcus Aurelius (180 ce). They were usually in response to events associated with political unrest. Systematic anti-​divination legislation began after 312 ce, when Constantine converted to Christianity: government actions against astrology and Christian opposition to it tended to coincide. Astrology was grouped with paganism and classed with divination, and it was thus subject to persecution and legal restrictions. By 358 ce, astrology was classed with both magic and divination, which were among the five major capital offenses. In 409 ce, the two emperors Honorius (r. 395–​423) and Theodosius II (r. 408–​450) required astrologers to burn their books in the presence of bishops or face exile. Christianity was, in general, opposed to (judicial) astrology, both because it clashed with Christian doctrines of freedom and moral responsibility, and because of its association with polytheism and the pagan establishment, but especially over the issue of foreknowledge: for Christians, only God can have such knowledge. However, Christians were ambivalent toward astrology, since, according to the Gospel of Matthew (2:1–​12), a star led the Magi, astrologers from the East, to the infant Jesus. Christian attitudes toward astrology were complicated by the fact that astrology was favored by the Gnostic heresy (2nd–​3rd century ce), which taught that the soul ascended through the stars to its liberation from evil matter. Tertullian’s position was an odd compromise:  God permitted astrology to operate until the time of Christ’s ministry, after which he freed mankind from the power of the demons (On Idolatry 9; Hegedus 2007, 308–​309). Tatian’s view was that pagans are trapped in astral fate, from which Christians are liberated at baptism (Oratio ad Graecos 8; Hegedus 2007, 125–​127). One bishop, Zeno of Verona (d. 380 ce), taught newly baptized converts that they were born again under a new set of constellations that destined them to heaven (Tractatus de

Astrology   397 XII signis ad neophitos: Löfstedt 1971, 105–​106). Origen (Against Celsus 5.6–​13; Hegedus 2007, 329–​333) and Eusebius, however, envisioned a kind of “nonfatalist” astrology, the basis for the natural astrology that dominated intellectuals for the next age (Preparatio Evangelica bk. 6; Hegedus 2007, 129). The most eloquent Christian opponent of astrology was Augustine (354–​430 ce), who knew the subject well from his earlier involvement with Manicheism, discussing astrology in the City of God (bk. 5). He indicates that many Christians still adhere to this ancient and evil practice, which he wants to see obliterated. The danger, as Augustine understands it, is that people confuse the power of God with those powers traditionally associated with astrology, which are actually the work of demons. In spite of these efforts, Christianity failed to eradicate astrology, which continued to be used well into the Byzantine period and beyond. Astrology, because of its usefulness for medicine, eventually became entrenched within the curriculum of the medieval universities, where it flourished in a form that had been further developed by Arabic authors, such as Abu Ma’shar (787–​886), who elevated astrology to a “master science,” which subsumes, and serves as an end for, all lower disciplines.

8.  An Ancient Example: The Horoscope of Hadrian For a practice and worldview that was so pervasive, it is curious that very few sources discuss how an actual consultation took place. Furthermore, very few horoscopic diagrams survive, outside of literary works. However, Evans (2004) has convincingly reconstructed part of how it was done, based on later testimony and surviving fragments of Zodiac boards. The astrologer would calculate planetary positions, noting this information on a scrap of papyrus or an ostrakon. When meeting with his client, he placed colored stone counters representing the planets on one of these boards, in their appropriate houses. Apparently, a Sign-​Place system of reckoning the astrological Places was used: the Sign in which the Ascendant lies corresponds to Place 1, Place 10 corresponds to the Sign with the Midheaven. These tablets have dual concentric outer circles that provided a convenient method for the comparison of charts, such as when determining compatibility with a potential spouse. Before Ptolemy’s Handy Tables became available sometime in the 3rd century ce, to obtain planetary positions astrologers used the Perpetual Tables (aiōnioi kanones, cf. Almagest 9.2), which appear to have been based on Babylonian planetary period relations and simple geometrical models. Preparation of such charts was the fundamental activity of the astrologer, hence they were called mathematici (calculators). Ptolemy’s Handy Tables were a significant improvement on these tables, which he criticized as being based on faulty geometrical models.

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8.1 The Chart To illustrate the practice of Greco-​Roman astrology, an example natal chart—​that of Emperor Hadrian (76–​138 ce), as drawn up and discussed by Antigonus of Nicaea (125–​175 ce), a physician and astrologer—​is described and interpreted (­figure C8.1.). This chart has survived in the Apotelesmatica of Hephaistion of Thebes (380–​450 ce), a collection of horoscopes of famous people (2.18.22–​52; Pingree 1973, 1.157.28–​162.30). Antigonus’ postmortem analysis aimed to explain Hadrian’s life retrospectively. Accordingly, it focuses on known biographical details, including the manner of his death. The present discussion will make use of Firmicus Maternus for additional commentary, since his was the latest (nearly) complete handbook. The example chart attempts to represent as many features as possible, for purposes of illustration, although no surviving chart is as complete. Its planetary positions, which differ somewhat from modern calculations (Neugebauer and van Hoesen [1959], 1987, 90–​91), were doubtless generated from tables such as the Perpetual Tables. The present discussion is based on Antigonus’ values. The chart is presented in the modern circular form, which renders relationships visually much easier to grasp. While circular charts are attested, the ancient authors—​Antigonus included—​seem to have preferred square charts, which are divided into smaller squares and triangles to represent the twelve Places. When one tries to interpret an ancient chart using a handbook such as Firmicus’ Mathesis or Vettius’ Anthologies, it soon becomes clear that no handbook, or all of them together, will suffice to instruct how it was done. There is nothing as clear as: Sign X indicates unambiguously outcome Y. Rather, the handbooks provide a mass of mutually inconsistent outcomes. The problem is too much and contradictory information. This accords with recent scholarship; namely, in the ancient world, one needed to learn astrology (and medicine) from a teacher within a living tradition; the handbooks functioned both as aides-​mémoires for the practitioner and to show the knowledge and skill of the teacher to attract students and clients—​and, furthermore, that one would use some nonrational preference to select predictions (Barton 1994b, chap. 3).

8.2 Diversity of Methods of Interpretation There was no universally agreed upon method of astrological interpretation in Greco-​ Roman antiquity. The existence of a diversity of methods supports Ptolemy’s view that astrology is merely conjectural (Tetrabiblos 1.1–​2) because where certainty is involved we should expect more agreement. This inherent fuzziness gave the Skeptics ammunition in their attack on astrology. The tendency was for the parameters on the chart to increase in number and complexity, giving astrologers more material to work with: the more predictions, the more likely that some will hit a mark. Furthermore, the accumulation of the experience of generations of astrologers, lent astrology the appearance of

Astrology   399

Figure C8.1  Natal chart of Hadrian, as cast by Antogonus of Nicaea. Drawing by author.

being empirical. Nevertheless, astrology forms a complete semiotic system, involving relationships and meanings that are known and stable, in contrast with the esoteric and elite oracles, which were then in decline. The rise in popularity of astrology thus may be understood to be a democratization of prophecy.

400   Hellenistic Greek Science The natal chart is a two-​dimensional diagram of the state of the heavens at a particular moment and place on the earth. Here, Hadrian’s birth at Italica (near Seville), Spain, 37° 30′ N. latitude, 6° 5′ W. longitude, about 6 a.m. on January 24 of 76 ce is indicated. The most striking feature of the astrological worldview (to us) is its geocentricity. The planets move around and influence the native at the center of the cosmos. The Signs are coordinates for showing the longitudes of the planets, which move within a narrow band along the ecliptic. The traditional orientation is like a clockface, with the cardinal points (kentra), namely, Ascendant (horoskopos) placed at nine o’clock (ASC), the Midheaven (medium coeli MC) at (approximately) noon, the Descendant (DSC) at three o’clock, and the Lower Midheaven (imum coeli IMC) directly opposite the Midheaven. Several circles are involved in this scheme. The chart, a flat projection of solid reality, distorts the actual relationship of these circles and is thus a schematic map of the heavens, rather than a precise projection. The Celestial Equator is inclined with respect to the horizon, according to the local latitude, and the ecliptic, or path of the sun, is inclined with respect to the equator by about 23.5°. In the chart, the horizon is represented by the line with ASC (Ascendant) and DSC (Descendant) on either end. The meridian, directly overhead, is represented by the line perpendicular to it, and the MC (Midheaven). The ecliptic circle is divided into 12 Signs, which comprise the Zodiac. Because the ecliptic circle is inclined both with respect to the local horizon and with the equator, it has a somewhat irregular apparent motion. The Ascendant, the degree of a particular Sign rising on the eastern horizon at the moment of birth (here Aquarius 1°), is the point from which the Places (topoi) are determined. Ptolemy developed trigonometric methods to calculate the Ascendant precisely (Almagest 2.8), but in practice it was often estimated using crude arithmetic methods. The Midheaven (MC) and its opposite (IMC), however, present a problem. Because of the inclination of the ecliptic circle, the angle between the Ascendant and the Midheaven measured along the ecliptic circle oscillates throughout the day, depending on latitude, and the actual Midheaven (MC*) must be determined from the Table of Ascensions (Almagest 2.8) or by using planispheric astrolabes, which were developed in Late Antiquity, on the basis of Ptolemy’s method of stereographic projection. On Hadrian’s chart, the precise MC* is Scorpio 21° 23′, which is less than 90° from the Ascendant. The effect of the oscillating Midheaven was usually ignored in practice—​ many astrologers used a simpler rule, namely, taking the Midheaven to be 90° or three Signs from the Ascendant. The oscillation of the Midheaven actually rendered the Place boundaries (cusps) variable throughout the day, a feature for which a universally agreed upon method has never been devised. One early method of determining intermediary cusps was to trisect the arcs between the Ascendant and the MC*, and between the MC* and the Descendant. Firmicus (2.15; 3.6) observes that the Midheaven may sometimes be found in the 11th Place. Oddly, however, he leaves the equal house system in place. On this basic framework astrologers laid out the 12 Places (dodekatopos), counted from the Ascendant counterclockwise, which divided the sky into regions that govern

Astrology   401 aspects of the native’s life, such as wealth, marriage, journeys, and so forth (See ­figure C8.1, lower right; “FM” stands for Firmicus Maternus, Mathesis.) These Places provide an additional interpretative framework for the planetary positions. There were variations, however: Ptolemy began the Places from 5 degrees before the Ascendant, and another method, attributed to the Egyptians, made the Ascendant the midpoint of the first Place. The simplest method, the Sign-​Place system, equated Signs and Places, that is, the Sign in which the Ascendant is found is coextensive with Place 1. An earlier method used eight Places (oktotopos) instead of 12. A variant Place system, counted from the Lot of Fortune rather than from the Ascendant, is attested in Manilius (3.43–​159) and Vettius Valens (2.41). The circle of the Places is the most arbitrary of all the elements of the chart, and astrologers have tried to support it by analogies from the human world, such as the drama of a typical human life.

8.3 The Planets and their Valences The planets, and sometimes the lunar nodes (head and tail of the dragon)—​not indicated on Hadrian’s chart—​are marked on the chart by their sigla and according to the degree of the Sign in which they fall, measured counterclockwise from the beginning of the Sign. Consistent with his efforts to render astrology on as sound a scientific basis as possible, Ptolemy (Tetrabiblos 1.5) assigned each planet a dominant quality, which it tends to produce in a patient’s body, that is, warming, drying, and so on, consistent with Aristotelian physics. (See Evans, chap. D10, this volume.) Venus (warming and moistening) and Jupiter (heating and moistening) are the benefics; Mars (heating and drying) and Saturn (cooling and drying) are the malefics; and Mercury (sometimes drying and sometimes moistening), sun, and moon are neutral, which means they combine their power with whatever planet they are near. According to Firmicus (5.1.29–​31), the MC in Scorpio means that Hadrian will be brave and his life will be filled with harsh experiences. He will travel much. His early life will be troubled from wife and children, but then he’ll receive fortune from others’ notice. The IMC in Taurus means that Hadrian will achieve greatness and be friends with many powerful men, and because of his integrity he will have others’ income and important projects entrusted to him.

8.4 The Lots The lots (klēroi /​sortes) provided a simple way to generate new interpretive material for the astrologer to work with. The lots are calculated by measuring the angular arc between two planets on the chart, and transferring this arc to another entity on the chart, and locating the lot at the end of the resulting arc. There were diverse methods for doing this; on Hadrian’s chart, Firmicus’ method has been followed (4.17). Multiple lots are mentioned in the handbooks: Fortune, Daimon, Eros, Necessity, and Basis, among others.

402   Hellenistic Greek Science To calculate the Lot of Fortune (klēros tuchēs) for Hadrian’s chart, take the angular distance from the sun to the moon (253°), and count off this arc counterclockwise from the Ascendant. The result is Capricorn 24°. The lots are used like the planets: if they are aspected by favorable planets, this is beneficial. Although Antigonus did not mention the Lot of Fortune in Hadrian’s chart, its presence amidst the morning planetary cluster would have been a favorable indicator.

8.5 Aspects Once the Places are oriented from the Ascendant, and the planets are placed in their locations, the aspects were determined, namely, the configuration of the planets with respect to each other and to the major features of the chart. Aspects are determined from the Signs the planets are in. Most significant were conjunction and opposition. In the former, the planets’ powers are combined in one Sign. In the latter, the Signs are 180° apart, and the planetary powers compete or conflict with each other. Ptolemy grouped the Signs into triplicities (120° apart), and quadruplicities (90° apart), and planets located in any of these were considered to be in a trine or a quartile in relation to each other. An example triplicity: Aries, Sagittarius, and Leo; a quadruplicity, Leo, Taurus, Aquarius, and Scorpio. Ptolemy pairs each triplicity with one of the four elements. The trine, or triangle, and its lesser version, the sextile (60° apart), were considered the most harmonious and favorable aspects. The quartile, or square, was considered to be unfavorable, partaking of the same bad qualities of opposition, but to a lesser degree. In Hadrian’s chart, the conjunctions are all of benefics, so this indicates good fortune. Aspects can affect the basic character of a planet. In the chart, Jupiter, normally a benefic, is in opposition with several benefics. This lessens their power somewhat, though not nearly as much as opposition with a malefic. On the chart, the aspects are indexed in a table in the lower left.

8.6 Sign Rulership: Houses (oikoi) Each Sign has a special affinity for a specific planet, as indicated in the chart. When a planet is found within its own Sign, its power is enhanced. The sun and moon each govern one Sign, and the other five planets govern two Signs, one of each gender. On Hadrian’s chart, this is indicated in the third concentric band from the outside by the planet’s siglum next to the Sign’s siglum.

8.7 The Terms (horia) The planets’ affinities are distributed somewhat irregularly among the degrees of each Sign by yet another method, based originally on rising times. These terms are depicted in the outermost band of the chart, five to a Sign. The effect of the terms: when a planet is in

Astrology   403 a foreign Sign, if it is in its own term, it has the same power it would have if it were in its own Sign. On Hadrian’s chart, although Mars is in Pisces, a Sign ruled by Jupiter, it is in its own term. Thus, it retains some of its malefic power. This is not mentioned by Antigonus.

8.8 The Decans Originally a coordinate system invented by the Egyptians to mark the annual course of the year in terms of the constellations rising just before sunrise, the astrological decans are 10° segments of the Signs, each governed by one of the Signs, and are indicated on the chart in the outermost band. (See Quack, chap. A2b, this volume.) When a planet is in a decan governed by the Sign of which it is ruler, it exerts the same influence as if it were in its own Sign. Firmicus notes (2.4.4) that some astrologers divide each decan further into three parts, giving nine munifices for each Sign, each governed by a planet, and functioning similarly to the decans with regard to planetary influence.

8.9 Planetary Exaltation and Dejection This system was originally Babylonian. The greatest good fortunes are indicated when a planet is near its own exaltation (hupsōma), and the opposite when near its dejection (tapeinōma). When most of the planets are at the exact degree of their exaltation, this indicates the greatest prosperity. Antigonus does not discuss them.

8.10 Analysis by Antigonus of Nicaea Antigonus’s analysis (Cramer [1954], 1996, 164–​168; Neugebauer and van Hoesen [1959], 1987, 90–​91) demonstrates why Hadrian became emperor and illustrates how an astrologer, familiar with the native’s life, sifts through the multiplicity of possible predictions from every feature, eliminating those that in retrospect do not apply. The sun and the moon together with Jupiter in Place 1, along with the fact that Jupiter, though hidden by the sun’s light, was going to reappear in seven days, all indicate that Hadrian was destined for the purple. Furthermore, the sun and moon, which are here taken to be metaphors for the native, have a complex series of attendants, as in a heavenly imperial procession. The moon is followed by her attendants (doryphoria, spear carriers), the sun, Venus, and Mars. The sun, as universal ruler, rises next, and he was preceded by his attendants, Mercury and Saturn. The moon was also approaching a bright, fixed regal star at Aquarius 20° (which was Formalhaut, in the Southern Fish, conjectures Beck 2007, 126). Firmicus lists four such stars, one each in Leo, Scorpio, Aquarius, and Taurus, and observes (6.2.3) that the moon must be full and rising with the Ascendant for this star to indicate the imperial dignity. Hadrian’s moon, however, is a waning crescent, but that is ignored by Antigonus.

404   Hellenistic Greek Science Antigonus explains the imperial metaphor: Hadrian received the proskynesis (prostration: reverence due an imperial person) because Jupiter was here the sun’s attendant, and because both luminaries were attended by five other planets, clustered in one part of the chart, and this effect is intensified by being in Place 1 (i.e., on the Ascendant). Antigonus attributes Hadrian’s robust size and gracious personality to the luminaries being both in the Ascendant and in Aquarius, an anthropomorphic Sign. His wisdom and education derived from the appearance of Mercury in the morning before the sun, accompanied by Jupiter. The morning rising of these planets indicates that these qualities were engendered in the native from his youth. This reflects an analogy with the beginning both of a human life and of the chart. Next, Antigonus examines the lord of the Midheaven (Mars governs Scorpio), which, being in one of its own terms (in Pisces) is well situated, making the native famous and powerful. All was not roses, however. Hadrian had many adversaries and plotters against him. These were caused by the sun and moon being completely enclosed by the malefics Mars and Saturn. The fact that Hadrian overcame them all was due to Mercury (a benefic) being in conjunction with Saturn in Saturn’s own house, and being in Place 12 (enemies). This last feature, along with Saturn and Mercury being attendants for the sun, made Hadrian wise but treacherous. He was honored and worshipped as a god because Jupiter was an attendant to the sun. The moon being brought to its new moon phase, with Venus in Place 2 in conjunction with Mars, indicates Hadrian will be wed to one woman. The reason he had only one sister was due to the moon’s being in conjunction with Jupiter along with the sun. If the moon had been conjoined with more planets, especially benefics, Hadrian would have had more siblings. (The malefic planets deprive one of siblings.) Furthermore, the Sign in which this occurs can affect the outcome: a bicorporeal Sign, such as Gemini, Sagittarius, or Aquarius, for example, will increase the number. A sister is indicated by the masculine gender of Aquarius, because when the sun and moon conjoin in a masculine Sign, this reduces the number of male siblings. He was adopted (by his relative, Trajan) because Jupiter and the moon were together in proximity to the Ascendant. Hadrian’s childlessness was caused by the sun being in the Ascendant. Saturn and Mercury being in Place 12 (Enemies) was the cause of his trouble with family members. Antigonus says that Mercury is in stasis (rebellion) with Saturn, so they are in conflict in Place 12. Hadrian’s dropsy was caused by the luminaries being surrounded by the two malefics and being in a watery Sign, Aquarius, and the Descendant being surrounded by Places that were under the nefarious influence of the malefics Saturn and Mars, in a terrestrial Sign. Being enclosed by malefic planets and watery Signs suggests suffocation. Antigonus insists that the natal chart alone is insufficient, but one must examine the charts for the third, seventh, and 40th days after birth. (This is called “progressing the chart” and is a method of generating fresh material for interpretation). Doing so, on the 40th day, Mars will be in Aries and the moon in Cancer, with the result that the moon, the planet most closely connected with health, is now attacked by Saturn in opposition, and Mars attacks it from a square aspect, which furnish clues as to Hadrian’s ill health.

Astrology   405 Antigonus next describes how to calculate Hadrian’s lifespan. Saturn in his own house allots 56 years. Venus is in favorable aspect, so she lends an additional eight years, giving Hadrian a life expectancy of 64 years. However, after 61 years 10 months, the Ascendant and the moon came into quartile with Saturn, indicating a serious health crisis. The favor of Venus, however, preserved his life, though not for much longer, as he died at about 62 years six months. This matches the known facts. At age 60, Hadrian became afflicted with a lethal disease, and eventually died of asthma and dropsy. For a retrospective reading, Antigonus has done well. Such examples were collected in an empirical effort to correlate specific features in these charts with definite future outcomes. The following comments from Firmicus Maternus serve to illustrate the nature of predictions drawn from handbooks and as further commentary on Hadrian’s chart. Saturn in Place 12 indicates an uprising of slaves or serious illnesses (3.2.26), but is mitigated by being in aspect with the benefic, Venus (sextile). Jupiter on the Ascendant makes the native famous and powerful, the ruler of a great state, in addition to being cheerful, benevolent, and rich (3.3.1). Mercury in Place 12 makes Hadrian intelligent, and if it is a morning rising, it makes him an important administrator of the public welfare (3.7.24–​5). The waning moon moving toward Venus indicates a position of power, honor, and authority (4.6.2). Saturn in Capricorn indicates a challenging life, filled with reverses attaining the height of fortune, only to lose it (5.3.42). Jupiter and Saturn in conjunction, with Jupiter moving away from the sun in a morning rising, indicates high position and great honor (6.23.3). And lastly, in a section entitled “Royal Charts,” Firmicus states that the sun and moon in a masculine Sign, with benefics in attendance, as in Hadrian’s chart, produces powerful kings ruling great states (7.22.1).

Bibliography Barton, Tamsyn. Ancient Astrology. Edited by Roger French. London, New  York: Routledge, 1994a. —​—​—​. Power and Knowledge:  Astrology, Physiognomics, and Medicine Under the Roman Empire. Ann Arbor: University of Michigan Press, 1994b. Bassi, D., Fr. Boll, P. Boudreaux, Fr. Cumont, A. Delatte, J. Heeg, W. Kroll, E. Martini, A. Olivieri, Ch.-​Ém. Ruelle, M. A. F. Sangin, St. Weinstock, and C.O. Zuretti, eds. Catalogus Codicum Astrologorum Graecorum. 12 vols. in 20 parts. Brussels, 1898–​1953. Beck, Roger. A Brief History of Ancient Astrology. Oxford: Blackwell, 2007. al-​Biruni, Muhammad ibn Ahmad Abu al-​Rayhan. The Chronology of Ancient Nations:  An English Version of the Arabic Text of the Athâr-​ul-​Bâkiya of Albîrûnî, or “Vestiges of the Past,” Collected and Reduced to Writing by the Author in A.H. 390–​1, A.D. 1000. Translated and edited by C. Eduard Sachau. London: W. H. Allen, 1879; repr., Frankfurt-​am-​Main, 1984. Bohleke, Briant. “In Terms of Fate:  A Survey of the Indigenous Egyptian Contribution to Ancient Astrology in Light of Papyrus CtYBR inv. 1132(B).” Studien zur Altägyptischen Kultur 23 (1996): 11–​46. Bouché-​Leclercq, Auguste. L’astrologie Grecque. Paris 1899; repr., Culture et Civilisation, Brussels, 1963. Brown, David. Mesopotamian Planetary Astronomy-​Astrology. Groningen: Styx, 2000.

406   Hellenistic Greek Science Cooper, Glen M. Galen, De diebus decretoriis, from Greek into Arabic: A Critical Edition, with Translation and Commentary, and Historical Introduction of Ḥunayn ibn Isḥāq, Kitāb ʾayyām al-​buḥrān, Medicine in the Medieval Mediterranean. London: Ashgate, 2011a. —​—​—​. “Galen and Astrology: A Mésalliance?” Early Science and Medicine 16.2 (2011b): 120–​146. Cramer, Frederick H. Astrology in Roman Law and Politics. Philadelphia:  American Philosophical Society, 1954; repr. Chicago: Ares, 1996. Cumont, Franz. Astrology and Religion Among the Greeks and Romans. New  York, London: Putnam, 1912; repr. New York: Dover, 1960. Evans, James. “The Material Culture of Greek Astronomy.” Journal for the History of Astronomy 30 (1999): 237–​307. —​—​—​. “The Astrologer’s Apparatus:  A Picture of Professional Practice in Greco-​Roman Egypt.” Journal for the History of Astronomy 35 (2004): 1–​43. Gundel, Wilhelm, and Hans Georg Gundel. Astrologumena:  Die Astrologische Literatur in Der Antike und Ihre Geschichte. Edited by Joseph E. Hofmann, Karl Rothschuh, Heinrich Schipperges, Rudolf Schmitz, Johannes Steudel, Bernhard Sticker and Rudolph Zaunick. Vol. 6:  Sudhoffs Archiv:  Vierteljahrsschrift für Geschichte der Medizin und der Naturwissenschaften der Pharmazie und der Mathematik. Wiesbaden: Franz Steiner Verlag GMBH, 1966. Hegedus, T. M. Early Christianity and Ancient Astrology. New York: Peter Lang, 2007. Hesiod. Theogony. Edited by M. L. West. Oxford: Oxford University Press, 1966. Holden, James Herschel. A History of Horoscopic Astrology. Tempe, AZ: American Federation of Astrologers, 2006. Jones, Alexander. “The Place of Astronomy in Roman Egypt.” In The Sciences in Greco-​Roman Society, ed. T. D. Barnes, 25–​51. Edmonton, Alberta: Academic, 1994. —​—​—​. Astronomical Papyri from Oxyrhynchus:  Volumes I  and II. Philadelphia:  American Philosophical Society, 1999. Löfstedt, Bengt, ed. Zenonis Veronensis Tractatus = Corpus Christianorum, Series Latina 22. Turnhout, Belgium: Brepols, 1971. Maxwell-​Stuart, P. G. Astrology:  From Ancient Babylon to the Present. Stroud, Gloucs., UK: Amberley, 2010. Neugebauer, Otto. “Demotic Horoscopes.” Journal of the American Oriental Society 63.2 (1943): 115–​127. —​—​—​. A History of Ancient Mathematical Astronomy, Part One. New  York, Heidelberg, Berlin: Springer-​Verlag, 1975. Neugebauer, Otto, and H. B. Van Hoesen. Greek Horoscopes  =  Memoirs of the American Philosophical Society 48. Philadelphia: American Philosophical Society, 1959; repr. 1987. Pingree, David. “Political Horoscopes from the Reign of Zeno.” Dumbarton Oaks Papers 30 (1976): 133–​150. Powell, Robert. History of the Zodiac. San Rafael, CA: Sophia Academic Press, 2007. Rochberg, Francesca. The Heavenly Writing:  Divination, Horoscopy, and Astronomy in Mesopotamian Culture. Cambridge: Cambridge University Press, 2004. Rochberg-​Halton, F. “New Evidence for the History of Astrology.” Journal of Near Eastern Studies 43.2 (1984): 115–​140. —​—​—​. “Elements of the Babylonian Contribution to Hellenistic Astrology.” Journal of the American Oriental Society 108.1 (1988): 51–​62. Tarán, Leonardo. Academica:  Plato, Philip of Opus, and the Pseudo-​ Platonic Epinomis. Philadelphia: American Philosophical Society, 1975.

Astrology   407 Tester, S. J., ed. A History of Western Astrology. Woodbridge, Suffolk, UK: Boydell Press, 1987. Walcot, Peter. Hesiod and the Near East. Cardiff, Wales: University of Wales Press, 1966. West, M. L. Hesiod: Theogony and Works and Days. Oxford: Oxford University Press, 1988. Winkler, A. “On the Astrological Papyri from the Tebtunis Temple Library.” In Actes du IXe congrès international des études démotiques Paris, 31 Août—​3 Septembre 2005, Bibliothèque d’étude 147, ed. G. Widmer and D. Devauchelle, 361–​ 375. Cairo:  Institut Français d’Archéologie Orientale, 2009. —​—​—​. “Some Astrologers and Their Handbooks in Demotic Egyptian.” In The Circulation of Astronomical Knowledge in the Ancient World, ed. J. Steele, 245–​286. Leiden: Brill, 2016.

chapter C9

T he L ongu e Du ré e of Al ch e my Paul T. Keyser

Every science evolves over time by small steps, as practitioners develop richer and more powerful understandings. The ancient Greek science of materials, their properties and transformation, came in time to be called alchemy and to comprise models and procedures that focused on the production, or imitation, of valuable substances, especially silver metal, purple dye, and certain gems. What constituted success for the practitioners of that state of the art has often struck scholars after the work of Lavoisier (1789) as delusional or dishonest. But long before Lavoisier, many highly effective techniques had been mastered, and the earlier models of the properties and transformations of materials were consonant with models of the same eras purporting to explain disease or living beings or the cosmos. Because I argue for a long and continuous evolution, this chapter begins at a very early date, indeed; and evidence from prehistoric cultures, as well as from Egypt and Mesopotamia in eras long before Homer, will be important. We do not have access to the theories and models of those prehistoric cultures, and we have only minimal access to the theories and models of the Egyptian and Mesopotamian practitioners. Nevertheless, the techniques being developed display a focus on certain goals and follow specific evolutionary paths. Those goals and paths in turn inform our understanding of the models we do have from early Greek thinkers. The structure of the chapter represents that, as follows: sec. 1, Fire; sec. 2, Colors; sec. 3, Ceramics; sec. 4, Fermentation; sec. 5, Fusible Stone; sec. 6, Artificial Stone; and sec. 7, Theories and Models. (I have advocated this interpretation in Keyser 1990; see also Irby-​Massie and Keyser, 2002, chap. 9, introduction; and Lambert 2005.) The account is roughly in chronological order, with geographical details, because it refers to specific data, but nothing depends on the particular dates or locales used: rather, they emphasize the depth of time and diversity of locale. To cover the wide range of cultures and practices, a capacious definition of alchemy is implicitly at play in this chapter. What later became more precise and focused remains here a collection of related practices and goals, elements from which were later

410   Hellenistic Greek Science compounded and fused into what became known as “alchemy.” This chapter thus deals with what can validly be called the prehistory of the ancient Greek science of materials, their properties, and transformation. Those elements were, as far as we can now tell, first compounded into the Greek art of alchemy by Bolus, on whom see Fraser, chap. D7, this volume, “Alchemy.”

1.  Fire: Transformative and Alive Stone struck on stone to knap a blade will strike out also, from some kinds of stones, sparks, which the Greeks called zōpuron (ζώπυρον), “living-​fire.” When those lively seeds fall upon tinder, fire may sprout. Fire feeds upon, and transforms, its fuel, causing changes of color, texture, and taste. Fire is thus both a material transformation itself and a producer of further transmutations. Fire seems to have another ambiguous nature, existing between life and stuff. Most stuffs are more or less static, maintaining their character over time: bone, earth, rock, wood, and even water—​although it flows and when flowing is called “living” in some cultures (e.g., in Hebrew, mayim-​hayim, as at Numbers 19:17 and Zechariah 14:8). Living things grow, change, spawn offspring, and die. Fire seems to straddle that divide—​it is a stuff and also alive. Fire plays a central role in alchemy, and the technology and science of material transmutation that eventually evolved into Hellenistic alchemy commences at the origin of human technology. Early humans dealt with their world in a variety of what must have been rich and effective ways, since they survived. One particularly powerful means of dealing with their world was fire. Evidence continues to accumulate that humans practiced making fire, in less to more controlled ways, from around 400,000 years ago (Karkanas et al. 2007; Goldberg et al. 2010; Roebroeks and Villa 2011; Berna et al. 2012). The production and control of fire almost seems to define humans as distinct from all other living beings on the earth, as Lucretius (for example) argues (probably following Epicurus), setting fire at the dawn of human social development (5.1091–​1100). When Greeks created etiological myths, they often placed fire at the root of human mastery of nature, for example, in Hesiod’s poems, Works and Days 49–​52 and Theogony 565–​569, and also in Aeschylus’ Prometheus Bound 7–​8. Aeschylus locates fire at the focus of human technology, by naming it πάντεχνος (pantekhnos), which seems to mean “all-​fashioning.” Our mastery of fire was a radical break from prior technology, enabling us to transform and improve stuffs (compare Wertime 1973). Among the uses of fire were treating materials to improve them for our further use. We dried, or smoked, or cooked food, making it easier to digest or store. Stuffs from which we made things, stuffs like wood, and bone, and flint, were fire treated to alter their qualities. Flint is made more knappable after annealing, a technique practiced for over 100,000  years (Domanski and Webb 2007; Richter et al. 2007). On the other hand, certain stones had fire inside them, it seemed, and surviving bits of flint and pyrites appear to have been used to strike sparks to light fires, at least by 50,000 years ago (Stapert and Johansen 1999).

The Longue Durée of Alchemy    411

2.  Colors: Dark, Light, and Red All Over The world is full of marvelous materials: from stones of varying color and frangibility, to flowers and fruits of gaudy hues and diverse tastes, to brilliantly colored birds, bugs, frogs, and snakes. Vision and the eye are so valuable to animals that they have evolved repeatedly, independently among arthropods, among mollusks, and among chordates (Serb and Eernisse 2008), and even some cyanobacteria can “see,” the entire cell constituting a very simple eye (Schuergers et al. 2016). But color vision appears in only some species, for reasons that are not yet clear (Osorio and Vorobyev 2008). Human color vision depends on receptors that, for the most part, perceive three overlapping ranges of the spectrum of light, and different human societies have parceled out their understanding of the colors they perceive in different ways. It is unclear how fundamental or fixed are the terms and structure of human color concepts (Kay and Maffi 1999), but some terms and concepts are found far more widely than others. In many languages, a major aspect of understanding color is a contrasting pair of terms that seem to refer to “black” and “white” or else to “dark” and “light”—​although rarely does that pair of terms form the complete set of color terms. In Greek, the pair is λευκός (leukos: light or white) and μέλας (melas: dark or black); the Latin system is more complex, offering both ater and niger for black or dark, and both albus and candidus for white or light (the distinction may perhaps have been that, originally, candidus and niger referred to shining things, whereas albus and ater to duller things: André 1949). Moreover, very few languages lack a term for “red”—​in Greek, the term is ἐρυθρός (eruthros), and in Latin it is ruber (for further discussion, see Lyons 2003). The artists’ palettes used in the cave paintings of Altamira, Lascaux, Niaux, and Chauvet, among others, appear to be primarily shades of red and black applied to a more-​or-​less white surface (Groenen 1991, 9–​15; Couraud 1992, 18; Clottes 1993). All three terms exist in ancient Mesopotamian languages (Landsberger 1967), in ancient Egyptian (Baines 1985), and in classic Maya (Tokovinine 2012). Those languages, and many more, also have terms for other colors, or other visual aspects of objects (Lloyd 2007, 9–​24), such as luminosity (dark and light and shiny and dull) or saturation (pure or gray). The relevant common denominator among all these systems of terms is that we attach importance, and sometimes even significance, to the colors or luminosities that objects possess, especially the triad λευκός, μέλας, and ἐρυθρός, whatever they refer to (Gage et al. 1999; Petru 2006; Hemming 2012). We attach meaning to colors, and we attach colors to objects we make, and even to ourselves. That is, we seek to change visual aspects (color or luminosity) of what we consider to be our own. Throughout time and space, humans apply dyes and pigments to ourselves and our things, and we do so eagerly. (There is no radical distinction between dye and pigment—​ both are colorants, differently carried in their vehicles, with dye typically intended to refer to a colorant that has dissolved in its vehicle, and pigment one

412   Hellenistic Greek Science that is merely mixed with its vehicle: the same substance may be a pigment in one vehicle and a dye in another.) Dyes derived from plants, especially those that produce browns, reds, and yellows, are frequent in many cultures, despite being often fugacious (Barber 1991, 223–​243). Three colors stand out for their intensive use in multiple cultures: red, the green-​blue range, and purple. There is ample evidence that as early as 100,000 years ago humans collected red ochre, an iron-​oxide mineral, and used it in various contexts (Hovers et al. 2003; d’Errico et al. 2010; Roebroeks et al. 2012). Moreover, there is some evidence that by the same period humans collected yellow ochre, a related iron-​oxide mineral, and heat treated it to produce red ochre (Groenen 1991, 14; d’Errico et al. 2010, 3107). Much later, by ca 7500 bce, some cultures collected red cinnabar, a toxic mercury sulfide mineral much rarer than ochre, which they seem to have used primarily as a pigment (Domingo et al. 2012; Gajić-​ Kvaščev et al. 2012). In some cases the cinnabar was applied to human bones, apparently as an element of mortuary practice (Martin-​Gil et al. 1995). Many prehistoric cultures exploited a wide variety of pigments (for example, in the Mesolithic cave paintings), and scholars have suggested that red was perhaps used to indicate life or health. However, we do not know what prehistoric cultures thought about red, or why they used red pigments. The red pigments may have been symbolic of life, or perhaps of fire, or they may have been somehow purificatory, or even pragmatic: disinfectants for example (Velo 1986, noting that ochre is indeed antiseptic). It may even be that pragmatic uses not infused with symbolism would explain the wide use of ochre, for example, as an essential ingredient in leather tanning (Debreuil and Grosman 2009; Rifkin 2011). If so, then the mortuary use of ochre or cinnabar may indeed have been as a kind of preservative or “embalming agent” (Martin-​Gil et al. 1995). It has also been suggested that ochre was ingested (perhaps unintentionally), which promoted maternal and infant health: that is, the extensive use of ochre for whatever purpose was an adaptively favored behavior, and the people exploiting ochre need not have been aware of the selection pressure (Duarte 2014, who draws a parallel with the extensive shellfish consumption by early humans). Moreover, practice often precedes ideology or theory, and the significance imputed to an activity by its agents likely varied over time: symbols are often multivocal and/​or epiphenomenal. Mineral pigments or vegetable dyes having colors that we designate in English as blue and green are not found as frequently as those labeled red or black (and white pigments are plentiful). Many things that are blue, like the sky and water and some feathers (if and when they are perceived that way), cannot yield a stuff that would impart color to other stuffs. Although there are also some green things, like feathers or scales, that yield no dye or pigment; most things that are green, like the leaves of plants, yield a substance whose color is fugacious. Some rare green or blue stones—​jade, malachite (with its rarer relative azurite), and lapis lazuli—​were collected, valued, and exported. Several cultures did discover a means of producing color-​fast pigments in the blue-​ green range, and in those cultures those pigments were highly valued (Pozza et  al. 2000; Berke 2007). From ca 4500 bce, Egyptians produced a blue to green material that we call “faience,” made by fusing sand, salt, lime (from shells or stone), and

The Longue Durée of Alchemy    413 some copper mineral, probably malachite (Nicholson and Peltenburg 2000; Lee and Quirke 2000, 108–​113; Hatton, Shortland, and Tite 2008). The recipe was also known in Mesopotamia, at least by ca 1500 bce, and the substance was produced in a variety of colors (Moorey 1994, 166–​186). The material appears to have been produced, or at least exploited, in Mycenaean Greece, where it was given a name that is probably the ancestor of the word κύανος (kuanos: Nightingale 1998). The Greek epics record its continued use and value (Iliad 11.24, 35; Odyssey 7.87), and later writers mention its means of production (Theophrastus, Stones sec. 55, and Vitruvius 7.11). A pigment very similar to Egyptian blue was produced and valued by the Han dynasty Chinese (Berke and Wiedemann 2000). Another blue material, indigo dye, was in some times and places extracted from the Indian legume Indigofera tinctoria L., or in other times and places from woad, a plant in the mustard family, Isatis tinctoria L.  (Balfour-​Paul 2000, 91–​96, listing also numerous other species used in other times and places). The color and dye are attested in cuneiform from ca 1700 bce as uqnâtu (lapis-​lazuli color, from uqnû, lapis lazuli: Gelb et  al. 2010, 193–​202). There is some evidence that Mycenaeans used a dye that was blue (Melena 1987, 224–​226; Palaima 1991, 293). In China by the early Han dynasty (ca 200 bce), indigo dye was extracted from a plant in the buckwheat family (Needham, Daniels, and Menzies 1996, 15–​19: Polygonum tinctorium Aiton 1789). In all cases, the dyeing process requires the reduction of the blue extract to a colorless but soluble material (chemically a very close relative of the purple dye, below), into which the yarn or fabric is immersed, and infused with the material, with the result that subsequent exposure to the (oxygen in the) air renders the colorless material again blue, thus dyeing the yarn or fabric (Beijerinck 1899; Koren 1995, 121–​123; Balfour-​Paul 2000, 100–​107). The Maya made and valued a blue pigment by infusing a certain clay with indigo (Arnold et al. 2008). Beyond the shades of red, and the blue-​green range, the color purple was valued by cultures that managed to produce it (Herzog 1987; Koren 1995, 117–​119; James et al. 2009, 1114). Only recently has the production of a purple pigment during the Han dynasty been recognized (FitzHugh and Zycherman 1992; Pozza et al. 2000; Berke 2007), but long before that dynasty, purple was produced and intensively used. In addition to gathering saffron pollen, whether for medicine or for dyeing, from ca 1600 bce the Minoans also gathered the sea-​snails from which a purple-​dye precursor could be extracted (Reese 1987). Moreover, they extracted and processed it into purple dye (Aloupi et al. 1990) and used it as a pigment in frescoes to depict purple-​dyed cloth (Sotiropoulou and Karapanagiotis 2006). The industry was practiced on the east coast of the Mediterranean by ca 1400 bce, and Tyre became famous for producing the dye. The highly valued dye was also produced, or at least exploited, in Mycenaean Greece, where it was given a name that is probably the ancestor of the word πορφύρεος (porphureos:  Palaima 1991, 289–​291). The Greek epics record its continued use and value (Iliad 8.221, 24.796, etc.; Odyssey 4.115, 19.242, etc.), and later writers describe the harvesting of the snails (Aristotle, History of Animals 5.15 [547a4–​b1]; Vitruvius 7.13; Pliny 9.125–​132) and even attempt to give the recipe for producing the dye from the snails (Pliny 9.133–​135; cf.

414   Hellenistic Greek Science Steigerwald 1986). That recipe was complex and marvelous, requiring that a tiny gland from the snail be gathered, then warmed and fermented with salt or urine in a tin-​plated vat; the presence or absence of sunlight may have played a role (Michel and McGovern 1987, 1988, 1990). The sufficiently ancient and mysterious origins of purple dye opened a space in the Greco-​Roman imagination for a legend of accidental discovery by Heracles’ dog, chewing snails on the beach and dyeing his muzzle purple (Pollux 1.45–​49).

3. Ceramics: Marvelous Mud The earliest stones that we altered by fire seem to have been reddened ochre and annealed flint. The first artificial stone seems to have been moist clay or loess that had been baked in the fire; next came plasters created out of fired white stones ground and mixed with water. Humans laid their fires on sand, rock, or any convenient surface of the earth, and normally an open hearth on the ground will discolor and dry its bed. In some cases, ca 28,000 years ago, hearths were deliberately constructed from wet clay, which was hardened by the superposed fire (Karkanas et al. 2004). The discovery that clay and loess, two soft “earths,” could be baked to a stony hardness may have seemed marvelous. (Clay and loess are two distinct kinds of soft fine-​grained silicate minerals that become plastic when sufficiently wet and have a relatively low fusion temperature.) The earliest evidence for this practice of cooking mud is dated to ca 26,000 years ago, from a place now called Dolní Věstonice, where loess was hardened and even shattered (Vandiver et al. 1989). Technical analyses suggest that the loess was wet enough when put into a hot enough fire that the objects shattered (as thick, wet clay will do when heated excessively). The objects formed were figurines and irregular forms, none of which was shaped as a conventional container or vessel: that is, these early things were not “pottery” because they were not “pots.” Nevertheless, the transformation itself was accomplished, and amounts to a transformation of a soft, wet plastic substance into a hard, dry, brittle substance. The same transformation was later used to create fired clay containers. The Jomon pottery of Japan, dated to ca 13,000 years ago and later, was regarded by archaeologists, from 1960 through the early 2000s, as the earliest pottery in the world (Rice 1999, 14–​15). But subsequent research based on newly available evidence now suggests that baking clay into container shapes began by about 20,000 years ago, in East Asia (as suggested by Kuzmin 2006; soon confirmed through radiocarbon dates by Wu et al. 2012; and then discussed by: Kuzmin 2013; Silva et al. 2014; and Gibbs 2015). A more elaborate transformation was the artificial production from stones of what we may call “white mud” and its subsequent reconstitution as a stone, once again resistant to water. Many rocks are composed primarily of calcium carbonate (notably, “limestone” and marble), and some are composed primarily of calcium sulfate (notably, alabaster and gypsum). Such rocks, when baked at a high enough temperature, are transformed into white and crumbly material, “lime” (calcium oxide). When this is

The Longue Durée of Alchemy    415 powdered, it can be mixed with water to produce a “white mud” that gets hot and soon hardens into a moderately water-​resistant “rock,” that is, plaster. Moreover, the plaster will be much more water-​resistant if one adds to the mix enough of the right kind of powdered stone (silicates such as volcanic ash, for example); the result is referred to as “pozzolanic” cement. Simple plasters were produced by ca 14,000 years ago, in the Sinai Peninsula, and used as adhesives (Kingery et al. 1988, 226–​227). They were also used in greater bulk as components of architecture (walls, floors, benches, and the like), at various sites in the eastern Mediterranean, from at least 7500 bce (Kingery et al. 1988, 223–​226; Carran et al. 2012, 118–​119). Around the same period, also in the eastern Mediterranean, these simple plasters were used to coat baskets, producing a container capable of holding liquids (Kingery et al. 1988, 227–​231): these containers are distinct from those made of baked clay, which are not found in this region until over a millennium later. The “lime” can be produced in simple open-​hearth fires, or in fire pits, as found in contemporary sites (Goren and Goring-​Morris 2008). Calcium sulfate rocks, when baked at a much lower temperature, produce a different white and crumbly material, which when mixed with water produces a “white mud” that also hardens, but is not very water resistant. This gypsum plaster (our Plaster of Paris) is attested in Mesopotamia from around the same period, and was used in architecture and vessels (Kingery et al. 1988; Moorey 1994, 330–​332). On the other hand, the more water-​resistant plaster, the pozzolanic cement, is also attested ca 7500 bce, at a site in Anatolia (Hauptmann and Yalçın 2000), and often later in the Mediterranean area (Theodoridou et al. 2013), as well as among the Maya (Gillot 2014). The description by Vitruvius of the Roman version of the process includes ingredients, proportions, and observations about the heat created when the mixture forms (Vitruvius 2.5.1–​2, 2.6.1–​4, and 5.12.2–​3; cf. Pliny 35.166; Jackson and Kosso 2013). Moreover, lime plaster was used to create human sculptures and to coat human skulls at Jericho and elsewhere, ca 8000 to ca 5000 bce (Kingery et al. 1988, 231–​234; Goren et al. 2001; Özbek 2009). The plaster on the human skulls was often painted with a thin outer layer of plaster mixed with red pigment, along with other modeling techniques that were used to create an overall lifelike appearance. This should be compared with the technique of painting human bones with red (sec. 2): in both cases, scholars have perceived a symbolic revivification of the fleshless remains (cf. Ezekiel 37:1–​14; Kuijt 2008).

4.  Fermentation: Unseen and Enlivening Powers Fire is transformative, and already some Greeks and Romans imagined that the first or foremost transformation wrought by fire was cooking: either cooking was foundational (Hippocrates, On Ancient Medicine sec. 3, Littré 1.576–​578), or else, the first

416   Hellenistic Greek Science thing we did with fire was to cook (Lucretius 5.1101–​1104). That notion has been hotly disputed by modern scholars, but evidence accumulates to show that humans cooked from very early times (Organ et al. 2011; Gowlett and Wrangham 2013; and Carmody et al. 2016). Food could be transformed by fire—​it could also be transformed by another, less manifest, power. When our diet came to include a larger proportion of seeds, we processed those into porridge or even into dough, both of them cooked. But a crucial transformation occurred when clay-​like dough, or stewed fruit, was infected with the invisible power of yeast. From dough that power produced leavened bread, and from stewed fruit that power produced wine, each of them a substance with properties entirely dissimilar from the parent stuff. The first artificial food, whether bread or wine, was produced from ordinary food by mysterious and fickle forces. Those forces were mastered to produce a wine-​like potion from bread itself: beer. Residues in pots show that a fruit and honey wine was being made by 6500 bce (McGovern et al. 2004), and inscribed records from Egypt and Mesopotamia attest to the regular production of beer from bread by a multistage recipe (Deheselle 1994; Samuel 1996). It seems likely that some form of brewing was practiced by ca 9500 bce (Hayden et al. 2013). Wine and beer, of course, contain a power that serves to transform our selves, or at least, our experience of ourselves.

5.  Fusible Stone: Metals as Failed Flints Shiny yellow pyrites (πυρίτης) was our “fire-​stone” from which we expelled inherent sparks (Dioscorides 5.25; Pliny 36.137–​138; Stapert and Johansen 1999). But other bright heavy stones of similar colors, though useless for starting fires, were found soft enough to carve, in the way that tough wood or bone can be carved, then to pound out like stiff clay or dough: first copper and then gold were found “native” and hammered for decoration and tools. It seems that this practice, starting around 12,000 years ago, may have initially been practiced to produce objects for decoration, and their use in tools did not displace the use of the many other stones used for tools (Craddock 2000; Roberts et al. 2009). Flint is improved by annealing it in fire (sec. 1), whereas copper becomes softer if heated and then quenched (but becomes  harder when allowed to cool slowly)—​ annealed copper is found as early as ca 10,000 years ago (Roberts et al. 2009, 1013). Moreover, gold and copper in a hot enough fire do not harden like wood or clay, or burn like limestone, but melt like fat, ice, or wax. The temperature range in which clay or loess permanently harden, and in which limestone burns, is very close to the temperature range in which copper and gold melt (all ca 1000ºC). The casting of native copper and gold was practiced by ca 8,500 years ago, in the highlands of Iran (Craddock 2000, 153–​ 154; Roberts et al. 2009, 1013).

The Longue Durée of Alchemy    417 A further and possibly unique development, by ca 7,000 years ago, was the smelting of soft, red copper from various hard rocks, colored green or blue, that is, rocks that look nothing like copper (Craddock 2000, 155–​161; Roberts et al. 2009, 1013; Thornton 2009, 308–​316; Radivojevic et al. 2010). This appears to be the first artificial production of a natural substance: copper had been known for thousands of years, but now it could be cooked up, that is, produced by transforming certain colorful heavy rocks through a complex fire-​based process. Another heavy rock, but one easier to cook, was galena, a shiny, gray lead mineral that, when cooked at relatively low temperatures in the right conditions, yields a new substance, rarely or never seen before: white silver, produced regularly by ca 4000 bce (Roberts et al. 2009, 1015). This was a new material, with properties similar to, but distinct from, those of copper and gold. From our point of view, there were now three “metals” in use—​but we should be wary of retrojecting the category “metal” into these cultures (see sec. 7). By ca 3500 bce, for reasons that are not yet clear, some of the people smelting copper were also creating yellow bronze, either by using special copper-​arsenic ores or else by co-​smelting copper ores with varicolored arsenic or tin ores (de Ryck et al. 2005; Roberts et al. 2009, 1016–​1018). Color transformations were long and widely familiar from pottery, and dyes used in woven cloth (sec.2): now metals too could be colored (compare Aristotle, Generation and Decay 1.10 [328b13–​14]; Theophrastus, On Stones sec. 49). Moreover, the yellow-​colored metal was easier to cast, and tools made from it could be made harder, sometimes a desirable quality. Around 2500 bce, somewhere north of Mesopotamia or west of China, the smelting of silvery iron was achieved from red ocher, long a personal and ceramic pigment (Yalçın 1999). Here again, as for copper, a long-​known but rare substance could be cooked up in a complex fire-​based process. The new material was harder to produce than bronze, at first worth far more than its weight in gold, and did not become widespread until ca 1500 bce. Iron had been known since ca 3200 bce, as a rare material, a star-​stone, that is, a meteorite, dropped from heaven (Rehren et al. 2013). Just as for copper, this was the reproduction of a natural material by artificial means.

6.  Artificial Stone: Glass The Egyptians fused sand and other materials to produce the blue to green material that we call “faience,” which was used and perhaps even produced in early Greece, as κύανος (sec. 2). The smelting of metal from ores will often produce a glassy slag, and either that, or the making of “faience,” may have influenced the development of glass itself (Mass et al. 2001). Besides glassy slags, another connection between metal and glass is that what we call metals, as well as glass, plus some stones, all shared the mysterious property that they could be melted like fat, ice, or wax, and when cooled they solidified again. However, the other properties of glass, such as frangibility and color, seemed to

418   Hellenistic Greek Science distinguish it from metal: cf. pseudo-​Aristotle, Colors sec. 3 (793a13–​19), on the sheen of metals, in contrast to the watery surface sheen of transparent glass (794a2–​6). In any case, glass seems to have been made occasionally as early as ca 2300 bce and became a regular item of commerce and use from ca 1500 bce, in both Egypt and Mesopotamia (Henderson et  al. 2010); scholars hypothesize invention in Syria (Oppenheim 1973; Rehren and Freestone 2015). Mesopotamian writers recorded precise and careful recipes for the production of glass (Oppenheim 1970), and we know that a key ingredient was plant ashes, for which “natron,” a salt-​like mineral found in Egypt and elsewhere, was substituted in Greco-​Roman times (Shortland et al. 2006). This new material was perceived—​and traded—​as a valuable and artificial stone. For much of its history, glass was not a “fake” gem, but a gem artificially produced, which the Egyptians called “molten stone,” according to Herodotus 2.69.2 (Duckworth 2012; Nicholson 2012). Trade in various colors of glass, that is, in various kinds of artificial gems, was extensive (Henderson et al. 2010), and technical analyses show that Egyptian and Mesopotamian glass reached Mycenaean Greece (Walton et al. 2009).

7.  Theories and Models: Inward Causes of Outward Changes The foregoing account emphasizes processes that transform the color or other properties of substances or that extract (create) substances from materials that do not seem to “contain” them. Some of the extracted (or created) substances were novel, such as ceramics (before 20,000 bce), “faience” (ca 4500 bce), silver (ca 4000 bce), glass (ca 2300 bce), or purple dye (ca 1600 bce); others were long known (copper, gold, iron); and some were altered and improved versions of known substances (wine from fruit, plaster from limestone, bronze from copper, and beer from bread). We have no access to the models that those prehistoric cultures created and used to understand and explain the transformations they practiced. We can, however, examine both the variety of Greek models, as well as at some data from outside Greco-​Roman culture. For example, the Chinese “five phases” (wu hsing, 五行), wood, fire, earth, metal, and water, were conceived not as underlying immutable “elements” but as observable stations or “phases” of an endless cycle of transformations (Lloyd 2012, 21–​26). The earliest Greek thinkers wondered what was the ultimate stuff of the cosmos, guessing water or air or fire or earth—​or all four (Kirk, Raven, and Schofield 1983). That is, in contrast to Chinese thinkers, the Greek thinkers sought a stable stuff, or small set of stuffs, that lay beneath the transformations visible in the world and in the workshop. That early choice established a kind of paradigm within which later Greek thinkers worked. Moreover, having chosen “elements” as the fundamental paradigm, the problem became to explain change; in contrast, with a cycle of ever-​changing “phases” as the foundation, the problem would be to explain persistence and stability.

The Longue Durée of Alchemy    419 Given the central role of metals and their transformations in alchemy, it is also crucial to note that no Greek theory considered metals, any more than glass, as elemental in themselves. Before considering the early Greek theories of material transformation, we need to look at how “metals” were perceived and conceived. In Greek thought, metals were never elemental in themselves. Moreover, even a Greek or Roman concept of “metal” in itself is only weakly attested at best; and certainly there was no concept of “metal” in our sense of a material that is fusible, malleable, opaque, specular, and miscible or susceptible of alloying with others of its kind. There was no agreed Greek term that maps exactly to our “metal,” and μεταλλ-​(metall-​: literally, “(found) with others”) usually refers to things “mined.” Aristotle may approach the concept of “metals” in Meteorology 3.6 (378a19–​28), where he distinguishes ὀρυκτά, the “dug-​ups” (orukta, e.g., realgar, sulfur, ochre, and cinnabar) from μεταλλευτά, the “found-​withs” (metalleuta, e.g., iron, gold, and copper; cf. On Sensation sec. 5 [443a15–​21]). However, in Meteorology 4.10 (388a10–​13), he lists “stone” among the metalleuomena. (Theophrastus, Stones sec. 1, indicates that the metalleuomena were created from water, in contrast to other substances created from earth.) Materials such as gold, silver, copper, and so on, had fusibility as a primary characteristic, since the time of Plato or before. However, both Plato, Timaeus 59b–​c, 61a–​c, and Aristotle, Meteorology 4.10 (389a7–​9), include glass, some stones, and some metals as fusible substances, composed primarily of the element “earth.” Our concept of “metal” is perhaps first in view in Isidore, Etymologies 16.17.2, as metalla, where he lists precisely seven species: aurum, argentum, aes, electrum, stagnum, plumbum, and ferrum (approximately: gold, silver, copper-​and-​bronze, silver-​gold-​alloy, tin, lead, and iron; see Halleux 1974, 19–​60). Two examples, mercury and iron, will highlight this contrast. We commonly think of mercury as a metal, which happens to be molten at standard temperatures: but it was not widely recognized in Greek or Roman thought as a member of the same category as gold, silver, copper, tin, lead, and their alloys (Halleux 1974, 108, 179–​188). A few authors, however, do refer to mercury by catachresis as χυτὸν ἄργυρον (khuton arguron), that is, “molten silver”: Aristotle, On the Soul 1.3 (406b18–​22, perhaps from Democritus), plus Meteorology 4.8 (385b1–​5, things that cannot be frozen, like oil and honey), and Theophrastus, Stones sec. 60 (see below). On the other hand, although iron was usually listed with gold, silver, copper, and so on, and was thus implicitly a “metal” (explicitly so in Pliny 34.142–​143), there seems to be no Greco-​Roman text that states clearly that iron was fusible—​because the normal melting point of the iron alloys known in ancient Europe and western Asia was higher than could be attained in their kilns. (The text that comes closest is Aristotle, Meteorology 3.6 [378a27–​28], who gives iron as one example of substances that are either fusible or malleable, with two other examples, gold and copper, that are each both fusible and malleable. However, in Meteorology 4.6 [383a30–​ b5], he describes some stage of the smelting of iron as “growing soft” like horn, not melting; cf. 4.9 [385b6–​12], 4.10 [388b30–​33]; Pliny 34.146; and Halleux 1974, 189–​198.) That is, although listed with other “metals,” iron seemed to lack a characteristic of those other “metals” that had been considered essential since the time of Plato and Aristotle.

420   Hellenistic Greek Science Turning now to the early Greek theories, possibly as early as Alcmaeon of Croton (around 500 bce), there was a guess that living bodies were formed of a blend of several internal juices. That idea of a limited list became also a kind of foundational choice for later theories. Alcmaeon’s near-​contemporary, the famously cryptic aristocrat Heraclitus of Ephesus, argued for the inherent unity and dynamic balance of opposites, manifested in the continual and eternal changes of the cosmos and its stuffs. For Heraclitus, “fire” seems almost to mean “energy” and is the immortal fundamental principle of the world. This recognition of a special place for fire within a limited list of “elements,” and as playing a key dynamic role in an elemental system, was to persist in later models. The aristocrat Empedocles of Acragas (ca 455 bce) hypothesized that the whole cosmos had been cooked up from four essential divine ingredients: earth, water, air, and fire. These could mix and separate, but none of the four could ever die or decay. Empedocles theorized that fire is “bright” and water is “dark” (cf. sec. 2 above), and the other colors, such as red or green or blue, seem to be produced by suitable mixtures of the two primary colors (Ierodiakonou 2005). His near-​contemporary Anaxagoras of Clazomenae, working in Athens, proposed instead that every sensible quality was due to infinitesimal “seeds” pervading each part of the cosmos. That is a model that can well explain any transformation, at the price of giving no guidance on which transformations are more possible or in what way. Democritus of Abdera (writing ca 430 bce) chose as his elements a pair of concepts, indivisible units (atoms) strewn and mixed in a void, and those atoms generated sensible qualities by their mutual arrangements and motions in that endless void. On this theory, lead was softer and heavier than iron because its atoms were more closely and more regularly packed. For Democritus, the atoms of gold, for example, or fire, were in themselves immutable, but any particular quality manifested in an observable material could be created by possibly multiple combinations or arrangements of atoms. Theophrastus records that Democritus hypothesized four primary colors: white, black, red, and green (cf. sec. 2 above; On Sensation sec. 73–​75, Democritus fr. 68 A135 DK), which Democritus probably argued were produced by four distinct kinds of atomic arrangement (Furley 1993). Plato of Athens sought to found a maximally probable account of colors and stuffs upon a mathematical basis, constructing the four Empedoclean elements from fundamental triangles grouped into four of the five regular polyhedra (the dodecahedron representing the zodiac); cf. Gregory, chap. B1, this volume. Plato explained elemental transformation and chemical combination by their rearrangements, and sensible and physical qualities by their shapes (Timaios 52–​64; Lloyd 2006). Plato, like Pindar before him (Olympians 1.1, Isthmians 5.1–​3), saw metals as watery because they were fusible. Plato’s student, Aristotle of Stageira, returned to the primitive and unanalytic notion that qualities such as color, density, hardness, and so on, were essential and primary entities which attached to quality-​less substrate matter; in his model, every stuff was mixed from some of the four Empedoclean elements, which were themselves explained as products of inseparable primary opposites hot/​cold and wet/​dry (Bolzan 1976). Elemental transformation occurs because of a change in a substance’s

The Longue Durée of Alchemy    421 constituent opposites, so water becomes earth when wet departs so that dry arrives. Most ordinary substances of the earth are formed by the agency of a pair of “exhalations” (anathumiaseis), “metals” (metalleumena) primarily by the moist one, and stones by the dry (or smoky) one. All metals except gold are affected by fire and contain some earth (from the dry exhalation); apparently the baser metals were “dryer.” In addition to the theory expressed by Aristotle in Meteorology book 4, he also addresses issues of mixing and transformation in his book Generation and Decay (whose title may also be translated in other ways, such as, “Coming to Be and Passing Away”). There he uses the reciprocal transformation of water and air as a running example of how elements are transformed, whereas their underlying “matter” (hulē) persists, and he explains other transformations in the same way: 1.1 (324b26–​315a3), 1.2 (317a27–​29), 1.4 (319b14–​24), 1.6 (322b1–​21), 2.1 (329a24–​329b3), and 2.4 (331a7–​332a2). He points out that monists explain change as the alteration of the underlying single substance, whereas pluralists explain change via the mixing of their several primordial stuffs: 1.1 (314b1–​12). His own theory can indeed be analyzed as an attempt to combine the features of monism (the single underlying quality-​less hulē), with the features of pluralism (the multiple fundamental qualities, hot/​cold, wet/​dry). Aristotle’s model of mixing allows for transformation, it seems, so that when mixing occurs among ingredients that are more or less balanced in powers, each small bit of one ingredient meets and merges with a small bit of another, with proportionately blended properties (Cooper 2004). On this model, much more could be done to analyze compounds than on prior models (Viano 2015). This model also provides an opening for explaining or proposing that some ingredients have a disproportionate effect. Unlike a small piece of wood put in a large fire, or a small drop of wine in a large jug of water (Generation and Decay 1.10 [328a26–​28]), some ingredients might transform the larger substance. Perhaps tin in copper (see sec. 5 above: Generation and Decay 1.10 [328b13–​ 14]; and Theophrastus, Stones sec. 49), or dyes in cloth, or spices in food, were examples of this kind of disproportionate transformation. For Aristotle, color was a secondary quality produced either by the interaction of our eyes with stuff or perhaps from the particular mixture of the four elements in the colored thing. After Aristotle, the debate widened, and various philosophers suggested various alternative theories or adjustments to existing theories. Theophrastus problematized “fire” as an element, by pointing out that unlike the elements air, water, and earth, it required fuel, could be generated, and had many other peculiar properties, and Theophrastus seems to suggest that perhaps fire was not elemental, but that instead heat was (Robinson 1959; Keyser 1997, 377). Theophrastus composed a number of short works (one papyrus roll each) on a variety of topics, and one of those that survives concerns fire. In that work, Theophrastus points out that the element fire has special properties compared with the other elements: it generates itself, it destroys itself, and most forms of fire are “with violence” (μετὰ βίας), that is, implicitly “unnatural”: sec. 1. Unlike other elements, fire requires a substrate, its fuel: sec. 3–​4. As Heraclitus said (above), the element fire penetrates everywhere and is universally distributed:  sec. 9.  Similarly, in his monograph On Stones, Theophrastus not only includes recipes (below) but also theorizes the

422   Hellenistic Greek Science stuffs that emerge from the earth; he also treated things from the earth in a lost work “on metals,” but we do not know exactly what was included in that work. In On Stones, sec. 1, he distinguished the metalleuomena as being created from the element water, in contrast to other substances created from the element earth. He also records the marvelous transformative properties of some stones (sec. 4, 23, 28–​29, 45) and remarks that stones “grow” and “give birth” (sec. 5, as also in Pliny 10.12, 36.149–​151, 37.154, and 37.163). Straton of Lampsacus may have attempted the opposite, that is, widening the list of elements to include many perceptible properties, not necessarily arranged in a system of opposites (Keyser 2011). That would allow for better explanations of the complexity of mixture and transformation, but might not guide exploration very well, except where perceptible properties happen to be closely tied to composition. Because alchemy has seemed to scholarship to be primarily about recipes and practices, only texts that include explicit recipes or practices have usually been accounted as evidence of a genre “alchemy.” However, that introduces a false dichotomy since most Greek texts that survive from the period before ca 200 bce are oriented toward theory, not practice, so that for any science, what survives from that period is primarily the models, not the procedures or recipes. Even the Aristotelian Meteorology book 4, which treats the properties and composition of substances in great detail, is primarily theoretical and analytic, and offers not a single recipe. One example of an early “alchemical” recipe is found in Thucydides, who twice records (2.77.3 and 4.100.2–​4) the approximate recipe for an incendiary mixture (wood, sulfur, and pitch) analogous to “Greek Fire”—​presumably only because it was of interest for his account of the war. One notable exception to the loss of early recipes is the book On Stones by Theophrastus, written ca 315 bce, where he records a number of recipes. He reports on substances that are produced both by nature, as well as by human artifice: the first he calls αὐτοφυής/​autophuēs, or else αὐτόματος/​automatos; the second he calls τεχνικός/​ tekhnikos, or σκευαστός/​skeuastos “prepared,” or κατ’ ἐργασίαν/​kat’ ergasian “from the workshop.” In particular, he records recipes for several artificial stones, mainly pigments (cf. sec. 2, above). Several of the recipes involve transformations between a metallic and a stony substance. The enabling power of the transformation is usually either fire, or else sour wine, that is, the power of fermentation is used (cf. sec. 4 above). Several are complex and marvelous. Theophrastus records these six recipes: • Sec. 53–​54: yellow ochre (ὤχρα/​ōkhra) when heated in closed, airtight pots turns to red ochre (μίλτος/​miltos), allegedly discovered by Kudias (Cydias) the painter (ca 355 bce), but perhaps only first published in Greek by him since it had been known for a very long time. • Sec. 55: the artificial and natural κύανος/​kuanos (he does not actually give the full recipe, but indicates it is produced in Egypt using fire and grinding). • Sec. 56:  from the metal lead (usually characterized as black), the white stony pigment ψιμύθιον/​psimuthion is produced, using sour wine, followed by repeated washing and grinding (this is the pigment “white lead,” a lead carbonate).

The Longue Durée of Alchemy    423 • Sec. 57: from the red metal copper, the green stony pigment ἰός/​ios is produced, also using sour wine, and the same washing and grinding process (this is the pigment “verdigris”). • Sec. 58–​59:  from a certain sand, Callias of Athens discovered that cinnabar is produced by grinding in stone vessels and washing in copper ones. • Sec. 60: from the red stone cinnabar, the strange substance “molten silver” (χυτὸν ἄργυρον/​khuton arguron) is produced, by grinding the red sandy substance mixed with sour wine in a copper mortar with a copper pestle. Theophrastus, On Stones, thus records an early stage of the development of the kind of Greek theories and recipes that would later be included in the genre of “alchemy.” Moreover, his was not the only book to offer such recipes, since he cites several others (sec. 53, 59), long ago lost. Later works preserve other complex and marvelous recipes, for Egyptian blue (Vitruvius 7.11), purple dye (Pliny 9.133–​135), and for making pozzolanic cement (Vitruvius 2.5.1–​2, 2.6.1–​4). Greek philosophers were interested in why and how the colors of things could change (Ierodiakonou 2015), given that the things were composed of unchanging elements: different elemental mixtures might well manifest different colors, but how could a substance change its color? Lucretius, probably reproducing the theory of Epicurus, offers the explanation that the color of the sea changes, just because its atoms rearrange (2.757–​767); the Stoics, on the other hand, seem to have held that changes in color without change in composition can only be due to change in perception (Seneca, Natural Questions 1.7.2). For Stoics, beneath the four elements lay the even more fundamental principles of god and matter: this was a matter that had qualities (like extension) but acquired “secondary” qualities like color and hardness in various contingent ways (Gourinat 2009), thus opening up the prospect of transformation of stuffs, such as the rock galena into the metal silver. The Stoic Chrysippus, ca 240 bce, argued that the four elements were produced out of an original “fiery” state, which was also elemental (Cooper 2009). Moreover, his model of mixture allowed for compounds in which the proportions were far from similar, so that, for example, he rejects Aristotle’s assertion that a drop of wine in a large container of water would lose its vinous character, and he explicitly allows that gold could be extended by being mixed with certain powerful substances (φάρμακα/​pharmaka, as in Theophrastus, On Stones sec. 55; Long and Sedley 1987, sec. 48: 1.290–​294, 2.287–​291). His theory would thus allow for small amounts of tin changing the color and other properties of a large amount of copper. It is Bolus of Mendes who is usually credited with combining Greek theories with Egyptian techniques to found “alchemy”; he wrote around 200 bce, apparently often under the name Democritus, but as noted, earlier writers (such as Theophrastus) were already providing recipes. (There is evidence that recipes from this tradition, for the production or augmentation of silver, were in use well before 200 bce: Keyser 1995/​6.) After Bolus, there are many texts, hard to date precisely, and often attributed to “Democritus.” The primary goals of alchemy, as laid down in these early Hellenistic texts, were the production or augmentation of gold, the same of silver, the production of gems, and the

424   Hellenistic Greek Science production of valuable dyes, especially purple; in addition, some texts either use fermentation as a guiding metaphor or even speak of personal transformation. It is clear how closely those goals adhere to the long-​known processes delineated above. (For the further developments, in the Greco-​Roman and Late Antiquity periods, see the essays by Fraser, chap. D11, and Viano, chap. E5, this volume.) Thus, much of ancient Greco-​Roman alchemy was no delusion or deception: it was instead the oldest, broadest, and most accomplished of the ancient sciences, deserving a place in scholarship equal to that usually granted to “astronomy” and “medicine.” If many of its theories, and some of its goals, would no longer pass muster as valid, let us recall that neither would the theories of geocentric astronomy nor those of humoral medicine, and yet ancient Greek astronomy and ancient Greek medicine are typically regarded as the “best” of the ancient sciences. Inadequate theories will produce bad predictions and goals along with the good:  the theories of ancient alchemy allowed workers to produce a wide variety of outcomes they desired, dyes and pigments, glass and metals, objects of use and beauty.

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chapter C10

Parad oxo g ra ph y Klaus Geus and Colin Guthrie King

1. Introduction Strangeness attracts. The odd and the wondrous fix our attention and beg for explanation. There is therefore nothing strange about the fact that Greek literature, from the very beginning, features objects of wonder. In Homeric epics we find things (in particular, products of craft) that are “a wonder to behold” (thauma idesthai: Iliad 5.725, 18.377; Odyssey 6.306, 7.45). Herodotus announces as a purpose of his inquiry the preservation of “deeds great and wondrous” (erga megala kai thōmasta: Histories 1.1.3), and this includes both natural wonders (e.g., noteworthy geographical features or animal behavior: Histories 3.113.1, 4.53.3) and human and technical achievements “well worth seeing” (axiotheētos, e.g., with relation to Egyptian architecture, Histories 2.163.1, 2.176). The collecting of lore concerning wondrous places, peoples, and things is characteristic of such accounts, which are by turns geographical and ethnographic. This modus operandi became explicit and programmatic in a genre of literature dedicated specifically to the collection of what might be called oddities. The main source for this literature was not observation or experience, but other literature. Historiography, poetry, and especially the natural science of Aristotle and the early Peripatos served as the sources for this new genre, formed at the end of the 4th century bce. They were mined for the extraction of accounts concerning “wonders” (thaumata), “singular” things (idia), and those that occur against expectation (paradoxa). The purpose of this article is (1) to describe the genesis and development of the genre and define its common characteristics; (2) to introduce its main authors; and (3) to explain its importance for the history of ancient science. With this aim in view, we shall also identify and analyze the epistemic norms of plausibility and regularity implicit in this literature, norms which guided paradoxographers in the selection and treatment of their objects.

432   Hellenistic Greek Science

2.  Genesis and Development of the Genre and Common Characteristics Paradoxography is apparently a postclassical neologism of Byzantine origin. Johannes Tzetzes (1110–​1180 ce), Chiliades 2.35.131, is generally considered to have first coined the term; it is not attested in ancient authors. Accounts dedicated to the strange and wondrous can be identified in titles such as On Wondrous Things (Peri thaumasiōn, Phlegon of Tralles, 2nd century ce); Wondrous Stories (Historiai thaumasiai, Apollonius Dyscolus, 2nd century ce); A Collection of Wondrous Things (Isagōgē thaumasiōn, Agatharchides of Knidos, 2nd century bce); Inquiry on the Strange (Paradoxos historia: a title attributed by the Suda Π–​7 1, s.v. Palaiphatos, to Philon, sc. Herennius Philon of Byblos?); and A Collection of Inquiries on the Strange (Historiōn paradoxōn sunagōgē, Antigonus of Carystus, 3rd century bce). The first modern (i.e., critical) editions of this literature consisted in a more or less inclusive selection of works with such titles. Westermann ([1839], 2009)  prints a roughly chronological collection under the heading of Paradoxographoi, thus establishing this term in modern scholarship. Westermann’s edition includes pseudo-​ Aristotle, On Marvelous Things Heard; Antigonus of Carystus, Apollonius Dyscolus, Phlegon, and Michael Psellos’ (11th century ce) On Strange Readings (Peri paradoxōn anagnōsmatōn), followed by fragments from more than a dozen other authors. Some years later, certain of these authors are edited again as Minor Greek Writers on Natural Things (translation of the title of Keller 1877), including Paradoxographus Vaticanus, which is not in Westermann (1839/​2009). Öhler (1914) then published a further edition and first commentary on Paradoxographus Florentinus. In the most recent edition of relevant literature, Giannini (1966) collects yet another group of authors and texts under the title (i.e., “Remains of the Greek Paradoxographers”), which now begins with Callimachus (4th–​3rd century bce) and places pseudo-​Aristotle near the end, after Phlegon. Giannini (1966) also includes several new paradoxographoi and excludes others, either as authors of dubious works or as authors whose works are not properly topical to paradoxography, that is, “pseudo-​paradoxographical” authors. Though the term paradoxography is well established, it is still to some degree unclear to which authors and works it properly applies, and how they relate to one another. What, then, makes an author or text paradoxographical? The bifurcation of the question arises from two interdependent approaches to paradoxography: one by way of identifying common characteristics of certain authors and their supposed audiences, the other by way of investigating the characteristics germane to certain texts. Clearly, the two are interconnected. Paradoxographical texts have been characterized variously as lists of facts that are considered wondrous, as a sensationalist and consumer-​oriented type of writing (Giannini 1963, 248, n.3), or, in a similar vein, as the second-​rate product of extraction from proper historical and scientific authors, a “parasitic growth on the tree of historical and natural-​scientific literature” (Schmid and Stählin 1920, 2. Theil,

Paradoxography   433 1. Hälfte, 237) and a “derivative form of literature” (Schepens and Delcroix 1996, 409). Paradoxographical authors are thus characterized as “‘collectors’, not . . . researchers” and “‘consumers’ of the ideas of others” (Schepens and Delcroix 1996, 409). Their purpose was to “fabricate the marvelous” (Jacob 1983) using the materials of proper historiographical, zoological, and geographical research, while writing for a popular audience unaccustomed to real science (see Schepens and Delcroix 1996, 407–​408 for a circumspect defense of this view). This general consensus in the literature on paradoxography, which we cannot examine in detail here, raises (and sometimes begs) some important questions in the history and theory of science. What distinguishes literary collectors from real researchers? How did their methods and interests differ from those of their sources? And what is the difference between proper and “popular” historiography and science? We shall suggest an approach to some of these questions by identifying the epistemic priorities and values of the paradoxographers (see section sec. 5 on the purpose and meaning of paradoxography). First, however, it will be useful to contextualize the genesis and development of the genre. It is usual to place Callimachus of Cyrene (4th–​3rd century bce) at the origin of paradoxographical literature in the proper sense (see, e.g., Ziegler 1949, 1140–​1141; Giannini 1963; Schepens and Delcroix 1996). According to the Byzantine lexicon known as the Suda (ca 970 ce), Callimachus wrote a Collection of Wondrous Things Over the Whole Earth According to Places, but this title contains some orthographical and grammatical irregularities (Thaumatōn (?)  tōn eis (?)  hapasan tēn gēn kata topous ontōn (?) synagōgē). One conjecture has it that the real title of the work should be reconstructed as On Marvels of Each Kind According to Their Places (Peri tōn ana panta genē kata topous thaumasiōn) (Ginannini 1966, 15). In any case, the proper title of Callimachus’ work is difficult to reconstruct on the basis of the textual evidence, which is preserved in another, partially extant, work by Antigonus of Carystus (3rd century bce), a Collection of Inquiries on the Strange (Historiōn paradoxōn sunagōgē). These passages are excerpts of excerpts, which Antigonus introduces with the words “Callimachus of Cyrene also composed a certain selection of strange things (paradoxa), from which we shall write up as much as seems to us to be worth being heard” (Antigonus 129). The practice of excerption, which is so characteristic of paradoxographical literature in general, is most evident here, where perhaps the first paradoxographical work itself becomes cannibalized by an emulator. What then follows (Antigonus 130–​173) are about 45 briefly described wonders related to waters, organized by place (e.g., “in the Indian sea,” “in the sea around the Aeolian islands”), with reference to an author on whose testimony each wonder rests (Aristotle, Eudoxus, Theophrastus, Timaeus, and Polycritus are just some of the sources; see Schepens and Delcroix 1996, 383 for a more complete list). Antigonus dutifully includes this last aspect of Callimachus’ work, giving the sources that Callimachus cites in indirect discourse. To judge from these excerpts, paradoxography would seem at its inception to resemble some of the learned practices of canonical texts involved in philological research. The paradoxographer collects bits of (largely decontextualized) information

434   Hellenistic Greek Science on the basis of written sources with a view to certain criteria of relevance. And the texts on which this operation is performed are canonical in the sense that the authority of their authors serves as the foundation for the plausibility of the information derived from them. The emphasis on credibility is a general feature of paradoxographical literature (Schepens and Delcroix 1996, 382–​389), but there are different ways how it is sought. Antigonus supports the credibility of the information he reports not just through his sources but also by criticizing these sources and their credibility (see Antigonus 15 and 45 for telling examples). This was not always the case; later paradoxographers were more concerned with supporting their credibility through the addition of adventitious geographical details, and some did not include any marker for testimony (such as “they say”). Paradoxography at its inception, however, can be characterized as a literature that presents assertions about things that are strange but true, and in which the credibility of these strange truths is supported by the credibility of sources. Historically, the birth of paradoxography depends on the formation and availability of a body of literature—​ historiographical, zoological, ethnographic, geographic, natural-​scientific—​that could be so mined (Flashar 1972, 51). Antigonus is also very much concerned with documentation. Besides Callimachus, whose work he excerpts, Antigonus copiously and explicitly extracts accounts from Aristotle (two main blocks: 27–​60, 61–​115), and “cites” him on several occasions (e.g., 16, 19, 37, etc.). Aristotle is the most cited and excerpted author in Antigonus, but the range of other named sources is remarkable; it includes among others Eudoxus of Knidos, Timaeus, the Lesbian Myrsilus (first attested by Antigonus), but also Herodotus and poets such as Homer, Alcman, and Aeschylus (for particular passages see Schepens and Delcroix 1996, 384–​385). As we can see in Antigonus, the naming and particularly the qualification of a source for wonder-​reports make an important difference: the plausibility of the alleged fact is based on a (sometimes qualified) authority. This can be contrasted to later paradoxographical literature such as Isigonus of Nicaea’s Unbelievable Things (Apista) (ca 1st century bce or 1st century ce), where wonders are presented without reference to or qualification of their literary sources. That some later writers in this genre did not “cite” particular sources of information on wonders has several possible explanations. Perhaps they were unable or reticent to attribute wonders by name because they themselves were working on the basis of compilations. This would seem to be the case in the anonymous Paradoxographus Florentinus (Ziegler 1949, 1161–​1162). It is also possible that the wondrous and sensational was itself the main object of their interest, and the identity of the author of a report was—​at least for them and their audience—​an irrelevant detail. Whatever the reason, the naming of sources versus its absence marks an important difference between types of paradoxographical writing, and also a change in its development. Later writing on strange things, as represented for example by Phlegon (2nd century ce), differs in yet other respects. His Book of Wonders contains reports concerning ghosts and sex changes that are sensational rather than simply unusual. The concern for credibility so characteristic of natural inquiry and historiography is completely lacking here.

Paradoxography   435 A third early, but difficult to date, piece of paradoxography is the pseudo-​Aristotelian On Marvelous Things Heard (Peri thaumasiōn akousmatōn). It differs from the works of both Callimachus and Antigonus in the important respect that it does not cite its sources. This may be due to yet another circumstance not yet considered: it was composed within a school on the basis of literature that was considered proprietary, and thus in no need of being “cited.” Written in the Peripatos using Aristotle, Theophrastus, and Timaeus as its main (but unnamed) sources, the largest part of it may be dated to the first half of the 3rd century bce (Flashar 1972, 39–​50). Like Antigonus’ Collection, this work too may have been written in response to Callimachus (Regenbogen 1940, 1371); it certainly shares some of the sources on which Antigonus relies. The last part of the text (152–​178) seems to have been added afterward; it includes material that is much later than the 3rd century bce. As a text that relies heavily on Peripatetic material that we have, On Marvelous Things Heard is a valuable source for the study of the paradoxographical method of excerption. Consider the following case, where a passage from Aristotle’s History of Animals has become the object of paradoxography. The passage in Aristotle is as follows: The marten is about the size of a small Maltesian lap-​dog, white and hairy on the underside, and in character nasty like the weasel; even if it becomes domesticated it will still ruin hives, for it loves honey. It is a bird-​eater, like the cat. Its sexual organ is bony, as has been said, and the penis of the marten seems to be a remedy for strangury; they administer it in pulverized form. (9.6, 612b10–​17).

Compare the following paradoxographical extracts: • It is said that the sexual organ of the marten is not similar to the nature of other animals, but that it is rigid throughout like bone, no matter what state it happens to be in. They say that it is one of the best remedies for strangury, and that it is administered in pulverized form. (pseudo-​ Aristotle, On Marvelous Things Heard 12) • The sexual organ of the marten [is said] to be bony; it seems to be a remedy for strangury. (Antigonus 108) The passage from History of Animals 9.6 can be read against the background of a comparative study of physiological differences between kinds of animals in History of Animals 2.1. There Aristotle remarks that there are many differences with respect to the male sexual organ and notes that some animals have a cartilaginous and fleshy organ like men, whereas others have a sinewy organ, like the camel and the deer (History of Animals 2.1, 500b20–​23). Still others have a bony organ, like the fox, wolf, marten, and weasel, “for in fact (kai gar) the weasel has a bony penis” (500b23–​25). Clearly the focus of interest in this passage from History of Animals 2.1 is on physiological comparison: having a bony penis is a distinguishing trait common to several different kinds of animal. The animals with which the marten shares this trait are no longer mentioned in

436   Hellenistic Greek Science (the perhaps Theophrastean) History of Animals 9, which is focused instead upon the peculiar features of certain types of animals. Nor is it to be found in pseudo-​Aristotle’s On Marvelous Things Heard and Antigonus’ Collection. It is telling that the information concerning the marten is extracted from History of Animals 9, containing a collection of remarkable animal traits and behavior, and not the more comparative History of Animals 2. The decontextualization of this information by both paradoxographers has the effect of making the bony character of the marten’s penis seem to be just a curiosity. But both use indirect discourse to indicate that this information is based on a report. The language of both passages from History of Animals suggests, in contrast, direct acquaintance (see, e.g., “for in fact the weasel has a bony penis,” History of Animals 2.1, 500b25). The statement that the marten’s organ possesses curative properties for urination problems is preserved in even the very brief extract in Antigonus, which reflects a reduction of the original information to the two sole salient points: the bony nature of the marten’s member, and its alleged medicinal potency. The practical matter of how it is used medicinally, which pseudo-​Aristotle preserves, was either no longer relevant, or (despite the verdict of Wilamowitz [1881], 1965, 18, n. 4) no longer accessible to Antigonus. We see here a tendency of increasing isolation and decontextualization of information through a process of extraction guided by epistemic priorities quite different from the source-​texts. We shall turn to a study of these norms in our concluding remarks (sec. 5) on the purpose and meaning of paradoxography.

3.  The Topological and Geographical Principles of Organization As stated, the title of Callimachus’ work cannot be reconstructed with certainty, a possible emendation being On Marvels of Each Kind According to Their Places (Peri tōn ana panta genē kata topous thaumasiōn). Be that as it may, it is clear that Callimachus ordered his paradoxa according to places, thus introducing a topographical principle that can be found in most paradoxographical lists: every thaumasion is attached to a certain place and is specific to a place. Typically, paradoxographical texts provide a place for the mythological, zoological, ethnographic, and geological information they contain, which is itself often organized geographically or topologically (i.e., according to areas encompassing several places). This topological principle of organ­ ization of information alone would earn paradoxographical literature a place in the history of ancient science, even when theory making and explanation are noticeably absent from it. By examining how geography is used, we may observe its significance in paradoxographical writing. Paradoxographical authors took great pains to attribute their paradoxa to specific locations. “Such geographical precision had, in fact, been paramount from the beginnings of the genre in Callimachus’ Collection of Marvels of the World,

Paradoxography   437 Arranged Geographically” (Stern 2008, 439–​ 440). This aspect prevails in most paradoxographers, notably in the Paradoxographus Florentinus, which lists 45 water marvels in 43 chapters. The strangeness of particular water phenomena is only one source of wonder in this paradoxographer; the cumulative topographical diversity of water wonders is another. The topographical principle can be refined. In the 178 chapters of the pseudo-​ Aristotelian On Wondrous Things Heard (which contains 187 single items), only 15 items (about 8%) fail to yield geographical information. Thus, naming a topos for a paradoxon was clearly the norm, since it enhanced the credibility of the information. Most of the items that are devoid of geographical information come in clusters, like in sec. 11–​15, where our author draws on a single source—​most probably the pseudo-​Aristotelian book 9 of the History of Animals or Theophrastus’ Peri zoōn ēthous kai phronēseōs (On the disposition and intelligence of animals), where the geographical information was already missing in the “Vorlage” or textual exemplar that served as the original. In other cases like sec. 147 or sec. 165, the item is to be understood as an extension, annex, or corollary to the previous chapters and should not be regarded as isolated (and hence should not be assigned its own number in the edition). As comparison shows, in both cases the information derives from the same source as in the previous chapters, which makes it even more plausible that the author considered these as belonging together and therefore saw no reason to give additional geographical information. What is more, one can see that the author aimed to lump together information about strange events and things that took place at the same location. For example, in sec. 89–​92 we find some very heterogeneous information about a lake, the ability to shoot with a sling, women giving birth to babies while working, and a wondrous river. All this happened in the region of the Ligurians. Of course, this geographical organizing principle is subordinate only to the topographical one, since paradoxa may be mentioned without an indication of their locality (albeit few), but places are not discussed without paradoxa. A peculiar geographical organizing principle can also be detected from sec. 85 onward. The author mentions a road called “the Heraclean,” named after the demigod who connects the lands of the Italians, Celts, Celtoligurians, and Iberians. He then goes on to describe various paradoxa in a fashion reminiscent of a periplous or perihēgēsis. He begins his “voyage” in Iberia and the islands off the Iberian coast, moves to the Massaliotes, then to the Ligurians, then to the Tyrrhenians in Italy, then to Italy proper, then to southern Italy and Sicily (where the Carthaginians are also mentioned), and comes to Promontorium Iapygium in Calabria. After an inexplicable item on Boeotian Orchomenos (see Flashar 1972, 117; Vanotti 2007, 179), the author adds paradoxa from the islands in the Tyrrhenian Sea (Sardinia, Lipara, the islands of Seirenusae, and two places expressly connected to islands). He then turns to the cities and regions in the Sicilian and Adriatic Seas, namely Sybaris, Tarentum, Croton, and Metapontum, moving inland to Daunia and the Peucetii in Apulia. The following chapters, from sec. 111 onward, concern Sicily; hence they are also connected geographically, though the author probably draws here on yet another source (Lycus instead of Timaeus of Tauromenium).

438   Hellenistic Greek Science This can be described as a “hodological” way of ordering and narrating information. The items are connected on a topological level like cities via roads. This particular style of narration may be observed in geographical authors like Pomponius Mela, pseudo-​ Scymnus, Dionysius Periēgētēs, but also—​an even better parallel from antiquarian and encyclopedic authors—​in Pliny the Elder. Interestingly enough, this geographical ordering principle is so dominant here that the author makes no distinction between Greek and native paradoxa. The Greek-​Barbarian dichotomy so prevalent in some Hellenistic authors is clearly avoided here. Timaeus of Tauromenium is the most prominent, probably even the sole, source for this whole section. Given the interest of Timaeus in foreign nations like the Carthaginians or the Sicilian and Italian peoples, it seems a safe guess to attribute the geographical structure (and even the hodological principle) of the text cited by pseudo-​Aristotle to Timaeus himself. If we are right about this, it would make a good case for thinking that the so-​called prokataskeuē of Timaeus, that is, the introduction of his Sikelikai historiai in five books, was organized according to this hodological structure. An exception to the rule of geographical ordering of paradoxa seems to be the Collection of Inquiries on the Strange (Historiōn paradoxōn sunagōgē) of Antigonus of Carystus (3rd century bce). Of the 173 chapters, many do not name a topos. But a closer look confirms that topos and atopia are not distributed by default. After the first 18 chapters where every single paradoxon is attributed to a certain place, in none of the dozen examples (with one dubious exception) is there mention of a place. In other words, Antigonus also paid attention to this element. Even the underlying structure of paradoxographical lists is geographical.

4.  Paradoxographical Authors and Their Sources In their comprehensive Encyclopedia of Ancient Natural Scientists (2008, 1011), Paul Keyser and Georgia Irby-​Massie list 61 ancient authors as paradoxographoi. Some, like Eudoxus of Rhodes or Callixeinus of Rhodes, surely wrote about strange things, customs, and places, but their works were not paradoxographical per se, and therefore should not be included in an edition of paradoxographical authors (like the new fourth volume of Fragmente der Griechischen Historiker). On the other hand, some 20 authors are missing from their list, the most prominent among them being Varro and Cicero. Despite this, Keyser and Irby-​Massie give the right impression: “paradoxography” was a thriving literary field (to avoid the term genre) from Early Hellenistic times on, and more ancient authors were concerned with collecting and writing paradoxa than with, say, writing about alchemy (56), architecture (44), doxography (38), harmonics (54), metrology (29), psychology (48), or veterinary medicine (41 instances) (see Keyser and Irby-​Massie 2008, 990–​991, 991, 997, 1000–​1001, 1010, 1017–​1018, and 1018 respectively).

Paradoxography   439 Nevertheless, despite the abundance of names, it is difficult to get a clear picture of what these ancient authors were doing and why. This can be attributed in the main to that most paradoxographical authors survive only in fragments. Only the pseudo-​ Aristotelian work On Marvelous Things Heard and three anonymous lists, commonly called Paradoxographus Florentinus, Palatinus, and Vaticanus, are (probably, some doubts still linger) fully preserved. And, even in these cases, we find no introduction or scholarly statements in which the author permits us some insight into his methods and aims. In the following conspectus, we must limit ourselves to outlining the basic features of paradoxographical writings in the most famous and cited authors. We exclude authors like Theopompus, Philostephanus, or Phlegon, whose works are either not paradoxographical in our modern sense (Phlegon), or whose fragments seem to derive from works with different literary character (Theopompus, Philostephanus). Since we have already discussed the role of Callimachus and the pseudo-​Aristotelian work On Marvelous Things Heard, we will now discuss briefly Antigonus of Carystus, Isigonus of Nicaea, Nicolaus of Damascus, and the anonymous authors of the three lists mentioned above. Antigonus, born in Carystus (Euboia) at the beginning of the 3rd century bc, lived at Athens, where he is said to have worked with members of the Academy, most notably Arcesilaus. Later, he was summoned to the “muse court” of the Pergamene king Attalos I (241–​197 bc). One may guess that his well-​known “biographies,” or rather “character sketches,” prompted this invitation. Different in style is his Historiōn paradoxōn sunagōgē, “eine höchst kunstlose, ja armselige Zusammenstellung” (“a most unartistic, even pathetic compilation”; Susemihl 1891, 1.472). This work is comprised of five parts with five respective introductions. Only the first (sec. 1–​25) and the fourth (sec. 116–​128) transmit excerpts from other authors; the second (sec. 26–​60) contains excerpts from the dubious book 9; the third (sec. 60–​115) from all books of Aristotle’s History of Animals; the fifth and last part relies on Callimachus’ Thaumasia. Antigonus cites not only examples from literary sources but also includes mirabilia of Carystus and its surroundings, as well as from Pitane, Delphi, and Kos, drawing on personal experience and historiē. His polemics against Callimachus and Archelaus may be explained by the antagonism of the Alexandrian and Pergamene “schools.” Antigonus wrote his work shortly after 240 bce (Wilamowitz [1881] 1965, 23–​24; Susemihil 1891, 2.474, n. 64). Its 173 chapters rival the pseudo-​Aristotelian work On Marvelous Things Heard in scope and length. Isigonus of Nikaia is called a “historian” by Tzetzes (schol. Lyc. 1021= F 14 Giannini) and as such is distinguished from the “philosophers” Sotion and Agathosthenes (both also known nowadays as paradoxographers). It is unclear if we can surmise from this that Isigonus wrote before them. But his date is not totally unknown as Ziegler (1949, 1155–​ 1156) and Flashar (1972, 93) claim. On the one hand, Isigonus draws on Varro (and probably also on Nicolaus of Damascus, although not according to Rohde 1871, 29–30 and Susemihl 1891, 1.481); on the other hand, he is cited by Pliny the Elder; he must have lived in the first half of the 1st century ce. Isigonus wrote Apista, drawing on Theophrastus’ On Water, the pseudo-​Aristotelian On Wondrous Things Heard, and, according to Rohde,

440   Hellenistic Greek Science also on Antigonus and another paradoxographer called Nymphodorus. Despite citing mirabilia from all over the oikοumene, the abundance of Italian examples is striking. Nicolaus of Damascus (born ca 64 bce) is considered by ancient writers a Peripatetic, which in his case does not mean being an “official member of the school of Aristotle,” but rather indicates he was an adherent of Aristotelian doctrine and especially of a certain style of conducting research. He entertained an eventful and varied life, having access to the illustrious circles of Herod the Great and Agrippa. The latter even introduced him to Emperor Augustus in Rome. The talented Nicolaus was active in various literary areas, for example, botany and historiography. We have fragments of a history of Augustus, and also of an autobiography and a universal history. Stobaios transmits no less than 47 fragments of a Paradoxōn ethnōn sunagōgē in his “anthology” (and we probably have to add another 13 fragments, which coincide with chapters in the Paradoxographus Vaticanus). Hence Susemihl and others have speculated that the Sunagōgē was not a work by Nicolaus himself but was a later collection. The ill-​fitting title may have been caused by the fact that the excerpts were made from the universal history of Nicolaus. If paradoxography consists basically—​at least in subsequent stages of its development—​in assembling lists or catalogues of strange things, it is embodied best by three anonymous works named according to the repository of the (main) manuscripts which contain them:  Paradoxographus Florentinus, Paradoxographus Vaticanus, and Paradoxographus Palatinus. Probably the oldest one of the three, the Paradoxographus Florentinus, was attributed by Öhler 1914 to the era before 100 ce on linguistic grounds, but the use of epitomized sources, among them especially Isigonus, may skew this picture (and the work may be much later). What is interesting is that the 43 chapters of the Florentinus consist only of water mirabilia, but the kind of water—​ sea, river, spring, canal, and so on—​ is not an ordering principle. Also, the author seems to have made a conscious effort to cite his source texts. Only in 13 chapters are the original sources not stated. Since these lacunae come in clusters, they may already have been omitted in the sources of the anonymous author. In only one instance (sec. 19, where there seems to be a textual corruption of the strange name Amomentos/​Ammonos, or a textual loss) does the author fail to name a location. Nearly all mirabilia of the Paradoxogaphus Vaticanus, arranged in 62 chapters, incorporate locations, too. The only exceptions concern general (i.e., not local) things like birds, fish and land animals, or commonly known things and persons like the Trojan River Scamander, Proteus, or Alexander the Great. If Geus 2016 is right in rearranging a cluster of chapters, the whole text is divided in three distinct parts, the borders of which the author intentionally tried to overlap and blur: sec. 1–​9.2 contain paradoxa of animals, sec. 10–​22 and 30–​39 paradoxa of water, sec. 23–​29 and 40–​62 (without any citations) paradoxa of customs and rituals of different peoples. It is clear then that the Paradoxographus Vaticanus is no mere list, copied from one or several sources but a sensibly and subtly arranged work. The effort to interlock and allude to the many heterogeneous mirabilia by association, conspicuous words, or topographical and topical parallels, is reminiscent of literary techniques employed in similar works like the Animal History of Aelianus (3rd century ce) or the Physiologus (2nd century ce).

Paradoxography   441 The Paradoxographus Palatinus is transmitted in two versions, a longer and a shorter one. The longer one contains 25 mirabilia in 21 chapters. Only eight include topographical indications, and even in these cases, three may be considered as belonging to the prior chapters, making the location superfluous. Of the remaining five, four come at the beginning in a cluster that points to a “Vorlage” where no location was indicated. Again, we sense the urge of the paradoxographer to give a topographical reference for strange phenomena. In the case of the Palatinus, exotic locations prevail. Nearly all locations are unknown or belong to regions outside the Greek homeland. Eleven different authors are cited in its 21 chapters. Only a certain Polyclitus is named twice (but since both citations come directly after one another, we should rather speak of one fragment). This is clearly not by default. The compiler of the list is fond of assembling strange things in exotic landscapes but also of presenting various and unfamiliar authorities. (According to Ziegler 1949, 1164, Paradoxographus Palatinus wrote after Athenaeus.) The author even mentions Cato’s Origines as one of his sources. The relationship between the three anonymous paradoxographers is very loose. They seem to have written with different aims and at different times. They attest to a principle common for similar works like the Physiologus, which resembles paradoxographical writing in some regards:  folktales, especially anonymous ones, became popular and common in imperial and Byzantine times. According to individual needs, contexts, and occasions, such works could be changed by inclusion, exclusion, and variation of chapters. One final observation: by our calculations, we have more than 100 authors and works mentioned as “sources” in the entire Corpus Paradoxographicum. And nowhere, as far as we know, is a geographical author or treatise cited: we find no mention of Hecataeus, Eratosthenes, Hipparchus, or Strabo. Dicaearchus and Artemidoros are cited only once, and in both cases it is far from clear that the fragments are derived from their geographical works. Nevertheless, we find many parallels and connections between geographical and paradoxographical authors, especially in Mela but also in Strabo. So, where did the geographical authors get their information? One guess would be that both kinds of authors independently drew on the same stock of information, that is, scientific and historical writings, especially of the Peripatos. But could there be another explanation? Might geography and its “parasitic” neighbor, paradoxography, be mutually interdependent? Could it be that it was not just the paradoxographer who mined geographical treatises for paradoxographical “facts,” but that the geographers made use of paradoxographical lists for their own works? This hypothesis merits further investigation.

5. Conclusion So far, we have treated paradoxography as a literary genre. The paradoxographer is a literary extractor who culls information from other sources on the basis of epistemic criteria:  what is sought is the “unbelievable” (adoxon), the “singular” (idion)—​in

442   Hellenistic Greek Science general, that which goes against expectation (paradoxon). As we have argued, the paradoxographer informs the material selected by these criteria through his principles of geographical and topological organization. Still, paradoxography is not literature about literature, but literature about the (sublunary) world, and its express purpose is to identify and describe certain features of this world. The epistemic value of “factuality” is apparent in the paradoxographer’s selective use of literary testimony; information must be given by a respectable author in order to be admitted, mythical literature is excluded (see Schepens and Delcroix 1996, 388). As literature about the world based explicitly on literary testimony and a kind of natural historiography, paradoxography presents us with an interesting and as yet largely undiscussed ancient case of the use testimony for knowledge. In closing, we shall briefly touch upon the historiographical issues underlying this case, and locate the position of the paradoxographer in relation to it. The modern debate concerning the use of what others report (by writing or in speech) was decidedly influenced by David Hume. Hume states that, since the reports of others usually conform to what we observe to be the facts, testimony itself is rightfully treated as valid evidence about the world (Hume [1748] 2000, 84). In keeping with his critique of claims to “innate” sources of knowledge, Hume puts our tendency to trust reports down to a kind of cognitive habit, one which need not reflect the “connections” of things as they really are (85). Yet it is a habit that permits us to treat reports with caution when they contain things not analogous to our experience. Hume singles out a particular, extreme sort of testimony to make his case, that concerning miracles: “It is no miracle that a man, seemingly in good health, should die on a sudden . . . but it is a miracle that a dead man should come to life; because that has never been observed in any age or country” (87). He then concludes that miracles are those events that run contrary to “uniform experience,” otherwise “the event would not merit that appellation” (87). In this context, Hume formulates a position regarding the relationship between observation and the treatment of historical testimony that is endemic in early modern science. The testimony of the senses, as it were, overrules historical testimony and even the reports of contemporaries. The proper treatment of reports is directly controlled by “our” experience. And Hume distinguishes between that which is “only marvelous” and what is “really miraculous,” in claiming that even the greatest authority could not support something that goes against all human experience (86). The treatment of reports of natural wonders in ancient paradoxography reflects a very different approach to testimony. Modern readers with empiricist intuitions have been prone to fault the paradoxographers for putting their epistemic store in stories, when they should have used observation to verify the reports of strange waters, odd animal behavior, and unbelievable places. But theorists of science have since come to appreciate that there are many irreducible social components of the individual’s observation that involve testimony (beginning, of course, with “our” experience). Paradoxography is remarkable in that it often contains forthright acknowledgment of the role of authority in “observation.” The interest in paradoxa is motivated by the fact that they go against common experience, yet the basis for discussing them is not autopsy, but rather the

Paradoxography   443 historical and literary method of assembling testimony, organizing it thematically, topologically, geographically, and scrutinizing not only its consistency but also the reliability of its source. This historical approach to natural wonders may not be experimental, but it does reflect evolved practices in the treatment of testimony and a coherent hierarchy of epistemic values in its treatment—​which is not too bad for a “parasitic” genre of “sub-​ scientific” literature.

Bibliography Articles in EANS: 40–​41 (Agatharkhidēs of Knidos), 93 (Antigonus of Karustos), 152 (pseudo-​ Aristotle, De Mirabilibus Auscultationibus), 446 (Isigonos of Nikaia), 463 (Kallimakhos of Kurēnē), 565–​566 (Mursilos of Mēthumna), 577–​578 (Nicolaus of Damascus), 624 (Paradoxographus Florentinus), 624 (Paradoxographus Palatinus), 625 (Paradoxographus Vaticanus), 653–​654 (Philōn of Bublos, Herennius), 811–​812 (Timaios of Tauromenion). Flashar, H. Aristotelis Opuscula II: Mirabilia. Berlin: Akademie-​Verlag, 1972. Fraser, Peter M. Ptolemaic Alexandria. 3 vols. Oxford: Oxford University Press, 1972. Geus, Klaus. “Paradoxography and Geography in Antiquity:  Some Thoughts About the Paradoxographus Vaticanus.” In La letra y la carta:  Descripción verbal y representación gráfica en los diseños terrestres grecolatinos: Homenaje al Prof. Pietro Janni con motivo de su octogésimo aniversario, ed. Francisco J. González Ponce, Francisco Javier Gómez Espelosín, and Antonio L. Chávez Reino. Servicio de Publicaciones, Universidad de Alcalá de Henares, 2016: 243–​258. Giannini, Alexander. “Studi sulla paradossografia greca I: Da Omero a Callimaco: motivi e forme del meraviglioso.” Rendiconti dell’Istituto Lombardo, Accademia di Scienze e Lettere 97 (1963): 247–​266. —​—​—​. “Studi sulla paradossografia greca II.” Acme: Annali della Facoltà di Lettere e Filosofia dell’Università degli Studi di Milano 17 (1964): 99–​140. —​—​—​. Paradoxographorum Graecorum reliquiae recognovit, brevi adnotatione critica instruxit, latine reddidit. Milano: Istituto Editoriale Italiano, 1966. Gómez Espelosin, F. Javier. Paradoxógrafos griegos:  Rarezas y maravillas; introducción, traducción y notas. Biblioteca clásica Gredos 222. Madrid: Editorial Gredos, 1996. Hume, David. An Enquiry Concerning Human Understanding. London: Millar, 1748. Repr. Tom L. Beauchamp, ed., Oxford: Clarendon, 2000. Ibáñez Chacón, Álvaro. “Poesía y paradoxografía.” Maia 60 (2008): 393–​404. Jacob, Christian. “De l’art de compiler à la fabrication du merveilleux: sur la paradoxographie grecque.” Lalies 2 (1983): 121–​140. Keaney, John J. “A New MS of the Vaticanus Paradoxographus.” Classical Philology 74 (1979): 156–​157. Keyser, Paul, and Irby-​Massie, Georgia L. The Encyclopedia of Ancient Natural Scientists: The Greek Tradition and Its Many Heirs. London and New York: Routledge, 2008. Öhler, Henricus. Paradoxographi Florentini Anonymi opusculum de aquis mirabilibus ad fidem codicum manu scriptorum editum commentario instructum. Tübingen: Heckenhauer, 1914. Pajón Leyra, Irene. Paradoxografía griega: estudio de un género literario. Diss. Madrid 2008. Madrid: Universidad complutense de Madrid, 2009. —​—​—​. Entre ciencia y maravilla: El género literario de la paradoxografía griega. Monografías de filología griega 21. Zaragoza: Universitarias de Zaragoza, 2011.

444   Hellenistic Greek Science Rohde, Erwin. “Isigoni Nicaeensis de rebus mirabilibus breviarium ex codice Vaticano primum edidit.” Acta Societatis Philologae Lipsiensis 1 (1871): 25–​42. Schepens, Guido, and Kris Delcroix. “Ancient Paradoxography: Origin, Evolution, Production and Reception”. In  La letteratura di consumo nel mondo greco-​latino. Atti del convegno internazionale, Cassino, 14–​17 settembre 1994, ed. Oronzo Pecere and Antonio Stramaglia, 375–​460. Cassino: Università degli studi di Cassino, 1996. Schmid, Wilhelm, and Otto Stählin. Geschichte der griechischen Literatur. 2.  Theil:  Die nachklassische Periode der griechischen Literatur. 1. Hälfte: Von 320 vor Christus bis 100 nach Christus. 6th ed. München: Beck, 1920. Stern, Jacob. “Paradoxographus Vaticanus”. In In Pursuit of Wissenschaft:  Festschrift für William M.  Calder III zum 75. Geburtstag, ed. Stephan Heilen, Robert Kirstein, R. Scott Smith, Stephen M. Trzaskoma, Rogier van der Wal, and Matthias Vorwerk, 437–​466. Hildesheim and New York: Olms, 2008. Susemihl, Franz. Geschichte der griechischen Literattur in der Alexandrinerzeit. 2  vols. Leipzig: Teubner, 1891. Wenskus, Otta, and Lorraine Daston. “Paradoxographoi.” Translated by T. Heinze. In Der Neue Pauly: Enzyklopädie der Antike, ed. Hubert Cancik and Helmuth Schneider, vol. 9, 309–​314. Stuttgart and Weimar: Metzler, 2000. Westermann, Anton, ed. ΠΑΡΑΔΟΞΟΓΡΑΦΟΙ:  Scriptores rerum mirabilium Graeci; insunt [Aristotelis] mirabiles auscultationes, Antigoni, Apollonii, Phlegontis historiae mirabiles, Michaelis Pselli lectiones mirabiles, reliquorum eiusdem generis scriptorum deperditorum fragmenta. Accedunt Phlegontis Macrobii et olympiadum reliquiae et anonymi tractatus de mulieribus etc. Braunschweig: Westermann and London: Black and Armstrong, 1839; repr. Amsterdam: Hakkert, 2009. Wilamowitz-​Moellendorf, Ulrich von. Antigonus von Carystus. Berlin: Weidmann, 1881. Repr. Berlin and Zürich: Weidmann, 1965. Ziegler, Konrat, “Paradoxographoi”. In Paulys Realencyclopädie der classischen Altertum­ swissenschaft. vol. 36.2, 1137–​1166. Stuttgart: Alfred Druckenmüller, 1949.

chapter C11

M u sic a nd Harmonic T h e ory Stefan Hagel

1. Introduction From time immemorial, harmonic knowledge was encapsulated in the transmission of musical skills. How much of this information needed to be verbalized and thus elevated to a distinctively higher level of consciousness, available to symbolic representation and operation, however, differs widely with the circumstances. The human voice, as well as many woodwind instruments, is not likely to give rise to conscious reflection on pitch relations. The case is different with instruments that need to be tuned, either as part of the manufacturing process or right before every single performance. A typical instance of the former class is the panpipe (sýrinx), where a row of pipes are stopped at different lengths to form a scale, whose constituent pitches can barely be modified by means of playing techniques. In the latter class fall the stringed instruments, whose tuning is quickly lost (or arbitrarily disposed of). Here the first thing any apprentice must learn is to tune their instrument, setting up a series of pitches in a predefined relation—​however roughly defined it may be. That is probably why stringed instruments form the conceptual background of the earliest testimonies of “western” musical terminology, preserved in cuneiform texts from as early as the first half of the second millennium bce. This tradition employed diatonic heptatonic scales, based on resonant fifths and fourths (conceptually opposed to the “impure” tritone interval): physical resonance and its physiological counterpart, perceived consonance, naturally play a more substantial role when more than one sound is elicited simultaneously, foregrounding instruments such as lyres, harps, and double pipes, against panpipes and single-​duct woodwind. The cuneiform sources unfold a terminology of immediate practical impact, which could even be employed for a rudimentary musical notation, but hardly any sign of

446   Hellenistic Greek Science more abstract “harmonic” reasoning has so far emerged. In sharp contrast, we witness an outburst of music-​theoretical activity in the Greek world beginning around 500 bce, which, after about two centuries of lively discussion, crystallized in theoretical edifices whose principles remained largely unchallenged until Late Antiquity. On the one hand, this process is included in the general surge of systematization and intellectual penetration known as Pre-​Socratic philosophy. On the other, Greek music displayed features that particularly encouraged its inclusion. Firstly, it employed well-​defined pitches and recognized intervals that would lend themselves to theoretical inquiry in the first place. Just as the first extant (and never challenged) definition of the singing voice characterizes it by the absence of pitch slides (Aristoxenus, Harmonics 13.8–​15.3 Da Rios), the most-​esteemed instrument was the lyre, presenting a row of open strings straightforwardly emitting one note each. Secondly—​a characteristic shared with the Near East—​the notes of lyre strings were not only arranged in various tunings but also ordered according to pitch, which made an analysis in terms of scales straightforward. Thirdly, ancient Greek musical culture incorporated a strong competitive element, already evident in the oldest texts. The ensuing susceptibility for innovation supported the evolution of more complex and varied structures, which in turn required a careful analysis of the underlying traditional scales. Scales, indeed, were the concern of the science that the ancients named harmonikḗ. Quite understandably so, since other aspects of music making are not as easily analyzed. Scales patiently sit on the instruments, and, in the course of time, tools were devised to measure them out. Rhythm, in contrast, only instantiates itself within time, and without either the means of recording a performance or measuring its small constituent time spans as they flow by, its assessment depended entirely on mental processes, ultimately counting abstract “time” instead of primarily perceived units such as syllables or beats. Consequently, it seems, rhythmical theory only became fully distinct from syllable-​ based metrics after some time, resulting in confusions between the two related fields, which have survived into modern scholarship. Another aspect of music, which some considered of the highest importance, was even more difficult to grasp: its effect on the human psyche. Most prominently, Plato considered selecting the right types of music paramount to the education of the ideal citizen, both in the Republic and the Laws. However, Plato apparently knew well enough that a usable psychology of music was far beyond contemporary resources. Thus he avoided giving any technical details in the more practice-​oriented Laws, while the rigorist restriction of instruments and modes in the Republic must be understood to contain a good deal of irony. Half a century later, Aristoxenus, antiquity’s greatest music theorist, equally refrained from associating technical details with ethical values, regarding musical judgment as a complex ability basically gained through appropriate education (Barker 2007, 233–​259). How wisely this was done becomes apparent through the work of Aristides Quintilanus (2nd/​3rd century ce), who finally undertakes the Platonic project by fitting gender labels to single notes, rhythms or instruments.

Music and Harmonic Theory    447

2.  The Earliest Stage of Greek Musical Theory In studying ancient musical science, the main focus must therefore be given to pitch, including physical and mathematical models. Unfortunately, the origins of such models are largely a matter of speculation. Extant technical sources more or less start with the Peripatos, above all the remains of several works by Aristoxenus, whose genius eclipsed most of what had been written earlier. But even of his writings, only a minuscule part survived, which deals with technical basics; quotations in later authors offer dim vistas on the extensive losses. From what must have been the most exciting period, we have almost nothing: a few quotations, and a few brief references mainly in Aristoxenus’ texts. Inevitably the ground becomes the more slippery, the further one goes back in time. Where our sources seem to provide quite precise information on musical developments in the Archaic period, we can hardly take these at face value (as too often was done) (cf. Barker 2014). Music-​historiographical interest mainly developed in the 4th century bce and constructed narratives mostly based on poetic texts or conventional ascriptions of traditional music to outstanding, often more legendary, figures of the past. The evaluation of particular statements is further encumbered because these usually lack their original context: they are excerpts of quotations or quotations of excerpts. With some extrapolation, we may nevertheless trace some general strands at least to the first half of the 5th century: our first explicit sources use concepts and terms that must have been established in a broader discourse and over a considerable span of time. To illustrate this, we can conveniently start from one of the earliest and most famous testimonies, a fragment from Philolaus (fr. 6a), allegedly the first Pythagorean who composed a book, around the end of the 5th century: The size of harmonía is a fourth [syllabá] and a fifth [di’ oxeiân]. And the fifth is larger than the fourth by the ratio of 9:8 . . . The fourth is 4:3, the fifth 3:2, the octave [dia pasân] 2:1. Therefore the harmonía is five ratios of 9:8 plus two diéseis, the fifth is three ratios of 9:8 plus a díesis, and the fourth two ratios of 9:8 plus a díesis.

There is a lot of mathematics in the passage, but for the moment we will focus on a much more basic fact: Philolaus can evidently rely on commonly accepted terms for intervals of given sizes. This is by no means an ubiquitous characteristic of music culture, as a comparison with the musical cuneiform sources shows: although their system conceptually distinguishes between intervals of the fifth/​fourth and the third/​sixth types and also presupposes the functional identity of notes an octave apart, so far no Akkadian general terms for intervals of a particular size have surfaced; instead, terminology was attached to scale degrees—​ultimately individual strings (West 1994; Kilmer 2001; Hagel 2005a). We do not know how recent the abstract notion of intervals in the modern sense

448   Hellenistic Greek Science was in Philolaus’ time; yet the fact that two out of three terms differ from later standard terminology is a sign of an ongoing process. The case is of special interest also because it highlights the influence of very practical details on the formation of the science. All later technical sources call the fourth “dia tessárōn” and the fifth “dia pénte,” indicating the distance of respective scalar degrees by inclusive counting, similarly to the modern English terms (which depend on the Greek via mediation of Latin writers). Such counting of course presupposes a heptatonic system; if there are only five notes in the octave, for instance, the fourth would literally be a “third.” Philolaus’ terms, however, avoid counting throughout. His fourth is a “syllabá,” his fifth “di’ oxeiân.” The latter only becomes understandable from the tuning of the traditional seven-​stringed lyre, whose outermost strings were tuned an octave apart, so that the remaining five could not possibly establish a complete heptatonic scale. The “gap” of one “missing” degree was present in the higher part of the scale, so that the archetypal fifth was sounded between the central and the highest strings: di’ oxeiân [khordân], “through the high [strings].” Notably, though, Philolaus applies the same term to another fifth that starts from the lowest note: obviously a term that had originally denoted a particular pair of strings already was commonly used to indicate any interval of the same size, regardless of whether it spanned four or five notes on the lyre, and regardless of its literal meaning. But what about the term for the fourth, “syllabá,” literally “what is taken together”? It has been considered that it referred to intervals typically used in performance, which is doubtless possible. But syllabá had at the same time acquired its grammatical acceptation as the syllable, a building block for words, itself consisting of several letters/​sounds as elementary units. This, in turn, offers such a striking parallel to the function of the fourth in later Greek music theory that this interval’s designation as syllabá may seem a token of such a conception in an early stage. The question, in fact, bears on the very core of the harmonic science: scalar analysis. In the extant sources, from the late 4th century on, it is all about tetrachords: units of four notes spanning a fourth, from which larger systems are formed by different ways of juxtaposition. Aristoxenus credits himself as having first sorted out the rigid rules according to which some shapes of fourths are susceptible to all kinds of combination while others are not; which implies that he inherited some looser set of ideas from his predecessors. Some of these, he says, asserted that “starting from the fourth, the mélos divides in two in either direction, though without defining whether this is true for any one, nor saying why it is true . . . ” (Aristoxenus, Harmonics 9.16–​20 Da Rios; cf. Hagel 2009a, 373–​377). Whatever the shortcomings may have been in detail, the general idea is clear: “the fourth” is regarded as the core element of harmonic theory, central to understanding the fabric and interrelations of musical structures. Both at its upper and its lower end, there are two possible ways of continuing the scale by adding another, similar, “fourth”: either immediately, so that the two share a common pitch (synápheia), or keeping them separate by inserting a whole tone in between (diázeuxis). As a result, pitch space expands as a network of fourths, within which one can map out the larger systems of musical practice. The boundaries of the fourths, where “the mélos divides” are points of possible modulation between the scales (see figure C11.1).

Music and Harmonic Theory    449 b

e’

a

a’

d’ c’ synápheia (conjunction)

g’ f’ diázeuxis (disjunction)

Figure C11.1  Pitch space understood as a network of fourths (bold), each with two possible continuations at either end (horizontally one moves through pitch, vertically through “keys” in the circle of fifths; “regular” scales are formed by the shortest connections between points of identical height).

Aristoxenus himself also utilizes the image of melodic roads. But it is much older; the earliest testimony to the general paradigm takes us back almost to the middle 5th century bce, when Ion of Chios poetically addresses the novel eleven-​stringed lyre as supporting “concordant crossroads of harmonía” (συμφωνούσας ἁρμονίας τριόδους: in Cleonides 12, 202.14–​17 Jan; West 1992a, 23–​28). Apart from the image of parting paths, the notion of concordance, in antiquity reserved for octave, fifth, fourth and their combinations with octaves, is evocative of the analysis in divisions spanning a fourth or, in the case of diázeuxis, a fourth plus a tone. What in Aristoxenus only surfaces in an entirely abstract discussion is here still embedded within a lively instrumental context. And yet this should not hide the fact that a great deal of abstract reasoning is presupposed by Ion’s statement. The design of the lyre with its plain succession of indiscriminate strings ordered according to pitch gives no indication of the inherent crossroads of possible modulations; these only exist in the mind of the musician. Consequently we must assume that the underlying ideas had started to evolve even earlier, at least as early as the first half of the 5th century. A plausible stimulus for such an analysis is the comparison of different instrumental tunings, which becomes necessary if one wants to have available more than one of the traditional structures at once, as was doubtless the case on Ion’s lyre. The rough chronology is confirmed by a passage, probably quoting Aristoxenus, which states that the position of the diázeuxis in the Mixolydian had been subject to discussion in the earlier 5th century (pseudo-​Plutarch, Music 1136de). Since the very notion of diázeuxis (“disjunction”) presupposes the recognition of elements that can be disjoined or not, this appears to push the terminus ante quem for tetrachordal analysis in particular back to not long after 500 bce. So, whatever the semantic origin of Philolaus’ term syllabá, in his times it was well established as the intermediate level of musical structures, between single pitches (phthóngoi) and self-​ contained systems (harmoníai)—​just as the syllable of speech provides a useful level of analysis between phonemes and words. The general lyre tuning that Philolaus takes for granted exemplarily exhibits diázeuxis: an octave consists of two fourths, separated by a tone. This structure obviously constitutes what Philolaus calls “the harmonía” (as opposed to dia pasân for

450   Hellenistic Greek Science the octave as an unstructured interval). Its analysis in terms of named interval sizes, however, is only the ground on which he builds the edifice of a mathematical description, identifying interval sizes with ratios of integers. Again, we have no idea how old this mathematical approach is. Later sources usually associate it with Pythagoras, but their accounts have no historical value. In any case, it is clear that simple integers and their relations inspired the Pythagorean worldview. Since few aspects of the material world, however, lend themselves to such elegant mathematical renditions as do consonant intervals, it is quite likely that musical arithmetic had been playing a key role from Pythagoras’ times on. But how had the association of intervals and ratios been observed, in the first instance? Once more corresponding knowledge fails to show up in Babylonian sources—​or Egyptian sources, at that, facing the legendary connection of Pythagoras with the presumed arcane wisdom of both cultures. On the other hand, a sort of practical familiarity with the basic relations was likely available in the workshops of certain instrument makers, namely those concerned with lutes and woodwinds equipped with finger holes: here stopping the string at half its length or drilling a finger hole halfway down the pipe would result in a pitch shift of an octave, for example. Lutes, however, are conspicuously absent from archaic Greek texts and images, while pipes are omnipresent in the form of the aulos (a pair of reed-​blown tubes played simultaneously). The manufacture of the latter therefore provides a plausible starting point for mathematical harmonics. Once more, a considerable amount of abstraction was involved in transforming pipe-​makers’ rules of thumb to the generalized arithmetical treatment exposed by Philolaus. Not only are intervals and ratios ontologically identified here—​ the octave is not expressed or described by a particular ratio, it “is” 2:1—​but they also are efficiently added to and subtracted from each other in terms of ratio arithmetic. The text does not manage to logically derive the respective results, it rather quotes them in random order. But it is clear that the ratio for the tone is derived from those for the consonances, 9:8 = 3:2 ÷ 4:3. At the end, the fragment sets out upon measuring the intervals in terms of their smallest constituents within a diatonic scale, tones of 9:8 and diéseis, a term that here means the “smaller semitone,” better known as the leîmma. Its ratio, 256:243, is not calculated in the extant quotation, but if we can trust Boethius’ account, Philolaus used it, in a mathematically problematic way, to derive also smaller hypothetic microintervals down to a “kómma,” which he seems to have regarded as a sort of—​though not indivisible?—​unit (Philolaus fr. A26 DK = Boethius, De institutione musica 3.5, 276.15–​277.18 Friedlein; and fr. 6B = Boethius 3.8, 278.11–​16 Friedlein; cf. Barker 2007, 272–​286; Hagel 2009a, 143–​151). Now, while we can associate each aspect of scalar analysis with actual practical needs of musicians, this is not true for interval mathematics. Even though it is probably grounded in practical knowledge, the numerical manipulation of ratios has no bearing whatsoever on matters of music-​making. Here, therefore, we have the hallmarks of science for its own sake; at the same time, it was exactly because of its isolation from practice that this branch of harmonics could more easily acquire a sterile tinge.

Music and Harmonic Theory    451

3.  Development of the Two Major Paradigms In the following centuries, the two approaches developed largely independently and were eventually construed as being in sharp contrast to each other, attaching themselves to the names of Aristoxenus and Pythagoras respectively. The cause of this dichotomy was not yet apparent in the 5th century but surfaced soon afterward, as the question of commensurability. On the one hand, musicians evolved comprehensive systems of scales, which became very important in the construction of a new modulating type of aulos, where an optimal matching of notes and therefore finger holes across the various playable modes was a physical necessity. This was achieved by adopting a simple and entirely commensurable scheme, in which the quartertone (díesis in its typical acceptation) became the unit of measurement (quoted as such by Aristotle): two quartertones giving a semitone, four a tone, and 24 filling the octave. Within an interval of a ninth divided into 28 quartertone steps, one influential system was thus able to arrange the notes of all important musical modes into a coherent system, apparently drawing on traditional relationships between them, as well as establishing new ones (Barker 1978; Hagel 2000, 181–​182; Hagel 2009a, 384–​385). It seems that the first comprehensive diagrams of scales were published in this milieu, perhaps labeled with the signs of the newly developed musical notation. In much the same period, however, the more mathematically minded started to wonder about what all this might mean, given the established ratio of 9:8 for the tone. Evidently, six tones of 9:8, stacked one above the other, will never work out to an octave of 2:1, as the commensurabilist “harmonikoí” presupposed: (9:8)6 ≠ 2. Similarly, it is not possible to give a ratio of integers for a true semitone conceived as the half of a tone of 9:8, as the Pythagorean writer Archytas of Tarentum, a contemporary of Plato, was able to prove—​nor, a fortiori, for a true quartertone. Now one might have objected that the rational nature of all musical intervals was not to be treated as a given. But this would not have helped in the face of the octave problem, as long as it was conceded that the fifth and fourth corresponded to their elegant ratios, which gave such an attractive “explanation” for their concordance. As a result, the science as a whole was stuck:  a physical-​mathematical inquiry would not give up the ratios, but was incapable of providing the modulating systems so urgently needed in musical practice; on the other hand, the harmonikoí could proceed with their business only by ignoring the mathematical branch. Did the latter try to put their endeavors on a theoretical basis, apart from the quartertone that was evidently adopted only for convenience? A passage from Plato’s Republic might hint in this direction, in which Glaucon and Socrates ridicule a certain group of music theorists, set apart from those doing mathematical studies, who executed experiments on strings to settle on a smallest interval, “which one must use as a measure” (Plato, Republic 531ab). From a post-​Aristoxenian viewpoint, such an exercise

452   Hellenistic Greek Science

méson

“bottommost” A

B

“central” e

a

diezeugménon “disjunct” synemménon “conjunct” b d

hyperbolaîon

hyperbolaía

diezeugméne-

synemméne

mése-

hýpaton

hypáte-

is of course pointless because its results would depend on the aural capabilities of the experimenter. Yet this view presupposes the assumption that pitch is a continuum, which the theorists in question apparently doubted: in analogy to the contemporary physical atomist theory of Democritus, they may have been after an atomist (or better: quantum) theory of pitch, hoping that the smallest entities of pitch would reveal themselves within the realm of the audible. Anyway, their attempt was bound to fail. Consequently the proponents of commensurable scale systems retreated to basing their claims on perception as the ultimate judge of musical matters; this, at least, is the stance of Aristoxenus, who brought the commensurable approach to its summit. In Philolaus, we have encountered the analysis of a musically structured octave. A century later, a reference system had emerged that spanned a double octave, and which we know as the “Perfect Scale” (sýstēma téleion). It expanded the two disjunct fourths of Philolaus’ lyre octave by another fourth in each direction, supplemented by another tone at the bottom, matching the central disjunctive tone (“Greater Perfect Scale”). If another fourth was also added right above the central tone, as the conjunct alternative, the result was often called “Unmodulating Scale” (sýstēma ametábolon), in contrast to larger diagrams that incorporated modulation by accounting for more than one key (figure C11.2). At least in the stage we know of, the possible structural variety of the involved fourths was now restricted to what became the standard forms of “tetrachords,” with the smallest intervals at the bottom. In order to identify each note, a system of two levels was used: on the one hand, the old string names in the central octave were duplicated in the new adjacent tetrachords; to distinguish them, the name of the tetrachord was added, which in turn was associated with its highest note. This model scale became a key ingredient of musical thinking until Late Antiquity, informing mathematically minded theorists no less than the notation used by professional singers. When was it conceived, and what was its original purpose? All we know for sure is that it predates Aristoxenus, who trusts the students of his introductory course to understand its terminology without further explanation (Harmonics 50.6–​7 Da Rios). As to its origin, there are (at least) two possibilities—​not necessarily mutually exclusive—​one practical, the other rooted in abstract theory. The proponents of a

“overshoot” e’

a’

“central octave”

Figure C11.2  The tetrachords of the “Perfect Scale” (in the lower part, tetrachord names derive from their higher bounding notes, in the higher part, those note names from the tetrachords; pitch ascends from left to right).

Music and Harmonic Theory    453

a

-‘ - hyperbolaíon nete

(g) méson

-‘ - hyperbolaíon paranete

likhanós mesôn

e (f)

-‘ - dieeugménon nete tríte hyperbolaíon

hypáte mesôn parypáte- mesôn

(D) hýpaton

-‘ - dieeugménon paranete

likhanós hypatôn

B (C)

paramésetríte- dieeugménon

hypáte- hypatôn parypáte- hypatôn

A

mése-

proslambanómenos

theoretical derivation point to the fact that two octaves are required to map all possible shapes of the octave (eídē toû dia pasôn) onto a single scale (cf. figure C11.3). Aristoxenus indeed testifies to a related endeavor, carried out by previous theorists (Harmonics 11.3–​5 Da Rios). These shapes of the octave seem to have been a particularly theoretical concept. Structurally they were related to more irregular scales, apparently used on the aulos (Hagel 2009a: 379–​393) and doubtless also to lyre tunings of which we know almost nothing. In any case, the similarities were significant enough as to derive the regularized octave shapes’ names from the old modes. The succession of shapes could be understood as generated by successively transferring the outermost interval from one end of the scale to the other, in a circular procedure, which arrives at its starting point right when the run through the Perfect Scale’s double octave is completed. As a consequence, the double octave could be represented as a circle (Ptolemy, Harmonics 3.9, 101–​104 Düring)—​and not the octave, as might seem more natural. But there is also a very practical aspect. In Egypt, wooden auloi have been found whose design shows close association with the Perfect Scale (Hagel 2005b). Their date is of course much later, but since Greek soil rarely yields wooden instruments, we cannot know how old the type is. An arcane quotation of numerological speculation in Aristotle links the aulos to cosmology. The general connection does not come as a great surprise: astronomy, the different branches of mathematics, and “not least” music had been declared “siblings” by Archytas, and the same Archytas purportedly also worked on auloi (Archytas fr. 1; Athenaeus 4.184e). More specifically, however, the figure Aristotle appears to cite fits the smallest numerical description of the scale skeleton

b (c) (d) e’ (f’) (g’) a’ diezeugménon hyperbolaîon

Locrian / Hypodorian Mixolydian Lydian Phrygian Dorian Hypolydian Hypophrygian Locrian/ Hypodorian

Figure C11.3  Mapping shapes of the octave on the “Greater Perfect Scale.” Solid lines represent the “fixed” notes of the tetrachordal framework of harmonic theory, dotted lines the “movable” notes whose pitches depend on the “genus” and “shade” of the tetrachords.

454   Hellenistic Greek Science displayed in figure C11.2, and a connection between it and the spheres of the planets is made by Ptolemy, very likely continuing an existing tradition. Possibly, therefore, the “Perfect Scale” was part of a common ground between all kinds of music theorists not later than the early 4th century. However, its astronumerical connection treats it as a structure of empty fourths, attaching significance only to their bounding notes. The same scale skeleton appears in the Division of the Monochord from the end of the 4th century, in what presumably was the original concluding chapter (Sectio Canonis 19; Hagel 2009b). In standard musical terminology this set of notes became labeled as the “fixed” ones, while those within the tetrachords were considered as “moving,” that is, they depended on the particular type and flavor of the tuning. Of course interest in the internal notes and their possible pitches had also begun much earlier, but its history is particularly puzzling. In Aristoxenus’ system, there were three categories (génē, often rendered as “genera”) within one of which musical perception would put each of the infinite possible tuning shades (khróai): harmonía (enharmonic), khrôma (chromatic), and diatonic. In this way, Aristoxenus both set up a comprehensive abstract system and addressed the philosophical problem of providing a theory in the face of a potential infinity inherent in the phenomena. At the same time, the lasting success of his classification mostly eclipsed former approaches. Probably, the three genera derive from very different musical contexts. The easiest to account for is the diatonic, which is already found in the cuneiform sources and whose straightforward type, with perfect fourths and fifths throughout, as readily obtained in the tuning of strings, was mathematically analyzed as early as Philolaus. The enharmonic, on the other hand, was associated with wind instruments, where half-​stopping of finger holes yielded the famous “quartertones”—​which were originally larger, it seems, closer to three eights of a tone. The chromatic, finally, characterized by semitones, may have had its origin in modulation, which established “coloring” notes besides the basic tonalities. Although it was Aristoxenus’ merit to establish rules that would account for all three, he was not the first to consider possible relations. It was once more Archytas who had devised ratios for the diatonic and the enharmonic—​the two varieties in use on early auloi—​and provided a clue on how to find “the chromatic note” in relation to these. Some of the conceptions are also inherent in Greek musical notation, probably devised in the 5th century. For Aristoxenus, the genera were more than just a neat way of accounting for a set of traditional options; he made them one of the two pillars on which his entire system rests. The other pillar is his rule of melodic continuity (synékheia /​to hexês), which logically condenses the idea of a modulating network of tetrachords to a very brief form (Harm. 67.6–​9): each note in the system must make a concord of a fourth with the fourth note in succession, or of a fifth with the fifth (or both). This rule, says Aristoxenus, is a requirement for any musically well-​formed system, but not self-​sufficient; possible sequences of intervals are further restricted by the rules for the genera. These, however, are largely descriptive instead of derived from more general principles: in accord with Aristoxenus’ viewpoint, Harmonics once more emerges as governed by musical

Music and Harmonic Theory    455 “perception.” Aristoxenus conceived of the “moving” notes as each governing a definite range of pitch, within which it can occupy any position, though not all theoretically possible combinations are allowed. The details are set out in figure C11.4. Laying out melodic space on the basis of such abstract rules was the core of Aristoxenus’ achievements, and his partition of the harmonic science into chapters remained canonical: starting from the definition of pitch and its movement it proceeded through intervals (diastḗmata), genera (génē), scales (systḗmata), keys (tónoi), and modulation (metabolḗ) up to matters of composition (melopoiía). His adherence to the commensurable description enabled Aristoxenus to arrange the musical keys in a full circle, augmenting their number to 13 and thus providing for all possible modulations. His system therefore combines the theoretical advantages of equal temperament, governing the tetrachordal framework of “fixed” notes, with a high degree of flexibility regarding the actual attunement of individual performances, defined in terms of the “moving” notes. Inevitably such a comprehensive system was directly opposed to the mathematical standpoint, which neither allowed for a true semitone nor a true circle of fifths. Aristoxenus countered such arguments by devising a demonstration, which he probably carried out on a 12-​stringed instrument. It focuses on the question of the semitone but essentially proves that a series of 12 perfect fifths and fourths reverts to the original pitch. This would have worked out perfectly, since the difference between the mathematically “ideal” intervals and their equally tempered counterparts, less than the hundredth part of a tone, was undetectable by the available means. Thus Aristoxenus had confined harmonics to the study of music in a very “modern” sense, not far removed from the notions of his colleague Theophrastus, who emphasized music’s basically psychological nature against attempts of quantification (Barker 2007, 411–​436). The price was considerable: effectively to deny the significance of the fact that elegant numerical ratios of physical properties in sound-​generating objects correspond to the musical quality of consonance. Aristoxenus did so by strictly applying the Aristotelian notion 2/3 1/3

tone

tone enharmonic chromatic diatonic

e e f

f#

g

a

range of the range of the parypátelikhanós

Figure C11.4  The ranges of the “moving” notes within the tetrachord according to Aristoxenus. For each position in the continuum of possible upper moving notes (likhanoí) one may find the associated possible range of lower moving notes (parypátai).

456   Hellenistic Greek Science that one science must not employ, in its demonstrations, principles belonging to another (Aristotle, Posterior Analytics 75b; cf. Barker 2007, 105–​112); hence, the physics of sound are extraneous to the study of music. Exactly the opposite program is carried out in the Division of the Monochord, transmitted under Euclid’s name and probably composed not long after Aristoxenus’ writings, perhaps even as a reaction to them. It consists in a series of rigid—​though not entirely faultless—​mathematical propositions with musical implications, establishing, along basic interval mathematics as had been used since before Philolaus, doctrines such as the impossibility of bisecting a tone of 9:8—​or any interval of a ratio (n+1):n—​into equal parts, or that six such tones add up to more than an octave of 2:1. The reasoning is arithmetical throughout, even though the proofs are accompanied by quasi-​geometrical diagrams consisting of lines representing integers or ratios, and even though the work culminates in the truly geometrical construction of the Perfect Scale on the monochord (Creese 2010, esp. 22–​50, 72–​80, 151–​156). Geometry intrudes only through the physical nature of the string as a line. Ironically, procedures such as the construction of a true semitone would be straightforward if envisaged in terms of geometry: the entire approach of the Division depends on denying its possibilities and relying on integer arithmetic instead. This puzzling fact can only be explained historically. The experimental device of the monochord, a string divided by one or more movable bridges, was adopted only late, when the arithmetical nature of harmonic reasoning was already firmly established. Nevertheless the author of the Division felt the need to justify the integer approach, after all. This is done right at the start, by outlining a comparatively advanced theory of pitch in terms of movement density—​effectively density of single impacts, as other sources make clearer. From the notion of countable impacts it is derived that their relation is describable in integer ratios (however wrongly, since the impacts would be separated by noncountable and therefore potentially noncommensurable quantities of time and/​or space). Finally, the idea of mathematical elegance is attached to the Greek lexicon, where ratios of n:1 as well as (n+1):n are expressed by single words.

4.  Hellenistic Developments By about 300 bce, therefore, all basic ingredients of Greek harmonic science have appeared on the stage and produced reference works of lasting importance. What was left to the following centuries was, as far as we can see, refinements such as the design of mathematical variants, more or less playful, the production of various handbooks, and above all, efforts to evaluate, to bridge, or at least ignore, the rift between the “mathematical” or “Pythagorean” approach on the one hand, and the “Aristoxenian” view on the other. During this process, the latter remained largely monolithic. Only in the case of the musical keys can we detect significant innovation. Whereas Aristoxenus had augmented

Music and Harmonic Theory    457 their number to a structurally meaningful 13, wherever necessary duplicating existing names to a “high” and a “low” variant a semitone apart, the Late Antique handbooks give a system of 15 tónoi. Three of these merely continue another, one octave higher; anyway, the motivation was hardly to include a few extra-​high notes, but rather the creation of five triads, expressed in a refurbished nomenclature. The traditional modes, Dorian, Phrygian, and Lydian, of course, still retained their names, as well as the respective scales a fourth below, Hypodorian, Hypophrygian, and Hypolydian, whose symmetry had emerged in the 4th century. Now two more basic names were invented instead of Aristoxenus’ “low” duplicates: Iastian and Aeolian, apparently without any connection to earlier modes of the same designation. The term Mixolydian was dropped altogether, and instead every basic scale also got a neighbor a fourth higher, designated by the prefix “Hyper-​.” The fact that it had become possible to put terminological symmetry on top of conventional names indicates that at least the old Mixolydian mode had by then lost its musical identity, and so probably had the others, if to different degrees. The mathematical branch of harmonics, in contrast, produced a number of novel solutions to the problem of an adequate numerical representation of musical tunings:  how to represent the intervals within the tetrachord in ratios. On the one hand, the “Pythagorean” diatonic with two tones of 9:8 and a remaining small semitone (leîmma) of inelegant 256:243 at the bottom remained important for several reasons. Firstly, it reflected the most straightforward lyre tuning and was therefore of permanent practical relevance; secondly, its association with the circle of fifths also associated it with the process of modulation to neighboring keys; and finally, Plato had attached his authority to it by incorporating it within the structure of the world soul in his highly influential Timaeus. On the other hand, however, theorists kept looking for aesthetically more convincing numbers. Archytas had already proposed a system in which enharmonic and diatonic were expressed in terms of ratios of the form (n+1):n throughout. His solution was at odds with principles that became generally recognized from the later 4th century (he assumed a common lowest interval for both genera), but the ideal of “epimoric” ratios remained effective. The next one to use it, as far as we know—​almost all our relevant information comes from a single source, Ptolemy’s Harmonics—​was Eratosthenes. However, he applied it only to the chromatic and the enharmonic, while embracing the “Platonic” version of the diatonic. In the chromatic, he replaced the leîmma with the excellent approximation of 20:19. His representation of the two small lower intervals in the chromatic and enharmonic, which Aristoxenus assumes to be identical, has two faces. On the one hand, he makes them “near-​identical” by assigning subsequent epimorics to them—​20:19 and 19:18 for the chromatic, 39:38 and 40:39 in the enharmonic—​a procedure that figures large also in Ptolemy. On the other, they can be understood as transposing Aristoxenus’ intervals to the monochord, in a mathematically illicit but in this case nevertheless acceptably accurate transformation of microtonal units to units of string length. If his goal was the integration of the two rivaling accounts at least on the level of the single scale, as seems likely, we cannot but admire his success.

458   Hellenistic Greek Science A certain Didymus, who may have lived in the 1st century of our era and is otherwise only known for his discussion of the criteria on which different schools of music theory based their attitudes, found another set of numbers. Again the little we know comes from Ptolemy. Didymus’ special interest seems to have been in mathematical symmetry; he sought for note pairs within the scale whose respective string lengths on the monochord would sum to the length producing the lowest note of the Perfect Scale: in this way, a single bridge position on the monochord could produce two valid pitches. Adrastus of Aphrodisias adopted the idea for the humbler procedure of demonstrating the concords. More importantly, Adrastus addresses a methodological problem in using the monochord (although he fails to notice that it turns against his own procedure much more than it affects the target of his attack: Creese 2010, 254–​256; Hagel 2012): unlike the ideal point in the geometrical division of an ideal line, the material bridge takes up some space on the material string, so that the experiment cannot precisely reflect the proposition. The flawed application of this insight by Adrastus may indicate that it was not his discovery, after all; at any rate, by the 2nd century ce one had become aware of the problematic nature of the very instrument on which the demonstration of “Pythagorean” harmonics was now traditionally relying. There were other, more immediately practical problems as well. Whenever theorists set out to compile tables of numbers for “dividing the monochord” in accordance with a larger scale such as the Perfect Scale, numbers quickly became uncomfortably high. On paper, and with the help of an abacus, they were not very difficult to work out, of course. But as soon as it would have come to applying the figures to the experimental instrument, one could not possibly divide the material ruler into the 10368 units demanded by the division transmitted in the pseudonymous “Timaeus Locrus” (probably based on Crantor), the 41472 called for by Thrasyllus, Gaudentius’ chromatic 20736, Boethius’ three-​genera 9216, or even Aristides Quintilianus’ 4608 (Thesleff 1965, 209–​213, cf. Hagel 2009a, 161 n. 70; Thrasyllus, in Theon of Smyrna, Mathematics Useful for Reading Plato 91–​93 Hiller; Gaudentius 16, 344.22–​24 Jan; Boethius, De institutione. musica. 4.11; and Aristides Quintilianus 3.2, 97.17–​98.21 Winnington-​Ingram). Not specifying a way of how to transpose their numerical diagrams to the monochord, all these endeavors were apparently of a purely speculative nature. Quite likely, therefore, teachers and philosophers generally contented themselves with experimentally demonstrating the basic concords in classroom, but hardly ever a complete musical scale. In this way, potential discrepancies between theory and musical experience would comfortably remain undetected.

5. Ptolemy To change this, it took one of the most brilliant minds of antiquity, who was as much interested in an aesthetically satisfying mathematical foundation of music as undaunted by the intricacies of musical reality and the complications involved in constructing

Music and Harmonic Theory    459 reliable instruments. Claudius Ptolemy combined the Alexandrians’ recognized expertise as a musical connoisseur (cf. Athenaeus 4.176e) with the astronomer’s familiarity with custom-​made precision instruments and the practical scientist’s fluency in transposing unwieldy integer ratios into sexagesimally expressed approximations. His Harmonics are outstanding in many respects, most notably the design of true experiments. But he already ventures to surpass his predecessors, that is, earlier writers of a broadly “Pythagorean” hue, in in his introductory chapters regarding the classification of intervals in terms of consonance and melodic usability. His expressed aim is to use epimoric intervals throughout, wherever possible obtained in a twofold procedure, first bisecting the fourth in two epimorics, one of which is subsequently bisected in turn, producing the required total of three intervals within the tetrachord, which are ordered according to musical principles much like the Aristoxenian ones (with the exception that the lowest interval in the chromatic and enharmonic is only about half the size of the one above it—​apparently an expression of a changed musical taste). The resulting tetrachords are combined to octave scales, which are subjected to the musical judgment of the reader. To make this possible, two practical issues are addressed. One is the construction of a reliable instrument, whose geometry is discussed, as well as a method of testing the uniformity of the strings. Most importantly, Ptolemy expands the monochord to an instrument of eight, later 15 strings, a prerequisite for effectively playing melodies, which alone guarantees the musical experience on which any judgment of the scales’ appropriateness must be based. Secondly, for practical purposes all the ratio-​ determined bridge positions are broken down to approximations along a scale of 120 units, further subdivided to fractions of 60, in accordance with astronomical practice. This gave a double advantage: not only can these figures be immediately applied to a single standard ruler laid out along the string; they are also directly comparable, while comparison between entries in different integer tables normally requires further multiplication leading to even larger figures. In this way, Ptolemy claims, the contemporary reader would be able to determine, beyond doubt, which of the mathematically possible tetrachord divisions actually corresponded to ones actually in use, and would discover that construing them according to purely mathematical principles has lead to such a precise intonation that no expert would find the least fault with it. All this is unprecedented, as far as we see, but Ptolemy is not content. In a second go, he devises a set of even more powerful experiments. Here the reader is asked to tune scale snippets from commonly used lyre tunings on the eight-​stringed canon solely by ear; then from the relationship of certain resulting bridge positions the mathematical nature of the tunings is derived. This latter procedure is not entirely stringent if viewed from outside Ptolemy’s paradigm, since the interpretation presupposes the validity of his principle that melodic intervals must be epimoric; even so, the results appear highly reliable (Hagel 2009a, 194–​216). Ptolemy’s harmonic program culminates in a set of 15 extensive tables, from which all lyre tunings in contemporary use can be read, compared, and set out on the canon: twice seven keys, each in five variants covering various mixtures of tetrachord divisions, plus a compilation of the different

460   Hellenistic Greek Science bridge positions associated with each string, which vary from seven to ten. In between, Ptolemy expounds on further technological advancements of the many-​stringed canon, ingeniously applying the intercept theorem to transform the traditional concept of bridge positions into lateral distances between parallel strings running across a common straight diagonal bridge. By making this bridge pivot around a point in line with the string ends on one side of the instrument, the scale can be transposed to another pitch wholesale. Throughout his program, Ptolemy gives equal attention to both its methodological poles: on the one hand, he addresses small details of construction which might help or encumber the practical use of his proposed instruments; on the other, he takes pains to keep their design reconnected to the mathematical propositions by rigid proofs about their geometry or physics. Outstanding examples are his concern about a possible interference of a bridge moving under one set of strings with a string belonging to another set, or his logical treatment of the question—​instead of accepting the fact as self-​evident—​whether experimental results remain valid if the single string of the monochord is replaced by several of identical length and pitch. On the one hand, Ptolemy had thus been able, almost certainly for the first time, to give a largely accurate mathematical description of tonal structures based on intervals other than pure fifths and fourths that were actually heard at the period. His novel methodology would have seemed to rescue the project of mathematical harmonics, whose Pythagorean proponents had been said to blame musical perception where it did not approve of their “rational” constructs (Ptolemaïs, in Porphyry, Commentary on Ptolemy’s ‘Harmonics’ 23.24–​31 Düring). On the other, although his work remained known, his methods seem not to have been emulated by anybody later on. This may be partly due to the refined technology that his equipment exhibited, especially where laterally moving strings were involved, partly also to his difficult style and demanding lines of argument, quite unusual in the context of Roman-​period harmonic handbook production, where originality was scarce and surprisingly silly writers could still hope to be quoted. On top of this, ironically, to reflect actual practice in his theory, Ptolemy had to sacrifice commonly used terminology for something more arcane. Instead of representing the full circle of fifths, incompatible with the mathematical approach, he reintroduced a set of only seven keys, in accordance with the seven shapes of the octave. Consequently, he associated these keys with the respective shapes’ names, making Dorian, since Plato the most esteemed of modes, the center of the system. However, this was at odds with the musicians’ use of notation, where the Dorian key was marginal—​so it is hardly surprising that Ptolemy’s practical viewpoint failed to be appreciated. Anyway, his extensive tables and experiments apply only to the lyre, whose strings yielded exact pitches, similar to those from the canon; covering all kinds of music in their traditional mutual relation would have demanded more than seven keys (a paragraph from a practically oriented treatise, surviving in the compilation of Anon. Bell., 2, sec. 28, lists a total of 11 keys used on the cithara, the aulos, the hydraulis, and for “orchestic” music). Only a few methodological problems remain even in Ptolemy’s work. Perhaps the most serious was mentioned earlier: the more powerful of his experiments ultimately

Music and Harmonic Theory    461 depend on the ontological assumption that musical intervals must be epimoric even if they are not classified as consonances. Within the program of mathematical harmonics, one or other similar a-​priori assumption doubtless had to be made; but it is as significant as it is characteristic for ancient scientific writing that Ptolemy would rather hush up evident problems within his method than admit the possibility of another viewpoint (in this case, the Aristoxenian). For example, compare the rhetoric by which Ptolemy dissimulates that his elegant method yields neither the most frequently employed tetrachord division (his “tonic diatonic”) nor the “Pythagorean” diatonic (which he calls “ditonic diatonic”), indispensable for modulation and therefore not only contained in some cithara attunements but also governing the mutual relations of Ptolemy’s tables of keys (Hagel 2009a, 203–​204). Anyway, it is certainly significant that, to elevate the science of harmonics to such a degree of rigor, it took an author who was not only willing to reevaluate previous approaches and intellectually capable of doing so but also accustomed to the demands of the exact science of astronomy, which is based on phenomena that are observed visually, and therefore more easily measured and less prone to methodological obfuscation. In this way, Archytas’ statement that the mathematical sciences, astronomy and music are siblings, which stands fairly at the beginning of the preserved direct testimonies on our subject, is true for Ptolemy’s work as the pinnacle of the same tradition not only explicitly, insofar he avails himself of arithmetical just as well as geometrical resources to build his edifice of music theory and eventually to associate its features with elements of astronomy, astrologically conceived, but also on a deeper, methodological level: he was the one to reclaim contemporary scientific standards for the study of pitch structures, which had been in the process of both digressing towards speculation unrelated to experience and fossilizing into handbooks of sometimes questionable quality, even though it might once have provided the major stimulus for the mathematical orientation of parts of Greek natural philosophy.

Bibliography “Da Rios”: Rosetta da Rios, ed., Aristoxeni elementa harmonica. Roma: Typis Publicae Officinae Polygraphicae, 1954. “Düring”: I. Düring, ed., Die Harmonielehre des Klaudios Ptolemaios. Elander: Göteborg, 1930. I. Düring, ed., Porphyrios Kommentar zur Harmonielehre des Ptolemaios. Elander: Göteborg, 1932. “Friedlein”:  G. Friedlein, ed., Boetii De institutione arithmetica /​De institutione musica. Teubner: Leipzig, 1867. “Hiller”: E. Hiller, ed., Theonis Smyrnaei, philosophi platonici, Expositio rerum mathematicarum ad legendum Platonem utilium. Leipzig: Teubner, 1878. “Jan”: C. v. Jan, ed., Musici scriptores Graeci. Teubner: Leipzig, 1895. “Winnington-​Ingram”: R.P. Winnington-​Ingram, ed., Aristidis Quintiliani De musica libri tres. Leipzig: Teubner, 1963.

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Modern works Barker, A. “οἱ καλούμενοι ἁρμονικοί:  The Predecessors of Aristoxenus.” Proceedings of the Cambridge Philological Society 24 (1978): 1–​21. —​—​—​. “Aristides Quintilianus and Constructions in Early Music Theory.” Classical Quarterly 32 (1982): 184–​197. —​—​—​. Greek Musical Writings II:  Harmonic and Acoustic Theory. Cambridge:  Cambridge University Press, 1989. —​—​—​. “Greek Musicologists in the Roman Empire.” In The Sciences in Greco-​Roman Antiquity, ed. T. D. Barnes, 53–​74. Edmonton, Alberta. Reprinted from Apeiron 27.4 (1994). —​—​—​. Scientific Method in Ptolemy’s “Harmonics.” Cambridge:  Cambridge University Press, 2000. —​—​—​. “Early Timaeus Commentaries and Hellenistic Musicology.” In Ancient Approaches to Plato’s Timaeus, ed. R. W. Sharples and A. Sheppard. Bulletin of the Institute of Classical Studies Suppl. 78 (2003): 73–​87. —​—​—​. The Science of Harmonics in Classical Greece. Cambridge:  Cambridge University Press, 2007. —​—​—​. “Shifting Conceptions of ‘Schools’ of Harmonic Theory, 400 bc–​200 ad.” In La Musa dimenticata. Aspetti dell’esperienza musicale greca in età ellenistica, ed. M. C. Martinelli, 165–​ 190. Pisa: Edizioni della Normale, 2009. —​—​—​. Ancient Greek Writers on Their Musical Past. Studies in Greek Musical Historiography. Pisa: Fabrizio Serra, 2014. Creese, David. The Monochord in Ancient Greek Harmonic Science. Cambridge: Cambridge University Press, 2010. Hagel, Stefan. Modulation in altgriechischer Musik:  Antike Melodien im Licht antiker Musiktheorie. Frankfurt am Main: Lang, 2000. —​—​—​. “Is nīd qabli Dorian? Tuning and Modality in Greek and Hurrian Music.” Baghdader Mitteilungen 36 (2005a): 287–​348. —​—​—​. “Twenty-​four in Auloi:  Aristotle, Met. 1093b, the Harmony of the Spheres, and the Formation of the Perfect System.” In Ancient Greek Music in Performance, ed. Stefan Hagel and C. Harrauer, 51–​91. Vienna: Österreichischen Akademie der Wissenschaften, 2005b. —​—​—​. Ancient Greek Music:  A New Technical History. Cambridge:  Cambridge University Press, 2009a. —​—​—​. Review of Barker 2007. Classical Philology 104 (2009b): 243–​248. —​—​—​. Review of Creese 2010. Aestimatio 9 (2012): 337–​351. Kilmer, A. D. “Mesopotamia.” In The New Grove Dictionary of Music and Musicians, 2nd ed., 480–​487. New York: Grove’s Dictionaries, and London: Macmillan, 2001. Rocconi, Eleonora. Le parole delle Muse. La formazione del lessico tecnico musicale nella Grecia antica = Seminari Romani di cultura greca Quaderni 5. Roma: Quasar, 2003. Thesleff, Holger, ed. The Pythagorean Texts of the Hellenistic Period. Åbo: Åbo Akademi, 1965. West, M. L. “Analecta Musica.” Zeitschrift für Papyrologie und Epigraphik 92 (1992a): 1–​54. —​—​—​. Ancient Greek Music. Oxford: Oxford University Press, 1992b. —​—​—​. “The Babylonian Musical Notation and the Hurrian Melodic Texts.” Music & Letters 75 (1994): 161–​179.

chapter C12

An cient Agronomy as a Literature of Be st Practi c e s Philip Thibodeau

1. Introduction Of the one hundred or so Greek and Roman agronomical writers whose names we know, about two dozen have left us substantial collections of fragments, and nine wrote texts that survive complete: Hesiod (Works and Days), Xenophon (Oikonomikos), Cato the Elder (De agri cultura), Varro (De rebus rusticis), Vergil (Georgica), Columella (De re rustica), Pliny the Elder (Historia naturalis, bks. 14–​15, 17–​20), Palladius (Opus agriculturae), and Cassianus Bassus (whose Peri georgias eklogai forms the core of the Geoponica). Aristotle’s writings on animals, Theophrastus’ on plants, and the veterinary works of Vegetius, Pelagonius, and the Hippiatrica also constitute an important part of this tradition. These texts cover a period of history of nearly 1,700 years and offer insights into a broad range of agricultural practices from the ancient Mediterranean, particularly during the Roman era, when our sources become especially rich. They vary widely in content and tone and in the amount of attention they give to prior tradition and the authors’ own personal experience. Most make the case for farming, or georgica, as a source of honor and enjoyment, and all present it as something necessary and profitable. Yet however useful these texts may be in helping us understand ancient farming, the contribution they made to agricultural practice in their day is less obvious. Among the 90% or so of the Mediterranean population who spent their days performing agricultural-​related tasks, rates of literary must have been very low, as we can infer from comparisons with other premodern populations—​perhaps 10%, at best. This tells us something important about the lore that guided actual practice on actual farms: it was largely oral, passed on, learned, and implemented without assistance from written texts.

464   Hellenistic Greek Science If the entire corpus of agricultural literature had been confiscated and burned one day in 100 bce, it is unlikely that anyone in Athens or Rome would have lacked for food or drink that year as a result. What function then did these texts serve? To answer this question it is important to bear in mind that they were written by philosophers, scholars, poets, and wealthy landowners for persons of a similar background: Hesiod writes for a brother who held the lion’s share of the family inheritance, Vergil for his patron Maecenas, Columella for a number of well-​educated farmer friends, Varro for his aristocratic wife. The authors take for granted that their readers own property on which cultivation is ongoing and are ready to learn how to do things better. Inevitably they touch on agricultural practice as it was conducted in their day, but they did not write to document such. As a rule, it is not the common practices of agriculture that their works set out to describe, but the best practices. What specifically is meant by the term “best” depends of course on the standard of evaluation. It might, for instance, be understood in a social context as a synonym for the word “aristocratic”; an element of class snobbery occasionally constrains our sources from getting into gross details, especially where animals were concerned. But most often the appropriate sense of “best” is economic. The agronomists set out to teach their readers how to succeed at farming in a material way—​as Varro puts it, how to increase the quantity and quality of agricultural yield, and avoid losses (De rebus rusticis 2.4). Farming manuals develop from, and often return to, the discourse of oikonomika, the profitable and sustainable exploitation of one’s landed property. For the majority of ancient writers social and economic excellence is the only excellence that counts. Others took the view that best practice should be founded on knowl­ edge of natural causes. This kind of writing is more recognizably scientific, since it makes an appeal to principles rooted in the discourse of botany, zoology, or physics; however, as we shall see, the scientific perspective is a rare bird. More common in agronomical writing is a strain of discourse that can be classified as paradoxography—​texts that invite readers to contemplate unusual instances of agricultural success or explain how to manipulate nature through paradoxical means (means often labeled “magical”). Here the writer’s attention to best practice causes him to focus on things that are valued for their exclusivity: crops, animals, or techniques that are rare, exotic, out of the ordinary, or somehow “contrary to normal expectation” (para-​doxa in its root sense). These three forms of discourse—​economic, natural scientific, and paradoxographical—​constituted much of the literature of ancient agronomy. There are numerous edifying surveys of the practices of farming in Greco-​Roman antiquity, as reconstructed through a study of literary sources, archaeological and archaeo-​botanical finds, and comparative agronomy (White 1970; Flach 1990; Isager and Skydsgaard 1992; Kron 2008). This article offers a sketch of the body of agronomical knowledge that was communicated through books (Oder 1890–​1893; White 1973; McCabe 2007). I begin by documenting the gradual expansion of written knowledge as it came to cover more topics and treat them in greater detail. The distinctive features of economic “best practice” are outlined next. There follows a survey of the uses of scientific

Ancient Agronomy as a Literature of Best Practices    465 explanation, and a case study of the interaction between agronomy and a more mature ancient science (astronomy). To conclude I trace some of the uses of paradoxography in agronomical literature.

2.  The Expanding Scope of Agronomy From the Iron Age onward, the history of farming in the ancient pagan Mediterranean followed an arc of slow but meaningful technical progress; it is possible to trace the development over time of new strains of cereals, new varieties of fruit, new methods of plant propagation, better kinds of animal feed, more complex forms of veterinary medicine, and improved methods for storing and shipping agricultural produce. With the coming of literacy, the ensuing agronomical literary tradition would likewise evolve, sometimes in ways that mirror real-​world developments, sometimes in accordance with its own logic. It may help to divide this literary evolution into two broad phases. In the first, running from Hesiod to Mago of Carthage (8th to 2nd century bce), we see the range of topics treated by agricultural writers gradually expand, with what had been a nearly exclusive focus on cereals eventually coming to embrace all the major subdivisions of agronomy. In the second phase, which runs from Mago to the Geoponica (2nd century bce to 10th century ce), an established core of agronomical lore is constantly refashioned and reconfigured, even as new forms of specialized knowledge take on written form for the first time. The agricultural literary tradition starts with Hesiod of Ascra, the composer of a didactic poem that has come down to us under the title Works and Days. The first half of the poem (1–​382) does not speak of farming per se; Hesiod muses on justice and the origins of human suffering, and advises his brother Perses to seek wealth by honest means. It is the second half of the poem, with its memorable depictions of farm work and rustic leisure, that justifies its title. Within the “Works” section (lines 383–​617) Hesiod presents advice on plowing, planting, harvesting, threshing of grain, woodcutting, and the construction of a plow. He mentions vine pruning and the care of oxen, goats, and sheep but without much elaboration. Although the poet is acquainted with olive oil and figs, he never speaks of the cultivation of their trees. The times for annual tasks are indicated by the appearance of certain stars, birds, and animals, and those for monthly tasks by the days of the moon (765–​828). For Hesiod, it is the job of the farmer to observe justice and manage his inheritance well; beyond that, his primary task is working the soil (a task that provides the Greek word for farming, ge-​orgia, its etymology) to raise cereals. About two centuries pass before the next Greek agronomical work appears: Xenophon’s essay on household management and farming, the Oikonomikos. Like Hesiod, Xenophon begins by talking about moral and social concerns, discussing first how a good aristocrat should instruct his young wife and manage his slaves (Pomeroy 1994). As in Hesiod, a review of the basic techniques of farming is reserved for the end of

466   Hellenistic Greek Science the treatise (15–​19). There Socrates is made to learn from Ischomachus that a farmer can learn all he needs to know by watching his neighbors and learning from them: this and some common sense will supply him with answers to any questions he may have about tilling the soil, growing cereals, or planting trees. In speaking of the latter, Xenophon specifically mentions grapevines (classified as trees by the Greeks and Romans), fig trees, and olive trees. Xenophon’ insistence that farming is easy to understand and does not require book knowledge (15.10–​16.2) places him somewhat at odds with the mainstream agricultural tradition—​though as noted in the introduction, his stance is consistent with the social realities of ancient farming. He criticizes previous writers on agriculture who insisted “the man who plans to farm correctly must first understand the nature of the soil” (16.2). It is possible he is referring here to prose treatises by men like Charetides of Paros or Apollodorus of Lemnos, two early authors cited by Aristotle (Politics 1.11, 1258b39). But a more likely target is the philosopher Democritus, who is reported to have written a treatise on farming, Peri georgias. Many if not most of the texts ascribed to Democritus in antiquity seem to stem from the “Democritean” writer Bolus of Mendes (Wellmann 1921), but some plausible-​looking fragments discuss soil quality, fencing, planting times, and winemaking. After Xenophon a certain Androtion, thought to be identical to the Athenian atthidographer (385–​355 bce), wrote a treatise on farming that discussed best practices for cultivating trees such as the fig, apple, pear, olive, pomegranate, and myrtle. Together these texts make clear that, by the end of the 4th century, prose works on farming were discussing all the members of the “Mediterranean triad”—​wheat, olives, and wine—​as well as fruit trees. By contrast, animal husbandry appears to have occupied a marginal place at this stage in the written tradition. Simon of Athens and Xenophon wrote about horsemanship, but with a focus on riding and training. Aristotle frequently reports the lore of cattle breeders, goatherds, and shepherds in his zoological works (Louis 1970), but never identifies written sources for animal care. He seems to have distinguished the raising of animals from farming proper. In the Politics Aristotle writes (1.11, 1258b12–​22): The practically useful branches of the art of wealth-​getting are first, an expert knowledge of livestock, what breeds are most profitable and in what localities and under what conditions, for instance what particular stock in horses or cattle or sheep . . . secondly, the subject of farming proper (georgia), and this again is divided into cereal-​growing and tree-​planting; also, there is bee-​keeping, and the breeding of the other creatures finned and feathered which can be used to furnish supplies. These then are the branches and primary parts of wealth-​getting in the most proper sense. (Trans. Rackham, slightly adapted)

Note the claim that georgia deals only with cultivating plants, not with raising livestock or other animals. It is also noteworthy that Aristotle treats agricultural knowledge in the same way Hesiod and Xenophon did, not as an independent field of study but as an adjunct to the art of wealth getting, khrematistike.

Ancient Agronomy as a Literature of Best Practices    467 After Aristotle and Theophrastus, there is a span of some 200 years for which our knowledge of georgic literature is very poor—​little more than a list of 52 authors, preserved by Varro in alphabetical order (De rebus rusticis 1.1.9), whose writings date to this period. To be sure, not all of those Varro names were agronomists in the strict sense: some were doctors or herbalists (Apollodorus of Taras, Hicesias), others historians writing about the agriculture of foreign nations in an ethnographic vein (Bion of Soloi, Dinon of Colophon); but most must have been farmers. The rise of the specialized monograph testifies to the growing complexity of the literature at this time. A certain Moschion wrote an entire book about radishes (Pliny 19.87); Amphilochus of Athens dedicated a volume to the important feed plants alfalfa and shrub-​medick (13.130); Menecrates of Ephesus composed a poem on beekeeping (Varro 3.16.18). The first treatises on animal husbandry seem to have been composed during this time, since a Hellenistic writer named Euboulus is cited in the Hippiatrica for the treatment of diseases in horses (McCabe 2007). Only one text from this era has come down to us in a way that allows us to form an impression of the original work. Nicander of Colophon, best known for his didactic poems on poisonous animals and cures for their bites, also wrote a poem in two books entitled Georgica, of which approximately 150 lines are preserved in quotation by Athenaeus (Gow and Scholfield 1953). The title suggests a treatise on farming, yet the fragments deal solely with the cultivation of vegetables, flowers, and herbs. That georgica could be taken to mean “gardening” points to the expanding denotation of the term. Cato the Elder’s De agricultura (ca 160 bce) is a unique text in several respects. It is the first work of Roman prose to survive in its entirety, written in an unadorned, archaic Latin. It is the most forthcoming agricultural treatise when it comes to such quotidian details as how many buckets an oil press-​room should have, or what it costs to buy a press at Pompeii. It is also, at the level of farming technique, very sophisticated, written with a keen eye for efficient technique and the vagaries of a working farm. Like prior Greek writers, Cato is not concerned to cover all of agronomy but to give as detailed a portrait as possible of its most profitable divisions. Cereals and livestock receive some attention, but olives, vines, and fruit trees stand front and center. Cato also speaks in great detail about farm buildings, folk medicine, religious observance, and food storage. Cato was followed a few decades later by two Romans with a farm in Cisalpine Gaul, the father and son Hostilii Sasernae, who wrote in a similar vein about costs and efficiencies; they discussed staffing, climate, vineyards, manure, folk remedies, and the operation of clay, stone, and sand pits (White 1973). It is a curious fact that the single most important work on agriculture from Greco-​ Roman antiquity was not written in either Greek or Latin: the Carthaginian nobleman Mago spoke and wrote Punic. The Punic title of his work is unknown, but not its size: 28 books, larger than any other ancient treatment of the subject. A survey of the fragments suggests the comprehensiveness of its coverage: property management, cereals, vines, olives, fruit trees, nut trees, herbs, flowers, the storage of produce, raising cattle and ovicaprids, poultry, and beekeeping (Speranza 1971); the material on veterinary medicine alone was enough to fill a book (Varro De rebus rusticis 2.5.18). Given the loss of

468   Hellenistic Greek Science earlier Hellenistic materials we cannot tell for sure whether Mago pioneered discussion in any particular field, but he appears to have been the first to treat all of these subjects together. Pliny informs us that around 146 bce the Roman Senate commissioned a group of translators to render Mago’s encyclopedia into Latin (18.22–​23); unfortunately, nothing of this translation project remains. Instead, later writers read their Mago in Greek, thanks to an effort in the 1st century bce that Varro describes after giving his list of 52 Hellenistic agronomists (1.1.10): Mago of Carthage, writing in Punic, has surpassed all of them in fame, encompassing a wide range of topics in 28 books. Cassius Dionysius of Utica translated these into Greek in 20 books and dedicated them to the praetor Sextilius, after adding to these rolls quite a bit drawn from the sources I have just mentioned and taking from Mago the equivalent of 8 books. Diophanes of Bithynia helpfully reduced this collection to 6 books and dedicated it to King Deiotarus.

This notice allows us reconstruct a two-​stage process of translation and anthologization. Around 90 bce Cassius Dionysius, a Greek freedman, translated Mago’s work from Punic into Greek. He also excerpted it, thus reducing it to eight books worth of Carthaginian material, and combined this with 12 books worth of excerpts from the aforementioned Hellenistic agronomists. A generation later, around 60 bce, Diophanes condensed Dionysius’ work into six books. Both of these collections proved popular and became the primary channel through which later writers knew Mago and other Hellenistic writers. The occurrence of parallel passages in later sources is very often due to their origin in the Mago-​Dionysius-​Diophanes triad. The compact but comprehensive agronomical encyclopedia dealing with most of the topics treated by Mago would remain a popular format for the remainder of antiquity. Later writers came up with different ways of rearranging or simplifying its materials and often added insights gleaned from their own experience as farmers. Varro’s work De rebus rusticis is a good illustration of this. In the introduction he characterizes his three book treatise as an attempt to make the writings of Mago-​Dionysius-​Diophanes even more compact and accessible (1.1.11). One of his most noticeable contributions is the organization of material according to notional matrices: book 2, for instance, has 81 subdivisions, to cover nine different kinds of quadruped animal and nine different forms of animal care (Skydsgaard 1968). Another innovation is Varro’s identification of a third branch of agriculture, complementing plant growing and animal husbandry, which he calls uillatica pastio, or “boutique zooculture”: the raising of fowl, both common and exotic, dormice, snails, and bees. Varro gives the credit for this innovation to a certain Marcus Seius who collected “the scattered and unsystematic” remarks of Mago and Dionysius on the subject and implemented them with profitable results (3.2.13). Roman writers from the Imperial era continued to treat a wide range of subjects, no matter how brief or expansive their work. The poet Vergil would adapt Varro’s division

Ancient Agronomy as a Literature of Best Practices    469 of topics in composing his Georgics, devoting one book to Hesiodic themes and cereals, one to trees, one to animal husbandry, and one to beekeeping. Cornelius Celsus, best known for his surviving De medicina, also wrote five lost books on agriculture and appears to have aimed at complete coverage, tackling such matters as labor, plowing, ovicaprids, beekeeping, and poultry farming. Columella’s 12 book De re rustica is one of the most attractive introductions to ancient agriculture and one of the most thoughtful, with the author repeatedly bringing to bear his personal experience, particularly when talking about vineyards and fowl; the Magonian curriculum is fully represented in his work. Like Celsus, Pliny the Elder incorporates a complete survey of agronomy into his larger encyclopedia project, through books 8 (quadrupeds), 10–​11 (birds and insects), 14–​15 (vines and trees), and 17–​20 (trees, cereals, gardens). Finally, the Opus agriculturae of the late Roman writer Palladius (ca 375–​450 ce) presents this traditional core of information within a novel format based on the Roman calendar. Greek agronomical encyclopedias were no less numerous. The brothers Quintilii, who were both Roman consuls during Marcus Aurelius’ reign, put together the first Greek agricultural survey since Diophanes. Vindonius Anatolius of Berutos (ca 350 ce) authored a 12-​book work entitled Collection of Farming Practices whose success can be measured by its subsequent translation into Syriac, Arabic, Old Persian, and Armenian. At some point in the 6th-​century ce, the scholar Cassianus Bassus combined Anatolius’ collection with a 15-​book farm compendium by Didumos of Alexandria to create a work, Excerpts on Farming, which later served as the basis for the Byzantine treatise known as the Geoponica (Rodgers 2002). This compilation, which survives complete in 50 different manuscripts, embraced every form of literary farm lore known in the Greek east during the first millennium. It covers the following topics: weather lore, site location, water and soil types, the Mediterranean triad (cereals/​legumes, vines, and olives), nut and fruit trees, garden and medicinal plants, vegetables, pests, poultry, bees, horses, cattle, sheep, goats, dogs, swine, game, and fish. Yet like mice among mountains, short, specialized works of agriculture continued to be composed in both Greek and Latin, works designed to deal more systematically with subjects that had received superficial handling in the compendia. Prose treatises devoted specifically to gardening appear for the first time during the Augustan era, bearing generic titles (Cepurica, Gardening), with five different authors attested (Pliny 1.19). A  number of handbooks discussing the storage of agricultural foodstuffs were written in the same period (Columella 12.4.2). One Philiscus of Thasos, nicknamed “The Wildman” for his residence in a deserted backwater, left behind a handbook on beekeeping, as did Aristomachus of Soloi, who could draw upon 58 years of personal experience with his hives (Pliny 11.19). Between the 3rd and 7th-​centuries ce, several Greek authors wrote treatises on horse medicine, substantial fragments of which survive in the Byzantine compilation Hippiatrica (McCabe 2007). Others who specialized in agricultural magic and paradoxography will be discussed below.

470   Hellenistic Greek Science

3.  The Language of Best Practice Ancient agronomical texts often speak of the common practices of agriculture, or what the author perceives to be common practice: many a sentence reports what “they”—​ that is, farmers in general—​do when they plant or raise animals. Yet authors took the trouble to write to publicize agricultural practices they believed better than the norm. These might be practices known through firsthand experience, observation of others, or from books; whatever their source, the articulation of best practice forms the heart of each text. This means that the practices described by our sources were not always representative of how most farmers in the author’s place or age farmed; best practice might have been the norm but it is unrealistic to expect that this was always so. Identifying a piece of lore as best practice also must be done with care; fortunately, an author’s recommendation of some practice often leaves a mark on the rhetoric of his (or her) text.1 One common indicator of a best practice is a tone of polemic or disagreement. Hesiod, for instance, concludes his disquisition on lucky and unlucky lunar days by calling his calendar “a great boon for mortals . . . one man praises one day and another, another, but few know” (822–​824), the implication being that he himself knows and that his classification of days is superior to others’. Varro warns his readers against accepting the rules laid down by Cato and the Sasernae for staffing vineyards: neither admits of being scaled up or down properly, nor do they take into account the varying qualities and capacities of different soils in the way Varro would (1.18.3–​7). A passage from Columella offers an interesting glimpse of a controversy arising even in the course of publication (4.1.1): You reported, Publius Silvinus, that after you read the book I  wrote on vineyard planting (sc. bk. 3) to a group of persons interested in agriculture, you found that some spoke well of the majority of my recommendations, but criticized one or two: in particular, they thought I made the pits for sowing the vines too deep, a half-​ foot more than the depth of two feet which Celsus and Atticus recommend.

This issue was important enough to divide opinion:  Silvinus’ friends, insisting that Celsus and Atticus were right about two feet, stood opposed to Columella, who was sure that another half foot would make a difference. Another clear token of preference is an agronomist’s ranking. Theophrastus cites Charetides (probably: the name is reported as “Khartodras”) for the view that human manure is the most pungent and therefore the best of all dungs, followed in order by that from pigs, goats, sheep, oxen, and mules (Historia plantarum 2.7.4); Cassius Dionysius countered with a different ranking: droppings from pigeons first, followed by human, goat, sheep, ass, and horse dung (1.38.2–​3). Cato gives a ranking of land usages that seems arranged in descending order of profitability (1.7): a top-​notch vineyard, an irrigated

1 

One ancient agronomist, from the list of Varro 1.1.10, had a name that in Greek is feminine: Persis.

Ancient Agronomy as a Literature of Best Practices    471 market-​garden, a willow grove (for making ties), an olive yard, a grazing meadow, grain land, a forest for timber, an orchard, and an acorn-​bearing forest (to feed pigs). The position of each item in its list serves to distill a wealth of experience into a simple set of comparisons. Yet another sign of advocacy for a specific way of doing things is the introduction of extraordinary detail. In one of Mago’s books on trees, he wrote that not all pears should be planted at the same time: round or oblong ones should go in during late fall, and the rest in the season following (Pliny 17.131); the implication is that this distinction was not always observed by other farmers. When Cato talks about building an olive crusher, he spells out a number of contingencies to avoid, such as a situation where the central pivot is misaligned or where one stone that should turn freely rubs against another (20–​22). A well-​designed and well-​built press would not have these problems; one must follow Cato’s detailed advice to escape them. The citation of authorities can be a sign of best practice in certain contexts. For an account of how to prepare a nursery bed for cypress seedlings, Cato refers to the demonstration of an otherwise unknown Minius Percennius (151), the recommendation receiving extra weight from the fact that, except for “the Manlii” in the next chapter (152), Cato names no other sources. Cato was in turn often quoted by later Roman agronomists, like Varro (1.22.3, 24.1) and Pliny (18.25, 18.34, etc.), whose copying constituted an implicit acknowledgment of the value of their predecessor’s advice. The anthologies drawn up by Cassius Dionysius, Diophanes, and Julius Hyginus, and the collections that were combined to form the Geoponica and the Hippiatrica likewise testify to a long process of selection and sorting of best texts; we rarely have any sense of the criteria underlying the decision to quote or paraphrase a predecessor, but it is reasonable to think that the authors’ personal experience with the subject often played a part. Finally, the first-​person is commonly used to set a seal of approval on a piece of advice. Cato says, “If you ask me what kind of farm is best, I will say, a hundred iugera of land with every form of land-​use and an excellent location” (1). Columella repeats a recommendation that seeds be treated with the juice of a plant called sedum to prevent pests “and experience has taught us that this is correct” (11.3.61). Photios describes Anatolius’ whole agronomical collection as “a useful book, as we have often found by direct experience” (163). A remedy from the Hippiatrica ends with the simple phrase: “Tested” (McCabe 2007). The language of personal recommendation and testing can even attach to practices we may not consider “best.” Consider the following from Anatolius: And this treatment as well has been approved by experiment: let someone take in his right hand a tortoise on its back which is found in the marshes and carry it to the vineyard, and going in let him put it down, alive, on its back, piling up a little earth around it so it will not be able, by turning itself over, to go away . . . and when this has happened, the hail does not fall either on the field or the whole area. There are some who say that the carrying around and placing of the tortoise ought to take place in the sixth hour of the day or night. But we, even without this, not observing the hour

472   Hellenistic Greek Science carefully, did not repent of it, and we think that this suffices, which has often been proved by experiment. (Trans. Rodgers; Rodgers 1980, 2)

It is entirely possible that on one or more occasions Anatolius placed an overturned tortoise in his vineyard before a hailstorm and the vines escaped damage. For nonphilosophers modern and ancient, hard questions about causality can be skirted so long as experience has shown that a procedure works.

4.  Causal Explanations of Practice Since the Greek and Roman agronomists boasted of the value of their techniques, and since those techniques sufficed to raise yields and nutritional quality to levels that would not be reached again in Europe until the 18th or 19th centuries (Kron 2008, 2012), it is worth considering whether their success was due to something resembling modern agronomical science. This matter can be addressed by considering the appearance in our texts of etiologies—​that is, explanations of plant growth, animal life, or farming technique which make an appeal to underlying causes. If all of our texts resembled Theophrastus’ Causes of Plants, the case in favor would be a strong one indeed. This work is one of our most important sources for early Greek plant agronomy and makes a concerted effort to give causal explanations for phenomena of plant life and the effectiveness of agricultural procedure. Theophrastus justifies his inquiry by stating that knowledge of causes makes one a better farmer (Causae plantarum 3.2.3): For a given procedure (sc. of farming) there is an account that gives its cause, and the cause must not escape us. For the man who carries out the procedure in ignorance of the cause, guided by habit and by events, may perhaps succeed, but he does not know (just as in medicine); and complete possession of the art comes from both.

Over the course of six books, Theophrastus moves from one scientific explanation to another, like this (1.15.1): Trees left untended will blossom earlier than cultivated trees like vines, apples, olives, figs, and so on because they have more heat when the earth is not dug up and their roots are not laid bare, and heat is the source of their motion.

Among other topics his study covers plant growth, plant reproduction, times of sowing and harvest, and preparation of the soil. However, this part of Theophrastus’ botanical corpus was not well received—​Varro calls it “more suited to those who cultivate philosophers’ lecture-​halls than those who want to cultivate their land” (1.5.2)—​and outside his work, examples of agricultural etiology are few and far between. A fragment of Democritus justifies a date for sowing grain by citing natural propensities (Geoponica 2.14.4):

Ancient Agronomy as a Literature of Best Practices    473 Democritus, in his recommendation that one sow specifically near the setting of the Crown (sc. Corona Borealis, an early constellation), passes along an observation of nature, namely, that at that time not only is it normal for frequent showers to occur, but the earth too has a natural, receptive impulse which makes seeds sown then more fertile.

Some Roman writers also indulged in scientific digressions. Varro states that there are five basic causes of illness in animals: excessive heat, excessive cold, too much or too little work, or moderate work followed too soon by eating or drinking (2.1.23); the principles may be simple, but they are comprehensive. Columella adverts to a principle of inheritance that his uncle demonstrated through an experiment. One day the uncle spotted at Gades a number of colorful but shaggy wild rams that had been imported from Africa for the public shows. Intrigued, he purchased some and took them home to breed with his ewes. When the offspring turned out colorful but still too shaggy, he mated them with some Tarentine ewes, a breed famous for their soft fleeces. The offspring of this match proved to be the best of both worlds, showing the delicate wool of their mothers and bright color of their male progenitors. “So, on the basis of this analogy, he used to say that any trait present in wild animals would reappear in later stages of descent with its wildness diminished” (7.2.4–​5). This would have been an interesting investigation to pursue further, since the phenomena of inheritance become more complex and surprising when pursued over multiple generations. But one looks in vain for edifying accounts of cause or experimentation in Xenophon, Cato, Palladius, or the fragments of Nicander, Mago, or the Geoponica authors. Moreover, the examples one does encounter are ad hoc, not underwritten by any theory or set of principles beyond, for example, belief in four elements or common notions about the inheritance of traits. When etiologies do go a little deeper, it is to no effect. Varro’s book includes this remarkable observation (1.12.1–​2): If you are forced to build your villa by a river, take care that the river does not face it, for in the winter it will get very cold and in the summer it will be unhealthy. One should also watch out for swampy places, both for the aforementioned reasons and because tiny creatures grow there, hard for the eye to follow, which travel through the air to enter the body through the mouth and nose and produce illnesses that are hard to manage.

This is remarkable, because instead of attributing the unhealthiness of wetlands to some ill-​defined miasma, it places the blame on hard-​to-​see creatures that suggest either microbes or malaria-​bearing mosquitoes. Yet despite the interest of this explanation it has no known roots in prior medical theory and occasioned no follow-​up by later writers. Another sign of the conceptual immaturity of ancient agronomy is its lack of organized factions. Our authorities disagree and dispute with one another, but not on the basis of principles defended and codified by schools. Platonists and Sophists, Stoics and Epicureans, Dogmatists and Methodists did not advance rival explanations of

474   Hellenistic Greek Science agricultural phenomena. When agriculture is mentioned in works that seek to define the nature of tekhne or episteme, it serves as a prime example of a body of knowl­ edge that could be implemented effectively based on ordinary experience, without an appreciation of causes, a science that was wholly empirical (Cicero, De oratore 1.249; Philodemos, Oeconomica, col. 7.30–​33 Jensen; Celsus De medicina pref.32; Columella, pref.11; and Galen, On Medical Experience 98–​99 Walzer). The absence of causal explanations from most agronomical writing is not an accident of transmission, then, but a basic feature: the impressive achievements of Mediterranean farmers were due to their trying out, and perfecting, new techniques without assistance from theory. Agricultural knowl­edge in Europe would remain in a similar condition until the 18th century, when pioneering agronomists like Jethro Tull (1674–​1741) began to write and polemicize on the basis of a fruitful mixture of theory and experiment.

5.  A Scientific Framework: Farmer’s Calendars If ancient agronomy lacked a distinctive scientific discourse or theory of its own, it nevertheless had productive interactions with other more developed sciences. By way of illustration I offer the interaction between the timing of annual farm tasks and knowledge of astronomical and calendrical cycles. Agriculture was one of the areas where the science of astronomy had important practical applications, since farmers needed to know when to do what. In most parts of the Mediterranean, fields were plowed throughout the summer, sown with grains and legumes in the fall, and the crop harvested at the end of winter. The sowing had to be well-​timed: too early, and the seeds would germinate before the autumn rains brought a consistent supply of moisture; too late, and the crop would not have enough time to mature. The harvest likewise required precise timing: a farmer would want to wait to let his crop become as mature as possible, but not so long that the plants would drop their seeds or be exposed to too much dangerous weather. Similar considerations applied to the planting and harvesting of fruit trees, and the breeding of livestock. Because the key cycles followed the natural year, the phenomena of the heavens offered the most reliable set of cues for keeping track of time. Hesiod identifies the most critical periods using a set of signs that would become canonical for later writers. The setting of the Pleiades and Orion in the west at dawn (early November) marked the time to plow and sow; the rising of Arcturus at dusk (late February) was a sign to prune vines. The rising of Pleiades in the east at dawn (mid-​May) indicated the start of the sailing season and the time to harvest grain. Threshing was done around the summer solstice (late June), when Orion had risen into the morning sky. The Dog Days, when Sirius was too close to the sun to be seen, were the best time to sail. In mid-​September the rising of Arcturus in the morning sky signaled that the

Ancient Agronomy as a Literature of Best Practices    475 grapes were ripe and ready to be harvested. Observation of these phenomena would keep any chore from being accomplished out of season and thus reduce the risk of loss (West 1978). The next stage in the development of this tradition involved an expansion of the number of stellar signs and their correlation with weather events. Much of this work was done in the period 450–​350 bce by figures such as Euctemon of Athens, Democritus, Eudoxus of Knidos, and Callippus of Cyzicus (Lehoux 2007). All of them published parapegmata—​texts that listed the celestial and meteorological events of the year with day counts from one to the next. Other constellations were brought into the system, such as Corona, Delphinus and Aquila, as well as the signs of the zodiac. A belief that in a given locale the same kinds of weather (wind, rain, or storm) tended to occur on the same day of the astronomical year motivated the recording of meteorological data that could help farmers plan their work even more precisely, if they wished to know whether to wait a day or two for rain or clear skies. Early Greek and Roman authors did not tie the farmer’s cycle of chores to the civil calendar, for the simple reason that their civil calendars were generally out of step with the natural seasons by weeks or even months. There are exceptions: Aristotle and Theophrastus occasionally link times for animal breeding and plant growth to months of the Athenian calendar (e.g., Historia animalium 6.21, 575b15, and Historia plantarum 4.15.3), presumably because in their day it was properly intercalated. But the norm was to use astronomical phenomena as reference points. Mago of Carthage, for instance, times the planting of fruit trees to the setting of Arcturus, the Pleiades, Sagitta, and Aquila (Pliny 17.131). Cato marks the year by the equinoxes and other natural phenomena (44, 161). Varro, though he alludes to the Julian calendar reform (1.28.1), makes no use of it for his own schedule of annual tasks, which is punctuated by the equinoxes, the solstices, the first sign of the west wind, and the risings of Sirius and the Pleiades (1.28–​36). The earliest attested example of a farm schedule fully correlated to the civil calendar is a beekeeper’s calendar which was created by Julius Hyginus, who was freedman of Caesar; his text specified which tasks should be performed during each month of the Julian year, and left out astronomical data (Columella 9.14). In his eleventh book Columella gives a schedule of annual tasks designed for use by a bailiff; it is arranged by Roman calendar month and connects the risings and settings of stars to specific Roman days (11.1.29–​2.2). The elder Pliny attempted something similar in his book on cereal cultivation, creating in the process a rather unwieldy mix of civil calendar, astronomical calendar, and schedule of significant tasks (18.224–​320). In Greek, the Quintilii (Geoponica bk. 3) composed the first farmer’s calendar arranged by Roman months. Palladius took this development one step further by organizing his entire Opus agriculturae around a core of 12 books spelling out the tasks to be performed during each Roman month, starting with January. There is no longer any mention of the rising or setting of particular stars, although as if to pay tribute to the astronomical tradition he appends monthly tables of shadow lengths for each hour of the day. This novel arrangement of traditional material made Palladius’ work very useful—​it was the central agronomical text in the west from Late Antiquity through the medieval period,

476   Hellenistic Greek Science perhaps because of Cassiodorus’ recommendation (Institutes 1.28.6)—​and it may be no coincidence that after Palladius, new writing on agriculture in the Roman west ground virtually to a halt. When it resumed in the Renaissance, the Palladian format hybridized with the astronomical table tradition to produce the genre now known as the farmer’s almanac.

6.  Paradox and Practice One strain of agronomical discourse that looms nearly as large in ancient texts as that of the sciences is paradoxography. Writers introduced paradoxographical material for two different reasons. In some cases it was for the sake of curiosity: instances of unusually prolific vines or strange sheep or fertile lands are cited simply to make the reader marvel at the diversity of nature and the power of cultivation. In others, paradoxography becomes a practical affair, as authorities provide recipes for reproducing marvels on one’s own farm. Both kinds occur in our texts, although the latter came to assume an increasingly prominent role over time. This second mode is often discussed under the rubric of magical or superstitious practice, but seeking to cordon off irrational styles of farming from the rest does more to obscure the purposes of these texts than to illuminate them. Lore about the agricultural wonders of remote lands enters the ancient tradition first via myths and travelers’ tales, and later as a side-​effect of Greek and Roman imperial conquest. Greek myths held that somewhere in the distant north or west a team of nymphs named the Hesperides kept a garden in which a tree that bore golden apples grew. At the palace of Alcinous, Homer’s Odysseus encountered a royal garden where wonderful trees bore fruit “that is never ruined and never fails, neither in winter or in summer, but grows year round” (7.117–​118). Herodotus reports that the land of Assyria bore no figs, vines, or olives but produced wheat yields nearing 300:1 on plants with leaves four fingers wide (1.193.3). After Alexander’s conquest of the east, witnesses returned to Greece reporting all manner of exotic flora, including a “fig tree” in India that has roots sprouting from its branches and spanned nearly 40 paces (the banyan: Theophrastus, Historia plantarum 4.4.4). For Varro, the Atlantic coast of the Iberian Peninsula was a source of stories about mares that could be impregnated by the wind (2.1.19) and sows fat enough to furnish cuts of ham one-​foot thick (2.4.11). Pliny reports a magical oasis in Tacape in North Africa with giant palm trees under which olives grew—​and where figs grew under the olives, pomegranates under the figs, vines under the pomegranates, and grain and vegetables under the vines; this miraculous fertility all made possible by the waters of the oasis’ spring (18.188). The expansion of trade and travel in the Mediterranean did as much to confirm the truth of such stories as it did to refute them. When the golden-​yellow fruits of the citron were first brought to Athens from trees in the Near East during the 4th century, people identified them as the apples of the Hesperides—​perhaps not gathered from

Ancient Agronomy as a Literature of Best Practices    477 the garden, but originating from trees of the same kind (Athenaeus, Deipnosophistae 3.84d). When Theophrastus set down the first detailed description of the citron tree, he attached to it the geographically correct name “Persian or Median apple”; yet the tree’s magical reputation was not diminished, since, as Theophrastus correctly notes, the citron bears fruit and flowers year round, just like the trees in Alcinous’ orchard (Historia plantarum 4.4.2–​3). Eventually citron trees themselves, not just the fruit, were imported to Greece and Rome, although Pliny reports that farmers in his day had little success growing them (12.16). Palladius, by giving the first account of successful citrus cultivation (4.10.11–​18), in a way records the fulfillment of the culture’s 700-​year-​old dream (Andrews 1961). Paradoxography was thus in service to ancient agricultural science, not in competition with it. And the science returned the favor: the two most rigorous ancient studies of animals and plants—​Aristotle’s zoological writings and Theophrastus’ plant writings—​ were also two of the most important sources for Hellenistic paradoxographers. An early text, Apollonius’ Inquiries into Marvels, quotes extensively from both writers (16, 27–​29, 31–​34, etc.), and one of the authors from Varro’s list, Aristandros of Athens, who specialized in agronomical portents, took from Theophrastus his anecdotes about trees which changed species (Pliny 17.243; Historia plantarum 2.3). Varro himself cites Theophrastus as often for botanical wonders as he does for scientific explanations (1.7.6–​8, 37.5). When Diophanes included in his collection a book devoted entirely to paradoxa (Photios Bibliotheca 163), agricultural paradoxography became a proper literary genre. The most significant figure in this tradition was Bolus, who hailed from Mendes in Egypt; although conventionally dated to around 200 bce, it was not until the age of Augustus that his work made its presence felt in agricultural writers. The study of Bolus is complicated because numerous texts on farming that our sources ascribe to Democritus were in fact Bolus’ compositions. We may sidestep this complication by reviewing three fragments that have come down under Bolus’ own name. First, a short item (Scholia to Nicander Theriaka 764): Bolus the Democritean in his work On Sympathies and Antipathies says that Persians had a poisonous tree in their country and planted it in Egypt, hoping that many would die from it, but since that land is good, the tree changed into its opposite nature and bore the sweetest fruit.

Aside from the interesting note of Egyptian nationalism, this anecdote is nothing but a typical botanical marvel. However, another text makes an important shift from the contemplative to the practical realm. Columella records the following technique for growing cucumbers in the Mediterranean winter (11.3.53): Bolus teaches that in a sunny and well-​manured location one should have a garden of fennel plants and brambles sown in alternating rows, which, at the fall equinox, should be cut down a little below ground. The center of the bramble or the fennel stalks are filled with manure using a wooden stylus and cucumber seeds planted inside, with the result that as they grow they will mate with the brambles and the

478   Hellenistic Greek Science fennels (for they will be nourished not just by their own but by a kind of maternal root); this ingrafted stock will supply cucumbers even in the cold.

This recipe counts as a paradoxon because we might not expect plants as dissimilar as cucumbers and fennel to be able to grow together; presumably, a natural sumpatheia or affinity between the plants made the process viable. This may not be a very practical method for growing cucumbers in the cold; however, had it worked it would have been a noteworthy spectacle. Finally, Columella paraphrases one of Bolus’ veterinary remedies (7.5.17): But Bolus of Mendes, a notable author from the Egyptian nation, whose collections, called Kheirokmeta in Greek, circulate under the counterfeit name ‘Democritus’, thinks that due to this disease (sc., erysipelas) one should inspect the backs of one’s sheep often and well, and that if this defect is encountered in any of them, we should quickly dig a ditch at the threshold of the sheepfold and bury the afflicted animal alive and upside down in it, then have the entire flock pass over the buried animal, because this action will drive away the disease.

The elements of sympathetic and contagious magic are obvious: the burial of the animal upside-​down “reverses” the disease, and the other animals pick up the cure by making contact with the animal through the ground. Bolus, however, does not talk about causes; he merely spells out the procedure. In the eyes of his contemporaries, its chances of success would perhaps have been no worse than those of the cucumber-​fennel graft. One of the most famous paradoxical procedures from ancient agronomical lore is bougonia, the generation of bees from the carcass of an ox; the history of its literary representation further illustrates a shift from the contemplative to the practical. Starting in the Hellenistic era, several poets bestowed on bees the epithet “ox-​born.” This epithet was explained by the paradoxographer Antigonus of Carystus (300–​250 bce), who wrote that in Egypt, a slaughtered ox buried in the sand up to its horns would produce bees as it decomposed (23). For early writers, bougonia is merely a surprising piece of natural history associated with Egypt. A fragment of “Democritus,” presumably derived from the writings of Bolus, converts this piece of lore into a recipe: if any beekeeper loses his hive, he should build a small, airtight wooden house and place a freshly slaughtered ox inside, surrounding it with fragrant herbs; after a few days the flesh will dissolve and turn into bee larvae, then into bees (Geoponica 15.2.21–​36). Vergil repeats the same account and gives the practice a mythical aetion that involved the deaths of Orpheus and Eurydice (Georgics 4.281–​558). Celsus, and with him Columella (9.14.6), expressed doubts about the process, not questioning its effectiveness, but asking whether it was worth the effort, since bees never die off in such large numbers. Tellingly, its viability was not at issue—​only the economics of the procedure put people off. Paradoxical recipes of this sort proliferated and became a major part of the agricultural tradition; they featured prominently in the works of Julius Africanus, Anatolius, and one ascribed to the Roman sophist Apuleius (Rodgers 1980). They complement but do not drive out the Magonian core of best practices; the Late Antiquity compilations

Ancient Agronomy as a Literature of Best Practices    479 merely expand to accommodate them. Here then is yet one more indication that ancient literary agronomy was a body of knowledge marked by ecumenism and an optimistic if sometimes naive empiricism, which preserved the written riches of centuries. And as vast as it is, it represents only a small sample of the deeper stores of know-​how handed down by generation after generation of (mostly illiterate) ancient Mediterranean farmers who managed to make breadbaskets out of many lands that today are deserts.

Bibliography Ambrosoli, Mauro. The Wild and the Sown: Botany and Agriculture in Western Europe, 1350–​ 1850. Cambridge: Cambridge University Press, 2009. Andrews, Alfred C. “Acclimatization of Citrus Fruits in the Mediterranean Region.” Agricultural History 35 (1961): 35–​46. Bartoldus, Marco Johannes. Palladius Rutilius Taurus Aemilianus: Welt und Wert spätrömischer Landwirtschaft. Augsburg: Wissner-​Verlag, 2012. Beagon, Mary. Roman Nature:  The Thought of Pliny the Elder. Oxford:  Oxford University Press, 1992. Burford, Allison. Land and Labor in the Greek World. Baltimore, MD:  Johns Hopkins University Press, 2000. Christmann, Eckhard. “Bemerkungen zu Autoren und ihrem Publikum in der römischen Landwirtschaftlehre,” In Antike Fachschriftsteller: Literarischer Diskurs und sozialer Kontext, ed. Marietta Horster and Christiane Reitz, 121–​151. Stuttgart: Franz Steiner Verlag, 2003. Decker, Michael. Tilling the Hateful Earth:  Agricultural Production and Trade in the Late Antique East. Oxford: Oxford University Press, 2009. Drachmann, Aage Gerhardt. Ancient Oil Mills and Presses. Copenhagen: Levin & Munksgaard i komm, 1932. Edwards, Anthony T. Hesiod’s Ascra. Berkeley: University of California Press, 2004. Flach, D. Römische agrargeschichte. Munich: Beck, 1990. —​—​—​. Marcus Terentius Varro. Gespräche über die Landwirtschaft. 3  vols. Darmstadt: Wissenschaftliche Buchgesellschaft, 1996–​2002. Foxhall, Lin. Olive Cultivation in Ancient Greece: Seeking the Ancient Economy. Oxford: Oxford University Press, 2007. Frayn, Joan M. Subsistence Farming in Roman Italy. London: Centaur Press, 1979. —​—​—​. Sheep-​Rearing and the Wool Trade in Italy during the Roman Period. Liverpool: Francis Cairns, 1984. García Armendáriz, José-​Ignacio. Agronomía y tradición clásica. Seville:  Universidad de Sevilla, 1995. Gow, A. S., and A. F. Scholfield. Nicander:  The Poems and Poetical Fragments. Cambridge: Cambridge University Press, 1953. Horden, Peregrine, and Nicholas Purcell. The Corrupting Sea:  A Study of Mediterranean History. Oxford: Blackwell, 2000. Isager, Signe, and Jens Erik Skydsgaard. Ancient Greek Agriculture: An Introduction. London: Routledge, 1992. Keyser, Paul T., and Georgia L. Irby-​Massie, eds. The Biographical Encyclopedia of Ancient Natural Sciences. London: Routledge, 2011.

480   Hellenistic Greek Science —​—​—​. “Food Production.” In The Cambridge Companion to the Roman Economy, ed. W. Scheidel, 156–​174. Cambridge: Cambridge University Press, 2012. Kron, Geoffrey. “Animal Husbandry, Hunting, Fishing, and Pisciculture.” In The Oxford Handbook of Engineering and Technology in the Classical World, ed. J. P. Oleson, 175–​222. Oxford: Oxford University Press, 2008. —​—​—​. “Food Production.” In The Cambridge Companion to the Roman Economy, ed. W. Scheidel, 156–​174. Cambridge: Cambridge University Press, 2012. Lehoux, Daryn. Astronomy, Weather, and Calendars in the Ancient World: Parapegmata and Related Texts in Classical and Near-​Eastern Societies. Cambridge:  Cambridge University Press, 2007. Louis, Pierre. “La Domestication des animaux à l’époque d’Aristote.” Revue d’histoire des sciences 23 (1970): 189–​201. McCabe, Anne. A Byzantine Encyclopaedia of Horse Medicine: The Sources, Compilation, and Transmission of the Hippiatrica. Oxford: Oxford University Press, 2007. Oder, E. “Beitrage zur Geschichte der Landwirtschaft bei den Griechen.” Rheinisches Museum 45 (1890): 58–​99, 212–​222; 48 (1893): 1–​40. Osborne, Robin. Classical Landscape with Figures. The Ancient Greek City and Its Countryside. London: George Philip, 1987. Pomeroy, Sarah B. Xenophon Oeconomicus:  A Social and Historical Commentary. Oxford: Oxford University Press, 2001. Rodgers, Richard H. “Hail, Frost, and Pests in the Vineyard: Anatolius of Berytus as a Source for the Nabatean Agriculture.” Journal of the American Oriental Society 100 (1980): 1–​11. —​—​—​. “Kepopoiia:  Garden Making and Garden Culture in the Geoponika.” In Byzantine Garden Culture, ed. Antony Littlewood, Henry Maguire, and Joachim Wolschke-​Bulmahn, 159–​175. Washington, DC: Dumbarton Oaks, 2002. Sallares, Robert. The Ecology of the Ancient Greek World. Ithaca, NY:  Cornell University Press, 1991. Skydsgaard, Jens Erik. Varro the Scholar:  Studies in the First Book of Varro’s De re rustica. Copenhagen: E. Munksgaard, 1968. Speranza, Feliciano. Scriptorum Romanorum de re rustica reliquiae. Messina: Università degli Studi, 1971. Spurr, M. S. Arable Cultivation in Roman Italy c. 200 b.c.‒c. a.d. 100. London: Society for the Promotion of Roman Studies, 1986. Tchernia, André. Le vin de l’Italie romaine. Rome: École française, 1986. Teall, John L. “The Byzantine Agricultural Tradition,” Dumbarton Oaks Papers 25 (1971): 35–​59. Thibodeau, Philip. Playing the Farmer:  Representations of Rural Life in Vergil’s Georgics. Berkeley: University of California Press, 2011. Thurmond, David L. A Handbook of Ancient Food Processing in Ancient Rome: For Her Bounty No Winter. Leiden: Brill, 2006. Wellmann, Max. “Die Georgika des Demokritos.” Abhandlungen der preußischen Akademie der Wissenschaften 4 (1921): 3–​58. West, Martin L., ed. Hesiod Works and Days. Oxford: Oxford University Press, 1978. White, Kenneth D. Roman Farming. London: Thames and Hudson, 1970. —​ —​ —​ . “Roman Agricultural Writers I:  Varro and His Predecessors/​ ” In Aufstieg und Niedergang der römischen Welt 1.4, 439–​493. Berlin: de Gruyter, 1973. —​—​—​. Farm Equipment of the Roman World. Cambridge: Cambridge University Press, 1975.

chapter C13

Op tics and  V i si on Colin Webster

1. Introduction Vision is a compound phenomenon, integrating such diverse aspects as images, objects, shapes, light, darkness, color, spatial orientation, size determination, distance perception, motion, binocular vision, double vision, myopia, visual illusions, reflection, and refraction. No two authors in antiquity agreed on precisely which elements should be included in a useful and credible account of visual perception, and because of the considerable physiological, epistemological, ontological, technological, and aesthetic factors bound up with vision, authors adopted substantially different assumptions when they discussed “sight.” Some incorporated perspectival “scene drawing” or dealt with rainbows. Others focused on the soul’s perceptive capacities. Yet scholarly treatments of the subject tend to privilege mechanical models, considering all contributions to be equivalent “theories of vision” regardless of the contexts in which they are found. This comes at the expense of a more holistic approach that pays attention to how each author functionally defines sight by making certain factors crucial and not others. To put this in another way, “vision” is a contingent construction whose operational definition shifts according to the concerns of each theorist. The boundaries of sight are fluid. As a result, considering all authors to be engaged in an individual enterprise that investigates a single, selfsame phenomenon would be to underestimate how significantly conflicting goals can alter assumptions about what the visual experience constitutes and which of its aspects demand explanation. For our purposes, we can assert that philosophical or “scientific” explanations of vision first arose during the 5th century bce as part of the general pre-​S ocratic program of explaining the “nature of things.” Such theorists as Alcmaeon, Anaxagoras, and Diogenes began by modeling the eye’s functional mechanism on the mirror. Empedocles instead conceptualized vision as a type of color transfer,

482   Hellenistic Greek Science while Democritus figured vision primarily as a type of image transfer across a medium. By the time of Plato, a relatively consistent set of phenomena came to define sight, including color, image transfer, reflection, and night vision. Aristotle broke from this mold to incorporate sight within a broader metaphysical account of perception and the soul, while the Epicureans fixated on the epistemological consequences of optical illusions. In the Hellenistic period, geometrical optics (and its sibling discipline catoptrics) rose to greater prominence, utilizing diagrams to explicate and systematize vision. As a result, this mode of articulating the visual experience introduced certain assumptions about the visual cone and its constituent rays. These assumptions crept back into physical theories, including those of the Stoics and Galen. It was not until the 2nd century ce that Ptolemy finally wrote a treatise that systematized and synthesized both the geometrical and philosophical approaches to sight. Because multiple disciplines deal with these visual explanations, scholarship tends to be field specific. Nevertheless, several surveys of ancient visual theories have been produced, some more and some less sensitive to the heterogeneity of ancient approaches (the recent work of both A. Mark Smith and Michael Squire represents a tremendous contribution in this regard; see Smith 2015; Squire 2015; cf. Beare 1906; Lindberg 1976; Park 1997; Darrigol 2012). In general, however, historical overviews tend to break down ancient theories into one of two camps: intromissionist (we see by means of something entering the eye) or extramissionist (we see by means of something exiting the eye). Although some reservations have occasionally been voiced about this strict intromissionist/​extramissionist binary (hereafter I/​E), employing it remained the dominant way to approach ancient ideas about vision until very recently. To be sure, this categorization does have its strengths, and this chapter will exploit the I/​E model to describe certain theoretical commitments where appropriate. That said, this dichotomy has its own history, appearing as a minor rubric in Aristotle and Theophrastus and only gaining prevalence in subsequent doxographical accounts. Before the rise of geometrical optics in the late 4th century bce, however, the I/​E categorization conceals more than it reveals, and only a few theories fit neatly into one of its two camps. What the I/​E categorization does highlight, however, is the modern shock at the fact that no ancient theory utilized light as the primary vehicle of visual information. Various theorists considered light to be a catalyst or necessary condition of vision, but no author in antiquity argued that light entered the eye to produce a visual perception on its own. Instead, authors posited other mechanisms, some of which indeed involved substances extending from the eye, others substances entering into it, while still others integrated both elements of I/​E. Rather than employ this dichotomy, however, or argue for an alternative schema, this chapter proceeds by examining the treatment of eyesight more or less chronologically, examining how different pressures led authors to structure the investigation of vision in different ways.

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2. Early Philosophical Authors 2.1 Vision as Reflection: Alcmaeon, Anaxagoras, and Diogenes For the physikoi of the 5th and 4th centuries bce, investigating the “nature of things” seems to have included providing an account of vision. We owe most of our information about these early Greek models to Aristotle and Theophrastus, both of whom wrote treatises called On Sense and Sensibles. Yet the earliest optical “theory” appears in neither of their texts, but is preserved in Aëtius’ reconstructed Placita (1st century bce). This lemma addresses the “Pythagoreans,” stating that they compared reflection to a hand that reaches out to its object before bending back at the elbow to touch the shoulder (Aëtius 4.14.3). Since the passage does not describe sight per se, but reflection, it is unclear whether the arm accounts for the general mechanism of the eye or merely the optical effects of a staring directly into a mirror. Nevertheless, this Pythagorean formulation seemingly answers the most basic question about vision: “How can we see objects at a distance?” It does so by constructing visual perception on the model of touch, whereby sight exits the eye to “grasp” what it sees. And even at this earliest stage, reflection seems to be a crucial part of explicating what constitutes the visual experience. Reflection also plays a key conceptual role in the account of Alcmaeon, the earliest individual Greek author whose theory of vision can be reconstructed. Alcmaeon attributes the basic mechanism of vision to the image appearing in the moist ocular surface, holding that we see because the water surrounding the eye “reflects back” by means of its “gleaming and diaphanous nature”—​ a characteristic that he attributes to the fire in the eye’s composition (Theophrastus, On Sense and Sensibles 26; cf. DK 24 A10). By reflection—​or, more literally, “immanent appearance” (emphasis)—​Alcmaeon is referring to the tiny image that appears when you look into someone else’s eye. This phenomenon famously gave the Greeks their word for pupil, korē, which refers to the miniature “puppet” version of the viewer mirrored back in the ocular surface (cf. Plato, Alcibiades I 132e7–​133a5). Along with discussing the mechanics of image transfer, Alcmaeon was also reportedly the first to excise the eyes and discover “channels” behind them (no doubt the optical nerves), but his explanations do not seem to involve complex physiological arguments or systematic dissections (DK 24 A10; Longrigg 1963, 156–​157; 1993, 53–​60; Lloyd 1979, 156; cf. Aristotle, On Sense and Sensibles 2, 438b12–​16). Rather, for him, the external features of the eye were sufficient to explain the mechanism of sight. His account pointed to the visible manifestation of an image on the eye’s surface while associating it with traditionally conspicuous visual phenomena (brightness, shininess, and reflection).

484   Hellenistic Greek Science The idea that the reflection on the eye’s surface provided its functional mechanism proved persuasive for multiple thinkers of this era, with each theorist adapting it to his own philosophical program. For instance, Anaxagoras suggests “the eye sees by reflection in the pupil” but argues that it does so by means of alteration by opposition, whereby stronger colors are reflected in weaker (Theophrastus, On Sense and Sensibles 27; cf. 37). Like Alcmaeon, Anaxagoras holds the eyes to be composed of fire, but he adds that visual perception must always involve pain—​even if we cannot discern it—​since the opposition required for any change will produce distress (cf. Theophrastus, On Sense and Sensibles 28). Diogenes of Apollonia likewise attributes vision to reflection, but adds that reflection only “causes perception when it is mixed with the internal air” (Theophrastus, On Sense and Sensibles 39; cf. 47). He is thus the first in a long line of theorists to give air, or pneuma, a vital role in perception and sensation. Although his physiological assumptions are therefore somewhat different than Anaxagoras’, he adopts his predecessor’s notion that reflection occurs because of difference, insisting that dark eyes see best in the daylight, since they contrast with brightness, while lighter eyes see better at night, since they better reflect darkness (Theophrastus, On Sense and Sensibles 42). This could point toward the fact that Greek mirrors were not colorless, but most often made of bronze, and therefore would have indeed produced better images of darker objects that contrasted more substantially with the reflective material. The theory of vision-​as-​reflection also appears outside the philosophical tradition, popping up in the Hippocratic treatise On Fleshes, where the author argues “light and all bright things shine back by this transparency [in the eye]; and so one sees by this reflecting” (Hippocrates, On Fleshes 17.8–​10, Littré 8.606 = Places in Man sec. 2, Littré 6.278). Explaining vision by means of reflection was so widespread that Theophrastus could state that “some opinion concerning reflection is common; for basically everyone understands seeing in this way, namely by reflection occurring in the eye” (On Sense and Sensibles 36). Yet, although all these reflection theories rely on a similar set of associations, they tend to be pulled from treatises explicating whole worldviews rather than investigating sight in all its complexity. Thus, to consider these as explanations of “vision,” one must understand that vision is here seen through the lens of the early philosophical commitment to explain “the behaviors of the heavens and earth” more broadly (cf. Plato, Phaedo 96b9–​10). In other words, vision presented an opportunity to showcase a philosophical program as much as it demanded thorough and full investigation. Moreover, although it certainly could be a by-​product of the limited historical record, these authors seem to have viewed sight rather narrowly, construing it primarily as an instance of image formation (perhaps involving colors), which occurred with greater or lesser success in the dark, depending on the animal. At the same time, they granted the mirror a key role in conceptualizing both the mechanics and the boundaries of vision, while functionally ignoring features like depth perception, perspective, and binocular vision.

Optics and Vision   485

2.2 Empedocles: Effluence/​Pore Theory As the philosophical tradition developed, so too did accounts of vision, as thinkers incorporated additional components of the visual experience into their explanations. Empedocles, Democritus, and Plato all fit this pattern, and each of them expanded the visual mechanism beyond the ocular surface to include dual-​direction stimuli. Moreover, each author integrates vision within a larger treatment of the senses more generally. For instance, Empedocles proposes an effluence/​pore model to explain all five senses, vision included, suggesting that every object constantly sends off effluences of varying sizes, which are discerned by the appropriately sized pores of each sense organ. Only those effluences that are “commensurate with sight” fit precisely into in the eye and cause visual perception (Plato, Meno 76c7–​d5; cf. DK 31 A86). These visual effluences are composed of two elements, fire and water, and each enters its own respective pore in the eye, thereby producing light and dark respectively (cf. Aëtius 4.9.6; Theophrastus, On Sense and Sensibles 7). The collective effect of these fire and water effluences produces a unified color sensation in the eye, which is what Empedocles could potentially mean by the context-​less fragment “one sight arises from both” (DK 31 B88). From this evidence, scholars have often classified him as an “intromissionist.” His two-​element effluence explanation seems to rely on the most common ancient theory of color, namely, that black and white do not merely represent the poles of the spectrum but supply color’s constituent elements (Theophrastus, On Sense and Sensibles 59 = DK 31 A69a; cf. Prantl 1849; Kranz 1912; Ball 2001; Pastoureau 2001). Such a system was seemingly accepted by Parmenides (DK 28 B8, lines 38–​41), Anaxagoras (DK 59 B4; cf. Theophrastus, On Sense and Sensibles 59), Plato (Timaeus 67c4–​68d7), and Aristotle (On Sense and Sensibles 3, 439b15–​440b25; 4, 442b21–​29). This binary system led Empedocles to conclude that neither earth nor air produced sensation in the eye (Ierodiakonou 2005a; Rudolph 2015). In contrast to authors providing reflection models that tend to treat vision as a type of image reception, Empedocles is not known to have attempted to explain the mechanism by which we reconstruct whole impressions and instead construes the basic visual experience as a type of single color-​formation. Although both Plato and Theophrastus attest to Empedocles’ intramissionist effluence model, one major interpretative difficulty surrounds his theory: Aristotle suggests that Empedocles also promoted an extramissionist account of visual perception, whereby fire streamed from the eye to reach its objects. Aristotle shares a long simile in which Empedocles compares the eye to a covered lamp. The eye contains an interior compartment of fire surrounded by water threatening to extinguish it. The two elements are kept separate by membranes (windscreens in the simile), and just as light streams through the screens of the lamp, rays of fire travel through eye’s membranes and out into the winds (Aristotle, On Sense and Sensibles 2.437b26–​438a3 = DK 31 B84; Theophrastus, On Sense and Sensibles 7). Considerable debate has surrounded how these details relate to ocular anatomy (especially in regard to what the water represents), but since very little

486   Hellenistic Greek Science was known about the eye’s interior structures, it seems unnecessary to hew too closely to its actual components. The most plausible reconstruction, to my mind, involves positing an interior chamber of fire surrounded by a chamber of water (identified as the ocular fluid rather than the lacrimal moisture on the eye’s surface). The visual pores lead to each of their respective chambers, and fire from the interior chamber passes through passageways into the air (see figure C13.1). Nevertheless, it is still unclear whether Empedocles ascribes any active role to the fire exiting the eye like the light moving through the lamp screens, and if so, (1) how it manages to avoid interfering with the incoming effluences, and (2) why does it not trigger a visual perception on its own when occupying the sensory pores. Yet Aristotle himself hedges on whether the lamp simile portrays Empedocles’ actual explanation of vision (Aristotle, On Sense and Sensibles 2.437b24–​438a5; cf. O’Brien 1970:  142–​ 143), and as such, while many commentators have attempted harmonize both aspects (Ross 1906, 137–​138; Taylor 1928, 280–​281; Verdenius 1948; Long 1966; Sedley 1992; Kalderon 2015, 8–​9), the most likely account accepts that the simile explains the eye’s gleam rather than its operative mechanism (Cherniss 1935, 318, n. 106; O’Brien 1970, 144; Ierodiakonou 2005a). That being said, Empedocles does use the internal fire to account for night vision elsewhere, suggesting that animals with more fire in their eyes can see better in the darkness, since the substance “fills up” for the lack of light. This contradicts his pore model, however, since its “like with like” mechanism more easily implies that increased fire would improve the eye’s capacity to recognize light/​white, not dark/​black (Theophrastus, On Sense and Sensibles 8; cf. 18; Aristotle, Generation of Animals 5.1, 779b12–​20; DK 31 A91). As such, although the lamp simile cannot describe Empedocles’ mechanism of visual perception, which relies on the effluences/​pores model, he still utilizes elements of the analogy when it suits his proximate explanatory goals. In short, he is inconsistent when addressing different aspects of sight. This in turn illustrates how little attention he pays to falling on one side of the I/​E binary rather than the other.

Water Fire Fire

Fire (?) Water

Figure C13.1  Empedocles’ model of the eye. Drawing by author.

Optics and Vision   487

2.3 Democritus: Imprint Theory Like Empedocles, Democritus, too, puts forward a theory of vision that frustrates the I/​ E dichotomy, proposing a mechanism that involves both inward and outward forces. Moreover, Democritus adopts elements from both previously dominant models, arguing that “seeing occurs because of an effluence and a reflection in the eye” (Theophrastus, On Sense and Sensibles 80). Despite employing these familiar ideas, however, he construes them in his own way. First, like Empedocles, Democritus suggests that all objects release effluences, but unlike Empedocles, he considers these to be skin-​like films, not streams of fire and water. Moreover, Democritus argues that these effluences do not travel directly to the eye but make an “imprint” (entupōsis/​deikelon) on the air between the visible object and the eye, a process that he compares to imprinting a mark in wax (Theophrastus, On Sense and Sensibles 51). Because of the dual pressure exerted by “the thing seen and that which sees it,” the intermediate imprint “shrinks down” in order to fit in the eye. When it strikes the moist ocular surface, it creates a reflection, or “immanent appearance,” which seems to be understood as another imprint (Theophrastus, On Sense and Sensibles 50‒52). In fact, Democritus incorporates light into this wax-​imprint heuristic as well, stating that sunlight prepares the air by pushing and condensing it, thus making the air a more receptive medium of a visual impression (Theophrastus, On Sense and Sensibles 54). Light thus acts as a catalytic agent for sight, as it were, rather than causing visual perception itself. While Democritus describes vision as an immanent appearance on the eye’s surface, he also assigns a role to the ocular interior, suggesting it transmits the visual imprint by being “as spongy as possible and empty of dense and resistant flesh, or, still, thick and oily liquid.” The imprint passes through this material to the back of the eye, where it meets “veins” that should be both “straight and dry, so as ‘to be of the same shape’ as the things being imprinted” (Theophrastus, On Sense and Sensibles 50). What precisely Democritus means by these descriptions is imprecise and has caused much confusion, but it seems possible that he is incorporating the wax-​imprint model to understand the eye’s interior mechanisms (which explains the need for smooth, nonresistant and not overly “oily” material, whereby the “condensed” air is matched by the smooth, “dense” surface of the eye). If this is true, the impressions on the ocular surface are transferred through the eye in an analogous fashion to the way they were transferred through the air. Alternatively, Democritus could be imagining the impressions now to be independent objects (rather than imprints moving along a medium), which pass through pores in the eye themselves (see Rudolph 2012 for an alternate account). Controversy surrounds this and other key details of Democritus’ theory. For instance, according to Aristotle, Democritus held that the intermediate air acted as an impediment to sight rather than supplying the necessary visual medium (Aristotle, On the Soul 2.7, 419a16–​18), but most scholars now accept that this misrepresents Democritus’ position. Commentators also debate whether the pressure to compress the incoming imprint—​ which is  supplied by “that which sees”—​ comes from the eye itself or some effluence ejected from it (for the former interpretation, see Bicknell 1968; Baldes 1975; and Taylor

488   Hellenistic Greek Science 1999; for the latter, see English 1915; Guthrie 1965, 442-​443; Mugler 1959; Burkert 1977; Sassi 1978, 108–​109; Barnes 1982). In either case, to my mind, we should not conflate the imprint-​shrinking pressure exerted by the eye with the notion that Democritus promoted a fully articulated geometrically determined ray theory (pace Rudolph 2011), especially since Theophrastus claims that his predecessor attempted to explain how magnitude and distance appear in the eye, but only unsuccessfully so and without providing a demonstrative account (Theophrastus, On Sense and Sensibles 54). Along with these direct discussions of visual mechanics, Democritus also proposes a detailed account of color, although it is uncertain how closely the two explanations relate. Unlike his predecessors, he considers four colors elemental: black, white, red, and pale yellow (Theophrastus, On Sense and Sensibles 73–​78; DK 68 A125). Whiteness arises from smooth atoms, black from rough, red from fire-​like atoms, and pale yellow from solid and void. Yet even after having provided the material properties responsible for color, Democritus insists that color is not an objective quality adherent in either atoms or visible objects but a subjective creation of the mind, existing only by “convention” (DK 68 B9; B125). In sum, Democritus expanded on the theories of his predecessors, while incorporating substantially more aspects of vision into his philosophical account, including experiential, theoretical, and epistemological features.

2.4 Plato: Intermingled Fire Plato—​at least as evidenced by the Timaeus—​bases his model of vision on the assumption that some type of ocular fire provides the operational mechanism of sight. He suggests that the eye contains a certain fire that produces a gentle light but does not blaze hot enough to burn our flesh. This fire collects around the middle of the eye, and the purest part filters through the pupil, forming a smooth and dense “current of sight.” Outside of the eye, this current mixes with its “sibling” substance, daylight, to create an active channel “along the straight line of the eyes.” Wherever this stream touches an external object, “motions” (kinēseis) are transferred down its length, through the eyes and into the body, ultimately reaching the soul, which then “provides this perception which we call seeing” (Timaeus 45b2–​d3). After providing these details, Plato then explains reflection, claiming it occurs when inner and outer fires coalesce on a smooth surface, such as a mirror, while also discussing the special case of image inversion in a semi-​cylindrical reflective surface (Timaeus 46a2–​c6). Moreover, just as Democritus and Empedocles before him, Plato attempts to explain color, arguing that it streams from all bodies in the form of a flame composed of particles “commensurate to sight.” Those particles proportionate to the visual stream do not affect it (and are thus transparent); those that are larger “dilate” the visual stream to create white, while those that are smaller “contract” it to create black (Timaeus 67c4–​68d6; cf. Theophrastus, On Sense and Sensibles 86, 91; cf. Ierodiakonou 2005b). The dilation widens pores in the eye and allows more fire and moisture to exit and meet with the incoming flame, and the consequent mixture produces both dazzling

Optics and Vision   489 brightness and the full spectrum of colors. Yet despite construing color as a product of the interaction between an external substance and the visual stream, Plato grants color an objective reality, establishing it as the object of vision. In creating these theories, Plato adopts several features from his predecessors. For example, when establishing the necessary conditions for sight, the visual stream acts as flowing substance (and thus resembles Empedocles’ lamp fire), but when transmitting visual perceptions, it functions as a single haptic body (and thus resembles the Pythagorean arm). When describing color, however, Plato utilizes the Empedoclean concept of incoming effluences, construing color as a stream of particulate matter. Yet, insofar as the dilations of the visual stream could be said to constitute the visual information (rather than the incoming fire), Plato’s account could be said to incorporate a type of visual medium in the manner of Democritus. In any case, his account does not fit the I/​E paradigm with ease, instead representing another instance of a theory incorporating both inward and outward components. Lastly, although we should shy away from constructing a simple historical progression, Plato’s account is the first to be expressly rectilinear. In short, by the beginning of the 4th century bce, a common cluster of features had emerged as part of what it meant to “explain vision” within the philosophical tradition. Authors needed to provide an account not only of image transfer but also of reflection and night vision. They needed to articulate the nature of color, how light participated in visual mechanics, and the basic physiology of the eye. Yet other features like depth perception and binocular vision still remained absent from the core conceptualization of vision.

2.5 Aristotle: The Transparent Visual Medium Aristotle did not focus solely on this standard cluster of features, and instead put more effort into establishing the general metaphysical framework underlying all perception. To this end, he argued that each of the five senses has its own unique “proper sensible” that it alone can discern. For example, the proper sensible for hearing is sound, while for vision it is the “visible.” Aristotle then further clarifies that the “visible” is color, as well as the related quality of luminescence (On the Soul 2.7, 418a26–​28; cf. 419a4–​5; On Sense and Sensibles 2, 437b6–​7). In other words, we see color by virtue of itself, but perceive all other visible characteristics by virtue of color. Still, color still needs to get from object to eye somehow, and Aristotle holds that some substance cannot simply fly through the air, or else we would see its journey across the sky. Instead, visual perception must take place across some medium. Yet for Aristotle this medium cannot be identified as a particular substance and should instead be considered a characteristic common to the multiple materials through which we can see, including both air and water. He therefore establishes the visual medium as the “transparent” (to diaphanes). Within this framework, light is understood to be the presence of fire (or something like fire) in the air (or some other potential visual medium), such that light is itself the activity of the transparent medium being

490   Hellenistic Greek Science transparent (On the Soul 2.7, 418b9–​419a1). In other words, light is the actualization of a potentially transparent substance—​ the activity that alters it from darkness into a medium through which colors can be seen. Having established the characteristics of the visual medium and the necessary parameters of perception, Aristotle describes the visual act in simple terms, stating only that colors produce some form of instantaneous qualitative alteration across the transparent medium. The eye receives this color insofar as it, too, is transparent (being composed of water) and thus “receptive of light” (On Sense and Sensibles 2, 438b3–​11; cf. 2, 438a14–​20). That being said, Aristotle provides the stipulation that the alteration in the eye must be nondestructive (i.e., not the type where F becomes not-​F) and must keep the transparent’s capacity to receive color intact. The coloration in the eye therefore functions as a type of second-​order actualization, like a teacher actively using knowl­ edge to solve a mathematical equation (and thus changing from “smart” to “employing smartness”), rather than a student learning the skill for the first time (and thus changing from “ignorant” to “not-​ignorant”) (On Sense and Sensibles 2, 438b2–​5; cf. On the Soul 2.7, 419a13–​14). Aristotle further describes the activity of sight as the transparent eye adopting some relevant quality of its object—​its form without its matter—​whereby it “becomes like” that which it perceives (On the Soul 2.6, 418a3–​6). Considerable controversy surrounds what this means (the so-​called literalist/​spiritualist debate), since it is unclear whether Aristotle indicates that the interior transparency of the eye literally adopts the color of its object through some material alteration (Slakey 1961; Sorabji 1972, 1974, 1992; Sisko 1996), or whether the visual faculty simply becomes psychologically aware of its object without material change (Burnyeat 1992, 1993, 2001, 2002; Broadie 1993; Johansen 1997; Sisko 1998; Murphy 2005; Lorenz 2007). Some scholars advocate what might be called variants of a hylomorphic position, suggesting that any material change would either constitute or subtend alterations to the sense organs’ form, which therefore collapses (according to them) any relevant distinction between physical and psychic alteration (Everson 1997; Charles 2011; cf. Nussbaum 1978; Nussbaum and Putnam 1992; for other variants, see Scaltsas 1996; Caston 2004; Shields 2007; Marmodoro 2014, 111–​118). To be sure, it is clear that for Aristotle the seeing eye cannot turn red in the same way that white cloth becomes red with the addition of dye (and thus destructively not-​ white), since this would violate Aristotle’s stipulation that perception constitutes an act of nondestructive qualitative alteration. Nevertheless, there may be some leeway for the transparent eye to change physically (i.e., not exclusively psychically), insofar as all destructive alterations must take place between opposites (i.e., from F to not-​F), and the transparent is not the opposite of any color (since colors operate between the opposites white and black). A transparent substance can therefore become red without technically becoming not-​transparent—​especially since transparency is that which hosts color in the first place (On Sense and Sensibles 3, 439b8–​10). Whichever interpretation holds, however, it is clear that Aristotle makes the transparent visual medium a necessary condition of vision (On the Soul 2.9, 423b17–​23). In fact, he claims that all five senses must involve some medium, and it is in part this universalizing project that

Optics and Vision   491 creates interpretative difficulties (On the Soul 2.7, 419a26–​b4; cf. Lloyd 1996, 126–​137; Sisko 1998). In sum, Aristotle takes a far more systematic and sensitive approach to visual perception than his predecessors, and in the process, he constructs sight as an act of color transfer rather than image formation while leaving distance perception, binocular vision, and other aspects unexamined. Along with presenting a philosophically sophisticated account of vision, Aristotle also collected many of his predecessors’ arguments, and it was he who first began to recast them along I/​E lines, partially as a way to present his own theory of instantaneous transfer as an answer to some of the aporiai left by their assumptions (On the Soul 2.7, 418b21–​27, 419a13–​20; On Sense and Sensibles 1, 437b10–​438b16). Still, the I/​E dichotomy was not his sole—​or even his primary—​interpretative rubric, and he also examined whether his predecessors hypothesized fire or water as the eye’s active element and whether they placed its operative mechanism on its surface or interior. Similarly, Aristotle’s successor Theophrastus occasionally employs the I/​E dichotomy (On Sense and Sensibles 5), but his fundamental division addresses whether theorists attribute the visual mechanism to the congruence of like substances or the interaction of opposites (On Sense and Sensibles 1). Nevertheless, with the rise of the Epicureans, the I/​E binary became more important, even as motivations for investigating vision shifted ever more toward addressing certain epistemological anxieties.

2.6 Epicurean Eidōla theory Although the doxographical tradition lumps Epicureans together with the Atomists on the subject of vision, Epicurus actually produced a distinct variant of the atomistic imprint theory. He accepted Democritus’ idea that every object continuously sloughs off extremely thin, film-​like effluences, but he dispensed with the notion that the air acts as a medium between object and eye. Instead, he argues that the effluences, which he called “images” (eidōla; simulacra in Latin), rushed through the air and entered the eye (or soul) themselves (Epicurus, Letter to Herodotus 46; Diogenes Laërtius 10.47–​59, 68–​ 69). Epicurus seems to have taken the vocabulary of eidōla from Democritus’ account of dreams and prophecy, which involve free-​floating images entering into our souls while we sleep (DK 68 B10a; Aristotle, On Prophesying in Sleep 2, 464a6–​14; Theophrastus, On Sense and Sensibles 51; Aëtius 4.9.6; cf. Schneider 1821; Alfieri 1936, 144; Burkert 1977, 103–​104; Gottschalk 1980: 97–​98). Indeed, Lucretius, who provides the most extensive evidence for the Epicurean theory, suggests that the thinnest eidōla can cause dreams and hallucinations by entering the body directly—​even before he mentions the role that the effluences play in vision (4.26–​40, 722–​748). For Epicurus, the eidōla move at a tremendous velocity from object to eye, all while maintaining their shape (including three-​dimensional topography) and collectively conveying color (atoms themselves being colorless; cf. Lucretius 4.54–​218). The individual eidōla are too thin to affect perception on their own, so only a sufficient succession of them can cause vision (Lucretius 4.86–​89, 110–​128; cf. Epicurus, Letter

492   Hellenistic Greek Science to Herodotus 46–​47, 50). Yet unlike Democritus, Epicurus held that colors maintain an objective, if transient, reality (Ierodiakonou 2015). Moreover, neither Epicurus nor Lucretius mentions whether or how the eidōla shrink to fit into the eye, and ancient commentators disagree as to whether the Epicureans held such a position at all. Some seem to suggest as much (cf. Sextus Empiricus, Against the Mathematicians 7.209, Plutarch, Against Colotes 1121), while others argued that only part of each eidōlon enters the eye, with a full image arising only by piecing together patches of successive images (Alexander of Aphrodisias, On Aristotle’s ‘On Sense and Sensibles’ pp. 56.6–​58.22; cf. Avotins 1980). In any case, without positing a visual medium, the Epicureans had difficulty explaining why we cannot see the constantly emitted eidōla in the dark, since there was no clear role for light to play in the mechanics of vision. Lucretius never addresses this issue satisfactorily, claiming that light atoms are necessary to perceive colors (2.795‒798) and stating that the sun sends out many beams of light that suffuse the world with incredible speed, but he does not truly articulate how light interacts with the eidōla (2.142‒156; 4.161–​190). Instead, he proposes that we cannot see shaded objects when standing in the light because the dark air somehow blocks the pores of the eye (4.337–​353). The relative lack of attention Lucretius pays to the mechanics of light helps reveal that  the primary motivations behind the Epicurean account of visual perception lie more in the epistemological ramifications of fallible senses than in the physical mechanics of vision. Indeed, Epicurus holds that the perceptions themselves cannot be false, only the inferences drawn from them (Diogenes Laërtius 10.33–​34, 10.62; Epicurus, Letter to Herodotus 50–​52; Lucretius 4.379–​499; Aëtius 2.21.5; see also Glidden 1971; Striker 1977; Taylor 1980; Everson 1990), and it is for this reason that Lucretius spends considerable time explicating certain false appearances, including reflection, a square-​ tower appearing rounded, misapprehended relative motion, misapprehended distances, colonnades and their vanishing point, bent oars, double vision, and the misapprehension that we are awake when sleeping (4.268–​461). Moreover, Epicurus appears to have been the first to offer a full account of distance perception, proposing that the eye discerns distance by the amount of air that an eidōlon pushes into the pupil in front of it (4.244–​255, 268–​291). This in turn helps explain the “illusion” of large objects appearing small at a distance. Regardless of the problems inherent in Epicurus’ account (especially in his model of distance perception), his simplified visual mechanics dominated in the doxographical tradition, supplanting and suppressing Democritus’ earlier theory (an outcome no doubt aided by Aristotle’s mischaracterization of the Atomists as holding the intermediate air to impede rather than enable vision). As Epicurus and Lucretius both evince, the rise of skeptical arguments against the reliability of the senses altered what constituted an adequate account of “sight” (cf. Berryman 1998; Ierodiakonou 2015). To be sure, philosophers as far back as Parmenides had been concerned about the unreliability of the senses. Alcmaeon references differing levels of visual acuity, and Plato discusses several paradigmatic visual illusions, including objects “bending” in water, equal magnitudes appearing to be different sizes because of their relative distances, and trompe l’oeil “shadow” painting (Plato, Republic

Optics and Vision   493 10, 602c9–​d5; cf. 7, 523c1–​6). A concern with the epistemology of vision was nothing new. Nevertheless, the Hellenistic fascination with the limits of knowledge made false appearances the primary locus of anxiety when dealing with sight, thereby rendering them as one of the main features of vision demanding explanation (cf. pseudo-​Aristotle, Problemata, Book 31).

3. Geometrical Optics 3.1 Early accounts Along with the philosophical treatments of vision, a separate tradition emerged in the early 4th century bce that dealt with sight geometrically: optics. This approach utilized diagrams to explain visual appearances, constructing vision according to the practices of mathematical proofs. Such a practice altered notions about the physical mechanisms involved in sight in subtle but significant ways, establishing the assumption that multiple visual rays extended from the eyes and introducing the concept of a visual cone. These mathematical descriptions influenced subsequent philosophical accounts, which thereby suggests that we should not erect a strict barrier between geometry and natural philosophy. Still, we should recognize that geometrical optics maintained its own goals and should not view it as an attempt to explain precisely the same phenomena by different means, but a subject field that has its own origin story and concerns. The first mention of a geometrical optics occurs in Aristotle, who discusses it as if it were already an established discipline (Physics 2.2, 194a7–​12; Metaphysics 3.2, 997b20–​21; 13.2, 1077a4–​7; 13.3, 1078a14–​15; Posterior Analytics 1.7, 75b14–​17; 1.9, 76a23–​25; 1.12, 77b1–​ 4; 1.13, 78b36–​1.14, 79a21). By contrast, Plato never mentions optics by name and instead refers to “the measuring art” as that which determines whether distant objects are as small as they appear (Protagoras 356c4–​e4). Therefore, it seems likely that optics arose in the early 4th century bce, sometime during Plato’s lifetime. Three known candidates stand out as possible originators within that time span:  Democritus, Archytas, and Philip of Opus (although better cases can be made for the latter two). Democritus wrote a now-​lost work entitled Ray-​drawing (aktinographiē), which multiple scholars assume was an account of geometrical optics and perspective (LeJeune 1957, 4; Burkert 1977, 100; Rudolph 2011; Menn 2015, 19). This conclusion, however, is largely based on Vitruvius’ assertion that Anaxagoras and Democritus both wrote about perspectival drawing, or scaenographia (Vitruvius 7. proem.11; cf. 1.2.2; see Tanner 2015). Yet Democritus’ treatise on rays more likely discussed celestial illumination, since Thrasyllus lists it in a tetralogy devoted to astronomy (Diogenes Laërtius 9.48 = DK 68 A33), and Democritus elsewhere only uses “aktines” to refer to light beams projecting from the sun and other light sources, not a visual ray projecting from the eye (DK 68 A91, line 5; DK 68 A135, line 41). Although it is possible that Democritus produced some account of perspectival drawing for the theater, Vitruvius’ comments certainly project

494   Hellenistic Greek Science anachronistic assumptions back on Anaxagoras, who used diagrams to discuss celestial astronomy, not optics, and the same could easily be true for Democritus. A slightly better case can be made for Archytas as the originator of geometrical optics, since—​at least according to Apuleius—​ he held a ray theory, and a controversial fragment of Aristotle preserved by Iamblichus mentions an unnamed Pythagorean who used diagrams to construct optical proofs (Apuleius, Apology 15; Iamblichus, On the General Mathematical Science 25, 78.8–​18; cf. Burnyeat 2005). The most concrete case, however, can be made for Philip of Opus (fl. ca 350 bce), a member of Plato’s Academy and contemporary of Aristotle, since the Suda states that he wrote both an optikōn and an enopt(r)ikōn (Suda φ–​418 = 4.733, 24–​34 Adler). Philodemus also mentions advances in optics in the Academy while Plato was still alive (although Philodemus’ text is regrettably damaged at this point; see Academicorum Philosophorum Index Herculanensis p. 17, col. Y, lines 15–​17; cf. Mueller 1992, 172–​173). In many ways, however, trying to locate a single moment for the inception of optics is misguided, since the field did not emerge suddenly as a straight expansion of the philosophical theories dealt with so far. Rather, a properly geometrical optics arose in part as an offshoot of the mathematical investigation of celestial illumination and other meteorological phenomena (cf. Netz and Squire 2015).

3.2 Peripatetic Ray Theory and the Visual Cone The first extant example of the mathematical representation of a visual ray occurs in Aristotle’s Meteorology, and even this origin hints at the connection optics originally bore to atmospheric and celestial geometry. Indeed, despite the fact that Aristotle constructed vision as a nondestructive qualitative alteration across a transparent medium in On the Soul and On Sense and Sensibles, when explaining the circular shape of the rainbow’s arc in the Meteorology, he adopts a theory of a projecting visual ray. He claims that the rainbow results from reflection in the clouds, a process that he depicts in a diagram (figure C13.2). He posits the clouds to be a perfect hemisphere (A) resting on the horizon and suggests that sight extends from the viewer (at K) to some point on that hemisphere (at M), from which it reflects to the sun (at H). Some constant, but unspecified ratio determines where the sight meets the clouds, but regardless of where the visual ray lands, this point can be rotated around the geometrical pole (Π) to form a perfect arc on the hemisphere. The higher the sun rises in the sky, the lower the rainbow appears, and the more that is cut off by the horizon. Because this extramissionist account contradicts what Aristotle says elsewhere, multiple commentators—​even in antiquity—​have argued that the explanation is merely a geometrical convenience and does not illustrate any commitment to a visual ray theory (Alexander of Aphrodisias, On Aristotle’s ‘Meteorology’ 141 Hayduck; cf. Boyer 1959, 50; Gottschalk 1965, 79–​80; Simon 1988, 48–​51; Smith 1999, 150). Yet several features betray the fact that Aristotle here granted the visual ray real physical existence, including his assumption that it possesses both magnitude and density, weakens over distance,

Optics and Vision   495 A M

H

K

O

Π

Figure C13.2  Aristotle’s rainbow (Meteorology 3.5, 375b19–​29). Diagram modeled after Paris grec 1880, folio 95, with second part of proof omitted from the image. Drawing by author.

can push through mist, and can fail to reach its object (Meteorology 3.4, 373a35–​b9; 3.4, 374b9–​15; cf. Jones 1994, 63; Merker 2002, 195). In fact, Aristotle also entertains extramissionist assumptions in the Generation of Animals, where he suggests that we see farther through tubes or through deep, furrowed brows, since these can prevent the substance leaving the eyes from scattering (Generation of Animals 5.1, 780b13–​781a12). Regardless, Aristotle’s portrayal of a visual ray in the Meteorology seems to have been part of a broader turn to ray theory within the Peripatetic tradition (cf. Theophrastus, On Dizziness 6–​9; pseudo-​Aristotle, Problemata Book 15, and De coloribus). In addition to articulating a geometrically inscribed visual ray, Aristotle’s Meteorology also provides a glimmer of what later becomes an almost universally assumed feature of how vision propagates: the visual cone. In the Meteorology, sight (opsis) forms a cone when tracing the arc of the rainbow, but there is no indication that eyesight naturally assumes this shape. Rather, it is the pseudo-​Aristotelian Problemata that explicitly names the visual cone as an inherent feature of vision for the first time. This occurs in Book 15, “Problems Concerning Mathematical Theory Generally and Those Connected to Celestial Matters,” which includes lemmata about why we count by tens, why the sun and moon appear flat, and why sunlight pouring through rectangular holes appears circular. It is only at this intersection of celestial illumination and visual appearances that the text refers to multiple visual rays (opseis) extending from each eye and falling in the shape of a cone (Problemata 15.6, 911b20–​21; cf. Berryman 1998, 185). All previous philosophical accounts construed the visual projection primarily as singular extension from the eye, whether it be a rigid body, a projectile, or a fluid stream. By contrast, the lemmata dealing with celestial illumination depict sight as involving multiple dispersed rays. Since this transition took place precisely in a geometrical context that depicted multiple solar rays projecting from the sun, often falling on spherical bodies (such as the moon in an eclipse) and forming a cone as a result (cf. Webster 2014b: 172–​219), it seems likely that the visual cone migrated from astronomical diagrams into the conceptualization of vision. This probability becomes even greater when we recognize (as scholars

496   Hellenistic Greek Science seldom have) that the visual cone is a geometrical conceit, not an experiential reality, and even a single eye sees a far broader cross-​section than the shape implies, while both eyes collectively cover almost 180 degrees horizontally and about 120 degrees vertically. The conical shape must have originated somewhere, and astronomical diagrams seem the most likely source.

3.3 Euclid’s Optics The astronomical background to geometrical optics becomes increasingly clear with the Optics attributed to Euclid—​the first fully geometrical treatment of sight. Unlike its philosophical predecessors, the Optics includes no physical arguments or justifications. Instead, it proceeds in the manner of an abstract mathematical treatise, beginning with seven definitions followed by 57 geometrical proofs. Scholars have long held doubts about the text’s authenticity, especially because two versions of the treatise remain extant (now referred to as versions A and B) and multiple propositions contain sloppy geometry deemed unbecoming of the mathematical talents of Euclid. Heiberg proposed that version A was authentic while B was an inferior redaction produced by Theon of Alexandria in the late 4th century ce (he thus called it the Recensio Theonis; cf. Heiberg 1882), but recent scholars have inverted the relationship (Knorr 1991; Jones 1994; Webster 2014a). Indeed, Geminus already appears to have some form of B in the 1st century bce, 300 years before Theon, since he quotes its unique first proposition (Geminus, Optical Fragments 22.14–​15 Schöne). While true Euclidian authorship of the Optics is still difficult to determine, no powerful arguments for rejecting it have emerged, and some legitimate reasons for supporting it exist (cf. Takahashi 1992; Knorr 1994). We can therefore consider it likely that version B of the Optics was written sometime around Euclid’s traditional floruit in 300 bce, most likely by him or at least by another mathematician adopting his formal traits. The Optics begins by establishing the basic geometry of sight, positing that discrete visual rays extend from the eyes (def. 1) and fall in the shape of a cone (def. 2), while only those points on which the rays fall are seen (def. 3). In addition, the wider the angle a visible object subtends in the visual field, the larger it “appears” (def. 4). Ray orientation also aligns with spatial orientation, both on the up/​down and left/​right axes (def. 5–​6; i.e., more leftward rays see objects lying more to the left; more rightward rays see objects lying more to right, etc.). Lastly, visual acuity increases with the number of rays falling on an object (def. 7). In sum, the text presents an angular optics, whereby the visual angle alone determines apparent size, so that a finger held close to the eye and a building in the distance can both “appear” to be the same size as long as they subtend equivalent angles. The Optics makes no attempt to incorporate distance perception or the anatomy of the eye, include any physiological mechanisms, or countenance the contribution of either color or light. Instead, it constructs sight as a phenomenon involving solely magnitudes, motion, distance, and angles, and imagines vision as taking place entirely within the confines of a geometrical diagram.

Optics and Vision   497 Since antiquity, the question has been whether this treatise relates a mathematically neutral account, concerned primarily with perspective (Geminus, Optical Fragments 24 Schöne; cf. Brownson 1981; Andersen 1987; Tobin 1990; Panofsky 1991, 35–​36; Sinisgalli 2012), or whether it commits to one particular mechanics of vision. Yet the first three propositions (especially when B is taken to be the original text) indicate that the Optics does implicitly endorse an extramissionist visual ray theory, whereby discrete physical rays proceed from the eyes (def. 1, prop. 1–​2), fall in a cone (def. 2), and can move back and forth to fill in the gaps between them (prop. 3, see figure C13.3). These rays must have physical existence, since they can oscillate (cf. Lindberg 1976: 13; Jones 1994; Berryman 1998), and must have some thickness, since without any breadth, the area on which they fall would be nonexistent (cf. Ptolemy, Optics 2.50–​51; Jones 1994). Despite the physical implications of these geometrical propositions, multiple problems arise from seeing rays as physical entities, since if they have any actual breadth, they would be either woefully insufficient to cover the visual field (having only the surface area of the pupil to spread across the entire sky), or far too substantial to fit into the eye. More concretely, the rays could not possibly have a single vertex as an origin point, since multiple physical objects would then need to occupy the same space. These difficulties betray the fact that Euclid does not utilize a geometrical diagram to express an abstraction of a preformulated physical ray theory; rather, his geometrical diagrams enable and construct many of his implicit physical assumptions. The resultant visual rays therefore possess “hybrid ontology,” acting as magnitude-​less geometrical abstractions at their common vertex in the eye, while representing actual physical rays where they meet the visible object (Webster 2014b, 189–​209). Euclid did not write his treatise solely to articulate the mechanics of the visual ray, however, and a closer look at the propositions reveals a multifaceted work. Sections deal with ray mechanics (prop. 1–​3), magnitudes and distances (prop. 4–​8), the “rounded square” illusion (prop. 9), direction and altitude (prop. 10–​17), size and similar triangles (prop.  18–​21), spheres (prop.  22–​27), cylinders (prop.  28–​29), cones (prop.  30–​33), Γ

K

V

A

B

Figure C13.3 Euclid, Optics, prop. 1, B (diagram after Paris grec 2350, folio 31v). “Nothing of the things being seen is seen whole all at once.” Rays ΒΑ, ΒΓ, ΒΚ, and ΒΛ move back and forth to fill in the gaps. Drawing by author.

498   Hellenistic Greek Science circles (prop. 34–​36), foreshortened circles (prop. 37–​41), motion and a single magnitude (prop. 42–​44), equality and inequality (prop. 45–​48), motion and multiple objects (i.e., parallax motion; prop. 49–​55), size and apparent distance (prop. 56), parallel lines (prop. 57), and the diameter of a square (prop. 58). Previous scholars have suggested that the Optics privileges “sight” rather than light (Simon 1988) or that it primarily concerns itself with false appearances—​notably the “rounded-​square” of prop. 9 (cf. Berryman 1998; Smith 1981), but neither of these descriptions fully accounts for the subject matter in the text. Prop. 18 does not involve the eyes at all, instead focusing on how to judge the height of an object from its shadow, while several of the propositions present geometrical fallacies that create appearances rather than explaining them away. For instance, prop. 37 argues that an eye resting on any point of a hemisphere will see its base as a full circle and not a foreshortened ovoid (this is a false assertion; cf. Knorr 1992), while prop. 27 argues that two eyes can comprehend a hemisphere whose diameter is equal to the distance between the eyes (also a false assertion; cf. Webster 2014a). These are “appearances” that never appear outside of Euclid’s faulty geometry. Therefore, insofar as the Optics can be said to maintain a single purpose, it cannot be to “explicate sight” or “explain false appearances” in any straightforward manner. Instead, the text must be more modestly characterized as an attempt to systematize vision and a few related phenomena within geometrical parameters. Along with revealing Euclid’s preoccupations, his mistakes uncover some of the sources he was drawing from. For example, the erroneous conclusion about hemispheres in prop. 27 results from borrowing a proposition from the geometry of celestial illumination (Webster 2014a), and indeed, the Optics long circulated in a manuscript termed the “Little Astronomy.” This astronomical background in turn helps us derive greater meaning from the fact that the Optics is the first extant treatise to use both aktines and opseis to refer to the rays extending from the eyes. Previous philosophical authors had been careful to keep visual rays separate from light rays, while poets had likewise employed aktines to refer to the projectiles hurled from the sun or the light projected from it. By extension, some used the term to refer to the “shine” or “gleam” of the eyes but without suggesting a functional mechanism of sight (Pindar, Encomia, fr. 123.3; cf. Isthmia 4.43; Aristophanes, Wasps 1032; Peace 755. For a borderline case, see Empedocles DK 31 B84, line 33). By contrast, the Optics conflates these two terms outright, no doubt aided by the fact that both types of ray appear identical in a geometrical diagram. Accordingly, Epicurus, Euclid’s contemporary, could now reject the notion that we see through aktines (Epicurus, Letter to Herodotus 49.4; cf. Diogenes Laërtius 10.49), and in the next generation, Chrysippus could refer to fiery aktines exiting the eye (Aëtius 4.15.3 = Stoicorum Veterum Fragmenta 2.866, line 6). This shift in vocabulary is nontrivial, since it once again highlights the fact that in contrast to previous philosophical accounts, Euclidian geometrical optics posits that multiple visual rays extend from each eye, not an individual stream or opsis. This shift resulted, no doubt, from the application of diagrams to the articulation of the visual experience. Geometrical optics therefore did not simply depict pre-​held assumptions about the visual cone and its numerous rays; it helped produce them.

Optics and Vision   499 The effects that optics had on theories of eyesight were many, but one salient feature was that diagrammatic depictions of vision became intrinsically associated with extramissionist ray theory. Despite the fact that the Pythagoreans, Plato, and Empedocles had all already proposed theories that involved at least some feature exiting the eye (even if not sight’s active mechanism), the optical diagram produced a more powerful expression of a visual projection, and as a result, the subsequent tradition held up the “mathematikoi” as the paradigmatic advocates of extramissionism (along with those associated Peripatetics who adopted a visual ray theory and also used diagrams). As a foil, authors took the Epicureans (and Atomists by extension) as the paradigmatic intromissionists. The simplicity of this scheme led most ancient authors to accept some version of this rubric when formulating their potted histories of previous optical theories. (Cf. Geminus, Optical Fragments 24 Schöne; Aëtius 4.13; Apuleius, Apology 15; Aulus Gellius 5.16; Galen, On the Opinions of Hippocrates and Plato 7.5.1–​2, Kühn 5.618; Alexander of Aphrodisias, On Aristotle’s ‘On Sense and Sensibles’ 27.20–​34.21; Porphyry, Commentary on Ptolemy’s ‘Harmonics’ p. 32.6 Düring = DK 68 A126a; Calcidius, On Plato’s Timaeus 236–​238; Euclid, Optics, preface (B), 152–​154). That being said, the I/​E divide was not an abstract discussion about whether vision could function by something entering the eye or some material extending from it. Rather, authors pitted visual ray theory against eidōla theory in particular, assuming these as the two main options for explaining visual perception. Yet the Epicureans and mathematikoi are not the only characters included in these lists, and Plato frequently appears as someone who proposed a dual-​action theory of sibling fires. Just as often, these overviews also include the Stoics.

4. Post-​Euclidian and Syncretic Approaches 4.1  THe Stoics Although the Stoics land squarely in the philosophical tradition of the 3rd century bce, their theories of eyesight bear traces of geometrical optics. Various adherents proposed slightly different models of visual perception, and we should therefore be wary of establishing a monolithic model. In general, though, the Stoics believe the soul is a continuum of innate pneuma—​a thin mixture of air and fire—​which is stretched to varying degrees of tightness throughout body and its parts (Stoicorum Veterum Fragmenta 2.439–​462, 2.738–​772, 3.84, 3.160; cf. von Staden 1978, 97). Vision occurs when the visual pneuma moves via the nerves to the eye, where it reaches the pupil and “pricks” the external air, thereby stretching it into a taut cone of “fiery rays” (Stoicorum Veterum Fragmenta 2.866 = Aëtius 4.15.3; cf. 2.867; 2.869). We see when objects impinge upon this stretched air. Chrysippus likens this act to feeling something by means of a “walking

500   Hellenistic Greek Science stick” (Stoicorum Veterum Fragmenta 2.864; 2.865; 2.867; 2.871), and although this comparison should not be interpreted literally, it allows the Stoics to conceptualize the mechanism of sight on the model of touch, which fits nicely with their commitment to a fully corporeal universe. The Stoics’ position thus adopts some of the entities formulated most clearly by geometrical optics (rays and cones), but reimagines them according to new physical commitments (pneuma, tension). A similar transposition takes place in the vocabulary used to describe how images reach the eyes via the cone. Chrysippus utilizes the basic Aristotelian vocabulary of “alteration,” while Zeno and Cleanthes employ the more Atomistic “imprint” (tupōsis)—​which they seem to understand literally as a physical impression made on the soul (see Stoicorum Veterum Fragmenta 2.55; 2.56; cf. Hankinson 2003: 62; Løkke 2008: 40–​41). Similarly, in their treatment of light, the Stoics explain that we cannot see in the dark because the visual pneuma cannot produce sufficient tension on its own, and the “stretching” of the external air only occurs when it is already illuminated and thus homogeneous with the “light-​like” visual pneuma (Geminus, Optical Fragments 24.11–​15 Schöne; cf. Stoicorum Veterum Fragmenta 2.868). In general, then, the Stoics appropriated preexisting vocabulary and assumptions, reinterpreting them to fit their broader physical philosophy. Lastly, while the above description details the physical mechanism of vision, in the extant fragments the Stoics afford far more attention to the process by which the leading part of the soul, the hēgemonikon, perceives what the eye presents to it. What we receive through the stretched cone is not actually a visual perception at all, but an involuntary affection called a phantasia. Visual perception does not properly take place until the brain consciously chooses or “accepts” the image presented to it, which they then call a cataleptic impression (phantasia katalēptikē; cf. Kerferd 1976; von Staden 1978; Sedley 2005). Considerable debate surrounds these terms and their translation, since it is uncertain whether the soul accepts the phantasia qua sense impression (e.g., yes, I see brown) or qua propositional statement (e.g., yes, that object is brown). A full account of Stoic epistemology cannot be dealt with here, but these issues highlight how investigations of “vision” could include complex interrogations of mental processes. The boundaries of the phenomenon moved according to the interests and anxieties of various authors.

4.2 Galen: Geometrical Anatomy By the mid-​3rd century bce the major philosophical schools in antiquity had all put forward their respective theories and the basic geometry of vision had been established. Yet none of these authors dealt with the anatomy of the eye to any great extent. The philosophical tradition only addressed the basic ocular structures (if at all), and Euclid simply placed the vertex of the visual cone “at” the eye. Around the same time, Archimedes factored in the angle subtended by the cornea when utilizing the visual cone to determine the diameter of the sun, but his geometry ends up placing the cone’s vertex far

Optics and Vision   501 behind the eye and so cannot be said to integrate the eye’s anatomy to any great extent (The Sand Reckoner 138–​139 Mugler). Yet by the early 3rd century bce, two physicians, Herophilus and Erasistratus, had made significant anatomical advancements in Alexandria, not only identifying the motor and sensory nerves, distinguishing arteries and veins, discovering the ovaries and fallopian tubes and accurately describing the liver, but also discerning four separate membranes within the eye, including the “horn-​ like” cornea (keratoeidēs) and the “net-​like” retina (amphiblēstroeidēs) (Longrigg 1988, 462–​471; von Staden 1996). These anatomical features did not make it into contemporary philosophical accounts, and around 400 years passed before they featured highly in the theories of Galen, who expanded on these discoveries and incorporated the microstructures of the eye with a pneuma-​theory of vision in the 2nd century ce, all while providing a (rudimentary) geometrical analysis of the ocular anatomy. Although Galen’s text On Vision has regrettably been lost (cf. On the Usefulness of the Parts 10.6, Kühn 3.785–​786; 8.6, 3.641 Kühn), both Anatomical Procedures and On the Usefulness of the Parts supply systematic anatomical investigations of the eye, and On the Opinions of Hippocrates and Plato deals more fully with a physical theory. In gen­ eral, Galen’s model resembles the Stoics’ to a great degree: he, too, claims that vision occurs when psychic pneuma reaches the surface of the pupil, strikes the external air and stretches it into a taut cone with its apex in the eye and its base on the objects seen. Yet Galen seeks to distinguish himself from his Stoic predecessors by claiming that visual pneuma does not merely meet with the illuminated air but actually transforms the air into a sensate extension of the eye—​and ultimately the brain. In other words, Galen argues that visual pneuma converts the air into a quasi-​organ of sight (On the Opinions of Hippocrates and Plato 7.5.31–​32, Kühn 5.624–​625; cf. Ierodiakonou 2014). Despite his posturing, however, this model aligns with the Stoics in most respects, and where Galen differentiates himself more fully is in the level of anatomical detail that he incorporates. He describes how air enters the body during inhalation and then travels to the heart, where it is elaborated into “vital pneuma.” Some of this new substance travels through the arteries to the back of the brain, where it is further elaborated into “psychic pneuma” in the retiform plexus, a net-​like cluster of vessels (now called the rete mirabile), and this pneuma continues on through the tri-​layered optic nerves and retina to reach the primary organ of sight, the crystalline humor (krustalloeidēs)—​which we now call the lens (On the Usefulness of the Parts 10.1, Kühn 3.760). Galen argues that pneuma makes this crystalline humor sensate, which can then register alterations in the visual cone and discern images insofar as the humor is “white, bright, gleaming and pure” (On the Usefulness of the Parts 10.1, Kühn 3.761). The crystalline humor transmits information back along through the psychic pneuma to the brain, where the visual perception actually takes place. Galen’s detailed physiological account serves multiple purposes, but his overarching project in On the Usefulness of the Parts is to demonstrate that each and every structure in the body is optimally constructed to fulfill at least one specific purpose. For Galen, this argument confirms his teleological worldview and illustrates the technical skill of a divine demiurge. As part of this larger project, however, Galen stops abruptly to provide

502   Hellenistic Greek Science a small section on ocular geometry (On the Usefulness of the Parts 10.12, Kühn 3.812). Unlike the optical authors we have examined, however, Galen does not utilize geometry primarily to provide an account of the trajectory of visual rays (although he does supply a brief such exposition) but to explain the purpose of the optical chiasma, the X-​ shaped meeting of the optical nerves between the brain and the eyes. Galen ascribes two functions to this anatomical feature: (1) to allow the exchange of pneuma should one eye become damaged (or simply closed) (On the Opinions of Hippocrates and Plato 7.4.11–​17, Kühn 5.614–​617; On the Usefulness of the Parts 10.14, Kühn 3.831–​838); and (2) to ensure that both eyes remain on the same level plane, thereby preventing double vision. To demonstrate this second function, Galen employs a set of assumptions somewhat different than Euclid’s: he considers every visible object to be a magnitude necessarily bound by at least two visual rays (rather than potentially being reached by a single ray) and insists that each eye produces its own two bounding rays. Accordingly, he considers spatial perception not to be a function of individual ray orientation but to result from the superposition of a magnitude in the respective visual fields (see figure C13.4). To the left eye, A appears slightly to the right; to the right eye, A appears far to the left. The brain thus perceives A to rest at the middle point between these two locations (as if the respective visual cones were superimposed) and therefore sees A slightly to the left of center in its perceived visual cone. The same process occurs for B. In other words, a visual object appears in the “middle location as compared to when each eye produces an image of the object separately” (On the Usefulness of the Parts 10.12, Kühn 3.824). This formulation leads him to the odd conclusion that double vision does not and indeed cannot occur across a horizontal plane, since an object always appears midway between its location in each individual visual cone, regardless of where those locations are. Galen even claims to have confirmed this experimentally, insisting that wall-​eyed patients do not see double, whereas those who have an eye displaced upward do (On the Usefulness of the Parts 10.12, Kühn 3.825–​827). As such, Galen believes that he

B

A

Left eye (object appears to the right)

perceived visual cone

Right eye (object appears to the left)

Figure C13.4  Galen’s binocular image location. Drawing by author.

Optics and Vision   503

Optical Chiasma

Optical Nerves

Figure C13.5  Galen’s optical chiasma. Drawing by author.

needs only to demonstrate that the optical chiasma keeps the two eyes on the same horizontal plane in order to prove that the anatomical feature prevents all double vision. To this end, he reimagines the optical nerves as completely straight lines running from the brain to the base of the eyes. Since these two lines cross at the chiasma, both must lie on the same plane, and therefore the eyes must be level (see figure C13.5). Galen’s geometrical account falters in several important ways—​namely, the eyes can still rest on the same plane and not be level (just tilt your head), double vision can occur horizontally and vertically (just cross your eyes), and the optical nerves are not rigid, straight lines (they are flexible bodily vessels). Moreover, Galen has elsewhere insisted that the nerves do not cross but only meet before spreading back apart—​ thus invalidating the very basis of his geometrical argument. By adopting a syncretic approach to vision and including geometrical insights, Galen draws odd conclusions about visual experience, recreating the flesh and blood optical nerves as quasi-​abstract lines (cf. Webster 2014b, 255–​265). He produces a highly detailed account of ocular structures and lionizes anatomical precision, but by employing multiple approaches to vision, he creates hybrid entities and reduplicated, sometimes conflicting, justifications.

4.3 Ptolemy’s Optics The most extensive discussion of vision in antiquity was produced by Ptolemy (fl. ca 127 ce–​ca 141 ce), a Greco-​Roman astronomer, geographer, and mathematician

504   Hellenistic Greek Science working in Alexandria. Like his younger contemporary Galen, Ptolemy adopts a syncretic approach to vision, selecting elements from multiple physical theories, engaging with the philosophical ideas of Plato, Aristotle, and the Stoics and employing mathematical arguments well beyond the basic proofs provided by Euclid. What is more, Ptolemy places far greater emphasis on experimental confirmation than his predecessors, structuring much of his analysis on material apparatuses designed to investigate vision, its behaviors, and its characteristics. More than a geometrical text, Ptolemy’s Optics constitutes a full-​scale analysis of vision, a broad investigation into its physical and philosophical underpinnings. In this regard, it functions as a type of culmination of the traditions discussed heretofore. It represents the most sophisticated and comprehensive account of optics in the ancient world, unsurpassed until Ibn al-​Haytham (ca 965–​1040/​41) wrote his Kitab al-​Minazir, or Book of Optics, in the 11th century. The original Greek text of Ptolemy’s Optics has been lost, and instead we have only Eugene of Sicily’s 12th-​century Latin translation of an earlier Arabic edition. In the course of this transmission, the treatise has also suffered some losses, with the first of its five books missing and the last ending abruptly. Ptolemy fortunately recounts what Book 1 contained: a discussion about the nature of light and sight, their interactions, and their respective powers (Optics 2.1). In turn, Book 2 outlines the philosophical framework for vision before discussing binocular vision, image location, and distance perception. Books 3 and 4 deal with reflection in plane, concave, convex, and compound mirrors, and Book 5 investigates refraction. The transmission history of the text has led some scholars to question the work’s authenticity (cf. Knorr 1985, 27–​105; see Siebert 2014 for the most substantial arguments against Ptolemy’s authorship). Still, references to Ptolemy’s text occur in Late Antiquity and the medieval period (cf. Damianus, Optical Hypotheses 3 and Simplicius, On Aristotle’s On the Heavens 7.20.11 Heiberg; Simeon Seth, On the Nature of Things 4.74.12 Delatte), and most recent scholars have accepted it to be genuine (see Martin 1871; LeJeune 1956, 13–​26; 1957, 13–​25; 1989, 13–​26, 133–​138, 271; Smith 1996, 6, 13, 49–​50). Like Aristotle, Ptolemy begins (at least in Book 2) by establishing the metaphysical foundations of visual perception, delineating the hierarchy of qualities and capacities that it involves. At the most fundamental level, he holds the necessary condition of vision to be “luminous compactness” (lucida spissa), insisting objects need to be illuminated to be visible but must also be compact enough to impede the visual flux that extends from the eye. While luminous compactness is intrinsically visible, however, it is not that which is primarily visible, which Ptolemy holds to be color (as did Aristotle). In other words, all visual qualities require color to be discerned, and even when we see light, we see it by virtue of its color. Ptolemy goes on to propose a physical theory involving both visual rays and a projecting visual cone. Yet in stark contrast to Euclid’s Optics, Ptolemy argues that the visual cone is not a collection of individual rays but is composed of a continuous “visual flux” (Optics 2.50). As such, he sees rays as convenient geometrical constructs that operate as powerful analytic tools, and he insists that they do not represent real entities.

Optics and Vision   505 Moreover, his visual cone is continuous, but it is not homogenous: a visual axis runs down its center, along which the visual flux remains particularly strong and effectual. Visual acuity degrades toward the edges of the cone, where the visual flux weakens. Moreover, the cone degrades over distance, when the visual rays extend too far from their source (Optics 2.20). In short, unlike Euclid’s geometrically uniform visual entities, Ptolemy constructs a dynamic model of sight, utilizing physical arguments alongside diagrammatic depictions when constructing the mechanism of the eye. As for the act of perception itself, Ptolemy relies on a lax version of Aristotle’s account, suggesting that visible objects somehow qualitatively alter the visual flux, which thereby takes on their color (Optics 2.24). In other words, the cone sees white by “whitening” and black by “blackening”—​although Ptolemy does not outline whether this is meant in the same nondestructive manner as Aristotle stipulates. In any case, color produces a physical, objective affection in the visual flux. That being said, he still considers visual perception itself to be an intentional act, requiring a “rational interchange” between the affection in the visual cone and the governing faculty, which accepts that affection presented to it and infers all secondarily visible qualities (Optics 2.22). This doctrine resembles Stoic notions of cataleptic impressions and reveals Ptolemy’s continued interest in the epistemology of vision (which he also deals with in On the Criterion of Truth and the Governing Faculty; cf. Long 1989). Ultimately, however, Ptolemy’s syncretic approach defies straightforward classification, and while he certainly draws upon his predecessors, aligning him with a single philosophical outlook would be misleading. After having laid out his basic physical model, Ptolemy moves on to the geometry of sight, but unlike Euclid’s account, he does not make geometrical systematicity the main goal of optics, and as such, he leaves behind many of the proofs involving basic geometrical shapes. Instead, Ptolemy moves through multiple aspects of visual experience, turning first to color perception and then discussing the perception of place. Unlike Euclid, he claims we can obviously discern that a building in the distance is larger than a hand held up in front of it, and he argues that this distance perception arises from the fact that the lengths of the visual rays are themselves perceptible, with each eye possessing the capacity for depth perception individually (Optics 2.26). Ptolemy also discusses the attendant implications for size perception, which relies not only on the perceived breadth and distance of an object but also its angular orientation. For instance, a wall angling away from us will “appear” longer than one occupying the same visual angle but oriented horizontally (Optics 2.94–​62). More than presenting mechanical rules, however, Ptolemy acknowledges that distance and size perception are subject to human judgment and can rely on color cues as well—a phenomenon that painters use to their full advantage (Optics 2.123–​127). He establishes a general scheme for potential illusions, which he argues arise from either objective factors affecting the visual flux or subjective factors arising in judgment (Optics 2.84, 90, 104–​105). In general, however, Ptolemy does not establish the relative power of each factor, and so we are left with a number of variables, but no formula, so to speak. This could be leveled as a critique, but more accurately reflects his sensitivity to the squishiness of human perception.

506   Hellenistic Greek Science

4.4 Ptolemy’s Objective Illusions: Diplopia, Reflection And Refraction In each of the extant books, Ptolemy conducts an investigation of at least one objective illusion (double vision, reflection, or refraction), and in each case, he employs an experimental apparatus. In Book 2, he investigates double vision (diplopia) by means of a short ruler with two cylindrical pegs. Ptolemy recognizes that each eye sees the same object in a slightly different position in their respective visual fields, and as a result, a single object will only be seen in a single location when the central axis of both visual cones align upon it (Optics 2.27). When the object occupies any other location, double vision takes place. His ruler allows him to both interrogate and organize the geometrical circumstances of diplopia, explicating when the visual cones line up and when they do not (Optics 2.27–​45). On the one hand, this approach demonstrates his empirical approach to the question of visual illusions. On the other, it is hard to discern when Ptolemy actually tests his results and when he relies on his geometrical depictions of the apparatus to support his claims. In Books 3, 4, and 5, Ptolemy conducts a large-​scale investigation of reflection and refraction, which he considered to be special cases of each other. Refraction constitutes an instance where the visual ray is partially bent, whereas reflection is an instance where it is fully broken, and in this regard, we might instead think of them as reflection and deflection (Optics 2.105, 5.36). To conduct his analysis, Ptolemy draws on a long tradition of “catoptrics,” or the geometrical study of mirrors, which perhaps goes back as far as the lost enoptrikon of Philip of Opus (mentioned earlier). The first systematic treatise in the discipline, however, is the Catoptrics attributed to Euclid, which provides one of the first explicit—​albeit notoriously problematic—​articulations of the laws of reflection (Euclid, Catoptrics, def. 3–​5; cf. pseudo-​Aristotle, Problemata 11.23, 901b21–​23; 16.13, 915b18–​35). Indeed, like the Optics, Euclid’s Catoptrics attempts to provide a systematic geometrical treatment of its subject matter, and it does so by dividing reflection into plane, convex and concave mirrors. It, too, may have an astronomical background (Mota 2012). The Hellenistic period saw numerous other treatises about mirrors, including a now-​lost “huge volume” by Archimedes (cf. Apuleius, Apology 16), which reportedly covered a wide range of geometrical, meteorological, and practical topics; a treatise by Diocles called On Burning Mirrors, which demonstrates that a parabolic mirror can focus the strength of the sun’s rays on a single point; and the De speculis circulating under the name Ptolemy (but also attributed to Hero), which contains both a quasi-​philosophical “proof ” of the equal angle law (pseudo-​Hero, De speculis 6–​8) and instructions for how to construct mirrors that will distort the face, multiply the image, and reveal a hidden idol in a temple. In short, a number of different goals motivated the study of reflection in antiquity, and authors display interest in abstract questions about conics, practical concerns, and a fascination with thaumaturgy. This varied tradition lies behind Ptolemy’s discussions of reflection and refraction in his Optics, but his investigations attempt more directly to “save the phenomena” and

Optics and Vision   507 articulate the deeper regularities underlying these visual behaviors than to address all possible applications of mirrors (Smith 1981). Still, his modes of argumentation are multiform, employing both geometrical proofs and physical rationales, while also displaying his interest in empirical corroboration. For instance, in Book 3, Ptolemy investigates reflection in plane and convex mirrors, grouping them together because they both produce reflections that do not disrupt orientation—​even if convex mirrors can considerably distort shape. To do so, he establishes three basic principles of reflection: (1) we see along the rectilinear ray reaching the object through reflection; (2) the object appears to be located on the perpendicular dropped from the object through the mirror’s surface; and (3) reflection takes place at equal angles (Optics 3.3). He presents these principles as logical and indubitable, but he goes on to confirm them empirically nevertheless. To do so, he uses multiple experimental apparatuses, such as a bronze plaque made to hold a plane, convex, or concave mirror at its geometrical center and fitted with a sighting mechanism directed at this point (Optics 3.10), and a board with colored lines drawn on it to test the rectilinearity of sight lines (Optics 3.42). In Book 4, Ptolemy turns to concave and compound mirrors, grouping these together because they can both distort, invert, and multiply an image depending on the location of both the eye and the object. Analyzing these mirrors is accordingly far more complex. Ptolemy’s account therefore moves forward on a “case by case” basis (Smith 1996, 41), dealing with apparent distance, size, shape, orientation, displacement, and magnification in turn. In Book 5, Ptolemy investigates refraction and employs another experimental apparatus to do so, retrofitting his bronze plaque with a glass dish to determine the angles of incidence and refraction from air to water, air to glass, glass to air, and water to glass. Ptolemy seemingly wants to establish a direct proportionality between the visual density of an object and its refractive index/​impedance (i.e., the denser a material, the more it bends the trajectory of the visual ray) (Optics 5.2). He also proposes a law of refraction, claiming, “objects will be seen along the continuation of the [incident] visual ray, as well as along the normal dropped [from the visible object] to the water’s surface” (Optics 5.5). This is incorrect (cf. Lejeune 1957, 167–​169), but it clearly illustrates how Ptolemy attempts to understand refraction by extending his analysis of reflection. As for the refractive values that he finds in his experiments, they come fairly close to modern numbers but are certainly idealized, rounded to fit the tidy algorithm of “constantly diminishing first difference subject to decrease by constant second differences” adopted from Babylonian astronomy (Smith 1996, 45; cf. Neugebauer 1957). Yet without knowing the quality of the glass he used or the precision of his sighting mechanism, we cannot determine how accurately he reported his findings (cf. Lejeune 1946; Smith 1982). In sum, Ptolemy approaches both reflection and refraction with an empirical mindset, even while privileging regularity and mathematical elegance above all. Lastly, while some ancient authors separated the investigation of vision into optics, catoptrics, and scaenographia (cf. Geminus, Optical Fragments 26 Schöne), Ptolemy holds that analyzing and explaining these illusions is a fundamental part of what it means to comprehensively explain vision. “Sight” as a construct had expanded well beyond the simple

508   Hellenistic Greek Science act of image transfer to include a whole number of features, be they physical, geometrical, experiential, technological, or epistemological.

5. Conclusion In the years following Ptolemy, the trend toward greater inclusion did not continue, as Neoplatonic philosophers grew increasingly interested in the psychic aspects of vision, constructing complex systems around the role of the soul in the perceptive act (Smith 2015b, 130–​154). In the process, they became less interested in the other features so crucial to Ptolemy. In truth, Ptolemy’s monumental work had varying impact, with geometrical works in late antiquity like Anthemius’ On Burning Mirrors bearing no trace of its theories, while Damianus’ Optical Hypotheses recapitulated ideas and passages from it alongside those taken from Euclid (cf. Netz and Squire 2015; see Siebert 2014 for an alternate dating of Ptolemy’s treatise based of this lack of influence). Optics therefore follows the trajectory of most scientific disciplines, moving in multiple directions over time, rather than in a linear advance toward ever better discoveries. Indeed, the investigation of vision changed considerably from the 5th century bce to the 2nd century ce, shifting from the basic practice of incorporating visual perception into a particular physical philosophy into the full-​scale interrogation of sight, reflection, and refraction. Vision as a scientific phenomenon encompassed ever more aspects, both experiential and epistemological, while technology influenced assumptions about what constituted its fundamental behaviors. In short, the intellectual and material apparatuses surrounding visual perception altered what it meant to explain sight. The boundaries of this practice never stabilized, however, and later authors were free to emphasize certain epistemological aspects, while ignoring physical or geometrical facts, and vice versa. The history of visual explanations in antiquity should countenance this shifting terrain, recognizing that divergent goals motivated various authors, who in turn drew from different textual traditions. Even the same authors could possess conflicting goals when focusing on separate aspects of the visual experience. That being said, whether authors located the act of visual perception in rays, the cone, the eye, the brain, or the soul, whether they hypothesized some power left the eye, some imprint entered it, or some complement of both operated in tandem, they thought of the visual mechanism without making light the primary vehicle of visual information. That they could do so for so long illustrates the complexity of the visual experience and the number of competing variables included within it.

Bibliography Individual Authors See EANS entries on Aëtios, 37–​ 38 (Mejer); Alexander of Aphrodisias, 54–​ 55 (Fazzo); Alkmaiōn of Krotōn, 61 (Zhmud); Anaxagoras of Klazomenai, 73–​74 (Graham); Apuleius

Optics and Vision   509 of Madaurus, 119–​120 (Opsomer); Aristotelian Corpus, De Coloribus, 146 (Ierodiakonou); Aristotelian Corpus, Problems, 149–​150 (Hellmann); Arkhutas of Taras, 161–​162 (Zhmud); Calcidius, 203–​204 (Somfai); Chrysippus of Soloi, 212–​213 (Lehoux); Damianos of Larissa, 225 (Bowen and Todd); Dēmokritos of Abdēra, 235–​236 (Englert); Diogenēs Laërtios, 251–​252 (Mejer); Diogenēs of Apollōnia, 252 (Graham); Empedoklēs of Akragas, 283–​284 (Trépanier); Erasistratos of Ioulis, 294–​296 (Scarborough); Geminus, 344–​345 (Bowen and Todd); Hērophilos of Khalkēdōn, 384–​390 (Scarborough); Iamblikhos of Khalkis, 430–​ 431 (Lautner); Kleanthēs of Assos, 476 (Lehoux); Parmenidēs of Elea (Curd); Philippos of Opous, 647 (Mendell); Sextus Empiricus, 739–​740 (Bett); Simplicius of Kilikia, 743–​745 (Baltussen); Thrasullos, 806–​807 (Tarrant); M. Vitruuius Pollio, 830–​832 (Howe); Zēnōn of Kition, 846–​847 (Lehoux).

General Overviews Beare, John. Greek Theories of Elementary Cognition from Alcmaeon to Aristotle. New York: Oxford University Press, 1906. Darrigol, Olivier. A History of Optics:  From Greek Antiquity to the Nineteenth Century. New York: Oxford University Press, 2012. Lindberg, David. Theories of Vision from Al-​Kindi to Kepler. Chicago: University of Chicago Press, 1976. Park, David. The Fire Within the Eye: A Historical Essay on the Nature and Meaning of Light. Princeton, NJ: Princeton University Press, 1997. Smith, A. Mark. From Sight to Light: The Passage from Ancient to Modern Optics. Chicago:  University of Chicago Press, 2015a. Squire, Michael, ed. Sight and the Ancient Senses. New York: Routledge, 2015.

Early Philosophical Authors: Vision as Reflection Lasserre, François. De Léodamas de Thasos à Philippe d’Oponte. Témoignages et fragments. Édition, traduction et commentaire. Naples: Bibliopolis, 1987. Lloyd, G. E. R. Magic, Reason and Experience: Studies in the Origin and Development of Greek Science. New York and London: Cambridge University Press, 1979. Longrigg, James. “Philosophy and Medicine:  Some Early Interactions.” Harvard Studies in Classical Philology 67 (1963): 147–​175. Rudolph, Kelli. “Sight and the Presocratics: Approaches to Visual Perception in Early Greek Philosophy.” In Squire 2015, 36–​53. Solmsen, Friedrich. “Greek Philosophy and the Discovery of the Nerves.” Museum Helveticum 18 (1961): 150–​197; repr. in F. Solmsen, Kleine Schriften. 3 vols. vol. 1, 536–​582. Hildesheim: Georg Olms, 1968.

Empedocles: Effluence/​Pore Theory Ball, Philip. Bright Earth: The Invention of Color. London: Penguin, 2001. Booth, N. B. “Empedocles’ Account of Breathing.” Journal of Hellenic Studies 80 (1960): 10–​15. Bruno, Vincent J. Form and Color in Greek Painting. New York: W.W. Norton, 1977. Cherniss, Harold. Aristotle’s Criticism of Presocratic Philosophy. New York: Octagon Books, 1935. Ierodiakonou, Katerina. “Empedocles on Color and Color Vision.” Oxford Studies in Ancient Philosophy 29 (2005a): 1–​37.

510   Hellenistic Greek Science Kalderon, Mark E. Form Without Matter:  Empedocles and Aristotle on Color Perception. New York: Oxford University Press, 2015. Kranz, W. “Die Ältesten Farbenlehren der Griechen.” Hermes 47 (1912): 126–​140. Long, A. A. “Thinking and Sense-​Perception in Empedocles:  Mysticism or Materialism?” Classical Quarterly 16.2 (1966): 256–​276. O’Brien, D. “The Effect of a Simile: Empedocles’ Theories of Seeing and Breathing.” Journal of Hellenic Studies 90 (1970): 140–​179. Osborne, H. “Colour Concepts of the Ancient Greeks.” The British Journal of Aesthetics 8.3 (1968): 269–​283. Pastoureau, Michel. Blue: The History of a Color. Trans. M. I. Cruse. Princeton, NJ: Princeton University Press, 2001. Originally published as Bleu, Histoire d’une couleur. Paris: Éditions du Seuil, 2000. Platnauer, Maurice. “Greek Colour-​Perception.” Classical Quarterly 15.3 (1921): 153–​162. Pollitt, Jerome Jordan. “Περὶ χρωμάτων:  What Ancient Greek Painters Thought About Colours.” In Color in Ancient Greece, ed. M. A. Tiberios and D. S. Tsiafakis, 1‒8. Thessaloniki: Aristotle University of Thessaloniki, 2002. Prantl, Carl. Aristoteles über die Farben. München: Kessigner, 1849. Sedley, David. “Empedocles’ Theory of Vision and Theophrastus’ De sensibus.” In Theophrastus:  His Psychological, Doxographical, and Scientific Writings, ed. W. W. Fortenbaugh and D. Gutas, 20–​31. New Brunswick, NJ: Transaction, 1992. Siegel, Rudolph. “Theories of Vision and Color Perception of Empedocles and Democritus; Some Similarities to the Modern Approach.” Bulletin of the History of Medicine 33.2 (1959): 145–​159. Verdenius, W. J. “Empedocles’ Doctrine of Sight.” In Studia Varia Carolo Guilielmo Vollgraff, 155–​164. Amsterdam: North-​Holland, 1948.

Democritus: Imprint Theory Alfieri, Vittorio Enzo. Gli Atomisti: Frammenti e testimonianze. Bari: Laterza, 1936. Baldes, Richard. “Democritus’ Theory of Perception: Two Theories or One?” Phronesis 20.2 (1975): 93–​105. —​—​—​. “Theophrastus’ Witness to Democritus on Perception.” Apeiron 10.1 (1976): 42–​48. —​—​—​. “Democritus on the Nature and Perception of ‘Black’ and ‘White’.” Phronesis 23.2 (1978): 87–​100. Barnes, Jonathan. The Presocratic Philosophers. 2 vols. Rev. ed. New York: Routledge. 1982. Bicknell, P. J. “The Seat of the Mind in Democritus.” Eranos 66 (1968): 10–​23. Burkert, Walter. “Air-​Imprints or Eidola: Democritus’ Aetiology of Vision.” Illinois Classical Studies 2 (1977): 97–​109. English, Robert B. “Democritus’ Theory of Sense Perception.” Transactions and Proceedings of the American Philological Association 46 (1915): 218–​221. Guthrie, William K.  C. A History of Greek Philosophy. Vol. 2:  The Presocratic Philosophers. Cambridge: Cambridge University Press, 1965. Mugler, Charles. “Les theories de la vie et la conscience chez Démocrite.” Revue de philologie 33 (1959): 7–​38. Ross, G. R. T., trans. Aristotle: De Sensu and De Memoria. Cambridge: Cambridge University Press, 1906. Rudolph, Kelli C. “Democritus’ Perspectival Theory of Vision.” Journal of Hellenic Studies 131 (2011): 67–​83.

Optics and Vision   511 —​—​—​. “Democritus’ Ophthamology.” Classical Quarterly 62.2 (2012): 496–​501. Sassi, Maria Michela. Le teorie della percezione in Democrito. Florence: La Nuova Italia, 1978. Tanner, Jeremy. “Sight and Painting: Optical Theory and Pictorial Poetics in Classical Greek Art.” In Squire 2015, 107–​122. Taylor, C. C.  W. The Atomists:  Leucippus and Democritus. Toronto:  University of Toronto Press, 1999. von Fritz, Kurt. “Democritus’ Theory of Vision.” In Science, Medicine and History: Essays on the Evolution of Scientific Thought and Medical Practice Written in Honour of Charles Singer, ed. E. A. Underwood, 83–​99. Oxford: Oxford University Press, 1953.

Plato: Intermingled Fire Ierodiakonou, Katerina. “Plato’s Theory of Colours in the Timaeus.” Rhizai 2.2 (2005b): 219‒233.

Aristotle: The Transparent Visual Medium Broadie, Sarah. “Aristotle’s Perceptual Realism.” Southern Journal of Philosophy 31, suppl. (1993): 137–​159. Burnyeat, Miles. “Is an Aristotelian Philosophy of Mind Still Credible? A  Draft.” In Essays on Aristotle’s De Anima, ed. M. C. Nussbaum and A. O. Rorty, 15–​26. New York: Oxford University Press, 1992. —​—​—​. “Aristote voit du rouge et entend un ‘do’: Combien se passe-​t-​il de choses? Remarques sur De Anima, II 7–​8.” Revue Philosophique de la France et de l’Etranger 188 (1993): 263–​280; trans. “How Much Happens When Aristotle Sees Red and Hears Middle C? Remarks on De Anima 2 7–​8.” In Essays on Aristotle’s De Anima, ed. M. C. Nussbaum and A. O. Rorty, 421–​ 434. New York: Oxford University Press, 1995b. —​—​—​. “Aquinas on ‘Spiritual Change’ in Perception.” In Ancient and Medieval Theories of Intentionality. ed. D. Perler, 129–​153. Leiden: Brill, 2001. —​—​—​. “De Anima II 5.” Phronesis 47 (2002): 28–​90. Caston, Victor. “The Spirit and the Letter: Aristotle on Perception.” In Metaphysics, Soul, and Ethics in Ancient Thought, ed. R. Salles, 245–​320. New York: Oxford University Press, 2004. Charles, David. “Desire in Action: Aristotle’s Move.” In Moral Psychology and Human Action in Aristotle, ed. M. Pakaluk and G. Pearson, 76–​94. New York: Oxford University Press, 2011. Everson, Stephen. Aristotle on Perception. New York: Oxford University Press, 1997. Johansen, Thomas K. Aristotle on the Sense-​ Organs. New  York:  Cambridge University Press, 1997. Lorenz, Hendrik. “The Assimilation of Sense to Sense-​Object in Aristotle.” Oxford Studies in Ancient Philosophy 33 (2007): 179–​220. Lloyd, G. E. R. Aristotelian Explorations. New York: Cambridge University Press, 1996. Marmodoro, Anna. Aristotle on Perceiving Objects. New York: Oxford University Press, 2014. Murphy, Damian. “Aristotle on Why Plants Cannot Perceive.” Oxford Studies in Ancient Philosophy 29 (2005): 295–​339. Nussbaum, Martha C. Aristotle’s De Motu Animalium. Princeton, NJ:  Princeton University Press, 1978. Nussbaum, Martha, and Hilary Putnam. “Changing Aristotle’s Mind.” In Essays on Aristotle’s De Anima, ed. M. C. Nussbaum and A. O. Rorty, 27–​56. New  York:  Oxford University Press, 1992.

512   Hellenistic Greek Science Scaltsas, Theodore. “Biological Matter and Perceptual Powers in Aristotle’s De anima.” Topoi 15.1 (1996): 25–​37. Schofield, Malcolm. “Phantasia in De Motu Animalium.” In Moral Psychology and Human Action in Aristotle, ed. M. Pakaluk and G. Pearson, 119–​134. New York: Oxford University Press, 2011. Shields, Christopher. “Intentionality and Isomorphism in Aristotle.” Proceedings of the Boston Area Colloquium in Ancient Philosophy 11 (1995): 307–​330. Sisko, John E. “Material Alteration and Cognitive Activity in Aristotle’s ‘De Anima’.” Phronesis 41.2 (1996): 138–​157. —​—​—​. “Alteration and Quasi-​Alteration: A Critical Notice of Stephen Everson, Aristotle on Perception.” Oxford Studies in Ancient Philosophy 16 (1998): 331–​352. Slakey, Thomas. “Aristotle on Sense Perception.” The Philosophical Review 70.4 (1961): 470–​484. Sorabji, Richard. “Aristotle, Mathematics, and Colour.” Classical Quarterly 22.2 (1972b): 293–​308. —​—​—​. “Body and Soul in Aristotle.” Philosophy 49 (1974): 63–​89. —​—​—​. “Intentionality and Physiological Processes: Aristotle’s Theory of Sense-​Perception.” In Essays on Aristotle’s De Anima, ed. M. Nussbaum and A. O. Rorty, 195–​225. New York: Oxford University Press, 1992.

Epicurean Eidola theory Asmis, Elizabeth. Epicurus’ Scientific Method. Ithaca, NY: Cornell University Press, 1984. Avotins, Ivars. “Alexander of Aphrodisias on Vision in the Atomists.” Classical Quarterly 30.2 (1980): 429–​454. Bailey, Cyril. The Greek Atomists and Epicurus. 2nd ed. New York: Russell & Russell, 1964. Berryman, Sylvia. “Euclid and the Sceptic: A Paper on Vision, Doubt, Geometry, Light and Drunkenness.” Phronesis 43.2 (1998): 176–​196. DeWitt, Norman W. Epicurus and His Philosophy. Minneapolis:  University of Minnesota Press, 1954. Everson, Stephen. “Epicurus on the Truth of the Senses.” In Epistemology, ed. S. Everson, 161–​ 183. Cambridge: Cambridge University Press. 1990. Gottschalk, H. B. Heraclides of Pontus. New York: Oxford, 1980. Glidden, D. K. “‘Sensus’ and Sense Perception in the De rerum natura”. California Studies in Classical Antiquity 12 (1979): 155–​181. Harry, Brigid. “Epicurus: Some Problems in Physics and Perception.” Greece and Rome, 17.1 (1970): 58–​63. Hicks, Robert Drew. Stoic and Epicurean. New York: Russell & Russell, 1962. Ierodiakonou, Katerina. “Hellenistic Philosophers on the Phenomenon of Changing Colors.” In The Frontiers of Ancient Science: Essays in Honor of Heinrich von Staden, ed. B. Holmes and K.-​D. Fischer, 227–​250. Berlin: de Gruyter, 2015. Lee, Edward N. “The Sense of an Object:  Epicurus on Seeing and Hearing.” In Studies in Perception: Interrelations in the History of Philosophy and Science, ed. P. K. Machamer and R. G. Turnbull, 27–​59. Columbus: Ohio State University Press, 1978. Masi, Francesca G., and Stefano Maso, eds. Epicurus on Eidola. Peri Phuseos Book 2: Update Proposals and Discussions. Lexis Ancient Philosophy 10. Amsterdam: Adolf M. Hakkert, 2015. Rist, John M. Epicurus: An Introduction. New York: Cambridge University Press, 1972.

Optics and Vision   513 Schneider, Johann Gottlob. Theophrasti Eresii quae supersunt opera. Leipzig: Teubner, 1818. Striker, Gisela. “Epicurus on the Truth of Sense Impressions.” Archiv für Geschichte der Philosophie 59.2 (1977): 125–​142. Taylor, C. C.  W. “‘All Perceptions are True.’” In Doubt and Dogmatism, ed. M. Schofield, J. Barnes, and M. Burnyeat, 105–​124. Oxford: Oxford University Press, 1980.

Geometrical Optics: Early accounts Burnyeat, Miles. “Archytas and Optics.” Science in Context 18.1 (2005): 35–​53. Mekler, Siegfried. Academicorum Philosophorum Index Herculanensis. Berlin: Weidman, 1902. Menn, Stephen. “Democritus, Aristotle, and the Problemata.” In The Aristotelian Problemata Physica: Philosophical and Scientific Investigations, ed. R. Mayhew, 10–​35. Leiden: Brill, 2015. Mueller, Ian. “Mathematical Method, Philosophical Truth.” In The Cambridge Companion to Plato, ed. R. Kraut, 170–​199. Cambridge, MA: Cambridge University Press, 1992. Simon, Gérard. Le regard, l’être et l’apparence dans l’Optique de l’Antiquité. Paris:  Éditions du Seuil, 1988. Tarán, Leonardo. Academica:  Plato, Philip of Opus, and the Pseudo-​ Platonic Epinomis. Philadelphia: American Philosophical Society, 1975.

Peripatetic Ray Theory Boyer, Carl. The Rainbow: From Myth to Mathematics. Princeton, NJ: Princeton University Press, 1959. Brunschwig, Jacques. “Aristote et le statut épistémologique de la théorie de l’arc-​en-​ciel.” In Graceful Reason: Essays in Ancient and Medieval Philosophy Presented to Joseph Owens, ed. L. P. Gerson, 115–​134. Toronto: Pontifical Institute of Mediaeval Studies, 1983. Ferrini, Maria Fernanda, ed. and trans. i Colori. Pisa: Edizioni ETS, 1999. Gottschalk, H. B. “The Authorship of Meteorologica, Book IV.” Classical Quarterly 11.1 (1961): 67–​79. —​—​—​. “Strato of Lampsacus:  Some Texts.” Proceedings of Leeds Philosophical and Literary Society 11 (1965): 95–​182. —​—​—​. “The De Coloribus and Its Author.” Hermes 92 (1964b): 59–​85. Hahm, David E. “Early Hellenistic Theories of Vision and Perception of Color.” In Studies in Perception: Interrelations in the History of Philosophy and Science, ed. P. K. Machamer and R. G. Turnbull, 60–​95. Columbus: Ohio State University Press, 1978. Jones, Alexander. “Peripatetic and Euclidean Theories of the Visual Ray.” Physis 31.1 (1994): 47–​76. Knorr, Wilbur. “Pseudo-​Euclidian Reflections in Ancient Optics:  A Re-​examination of the Textual Issues Pertaining to the Euclidean Optica and Catoptrica.” Physis 31 (1994): 1–​45. Merker, Anne. “Aristote et l’Arc-​en-​Ciel:  Enjeux Philosophiques et Étude Scientifiques.” Archive for History of Exact Sciences 56 (2002): 183–​238. Smith, A. Mark. Ptolemy and the Foundations of Ancient Mathematical Optics: A Source Based Guided Study. Philadelphia: Transactions of the American Philosophical Society, 1999. Stothers, Richard. “Ancient Meteorological Optics.” Classical Journal 105.1 (2009): 27–​42. Taub, Liba. Ancient Meteorology. New York: Routledge, 2003. Webster, Colin. “Technology and/​as Theory:  Material Thinking in Ancient Science and Medicine.” PhD diss., Columbia University, 2014b.

514   Hellenistic Greek Science Euclid’s Optics Andersen, Kirsti. “Ancient Roots of Linear Perspective.” In From Ancient Omens to Statistical Mechanics: Essays on the Exact Sciences Presented to Asger Aaboe, ed. J. L. Berggren and B. R. Goldstein, 75–​89. Copenhagen: University Library, 1987. Brownson, C. D. “Euclid’s Optics and its Compatibility with Linear Perspective.” Archive for History of Exact Sciences 24 (1981): 165–​194. Burton, Harry Edwin. “The Optics of Euclid.” Journal of the Optical Society of America 35.5 (1945): 357–​372. Heiberg, Johan Ludwig. Literargeschichtliche Studien über Euklid. Leipzig: Teubner, 1882. Knorr, Wilbur. “On the Principle of Linear Perspective in Euclid’s ‘Optica.’” Centaurus 34 (1991): 193–​210. —​—​—​. “When Circles Don’t Look Like Circles: An Optical Theorem in Euclid and Pappus.” Archive for History of Exact Sciences 44 (1992): 287–​329. Lackenbacher, Hans. “Beiträge zur antiken Optik.” Wiener Studien 35 (1913): 34–​61. Mugler, Charles. Dictionnaire historique de la terminologie optique des Grecs. Paris: Klincksieck, 1964. Netz, Reviel, and Michael Squire. “Sight and the Perspectives of Mathematics: The Limits of Ancient Optics.” In Squire 2015, 68–​84. Ovio, Giuseppe. L’Ottica di Euclide. Milan: Hoepli, 1918. Panofsky, Erwin. Perspective as Symbolic Form. Cambridge, MA: MIT Press, 1991. Schöne, Richard. Damianos Schrift über Optik. Berlin: Reichsdruckerei, 1897. Sinisgalli, Rocco. Perspective in the Visual Culture of Classical Antiquity. New York: Cambridge University Press, 2012. Smith, A. Mark. “Saving the Appearances of the Appearances: The Foundations of Classical Geometrical Optics.” Archive for History of Exact Sciences 24.2 (1981): 73–​99. Tobin, Richard. “Ancient Perspective and Euclid’s Optics.” Journal of the Warburg and Courtauld Institutes 53 (1990): 14–​41. ver Eecke, Paul. Euclide, l’Optique et la Catoptrique. Paris: Bruges, 1938. Webster, Colin. “Euclid’s Optics and Geometrical Astronomy.” Apeiron 47.4 (2014a): 526–​551.

The Stoics Dufour, Richard. Chrysippe: Œuvre philosophique, tome I. Paris: Les Belles Lettres, 2004. Gould, Josiah B. The Philosophy of Chrysippus. Leiden: Brill, 1970. Hankinson, Robert J. “Stoic Epistemology.” In The Cambridge Companion to the Stoics, ed. B. Inwood, 59–​84. New York: Cambridge University Press, 2003. Ingenkamp, Heinz G. “Zur stoischen Lehre vom Sehen.” Rheinisches Museum für Philologie 114 (1971): 240–​246. Kerferd, George. “The Problem of Synkatathesis and Katalepsis in Stoic Doctrine.” In Les Stoïciens et leur logiques, ed. J. Brunschwig, 251–​272. Paris: J. Vrin, 1976. Løkke, Håvard. “The Stoics on Sense-​Perception.” In Theories of Perception in Medieval and Early Modern Philosophy: Studies in the History of Philosophy of Mind 6, ed. S. Knuuttila and P. Kärkkäinen, 35–​46. Dordrecht: Springer, 2008. Long, A. A., ed. Problems in Stoicism. London: Athlone Press, 1971. —​—​—​. Hellenistic Philosophy: Stoics, Epicureans, Sceptics. London: Duckworth, 1974. —​—​—​. Stoic Studies. Berkeley: University of California Press, 1996.

Optics and Vision   515 Pohlenz, Max. Die Stoa. 2nd ed. Göttingen: Vandenhoeck & Ruprecht, 1992. Rist, John M. Stoic Philosophy. New York: Cambridge University Press, 1969. Sandbach, F. H. “Phantasia Katalêptikê.” In Long 1971, 9–​22. Sedley, David. “La définition de la phantasia katalêptikê par Zénon.” In Les Stoïciens, ed. G. R. Dherbey and J.-​B. Gourinat, 75–​92. Paris: J. Vrin, 2005. von Arnim, Hans Friedrich August. Stoicorum Veterum Fragmenta, 3 vols. Leipzig: Teubner. 1903–​1924. von Staden, Heinrich. “The Stoic Theory of Perception and its ‘Platonic’ Critics.” In Studies in Perception: Interrelations in the History of Philosophy and Science, ed. P. K. Machamer and R. G. Turnbull, 96–​136. Columbus: Ohio States University Press. 1978. Watson, Gerard. The Stoic Theory of Knowledge. Belfast: Queen’s University Press, 1966.

Galen Cherniss, Harold. “Galen and Posidonius’ Theory of Vision.” American Journal of Philology 54.3 (1933): 154–​161. Ierodiakonou, Katerina. “Galen’s Criticism of the Aristotelian Theory of Colour Vision.” In Antiaristotelismo, ed. C. Natali and S. Maso, 123–​141. Amsterdam: Hakkert, 1999. —​—​—​. “On Galen’s Theory of Vision.” Supplement to the Bulletin of the Institute of Classical Studies 114: Philosophical Themes in Galen, ed. P. Adamson, R. Hansberger, and J. Wilberding (2014): 235–​247. Longrigg, James. “Anatomy in Alexandria in the Third Century b.c.” The British Journal for the History of Science 21.4 (1988): 455–​488. von Staden, Heinrich. “Body and Machine: Interactions between Medicine, Mechanics, and Philosophy in Early Alexandria.” In Alexandria and Alexandrianism, ed. K. Hamma, 85–​106. Malibu, CA: J. Paul Getty Museum, 1996. Siegel, Rudolph. Galen on Sense Perception. Basel: S. Karger, 1970a. —​ —​ —​ . “Principles and Contradictions of Galen’s Doctrine of Vision.” Sudhoffs Archiv: Zeitschrift für Wissenschaftsgeschichte 54 (1970b): 261–​276.

Ptolemy Dambska, Izydora. “La théorie de la science dans les œuvres de Claude Ptolémée.” Organon 8 (1971): 109–​122. Duhem, Pierre. To Save the Phenomena: An Essay on the Idea of Physical Theory from Plato to Galileo, trans. E. Doland and C. Maschler. Chicago: University of Chicago Press, 1969. Govi, Gilberto. L’Ottica di Claudio Tolomeo, da Eugenio, ammiraglio di Sicilia, scrittore del secolo XII, ridotta in latino sovra la traduzione arabe di un testo Greco imperfetto, ora per la prima volta, conforme a un codice della Biblioteca Ambrosiana, per deliberazione della R. Accademia delle Scienze di Torino. Torino, 1885. Katsoff, Louis. “Ptolemy and Scientific Method: A Note on the History of an Idea.” Isis 38.1 (1947): 18–​22. Knorr, Wilbur. “Archimedes and the Pseudo-​ Euclidean Catoptrics:  Early Stages in the Ancient Geometric Theory of Mirrors.” Archives Internationales d’Histoire des Sciences 35 (1985): 27–​105. Lammert, Friedrich. “Eine neue Quelle für die Philosophie der mittleren Stoa I.” Wiener Studien 41 (1919): 113–​121.

516   Hellenistic Greek Science LeJeune, Albert. “Les tables de réfraction de Ptolémée.” Annales de la Société Scientifique de Bruxelles, series 1, 60 (1946): 93–​101. —​—​—​. “La dioptre d’Archimède.” Annales de la Société Scientifique de Bruxelles, series 1, 61 (1947): 27–​47. —​—​—​. Euclide et Ptolémée:  Deux stades dans l’optique géométrique grecque. Louvain: Bibliothèque de l’Université, 1948. —​—​—​. L’Optique de Claude Ptolémée dans la version latine d’après l’arabe de l’émir Eugène de Sicile. Louvain: Bibliothèque de l’Université, 1956. —​—​—​. Recherches sur la catoptrique grecque d’après les sources antiques et médiévales. Mémoires de l’Académie Royale de Belgique: Classe des Lettres et des Sciences Morales et Politiques. 2nd series, vol. 52, fasc. 2. Brussels: Palais des Académies, 1957. —​—​—​. L’Optique de Claude Ptolémée. New York: Brill, 1989. Long, A. A. “Ptolemy on the Criterion: An Epistemology for the Practising Scientist.” In The Criterion of Truth: Essays Written in Honour of George Kerferd, ed. P. Huby and G. Neal, 151–​ 300. Liverpool: Liverpool University Press, 1989. Martin, Thomas-​Henri. “Ptolémée, auteur de l’Optique . . . est-​il le même que Cl. Ptolémée, auteur de l’Almagest?” Bullettino di Bibliografia e di Storia Delle Scienze Matematiche e Fisiche 4 (1871): 466–​469. de Pace, Anna. “Elementi Aristotelici nell’ Ottica di Claudio Tolomeo.” Rivista critica di storia della filosofia 36.2 (1981): 123–​138. Siebert, Harald. Die ptolemäische Optik in Spätantike und byzantinischer Zeit. Stuttgart: Franz Steiner, 2014. Smith, A. Mark. “Ptolemy’s Search for a Law of Refraction:  A Case-​Study in the Classical Methodology of ‘Saving the Appearances’ and Its Limitations.” Archive for History of Exact Sciences 26.3 (1982): 221–​240. —​—​—​. “The Psychology of Visual Perception in Ptolemy’s Optics.” Isis 79.2 (1988): 189–​206. —​—​—​. Ptolemy’s Theory of Visual Perception:  An English Translation of the Optics With Introduction and Commentary. Philadelphia: Transactions of the American Philosophical Association, 1996. —​—​—​. “Sight in retrospective: The Afterlife of Ancient Optics.” In Squire 2015b, 249–​262. Taub, Liba. Ptolemy’s Universe: The Natural Philosophical and Ethical Foundations of Ptolemy’s Astronomy. Chicago: Open Court, 1993. Toomer, G. J. “Ptolemy.” In Dictionary of Scientific Biography, ed. C. C. Gillispie, vol. 11, 186‒206. New York: Scribner, 1976.

Catoptrics Acerbi, Fabio. “The Geometry of Burning Mirrors in Greek Antiquity. Analysis, Heuristic, Projections, Lemmatic fragmentation.” Archive for History of Exact Sciences 65.5 (2011): 471–​497. Boyer, Carl. “Aristotelian References to the Law of Reflection.” Isis 36.2 (1946): 92–​95. Hogendijk, Jan P. “Diocles and the Geometry of Curved Surfaces.” Centaurus 28.3 (1985): 169–​184. Jones, Alexander. “On Some Borrowed and Misunderstood Problems in Greek Catoptrics.” Centaurus 30.1 (1987): 1–​17. Knorr, Wilbur R. “The Geometry of Burning-​Mirrors in Antiquity.” Isis 74.1 (1983): 53–​73. Lejeune, Albert. “Archimède et la loi de la réflexion.” Isis 38 (1947): 51–​53.

Optics and Vision   517 —​—​—​. “Les postulats de la catoptrique dite d’Euclide.” Archives Internationales d’Histoire des Sciences 2 (1949): 598–​613. Lorch, Richard. “Pseudo-​Euclid on the Position of the Image in Reflection: Interpretations by an Anonymous Commentator, by Pena, and by Kepler.” In The Light of Nature: Essays in the History and Philosophy of Science presented to A. C. Crombie, ed. J. D. North and J. J. Roche, vol. 110, 135–​144. Dordrecht: Martinus Nijhoof, 1985. Mota, Bernardo M. “The Astronomical Interpretation of Catoptrica.” Science in Context 25.4 (2012): 469–​502 Nix, Ludwig Leo Michael, and Wilhelm Schmidt, eds. Heronis Alexandrini opera quae supersunt omnia. Vol. 2: Mechanica et catoptrica. Leipzig: Teubner, 1976. Rashed, Roshdi. Les Catoptriciens grecs. Vol 1: Les miroirs ardents. Paris: Les Belles Lettres, 2002. Simon, Gérard. “Aux origines de la théorie des miroirs: Sur l’authenticité de la Catoptrique d’Euclide.” Revue d’histoire des sciences 47.2 (1994): 259–​272. Takahashi, Ken’ichi. The Medieval Latin Traditions of Euclid’s Catoptrica. Fukuoka:  Kyushu University Press, 1992.

chapter C14

Pharm ac ol o g y i n t h e Early Roma n E mpi re Dioscorides and His Multicultural Gleanings John Scarborough

1.  Life and Times Sometime around 68/​69 ce, Dioscorides of Anazarbus completed the five full scrolls of his carefully organized Peri hyles iatrikes (Lat. De materia medica), a rough date secured by Erotian’s mention of Dioscorides’ synonyms for aconite or leopard’s bane (Erotian Κ–​31  =  Materia Medica 4.76; cf. Riddle [1985] 2011, 13–​14). A  generation or so later, multiple copies were in circulation, attested by papyri (Bonner 1922; Flemming and Hanson 2001), as well as a derivative multilingual listing of plant names by a Pamphilus of Alexandria (ca 100 ce), as reported by Galen (Kühn 11.792–​798, 12.31, and 19.63–​64 and 69; Wellmann 1898, 1916). The five books encompassed two or three decades of field botany, the gathering of seeds and roots and stems and leaves of medicinal plants, investigations of medical mineralogy, verifications of folk tales enwreathing animal products, perusal and study of given Greek medical texts (e.g., Sextius Niger, ca 30 ce, appears fairly frequently, as do unattributed lines from Theophrastus:  Scarborough [2005] 2011, xvi–​xvii), meticulous observations on how drugs “worked” when given to patients (Riddle [1985] 2011), collections of physiological and medical folklore to be verified (or not: Scarborough 2012) in the Greek-​speaking eastern half of the Roman Empire, with forays to the urban and rural pockets of Greek inhabitants numerous in Italy and southern Gaul, added to botanical and pharmaceutical details as gathered in coastal North Africa, ranging as far west as Mauretania. Dioscorides was native to Anazarbus, a moderately sized city 100 kilometers northeast of Tarsus on a Roman all-​weather highway in rugged Cilicia. Both Pliny the Elder and Dioscorides quote independently from the (lost) works of Sextius Niger (Wellmann 1889; Scarborough, [1986] 2010; 2008d); thus Dioscorides likely was born during the

520   Hellenistic Greek Science reign of either Tiberius or Caligula, and he set down the remarkable Materia Medica in approximately the same decades as Pliny was assembling his own Natural History. If we can assume analogy to the age when Galen first took up the study of medicine (Riddle [1985] 2011, 219–​220; Nutton 2013, 223; cf. also Kleijwegt 1991; and Scarborough 1971), then in his middle teens Dioscorides became a student attending the lectures, demonstrations, and botanizing rambles of a group of medical teachers then residing in Tarsus (Fabricius 1972, 190–​192; Nutton 2013, 178 with. n. 31, p. 379). One of these teachers was Arius (ca 50 ce)—​Materia Medica was dedicated to him—​who was a famed expert in compounding drugs from ores and minerals, a talented physician and general pharmacologist. Arius composed a handbook on pharmacology (Andromachus in Galen, Compound Medicines by Kind 5.13 = Kühn 13.840), and Dioscorides contributed a styptic formula to his teacher’s book (Compound Medicines by Kind 5.15 = Kühn 13.857), suggesting Arius’ high regard for his young apprentice. Dioscorides may have served for short periods as a civilian physician in an eastern legion (Scarborough and Nutton 1982, 213–​217; Riddle [1985] 2011, 3–​4), most probably—​if so—​ in the Armenian Wars (55–​63 ce), but utterly ill-​founded is his “career” as a military physician, or as a kind of “inspector general of hospitals,” repeated in works on ancient pharmacology and medicine (e.g., Wilmanns 1995, 249–​251; Nutton 1997, 330). What the Materia Medica does show, however, is a traveling physician, whose increasingly experienced skills spanned many provinces and cultures in detailed observations of the medicinal properties of plants, animal products, and minerals. His journeys delineate his search for drugs, patients, and the understanding of variant ailments and their treatments among the ill in distinct topographical and geographic regions, each characterized by diseases of its own. Occasionally, pharmaceutical economics (the “drug trade”) also enabled Dioscorides to incorporate drug stuffs from Far Eastern sources (Schmidt [1924] 1979; Miller 1969; Tomber 2008, 54–​56; Sidebotham 2011, 189–​190). Such exotics as Socotrine aloe, the two cinnamons, pepper, ginger, and other “spices,” previously of erratic supply, now with the relative political stability following the reign of Augustus, became increasingly common in Roman Imperial drug lore (Warmington 1974, 180–​234; Casson 1984, 225–​246; Riddle [1985] 2011, 98–​111). Sometimes, the Materia Medica becomes a documentation of this far-​flung commerce, reaching to India and beyond (Scarborough [1982] 2010; Casson 1989, 164–​165).

2.  Roman Assimilation of Foreign Drug Lore: Dioscorides’ Expanded World In 77 ce, Pliny the Elder presented to Titus his 37-​book “on everything” in the world of man and nature, the massive and jumbled, multiple-​sourced Latin encyclopedia, the Natural History. With the exception of some items on medicine and pharmacology from Italy (Stannard [1965] 1999), Roman Germany, Gaul, and Spain, Pliny’s information on

Pharmacology in the Early Roman Empire    521 drugs came from monstrous gulps of written texts, some in Latin, some in Greek, all sandwiched in layers or simply joined together, as the polymath, with childlike glee, set down as revealed in his research what medical folklore related about medicines made from common plants would do to cure the most loathsome diseases, what midwives among the pagani might believe promoted successful pregnancies, why toxic substances and sneaky specialists in their use lurked especially in the households of the rich and politically powerful, rank astrological linkages to the lore of snakes and insects, and similar topics (Beagon 1995, 202–​240; 2005; Scarborough 2008b, 140–​142; 2011, 8–​9). Pliny’s catalogue accepts all sources as equal merit—​in contrast to Dioscorides, with his painstaking care and analysis, generally by means of personal observation, who came to a balanced and reasoned judgment about most of the 700-​odd simples in the Materia Medica (Wellmann 1924, 129–​132; Stannard [1982] 1999, 4–​5; Bonet 2003, 151–​154). And yet, both Pliny and Dioscorides provide the broad panoramas of what was the Roman Empire in its 1st century: multiethnic, multilingual, a cacophony of religions, geography and topography of wondrous variability, and numberless historical traditions—​all presumably yoked by Roman law, a forcefully imposed pax Romana, paved highways connecting provinces from the Atlantic to the Tigris, and the employment of Latin and Greek in speaking, writing, teaching, and learning. If Egypt is distant to Pliny, it is “in the neighborhood” of Dioscorides; if Roman Germany is familiar to Pliny, Dioscorides might record “what he has heard,” and simply say “so it is said” regarding purported properties of drugs native to some of the western provinces. As students of nature, both seek the “fruits of empire” (Totelin 2012, 126), sometimes on the foundations of earlier Greek and Hellenistic inquiries, sometimes selecting botanical and animal species as imperial displays of conquest in gardens and zoos (as well as showing them as “captives” in Roman triumphs), and sometimes elaborating on particular folk medical traditions that emphasized either remarkable healing powers or deadly poisonous effects. What follows here is a rather brief selection of the 700-​odd simples, and the multitudinous compounds assessed by Dioscorides in his Materia Medica. One can begin with a few topographical and geographic particulars to suggest some of Dioscorides’ methods of gathering, classification, and consequent recommendations, as well as how he utilized sources of information, both written and oral.

3.  Egypt’s Millennially Old Pharmacological Traditions A good historical novelist, well acquainted with the Materia Medica, could easily depict Dioscorides on one of his plant-​collecting journeys up the Nile, perhaps taking time to tour the famous pyramids and sphinx (who presumably had an intact nose), and going further beyond the first and second cataracts, reflecting on what he had set down about kyphi in his first scroll (Materia Medica 1.25; Beck 2011, 22–​23):

522   Hellenistic Greek Science Kyphi is an incense compounded to please the gods: the Egyptian priests employ it copiously. They also mix it with antidotes [to poisons] and administer it in drinks for the treatment of difficult breathing. There are numerous recipes for its preparation, and one among them is as follows: ½ xestes (ca 27 g) of [the tubers] of nut grass (Cyperus rotundus L.), ½ xestes of ripe juniper berries (Juniperus communis L.), 12 minai (ca 5.2 kg) of shiny dried grapes/​raisins, the seeds having been removed, 5 minai of purified pine resin, 1 mna of sweet flag (Acorus calamus L.), 1 mna of camel’s thorn [oil] (Alhagi camelorum Fisch.), 1 mna of camel grass [oil] (Cymbopogon schoenanthus Spreng.), 12 drachmai (ca 40 g) of myrrh (Commiphora sp.), 9 xestai of old wine, and 2 minai of honey. Having removed the seeds from the raisins, pound and triturate them with the wine and myrrh, and having pounded and sifted the rest of the ingredients, combine them all to soak for one day; then, having boiled the honey until it has a glutinous consistency, mix it carefully with the melted pine resin, and then, having carefully pounded together the rest of the ingredients, put [this incense] up into storage in an earthenware vessel.

Dioscorides shows that this is one of a number of similar recipes, certainly of an ancient heritage, going back into dynastic times, demonstrated by a kyphi formula in the Ebers Papyrus (Ebers 1874; Grapow 1955, 19). Moreover, this multiply useful salve/​incense/​drink enjoyed a long-​term popularity: Plutarch, in his Isis and Osiris 383E–​384C, records a similar recipe, with the addition of six more ingredients (Griffiths 1970, 569), and the multisubstance lunar kyphi in Paul of Aegina’s Medical Epitome (ca 630 ce) includes 28 constituents (Scarborough [1984] 2010, 231–​232). The priests of Isis in Egypt apparently were the sources of much practical information, since—​among many examples—​Dioscorides cites them for a detailed understanding of a kind of wormwood called seriphon (Materia Medica 3.23.5–​6) that is effective as a vermifuge against both flatworms and roundworms. In this short set of passages (the major species is likely Artemesia absinthium L. but Materia Medica 3.24 is probably A. abrotanum L.), our well-​traveled physician/​pharmacologist illustrates the dynameis (properties) of each, by listing varieties and sources not only from Egypt but also Cappadocia, Pontus, Thrace, the Taurus Mountains, Cyprus, Galatia (Asia Minor), Sicily, Syria, and Cisalpine Gaul. The common name for the remedy in Cisalpine Gaul is Santonicon, after a tribe living farther west in Gaul, and is recommended by Scribonius Largus 141, for exactly the same problems: Could both Scribonius and Dioscorides have been tapping the same folk medical sources at roughly the same time? Dioscorides says the wormwood Santonicon is less bitter and with fewer seeds than the Egyptian seriphon, but also functions as a good vermifuge. A  touch of personal botanizing is reflected by Dioscorides’ phrase, “there is a third type of wormwood growing with great abundance in the country of the Gauls along the Alps.” Not surprisingly, he notes that the Egyptians produced large quantities of sesame seed oil, of known benefit to consumers as combined with wine and rose oil, in the form of plasters, ointments, and eye salves (Materia Medica 2.99); and Egyptian garlic (the common Allium sativum L.), carefully cultivated for its special, inner cloves called aglithes, is deemed particularly effective

Pharmacology in the Early Roman Empire    523 against intestinal flatworms (Materia Medica 2, 152). Noteworthy is the manner in which designated “parts” of a medicinally active plant are singled out for sometimes careful description.

4.  Coastal North Africa: Cyrene’s Wonder Drug One can readily trace Dioscorides’ travels west of Egypt, as he documented plants, animals, and minerals, and the drug lore of Libya and points farther west. Cyrene had been a fairly prosperous Greek colony and had become famous for its main export of a plant called silphion (Theophrastus, Enquiry into Plants 4.3.1; 6.3.1–​7; 9.1.7), featured on some handsome silver tetradrachmas dating from the 6th through the 4th centuries bce (Baumann 2000, 57, plates 132–​136; cf. Imhoof-​Blumer 1889, 17 with figs. 3.1–​3 and 5; Penn 1994, 81, fig. 56; Robinson 1927, ccli–​cclviii, remains a useful collection of illustrations of the coins). Famous, too, is the Laconian kylix (also ca 560 bce), picturing a king of Cyrene supervising the loading of shipments of silphion, carefully weighed before they were placed aboard trading vessels, and Theophrastus, Enquiry into Plants 6.3.2, details the painstaking care taken at Cyrene in preparing and shipping silphion. Dioscorides visited Libya (as it was still sometimes called) and made a precise record of its famous cure-all, silphion. Numismatists and historians of botany have puzzled over the depictions of the silphion on the silver coinages and have noted that no species known resembles what is pictured (Totelin 2009, 158–​161), but it was so renowned among the Romans that simply writing “ho opos” (the juice) sufficed for identification (Galen, Properties and Mixtures of Simples, 8.14.12 = Kühn 12.90–​91). A careful reading, however, of the description in Dioscorides, Materia Medica 3.80.1–​6, reveals a rather distinctive accounting of the parts of this plant, likely the actual drugs as depicted on the coins (it should be noted that plant parts had been classified as “herbs,” as early as Theophrastus, ca 300 bce; roots, stems, seeds, flowers, etc. were each thought of as pharmaka in their own right: Scarborough 2006, 18). Thus Dioscorides begins by describing the “parts” (Materia Medica 3.80.1; Beck 2011, 218): Silphion. It grows in [various] places in Syria, Armenia, Persia (here Media), and Libya, where the stem is called the “leaf of silphion” (maspeton), and its [stem] resembles that of the giant fennel (Grk. narthex, Ferula communis L.), but the leaves are like those of a celery, and its seed is broad and flat like a leaf, and is termed a magydaris, “the inflorescence of silphion.” Its root is heating, engenders flatulence, belching, and is an extreme desiccant, and is difficult to digest, and noxious to the bladder. [The root] being combined with a wax-​salve, it is good for scrofulous swellings [among the glands of the neck], and it also eliminates the bruises from a black eye, when it is applied mixed with olive oil; for those who suffer from sciatica, a wax-​salve of iris-​rhizome (probably Iris florentina L., or Iris germanica L.),

524   Hellenistic Greek Science or an unguent wax of henna [leaves] (Lawsonia inermis L.) [mixed with the root of silphion] is remedial [for pains in the hips]; boiled in vinegar inside the husk of a pomegranate, and then applied as a plaster, the root of silphion used [as a suppository] removes hemorrhoids around the anus.

At Materia Medica 3.80.6, Dioscorides says, “another kind of silphion also grows in Libya” (also called magydaris), but that it is far less potent than the variety of the herb he has so carefully delineated in its “parts.” Stem, leaf, seed, flower, root—​all can be matched, more or less, with the coinage. But as Theophrastus had written (Enquiry into Plants 6.3.4–​5), silphion had to be harvested only in its wild state and apparently could not be transplanted to other regions of the Mediterranean littoral. Moreover, the magydaris flourishes in Syria (Enquiry into Plants 6.3.7), and not in Cyrene, and both sources say that the Syrian/​Median silphion has far weaker properties (dynameis) than the variety growing uncultivated in Cyrene. Overharvesting, or deliberate uprooting by Berber sheepherders (Applebaum 1979, 122‒123), would lead to the extermination of the Cyrenaic silphion, and it is likely that the ancient silphion (Latin’s laser or laserpicium) is a now-​extinct species in the genus Ferula, a close cousin of the Iranian Ferula assa-​ foetida L., still used (root incised for its gum) as an expectorant and laxative (Usher 1974, 252, col. 2; Langenheim 2003, 416–​417). Much as Dioscorides writes, the odor of silphion and its kin is distinctive, or as a modern text on pharmacognosy has it: “a strong, alliaceous odour, and a bitter, acrid and alliaceous taste” (Trease and Evans 1978, 465). Steier (1927) diligently collects ancient and Arabic references but comes to no definite conclusions regarding species identification. Strantz (1909) remains the best summary of texts and sources on ancient silphion, as well as the numerous guesses of its actual species (see also Steier 1931; Andrews 1941; Gemmill 1966; Koerper and Kolls 1999; and Dalby 2003, 303–​304).

5.  Mauretania and Morocco: Juba’s Euphorbion Continuing west, Dioscorides traversed what is now Tunisia, northern Algeria, and proceeded beyond the Atlas Mountains into Mauretania, at some point reaching as far west as a tribal area called Autololia, on the Atlantic coast of what is now Morocco (one MS gives the site as Tmolos). Perhaps Materia Medica 3.82 records the observations on euphorbion from the lost works of Juba II (48 bce–​23 ce: Roller 2004, 103–​107, four fragments; Roller 2003, 178–​179; Totelin 2012, 136–​140; but Wellmann 1906–​1914, 2.98, apparatus criticus #1, adduces the common source as Sextius Niger). Since Dioscorides fails to designate this section with his usual “as is said,” or “they say,” when he borrows a written text without naming its author, it is also equally likely that Dioscorides has himself gone into the reaches of western Mauretania to check the story for accuracy. The Greek gives a distinctive flavor of an eyewitness report (Materia Medica 3.82):

Pharmacology in the Early Roman Empire    525 Euphorbion. This is a tree [actually a shrub] that grows in the Libyan region called Autololia, near to Mauretania, and it is similar to the giant fennel (Ferula communis L.); it is full of a very acidic sap, gathered by the natives with great fear, due to its extremely hot property; thus, they bind to the shrub the stomachs of sheep, that have been cleansed, and then they cut the stem (with the stomachs attached) with spears, wielded from some distance away. The sap immediately gushes out, in great quantities from the stomachs similarly to a jar that has been broken, and thereby drops to the ground. There are two varieties of this sap: one is transparent like that of the sarkokolla (Astragalus fasciculifolius Boiss.), roughly the size of bitter vetch seeds (that is what has fallen to the ground hardening into small, globular pellets), whereas the other variety—​which remains in the stomachs—​is riddled with small pieces of debris, and becomes hard . . . this medicinal was discovered when Juba was the king of Libya.

Pliny (Natural History 25.77–​78) relates that euphorbium was named after Euphorbus, a physician in service to King Juba, and that Euphorbus was none other than the brother of Antonius Musa (Wellmann 1907), famed for saving the life of Augustus. However, if Wellmann is justified in allocating the account of euphorbium to the lost writings of Sextius Niger, this means that when Pliny writes “the book by Juba is still available,” he has at hand both Sextius Niger and Juba’s tract, or—​as is sometimes obvious in many sections of the Natural History—​Pliny has cited the “original” behind his “secondary” reference (Scarborough [1986] 2010, 75–​76). Whichever text underlies the Natural History 25.77–​78, it identifies the locale of euphorbium as the Atlas Mountains, rather more secure than what we have in the muddled manuscript traditions for Dioscorides’ Materia Medica. Three generations of medical botany are represented here:  Juba II (ca 10 ce), Sextius Niger (ca 40 ce), and Dioscorides (ca 70 ce). A recent study has reconstructed most of Juba’s “little book” (so Galen, Compound Medicines According to Place 9.4 = Kühn 13.270–​271), founded on the presumptive quotations and excerpts in Dioscorides and Pliny the Elder (Pietrobelli 2014, 169–​173). One can, indeed, argue that Juba did not “discover” euphorbium, but that he was one of the first to record a venerated folk medicine in what is now western Morocco. Euphorbus’ name lives today as the nomenclature for some 2,000 species in the genus Euphorbia, with E.  resinifera Berg. likely the type described by Dioscorides (Stadler 1907, col. 1171). Some European pharmacies still carry a “Gummi Resina Euphorbium” prescribed as an extreme laxative (Usher 1974, 246, col. 2; Howes [1949] 2001, 160; Boulos 1983, 83–​85 for uses in modern Morocco). The gummy latex from this cactus-​like plant is characterized by the toxic actions of resiniferatoxin, given its well-​known irritant diterpinoid esters, sometimes labeled phorbol esters (Harborne 1999, 724, no. 2776; Wink and van Wyk 2008, 320), enabling some modern fisherman to employ various species in the stunning of fish, and hunters in the preparation of an arrow poison (E. candelabrum Trém., tropical Africa, and others: Usher 1974, 245, col. 2). Dioscorides’ native gatherers were quite cautious, with good reason: a recent description of the toxic actions of the diterpenes/​phorbol esters includes “potent skin irritants . . . lead[ing] to painful inflammation especially of mucosal tissue and of the eye (can cause intermittent

526   Hellenistic Greek Science blindness). Strong uticaria and blisters . . . develop” (Wink and van Wyk 2008, 320; also 128: E. mauritanica latex toxic as a “fatal nervous disorder in sheep”).

6.  Animals, Their Parts, and Greco-​Roman Pharmacology Specific geographical locales demonstrate only a limited selection of pharmaceuticals in the Materia Medica, so that when Dioscorides tabulates medicinals derived from animals, he reveals a specialized and widespread expertise, a kind of natural history encompassing zoology fused with pharmacology. The range of species includes almost everything from insects and arachnids (honey and beeswax, as well as whole-​bodied bed bugs, beetles, cockroaches, cicadas, and spiders), earthworms, terrestrial mollusks and given parts of shellfish, fish, amphibians, snakes and other reptiles, birds, and mammal parts (animal products, of course, include urines, dungs, fats, milks, cheeses, and oils). Generally, he traveled to verify the tales and stories that often accreted around the dynameis of these sometimes supposedly wondrous drugs. His kantharides likely derived from folk medical traditions (also acknowledged by Nicander of Colophon, Theriaca 755 and Alexipharmaca 115), but Dioscorides at Materia Medica 2.61 shows he has observed the “harvesting” of these beetles, their preparations as blistering agents, along with their use as emmenagogues (they are blister beetles in the genera Lytta and Mylabris: Beavis 1988, 168–​175; Scarborough [1979] 2010, 13–​14 and 73–​80, “Remedies: The Blister Beetles”). Later citations by Aëtius of Amida, Tetrabiblon 2.174 (Olivieri, 2.216–​217), adapting those by Galen, Compound Medicines According to Kind 1.1 (Kühn, 12.363–​365, etc.), indicate that Dioscorides’ cautions regarding what we call cantharidin were carefully endorsed. Pharmacology melds with medical dietetics, as Dioscorides catalogues a wide variety of land snails (Grk. kochlias, usually among the very common Helix spp.: Thompson 1947, 129–​131; Dalby 2003, 304–​305), a geographical and topographic accounting that includes Sardinia, Libya, Astypalaea, Sicily, Chios, “and in the Alps over all of Liguria” (Materia Medica 2.9.1). However, the “river snail has a foul odor, as does the forest snail that clings on to brambles and shrubs (termed by some sesilos or seselita), and is not good for the stomach and causes vomiting” (Materia Medica 2.9.1). Burnt (i.e., calcined), shells of the snails, are excellent as a tooth powder, and the raw snails ground whole in a mortar can be used as pessaries in the vagina, “to bring down the menses” (Materia Medica 2.9.2), an obvious would-​be contraceptive.

7.  Pontus and Russian Beavers The texts of the Materia Medica mirror actual journeys and sojourns, and Dioscorides repeatedly traveled to the northern coastal fringes of Asia Minor along the Black Sea.

Pharmacology in the Early Roman Empire    527 Pontus appears frequently, with its panoply of useful drug stuffs: Pontic honey from Heraclea was reckoned one of the oddest varieties available (Materia Medica 2.82.4) since the bees making it frequented flowers that made a honey that caused heavy sweating; Pontic licorice ranked as some of the finest known (Materia Medica 3.5.1); a ground pine (Ajuga hamaepitys [L.] Schreber) of Heraclea was an antidote for hemlock poisoning (Materia Medica 3.158.2); and Pontic wormwood had its own peculiarly effective quality (Materia Medica 3.23.1). Fish glue (ichthyokolla) from Pontus presumably was the best, although in this instance, Dioscorides’ account is curiously uninformative, and the Greek reveals little about what fish (the sturgeon), or what part of what fish, might be used to manufacture this water-​tight glue (Materia Medica 3.88; Scarborough 2015), and he likely extracted this short account from a written text (Wellmann 1906–​ 1914, 2.109, apparatus criticus, again adduces Sextius Niger). Dioscorides has not verified details about the sturgeon’s air bladder, similar to the very brief entry on the electric ray (Materia Medica 2.15), which had widespread application, as one reads in the pages of Scribonius Largus (Finger and Piccolino 2011, 46–​47), along with the usual gathering of folk tales by Pliny the Elder. These lapses are in contrast to his careful description of how beaver castor was produced (Materia Medica 2.24). Heraclea, in particular, had one of the few sheltered harbors on the southern shores of the Black Sea, becoming a major trans-​shipping center from early Hellenistic times (Burstein 1976, 4–​6). Herodotus 4.109.2 is one of our earliest testimonials to beavers and otters in Russian rivers (Asheri et al. 2007, 658), and the Hippocratic gynecological works attest beaver castor’s use for female ailments (Totelin 2009, 161–​163). Sostratus ca 30 bce (Zucker 2008) noted that kastoros orchis came from “Scythia” (Scholia on Nicander’s Theriaca, 565a Crugnola), and Dioscorides ventured to Pontus and other regions of coastal northern Asia Minor to verify—​or refute—​the tale of self-​castration by beavers when pursued by hunters. Apparently Sextius Niger had already disproven this mythology about the beaver (so we read in Pliny’s Natural History 32.26, although Pliny accepts the tale as true), and some details about beaver castor are underneath Nicander, Theriaca 565. Beaver castor was an expensive commodity and formed an important part of what a recent scholar called the “Traffic in Glands” (Devecka 2013), so Dioscorides’ search for accurate details on how this substance was produced is very important to him. Significantly, he describes carefully the beaver’s internal anatomy, indicating that Dioscorides has, indeed, found the source of the real stuff (Materia Medica 2.24.2; Beck 2011, 100): In every instance, select orcheis that are connected at one end at the apex—​since it is not possible to find two of the vesicles attached together in a single capsule—​and in which the innards are wax-​like, [have] an odor that is overwhelming, a scent of decay, sharply cutting [to the nose], biting [as would a snake], [and the substance] is friable, often divided by thin membranes in its natural state.

Because of its market value, counterfeiting beaver castor was common, and Dioscorides tersely describes how an unwary shopper might encounter a “fake” castor that would fool the amateur pharmacologist, who probably would not know the “real stuff ” if it

528   Hellenistic Greek Science chanced to be available; the rank smell was the important selling point (Materia Medica 2.24.2; Beck 2011, 100): Some people make a counterfeit castor by dripping liquefied gum ammoniac, or Acacia gum, into the [emptied] vesicle, then kneading this with the blood of the beaver, and then setting it out to dry.

Beaver blood would stink, to be sure, and the consistency of dried Acacia gum would duplicate somewhat the true castor, but Dioscorides lets us know that he agrees with Sextius Niger’s refutation of self-​castrating beavers, and why these stories cannot be true—​and he makes abundantly clear that he has encountered the actual beaver and its parts, perhaps in a drug mart, or in his travels that took him to the shores of the Black Sea (Materia Medica 2.24.2; Beck 2011, 100): Absolutely absurd, however, is the story that the animal rips off its orcheis and pitches them away, when it is hunted, since it is [anatomically] not possible [for the beaver] to reach these organs, situated lying flat [in its body] similar to those found in a hog [or boar]. And having cut out [the orchis] from the animal’s pelt, one ought to take out the honey-​like fluid together with its enfolding capsule, and thereafter dry it and set it out in storage.

Since Sextius Niger’s works are lost to us, except for occasional quotations and fragments, one can reasonably conclude that some two or three decades before Dioscorides, Sextius Niger had also seen and handled the castor sacs of beavers, likely coming across the Black Sea to the Greek-​speaking settlements in the Bosporos and the eastern and northern coasts of Asia Minor. The fable of beavers castrating themselves, since their “testicles” (actually preputial follicles) were so prized, has a deeper counterpart in the lengthy history of castoreum as a medicinal. A modern description of the parts employed echoes the accuracy of Dioscorides, with a rather remarkable set of details (Müller-​Schwarze and Sun 2003, 41): Beavers possess a pair of unique pouchlike structures called castor sacs (Plate 12). They contain the yellowish fluid that is the castoreum. The two castor sacs are located between the kidneys and the urine bladder, opening into the urethra. They are large weighing about 60 gr., which represents about 0.3% of the body weight of an average adult beaver of 19 kg. The European species, Castor fiber, is somewhat smaller than the North American Castor canadensis, described here.

Likewise, the near-​modern employment of Russian castor is strikingly similar to what one meets in the words of Dioscorides (Wood and LaWall 1926, 1246, cols. 1–​2): Castor comes to us in the form of solid unctuous masses, contained in sacs about two inches in length, larger at one end than at the other, much flattened and wrinkled, of a brown or blackish color externally, and united in pairs by the excretory ducts

Pharmacology in the Early Roman Empire    529 which connect them in the living animal. In each pair one sac is generally larger than the other. They are divided internally into numerous cells, containing the castor . . . a variety of Russian castor . . . has a peculiar empyreumatic odor . . . [and] breaks like starch under the teeth.

Castor has been used in hysteria and dysmenorrhea (Todd 1967, 1513, col. 2). Dioscorides (Materia Medica 2.24.1) writes that if one drinks some castor with two drachmai of pennyroyal, this brings on the menses, and expels a fetus, along with the afterbirth (pennyroyal is Mentha pulegium L., a common contraceptive: Scarborough 1989; Riddle 1992, 243; toxic phytochemistry in Hayes et al. 2007, 462–​477). Notably, early 20th-​century dispensatories listed beaver castor as a stimulant antispasmodic and as an emmenagogue, an abortive with a long history, reaching back at least to Hippocratic times, where these “hysterical affections” were ordinarily assumed. Hippocratic pharmacologists, who put together the tracts we know as Diseases of Women and Sterility (or Barrenness) were well aware of beaver castor, both as an additive in wine and as a straightforward contraceptive and fertility drug (a dual function, typical of such substances since ancient Near Eastern cultures: Riddle 2010, 7–​17), applied in a vaginal pessary (Diseases of Women 1.71 and Sterility 221: Littré 1853, 8.150, 428; Potter 2012, 354–​355). Physiological chemistry also suggests why castor was valued for so long: not only have perfumers of all persuasions used it for its dense odor (a prominent constituent is hydrocinnamic acid, especially evident to the nose, when burned in an incense), but it is also rich in salicylic acid and salicylaldehyde, gained from a beaver’s natural diet of willows and related species (genus Salix), the basic ingredients in aspirin. Added are prominent amounts of benzoic acid, benzyl alcohol, borneol, catechol, and various phenols (Müller-​Schwarze and Sun 2003, 42–​43) giving castor a decidedly acidic and “cleansing” nature.

8.  Principles of Organization: Myrrh, Frankincense, and the Sea Urchin In the preface to book 2 of his Materia Medica, Dioscorides explains why most of the medicinals, derived from animals, are grouped with pot herbs and grains, reflecting his first preface to book 1, which discloses the poor organization of previous guides to pharmacology (Scarborough and Nutton 1982). Notable is his summary of the contents of book 1, as well as what book 2 includes and why (Materia Medica 2.pref.; Beck 2011, 94): In the preceding book, my dear Arius, the first of our writings on materia medica, we have given an account of spices, oils, and unguents, and of trees and their saps, [their] tears, and the fruits produced by them. In this second book, we shall recount both animals, honey, milk, animal fat, and the cereals as they are termed, as well as garden herbs, subjoining to them those herbs that are suffused with a pungent property (having a kinship [among] themselves), such as the garlics, onions, and

530   Hellenistic Greek Science mustard; thereby pungency [as a property] shall be grouped together among herbs of the same kind.

Important is the term translated as “tears” (Grk. dakrya), which designates the form in which many of the famous pharmaceuticals of antiquity were transported: hardened globs of resins were packed into bags, to be used as needed, melted down in hot liquids (much as Materia Medica 1.64 and 68 describe the gathering and use of myrrh and frankincense). Often, too, these were the solidified chunks of “drippings” from the barks of conifers and pines, also applied to the “drippings” of exotics, such as frankincense and myrrh, as well as the slowly oozing latex of the opium poppy capsules (Materia Medica 4.64), gathered as latex that hardens, then fashioned into small lozenges for transport (Scarborough [1995] 2010, 6–​12). Myrrh comes from trees in the large and diverse genus Commiphora (Langenheim 2003, 368–​373, with color plate 19), but frankincense comes from Boswellia species (Langenheim 2003, 363–​368, with color plate 42)  and is still gathered in much the same way as described by Dioscorides (Materia Medica 1.68.1): They cut it into small squares and then having put them into earthenware pots, they roll [the pots] around until the pellets become rounded; after a time this kind is termed Syagrios [an Arabian promontory, now Ras Fartak] and they turn golden yellow.

Comparison with a 20th-​ century account describing what then was the Italian Somaliland suggests this age-​old harvest of an oleo-​gum-​resin from a stubborn tree (Howes [1949] 2001, 150; Eichhorn et al. 2011, for suggested modern uses): Tapping is here carried out by scraping away portions of the bark and not by making ‘incisions’ only in the tree. A special tool (termed “mengaff ”) is used. This is said to resemble a double scalpel, one end having a sharp end, used for the decortication, and the other end being blunt and used in assisting to remove the resin when it is hardened.

“Pungent properties” is my translation (Beck 2011, 94, prefers “sharp properties”), since Dioscorides has attempted to unite smell and taste into a definition of how drugs were perceived, gathered, used, and stored. He knows Theophrastus’ theories about sense perceptions (Scarborough [2005] 2011, xvi–​xvii), and he has bluntly rejected the then-​popular pseudo-​philosophic concepts loosely labeled a kind of debased atom­ism (Materia Medica pref.2; Scarborough and Nutton 1982, 206–​208), presumably descended from the teachings of Asclepiades of Bithynia (fl. in Rome after 120 bce: Scarborough 2008a, but see Vallance 1990 and 1993, who denies any links with the pre-​Socratics Democritus and Leucippus, or even with Epicurus). Dioscorides’ “sense perceptions” extend to touch, as he groups some two dozen narcotics, analgesics, and poisons, as “cooling” or cold (Materia Medica 4.63–​85, corn poppy through pellitory). First, however, are the “pungent” foods and drugs, beginning with the sea urchin (Materia Medica 2.1; Beck 2011, 92):

Pharmacology in the Early Roman Empire    531 A sea urchin is good for the stomach, eases the bowels, and is a diuretic. Its raw shell is [made more] beneficial, when compounded with unguent soaps, and is beneficial in treatment of mange [and itchy rashes]; and reduced to ash (viz. “calcined”), the shell cleans greasy wounds and shrinks growths of fungus-​like flesh.

Echinus lividus is likely the species here, but Thompson (1947, 72) notes that there are at least five kinds of sea urchin eaten in the Mediterranean. Gastronomic references are fairly common (Dalby 1996, 74–​75, 123), and in the Greek and Hellenistic cookbooks, sea urchins are delicacies, depending on local tastes: the fragments of Archestratus of Gela (ca 350 bce; Olsen and Sens 2000, 345) suggest a complex tradition for the preparation of these oddly shaped sea creatures. Wellmann, app. crit. indicates parallel passages in Pliny’s Natural History, book 32, and in Athenaeus, Deipnosophistae 3.91a, quoting from the lost works on medical dietetics by Diphilus of Siphnos (ca 300 bce: Manetti 2008; cf. Nutton 1995, 36, 368), whose works on edible (and otherwise) fish gained some popularity. Galen, Simples 11.32 (Kühn 12.355) is a confused version (the urchin is both a land and marine creature), but he quotes the preparation techniques as given by Dioscorides. Sources for the consumption and medicinal preparation of sea urchins emerged in the early Hellenistic centuries, and Dioscorides knows these traditions, but he does not uncritically accept them. The ash of the sea urchin retained its medical importance until the turn of the 18th century (Théodoridès 1980, 738–​739). Throughout the Materia Medica, Dioscorides follows a fairly consistent template: first comes the chosen name (or names) for the plant or animal or mineral, and the drug or food derived from it. Second, there are occasional—​if brief—​taxonomic and morphological descriptions, generally confined to botanical specifications (implied frequently are his assumptions that “anyone would know this,” that is, a beaver is a beaver, a crocodile is immediately recognized as such, frankincense can only be frankincense, etc.). Then he provides geographic or topographical variations, if he deems them “regional” (many entries lack this designation, thus common to many areas). Fourth are the “properties” (almost always dynameis), and his reports of what the drugs “do” (Riddle [1985] 2011; labeled a “drug affinity system”), as they are administered for various ailments: for example, sweating, increased urination, diarrhea, excessive menstruation in women (cf. numerous pharmaka judged to be contraceptive or abortive), reddened skin, vomiting, and so on; but Roman therapeutics viewed these modern “side effects” as often beneficial pharmaceutical actions. Sometimes, Dioscorides reverses the tabulation of “side effects” to a second phase of description, but if read carefully, one can detect a four-​stage organization, often obscured through a conglomeration of observations on plant parts, geographic distinctions among similar species, or “what is said” about the remedy (these are, again, almost always, specifics not verified by Dioscorides himself). In his preface to book 4, he merely summarizes what has been considered in books 1–​ 3, and takes up minerals in book 5, juxtaposing these mining and metallurgical details with wines and wine additives, this last a rather fascinating account of substances used to make wine more palatable in these long centuries before Pasteur discovered the organisms that produce the alcoholic properties: too often the wines were sour, and

532   Hellenistic Greek Science since this was a common problem, there are many recipes containing vinegar. Dosages engender rather significant warnings in a number of passages set down by Dioscorides (Luccioni 2002), a primary concern in the consideration of narcotics and poisons.

9.  Narcotics and Poisons: Uses and Cautions 9.1 Hemlock Of all the poisons known to our Greek and Roman predecessors, hemlock (Conium maculatum L.) is the most notorious. Ill-​famed from its quaffing by Socrates in 399 bce (Sullivan 2001), hemlock was used to put Phocion to death in 318 bce (Plutarch, Phocion 36.2; Romm 2011, 225), and there are several references in Greek and Roman sources on capital punishment by means of hemlock (Gossen 1956). Theophrastus, Enquiry into Plants 9.16.8–​9 provides an account of the preparation and effects of hemlock (Scarborough [1978] 2010, 378–​379; 2006, 20–​22), and the texts reveal a clear understanding by 300 bce of the pharmacological technology necessary to produce the poison. It is Dioscorides, however, who informs us (Materia Medica 4.78) of why and how hemlock could be employed for other uses than execution:  even though this is one of those plants that are deadly, “putting one to death by making the whole body very cold,” hemlock’s sap is gathered (chylizetai) before the plant’s seeds have become brittle, and the juice is pressed from cuttings from the top-​most of the plant, and dried in the sun. Then—​presumably heated to melt into compound ointments—​this sap is employed externally on the skin “restorative to healthy states of those limbs affected by shingles, or erysipelas, when mixed with salves that are pain-​killing, prepared as plasters.” The transdermal recommendation is sensible: some of the active constituents in hemlock’s sap, especially coniine and caffeic acid, are potent antibacterial and antifungal agents (Harborne 1999, 278, no. 1020, and 521, no. 1961) effective against the cutaneous inflammations caused by β-​hemolytic streptococci. Next, Dioscorides relates how this ointment (or salve or plaster) promotes the physical fashions and fads of the 1st century in the eastern Roman Empire (Materia Medica 4.78.2; Beck 2011, 285): The whole herb, when ground up and applied as a plaster on a man’s testicles, prevents ejaculation during his sleep; a plaster applied to [a woman’s] genitalia, causes her milk to cease, and prevents unwedded girls’ breasts from growing too large, and [as a plaster] this causes a young boy’s testicles to wither away.

Tellingly, the “most powerful” of the hemlocks are native not only to his home province of Cilicia but also to Attica, Megara, and Crete. One would never know, otherwise, that small breasts were fashionable in the 1st century, or that masturbation was frowned upon, or that one of the presumably effective manners in “making eunuchs”

Pharmacology in the Early Roman Empire    533 was a plaster of hemlock leaves, stems, and seeds. Medicine suffers from its own fads and fashions, much as is true for what is considered “ideal” in physical appearances, both male and female (König 2005), also illustrated by Cornelius Celsus’ circumcision reversal surgery (De medicina 7.25; Rubin 1980).

9.2 Thornapple, Crateuas, and Mithridates VI If Dioscorides’ hemlock is culture-​and time-​bound, there is little doubt that thornapple (Materia Medica 4.73–​74:  two kinds, stryknon manikon and doryknion, both Datura stramonium L.; Scarborough 2012b) had widespread use and application, sometimes with deleterious results. Thornapple was used to obtain a “high,” if consumed moderately (Materia Medica 4.73.2; Beck 2011, 281): The root has a property (dynamis) that engenders not unpleasant mental images when one drinks a drachma [by weight] of it with wine, but if two drachmai [by weight] are quaffed, they cause one to lose his wits for as long as three days; if four drachmai [by weight] are drunk, they kill.

Here, the difference between a beneficial draught and one that causes death, is simple quantity:  one drachma brings on pleasant visions, not unlike what someone today will experience with marijuana, but four times that amount is fatal. It is patent that Dioscorides has read reports of thornapple in his written texts, as when he notes that Crateuas calls the prickly seed pods and the drug derived from them halikakkabon (Materia Medica 4.74), as contrasted to the standard name “doryknion” chosen for the Materia Medica. Even so, Dioscorides is reporting doryknion as less predictable than the stryknon manikon, since he closes this entry with his usual qualifications of “it seems” and “some say”: It seems that doryknion is likewise a sleep-​inducer (hypnotikon), and if too much is ingested it kills. And some say that its seed is taken [as an ingredient] in aphrodisiacs (philtra).

By placing doryknion immediately after his—​much more precise—​entry on stryknon manikon, Dioscorides is acknowledging the “two kinds,” but the second he knows basically from hearsay and a written text. Crateuas (ca 100–​60 bce) was famously a physician and pharmacologist in service to Mithridates VI of Pontus (Jacques 2008; Mayor 2010, 101–​102; Scarborough 2012a), whose career was marked by frequent war against the Romans, and who—​as legend has it—​was finally cornered in the Greek-​speaking coast of what is now the Crimea, had to be run through with a sword in 63 bce, since he could not commit suicide with poisons, so effective had been his continuous self-​medications of toxic substances building what today is termed an acquired immunity (Mayor 2010, 417–​418, n.  1). In the haul of booty, carried back to Rome (so Pliny Natural History

534   Hellenistic Greek Science 25.3.5–​8) was Mithridates’ library: Lenaeus, a freedman of Pompey, duly translated the books on medical botany into Latin. Dioscorides, of course, knows Crateuas’ works, first-​hand, but does not necessarily accept the wonder-​tales, and chastises him for omitting a number of useful roots (MM. pref.1; Scarborough and Nutton 1982, 195, 204). Thornapple contains goodly quantities of atropine and scopolamine (hysocine), thus verifying the narcotic effects, described by Dioscorides (Scarborough 2012b, 254).

9.3 Henbane, Opium, and Mandrake: Poisons as Analgesics and Anesthetics At Materia Medica 4.68.3, after noting that there are “three kinds” of henbane (Grk. hyoskyamos: one of some 30 species in the genus Hyoscyamus, here probably H. muticus L. or H. niger L.), Dioscorides tells us that the “third kind” is very useful as an analgesic, much better—​that is, more reliable—​than the latex of the opium poppy. Henbane is dangerous (esp. the so-​called black henbane, Hyoscyamus niger L.), since the seeds engender states of delirium (maniodeis: Materia Medica 4.68.1) and deep stupor, thus being “useless” for medicinal purposes. And in spite of Dioscorides’ recommendation of his “third kind” of henbane, no species lacks the neurotoxins and mind-​bending constituents including the tropane alkaloids scopolamine (hysocine) and hyoscyamine, that even nowadays bring on visions if imbibed as a “dream tea” (Wink and van Wyk 2008, 145). Fifteen of the seeds can kill a child. What Dioscorides’ cautions indicate is henbane’s unpredictable actions, especially if used as a narcotic, so applications are limited to such treatments as analgesic suppositories, plasters that help the pains of gout, and a mouthwash of henbane roots and vinegar for toothaches. And yet henbane’s freshly cut leaves, laid on like a plaster “are the most effective in alleviation of all kinds of pain” (Materia Medica 4.68.4), a use that continues today (Usher 1974, 313, col. 1). This apparent self-​contradiction is explained if one notices that Dioscorides does not commend henbane as a swallowed narcotic but limits its employment to mixing in externally applied plasters, ointments, and salves. There is a recognizable search for a narcotic—​a natural anesthetic—​both reliable and readily controlled in its dosage by the physician-​pharmacologist. To Dioscorides, the opium poppy (Papaver somniferum L.), and related species, was commonly available throughout the Mediterranean littoral of the Roman Empire (no special locales are mentioned), and its history of use goes back at least into ancient Egyptian times, with some evidence of its employment in the Homeric epics, the Hippocratic tracts, and Theophrastus’ Enquiry into Plants (Scarborough [1995] 2010, 4–​ 5). It is, however, in the Materia Medica 4.64 that one gets a uniquely full description of this semi-​disreputable drug, apparently handy if one chose to commit suicide (Pliny, Natural History 20.199–​200). Dioscorides’ fairly lengthy account provides many details about the varieties of the poppy latex, ranging from what are potherbs through strikingly deleterious preparations. First is a short summary of the dietary benefits of poppy

Pharmacology in the Early Roman Empire    535 seeds and the expressed oil, still employed in modern baking as a seasoning (the seeds have no narcotic properties), and Dioscorides says that this is a substitute for sesame seeds, when mixed with honey. Of the “three kinds” of poppy, the third grows wild and is thereby the more potent as a drug (Materia Medica 4.64.1: pharmakodestera). The latex itself (ho opos autos), however, is dangerous, and (Materia Medica 4.64.3), [it] is an analgesic and sleep-​inducer, and promotes digestion, being useful for coughs and intestinal ailments, but if one quaffs too much of the latex, it plunges one into a lethargy while he is asleep, and it kills.

Opium is thus not useful, except in carefully prepared quantities as a sleeping liquid (heated wine into which the opium pellets were dissolved), pill, or lozenge, and Dioscorides’ cautions about its employment have echoes in modern pharmacology (Scarborough [1995] 2010, 10–​17). As far as Roman physicians and pharmacologists were concerned, opium latex had no use as a general anesthetic, and harvesting the latex “while the capsules are still green” suggests gathering techniques still followed today in Afghanistan and elsewhere, limiting the use of the drug to a rather narrow botanical window during its growth. To be sure, morphine (the major alkaloid averaging some 16% by weight), codeine, and the several dozen more alkaloids present in the raw latex engendered physiological effects that soothed the bowels and brought on sleep, but its variable potency led some earlier pharmacologists to argue against its use. Dioscorides Materia Medica 4.64.6 quotes Erasistratus—​quoting Diagoras—​Andreas, and Mnesidemus as previous authorities who did not trust opium, but “these very opinions are wrong, refuted through experience, with the efficacy of the drug being observed in its results.” Diagoras was active perhaps ca 350 bce (Keyser 2008), Erasistratus is usually dated to ca 260 bce (Scarborough 2008c), Andreas died 217 bce (Irby-​Massie 2008), and Mnesidemus was active perhaps ca 200 bce (Deichgräber 1932), a range of dates indicating a debate and wide employment of the opium poppy in medicinal pharmacy going back at least four centuries. Dioscorides does not suggest dosages in his account of the opium poppy, unlike the precision in the description of mandrake (probably Mandragora officinarum L., among six species), beginning with data gained from his folk medical informants (Materia Medica 4.75.7; Beck 2011, 283–​284): Some say that [this kind of mandrake] puts one to sleep when as little as a drachma [by weight] is consumed in a drink, or when eaten in a barley-​cake, or when eaten in [any] prepared food. The individual falls asleep in whatever position he might have been in, when he ate it, and then feels nothing for three or four hours from the time it was given to him. Physicians about to perform surgery or apply the cautery employ it also.

It is, moreover, the rural and agricultural contexts that set these details as portions of long-​held folkloristic knowledge, and Dioscorides is one of the few sources we have from the early Roman Empire who readily acknowledges the depth of learning about

536   Hellenistic Greek Science plants as instilled in those who lived on and from the land. At Materia Medica 4.75.2, he reflects exactly this milieu (Beck 2011, 282): The leaves of the male kind, which is white (some have termed it morion), are smooth, somewhat similar to the leaves of a beet. Its fruit [the “apple”] is twice the size [as the other kind], is yellow-​saffron in color, and has an overpowering odor. Shepherds eat the apples, and are rendered unconscious in a state of stupor. The root of this kind of mandrake is like that of [the other kind] but is larger and whiter. It too is without a stem.

Dioscorides’ “other kind of mandrake” (morion) may well be the Iranian M. turcomanica L., “white mandrake,” sometimes identified with the soma of ancient Iran and India (Wink and van Wyk 2008, 167), but it is his rural farmers and likely rhizotomoi (“root cutters,” prominent in Theophrastus, Enquiry into Plants 9)  who effortlessly control technical details, and since they do, Dioscorides’ account of the drug preparation is clear and precise (Materia Medica 4.75.3; Beck 2011, 282): The bark of a mandrake’s root is collected fresh, by means of chopping it up and putting the pieces in a press [similar to that used for the production of olive oil]. Once collected, juice of the mandrake should be put up in storage in an earthenware pot. Mandrake juice is also extracted from the “apples,” but the juice from them [as contrasted to that from the roots] soon loses its potency. The bark is also peeled from the root, threaded with linen, hung up for later use. Some, however, boil the roots with wine down to a third [of the original volume], then strain it, and put this up into storage; they give one cyathos as a dosage to insomniacs, to those who are suffering from great pain, and those who undergo surgery or the cautery, those whom they wish to be without sensation.

But then comes this warning: When the juice [of mandrake] is quaffed in a quantity of two oboloi [by weight], mixed with hydromel [melikraton], it brings up phlegm and [black] bile, as does hellebore [probably Helleborus niger L.], but when one drinks too much, it drives out his life.

That mandrake juice is a common drug in Roman antiquity that brought on a slumber resembling death is verified fictionally in the famous “Speech of the Doctor” in the Metamorphoses (Golden Ass) 10.9.11–​12, by Apuleius of Madaurus (ca 125–​170 ce), in which the inserted tale of a young man thus medicated comes to a happy ending, when “the father took off the lid of the sarcophagus with his own hands and found his son just shaking off his death-​dealing coma and rising up, back from the realms of the dead” (Hanson 1989, 2.237). Or, as the 7th-​century Latin Alphabet of Galen puts it, “Mandrake is a plant known to everyone,” and the mandrake-​juice press mentioned by Dioscorides perhaps was manufactured specifically to “squeeze it out by a press,” to produce the resultant juice called in Greek mandragorochylon (Everett 2012, 280–​281).

Pharmacology in the Early Roman Empire    537 The implicit and explicit risks, as enunciated by Dioscorides, of mandrake alerted doctors and surgeons to be especially prudent in using it (e.g., Galen, Simples 5.14 = Kühn 11.751). As late as the era of the Crusades, one finds mandrake occasionally employed in surgery (Mitchell 2007, 198–​202), but its use became part of the widespread folklore associated with the “flying of witches” (Duerr 1985, 1–​12; Hansen 1978, 29–​42), even though the so-​called “soporific sponge” had fairly ordinary application in surgery through the 17th century (Juvin and Desmonts 2004). Once Friedrich Wilhelm Sertürner successfully isolated morphine from the latex of the opium poppy (1817), the long search for a reliable anesthetic took on the trappings of a medicinal chemistry, leading eventually to the exact administration of anesthetics in modern surgery. It is customary to remind practitioners of what is now often called “naturopathy” or “phytotherapy” that any natural or “raw” drug, possessing active pharmacological principles, is efficacious because it “depends on an interplay between the constituent groups [of biochemicals] rather than on individual substances” (Wichtl 2004, 631 col. 3). Such an interplay in the mandrake juice involves some powerful phytochemical constituents, including the tropane alkaloids belladonnine, scopolamine (hysocine), and hyoscyamine, along with the coumarins scopoletin and scopolin (Wink and van Wyk 2008, 167; Duke 1985, 295, no. 215). In conclusion, one can cite the painstaking care that Dioscorides exercised with most of his natural products, so that amateurs such as Orion the Groom (Nutton [1985] 1988, 145) might flourish for a day or two with hawked exotics, but good physicians became well acquainted with the Materia Medica, which soon was in wide circulation, sometimes revised into an alphabetical listing (e.g., the famous Vienna Dioscorides, dated to 512 ce), the ancestor of so many of the drug manuals of medieval and Renaissance Europe.

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chapter C15

Dietet i c s Regimen for Life and Health Mark Grant

1. Introduction Any discourse on dietetics raises more questions than can be answered and poses more problems than can be solved. Even today some dieticians recommend one group of foodstuffs, others another group, the gamut of sensible nutrition ranging from high protein to the modern Mediterranean diet to Far Eastern cuisine. Woody Allen neatly encapsulated this debate in his film Sleeper. Waking up in the future after cryogenic suspension, the protagonist learns that, contrary to what doctors in the 20th century erroneously believed, the ideal diet is eating cream cakes. If controversy therefore surrounds contemporary thinking, how much more difficult it is to ascertain what constituted dietetics in the ancient world? For a start, the sources are fragmentary, Hippocrates and Galen overwhelming much of the earlier evidence. Anything deemed opposed to Galen tended to fade from the manuscript tradition. Then there is the vexed issue of interpretation, some foodstuffs having changed through agricultural selection and breeding, other foodstuffs being of uncertain identification. Finally, the context in which ancient dietetics was debated may be impossible to recreate. Food historians place themselves along this spectrum:  Wilkins and Hill (1996, 2–​3) seem almost to deny the authenticity of any attempt to recreate the dishes of Greece and Rome, arguing that the unfamiliarity of flavors militates against appreciating the latent subtleties of flavor and texture. In a similar vein, when discussing pancakes as recorded in a passage by Galen, Powell (2003, 165) wonders if “in the absence of any binding agent like oil or honey . . . the result was merely a disintegrating mess.” By contrast Grocock and Grainger (2006, 77–​83) feel that, by employing charcoal fires, replicating ancient equipment and researching assiduously the identification of plants, a window is opened for as near authentic a view of classical food and dietetics as is possible.

544   Hellenistic Greek Science Amidst these arguments, perhaps an analogy can be made with music. An audience can enjoy a performance on modern instruments of an opera by Mozart. Original instruments can bring the sound ever closer to what the composer may have envisaged. Yet an audience at the time of Mozart would have remained neither silent nor still, whilst the whiff of unwashed bodies, stale clothes, and guttering candles would jar on modern sensibilities. Just as with an opera performance, a discussion of ancient dietetics must be sensitive to what can be known and what must be placed in the realm of conjecture.

2.  Writers on Diet It is a truism to state that Homer was central to ancient Greek literary culture. Any discussion of regimen for life and health ought therefore to start with the Homeric poems. When setting off on his journey to Pylos and Sparta, Telemachus takes on board his ship barley (Homer, Odyssey 2.289). Meat was ubiquitous at meals, whether roasted over a fire on the sea shore or served at a feast in a banquet hall. Onions, honey, and goat cheese, too, might feature in special dishes (Homer, Iliad 11.618–​643). But it was wine that served to restore health, lend strength, and aid social interaction (Papakonstantinou 2009, 5, 12). Later medical writers often quoted Homer, sometimes to display their sophisticated learning and sometimes to support their thesis, for example, Galen when discussing the culinary use of animal blood (Powell 2003, 131). Medicine was not always viewed with high esteem, its efficacy often being haphazard (Jouanna-​Bouchet 2009, 734–​735), and so such literary flourishes perhaps gave it a more burnished aura. Jouanna-​Bouchet (2009, 740–​741) even sees in the structure of the medical ingredients listed by the 4th-​ century ce medical writer Marcellus Empiricus a reference to Virgil and the description of the shield of Aeneas the pharmacopoeia of the physician being akin to the armor of the gods. Sometimes it seems as if the doctor were at the side of a patient more as a psychological support than an active practitioner (Flemming 2000, 68), although such a relationship almost certainly would have promoted well-​being and healing. Practicing perhaps on the Aegean island of Kos in the late 5th century bce, Hippocrates recorded his observations about diet and nutrition in such an authoritative style that his works became central to medicine in the ancient world. There may have been medical works written before this time, but they do not survive and the evidence is especially sketchy (Flemming 2000, 83). To the hand of Hippocrates are attributed many of the surviving treatises from this period, his name alone being sufficient to ensure that the texts continued to be copied, although the wide variety in style indicates multiple authorships. Indeed, in that period doctors did not have a standard vocabulary with which to discuss their ideas (Craik 1998, 12–​13). Over 500 years later, doctors were still wrestling with the possibility of a standard nomenclature, niceties of philology and dialect often obstructing objective scientific research (Grant 2000a, 121). Focusing on regimen and its concomitant vocabulary, it might be expected that Galen should mine extensively the Hippocratic work On Diet,

Dietetics: Regimen for Life and Health    545 but he “ne fait de cette œuvre que quelques rares citations” (only makes a few rare citations from this work; Joly 1984, 79), and what he does quote is generally found in On the Properties of Foodstuffs. For Galen to pass over Hippocrates suggests he did not always agree with his predecessor, yet in his reverence he cannot bring himself to criticize openly, since one of the key arguments he employs against rival physicians is to highlight when they stray from Hippocratic tradition. That Galen so meticulously presented what he vigorously believed to be the sum of medical knowledge often meant that other authors were no longer copied (Walzer and Frede 1995, xiii). Thus perhaps this hesitation over quoting from the Hippocratic work On Diet is due less to carelessness and had more to do with promoting slightly different views. Just as it is notoriously difficult to judge which medical works belong to Hippocrates, so too is ascertaining the correct authorship of cook books. Parker (2012, 365) suggests that is not so much whether the author of a cook book created the dish in question, but rather whether the author is accorded, when sourcing recipes, a status commensurate with a great name. Such a name is Marcus Gavius Apicius. About this person Grocock and Grainger (2006, 54–​58) make some sensible suggestions:  he was the archetypal gourmand during the reign of Tiberius in the 1st century ce, he held luxurious banquets, and he influenced the eating habits of the aristocracy. Connected with his name was the cook book that survives from the later Roman Empire, for after him any gourmet who collected recipes might describe himself as an Apicius (Grocock and Grainger 2006, 35–​ 36). The style of cooking delineated in Apicius survived into the medieval world, the fine juxtaposition of numerous seasonings and the characteristic balance between sweet and sour, and its echo can be noticed still in the traditional agrodolce sauces of Italian cuisine. A key ingredient in many of the sauces in Apicius is defrutum. This was made by reducing must, into which a fruit flavoring such as quince or fig had been added, to a rich thickness (Grocock and Grainger 2006, 345–​346). Besides defrutum there was a repertory of similar flavorings: caroenum, which was almost certainly a cooked wine syrup; passum, a raisin wine; and sapa, a reduced must without fruit flavoring. Alongside wine as a significant feature of the ancient cooking and diet was water (Dalby 2003a, 346).

3.  Diet and Ingredients Hippocrates delineated the properties he imagined waters from different localities possessed, and the purity was to be judged by consistency, taste, smell, and color. During testing there should be no hint of sweetness, saltiness, bitterness, or odor. His views were upheld by later writers; Galen (Grant 2000b, 63) somewhat tetchily stressing he would not brook any opposition to the declaration that good water is plainly cold and moist. Asked by Augustus how he had managed to reach old age, Pollio Romilius attributed his longevity to the application of olive oil to his outside and reduced wine to his inside (Pliny, 22.114). What this centenarian omitted was the bathing that would have taken place before the rubbing of olive oil.

546   Hellenistic Greek Science When serving under the Emperor Trajan as the curator of Rome’s aqueducts, Frontinus employed a tripartite classification of the use of water: its use for drinking and recreation, its employment as a defense against fire, and its contribution toward public health (Vannesse 2012, 469–​471). Interestingly, the dedicatory inscriptions for Roman aqueducts in general rarely mention public health but rather record usefulness as their key purpose, namely for public fountains and baths. Washing the body thus had as much to do with a salutary regimen for life and health as eating the right foods. To attend the baths was also to engage in exercise, whether a vigorous wrestling match or a gentle game of ball. Exercise was therefore a further component in the regimen, as were sleep, massage, pharmacology, and sexual activity (Flemming 2000, 111). Petronius is probably joking about this relationship when he describes Trimalchio playing a game with a group of long-​haired boys, the greenish color of the balls hinting at the humors (Grant 2004, 244–​245). The therapeutic method known as the diatritus affords an example of how regimen employed most forms of available therapy, including phlebotomy but excluding physical exercise; the main goal of the physician is to keep the patient away from food until the third day after the onset of symptoms (Leith 2008). Galen recounts his observations of a teacher called Protus (Grant 2000a, 127): a sustained pattern of bathing, walking, eating a balanced diet, and drinking a moderate amount of water and wine furnished his bowels with a regular movement. As Flemming (2000, 64) concludes, medicine may be about health, but health is not necessarily about medicine. Whatever the effect of Galen and his views on the transmission of earlier writers, the record between the 5th century bce and the 2nd century ce of authors on diet and cooking is especially fragmentary. In the main, the excerpts that do exist are quoted by Athenaeus in The Partying Professors and Oribasius in Medical Compilations (Dalby 1996, 161–​162). Among the more prominent of these writers can be placed Diocles of Carystus, who compiled a manual in the 4th century bce on a regimen for travelers (Dalby 2003a, 118); Mnesitheus of Athens, who in the 4th century bce wrote authoritatively enough about foods to be cited by Galen (Dalby 2003a, 220–​221); Diphilus of Siphnos, who wrote about foods around 300 bce while serving as the physician to King Lysimachus of Thrace (Dalby 2003a, 119–​120); and Phylotimus, who wrote about food and diet in the 3rd century bce (Dalby 2003a, 259). Of the poetry of Archestratus, written in Sicily in the early 4th century bce, sufficient fragments remain to create a detailed picture of cooking in the Mediterranean Greek world (Wilkins and Hill 1994). The fragments are notable for emphasizing fresh ingredients and simple recipes; for example, a fish with tender flesh needs only brushing with olive oil and a sprinkling of salt to bring out the delightfulness of its flavor (Wilkins and Hill 1994, 74). In the same period, the Roman expansion around the Mediterranean world brought these ideas about food and diet into conflict with the political connotations of fine private banquets (Zanda 2011, 51–​53). In effect food was being used as a bribe for support in the Senate and the popular assemblies. Whilst personal health was not necessarily being adversely affected by such dining, fair competition within the senatorial class was perceived as being undermined, so the sumptuary laws that were enacted may be seen as

Dietetics: Regimen for Life and Health    547 a moral regimen for life and health, the lex Orchia of 182 bce being regarded the first to focus on this area of luxury.

4.  Theories of Diet Trying to legislate what constituted luxurious food—​the changing gamut of rare, exotic, or complex dishes and their ingredients—​was one matter (Zanda 2011, 56). What went on in the body when food had been eaten was another matter and throughout antiquity continued to provoke fierce debate. Celsus (On Medicine, Prooemium, 20) set out the four main views that held sway up to the 1st century ce regarding digestion: Hippocrates thought it was concoction, Plistonicus putrefaction, Erasistratus grinding, and Asclepiades distribution. Galen amalgamated the first two of these theories, arguing that what normally happened was concoction, but that when illness interfered it was putrefaction. These differing theories draw attention to the distinct schools of medicine that existed in the ancient world, ranging from the Empiricists and Rationalists to Methodists and Pneumatists, about which Flemming (2000, 84–​90) provides a neat summary. In his On Medical Experience, which mainly survives in a mediaeval Arabic translation, Galen mocks what he regards as unreasonable assertions about the nature of digestion, observation through experience offering the definitive answer (Walzer and Frede 1985, 65). Drawing on his modern medical expertise, Powell (2003, 13–​18) affords a succinct and detailed discussion of Galen’s theories about digestion, a process that was “a tribute to both his logic and his imagination.” In later antiquity the idea of distribution became increasingly dominant; the actual physical process of digestion being regarded as obscure, but the flow of vital juices from whatever was ingested being readily apparent (Langslow and Maire 2010). By the 6th century ce, the digestive system was regarded as simply working like a stove. Provided that foods were eaten that suited the body, good digestion would ensue, but if unsuitable foods were attempted, indigestible fluids would be produced (Grant 1996, 41). Like a cook tending a stove, everyone was advised to maintain the heat in their stomach (Galen, Natural Faculties 2.4, Kühn 2.89). Thus too many cold drinks were to be avoided lest that heat should be diminished. As with fuel that when burning badly emits a lot of smoke, so a weak heat in the stomach might leave poisonous vapors to rise to the head. Galen (Simple Medicines 2.13, Kühn 11.491) also held that in people who had difficulty in digesting milk, the liquid gave off a greasy smoke in the stomach. Underpinning these outward aspects of regimen in drink, food, and exercise was an inward system of balance between the qualities. Constituting the primary qualities were heat, cold, dryness, and moistness, while density, rarity, lightness, heaviness, hardness, and fragility were among the secondary qualities (Siegel 1968, 146). To each of the four elements of earth, fire, air, and water at least two primary qualities were envisaged as providing their particular features, for example, fire was hot and dry, and water cold and moist. In the body from birth were the four humors: black bile, phlegm, yellow bile, and

548   Hellenistic Greek Science blood. These humors had also to be kept in balance. Considered to be excreted by the liver, black bile was sour and effervesced, its consistency of dark olive oil being too viscous to pass from the body by evaporation. As a result it could become lodged in crevices around the body, its effect being cancer, ulceration of the bowels, black pustules on the skin, and hemorrhoids. If it was noticed in vomit or excrement, the prognosis following this extreme cooking of the blood was nothing less than death. Produced in the stomach and mouth, phlegm could be seen in nasal mucus and in catarrh. Pale and flavorless in its raw state, it could absorb saltiness, bitterness, or sourness. It could arise from particular foods entering the initial stages of digestion in the stomach. What colored urine was yellow bile. The bitterness of vomit was also ascribed to this humor. Unlike the other three humors, blood could coagulate to form a clot. The best blood was held to be thick and red, but there was nothing untoward if it possessed a yellowy or dark tinge. It was the vehicle for water and nutrients to be carried around the body. In the absence of any chemical testing, physicians used their own sensory perceptions to analyze excretions—​ good blood tasted sweet and diseased blood was salty or bitter. Some caution, however, must to be taken regarding the seeming neatness of this system. Its many anomalies in ancient authors can be ascribed to medical uncertainty or perhaps just to the realization that the body is an especially complex system, the exact equivalence of four humors with four temperaments being a later development (Mattern 2013, 54). A disturbance in the balance of the humors, either through excess or deficiency, or an increase in the ratio of one or more of the qualities, led to disease. As Galen wrote in his treatise On the Causes of Disease (Kühn 7.1–​41; Grant 2000a, 53): Obviously the causes of composite illnesses are inevitably composite. So if, for example, a hot cause and a dry cause run concurrently, the illness will necessarily be hot and dry; and if the causes are hot and moist, the illnesses will be hot and moist. The same is true for the other two combinations, namely moist and cold, and dry and cold.

This emphasis on the qualities, rather than the humors, seems to have been characteristic of Galen when discussing disease (Mattern 2013, 233). In this respect, it would be fascinating to know whether male and female doctors took the same view of the humors and qualities. While the evidence might be fragmentary, what is particularly exciting is the growing realization that women were involved in medicine. Antiochis of Tlos in Lycia (Parker 2012, 373–​374) was probably appointed by the local council as the official doctor and her status allowed her to set up a statue in commemoration of her profession. When assessing the temperament of a patient, age and sex had to be taken into account (Grant 1996, 40). Children were believed to be more sanguine, old people, phlegmatic. Women were held to be cooler, men to be hotter. Personality, race, and climate could affect the balance. Yet temperament did not stay static but rather changed throughout one’s lifetime. Galen records treating his most eminent patient Marcus Aurelius (Prognosis 11.1–​9, Kühn 14.658–​660). After an especially magnificent banquet, the emperor had

Dietetics: Regimen for Life and Health    549 contracted a fever. He assumed that his stomach had become so overloaded that, having lost its heat, it had converted the ingested food into phlegm. After checking the invalid, Galen concurred with the diagnosis, and he duly prescribed pepper and Sabine wine, the former being heating, the latter drying. This case neatly illustrates how dietary regimen worked in practice.

5.  Diets in Practice Whatever the theories about the humors, it is generally held that very many people in the ancient world lived at subsistence level, their dietary needs dictated by whatever foodstuffs were available rather than what was good for them. Living close to the sea was an advantage when supplementing the diet. Use of the land and rivers required payment, whether for renting or for taxes, but fishing in the sea seems to have been free (Nielsen and Nielsen 1998, 18). Less free were the fears of those Romans who had to go fishing, while storms and wrecks overshadowed the Mediterranean (Faas 2003, 323); although for the Greeks, fish were a highly symbolic and highly valued part of the diet (Dalby 1996, 66). Whatever the chances of improving the diet, the overall evidence suggests that most of the ancient world suffered a moderate degree of chronic malnutrition (Sallares 2002, 140). This would have afforded some protection against malaria, shortages of vitamins and iron being inimical to parasites (Sallares 2002, 142), but conversely it might have increased the risk of tuberculosis, a richer diet perhaps providing resistance against this disease. Eating according to the accepted views about regimen in diet and health was understandably mostly for those who could afford to be particular about their food intake. Porphyry, writing in the 3rd century ce, apologized that vegetarianism was only suitable for philosophers who did not have to engage in heavy manual labor (Grimm 1996, 59). While many ancients suffered from malnutrition, in contrast was forced feeding as practiced by athletes in training for spectacles such as the Olympic Games. In connection with such sporting events, dietitians might recommend various types of regimens, from one based around meat and unleavened bread to another built on sexual restraint and plenty of sleep (Corvoisier, Didier, and Valdher 2001, 160–​161). Galen mentions how the gladiators of Pergamum ate beans and pearl barley to strengthen their bodies for the arena (Grant 2000a, 98). Athletic diets were viewed as especially rich in nutrition; trainers had such talent in building up the bodies of their protégés, they were regarded as holding a skill parallel to that of physicians (Grimm 1996, 46). Fasting and purging could be employed as part of a regimen during the treatment of madness (Pigeaud 1987, 195). To classify madness proved problematic for ancient physicians; the Greek term mania encompassed all sorts of clinical manifestations of mental disorder. While Galen focused primarily on the physical causes of madness through an imbalance of the humors, he hinted at earlier beliefs about its origins lying in divine providence (Black Bile sec. 7, Kühn 5.132). It may be that this religious aspect

550   Hellenistic Greek Science was so prevalent among every class in society that people were generally wary of seeking medical advice. Dividing madness into the type accompanied by fever and the type free from fever might assist prognosis, but did not necessarily hasten a cure. Phrenitis was the name given to feverish madness, its primary cause an excess of yellow bile, this humor being by nature hot, but excessive blood was also held to blame. Mania and melancholia were the labels for madness without a fever: the former triggered by excessive yellow bile and the latter by black bile. Food engendered black bile, melancholic vapor rising from the stomach to affect the brain. Hemp seeds were considered to be among the foodstuffs that created this vapor. A favorite Roman dish of lentils with bacon similarly increased the production of thick blood and black bile. The regimen a physician might prescribe to help a patient suffering from madness could begin gently, employing perhaps the soporific powers of poppy seeds (Galen, Powers of Foodstuffs 1.31, Kühn 6.548), the watery coolness of large gourds (Galen, Powers of Foodstuffs 2.3.2, Kühn 6.561), the soothing nature of lettuce (Galen, Powers of Foodstuffs 2.40.7, Kühn 6.627), or the deadening effects of withholding meals over a long period of time (Hippocrates, Nature of Man 9, Littré 6.56). If this gentle regimen was ineffective, recourse could be made to drugs, from the narcotic effects of hellebore to the violent purging of scammony or Syrian bindweed (Convolvulus scammonia L.). Venesection could be employed alongside foods and drugs; one-​and-​a-​half liters to be drawn until the patient fainted (Galen, Therapy by Venesection sec. 12, Kühn 11.288–​291). This may be why Galen refers uncharacteristically to the divine causes of madness. Unable to cure patients, physicians could blame divine causes, while restricted nutrition, loss of blood, and drugged daze would at least silence any potentially embarrassing members of a family able to afford such treatment (Grant 2000b, 69–​70). In the late Roman Empire, fasting might be used not to combat mental disturbances but spiritual assaults on the soul, a rather different regimen for life and health. In Judaism the dietary rules are set out very clearly, whereas in classical religion it was not thought the gods were concerned about how people ate. The early Christians may have struggled with the void left by the abandonment of this Jewish heritage, and there were no other clear guidelines in the world around them to take its place. Taken to its most extreme, as prescribed by Jerome in the late 4th century ce, fasting would have had serious consequences, for example, extreme weight loss and absence of sexual interest. Grimm (1996, 170) suggests that this sort of regimen, which also involved obsessing about bodily appearance and fear of eating, would have led to nothing other than anorexia. To ensure civilized deportment at a meal, table manners were taught to children, and conviviality played an important role in the good digestion and enjoyment of food (Nielsen and Nielsen 1998, 37–​39). Although, whatever the family arrangements, how and when to dine was the prerogative of the male head of the household, whether to entertain guests, eat alone, or respond to an invitation (Nielsen and Nielsen 1998, 51). The food served at a meal could contain some health benefits, cook books sometimes highlighted recipes that aided the digestion or even combatted chills (Grocock and Grainger 2006, 59–​60).

Dietetics: Regimen for Life and Health    551

6. Conclusion Cookery and regimens for health continued to adjust to new customs and ways of living. In the 3rd century ce, Quintus Gargilius Martialis made a compendium of remedies derived from vegetables and fruits, drawing partly on Galen and Dioscorides, but primarily on Pliny the Elder’s Natural History (Maire 2007, xxvii). The entries are detailed, focusing on the numerous afflictions and diseases that each item could supposedly assuage, yet in their practicality any underpinning theory is generally absent. At the most there is, from time to time, reference to heating or cooling properties. Either it is assumed the reader knows about dietetic theory or such musing is beyond what a blunt Roman officer like the author felt was necessary, if, indeed, he is one and same with the man whose name is on the tombstone from Auzia in Mauretania Caesariensis. Sometime after 511 ce, an exiled Greek doctor called Anthimus wrote a treatise on diet addressed to King Theuderic of the Franks. Just as there were regional differences in cooking during the Roman Empire (Dalby 1996, 179–​180), so with the influx of new peoples into the Mediterranean world as the Roman Empire fell apart other styles of cooking became prevalent. In his short work, Anthimus highlights both continuity and change: butter alongside olive oil, the disappearance of pine nuts, the survival of reduced wine preparations, the employment of spices contrasted with the use of a simple sauce of salt and olive oil (Grant 1996, 28–​29). The system of the humors and qualities hardly features, the focus being on the digestive system as a sort of stove, the stomach when hot promoting the digestion but when cold creating noxious vapors (Grant 1996, 41–​42). Dalby (2003b) outlines the survival of the classical tradition in the Byzantine Empire, reporting on the introduction of new flavors such as cinnamon and aubergine (eggplant), while noting that the study of this period is relatively still in its infancy. It is suggested that in Constantinople those who had the necessary means paid attention to their temperament and adjusted their diet according to the good or bad effect that food might have on the balance of their humors (Dalby 2003b, 47–​48). The longevity of this system is testimony to the persuasiveness of ancient science.

Bibliography Brock, A. J. Greek Medicine. London, Toronto: J. M. Dent, 1929. Corvisier, J-​N., Didier, C. and Valdher, M., ed. Thérapies, Médecine et Démographie Antiques. Paris: Artois Presses Université, 2001. Craik, E M. Hippocrates: Places In Man, edited and translated with introduction and commentary. Oxford: Clarendon Press, 1998. Dalby, A. Siren Feasts:  A History of Food and Gastronomy in Greece. London, New  York: Routledge, 1996. —​—​—​. Food in the Ancient World from A to Z. London, New York: Routledge, 2003a. —​—​—​. Flavours of Byzantium. Totnes: Prospect, 2003b.

552   Hellenistic Greek Science Faas, P. Around the Roman Table, trans. Shaun Whiteside. Basingstoke, Oxford: Macmillan, 2003. Flemming, R. Medicine and the Making of Roman Women: Gender, Nature and Authority from Celsus to Galen. Oxford: Oxford University Press, 2000. Grant, M., ed and trans. Anthimus On the Observance of Foods. Totnes: Prospect, 1996. —​—​—​. Dieting for an Emperor: A Translation with Commentary of Books 1 and 4 of Oribasius’ Medical Compilations. Leiden: Brill, 1997. —​—​—​. Galen on Food and Diet. London, New York: Routledge, 2000a. —​—​—​. “Dietetic Responses in Galen to Madness.” The Classical Bulletin 76 (2000b): 61–​72. —​—​—​. “Colourful Characters:  A Note on the Use of Colour in Petronius.” Hermes 132 (2004): 244–​247. —​—​—​. Roman Cookery: Ancient Recipes for Modern Kitchens. 2nd ed. London: Serif, 2008. Grimm, V. E. From Feasting to Fasting, the Evolution of a Sin: Attitudes to Food in Late Antiquity. London, New York: Routledge, 1996. Grocock, C. and Grainger, S. Apicius: A Critical Edition with an Introduction and an English Translation of the Latin Recipe Text Apicius. Totnes: Prospect, 2006. Hankinson, R. J., ed. The Cambridge Companion to Galen. Cambridge: Cambridge University Press, 2007. Joly, R. Hippocrates De Diaeta. Edition, Translation and Commentary. Corpus Medicorum Graecorum I.2.4. Berlin: Akademie-​Verlag, 1984. Jouanna-​Bouchet, J. “Composition littéraire et composition médicale: un exemple remarquable dans la littérature médicale latine: Marcellus Empiricus.” Latomus 68 (2009): 720–​741. Langslow. D. and Maire, B., edS. Body, Disease and Treatment in a Changing World: Latin Texts and Contexts in Ancient and Medieval Medicine. Lausanne: Éditions BHMS, 2010. Leith, D. “The Diatritus and Therapy in Graeco-​Roman Medicine.” Classical Quarterly 58 (2008): 581–​600. Maire, B. Se soigner par les plantes: Les “Remèdes” de Gargile Martial. Lausanne: Éditions BHMS, 2007. Mattern, S. P. The Prince of Medicine: Galen in the Roman Empire. Oxford: Oxford University Press, 2013. Nielsen, I. and Nielsen, H. N., eds. Meals in a Social Context: Aspects of the Communal Meal in the Hellenistic and Roman World. Aarhus: Aarhus University Press, 1998. Oleson, J. P., ed. The Oxford Handbook of Engineering and Technology in the Classical World. Oxford: Oxford University Press, 2008. Papakonstantinou, Z. “Wine and Wine Drinking in the Homeric World.” L’Antiquité Classique 78 (2009): 1–​24. Parker, H. N. “Galen and the Girls: Sources for Women Medical Writers Revisited,” Classical Quarterly 62 (2012): 359–​386. Pigeaud, J. Folie et cures de la folie chez les médecins de l’antiquité gréco-​romaine: La manie. Paris: Les Belles Lettres, 1987. Powell, O. Galen On the Properties of Foodstuffs (De alimentorum facultatibus), Introduction, Translation and Commentary. Cambridge: Cambridge University Press, 2003. Reinhardt, T. “Galen on Unsayable Properties.” Oxford Studies in Ancient Philosophy 40 (2011): 297–​317. Riddle, J. M. Dioscorides on Pharmacy and Medicine. Austin: University of Texas, 1985. Sallares, R. Malaria and Rome: A History of Malaria in Ancient Italy. Oxford: Oxford University Press, 2002.

Dietetics: Regimen for Life and Health    553 Siegel, R. E. Galen’s System of Physiology and Medicine. Basel, New York: S. Karger, 1968. Singer, P. N. Galen: Selected Works. Oxford and New York: Oxford University Press, 1997. Vannesse, M. “Les usages de l’eau courante dans les villes romaines:  le témoignage de l’épigraphie,” Latomus 71 (2012): 469–​493. Wilkins, J. M. and Hill, S. Archestratus, The Life of Luxury:  Europe’s Oldest Cookery Book, Translated with Introduction and Commentary. Totnes: Prospect, 2004. —​—​—​. Food in the Ancient World. Oxford, Malden, MA: Blackwell, 2006. Zanda, E. Fighting Hydra-​Like Luxury: Sumptuary Regulation in the Roman Republic. London: Bristol Classical Press, 2011.

chapter C16

Gre c o-​R oman Su rg i c a l Instrum e nts The Tools of the Trade Lawrence J. Bliquez

As in modern times, so in antiquity, surgery was in most instances considered a more radical intervention than regimen or pharmacy in treatment of injury and disease (Hippocrates, Aphorisms 7.87, Littré 4.608; Seneca, On Anger 1.6.2; Galen, Recognizing the Best Physician 10.2; and the Empress Livia’s remarks to Augustus in Dio, Roman History 55.17.1). It therefore comes as something of a surprise to learn that under the Roman Empire more than 100 different kinds of surgeries were being performed, at least in some places at some times. Fortunately, many of the instruments actually used survive. This summary focuses on the tools, every day and specialty, one might expect to see were one capable of entering a well-​stocked surgery in classical Athens or one operating in the High Roman Empire. For more extensive references and illustrations, see Bliquez 2015. The history of Greco-​ Roman surgical instruments falls conveniently into two divisions:  tools available in “Hippocratic” times (5th to 4th century bce) and instruments at the disposal of surgeons, mostly Greek or at least Greek speakers, from the late Republic through the Empire (1st century bce to 5th century ce). Of the former period, only cupping vessels taken from graves and perhaps a few odds and ends survive. On the other hand, instruments from the Empire abound in number and variety. These, too, are mostly extracted from graves, but they are also found in houses and shops, especially in the Vesuvian cities and now Rimini (Bliquez and Jackson 1994; Jackson 2009), bathing establishments (Künzl 1986), and rivers and marine shipwrecks (Spawforth 1990, Gibbins 1997). In contrast to the few bleeding vessels from the Hippocratic period, the preserved literary treatises of the time attest a much greater number of instruments available (Bliquez 2003). And, of course, these treatises and the relevant literature of the Empire are key to understanding the usages to which tools were put. Most important are the Greek testimonia provided by Soranus, Galen, and early Byzantine excerpters

556   Hellenistic Greek Science like Oribasius, Aëtius, and Paul Aegineta, who open the way to the lost works of famous practitioners of the High Empire like Antyllus, Heliodorus, and Leonides. Celsus and Soranus’ paraphraser/​translator Caelius Aurelianus supply information in Latin. The former is crucial in being the earliest extant Imperial source and in bearing witness to many tools that must have been developed or improved on in the otherwise black hole of the Hellenistic period, especially in Alexandria. Other useful sources are sculptured reliefs (Hillert 1990; Krug 2008) and, occasionally, coins (Penn 1994), paintings, papyri, and inscriptions. Of reliefs, a few dating to the Empire depict surgical tools for sale in shops.

1.  Materials, Manufacture, and Design On the whole, one gets the idea that most of an Imperial surgeon’s repertoire consisted of instruments professionally prepared in advance by smiths and made available for purchase, whereas the Hippocratic physician often created his own on the spot or had a tool prepared for an immediate need (examples:  Diseases of Women sec. 222.11–​25 [Littré 8.474]; Diseases 2.47 Potter). This scenario sometimes applied in the Empire, as Galen mentions tools prepared to his specifications (Avoiding Distress 4–​5 Boudon-​Millot), and a provincial Egyptian physician of the 4th century ce, Eudaimon, appears to send for copper sheeting to personally make instruments he needs (Oxyrhynchus Papyri 59.4001). Of related interest are inscriptions informing us of competitions in designing instruments in the reign of Antoninus Pius (Engelman, Knibbe, and Merkelbach 1980, 108–​112). In this connection, we also occasionally read in the literature of “virtuoso” instruments associated with a specific individual (e.g., “the lithotome of Meges,” Celsus 7.26. 2n–​o). One such invention likely survives (see puoulkos below). In the main, surviving tools are made of bronze or brass. Many are equipped with an instrument at each terminus as, for example, spatulas and spoons complemented with knobs or “olivary enlargements” useful for grinding, probing, and cauterizing; scalpels featuring blades mounted opposite handle-​dissector combinations (see sec. 3.2 “Surgical Knives”); or scoops and needles opposite retractors. We may conjecture such an arrangement will have facilitated an operation or procedure where both ends could be brought to bear and, at the same time, will have conserved metal. Cutting and puncturing instruments like scalpels, needles, and chisels were equipped with iron or steel blades luted with tin and lead solder into slots (Krug 1993; Jackson 1986, 133–​135). Galen preferred steel from Noricum, and insisted on the hardest iron for his chisels (Anatomical Procedures 8.6, [Kühn 2.682],9.1 [Kühn 2.709]; see also Horace, Epodes 17.71 ense . . . Norico). Most blades have rusted away over time, as was surely the fate of iron/​steel needles and most cauteries of iron. Very few of the latter are preserved, though blobs of iron clinging to copper alloy instruments recovered at Pompeii perhaps represent once-​intact specimens (Bliquez and Jackson 1994, 126, #71–​72). Tooth forceps,

Greco-Roman Surgical Instruments   557 the arms of levers/​elevators, shears, and the blades of some chisels, being more robust iron forms, fare better. Fine copper hooks, needles, and probes too are often gone or badly corroded. Tin and lead probes and tubes are also scarce in surviving instrument sets, perhaps because they were rarely used. On the other hand, many cylindrical cases of copper alloy serving as containers for instruments mounted on shafts and for drugs are preserved (figure C16. 2, far right; figure C16.3, middle row, figure C16.9, far left). Boxes of the same material, many compartmentalized, some featuring fine decor, also occur in lesser numbers. Most biodegradable items are lost, but sometimes one encounters bone probes, knife handles and boxes made of bone or ivory, and even wooden probes and containers (Künzl 1983a, 91, #. 5–​6, 95, 97; Gibbons 1989; Spawforth 1990, 9–​10). Instruments were manufactured by casting, forging, and cold work. Substantial forms of copper alloy, such as scalpel handles and sequestrum forceps, were cast in molds by the lost wax process, while catheters and tubes were cut, beaten, and twisted into shape from sheeting (note the seam on figure C16.13); iron/​steel instruments and components like blades were forged (Longfield-​Jones 1978; Krug 1993, 74, 86–​87; Jakielski and Notis 2000, esp.  387). Blades that were worn or damaged might be replaced. It is unclear whether lathes or just chisels were used to create the threading of the worms on specula (Deppert-​Lippitz et al. 1995, 41–​45, 180–​187; Bouzakis et al. 2008), and the threaded shafts of some spoon probes and needles. Most likely both methods were employed. The superior craftsmanship involved is reflected in skillfully turned handles on some scalpels (figure C16.2, top row; and figure C16.15), and by the rings and baluster and doorknob finials on retractors and forceps (figure C16.2, bottom row, far left; and figure C16.3, middle row, 4th, 5th, and 7th from right). Occasionally, pieces feature damascening or inlay in silver (figure C16.6 and figure C16.9) or niello or Corinthian bronze (Krunić 1995). Such refinements recall the references to gold and silver instruments in a jibe at incompetent doctors made by the 2nd-​century ce satirist Lucian (The Ignorant Book Collector 29).Longevity may have been considerable. A scalpel handle in the form of a bust of Hercules (see below), a type that seems confined to the 1st century ce, is recorded as recovered in Byzantine levels at Corinth (Davidson 1952, 191, #1406). If so, that particular tool was functional for centuries.

2.  Aesthetic Enhancement and Symbolism One is struck by the aesthetic care expended on Greco-​Roman instruments as opposed to those produced in modern times. As noted, this may consist of abstract motifs such as raised rings, lattice patterns, striation, and finials resembling balusters, door knobs, and so forth. Such enhancements might serve the practical purpose of securing the surgeon’s grip. But Lucian’s jibe hints that instruments, especially fine ones, were of

558   Hellenistic Greek Science particular importance in marking out and elevating the status of a physician (see also Herodotus 3.131); thus, in an age where inconsistent or ineffective use of antiseptics and anesthetics made surgery a treatment of last resort, attractive gear must have inspired confidence. In fact, confidence, by the patient in his surgeon and perhaps by the surgeon in himself, may have been reinforced by recognizable motifs, which often seem symbolic. Vegetable designs like ivy or acanthus, for example, with their rapid growth and rich foliage may express vigor, and life force (figure C16.1, middle row, handle on third from right; and figure C16.6). The head of a wolf can allude to Apollo Lykios, therefore Apollo Medicus, father of Asclepius, while the bust of Hercules or his a knotty club, at least once combined with a lion’s head on a retractor, suggests endurance in the face of suffering (figure C16.2, top row, 6th, 7th, and 9th from right; figure C16.8, far left; Bliquez 1992). The limb/​club design alone could also allude to Asclepius’ staff (figure C16.8, 5th from left), as the snake’s head on the steadying bars of specula clearly signifies the healing presence of that deity (figure C16.1, middle row, 1st and 3rd from right). A unique ram’s head found on a speculum at Pompeii (figure C16.1, middle row, 2nd from right) may reflect the perceived powers of Egyptian creator gods (Bliquez 2016).

3.  The Instrumentarium 3.1 Cupping Vessel As noted, the cupping vessel (sikua σικύα, Latin cucurbita) is virtually the only type of Hippocratic instrument to survive (figure C16.4a–​4b). The nine, perhaps ten, specimens we have differ from their ca 30 preserved Imperial counterparts (figure C16.1, top row) by having less accentuated profiles, although two, if they date from the 4th century bce, show the gradual tendency to become more angular. Representations of both Hippocratic and Imperial models appear on reliefs, and the odd painting or coin. More than any other instrument, the cupping vessel symbolized the medical art. One can see by perusing the medical writings of the Empire where there are over 300 references to cupping for a host of conditions ranging over the entire body. Cups were used in two ways. In the first, the cup was applied to the skin without an incision, a process called “dry cupping, ” which was a milder intervention. The purpose was to stimulate an area or to attract a deep seated humor, for example. If there was scarification, that is, if the skin was cut in advance, translators use the term “wet”, which was the second way. The theory behind wet cupping was to extract corrupted blood or matter, or to divert an excess of blood causing a disease or condition (summaries esp. in Celsus 2.11.3–​4, and Galen, Leeches, Revulsion, Cupping, etc. sec. 3 [Kühn 11.320–​321]). In either case, the cup was heated before application. As the cup cooled against the skin, a vacuum resulted that caused it to adhere and pull; the stronger the initial heat, the stronger the pull. For patients

Greco-Roman Surgical Instruments   559 afraid of fire, the horns of cattle might be substituted, the vacuum achieved by puncturing and sucking the horn’s apex and then sealing it with a finger or wax. All surviving cups are copper alloy, but silver and glass models are attested in Imperial literature, and even small clay vessels are mentioned. Save for differentiation in size and width or, in the case of Hippocratic models, angularity of profile, survivals are relatively uniform. Imperial literary sources describe models with wide mouths or flat, thin or arched lips allowing for placement to the desired area of the body. Many specimens were equipped for rings at their apex for removal or suspension when not in use (figure C16.1, top row, 4th from right).

3.2. Surgical Knives 3.2.1 The Scalpel In cutting or puncturing, the “scalpel” wielded by Hippocratic practitioners was most likely any suitable knife. Indeed, the term ordinarily applied was the usual name for knife, machaira /​μάχαιρα, or, most frequently, its diminutive machairion /​μαχαίριον. By the time of the empire, there was a standard form consisting of a rectangular or trapezoidal handle, or one octagonal in section, mounting a dissector shaped like a leaf, all made of copper alloy (rarely iron). The dissector served to separate and lever tissue and growths (Celsus 7.19.6–​7); in some cases, it was sharp enough to incise or lance (Aëtius 6.1.53). On the other end a blade of iron or steel was soldered or luted into a slotted or tubular socket, the former often flanked by rolled terminals. This model of scalpel is already common at Herculaneum and Pompeii and, therefore, was created prior to 79 ce. The name commonly applied in Greek was smilē /​σμίλη and especially its diminutives smilion /​σμιλίον and (rarely) smilarion /​σμιλάριον. In Latin authors we find the name we use, scalpellus, the diminutive form of scalper. As with the cupping vessel, references to the surgical scalpel abound in the literature and representations of it appear not infrequently on monuments (Krug 2008). No surprise then that the scalpel is the most frequently recovered of all the instruments designed primarily for surgical purposes. Almost every surgical set of any consequence contains at least one specimen. In the main, the scalpel was deployed to puncture, incise, and excise in numerous interventions, the more adventuresome being mastectomy, hysterectomy, excision of struma/​goiter, and repair of various hernias. But it might also be utilized for dissecting (see below), and its blade likely for cauterizing. Blades differing in size, shape, and character that are amply described in the literature are frequently found among surviving specimens, the shape now dubbed “D” being the most commonly recovered (figure C16.2, top row, 1st–​6th from right; and figure C16.5.1). When the common rectangular or polygonal handle mounting a dissector received a special blade, it received a special name. Among these are the “raven/​crow”

560   Hellenistic Greek Science (korax /​κόραξ in Greek, corvus in Latin) used on hernias (figure C16.5.4); the “suture” (anarrhaphikon smilion /​ ἀναρραφικὸν σμιλίον) or “pterygium knife” (pterygotomon /​ πτερυγοτόμον) deployed in eye interventions (figure C16.5.6–​7); and the curved “tonsil knife,” called antiotomon /​ ἀντιοτόμον and probably the same as the “uvula knife,” or staphulotomon /​σταφυλοτόμον (figure C16.7), all of which can be identified with reasonable certainty among completely intact survivals.

3.2.2 The Phlebotome The same was likely true for the phlebotome /​φλεβοτόμον, probably just an ordinary scalpel, the “sharp pointed knife” or skolopion /​ skolopomachairion (σκολοπομαχαίριον), especially serviceable for lancing and procedures in confined spaces, and the “half spatula,” which sounds as though it represents another name for the D-​shaped blade. If we are right about the phlebotome and the half spatula, many have survived. Possibly, lancet-​like cutters, like a fine piece combined with a cautery (figure C16.8, 7th from either side), allegedly from Ephesus, also may have been called phlebotome.

3.2.3 The Lithotomy and Other Knives Identifiable, too, in recovered examples is the λιθοτόμον /​lithotomon or “lithotomy knife” (figure C16.8, 1st and 2nd, far right), which substituted for the dissector a roughened hook or scoop for extracting bladder stones (Künzl 1983b). What looks to be a spatula knife excavated at Rimini inserts an oval-​shaped blade into a polygonal handle (figure C16.5.5), but the dissector is replaced by the olivary enlargement, commonly found on surgical probes and spoons under the empire (see below). No authenticated “polyp knife” (polupikon spathion /​πολυπικὸν σπαθίον), which featured a leaf-​shaped blade mounted opposite a scoop, or “fistula knife” (suringotomon /​συριγγοτόμον) in the form of a sickle has yet turned up, in contrast to bow shears of iron/​steel (psalis /​ψαλίς) most commonly used for preparing sutures and bandages (figure C16.1, bottom row, far right).

3.3 Needles Obviously during surgery, wounds and incisions would need to be stitched, blood vessels ligated, and so on. Consequently, we often read in the literary sources of these processes and the materials threaded through needles (belone βελόνη /​Latin acus) for them, ranging from linen (Paul 6.13.1) to human (Paul 6.13.1) and animal hair (Paul 6.18.1), and especially wool (Witt 2009, 112–​114). And, of course, in the absence of appropriate adhesives, bandages and splints also had to be stitched into position with needles. The most daring surgeries involving needles are gastrorrhaphia, or stitching of an abdominal wound, and correction of various hernias. No surprise then that we find eyed needles of copper alloy in surgical sets, some curved, some straight and of various lengths and mass.

Greco-Roman Surgical Instruments   561 Under the empire we possess more complicated models, each perhaps called in Greek parakentērion /​παρακεντήριον, designed for couching cataracts and dealing with other conditions affecting the eyes. The most interesting is a splendid set of five needles mounted on a shaft terminating at the other end with the olivary enlargement found on probes, the purpose of the enlargement being to measure off and mark the point for insertion between the pupil and the outer canthus. Dredged from the River Saône (Montbellet), they came packed in one of the common cylindrical carrying cases for instruments and medicaments (Feugère, Künzl, and Weisser 1985). All are copper alloy, four of them beautifully decorated along the shaft with a spiral, silver inlay (figure C16.9). Two are unusual in being hollow with retractable stems, allowing for the cataract to be removed by suction. Also to be included in this socketed class is a model that generally features an iron/​steel needle (one from Pompeii faintly preserved) at each end of a slender, socketed shaft decorated with a combination of striation, molded rings, and fine and broad lattice patterns. Frequently, one of the socketed ends is positioned at an angle to the shaft (figure C16.3, middle row, 10th from right.). A seldom-​encountered third type, all copper alloy, mounts one or two needles on a robust shaft (figure C16.3, middle row, 11th from right; figure C16.8, 5th from left). All of these needle types would have been useful in delicate probing, cutting, and cauterizing, especially around the eyes. They were likely employed far more often in these procedures than in cataract surgery.

3.4 Probes (Including Spatulas and Spoons) In all Greco-​Roman surgical texts, from the Hippocratic Corpus on, the generic name for probe is mēlē /​μήλη in Greek, specillum in Latin. In the main the mēlē was any serviceable shaft of metal (figure C16.3, middle row, 8th from left). Those recovered in archaeological excavation are mainly copper alloy. However, the literature refers as well to tin, lead, wood, and other natural substances, such as feathers, garlic stalks, and swine’s bristles. Taken collectively, the probe is probably referred to more frequently in the literature and preserved in greater numbers in surviving instrumentaria than any other kind of instrument. The classification is extremely broad; the types varying from simple rods to shafts mounting spatulas, spoons, scoops, and even hooks, each type identified by one or more names. One characteristic distinguishing Hippocratic models from the Imperial is the frequent presence on the latter of an olivary enlargement called in Greek purēn /​πυρήν and baca in later Latin. The applications of the probe and its purēn are likewise many and varied. These include preparation and application of medicaments (as on the slab shown in figure C16.3, bottom row, far left.) and plugs/​pledgets, in addition to measuring, exploring, cauterizing, piercing, dissecting, dilating, threading, cleaning, curetting, depressing, elevating, pressuring, protecting/​guarding, directing, and retracting.

562   Hellenistic Greek Science Survivals include plain shafts of metal but these are rare. Three common models are (a)  the dipurēnon /​διπύρηνον, a shaft terminating in two purēns (figure C16.2 bottom row, 4th and 7th from right; and figure C16.3, middle row, 11th from left); (b) the spathomēlē /​σπαθομήλη, a shaft mounting a spatula opposite a purēn (figure C16.3, middle row, 3rd–​5th from left); and (c) a shaft mounting an ovular or triangular-​ shaped spoon opposite a purēn, called among other names mēlōtis /​ mēlōtris (μηλωτίς /​ μηλωτρίς, see figure C16.2, middle row, 4th and 5th from right; and figure C16.3, middle row, 7th from left). All were capable of serving most of the functions listed above. Common and multifunctional as well are types we call ligulas. These mounted small spoons, often at an angle to a shaft rounded or pointed at its terminus but usually lacking the purēn (figure C16.3 middle row, 9th and 10th from left). Other surviving articles we might classify with probes are plain spoons (figure C16.3, middle row, 6th from left); strigils for preparation and administration of medication; styluses (figure C16.2, bottom row, 16th from right; and figure C16.3, bottom row, left, below cautery), which are recorded as serving such functions as applying medication and levering out teeth; and, finally, large spatulas of uncertain purpose mounted at each terminus of a short husky shaft (figure C16.2, bottom row, 6th and 7th from left). Not to be ignored is a “virtuoso” scoop for extraction of arrow heads invented by Diocles of Carystus. A specimen appears to have been found lately in Rimini (figure C16.17; De Carolis 2007 and 2009).

3.5 Cautery Cauteries (kautēr, καυτήρ, καυτήριον, ferramentum) are documented in many different operations, but, in general, they performed four principal functions: staunch bleeding, eliminate diseased tissue, open the way to other parts of the body, and produce counter-​irritation (Jackson 1986, 154; 1994, 178). Generally, the cautery was regarded as an extreme measure, because as, Celsus notes (7.15.1), burnt tissue heals more slowly than incised tissue. But a cautery was not always applied directly to the diseased part: often it was simply used as a stimulant to transfer heat when, for example, it might be wrapped in rags. Nor was it always fired white hot. There was less reluctance when the area to be treated and the cautery to be used were small, as in work on or near the eye. The written sources bear witness to many different shapes. Surviving cauteries reflected in the literature include a circular specimen in Baltimore from Colophon (Caton 1914, 117, #X); a set of three semicircular models in the Naples Museum from Pompeii (figure C16.2, middle row, 10th–​12th from right); a rather similar type combined with a lancet in Mainz from Asia Minor (figure C16.8, 7th from either side); a lunated cautery in Bingen (Paul 6.57.1; figure C16.10); and a small spatulate model in the British Museum said to be from Italy (Celsus 7.12.6; figure C16.3, bottom row, above stylus). One of the pieces in Naples is iron, as are those in Mainz, the British Museum, and Bingen; the others are copper alloy. This contrasts with the fact that “iron” (siderion, ferramentum)

Greco-Roman Surgical Instruments   563 was the name preferred by the Hippocratics and by Celsus, indicating that this was the usual material for the instrument. Iron was surely preferred because, as opposed to copper alloy, iron can take higher heat without melting. Unfortunately for us, iron also rusts, the result of which is few survivals, considering what must once have been a very considerable number.

3.6 Retractors and Hooks We have names for four types of retractors and hooks.

3.6.1 The Sharp Hook The sharp hook (angkistron /​ἄγκιστρον, hamulus acutus) was as basic an instrument as the scalpel and probe. It was particularly handy for piercing and raising tissue prior to lancing, excision, or repair; for example, in retracting the lips of a surgical incision or a tonsil for excision. Frequently, as many as three or four such hooks were applied at the same time. In a few cases, sharp hooks mount another instrument at the opposite terminus, usually an iron or steel needle, a probe, another sharp hook, or a blunt/​blind hook. Survivals are regularly mounted on nicely turned shafts terminating in a finial resembling a baluster, a doorknob, a raised button or even the head of the Nemean lion (figure C16.3, middle row, 4th–​6th from right; and figure C16.8, far left). Two hooks rarely appear at both termini or two hooks at one terminus (figure C16.8, 2nd and 3rd from left).

3.6.2 Blunt/​Blind Model The blunt/​ blind instrument (tuphlangkistron/​τυφλάγκιστρον, hamulus retusus) occurs less frequently and served mainly for retraction, dissection, and elevation, as in exposing hydrocele and enterocele (Paul 6.62.4, 6.65.2), or in prying fragments from a fractured skull (Oribasius, Medical Compilations 46.15.5). Perhaps a dozen examples of instruments we can consider as blunt hooks survive. All feature a broad plate, at one or both ends. The most common type consists of a shaft from which, at one or both terminals, a kite or flat leaf-​shaped plate extends vertically from the shaft (figure C16.3, middle row, 3rd from right; and figure C16.11.17); in some cases a sharp hook is mounted at the opposite end, supporting the identification of the plates on these pieces as representing the tuphlankistron (Jackson 1986, 142). A second type may be seen in a specimen preserving a roughened lithotomy hook opposite a blunt two-​pronged retractor in Mainz (figure C16.8, 3rd from right), indicating that the latter type could also be used in lithotomy (see sec. 3.6.4, “Lithotomy Hook”).

3.6.3 Varix Extractor According to the sources, the so-​called varix puller or extractor (kirsoulkos /​κιρσουλκός) was a special instrument for accessing and positioning a varicose vein for excision and assumed the form of “the letter gamma at its bend” (Bliquez 1985). Its function was to clear the way to the varix by piercing, retracting, and winding the skin over it, language indicating

564   Hellenistic Greek Science it was a special type of the sharp variety. The kirsoulkos might be generally represented by a gamma-​shaped hook in an instrumentarium from 3rd century ce Ephesus, now in the Römisch-​Germanisches Zentral Museum, Mainz (figure C16.8, 4th from left).

3.6.4 Lithotomy Hook This same instrumentarium in Mainz contains two lithotomy knives, each mounting a roughened hook opposite the now absent blades (see sec. 3.B.3 above, under lithotomy knife, lithotomon). However, the hook (lithoulkos /​λιθουλκός, uncus) may occur independently of the knife (figure C16.5.11, Rimini), either completely independently (figure C16.16) or complimented by another retractor such as the blunt two-​pronged model in Mainz.

3.7 Forceps Basic to the surgeon was the forceps; therefore, it is no surprise that so many Imperial models surface in surgical graves and sites. The Domus del Chirurgo (House of the Surgeon) at Rimini alone has provided over 30 specimens. There are numerous types: some two-​piece models revolving on a pivot, like a pair of hand pliers; others one-​ piece spring types. Legs can be slender and pointed or broad and ending in jaws; the latter, often dentated or serrated, may be hollow, straight, curve inward, or curve off together in one direction, called the coudée type. In many instances, forceps are equipped with sliding catches, allowing their jaws to be fixed/​bound in place. Sometimes a forceps is combined with another instrument: among examples, two forceps from Italy with slots, probably for blades (figure C16.3, middle row, 8th and 9th from the right). It is problematic coordinating the many Greek names given in literary testimonia with these forceps types because physical description of a particular name, for example, “bone forceps,” is often scanty or nonexistent, while in some cases, different names were surely applied to the same surviving type. In any case, received opinion recognizes the models described in the following sections.

3.7.1 Smooth-​Jawed Spring Forceps Smooth-​jawed spring forceps (labis /​λαβίς, tricholabis /​τριχολαβίς, volsella) resemble modern tweezers (figure C16.3, middle row, 7th and 8th from right). Like the modern version, its main functions were hair removal, and extraction of objects from the eyes, ears, nose, and so on (Oribasius, Handbook for Eunapius 4.31.3; Galen, Compounds by Place 3.1 [Kühn 12.659], 3.3 [Kühn 12.688]). The “forceps for holding down/​gripping the eyelid” (blepharokatochon mudion /​βλεφαροκάτοχον μύδιον) mentioned by Paul (6.8.2) is likely a member of this class with reasonably broad jaws to which he applied a fancy name.

3.7.2 Dentated Spring Forceps Examples of dentated spring forceps (mudion /​μύδιον, sarkolabon /​σαρκολάβον, volsella) from Pompeii and Rimini are shown in figure C16.2, middle row, and figure

Greco-Roman Surgical Instruments   565 C16.5.8. Specimens from Italy in the British Museum and from Pompeii and Rimini represent the variant known as coudée (figure C16.2, bottom row, 13th from left; figure C16.3, middle row, 9th from right; figure C16.5.9). There are over 20 testimonia regarding the use of the mudion /​ volsella by Greco-​Roman surgeons to position tissue for the scalpel in eye, oral, urogenital, anal, and skeletal surgeries. One specimen at Rimini is iron (See Jackson’s summary 2009, 83, 88).

3.7.3 Heavy-​Duty Plier-​like Models Pseudo-​Aristotle (Mechanica 854a16–​31, ca 300 bce) provides a detailed description of such a forceps type made of iron that he calls odontagra /​ὀδοντάγρα, or “tooth forceps.” Over 20 examples of a plier-​type forceps with these qualifications survive, seven from the Domus del Chirurgo at Rimini alone (Jackson 2009, 85, 89). Those that are well preserved have handles round or squared in section and terminate at one end in globular or disc-​like swellings (Dude 2005, 96–​97, 113–​114). At the other we find smooth, straight, or incurved jaws/​beaks that, seen from the side, are offset from the handles, as a bayonet. The jaws of several specimens feature a circular depression to grip the tooth (figure C16.11, no. 14). Celsus pulls teeth (7.12.1b–​c) and extracts broken roots that may occur in the process with a forfex, which must be the name in Latin. Also preserved is a second type of plier-​like forceps. Surviving specimens are all composed of copper alloy; jaws may curve off together in the same direction (figure C16.1, middle row, 4th from left; and figure C16.11, no. 16) or come evenly together (figure C16.11, no. 15). If iron specimens represent the tooth forceps, then these copper-​alloy models must be surviving bone, or “sequestrum,” forceps, called in Greek ostagra /​ ὀστάγρα). Both the odontagra and the ostagra were deployed to grip bone fragments, (as the skull fragments of an aborted fetus), and both were also associated with extraction of imbedded points in which case they assumed the name “missile puller” (beloulkos /​βελουλκός). In the House of Siricius in Pompeii there was a painting of the episode in Aeneid 12.404 showing Iapyx attempting to extract an arrowhead from the wounded thigh of Aeneas tenaci forcipe (Scarborough [1969] 1976, pl. 18).

3.7.4 Forceps with Spoon-​Shaped Jaws In Imperial Greek sources we hear of an instrument called staphulagra /​σταφυλάγρα. It was mainly utilized, as its name (uvula gripper) indicates, for strangling the uvula (staphulē) and also hemorrhoids prior to excision, thereby reducing the loss of blood (Paul 6.31.2, 6.79.1). No description is given of the instrument. However, if it was to clamp effectively, the staphulagra must have been a type of forceps; likewise spoon-​ shaped dentated jaws would have been desirable for gripping and encompassing. And if it was to reach the back of the throat, it must have had reasonably long slender handles. Approximately 20 surviving cross-​legged forceps answer to these specifications (figure C16.5, no.  12 illustrates the basic form). Of these, six were found in instrumentaria, affirming surgical application. Recovered specimens fall into two classes:  one with straight legs more useful for work in the throat, and one with bowed legs more suitable for hemorrhoidectomy. In a few cases, the jaws are pierced with a hole (figure C16.2), middle row, 9th from right) of uncertain purpose.

566   Hellenistic Greek Science Paul also recalls for treatment of inflamed uvula or hemorrhoid an instrument equipped with “hollows” that could be filled with medication to be held in place and burn away the offending condition. This instrument, which he terms staphulokaustēs /​σταφυλοκαύστης and alternately haimorrhoidokaustēs /​αἱμαρροιδοκαύστης, was designed for patients who were timid or where there was fear of hemorrhage (6.71.1). From his description we gain the impression of a forceps with deep spoon-​shaped jaws closing evenly on one another. Three cross-​legged forceps with Paul’s stipulations are preserved, one with other instruments (figure C16.5, no. 13). In contrast to Imperial sources, there are few references to forceps types in the Hippocratic Corpus. There we find one lonely reference to a tweezers (labis), and one reference to an osteologon /​ὀστεολόγον, literally “bone extractor.” This must be the ostagra of later times. Its sole occurrence comes in Diseases of Women sec. 70.5 (Littré 8.190.22), where it serves to remove the skull fragments of an impacted fetus, a function also performed by the Imperial model. Surfacing in Physician 9 (Potter) are the Imperial names odontagra and staphulagra. We are told nothing about their applications, just that a neophyte physician needs to be conversant with their use. The Hippocratic Corpus may not tell the whole story. One would very much like to know what lies behind the “physician’s pinchers” (karkinos iatrikos /​καρκίνος ἰατρικός) in an inventory of dedications recorded in the Athenian Asclepieum (Inscriptiones Graecae II2 47, early 4th century bce, lines 16–​19) that also references cupping vessels and surgical knives (μαχαίρια ἰατρικά).

3.8 Bone and Tooth Instruments 3.8.1 Saws, Drills We find the surgical saw (priōn /​πρίων, serrula) employed, as we might expect, in the amputation of limbs (Celsus 7.33 and Leonides in Paul 6.84), or in removing sections of rib corrupted by fistula (Oribasius, Medical Compilations 44.20.18). Galen distinguished two distinct kinds, the first of which was serrated, while the second assumed the shape and size of a knife, with perhaps moderate serration (Commentary on the Hippocratic ‘Fractures’ 18b.331 Kühn). That surgical saws were relatively small is indicated by Celsus’ preference for the diminutive form, serrula. If most saws were made of easily degradable iron and steel, that would explain why we have so few surviving examples. These include a curved iron saw with fine teeth recovered in the fabulous Rimini find, which resembles Galen’s “knife saw” type (Jackson 2009, 85, 89). The term priōn occurs several times in the Hippocratic Corpus but always in the sense of a crown drill for trephining. The literary sources of the empire give us a fairly full picture of the numerous situations for which drills were used to bore into the skull and other parts of the skeleton. Their principle function was to remove damaged or diseased bone, such as bone made carious by ulceration or fistula (Celsus 8.2.4; Antyllus /​

Greco-Roman Surgical Instruments   567 Heliodorus in Oribasius, Medical Compilations 44.20.12; Paul 6.77.3) or skull fracture (Celsus 8.4.14; Paul 6.90.5). From the treatments of Celsus (8.3), Galen (Method of Healing 2.214–​219 Johnston and Horsley), and Paul (6.90.5), we learn drill bits were of two main types, the circular or crown-​shaped model and the familiar pointed bit. The former was used for shallower drilling over a limited area and had a removable center pin to keep the instrument in position until the circular section had begun to bite. The second type was of two kinds: the straight bit used by artisans, like smiths and carpenters, the other wider or with some sort of protective collar immediately above its pointed tip before it narrowed again. This feature acted as a barrier to ensure that the drill sank into the bone to a limited extent. Among various Greek and Latin terms for the bit we find the familiar trepan (τρύπανον). Diminutive forms show that the sizes of drills clearly varied to meet changing situations (Galen, Method of Healing 2.220–​221 Johnston and Horsley). Drills could be rotated by hand, or spun more rapidly by wrapping them with a strap or thong that could then be drawn by the free hand; or again they could be wrapped with a thong or strap and worked back and forth with a bow (aris /​ ἀρίς in Greek), exactly as the drills employed by wood and metal workers, from whom this method must have been borrowed. As to survivals, we have as many as seven bows (figure C16.11, no.  20 and figure C16.12) and, from Bingen, one fine set of crown drills, all copper alloy (figure C16.12). The drills feature the removable centering pins mentioned by Celsus; one preserves the perforations through which was passed the strap or thong of the bow. No pointed bit can be authenticated, probably because bits of this kind were iron and have rusted away.

3.8.2 Guard/​Protector In operations involving cutting or sawing bone, underlying parts had to be protected (Paul 6.77.4). To this end a type of guard was applied, called meningophulax /​ μηνιγγοφύλαξ in Greek and membranae custos in Latin (Celsus 8.3.8, 8.4.17). Its name “protector of the meninges” reflects the use of the instrument in skull surgery. But it also functioned as a guard in other surgeries, such as weapons removal (Paul 6.88.8). It might also be applied to steady bone for excision or to lift out a section of skull cut through (Oribasius, Medical Compilations 46.11.27–​28). Basically, the meningophulax was a plate of copper alloy mounted on a handle (Celsus 8.3.8). On the whole it must have resembled a spatula probe because a spatula probe could be substituted for it (Galen, Anatomical Procedures 8.7 [Kühn 2.686]). As only the blunt/​blind retractor (see sec. 3.6.2) survives with these features; it has been suggested that meningophulax was the name applied to it when it was deployed as a guard (Jackson 1986, 142–​143).

3.8.3 Chisels and Gouge Obviously, the primary function of the chisel (ekkopeus /​ἐκκοπεύς, Latin scalper /​ scalprum) was to chip away pieces of bone, as in trepanning or in cases of bone corrupted

568   Hellenistic Greek Science by fistula (Paul 6.77.3). Otherwise, its uses ranged from amputation of supernumerary digits (Paul 6.43.1) and weapons removal (Paul 6.88.5) to the forced removal of a finger ring (Oribasius, Medical Compilations 47.17.4). As with many other instruments, chisels were of various sizes and shapes: stout, sharp, heavy, square, narrow, knifelike, round and pointed, and notched or clawed. While the shape and size of the surgical chisel are treated in the sources, nothing is said about its material makeup; so archaeology has to fill in the picture. Noteworthy is a fine matching pair composed of flat iron blades mounted on octagonally sectioned handles of copper alloy from an Italian instrumentarium now in the British Museum (figure C16.3, middle row, 1st and 2nd from right). The Rimini find alone provides 12 specimens, featuring in the main, tanged blades of varying length, breadth, and thickness inserted into copper alloy or wooden handles (figure C16.11, no. 19; Jackson 2003, 318). The gouge was classed by Greeks as a type of chisel; hence it too bears the name ekkopeus. We find the gouge mentioned exclusively in the context of skull fracture where it is used to chip away weakened bone and to clear the area to be cut through with the lenticular (see below). As its blade was concave in section, it was distinguished by being called “circular” or “hollow” (Galen, Method of Healing 2.214–​215 Johnston and Horsley). Survivals are rare, the Domus del Chirurgo at Rimini supplying three authenticated models (figure C16.11, no. 21). As we might expect, the Rimini specimens feature iron blades of varying gauge and profile. Their missing handles of wood or bone were attached to the blades by a short tang and a small bronze collar. A very specialized type of chisel was the lenticular, or phakōtos /​φακωτός ekkopeus. It was used exclusively for removing damaged bone in cases of skull fracture and featured a lentil-​(phakos) shaped guard; hence its name. The lentil-​like button was positioned longitudinally at one end of its cutting edge. This button protected and, if necessary, separated the meninges while the sharp edge of the blade sliced sideways horizontally through the bone. To allow for the trajectory of the lenticular a groove had to be gouged or a hole drilled if damage to the skull had not already created a proper opening (Galen, Method of Healing 2.222–​223 Johnston and Horsley). We have only four iron specimens lately excavated at Rimini (figure C16.11, numbers 22, 23). The lentil-​like projections of each vary subtly. Though chisel types might be driven by hand, as likely as not they were driven by a hammer, often described as small (malleolus in Latin). None survive, perhaps because the surgical hammer was wooden.

3.8.4 Curette, File The ancients applied the names xustēr /​ ξυστήρ and in Latin, scalprum , to the curette, an instrument suitable for scraping away hard substances, mainly bone. Functions extend from scraping smooth boney surfaces in cases of fracture (Celsus 8.10.7G) to distinguishing sutures from fractures of the skull by applying a curette to scrape away previously applied ink, a procedure first described in the Hippocratic On Head Wounds (14.2, 4, 7 and 19.4 Hanson). Four spoon-​like tools in instrumentaria from Bingen, Colophon, Melos, and Italy (figure C16.3, bottom row, below forceps) qualify as attractive

Greco-Roman Surgical Instruments   569 candidates. Each features spoons with serrated or sharp-​rimmed bowls that look to be especially suited for bone work. A curette was also employed by Paul of Aegina as a tooth scaler to remove tartar (6.28.1). He also applies a file (rhinē /​ ῥίνη, lima) for this purpose. Other authorities refer to the file for leveling large or broken teeth (e.g., Heracleides and Asclepiades, as preserved in Galen, Compounds by Place 5.4 [Kühn 12.848], 5.5 [Kühn 12.871–​872]). And of course it was deployed for bone work, as in leveling bone in the excision of a rib (Oribasius, Medical Compilations 44.8.8). Only Aëtius mentions a file “dull, purēn-​like and quite smooth at the point” (8.32.8). Otherwise, there is no information as to appearance, except that the preference for diminutive forms indicates the surgical file was small. As for preserved specimens, Rimini has provided, among its many tools for bone surgery, a finely striated iron file with a ring for attachment to its now missing handle (Jackson 2009, 85, 89).

3.8.5 Levers or Elevators The Hippocratic treatise Fractures (3.31bis.1–​25 [Littré 3.528–​530]) contains an extensive description of a levering device called variously sidērion /​σιδήριον and mochlos /​ μοχλός or its diminutive mochliskos. Mochlos and mochliskos occur again in Imperial authorities to be joined by a new name, anaboleus /​ ἀναβολεύς. In commenting on the passage in Fractures, Galen explicitly associates the mochliskos with the type of tool used by stoneworkers, although he notes that the surgical type is smaller (Commentary on the Hippocratic Fractures, Kühn 18b.592). Like the bow drill and the surgical chisel, the lever demonstrates how the design of some surgical tools was adapted from tools long in use in other trades, such as carpentry and stone cutting. Galen stresses the need to have a number of elevators available, each differing in length and in the width and thickness of their ends (Commentary on the Hippocratic ‘Fractures’, Kühn 18b.592). Levers of this kind were applied along with extensions to reduce compound fractures of the bone. Among other applications we find the lever prying out the stone-​like tumor called tophus (Oribasius, Medical Compilations 45.6.2 & 45.6.9), bits of skull in cases of fracture (Oribasius, Medical Compilations 46.11.26; 46.15.4), teeth (Galen, Commentary on the Hippocratic ‘Fractures’, Kühn 18b.592), and imbedded stones or sling bullets (Paul 6.88.9). Of later authorities, Paul (6.107.2) offers the most extensive information as to appearance. Like pseudo-​Hippocrates, he requires that the instrument be iron and thick so it won’t bend. It should be seven or eight fingerbreadths in length, and its end should be sharp, wide, and moderately curved. In reducing a fracture, its sharp end should engage the protruding bone while pressure is applied at the other end of the instrument along with extension to re-​engage the extremities of the fracture. Over 20 levers, dating from the 1st to the 4th centuries ce, have found their way to us. Some are entirely copper alloy, others entirely iron; but many are composite instruments, featuring handles of copper and therapeutic ends of iron/​steel (figure C16.11, no. 18; figure C16.15). Where therapeutic ends are well preserved, we find they assume various shapes, as the literary sources say they should: some broad, some narrow,

570   Hellenistic Greek Science some pointed, some squarish, splayed or shaped like a kite, and so forth. In many cases a number of elevators, differing in size and shape are found in the same instrumentarium, as Hippocrates and Galen advise. For tooth and bone (sequestrum) forceps, see sec. 3.7.3.

3.9 Tubes Purges administered anally were a regular feature in the promotion and restoration of health. In addition, injections through hollow tubes into the other orifices of the body are widely described in the literary sources. Other kinds of tubes were employed for draining and for treating irritated or infected areas. Many tubes could be used for both injection and draining. There were two basic types:  (a) tubes attached to an animal bladder by which a solution was squeezed out, and (b) tubes that were piston driven. The various kinds include the following.

3.9.1 Clyster Tubes A common procedure the Greco-​Roman physician might perform for a host of different conditions was the administration of an enema or douche. The delivery apparatus was of type (a). Both the solution and the injection apparatus went mainly by the Greek name klustēr /​κλυστήρ, from the verb kluzo “to wash away, drench, purge.” Oribasius (Medical Compilations 8.24-​38) and Caelius Aurelianus (Chronic Diseases 4.3.24–​35), among others, may be consulted for extensive treatment of clysters, their ingredients and application. In addition to its use for enemas and douches, the klustēr was also employed, for example, to introduce oral medications and nourishment in the case of recalcitrant children (Paul 4.57.6), as well as various concoctions to treat a severely sore throat (pseudo-​Galen, Drugs Easily Procured 2.12.2 [Kühn 14.439]) or chronic ulceration in the ear (Paul 3.23.4). The tube, varying in width and length, might be made of copper alloy or bone/​ horn (Galen, Glaucon, Method of Healing 2.10 [Kühn 11.125]). For the Hippocratic author of Fistulas (6 Potter) even the shaft of a feather would do. The tube might also be perforated all around (Oribasius, Medical Compilations 8.33.3; Cassius Felix 48.18) and flanged at one end to secure the bladder (Caelius Aurelianus, Chronic. Diseases 4.3.24). Among suitable survivals, housed in the Naples Museum, are two tapering, hollow specimens from Pompeii, 17.4 and 13.7 cm in length, open at their distal and proximal ends, suitable for anal injection (figure C16.1, bottom row, far left). One and possibly both were found in the House of the Surgeon in Pompeii (Bliquez and Jackson 1994, 26, 57, 79–​80, all treating items 233–​234). A copper alloy tube in the Smithsonian Institution, Washington DC, is closed at one end, flanged at the other, and features multiple lateral perforations (figure C16.13; Bliquez 1998, 89–​92). For uterine syringes in Naples, see sec. 3.10.1 “Uterine Douche.”

Greco-Roman Surgical Instruments   571

3.9.2 Nasal Clyster We occasionally hear of a clyster to inject the nose called rhinenchytēs /​ ῥινεγχύτης. Scribonius Largus (Prescriptions 7) calls it a “horn,” which leads one to think he means a tube of horn/​bone to which a bag was attached, in other words a small size version of type (a). Aretaeus of Cappadocia (Care of Chronic Diseases 1.2.6) injects euphorbium and other ingredients to evacuate phlegm in cases of chronic headache, through a tube (aulos) that he says is made of twin elements uniting in one stem, thereby irrigating both nostrils simultaneously. This looks to be distinct from Scribonius’ “horn.” Unfortunately, Aretaeus does not say whether his aulos delivers its injection by means of a bag or is piston driven, and there is no surviving specimen.

3.9.3 Pus Extractor A unique injection apparatus has come down to us in an instrumentarium recovered from a tomb at Nea Paphos, Cyprus (figure C16.14). It consists of a hollow reservoir tube, to which there is attached, at its closed end, a slender pipe, open at its tip and possibly having a second lateral opening. Remnants of wood on the interior of the reservoir tube suggest that a second tube of wood, used as a plunger, was fitted inside. In addition to this apparatus, there was also among the items excavated from the tomb a fragmentary small “handle,” also copper alloy. It is taken to be part to the same instrument; if so, it would have been attached to the wooden plunger (Michaelides 1984, 318, #20, 320, #33). This remarkable piece aligns well to a piston-​driven syringe proposed by Heron of Alexandria (1st century ce) in his Pneumatica (2.18). He calls his syringe puoulkos /​πυουλκός or “pus extractor.” As envisioned by Heron, his puoulkos could both inject fluid when the plunger was pushed and extract fluid when the plunger was withdrawn. The Nea Paphos tube and references in Imperial literature make it clear that Heron’s puoulkos existed and was employed by healers. Galen in particular attests both functions. In one passage dealing with an ulcer that penetrates through the thoracic wall, affecting lung, rib, and pleura, he says it is his habit to inject hydromel through the opening and then remove superfluous hydromel with a puoulkos before administering medications (Method of Healing 2.52–​53 Johnston and Horsley). The same authority makes it clear that the instrument came in bores of varying sizes (Compounds by Kind 2.5 [Kühn 13.500]).

3.9.4 Ear Clyster/​Syringe Celsus is partial to an injection apparatus that he calls oricularius clyster, the ear clyster/​ syringe. As its name suggests, Celsus found the instrument handy for washing the ear for accumulations of wax and intruding bodies, irrigating fistulas, and the bladder through a wound created in lithotomy operations (5.28.12M; 6.7.3B, 6.7.9B; 7.26.5E; 7.27.6). There are also numerous attestations in Greek sources, where the instrument goes by at least five names, among them ōtikos klustēr /​ ὠτικὸς κλυστήρ, and ōtenchutēs /​ ὠτεγχύτης.

572   Hellenistic Greek Science As to the appearance of the instrument, Galen classifies it along with the clyster, catheter, and uterine clyster as a surgical tube (Method of Healing 2.80–​81 Johnston and Horsley). Caelius Aurelianus relates that it is formed of a thin pipe (Chronic Diseases 2.1.23: tenue ex aulisco formatum) capable of being inserted into a catheter for irrigation of the bladder. This means that at least sometimes the tube or pipe of the instrument had to be fine enough and long enough to be introduced well into the urethra. The question is, What drove the injection through the tube of Celsus’ oricularius clyster? A case can be made for both (a), the bladder-​bag model, and (b), the piston-​driven type. In favor of (b) are Paul of Aegina (6.59.2), who contrasts the ōtikos klustēr with a bladder attached to a catheter, as if the two injectors were distinct, and the 10th-​century Arab authority Albucasis, who clearly describes and illustrates a syringe (Spink and Lewis 1973, 198–​199). Also, like Albucasis, Galen (Commentary on the Hippocratic ‘Epidemics’ bk. 6, Kühn 17B.267) tells us that the solution to be injected might first be heated “in the ōtenchutēs over a lamp or a wax torch.” Positioning a bladder over a flame would be a much clumsier operation than heating liquid in a metal tube kept in place by a plunger. On the side of (a) we have Cassius Felix (46.13 Fraisse) who, in treating bladder ulceration, prescribes “an ear tube (auliscum oticum), smooth, made of copper alloy, and not bone, so as to avoid breakage, or of silver and attached to a swine’s bladder.” Possibly there were two versions of this injector, which might explain why it went by so many Greek names. As to survivals, if the ear syringe was of type (b), its name, as well as the name puoulkos, might have been applied to the Nea Paphos instrument. The same instrumentarium contains an elegant little tube of gilded bronze 8.3 cm in length that, if fastened to a small bladder, could pass for Cassius Felix’ type (a) version.

3.9.5 Catheter The Greeks gave to the Romans and to us the name catheter, catheter /​καθετήρ. Astonishingly, we hear of its use as early as the Hippocratic treatise Diseases (1.6 Potter, there called auliskos). As with other instrument types, shape and size varied. Celsus requires three sizes for men, two for women, all copper alloy and smooth. In the case of males, they should be longer and more curved, measuring 15, 12, and 9 inches in length; in the case of women, shorter models are recommended, measuring 9 and 6 inches respectively (7.26.1B). Rufus of Ephesus (On Bones 12.2) and pseudo-​Galen (Introduction, or Physician sec. 19 [Kühn 14.788]) likewise distinguish male and female types, the former likening the male catheter to the collarbone, the latter to the Roman letter “S.” Galen several times refers to models with straighter bores (Method of Healing 2.34–​35, 48–​49 Johnston and Horsley). In general, the catheter was developed to evacuate the bladder, but it had many other applications: fitted with a bladder or a bag of animal skin, it could function as a clyster irrigating the urinary tract for abscesses and inflammation (Rufus , Diseases of Kidney and Bladder 10.3.1–​2); or it might act to position and guard the neck of the bladder when a fistula was being incised (Oribasius, Medical Compilations 44.20.63). Lubrication of the catheter by olive oil facilitated its introduction into the urethra (Paul 6.59.1).

Greco-Roman Surgical Instruments   573 There are ample survivals: 15 examples of the male model, and two of the female. All are copper alloy. The Italian instrumentarium now in the British Museum (figure C16.3, top row left) contains two male types of varying length and one female model, while another set from Colophon has two distinct male types (Caton 1914, 116, #V; cf. figure C16.1, bottom row, left, probably Herculaneum). These catheter sets, therefore, reflect the directives in the literature for different sizes available for different situations. Also in accord with stipulations in the literature, both male and female models have the head of the catheter closed with an opening, or “eye,” positioned nearby. On the male specimens from Colophon and Italy, the opposite end is flanged. This feature would prevent the instrument from slipping into the urethra and provide a way of removal. It would also make it easier to attach a bag for irrigation and, by providing a counter surface, to promote the injection itself.

3.9.6 Cannula Tubes for draining empyema are well-​known in the Hippocratic Corpus (Diseases 2.47 Potter). A  simple, small, straight tube—​cannula—​would have served this purpose. Imperial authorities like Celsus, Caelius Aurelianus, and Paul insert tubes through an abdominal incision for draining ascites or dropsy. These tubes are called fistula (Latin) and kalamiskos /​καλαμίσκος (reedlet) respectively; Celsus recommending a fistula of lead or copper alloy (plumbea aut aenea fistula, 7.15.1–​2), Paul mentioning copper alloy alone (6.50.2–​3). Both authorities warn against draining all the fluid at once in accord with Hippocratic directives (Aphorisms 6.27 [Littré 4.570]). The fistula inserted by Celsus for dropsy is either flanged on one end or is equipped with a ring or collar around its shaft, so as not to sink too far into the abdomen. Paul adds a further refinement: his tube has the end to be inserted beveled off like a stylus to facilitate drainage. Two tubes of copper alloy, in Naples, answer strikingly to these specifications (figure C16.1, middle row, 2nd & 3rd from left, 12.4 & 9.3 cm in length). One of them, featuring a beveled tip and a large ring, answers closely to combined details of the instrument in Celsus and Paul. The other tube differs in having two openings (as opposed to beveling) at its distal end and once sported a T-​shaped device running its full length inserted into the proximal. It probably acted as a stopper allowing the surgeon to drain at his convenience, as Celsus and Paul require. A similarly collared tube has lately been found at Allianoi (Baykan 2012, 136, #256, and 203; and Figg. 12 & 13).

3.9.7 Plain Tubes/​Pipes (Employed for a Variety of Purposes) Tubes served to protect surrounding tissue from probe-​like cauteries and, occasionally, were themselves employed as cauteries. Wide bored models were also found handy for freeing the barbs of missiles from surrounding tissue in the course of weapons extraction (Paul 6.88.4). And in treating the growth called myrmekia, Paul (6.87.1) burrows under and levers up the growth “with a small tube (suringion /​συρίγγιον) of copper alloy or iron/​steel.” Elsewhere tubes are employed for fumigation, especially in the Hippocratic

574   Hellenistic Greek Science gynecological treatises (e.g., Diseases of Women sec. 133.39–​62 [Littré 8.284–​286]), as straws for preparing and imbibing medications (Aëtius 7.106.43–​46), attached to a blacksmith’s bellow to inflate in cases of ileus (Alexander of Tralles, Therapies 2.363.13–​ 23 Puschmann), to blow medication into the nose and throat (Oribasius, Synopsis to his Son Eustathius 7.20.15), or to suck water from an ear (Alexander of Tralles, Therapies 2.97.7 Puschmann). From the Hippocratics (Diseases 2.59 Potter) to the late empire, we encounter tubes to prevent contraction and adhesion in the body’s orifices. In some cases they were anointed with medicament to treat the afflicted part. Such tubes might be inserted postoperatively into the nose (Paul 6.25.3), rectum (Antyllus and Heliodorus, in Oribasius, Medical Compilations 44.20.72), vagina (Celsus 7.28), urethra (Oribasius, Medical Compilations 50.9.8–​15), and between the glans penis and foreskin (Paul 6.55.2). They went by various names, most already familiar, including auliskos, suringion, sōlēn /​ σωλήν and its diminutives, and the Latin fistula. Tubes/​pipes of copper alloy have passed down to us that are suitable for some of these applications. These might be seen in the two in Naples cited above, one and probably both from the House of the Surgeon in Pompeii (see figure C16.1, bottom row, far left), and in the gilded bronze tube recovered at Nea Paphos (Michaelides 1984, 320, #30). The instrumentarium of the so-​called Surgeon of Paris contains a tube featuring a small shovel at one terminus designed especially for insufflation (Künzl 1983a, 77, #26). Many of the references cited here require tubes of lead or tin. The reason for this is probably that lead and tin are malleable, and the treatments under consideration may have required remolding the tube to suit the intended operation and the anatomy of different patients.

3.10 Gynecological/​Obstetrical Instruments 3.10.1 Uterine Douche In the literary sources a number of conditions are treated with douching. Some examples in Aëtius 16: irregular menstruation (61.41), hysterical suffocation (67.107), uterine inflation (73.31), uterine edema (74.21) and watery genital discharge (104.3). The first detailed description of a tube attached to a bladder used in injecting solutions into female genitalia is described in the Hippocratic Corpus (Diseases of Women sec. 222.11–​25 [Littré 8.474]). This is said to have a solid tip of silver and, after an opening nearby, a series of openings at intervals along the side of the tube. The multiple perforations appear to have remained a standard feature of the design and the name applied to have been mētrenchutēs /​μητρεγχύτης or “uterine injector” (Paul 4.57.15). While Galen and other authorities favor this particular tube as an instrument designed for uterine injections (Compounds by Place 10.8 [Kühn 13.316]), they also allow for the regular bladder-​driven clyster with a plain tube (Oribasius, Selected Remedies 147.14). Several tubes of copper alloy in the Naples Museum are mounted on cup-​like cylinders and feature a series of holes running the lengths of their shafts (figure C16.1, bottom row, middle, above awl). These might have served for anal injection; but, as they answer

Greco-Roman Surgical Instruments   575 perfectly to the injection tube recommended in Hippocrates and Paul and, as at least one of them (and very possibly both) were recovered along with gynecological instruments in Pompeii (Bliquez 1995), we are justified in thinking of them as representing the mētrenchutēs. Also worthy of mention is a tapering tube with numerous lateral perforations and a flanged upper rim (see sec. 3.9.1, “Clyster Tubes”) in the Smithsonian Institution, Washington DC. It is said to come from Jerusalem (Bliquez 1998, 89–​92).

3.10.2 Uterine Specula Treatment of female conditions, for example, uterine growths, cancer, ulceration, and abortion required dilation providing access to female internal genitalia. The uterine speculum (dioptra /​δίοπτρα) was applied in such situations. Consisting of a series of valves expanded by the turning of a worm/​screw, this large (as much as 31 cm in length) speculum is the most intricate of all Greco-​Roman surgical tools. Appropriately, it receives wide treatment in Imperial literature that is matched by the number of well-​ preserved survivals, first and foremost at Pompeii (figure C16.1, middle row, right). Three clinical houses in that city have produced two examples of the standard trivalve model and the sole preserved quadrivalve (Bliquez 1995). In all, nine intact specimens are securely identified, one possibly Byzantine (Künzl 1992). The Pompeian specula were manufactured before the disaster of 79 ce. It tempting to see such intricate tools as the creation of Hellenistic Alexandria, a center of substantial advances in understanding human anatomy, specifically interest in gynecology and screw-​driven devices as well (Bliquez 2010, 36). The rectal (hedrodiastoleus /​ ἑδροδιαστολεύς), perhaps also a product of Hellenistic Alexandria, is a smaller bivalve speculum operated by compressing its handles, as one might a pair of pliers. In addition to being useful for dilating the rectum to treat hemorrhoids and fistula, this bivalve also appears useful for dilation of the female genitalia. The language of Imperial authorities allows for such use (Paul 6.78.4, “to dilate the rectum with the hedrodiastoleus . . . as we do the vagina”), and one of the two Pompeian specimens (figure C16.1, middle row, 5th from left, 18 cm in length) was recovered in a gynecological context, that is, in the company of a trivalve, a birthing hook and a clyster for douching (Bliquez 1995). The instrument may also have been used to treat wounds. Celsus (7.5.2B) records a dilation of a wound to extract an embedded missile, a device he compares to a letter of the Greek alphabet. The figure of the letter has dropped out of the text; but if that letter was an uppercase upsilon (Υ), that would perfectly match the shape assumed by the small dilator when its valves are open (Jackson 1991). It is just possible that the rectal speculum was developed even earlier. In its treatment of piles, the Hippocratic treatise Hemorrhoids 5 (Potter) refers to a katoptēr /​κατοπτήρ (tool for inspecting) as “being opened,” terminology that allows for a speculum operating on a pivot. Altogether 11 bivalve specula survive.

3.10.3 Ring Knife for Dismembering Impacted Fetus The Christian apologist Tertullian refers in passing to a ring knife, or anulocultrus, used in abortion (De anima 25.5). As he mentions Hippocrates in the same context, he may have in mind the “claw,” or onux, mentioned in Superfetation sec. 7.5 (Littré 8.480). This

576   Hellenistic Greek Science instrument may have existed in Galen’s time as he remarks on a contemporary onux in his Hippocratic Glossary (Kühn 19.107, re: ichthuē /​ἰχθύη): “He/​it could also mean the iron/​steel onux we use in aborting the fetus by extraction (embruoulkia) and cutting (embruotomia).” This language allows for an embryo hook or a hook-​like knife, as well as for the Hippocratic knife attached to a ring. Celsus mentions such a hooked knife to cut through the neck in dismemberment of a fetus (7.29.7).

3.10.4 Stylet for Opening the Cranium of an Impacted Fetus In the passage mentioned immediately above, Tertullian also attests an instrument for dispatching an impacted fetus prior to aborting it. He calls the instrument a “little spike of copper alloy” (aeneum speculum) but says Greeks call it embruosphaktes (embryo killer). Unfortunately, Tertullian does not describe the tool. “Little spike” (and, by metonymy in Latin, “arrow” or “javelin”) suggests a needle, and that identification has received some support. On the other hand, all other testimonia to perforation of an infant’s skull in abortion, whether the infant is alive or dead, involve knives: polyp knife, sharp, pointed knife, and so forth. It may be therefore that a scalpel/​lancet assumed a special name like embruosphaktes when used for this particular purpose.

3.10.5 Cranioclast We first hear of a cranioclast in the Hippocratic Diseases of Women sec. 70.1–​7 (Littré 8.146–​148). There a dead and bloated fetus is removed with the help of a “squeezing tool” (piestron /​πίεστρον) to crush the infant’s head prior to pulling out the rest of the corpse. Galen in his Hippocratic Glossary (Kühn 19.104, 130, re: piestron) equates the name with embruothlastēs (embryo crusher), the name used in his time. Both names favor a plier-​ like apparatus. An element of such an instrument, thought to be Byzantine based on its peculiar linear décor, is unfortunately now lost (figure C16.16; Künzl 1992, 203–​205). Similar décor links it to a hook of copper alloy serrated on its inner side, which could serve as an embryo hook and/​or a lithotomy hook.

3.10.6 Embryo Hook (embruoulkos /​ ἐμβρυουλκός, uncus) Another device for aborting a deceased or an impacted fetus was a special retractor/​ hook described by Celsus as being “everywhere smooth with a short dull point.” His account (7.29.4–​8) and that of Soranus (Gynecology 4.9–​11 Ilberg = 4.5.1–​108 Burguière, Gourevitch, and Malinas) are primary. Such a device goes as far back as the Hippocratic treatise Diseases of Women (sec. 70.1–​7 [Littré 8.146–​148]), where it is referred to as an helkustēr (ἑλκυστήρ, or puller). Basically, the Imperial procedure involved insertion of the hook by the physician in a suitable place, such as the fetus’ eye or collarbone. Sometimes a second hook was set, both hooks being turned over to an experienced assistant who drew on them steadily, sometimes pulling them from side to side, while the physician maneuvered the position of the fetus. As the operation progressed, amputation or evacuation of parts of the fetus might prove necessary. Four sturdy hooks of iron (now mostly gone) pegged into handles of copper alloy have come to light at Pompeii (figure C16.2, middle row, far right; cf. figure C16.16). One and likely all were recovered in instrumentaria, including specula and other instruments of gynecology (Bliquez 1995).

Greco-Roman Surgical Instruments   577

3.10.7 Strigil or Spoon Used as Uterine Curette The Hippocratic author of Nature of Women (42 Potter) prescribes winding a bit of membrane around a “scraper” (xustra /​ ξύστρα) to curette thrombi formed on the cervix. It is uncertain whether a small strigil or some spoon-​like scraper is at issue. While there is no such operation in the preserved literature of the empire, it has been proposed that the curette types with smooth and serrated spoons cited in sec. 3.8 “Bone and Tooth Instruments” may have served as uterine curettes in addition to work on bone.

4. Conclusion These were the tools that surgeons of the Greco-​Roman world wielded. Given their variety and high quality, it is not difficult to understand why they are sometimes perceived as modern (Lyons and Petrucelli 1980, 534). It is therefore fitting that their names and, in some cases, their actual forms are still in use today, not to mention the very name of the activity they made possible: cheirοurgia (handiwork), or in the English language “surgery.”

Figure C16.1  Instruments from Vesuvian cities (shortly before 79 ce). Alinari Photo, no. 19086. Late 19th century.

Figure C16.2  Instruments from Vesuvian cities (shortly before 79 ce). Alinari Photo, no. 19087. Late 19th century.

Figure C16.3  Instrumentarium from Italy. Length of longest catheter 30.25 cm. 1st to early 2nd century ce. Photo courtesy of the British Museum.

Figure C16.4a  Cupping vessel, Corinth. Height 9.1 cm, ca 500 bce. National Archaeological Museum of Athens. Photo by author.

Figure C16.4b  Cupping vessel, Tanagra. Height 14.8 cm. Traditionally dated 500 bce but probably Hellenistic. National Archaeological Museum of Athens. Photo by author.

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6

2 5

7 8

4 3 20cm

10 9

10

11

12

0 13

Figure C16.5  Scalpel, forceps, and retractor types, Domus del Chirurgo, Rimini. 3rd century ce. Drawings by Ralph Jackson as they appeared in Ars Medica 2009.

Figure C16.6  Scalpel handle with ivy pattern damascened in silver and copper, Asia Minor. 2nd century ce. Photo: Römisch-​Germanisches Zentral Museum.

Figure C16.7  Tonsil knives, Domus del Chirurgo, Rimini. 3rd century ce. Drawing by Ralph Jackson.

Figure C16.8  Portion of instrumentarium allegedly from Ephesus. (Left to right): three sharp retractors, sharp retractor converted from stylus, double needle, spatula probe, lancet cautery, three spoon probes (two with roughened interiors), two-​prong stone retractor, and two lithotomy knives. Retractor at far left is longest item at 17.4 cm; retractor fourth from left is shortest at 8.1 cm. First half, 3rd century ce. Römisch-​Germanisches Zentral Museum, Mainz. Photo: Römisch-​Germanisches Zentral Museum.

Figure C16.9  Ophthalmic needles with container, dredged from river Saône (Montbellet), 1st–​ 2nd century ce. Length of container without lid 18 cm; length of longest needle 16.5 cm. Photo: Römisch-​Germanisches Zentral Museum.

Figure C16.10  Lunated cautery, Bingen-​am-​Rhein. Length 9.5 cm. First half 2nd century ce. Photo courtesy of Stadtverwaltung Bingen/​Rhein.

18

14 15

16 17

20cm

10 21

20

22

23

0

19

Figure C16.11  Instruments for bone surgery:  stump forceps (14), two sequestrum forceps (15‒16), blunt retractor probably serving also as bone guard (17), bone lever (18), chisel handle (19), bow drill (20), gouge (21), lenticulars (22‒23), Domus del Chirurgo, Rimini. Drawings by Ralph Jackson as they appeared in Ars Medica 2009.

(a)

2

3

1

(b)

Figure C16.12  Bow with crown drills, Bingen-​am-​Rhein. First half 2nd century CE. Drawing by Ralph Jackson.

Figure C16.13  Perforated tube, allegedly from the Holy Land (Roman Imperial era). Length 9.7 cm. Drawing by Alexander Hollmann.

Figure C16.14  Injection tube, likely puoulkos, Nea Paphos. Length 20.2 cm. Mid-​2nd to early 3rd century ce. With the kind permission of the Director of the Department of Antiquities Cyprus. Drawing by K. Kapitanis.

Figure C16.15  Scalpel handle and four bone levers/​elevators, Bingen-​am-​Rhein. Length (left to right) 10‒17.5 cm. First half 2nd century ce. After Como 1925.

Figure C16.16  One element of a cranioclast (now lost and as restored), and an embryo and/​or lithotomy hook, allegedly from Ephesus (Late Roman to Early Byzantine). Lengths 17 and 15.5 cm. Photo: Römisch-​Germanisches Zentral Museum.

Figure C16.17  Scoop of Diocles (?) Length 11 cm. Drawing by Alexander Hollmann.

Greco-Roman Surgical Instruments   587

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Greco-Roman Surgical Instruments   589 Jakielski, Katherine E., and Michael R. Notis. “The Metallurgy of Roman Medical Instruments.” Materials Characterization 45 (2000): 379–​389. Johnston, Ian, and G. H. R. Horsley, ed., trans. Galen, Method of Medicine. 3 vols. Cambridge, MA, and London: Harvard University Press 2011. Krug, Antje. “Römische Skalpelle, Herstellungstechnische Anmerkungen.” Medizinhistorisches Journal 28.1 (1993): 93–​100. —​—​—​. Das Berliner Arztrelief = Winckelmannsprogramm der Archäologischen Gesellschaft zu Berlin, 142. Berlin: de Gruyter, 2008. Krunić, Slavica. “Why and How Silver Had Been Used in the Manufacture of Medical Instruments.” In Silver Workshops and Mints, Symposia Acta, Nov. 15‒18, 1994, National Museum Belgrade, ed. Ivana Popović, Tatjana Cvjetićanin, and Bojana Borić-​Brešković, 216–​ 217. Belgrade: Musée National de Belgrade, Monograph no. 9, 1995. Künzl, Ernst. With the collaboration of F. J. Hassel and S. Künzl. Medizinische Instrumente aus Sepulkralfunden der römischen Kaiserzeit. Sonderdruck aus den Bonner Jahrbüchern 182 (1982). Repr. Bonn: Habelt, 1983a. —​ —​ —​ . “Eine Spezialität römischer Chirurgie:  Die Lithotomie.” Archäologisches Korrespondenzblatt 13 (1983b): 487–​493. —​—​—​. “Einige Bemerkungen zu den Herstellern der römischen medizinischen Instrumente.” Alba Regia 21 (1984): 59–​65. —​—​—​. “Operationsräume in römischen Thermen.” Bonner Jahrbücher 186 (1986): 492–​509. —​—​—​. “Spätantike und byzantinische medizinische instrumente.” In From Epidaurus to Salerno, Symposium Held at the European University Centre for Cultural Heritage, Ravello, April, 1990, ed. Antje Krug, 201–​244. PACT, Journal of the Centro Universitario Europeo per i Beni Culturali 34, 1992. Longfield-​Jones, G. M. “Uses of Metals, their Compounds and Alloys.” In Mining and Metallurgy in the Greek and Roman World, ed. J. F. Healy, 246–​251. London: Thames and Hudson, 1978. Lyons, Albert S., and R. Joseph Petrucelli. Die Geschichte der Medizin im Spiegel der Kunst. Köln: Dumont Reiseverlag, 1980. Michaelides, Demetrios, “A Roman Surgeon’s Tomb from Nea Paphos,” In Report of the Department of Antiquities Cyprus, pt. 1, 315–​332. Nicosia, Cyprus: Dept. of Antiquities, and Zavallis Press, 1984. Olivieri, Alexander, ed. Aetii Amideni Libri medicinales I‒IV. Leipzig, Berlin: Teubner, 1935. Pantermalis, Demetrios. “Η ΑΝΑΣΚΑΦΗ ΤΟΥ ΔΙΟΥ ΚΑΤΑ ΤΟ 1983 ΚΑΙ Η ΧΑΛΚΙΝΗ ΔΙΟΠΤΡΑ.” ΤΟ ΑΡΧΑΙΟΛΟΓΙΚΟ ΕΡΓΟ ΣΤΗ ΜΑΚΕΔΟΝΙΑ ΚΑΙ ΘΡΑΚΗ 7 (1993 [1997]):  195–​198. [Published in Thessalonika, by the Ministry of Culture, Ministry of Macedonia and Thrace, The Aristotelian University of Thessalonica; see: http://​www.aemth. gr/​el/​.] Penn, R. G. Medicine on Ancient Greek and Roman Coins. London: Seaby/​Batsford, 1994. Potter, Paul, ed. and trans. Hippocrates. Vols. 5–​6, 8–​10. Cambridge, MA: Harvard University Press, 1988, 1995, 2010, and 2012. Puschmann Theodor, ed., trans. Alexander von Tralles:  Original-​ Text und Übersetzung nebst einer einleitenden Abhandlung. Ein Beitrag zur Geschichte der Medizin, 2  vols. Vienna: Braunmüller, 1878–​1879; repr. Amsterdam: Hakkert, 1963. Raeder, J., ed., Oribasii collectionum medicarum reliquiae. 5 vols. Corpus medicorum graecorum 6.1–​3. Leipzig, Berlin: Teubner, 1926–​1933. Salazar, Christine F., “Getting the Point: Paul of Aegina on Arrow Wounds.” Sudhoff ’s Archive 82.2 (1998): 170–​187.

590   Hellenistic Greek Science Scarborough, John, Roman Medicine. Ithaca, NY: Cornell University Press, 1969, repr. 1976. Sconocchia, Sergio, ed. Scribonii Largi compositiones. Leipzig: Teubner, 1983. Spencer, W. G., trans. Celsus: De medicina. 3 vols. Cambridge, MA: Harvard University Press; London: Heinemann, 1935–​1938. Spink, M. S., and G. L. Lewis, trans., comm. Albucasis on Surgery and Instruments. Berkeley, Los Angeles: University of California Press, 1973. Spawforth A. J. S. “Roman Medicine from the Sea.” Minerva 1 (1990): 9–​10. Waszink, J. H, ed. Quinti Septimi Florentis Tertulliani De anima. Amsterdam: Meulenhoff, 1947; repr. Leiden, Boston: Brill, 2010. Weaver, David S., George H. Perry, Roberto Macchiarelli, and Luca Bondioli. “A Surgical Amputation in 2nd Century Rome.” Lancet 356 (Aug. 19, 2000): 686. Witt, Mathias. Weichteil und Viszeralchirurgie bei Hippokrates: Ein Rekonstruktionsversuch der verlorenen Schrift ΠΕΡΙ ΤΡΩΜΑΤΩΝ ΚΑΙ ΒΕΛΩΝ. Berlin, New York: de Gruyter, 2009. Zervos, Skevos, ed. Gynäkologie des Aetios sive sermo sextus decimus et ultimus: zum erstenmale aus Handschriften veröffentlicht. Leipzig: Fock, 1901. [Aëtius, book 16.]

D

G R E C O -​ROM A N SCIENCE

chapter D1

Traditional i sm a nd Original i t y i n Rom an Sci e nc e Philip Thibodeau

Everyone loves a good story, but not everyone wants to be part of one. In ancient Greece a culture of kleos touched many with a desire to be part of whatever story future historians might tell. This ambition motivated scientists and doctors no less than statesmen and generals. Take, for instance, this boast attributed to the elderly Democritus (88 DK B 299): Of all the men in my lifetime I  have traveled over the greatest part of the earth, investigated to the widest extent possible, and seen the most climates and lands, and apprenticed myself to the most learned men, and no one ever surpassed me in the composition of lines accompanied by geometric proofs, not even the so-​called “cord-​joiners” of the Egyptians, with whom I was on friendly terms for a total of eighty-​five years.

Like an intellectual Odysseus, the philosopher has toiled for his wisdom, setting a new standard he wants people to remember. The glorification of individual achievements, whether one’s own or those of others, colors the ancient record in ways that now make it easy, sometimes too easy, for scholars to write a history about the evolution of Greek study of the natural world. Bold ideas of every kind, from the novel cosmologies of the pre-​Socratics to the grand syntheses of Ptolemy and Galen, dot the record; the biographical tradition provides needed dates and context. The Greeks wrote their own accounts of intellectual progress, like the one that opens the Hippocratic treatise On Ancient Medicine, or the histories of astronomy and geometry compiled by Aristotle’s student Eudemus (Zhmud 2006). All the ingredients for a good story are already there. By contrast, when we come to Roman science and medicine (by which I specifically mean works aimed at understanding or controlling nature that were composed

594   Greco-Roman Science in Latin), it becomes much harder to corral the actors into a good story. One reason was a deep cultural habit that discouraged Roman intellectuals from presenting their own ideas as original or putting themselves at the culmination of a progressive tradition. Valorization of the mos maiorum and devotion to ancestors was a central feature of Roman culture, which among other things spawned a conviction that voices from the past possess more authority than those of the present. Vitruvius, speaking specifically about technical writers, says (9.pref.17):  “The opinions (sententiae) of learned authors, though their bodily forms are absent, gain strength as time goes on, and, when taking part in councils and discussions, have greater weight than those of any living men.” The corollary of this view is that any living-​and-​breathing Roman writer, trapped in his present day, could only advance views that would initially occupy the weakest possible position in terms of authority. Hence the elaborate self-​deprecation visible in the prefaces of many writers who play down their abilities and justify intellectual projects, not in their own terms, but by appeals to the author’s respectable use of leisure time or practical benefit to society (Janson 1964). Hence, boasts of novelty confined mainly to matters of language, presentation, or (think of Pliny) scope; ideas celebrated and championed only when they belong to figures from the past; and new ideas praised for being revivals of old ones. Roman writers tend to bury their observations and insights deep within their texts; brilliant conjectures—​the precession of the poles leads to climate change (Columella 1.1.4–​5), diseases are caused by organisms too small for the eye to see (“animalia quaedam minuta, quae non possunt oculi consequi”: Varro, Farming 1.12.2–​4; Sallares 2002, 55–​65)—​ are tossed off casually and not followed up. The effects of this attitude go right to the heart of our primary sources. There are exceptions to these rules, and acknowledgment of the authority of the past did not preclude debate and disagreement with it. But in general, Latin technical writers idealize established tradition in ways that serve to efface their own contributions. To illustrate this premise, the present article shows how Roman intellectuals from various ages put original ideas into circulation by ascribing them to a pair of individuals from the ancient period: Rome’s second king, Numa Pompilius, and the philosopher Pythagoras. These two figures were the oldest sources of technical knowl­ edge most Romans were familiar with, and thus the most authoritative. In our earliest texts Numa, Pythagoras, and a handful of Pythagoreans are the only sources regularly named. Most of these attributions were in fact confabulations; they were made to bestow legitimacy on original ideas or deflect attention from the modernity of the author’s sources. Since the range of studies Numa and Pythagoras could be plausibly given credit for was broad but not all-​embracing, there was a limit to the number of sciences that could explored under their auspices; initially these included the fields of calendrics, astronomy, four-​element theory, and medicine. In time this constraint was loosened, eventually expanding to a point where everything from paradoxography to metaphysics could be made to fit. The history of this practice is sketched here from the second century bce to the beginning of the first century ce; the focus lies on two periods of activity which bookend

Traditionalism and Originality in Roman Science    595 a long lull. Despite its erratic nature and fundamental disingenuousness, this early habit of doing science through the retrojection of ideas shaped the way Romans organized knowledge and left a visible imprint on Latin-​language science of the Empire and Middle Ages.

1.  Two Wise Men While Romulus, the first king of Rome, was, to the Romans, the prototypical patriarch, creator of hierarchies and master of the arts of war, his successor Numa Pompilius spoke to a different side of the culture, inaugurating customs designed to promote peace among the citizenry and good relations with the gods. Numa encouraged the Romans to farm, devised ritual procedures and ceremonial protocols, and founded several colleges of priests and augurs, including the cult of the Vestal Virgins. His activities impinged on the realm of natural sciences when he established observances designed to fix spatial and temporal boundaries. Numa introduced the cult of Terminus at Rome, a faceless deity whose main charge was to protect the stones that separate one property line from another; the special attention given to this function early on spurred the Romans’ subsequent devotion to proper surveying when laying out army camps, towns, and colonies settled on conquered land (Gargola 1995). Tradition also credited Numa with the creation of a 12-​month calendar that improved the 10-​month calendar of Romulus and kept the year in closer alignment with natural cycles; this remained in use largely unchanged until Julius Caesar’s calendar reform. Unlike the self-​taught Romulus, Numa received instruction in wisdom; his teachers included a goddess who was sometimes identified as Egeria, a local water spirit, and sometimes as Ca(s)mena, an Italic deity equated with the Greek Muse. Some legends spoke of him wresting secret knowledge from gods such as Faunus, Picus, and even Jupiter himself (Ovid, Fasti 3.259–​392). But the only mortal teacher ever assigned to Numa was the philosopher Pythagoras. The Romans were happy to give the Greek thinker a key role in the early story of their city thanks to his school’s presence on Italian soil; the sacred character of the Pythagorean way of life, with its stress on ethics, observance, and secrecy, was also approved and seems to have motivated the specific association with the priestly Numa. Roman appreciation for the wisdom of Pythagoras can be traced to ca 300 bce when a statue in his honor was dedicated at the edge of the Forum, in obedience to an oracle that required the Romans to pay tribute to the wisest of the Greeks (Pliny 34.26); the story of Pythagoras’ tutoring of Numa probably originated about this time (Humm 2014). By the 1st century bce, serious Roman scholars recognized that Numa’s putative date (ca 725 bce) was several generations earlier than Pythagoras’ (ca 525 bce), but the tradition survived serial debunking, a telling indication of its age and popularity. Like Numa, Pythagoras left behind nothing in writing (Burkert 1972, 218–​220). Numa’s doctrines were preserved by the priestly colleges he founded, while Pythagoras’

596   Greco-Roman Science were transmitted through his students. Paying implicit heed to this fact, most forgers of Hellenistic pseudo-​Pythagorea ascribed their works to Pythagoras’ early followers, such as Brontinus, Archytas, Epicharmus, Timaeus, and Ocellus (Thesleff 1965b). The “silences” of Numa and Pythagoras added to their mystique and gave those who would invoke their authority considerable interpretative license. As we will see, Roman Pythagoreanism preserves very few genuine doctrines of Pythagoras and the old Pythagoreans (Kahn 2001); most attributions of doctrine to Numa must likewise be taken with a large grain of salt. Indeed, the ideas ascribed to these ancient thinkers often turn out to be quite modern.

1.1 Marcus Fuluius Nobilior One of the earliest encounters between native Roman wisdom and mainstream Greek science took place in the domain of material culture. After the sack of Syracuse in 212 bce, which claimed the life of Archimedes, the Roman general Marcus Claudius Marcellus took from the plundered goods of the city two astronomical “spheres” that Archimedes had designed. One was a globe inlaid with images of the constellations, an object perhaps like the Farnese Atlas, but made of bronze rather than marble (Cicero Republic 1.21). Marcellus put this star-​globe on display in Rome inside the temple of Virtue and Honor, where it shared space with a very ancient bronze shrine of Casmena said to have been made by Numa himself (Seruius, Commentary on Aeneid 1.8). This juxtaposition of modern cosmos and ancient Casmena echoed a popular motif from Hellenistic art that showed the Muse Urania accompanying a celestial globe (Brendel 1977). Another Roman military conquest—​of Ambracia, in 187 bce—​led to a more elaborate symbolic display. The victorious general, Marcus Fuluius Nobilior, dedicated a temple to “Hercules of the Muses” (Richardson 1992, 187). He furnished it with statues of the Muses taken from Ambracia (Pliny 35.66), and moved Numa’s shrine of Casmena from Marcellus’ temple to the new building (Seruius, Commentary on Aeneid 1.8). Finally, Fuluius had painted or inscribed on the walls a full edition of the Roman calendar (Macrobius, Saturnalia 1.12.16). Calendars had been published before at Rome, but in a format akin to law codes, bare lists of labeled dates (Michels 1967). Fuluius’ publication was innovative in two ways: it was set up in a sacred space, and it was accompanied by commentary. This commentary explained the roles that Romulus and Numa had in naming the months and furnished their reasons for choosing the names (Rüpke 2012, chap. 11). The text was the first written source to give Numa credit for completing Rome’s 12-​month calendar, a claim sanctified by the presence of his sacred relic. It may also have explained how Numa decided on the number of days to give each month; one of his stated principles was to create more months with odd numbers of days, in accordance with the Pythagorean doctrine that odd numbers are lucky (Michels 1967, 124). This would represent the first attempt we know of to explain some aspect of Roman technical lore in terms of Pythagorean teaching.

Traditionalism and Originality in Roman Science    597 Aside from work on the calendar, Fuluius contributed to Roman intellectual life through his patronage of the poet Quintus Ennius, best known as the author of the Annales, the first historical epic composed in Latin hexameters. The epic opened on a boldly Pythagorean note, with the shade of Homer appearing to Ennius in a dream to declare that he had gone through several cycles of reincarnation before entering the poet’s body (fr. 2–​11 Skutsch). Ennius also recounted the story of Egeria and Numa (fr. 113), and noted, in passing, that a solar eclipse is caused by the interposition of the moon (fr. 153). In a separate poem named after the Syracusan dramatist-​cum-​philosopher Epicharmus, Ennius spoke about the four basic elements and the four qualities, the elemental constituents of soul and body, and the transformations of air into wind, wind into cloud, cloud into rain, and vice versa (Warmington 1935, 410–​415). Although four-​element theories were developed by several Greek philosophers (Plato, Aristotle, the Stoics), Roman sources tend to ascribe the idea to Pythagoreans, as, for instance, Lucretius (4.712–​721), Vitruvius (2.2.1), and Ovid (Metamorphoses 15.237–​251) do. These bits of natural philosophy may seem harmless, yet in 181 bce a curious incident revealed that, in some quarters, efforts to make hay out of the supposed ties between Pythagoras and Numa were unwelcome. That year a farmer digging trenches in a field below the Janiculum turned up two large stone chests. Inscriptions indicated that one contained the remains of Numa and the other his books. While the chest with the remains turned out to be empty, the other yielded two sets of papyrus rolls in mint condition, seven discussing pontifical law in Latin, and seven treating “Pythagorean” philosophy in Greek. The discoverer eagerly read the books and circulated them among his friends. Once the urban praetor got wind of this, he confiscated the texts, reviewed their contents, and ordered that they be burnt, declaring them detrimental to religion. After hearing an appeal from the farmer, the Senate upheld the praetor’s decision and allowed all the books to be cremated in public (Livy 40.29.9–​14, Pliny 13.84–​87). It is almost certain that these texts were forgeries, given their state of preservation, and the discovery itself some kind of hoax. But who staged it, and why? Not knowing who the authors were, we cannot be sure of its original purpose (Rowse 1964). Yet the official decision to have the books burned shows that the melding of Pythagorean thought and Roman tradition that Nobilior and others were trying to promote struck more conserv­ ative Romans as a dangerous thing. Still, the practice continued.

1.2 Gaius Sulpicius Gallus and Pythagoras The dynastic dreams of Philip II and Alexander the Great were finally extinguished on June 22, 168 bce, in a battle that pitted Greeks against Romans near the small Thessalian town of Pydna. The Greek forces were led by the Macedonian king Perseus, while the Romans were led by L. Aemilius Paullus, who, in one of history’s fine ironies, was a devoted Hellenophile (Gruen 1992, 245–​248). On the night before the battle a lunar eclipse took place that unnerved both armies; Paullus moved to calm the fears of his troops by conducting sacrifices (Plutarch, Aemilius 17.7–​12). The next morning, with anxieties

598   Greco-Roman Science over the omen lingering, Paullus invited an officer named G. Sulpicius Gallus to explain to the army what they had seen. Gallus, an amateur astronomer, made clear that the eclipse was a natural event that occurs from time to time whenever the earth lies between the moon and sun (Cicero, Republic 1.23–​24). The soldiers took heart from this lecture and marched off to win a victory that put Greece under Roman control. The next year Gallus was elected consul, and the eclipse story ended up becoming a classic illustration of the triumph of science over superstition (Pliny 2.53–​55). Gallus, a dedicated scholar of Greek literature (Cicero, Brutus 78), wrote a book later in his life on the subject of eclipses (Pliny 2.53; cf. 1.2). The book cited Pythagoras as a source; to see what “Pythagoras” said, we need to review Gallus’ astronomical knowl­ edge. The elderly Gallus reportedly possessed the ability not just to explain eclipses but also to predict them (Cicero, On Old Age 49): “How much enjoyment he got from foretelling eclipses of the sun and moon for us!” This ability helped spawn a variant of the Pydna story in which Gallus was able to foretell the eclipse to the troops before it occurred; however, this improved account only appears in late sources and is best regarded as a fiction (Bowen 2002). The idea that a Roman statesman might be able to predict eclipses at any point in his life may seem far-​fetched, yet there are good reasons to take it seriously. An anecdote from Cicero’s Republic points to a source for Gallus’ predictive skills (1.21–​22). According to the story, Gallus was gathered with several other men at the house of Claudius Marcellus’ grandson when the appearance of an omen was reported. He asked for the sphaera of Archimedes that grandfather Marcellus had looted from Syracuse to be brought out of storage—​not the famous constellation globe in the temple of Honor and Virtue, but another device which, while much less impressive in appearance, turned out on closer inspection to be even more incredible, containing parts that represented the motions of the sun and the stars and the five planets. It had been built in such a way that a single turn of an input device would cause the celestial bodies to move (22): When Gallus set this sphaera moving, it happened that, in the bronze-​work, the moon followed the sun through as many cycles as it does in the actual sky; as a result solar eclipses occurred in the sphaera, and the moon encountered the cone which is the earth’s shadow, with the sun opposite.

The sphaera described here sounds remarkably like the Antikythera device, the famous box-​shaped calculator that Greek divers recovered from a shipwreck off the coast of the island Antikythera in 1900 (Freeth 2009). Both mechanisms had displays showing the relative motions of the sun, moon, and planets; Archimedes’ device represented lunar and solar eclipses, while the Antikythera mechanism included a dial on its back panel that forecast lunar and solar eclipses based on the Saros cycle, most accurately during the period 205 to 187 bce (Carman and Evans 2014). Both instruments were made of bronze and relied on a single rotary input. The device made by Archimedes would have been constructed in Syracuse before 212 bce; the Antikythera device was probably built later, perhaps in Rhodes. The Syracusan device Gallus was using seems to

Traditionalism and Originality in Roman Science    599 be an earlier version of the instrument, with a different display but similar functionality. Despite the intricacy of its construction, it would not be beyond the ability of an informed and intelligent amateur to operate. Gallus’ access to Archimedes’ sphaera makes plausible his late-​life hobby of eclipse prediction. (How accurate his predictions were is not recorded.) Cicero reports that the elderly Gallus also devoted himself to “measuring out nearly every bit of the sky and earth” (On Old Age 49). Pliny provides some specifics (2.83): “Pythagoras, who was a man of great wisdom, deduced that the distance from the earth to the moon is 126,000 stades, that the distance from the moon to the sun is double this, and the distance [sc. from the sun] to the zodiac, triple; our countryman Sulpicius Gallus held the same view.” Now the fi ­ gure 126,000 stades is exactly one-​half of Eratosthenes’ estimate of the diameter of the earth. If we call the earth’s radius r, we can represent this system thus: Earth radius Earth to moon Moon to sun Sun to zodiac Total radius of the heavens

1r 1r 2r 3r 7r

126,000 stades 126,000 stades 252,000 stades 378,000 stades 882,000 stades

These ratios and distances are far too small to have come from any mainstream Hellenistic astronomer—​Eudoxus, who stood at the head of the measurement tradition, considered the sun to be nine times larger and farther away than the moon, Aristarchus made it 19 times larger and more distant, and Posidonius put the earth‒moon distance at two million stades. Yet this scheme cannot be ancient, since it draws on the work of Eratosthenes for its basic unit of measure. Gallus (cos. 166) was probably a teenager in the year Eratosthenes died (194), which leaves little room, time wise, for an intermediate source. It would seem Gallus put together this sun-​moon system himself, ascribing it to Pythagoras in the treatise he wrote on lunar and solar eclipses. Gallus’ 1r–​2r–​3r sequence breaks down the “perfect” number 6 in a way that reflects Pythagorean numerology (Censorinus 11.4). Another noteworthy aspect of the scheme is its situation of the sun exactly midway between the surface of the earth and the fixed stars. In Greco-​Roman astronomy there were two main traditions about the order of the sun, moon, and planets. Most older authorities, including Philolaus, Eudoxus, Plato, Aristotle, and Eratosthenes, took the order to be Moon-​Sun-​Venus-​Mercury-​Mars-​Jupiter-​Saturn. During the Hellenistic era an alternative arrangement gradually won out that put the sun in the middle: Moon-​Mercury-​Venus-​Sun-​Mars-​Jupiter-​Saturn. Our earliest named source for this revised order is Archimedes (Osborne 1983); the inscription on the Antikythera device also employs it (Freeth and Jones 2012). Since Gallus was familiar with a sphaera of Archimedean manufacture, his placement of the sun midway between the earth and stars likely reflects the influence of the latter. Indeed, the possibility exists that he derived his values for the relative size of the lunar and solar orbits by simply looking at the dial on his machine and naively measuring the distance between the indicators.

600   Greco-Roman Science To sum up: Gallus’ scheme for cosmic distances drew on two results from the most advanced astronomical investigations of his day, Eratosthenes’ measurement of the earth and Archimedes’ revision to the sequence of the planets. Yet he seems to have presented this system as Pythagoras’. The ascription would have lent an air of authority to his figures, but served to obscure the nature of his own contribution. As we shall see, Gallus’ “Pythagorean” distances left a mark on later Roman astronomy, being used as a starting point for further speculation. Gallus was connected through Aemilius Paullus to two other men who displayed an interest in astronomical instruments. In 164 bce, Q. Marcius Philippus, who was elected censor that year with Paullus, recognized that a sundial, which had been removed from Catana in Sicily 99 years earlier and placed in the Forum near the Rostra, was inaccurate; to fix the problem he had a new dial set up next to the old one, calibrating it to the latitude of Rome (Pliny 7.214). Five years later, P. Cornelius Scipio Nasica, who had been Aemilius Paullus’ second-​in-​command at Pydna, was made censor. Nasica set up Rome’s first public water clock, a device that allowed people to track the hours on cloudy days and at night (215). He installed the clock inside one of the largest buildings in the Roman Forum, the Basilica Fuluia et Aemilia, whose construction was initiated in 179 bce by none other than M. Fuluius Nobilior (Varro, Latin Language 6.2). Philippus and Nasica were continuing Fuluius’ legacy of regulating time for the public good—​a legacy that in Fuluius’ eyes had been inaugurated by Numa.

2.  Pythagoras’ Cabbage and Cato Pythagorean influence is seen most clearly in early Roman astronomy and calendrics, yet also touched on medicine in what might seem at first a rather unlikely source: the Roman statesman Cato the Elder. In addition to being a successful general, orator, and politician, Cato was a learned man who essentially founded the tradition of Latin prose (Astin 1978, 182–​239). He had close ties to Aemilius Paullus (his son married Paullus’ daughter), but he was much less open to Greek culture than that man. The censor held a notoriously dim view of Greek doctors, especially those practicing medicine on Romans. In a treatise addressed to his son he wrote (Pliny 29.14): I will prove their race [sc. the Greeks] is utterly useless and incorrigible, and consider me a prophet when I say: whenever that race gives us its literature, it will corrupt everything, and all the more so if it sends us its doctors. They have taken a mutual oath to kill all barbarians with their medicine, but they do this for money so that they may be trusted and more easily bring us to ruin.

Pliny links his hostility to Greek physicians to the bad feelings that arose in Rome after the arrival of the first official Greek doctor, Archagathus of Laconia. Archagathus set up a practice in Rome in 219 bce at the invitation of the Senate and was initially quite

Traditionalism and Originality in Roman Science    601 successful, but his surgical techniques led to claims of malpractice and brutality, and eventually he was shut down, having earned the nickname “The Torturer” (29.13). Cato, like many Romans of the Republic, distrusted invasive medicines, strange drugs, and treatment for a fee (Scarborough 1970). He felt that every paterfamilias should maintain a collection of remedies that would enable him to deal with any medical problem that might arise at home (29.15). In his book On Agriculture, Cato published numerous remedies, presumably to help his fellow patriarchs treat members of their households. The recipes are scattered through the last quarter of the book: they include wines mixed with medically active ingredients such as juniper and hellebore (sec. 114–​115, 122–​127), and a magical charm for treating dislocated bones (sec. 160). Cato apparently claimed all of them as his own; here, as in the parts of the book that deal with farming proper, mentions of sources are rare. The only persons given credit in the sections on farm lore are the Manlii, superior broommakers (sec. 152), and Minius Percennius of Nola, who invented a new method for propagating cypress trees (sec. 151). This contrarian focus on the contributions of obscure individuals finds a parallel in Cato’s Origines, a work on Roman history that suppressed all the names of military leaders, but identified by name a famous Carthaginian elephant, Surus (Pliny 8.11). Given Cato’s aversion to Greek doctors, and his refusal to pay obeisance to famous reputations, his mention of Pythagoras at the beginning of a long discourse on the uses of cabbage is surprising (sec. 157). Even more surprising is the sophistication and sensitivity of the medicine he there describes. We read that cabbage is a special plant because it combines multiple savors: moist, dry, sweet, bitter, and acrid (sec. 157.1). We are given proper botanical descriptions of three different varieties (sec. 157.1–​2). We hear that overeating causes sickness by filling the veins and preventing the movement of breath through the body (sec. 157.7). Cato describes different classes of sores (sec. 157.3–​4) and suggests a cure for breast cancer (sec. 157.4). Specialized treatments are recommended for boys, girls (sec. 157.5), and infants (sec. 157.10), better suited to their tender constitutions, and a gynecological therapy is detailed (sec. 157.11). Cato even recommends treating a hardened fistula with kind of surgical instrument: insert a hollow reed into a bladder, he advises, and use it to inject cabbage juice into the wound (sec. 157.14). Cato’s debt to contemporary Hellenistic medicine in this part of his treatise is patent. The sophistication of the medical knowledge—​ the claim about veins transporting “breath” is rooted in the theories of Erasistratus; several prescriptions match word for word those given by the doctor Mnesitheus of Cyzicus (cf. Oreibasios, Collection 4.4, = Corpus medicorum graecorum 6.1.1, p. 100)—​and the humanity of its concerns give him away. Yet how are we to square this debt with the intense animosity to Greek doctors outlined above? Part of the answer is that it was impossible for any technical writer during this time to keep completely free of Greek influence, especially in matters of terminology (Boscherini 1970). But surely another factor was the statement made in the heading of the section that all of these treatments employ “the cabbage of Pythagoras.” Apparently Cato had no problem with modern, foreign methods, so long as he could pretend they had the blessing of the old Italian wise man.

602   Greco-Roman Science

3. A Long Lull After a promising start, Roman efforts to elaborate on the putative legacies of Pythagoras or Numa were abandoned for a period of time extending roughly from the death of Cato to the 60s bce—​almost a whole century. This period witnessed almost no systematic writing in Latin on nature or medicine. During the first 50 years, the only attested Latin work is a translation by D. Iunius Silanus of the Carthaginian agronomist Mago’s work (Pliny 18.23); in the first four decades of the next century, we can place a book on sailing by Varro, Cicero’s Aratea, and perhaps works by the Sasernae on farming, and a Publius Septimius on architecture (see entries in Keyser and Irby-​Massie 2008, with the timeline, pp. 2131–​2139); that is, about one work per decade. The reasons for this slowdown are unclear. Varro, at the end of this period, observed that there was no need for Romans to write about subjects like philosophy in Latin, because anyone who was interested would prefer to read about them in Greek (Cicero, Academica 1.2). Yet this cannot be the full explanation, since this period witnessed the continued flourishing of oral and performative arts, such as oratory, drama, and poetry, which possessed Greek counterparts; grammarians and rhetoricians were likewise publishing actively in Latin (Kaster 1995). A more telling factor may have been a change in the way advanced Greek thought was absorbed during this time. Educated Romans were no longer dealing with isolated pieces of loot or lore, but were visiting, studying under, and even living with accomplished Greek intellectuals who were past masters of their respective traditions (Gruen 1992, 251). To cite just a few well-​known examples, Scipio Africanus and his associates formed a fraternity of sorts with the historian Polybius and the Stoic philosopher Panaetius; the great doctor Asclepiades of Bithynia lectured at Rome with enormous success, befriending prominent figures in the city (Rawson 1985; Nutton 2013, 170–​173); Piso maintained the Epicurean philosopher Philodemus at his home; and many young aristocrats traveled to Rhodes or Athens to study. Cicero claims that Romans of this era took philosophy so seriously that they were more interested in living it than writing it, but then adds, tellingly, that they were also worried anything they wrote would not pass muster with experts (Tusculan Disputations 4.5–​6). The presence of Greek philosophers left Romans both inspired and intimidated. If fear of judgment deterred them from expounding philosophy in writing, tackling other scientific disciplines would likely have spurred similar worries. The Greek philosophers remained, but the worries eventually subsided: by the start of the 50s bce Roman authors resumed writing on science and medicine confidently and with the alacrity of men trying to make up for lost time. Varro’s earliest treatises on natural science date to this period, as does the work of Pompeius Lenaeus, who rendered the pharmacological writings of Mithridates into Latin. Between 54 and 51 bce Cicero completed his Republic, a work of political philosophy whose ending, an extended piece of cosmological speculation known as the Dream of Scipio, would exercise an enormous influence on Roman scientific writing in Late Antiquity. In the mid 50s bce, Lucretius

Traditionalism and Originality in Roman Science    603 published his great Epicurean poem on nature, Varro of Atax composed didactic poems on astronomy and geography, and Julius Caesar contributed to the ethnography of Gaul and Britain. The next decade witnessed even more work, including Cicero’s philosophical dialogues, which with the exception of the Republic were all written in the span of just two years, 46–​44 bce. Two of the most prolific scholars ever to write in Latin, P. Nigidius Figulus and M. Terentius Varro, were active during this time as well. They merit special attention here since both wrote about science and both were linked to Pythagoreanism.

4.  Nigidius Figulus, Pythagorean Born around 100 bce in Perusia, Nigidius was a distinguished Roman senator; like Varro and Cicero he supported the optimate branch of the Roman elite and was an ally of Pompey the Great. He participated in the Battle of Pharsalus and was exiled after Pompey’s defeat, dying in 45 bce, a year before Cicero was able to plead a case for his recall before Caesar. He was one of Rome’s most erudite and productive scholars, and pushed the bounds of acceptable research, as suggested by the obituary notice for him in St. Jerome’s chronicle, which describes him as both “Pythagorean and Mage” (fr. 8 Swoboda). Several stories told about his involvement with magic make the second label apt (Dickie 2001, 169–​172), but the first is harder to account for. As Holger Thesleff noted (1965a), the problem is that there is no evidence that Nigidius ever applied the term “Pythagorean” to himself or sought to align himself with the Pythagorean tradition. Nor is help forthcoming from his numerous writings, which include (Swoboda 1889): 1. a treatise on grammar in 29 books dealing with Latin usage, semantics, and etymology; 2. a treatise on the gods in 16 books dealing with their classifications, names, and roles; this included a discussion of the Stoic ekpyrosis, the Magi, and an exposition of the sixteen divisions of the sky from Etruscan sources (Weinstock 1946); 3. a book on “private augury”; 4. a book on the interpretation of entrails; 5. a book on dream interpretation; 6. a 360-​day calendar giving predictions for each day if thunder is heard, ascribed to the Etruscan seer Tages (Turfa 2012); 7. a book on the constellations of Greek astronomy relating the myths for each zodiacal sign, based on the work of Eratosthenes and other Hellenistic mythographers; 8. a book on the constellations of Egypt and/​or Babylon; 9. a book on timekeeping or geography, giving the ratios of day-​to-​night hours on the solstice for countries at different latitudes, derived from Eratosthenes and other Hellenistic geographers;

604   Greco-Roman Science 10. a treatise on winds, in 4 books, including signs of approaching winds from Aratus; 11. a treatise on human anatomy, in 4 books, concerned with parts and terminology; and 12. a treatise on zoology in 4 books concerned with terminology, based partly on Aristotle, and partly on the writings of the Magi. Nigidius drew from a variety of sources, including Greek scientists and philosophers (1, 2, 7, 9, 10, 12), Etruscan texts (2, 6), and eastern writings (2, 8, 12). A recurring interest in semiotics, the interpretation of signs in the natural world, and divination is clear. But there is a noteworthy absence of Pythagoreanism: none of the texts focus on traditional Pythagorean themes such as numerology, harmonics, psychology, purification, or reincarnation, and none of the sources are Pythagorean (Thesleff 1965a, 47). The ultimate source for Jerome’s label “Pythagorean,” then, appears to be the preface to Cicero’s translation of Plato’s Timaeus, which was composed shortly after Nigidius’ death and was intended as a panegyric (Timaeus 1): I have written quite a bit against the natural philosophers in my Academica and often gone back and forth in the manner of Carneades with Publius Nigidius—​ a gentleman who was finely equipped with all the arts specifically suited to a free man, and a keen and careful investigator of matters that Nature has seemingly kept under wraps. It is my considered judgment that he stood prominent in the line of those famous Pythagoreans whose discipline had more or less passed away, even though it was strong in Italy and Sicily for several centuries, and he was one who renewed their discipline.

This passage does not show that Nigidius was a Pythagorean—​to the contrary, it suggests Cicero took his time (“It is my considered judgment”) to settle upon this word as the correct one (Thesleff 1965a, 45). What it does show is the sheer rhetorical power of the term “Pythagorean.” Cicero saw his friend Nigidius exploring occult lore, publishing material from recondite, foreign sources, and studying the natural world with the aim of establishing links to the divine—​all risky, potentially impious avenues of inquiry. Another anonymous contemporary had a word for what Nigidius was up to: sacrilege (pseudo-​Cicero, Against Sallust 5.14). Cicero concluded that the most favorable description he could give this activity was to call it a revival of the ancient and distinguished tradition of Pythagoreanism (which it was not). The function of the label remained what it had been, to provide a veneer of respectability for innovative research. But for the first time a Roman was using it to defend someone else’s intellectual experiments, not just his own, and to apply it to a large and diverse corpus of work, not just a single doctrine. The power of the term comes to the fore once again, and the expansion of its scope is clear.

5.  Varro and Pythagorean Science M. Terentius Varro of Reate was by common consent Rome’s most learned, prolific, and influential scholar (Cardauns 2001). In his early life he was an active politician; in

Traditionalism and Originality in Roman Science    605 his retirement, which followed Caesar’s rise to power, he devoted himself to research. His life’s work amounted to 620 books under 74 different titles, of which the only texts that we possess intact are six books from the Latin Language (De lingua Latina), and the three-​book treatise Farming (De rebus rusticis). Varro was older than Nigidius but completed much of his publication later, including a work, the Disciplines, which provided an important stimulus to the study of science at Rome. This series consisted of nine books, one for each of the liberal arts: grammar, rhetoric, dialectic, arithmetic, geometry, astronomy, music, medicine, and architecture. He died in 27 bce at age 89 and was reportedly buried in accordance with Pythagorean custom (Pliny 35.160). The bulk of Varro’s work involved reconstructing the cultural archaeology of Rome from its language and traditions. He argued, for instance, that Numa and Pythagoras must both have employed hydromancy to communicate with the gods (Augustine, City of God 7.35). To support this notion, he observed that Egeria, Numa’s teacher, was associated with water and traced her name to an etymology, “She who brings out” (from egero), which suggested it was her job to bring out the divination bowl. This sort of interpretation, memorable, rationalizing, anachronistic, and implausible, is typical of his individual aperçus. The real bases for his scholarly authority and influence were his skill at organizing large bodies of information (Rawson 1978) and his ability to draw connections between disparate fields in a way characteristic of the Romans (Lehoux 2012, 176–​199). Connections he drew under the auspices of Pythagoreanism can be seen in his works on embryology, astronomy, and geometry. In a book titled For Tubero: On the Origin of the Human Being, Varro expounded on a theory of embryology and its arithmetical foundations that he credited to Pythagoras (Censorinus 9–​11). Most Greek and Roman doctors maintained that there were only two kinds of viable pregnancy, one lasting seven months, or 210 days, and one lasting nine months, or 270 days; eight-​month gestational periods were thought to produce stillborn babies (Parker 1999). A medical theory with Pythagorean roots took this numerology further, holding that the fetus of the seven-​month child needed 35 days to reach human form. This stage was divided into four subperiods: 6 days in which the embryo remained fluid, 8 for it to become blood, 9 days for it to become flesh, and 12 days for it to take on human shape. On this account, the ratios of successive day periods (6:6, 6:8, 6:9, 6:12) corresponded to the basic ratios of harmonic theory (1:1, 3:4, 2:3, 1:2). Varro began his essay by spelling out this schedule for the seven-​month child in exact accordance with the Greek tradition (Censorinus 11.2–​5). At this point our Pythagorean Greek sources add a gestational schedule for the nine-​ month child, starting again from a base period of six days. Varro, by contrast, proceeds to give a gestation schedule for what he calls a 10-​month pregnancy that comes to term on the 274th day (Parker 1999, 520–​522). The derivation of this figure is explained in two different fashions. First, in terms of numerology: the child is born after 40 periods of seven days, with the last seven-​day period ending on its first day (Censorinus 11.6–​ 8; Aulus Gellius 3.10.7–​8). Second, in terms of the solar year: the period of gestation is equal to the amount of time it takes the sun to cover three sides of a square inscribed in the zodiac (Censorinus 11.8). Varro’s account is unique. It gives a day total without parallel elsewhere; it justifies its numerological scheme, based on the number seven

606   Greco-Roman Science rather than six, by appealing to Etruscan religion; and it explains its partition of the solar year using astrological reasoning. Its creator must be Roman and is probably Varro. Nevertheless, Varro credits it to Pythagoras (11.11). Our second example is a theory of the harmony of the spheres and the distances to the sun, moon, planets, and stars, probably deriving from the Disciplines’ book on astronomy (Rawson 1985, 164). The scheme is reported by Censorinus (13.2–​5); he ascribes it to Pythagoras, but cross-​references with other Roman authors establish Varro as Censorinus’ source (Heath [1913] 1981, 112–​114, Burkert 1961, 28–​43): Earth radius: Earth to Moon: Moon to Mercury: Mercury to Venus: Venus to Sun Sun to Mars Mars to Jupiter Jupiter to Saturn Saturn to Fixed Stars Total radius of the heavens

1r 1r 1/​2r 1/​2r 3/​2r 1r 1/​2r 1/​2r 1/​2r 7r

126,000 stades 126,000 stades 63,000 stades 63,000 stades 189,000 stades 126,000 stades 63,000 stades 63,000 stades 63,000 stades 882,000 stades

tone hemitone hemitone trihemitone tone hemitone hemitone hemitone

Varro’s starting point was Sulpicius Gallus’ Pythagorean scheme for cosmic distances, which was described earlier: like Gallus, Varro used Eratosthenic earth radii as a unit of measure, and he took over Gallus’ figures for the radius of the cosmos (7r) and distance to the moon. Varro combined this with a sequence of intervals between successive planetary spheres based on the eight tones that make up the octave. The sequence of tones may derive from a poem dealing with the music of the spheres by Alexander of Ephesus, a Greek poet coeval with Varro whose poems on astronomy and geography were well-​ known at Rome in the 1st century (Courtney 1993, 248–​249; Irby-​Massie and Keyser 2002, 65–​66); no other Greek source has the same. The planets are set at distances determined by the musical intervals, which results in the sun being 1/​2r further from the earth than Gallus made it. Like Gallus, Varro credits this system to Pythagoras. As noted above, its cosmic distances are laughably small by Hellenistic standards, but perhaps seemed appropriate for a thinker from the 6th century. This arrangement of the cosmos had a long afterlife in Latin literature, being repeated, with minor variations, by Pliny (2.84), Fauonius Eulogius (18.5–​18), and Martianus Capella (2.169–​98). For a third illustration we will look at Varro’s history of geometry, which features another synthesis of disparate sciences (Cassiodorus, Institutes 2.6.1): In Latin “geometry” means “the measurement of the earth,” for among the various forms of that discipline, some say the first was the dividing up of Egypt among individual landowners; the teachers of this discipline were called “measurers.” However, Varro, the most expert of the Romans, relates the following origin for this

Traditionalism and Originality in Roman Science    607 name, saying that at least in the first stage the measurement of the earth offered the blessings of peace for peoples whose boundaries had been drawn up in a vague or contentious fashion. Next, the circuit of the entire year was divided into a number of months, and that this is the reason months (menses) have their name—​for they measure (metiantur) the year. But after those discoveries were made, scholars who felt called to understand things they could not see began to ask how great a distance separates the moon from the earth and the sun from the moon and how large is the measure that extends all the way to the peak of the sky; a question the most expert geometers succeeded in answering, according to his report. At that point, he says, the measurement of the entire earth was inferred through a process of probable reasoning, and that is how the discipline of Geometry acquired the name that it has kept for many centuries.

Varro has a unique take on the history and the nature of geometry. For him it is not the complex of lemmas, proofs, and diagrams, building upon each other and operating at a certain level of abstraction, familiar to us from Greek science. Instead, it is a special art of measurement that applies to objects of nature, starting and ending with the earth itself. Geometers, he says, began by measuring pieces of land, shifted to the division of periods of time, sought to establish the dimensions of the cosmos, then returned, finally, to measure the entire globe. The history of the discipline unfolds according to a kind of inner logic as the mastery of increasingly difficult measurement challenges eventually allows geo-​metria, earth-​measuring, to live up to its name. The other noteworthy feature of this account is that all of the fields embraced by “geometry” have an Italian or Pythagorean pedigree. Surveying and calendrics were old Roman institutions that Numa had a hand in inspiring, as we have seen earlier. The measurement of cosmic distances is described here in terms that specifically recall Gallus’ work, and thus derives from “Pythagoras.” As for the measurement of the size of the earth, Varro certainly knew Eratosthenes’ measurement, but may have had in mind estimates supposedly made by early Pythagoreans, for instance, the one claimed for Archytas of Tarentum by Horace (Odes 1.28.1). Whatever the case may be, all four subdisciplines have ties to Pythagoras or Numa, which suggests Varro was trying to reconstruct a distinctively Italic enterprise. Varro’s idiosyncratic account of geometry left an imprint on later Latin science. His history became a template for defining the discipline, which henceforth encompassed any materials dealing in some way with “the measurement of the earth,” as well as those of a familiar Euclidean cast. Martianus Capella’s book on geometry (6) explains the subject by offering a long survey of terrestrial geography, followed by a brief list of Euclidean terms and definitions (Stahl 1991, 44–​48). Isidore of Seville in his article on geometry repeats the passage from Cassiodorus quoted above and appends some remarks on the terminology for plane figures (Etymologies 3.10–​14). Later handbooks on geometry were filled with excerpts from Roman treatises on surveying: the most important introduction to geometry in the Latin west between the 9th and 12fth centuries was the so-​called First Geometry of pseudo-​Boethius, which mixed “geometrical knowledge from Euclid’s Elements, fragments from treatises on Roman land surveying  .  .  .  and

608   Greco-Roman Science pseudo-​philosophical digressions related to geometry” (Zaitsev 1999, 524); conversely, works on gromatics by Frontinus were often transmitted under the title Geometria. As eclectic and confused as this tradition may seem, it was nevertheless faithful in spirit to Varro’s etymological reconstruction of the discipline’s evolution, which was designed to foreground Italic contributions and pay tribute to an Italian Pythagoreanism that he himself helped to invent or recover.

6.  Pythagoras and Numa Under the Roman Empire By the time of the emperor Augustus (r. 31 bce to 14 ce), the Romans had access to more and better information about Greek intellectual history than ever before, yet this did not halt new attributions of wisdom to Numa and Pythagoras; in fact, the sophistication of the doctrines attributed to the pair grew in tandem with increased awareness of Greek science. In his account of Numa’s establishments, for instance, Livy credits the king with having introduced an intercalation scheme into the Roman calendar that would ensure the solar years and lunar months were accurately synchronized after 19-​ year intervals (1.19). If true, this would imply that Numa somehow anticipated, by more than two centuries, the commonly used 19-​year intercalation cycle first introduced at Athens by Meton, ca 430 bce. It is unclear where Livy got this notice from (no other source mentions it), but its anachronism is obvious. One of the best-​known documents of Pythagoreanism from the age of Augustus is the long speech delivered by Pythagoras in book 15 of Ovid’s Metamorphoses (75–​478). The speech is delivered to impress a crowd at Croton, a crowd that includes Numa, who is visiting from Rome (7–​8, 479–​481). Within the epic its function is to carry the central theme of metamorphosis out of the realm of mythology and into the natural sciences; it also serves as a didactic poem in miniature, with Lucretian flourishes, lore taken from Hellenistic paradoxographers and geographers, and a surprising number of passages translated from Empedocles (Hardie 1995). In keeping with the character of the speaker, it begins and ends with exhortations to vegetarianism grounded in the doctrine of metempsychosis (75–​175, 453–​478). But the bulk of the speech presents no traditional Pythagorean doctrine, and some of the material, like the obvious Heraclitean tag “All things are in flux” (178), stands at cross-​purposes with his philosophy. The examples of change cited include several blatant anachronisms, such as a reference to the tsunami that destroyed Helice in 373 bce (293–​294). In ascribing doctrines to Pythagoras, Ovid cheerfully highlights implausibilities that prior Roman sources tend to suppress. In order to preserve a clear focus on Roman culture, I have to this point focused on scholars who wrote mainly in Latin. I conclude with two who wrote in Greek because (a) both were influenced by Roman contexts, and (b) both used the Roman valorization of Pythagoras in a highly aggressive manner to reclaim broad swathes of ancient

Traditionalism and Originality in Roman Science    609 Greek science for Italy. Thrasyllus of Mendes is probably best known as the Emperor Tiberius’ astrologer, but he was also a notable philosopher whose thought incorporated Pythagorean elements into a Platonic core (Tarrant 1993). Thrasyllus was responsible for the arrangement of Plato’s dialogues into tetralogies and did something similar for the works of Democritus, creating a collected edition that grouped his books into tetralogies (Leszl 2007). In the prologue to this edition, Thrasyllus let it be known that his interest in Democritus—​surprising in a Platonist, given Plato’s reported hostility to Democritus—​ was founded in a desire to reclaim him for the Pythagorean tradition. He asserted that the Abderite had copied Pythagorean material, spoken in admiring terms of Pythagoras, and, if the chronology allowed it, could have been his pupil, since “he appears to have taken everything from him” (Diogenes Laërtius 9.38). Thrasyllus’ charges of imitation and plagiarism apparently failed to convince Greek philosophers—​there was no renewed appreciation for Democritus among Platonists or Pythagoreans—​and most probably considered the thesis as perverse as modern scholars do. Yet Thrasyllus surely expected a receptive audience somewhere, and the most likely place for it was among the Roman intellectuals of Tiberius’ court, conditioned by native tradition to see Pythagoras as the source of all wisdom. Classical Greek philosophy was subject to another attempted hostile takeover at the hands of the Neo-​Pythagorean philosopher Moderatus of Gades, who, like Thrasyllus, was active in the first half of the 1st century ce. Moderatus wrote in Greek, but as his name and city of origin indicate (Gades survives today as the modern Spanish city of Cádiz), must have been raised in a milieu that was culturally Roman; he may well have been a relative of L. Iunius Moderatus of Gades, the Roman agronomist better known by his nickname, Columella. Moderatus was an important innovator both in the history of ideas and in metaphysics (Dillon 1996, 344–​351). His revisionist philosophical history centered on the notion that Plato, Aristotle, and other early Platonists and Peripatetics had stolen Pythagoras’ best ideas from him without attribution, and then, to distract attention from their thefts, promoted a caricature of his philosophy (Porphyry, Life of Pythagoras 53): Plato and Aristotle and Speusippus and Aristoxenus and Xenocrates appropriated for themselves what was fruitful with only minor touching up, while what was superficial or frivolous, and whatever could be put forward by way of refutation and mockery of the School by those who later were concerned to slander it, they collected and set apart as the distinctive teachings of the movement.

That Roman intellectual jingoism catalyzed this rewriting of the past is strongly implied by a peculiar theory one of Moderatus’ students advanced. The student, Lucius of Etruria, argued that several pieces of Pythagorean lore, such as the rule against stepping over a broom or allowing swallows to nest in one’s house, had their closest parallel in the taboos of the ancient Etruscans; this constituted proof, he said, that Pythagoras was not actually from Samos, as the Greeks claimed, nor that he had an Etruscan father, as others

610   Greco-Roman Science had suggested, but was born and educated in Etruria (Plutarch, Convivial Questions 8.7, 727b–​c)! Pythagoras, in short, was a true Italian, whose honor Moderatus sought to rescue. Moderatus’ revisionist intellectual history helped shape his methodology as a philosopher. This involved, first, interpreting “superficial or frivolous” bits of Pythagorean numerology as protreptic devices designed to prepare novice students for immersion in more profound metaphysical doctrines (Kahn 2001, 105–​107). These doctrines he in turn reconstructed from early Greek philosophical texts dealing with logic and ontology, where he believed genuine Pythagorean notions lay hidden. In one case, Moderatus excavated from Plato’s Parmenides a supposedly ancient Pythagorean teaching about levels of metaphysical unity, the doctrine of the Three Ones, which culminated in a One that was above Being (Dodds 1928). The result was an elaborate system of transcendental Pythagoreanism that exercised a significant influence on the thought of the philosophers Plotinus and Iamblichus. While building on the work of earlier Greek Neopythagoreans, Moderatus was also continuing the Roman valorization of Pythagoras, which he took to an unprecedented extreme.

7. Conclusion The Roman tradition of doing science after Numa and Pythagoras was characterized by numerous incidents of “inverse plagiarism,” which one may define as the act of giving credit to others for ideas that are actually one’s own. It was motivated at first by the need to obfuscate the sources of new ideas. Over time it allowed Roman students of nature to do original work and broke down some of the barriers between different areas of inquiry in ways that made new syntheses possible. Under the empire it metastasized, becoming, in some cases, a weapon of intellectual imperialism. It produced a historical tradition littered with ghost texts, confabulations, and misappropriated doctrines. It makes for a good story, but those who read it or write it must be on guard against the characters’ penchant for misdirection. In the middle of the 6th century ce, while poking around in the library at Constantinople for material to complete his book On Divination (De ostentis), the Imperial administrator John the Lydian came across an anonymous essay on prognostication from the signs of the moon that he decided to copy. Its preface opened by taking to task critics of divination for launching incoherent attacks and confusing their own superstition with piety. After laying out a case for the moon’s influence on terrestrial beings, it ended with this reflection (47.14–​23 Wachsmuth): Therefore it is a form of madness when they criticize the methods we use to make conjectures about the future. Nor does spending leisure-​time observing the stars put one outside of piety; to the contrary, one may observe the all-​wise providence of the

Traditionalism and Originality in Roman Science    611 Ineffable Father of All Things through his works, and marvel at the fact that, when God leads, a man’s soul is able to converse about the heavens as much as it can. That is what Fuluius says, sharing the story of Numa.

Whoever penned Lydus’ text seems to have been familiar with the Roman habit of invoking figures like Numa to authorize nontraditional forms of inquiry and also to have known about Marcus Fuluius Nobilior’s role in starting it. The neo-​Pythagorean terminology for the deity suggests a document written in the Common Era, and the quote attributed to Fuluius must be apocryphal. Still, it is a measure of the persistence of the habit that people were still making appeals to Numa and Fuluius at such a late date.

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chapter D2

Science for Ha ppi ne s s Epicureanism in Rome, the Bay of Naples, and Beyond Pamela Gordon

According to the 1st-​ century ce Stoic writer Seneca, the following was an Epicurean saying: “Do everything as though Epicurus were watching” (Letter 25.5: sic fac omnia, tamquam spectet Epicurus). Reverence for Epicurus and close adherence to his teachings were essential aspects of Epicurean identity throughout the centuries-​long history of the school as it spread across the Mediterranean, to Italy, and to Asia Minor. But despite their desire to be faithful, later Epicureans made their own contributions as they recontextualized Hellenistic philosophy, responded to later developments and current controversies, or presented Epicureanism in new genres. In addition to surveying the later Epicurean sources, this chapter outlines aspects of Epicurean scientific theory that first emerge—​in hostile and in friendly sources—​between the 1st century bce and the 2nd or 3rd century ce. Some of these features of later Epicureanism may be attested only for this period because earlier texts are lost, but others are later developments. Many scholars interpret all Epicurean texts as witnesses to the state of Epicureanism as it existed during the life of Epicurus. Others describe a flexible tradition that accommodated innovation and idiosyncrasy. This issue—​orthodoxy vs. heterodoxy—​is energetically debated today. Firm evidence for doctrinal development is often lacking:  we have extensive, well-​preserved Roman texts but relatively few intact texts by Epicurus with which to compare them. My intuition is that modern scholarship is sometimes unduly influenced by the Epicureans’ guarantees of authenticity, as well as by ancient stereotypes that mock the Epicureans for being incapable of independent thought. The most important sources for Epicureanism during the time of the late Roman Republic and early Roman Empire are Lucretius, Philodemus, Diogenes of Oenoanda, and Diogenes Laërtius, Major scholars and teachers whose work survives only in fragments or paraphrases include Zeno of Sidon and his younger contemporary

616   Greco-Roman Science Demetrius of Laconia (late 2nd to early 1st century bce). Less friendly sources on Epicureanism include Cicero (106–​43 bce), Seneca (ca 1 bce–​65 ce), Plutarch (especially active from 100 ce until ca 120 ce), Epictetus (mid-​1st to 2nd century ce), and Cleomedes (the Stoic, likely 2nd or 3rd century ce).

1. Lucretius T. Lucretius Carus (died ca 50 bce) is a Roman poet about whom we know little other than that he authored the De rerum natura, or On the Nature of Things, a six-​book hexameter poem on Epicurean science. Lucretius’ ardent presentation occupies a unique position in the canon of ancient Roman poetry and is our primary source of information on Epicurean physics. Extremely popular in some Roman circles, Epicureanism had been presented in Latin before, but in apparently clumsy and unimaginative prose (Cicero, De Finibus 1.22, 29, 2.30, 3.40). In contrast, Lucretius engages a broad literary heritage, paying tribute in particular to the poetry of Homer, Hesiod, Empedocles, and Ennius. This is a radical departure from the prose of Epicurus, who—​if we are to believe Cicero, Plutarch, and other hostile witnesses—​devalued poetry and traditional education in general (see Asmis 1995). Lucretius conveys the materiality of phenomena through analogy, alliteration, imaginative epithets, and vivid descriptions. He offers inspired Latinizations of the technical terms of Epicurean physics via live metaphor, wordplay, and periphrasis. Never using atomi as a transliteration for the Greek word for atom, Lucretius refers to atoms and—​apparently—​atomic aggregates with a range of suggestive terms such as semina rerum (seeds of things), genitalia corpora (generative bodies), corpora prima (first bodies), elementa (elements; as well as letters of the alphabet), and primordia rerum (first beginnings of things), some of which are translations of traditional metaphors used in earlier Greek atomism. To describe void he refers to hollows, pores, breathing holes, and caves (e.g., caua, cauernae, caulae, fauces, foramina, speluncae, spiracula). Similarly, he draws on ordinary phenomena in the visible world to prove that atoms move through the void or to explain through analogy how atoms behave. Thus he writes that lightning and sound can pass through the walls of a house because their atoms travel through the void in the deceptively solid-​looking wall (1.489–​490) and—​ famously—​that atoms tossing endlessly through the void are like dust motes in a sunbeam (2.114–​128). The philosophical goal of De rerum natura as a whole is to provide enough scientific knowledge to release the reader from two major causes of human unhappiness: the fear of the gods and the fear of death (Lucretius 1.62–​135). The complex contents of the 6 books of De rerum natura resist reduction to outline form, but may be described as follows: book 1 treats the fundamentals of Epicureanism, laying out the theory of atoms and void; book 2 describes how the motions and qualities of the

Epicureanism in Rome, the Bay of Naples, and Beyond    617 atoms explain phenomena; book 3 treats the nature and mortality of the soul or spirit (psyche in Epicurus, animus and anima in Lucretius); book 4 focuses on phenomena of the psyche and thus presents an Epicurean theory of psychology; book 5 treats the nature of the cosmos and its impermanence, and includes a history of human civilization; and book 6 offers explanations of storms, earthquakes, and other natural phenomena that wrongly inspire fear of the gods. Streamlining the outline further, Farrell (2007, 79) presents the progression of the six topics from book 1 through book 6 as the following succinct list: “elements, compounds, material soul, its affects, the world, its wonders.” Scholarship on Lucretius has long been divided by many versions of the orthodoxy vs. heterodoxy debate. The notion that Lucretius wrote as if in a vacuum, ignoring ideas that developed after the lifetime of Epicurus, is a pervasive one that many scholars have in recent decades attempted to overturn. Several have maintained, for example, that Lucretius offers his own tacit critiques of Stoic philosophy or of later Hellenistic Skepticism, that he responds to post-​Hellenistic developments in science, that his relationship to the texts of Epicurus is extraordinarily complex, or that he has connections with later Epicureanism (see especially:  Kleve 1978; Asmis 1982; Clay 1983; various essays collected in Algra, Koenen, and Schrijvers 1997; and Schrijvers 1999). Schrijvers in particular stresses Lucretius’ engagement with Greek writers who pre-​and postdate Epicurus, prime among then Aristotle, Asclepiades, the Peripatetic Dicearchus, Galen, and the Hippocratics. But Sedley (1998) changed the playing field by grounding the argument for orthodoxy in a thorough treatment of recently discovered fragments of Epicurus’ On Nature. According to Sedley, Lucretius is a “fundamentalist” who unfolds Epicurean physics essentially as it is presented in the first 15 books of Epicurus’ On Nature, unmediated and in isolation from contemporary philosophical discourse. For Sedley, it is highly significant that Lucretius presents aspects of Epicurean physics essentially in the same sequence as they are put forth in the fragments of Epicurus’ On Nature (though Sedley posits that Lucretius made radical structural revisions during the later stages of the writing process). But to claim that Lucretius’ direct philosophical source was a single text by Epicurus is not to deny that Lucretius’ Roman context is readily apparent. Even Sedley’s “fundamentalist” view allows for originality in Lucretius’ proems, ethical diatribes, and imagery. Lucretius opens the poem with allusions to current civil strife, and throughout it he offers Epicureanism as the escape from the cultural ills of the late Roman Republic (for bibliography and an opposing view see McConnell 2012). In addition to decrying traditional Greek conceptions of the gods, Lucretius censures Roman augury (e.g., Lucretius 6.83–​89). His caustic treatment of the stages of erotic passion has strong Roman overtones (4.1121–​1192), as does his description of the “hell on earth” experienced by the ambitious politician (3.995–​1002). He is also as engaged with Alexandrian poetics and current rhetorical styles as were many of his contemporaries. Few scholars deny these aspects of the De rerum natura, though many discount them as minor, superficial accommodations. But recognition of Lucretius’ Roman outlook can be stated more

618   Greco-Roman Science strongly. For example, Asmis has argued: “Lucretius seeks to shift humans from their position in the Roman social and political order to a place in the natural order of things” (2008, 141). In her view, the surface structure of the De rerum natura follows Epicurus’ exposition of physics, but its deeper structure uses a particularly Roman conception of a natural treaty to “to reshape Epicurean physics into an ethical text” (2008, 142). Recognizing a yet more fundamental departure, Don Fowler described how the richness of Lucretius’ language suggests “multiple approaches to the world,” whereas Epicurus, as a reductionist, offered “one true story” (2002, 442). Thus for Fowler the complexity of the De rerum natura puts the poem in tension with Epicurus, making it “as deeply un-​ Epicurean as it is deeply Epicurean” (2002, 443). Future work—​perhaps not defined by an orthodox/​heterodox polarity—​will need to articulate what is particular to Lucretius without entirely discounting Sedley’s work on the papyri from Herculaneum. For a survey of scholarship on Lucretius, see Oxford Bibliographies Online (Campbell 2011).

2. Philodemus Epicurean circles—​like other philosophical schools—​had moved beyond Athens during the 2nd and 1st centuries BCE. The many places where Epicureanism flourished included Syria, where the Epicurean scholar and poet Philodemus (active in the early 1st century bce, until ca 40 bce) was born in the town of Gadara (in present-​day Jordan). Philodemus studied in Athens under another Syrian, Zeno of Sidon (fl. ca 100 bce), whom Cicero called “the most acute” of the Epicureans (Tusculans 3.38). Even when polemicizing against Epicureanism, Cicero praised Philodemus, calling him “very accomplished not in philosophy alone, but also in the other studies, which almost all the rest of the Epicureans are said to neglect” (Against Piso 70). A range of sources fills out this portrait, placing the erudite Philodemus in the environs of the Bay of Naples during the 60s through 40s and associating him with Siro, the head of the Naples school. Philodemus’ philosophical works (all in Greek) are known only from an extensive collection found in the so-​called Villa of the Papyri at Herculaneum, the city near Pompeii on the Bay of Naples that was also destroyed by the eruption of Vesuvius in 79 ce (over a century after the death of Philodemus). These substantially carbonized, partially deciphered book-​rolls yield fragments ranging in size from a few characters to several columns of connected prose. Many scholars connect Philodemus himself with this largely Epicurean library, identifying the owner of the elegant villa as the Roman statesman Calpurnius Piso Caesoninus, the father-​in-​law of Julius Caesar, and Philodemus’ student and patron (against this consensus see Porter 2007 and Blank 2013). Scholars have posited that Piso sometimes turned the villa over to Philodemus, and some identify a belvedere overlooking the sea as the meeting place for his Epicurean friends and students. For Gigante, a garden adjacent to the belvedere indicates homage to the “Garden” (the original name of the Epicurean community at Athens). In any case,

Epicureanism in Rome, the Bay of Naples, and Beyond    619 the assumption that Philodemus was the leader of a group of Epicureans is supported in part by Diogenes Laërtius’ reference to “Philodemus and his circle” (Diogenes Laërtius 10.3). Far from a cultural backwater, Herculaneum was “right at the intersection of the Greek and Roman worlds, where, as the example of Piso’s villa illustrates, the ear of a wealthy and powerful Roman elite might easily be won” (Sedley 2009, 34). If the Roman poet Vergil (70–​19 bce) was the author of the Catalepta (poems attributed variously to the young Vergil or to an anonymous poet writing in the voice of Vergil), Vergil may have studied Epicureanism on the Bay of Naples and thus belonged to Philodemus’ broader community. Catalepton 5 mentions sailing for “the harbors of the blest” (harbors being a common Epicurean metaphor for Epicurean tranquility) “to seek the wisdom of great Siro,” and Catalepton 8 mentions living in Siro’s humble home. Some scholars would add other Roman poets to this circle of friends, but nothing other than a few fragments of the De rerum natura discovered in the Villa of the Papyri suggests any connection with Lucretius (on the papyri see Obbink 2007). Confirmation of the links between the Epicurean communities at Naples and Herculaneum (10 km apart) appears in a papyrus fragment from Herculaneum that mentions someone returning to “dearest Siro” in Naples, and his decision “to engage in active philosophical discourse and to live with others in Herculaneum” (PHerc. 314, col. 14, Sider). Like Lucretius, Philodemus was an exponent of early Epicureanism. But unlike Lucretius, who extolled Epicurus as the sole font of Epicurean wisdom (e.g., Lucretius 1.66, 5.7–​12), Philodemus recognized four first-​generation founders of Epicureanism, whom he valorized as hoi andres, literally “the men”:  Epicurus, Hermarchus, Metrodorus, and Polyaenus (for citations see Longo Auricchio 1978). The tradition of “the men” (a title that has the impact of “The Great Men”) is emphatic in Philodemus and was well-​known to Plutarch (e.g., Non posse suaviter vivere secundum Epicurum [That One Cannot Live Happily Following Epicurus] 1087b, 1088d, and 1091b). Philodemus devoted some of his work to researching the early history of the Garden and collecting the original letters of “the men,” evident from his Pragmateiai, or Works on the Records of Epicurus and Some Others (Papyri Herculanenses 1418 and 310). He also wrote a poorly preserved essay titled On Epicurus. Though adamant that intimate knowledge of the texts of “the men” was essential, Philodemus did not focus exclusively on explicating the early works but composed original treatises, preserved the innovative work of his teacher Zeno, and responded to later critiques of Epicureanism (as articulated by Stoic philosophers and others). Thus Philodemus’ departures from orthodoxy can sometimes be identified more securely than is possible in the case of Lucretius (but see Kechagia 2010 on the early Epicurean response to Stoicism). In Philodemus’ estimation, however, it was not uncommon for Epicureans to stray too far. Apparently paraphrasing his teacher Zeno’s lament about the deterioration of conservative Epicurean values, Philodemus writes that “some of those who call themselves Epicureans say and write many things that they have gathered, but also much that is their own, yet not in agreement with the writings” (Papyri Herculanenses 1005, fr. 107.9–​16, Angeli). As he protests in the same work, “the most atrocious thing” regarding most Epicureans is their “unpardonable laziness” (i.e. lack of research) “in the

620   Greco-Roman Science [original] books” (Papyri Herculanenses 1005, col. 14.13–​18, Angeli). Elsewhere he writes that some Epicureans who disagreed with Epicurus were almost parricides (Rhetorica 1, col. 7.18–​28 Longo Auricchio). Of course, his rivals may have presented Philodemus as the parricide. Citing a foundational text would be the way to win an argument among Epicureans, but the texts themselves were in flux: the Epicurean Demetrius of Laconia corrected and restored the damaged texts of Epicurus, and Philodemus’ teacher Zeno devoted some of his scholarship to removing from the canon those works he considered inauthentic (Snyder 2000, 50–​53). Philodemus was prolific, but most of his philosophical writing focuses on Epicurean ethics rather than on natural science, though he did devote some of his studies to scientific method (“canonic”), the Epicurean prerequisite to physics (the study of nature). Nonetheless, his essays on ethics draw upon Epicurean science, as will be explained below, sec. 5 “Epicurean Medicine.” His work On Music acknowledges the value of music as a pleasure while claiming it has no effect on moral character. Refuting in particular the music theory of the Stoic Diogenes of Babylon, Philodemus argues that lyrics convey meaning, while sound cannot (see Delattre 2007). Moreover, others may have authored some of the Herculaneum papyri often attributed to Philodemus, and many focus on the views of other Epicureans. Works generally considered his include On Anger, On Choices and Avoidances, On Death, On Frank Criticism, On the Good King According to Homer (which Philodemus dedicated to Piso), On the Gods, On Methods of Inference, On Music, On Phenomena and Inferences, On Piety, On Vices and Virtues, On Rhetoric, and On the Way of Life of the Gods (for editions and scholarship see Treves and Obbink 2005; Blank 2013). By necessity, current scholarship on Philodemus focuses on the technical restoration of the papyri and the establishment of readable texts (on the new techniques for reconstructing and deciphering the papyrus rolls see Obbink 1996: v–​vii, 24–​53). For a survey of scholarship, see the article on Herculaneum papyri in Oxford Bibliographies Online (Henry 2013). Studies that have explored Philodemus’ contributions to Epicurean philosophy include Asmis 1990, Obbink 1996, Tsouna 2007, and the commentaries published with editions of the various works.

3.  Diogenes of Oenoanda Diogenes of Oenoanda is known only from a fragmentary Greek inscription in a small city in Lycia (in present-​day Turkey). Displayed on the walls of a stoa (colonnaded porch), this monumental inscription broadcasts an extensive invitation to Epicurean wisdom. First discovered in 1884, the inscription presents a range of texts, including epitomes on physics and ethics, a defense of old age, and two sets of Epicurean maxims. Also included are letters addressed to Diogenes’ friends that attest to Epicurean circles in the nearby islands and in Athens, Thebes, and Chalcis. Diogenes’ references to his medium reveal that much of the inscription was composed for this epigraphical context

Epicureanism in Rome, the Bay of Naples, and Beyond    621 only. As he explains: “It is in case you have not yet [attained any] knowledge of these matters that we turned so many letters to stone for you” (fr. 116 Smith). Diogenes’ inscription was gargantuan: possibly 80 meters or 262 feet long and almost 4 meters or 13 feet high (Smith 1998, 125; 1993, 92–​93). The approximately 300 known fragments (as counted in 2012) contain well over 6,000 words, but the original word count may have been four times larger (Smith 1993, 83). New fragments have been discovered recently (cited within as “NF”), and a full excavation would likely reveal more. Various dates from the 1st to 3rd centuries CE are possible (Canfora 1992 and 1996; Hall 1979; Smith 1993, 35–​48). But as Smith maintains, the striking resemblance of the lettering to another, securely dated inscription suggests that Diogenes’s inscription belongs roughly to the same era. This other major inscription in Oenoanda’s urban center includes a letter from the Emperor Hadrian dated August 29, 124 ce (Smith 1993, 40–​43). Until recently, most scholarship on Diogenes of Oenoanda has approached the text as a traditional exposition that can aid in the recovery of otherwise lost early Epicurean doctrine, or, conversely, has focused on reconstructions that rely on texts of Epicurus. But although the inscription generally does not undermine what we know of the original teachings of Epicurus, Diogenes offers distinctive expansions and demonstrates the elasticity of Epicurean texts. A key example of the latter is Diogenes’ new version of the Principal Doctrines. Much of the text is recognizable despite departures from Diogenes Laërtius’ text that may indicate that the sayings had been simplified for memorizing and recitation (Clay 1990). Yet eight of Diogenes of Oenoanda’s Principal Doctrines are unique, and another corresponds not to a Principle Doctrine but to one of the Sententiae Vaticanae, a version similar to but longer than Diogenes Laërtius’ collection. Thus, Diogenes Laërtius and Diogenes of Oenoanda present us with two versions of the Principal Doctrines, neither of which necessarily matches a collection originally formulated by Epicurus or his immediate disciples. Another example of Diogenes’ divergence from earlier Epicurean texts may be his engagement with the Stoics, whom Diogenes—​like Philodemus but unlike Lucretius—​names directly. Even his choice of building (a stoa) may be an architectural allusion to Stoicism. Diogenes of Oenoanda’s very choice of medium—​large lettering on a monumental building—​represents a departure from Epicurean tradition. By erecting this urban, prominently displayed inscription, Diogenes reverses the Epicurean idea that one ought to withdraw from public life, an attitude epitomized in the Epicurean adage “Live Unnoticed” (on which see Roskam 2007). But Diogenes professes that superstition (pseudodoxia) is raging among his contemporaries, thus making them especially in need of the wisdom of Epicurus. As the garrulous Diogenes announces, “If only one person or two or three or four or five or six—​or as many more as you wish, reader, as long as there were not too many—​were in a bad way, I would address them one by one and do all in my power to give them the best advice” (fr. 3 Smith). A vast proclamation was in order, its audience to include “all Greeks and foreigners (barbaroi)” (fr. 32 Smith). If we are to believe Clement of Alexandria, Epicurus himself had asserted that Greeks alone were capable of philosophy (Stromateis 1.15). But Diogenes’ outlook is distinctly

622   Greco-Roman Science cosmopolitan: he hopes to reach “those who are called foreigners [xenoi], though they are not really so.” “For,” he continues, “while the various segments of the earth give different people a different country, the whole compass of this world gives all people a single country, the entire earth, and a single home, the world” (fr. 30 Smith). Diogenes does not specify the current superstitions he means to combat. But in several fragments he inveighs against oracular prophecy (fr. 23 Smith, and NF 143). There was an active oracle to Apollo in Oenoanda, and the oracular centers of the Greek east were enjoying a renaissance, particularly at Claros and Didyma (Milner 2000; Bendlin 2011). In an unexpectedly xenophobic new fragment, Diogenes also—​despite his professed cosmopolitanism—​vilifies Jews and Egyptians, whom he lumps together as the two most superstitious peoples, or, literally, “the most fearful of divine power” (NF 126). Here Diogenes promotes a stereotype expressed also by Seneca, Plutarch, Tacitus, and others, who label the Jewish creed a superstition (Gruen 2002, 43). Diogenes’ grouping of Jews with Egyptians is unusual, but the association was not unknown in Rome, where both could be regarded as practitioners of unwelcome alien cults (Gruen 2002, 30–​33, 52–​53). Significantly, Diogenes’ reference to people who suffer from pseudodoxia and his eagerness “to give them the best advice” appears in the preface to his treatise on physics. For an Epicurean the main point was to give an explanation of the natural world that placed humanity not under the rule of the gods but in the realm of atoms and void. The most up-​to-​date editions of Diogenes of Oenoanda are Smith 1993 and 2003, and the various publications of newer fragments (see Hammerstaedt and Smith 2012, with bibliography); references in this chapter follow the numerations standardized in these editions. Recent work stresses the Roman Imperial context of the inscription and represents a promising direction. See: Bendlin 2011; Clay 1989 [1998] and Clay 2000; Fletcher 2012; Roskam 2007; Scholz 2003; Snyder 2000; and Warren 2000.

4.  Diogenes Laërtius Diogenes Laërtius is the Greek author of Lives and Opinions of the Eminent Philosophers (perhaps of the 3rd century ce), a 10-​book compendium of the biographies and doctrines of the Greek philosophers. The entire tenth book is devoted to Epicurus and contains information about the history of Epicureanism, as well as the only completely intact texts of Epicurus: the Letter to Herodotus, the Letter to Menoeceus, and the Letter to Pythocles (the last possibly pseudepigraphic), which Diogenes follows with a collection of 40 Kuriai doxai, or Principal Doctrines. Although Diogenes Laërtius does not claim to be an Epicurean, he expresses enthusiasm for Epicurus and discounts the views of his many detractors (“these people are out of their minds,” 10.9). Because early Epicurean texts have survived only in fragments, it is difficult to determine whether Diogenes Laërtius’ selection of texts is representative. He asserts that the three letters —​which treat physical theory, ethics, and astronomy and

Epicureanism in Rome, the Bay of Naples, and Beyond    623 meteorology—​together summarize Epicurus’ “entire philosophy” (Diogenes Laërtius 10.28–​29), but they may be more reflective of post-​Hellenistic interests than is readily apparent. This chapter leaves that issue for future researchers and will not explore the cultural context of Diogenes Laërtius’ choice of Epicurean letters. For recent assessments of Diogenes Laërtius, see: Gigante 1992; Goulet-​Cazé 1999; Mejer 1992 and 2007; and Warren 2007. An adequate survey of Roman Epicurean science and medicine would require a close examination of all post-​Hellenistic texts, particularly Lucretius’ De rerum natura. If fragments of Epicurus’ On Nature continue to emerge from Herculaneum, sorting old from new would be an unending task. I  highlight below those aspects of Epicurean science that have attracted scholarly discussion because of the possibility—​and sometimes the likelihood—​that they represent departures from the original teachings of Epicurus.

5.  Epicurean Medicine The care of the soul is fundamental to Hellenistic philosophy in general, but later Epicureans are particularly adamant about the healing properties of Epicurean philosophy. They found good support in the texts of Epicurus, who had made the following analogy: “Just as there is no use for medicine if it does not cure the diseases of the body, so there is no use for philosophy if it does not throw out passion [pathos] from the psyche” (Porphyry, To Marcella sec. 31 Pötscher = Arrighetti 247). A doctrinal Epicurean saying makes the general outlook particularly clear and draws attention to the relevance of science to human happiness: “If we had never been oppressed by misapprehensions about the phenomena above us, or about death (which is nothing to us), or by ignorance of the limits of pains and desires, we would not have needed to study natural science” (Principal Doctrine 11). The later sources emphasize this fundamentally therapeutic purpose of scientific study via the persistent use of language that presents the wisdom of the Garden as a medical cure for human suffering. The most famous medical simile is provided by Lucretius, who describes his application of poetic honey to a philosophy that might at first seem bitter, just as healers rim the cup with honey when they administer bitter wormwood to children (1.935–​950 and 4.10–​25). Diogenes of Oenoanda offers “the remedies [pharmaka] that bring salvation” as the antidote to the superstition (pseudodoxia) raging among his contemporaries “who suffer from a common disease, as in a plague . . . and their number is increasing (for in mutual emulation they catch the disease from one another, like sheep)” (fr. 3 Smith). Philodemus reveals the Epicurean tetrapharmakos, an abbreviated version of the first four Principal Doctrines: “The gods do not concern us; death is nothing to us; what is good can be easily obtained; what is bad can be avoided” (Papyri Herculanenses 1005, col. 4.9–​14). In literal terms, the tetrapharmakos, or “four-​fold remedy,” was a compound of wax, suet, resin, and pitch that was used for various ills (Philo, On the Confusion

624   Greco-Roman Science of Languages sec.184 [SVF 2.472, 154.2–​5]). But Epicurean use of medical terminology is not exclusively figurative. More than a metaphor or analogy, the tetrapharmakos was a liberating panacea for human suffering, without which happiness was impossible. That is, the encapsulated wisdom was not like a cure, it was the therapy itself. Epicurean remedies—​whether offered in the form of a protreptic inscription, a memorable refrain, or a rebuke—​were to be applied to the psyche and thus might be termed a form of “psychotherapy.” But Epicurean psychotherapy is not entirely distinct from the care of the body, for in Epicurean theory the psyche is a material entity made up of particularly fine atoms that are closely integrated with the rest of the body. As Lucretius explains, “in our limbs and the entire body, intermingled is the hidden force of the spirit and the power of the soul” (in nostris membris et corpore toto /​mixta latens animi uis est animaeque potestas, 3.276–​277, cf. 3.136–​176). Thus Epicurean psychology falls under the rubric of physics. Both Lucretius and Philodemus expand upon the implications of Epicurus’ holistic conception of human beings as “temporary psychophysical (and ultimately atomic) units” (Gill 2007, 138). Lucretius explains that wind, air, and heat (all made of atomic compounds) are distributed throughout the body, their various amounts rendering someone prone to anger, or to fear, or to passivity (3.282–​313). But Lucretius adds that human beings are not entirely constrained by the nature of the specific atomic compounds that make up their individual psyches: human reason (ratio)—​ which is made up of fine atoms located in the chest—​can prevail, so any person can live “a life worthy of the gods” (3.319–​322). The atomic basis of human psychology figures prominently in Lucretius’ exposition of the sordidness and violence of sexual passion in the finale to book 4, which reduces erotic love to a physiological process (see Brown 1987). In the beginning of that book, Lucretius offers a material explanation of vision, in which atomic compounds are continuously shedding effluences or films (called eidola by Epicurus; simulacra by Lucretius) that are fine enough to enter the eyes of the beholder as images. Similarly, yet finer effluences wander through the air and can enter the mind itself, sometimes distorted and misconstrued, as in dreams about the deceased or visions of unreal creatures like centaurs (4.722–​748). Erotic love, as deceptive as a dream, is a kind of illusion based on the atomic visual influence of a particular human body (Brown 1987, 85). The suffering, insatiable lover exaggerates the importance of that specific body and will soon be disillusioned. To achieve Epicurean tranquility, “one must flee the effluences and ward off the fodder of love” (sed fugitare decet simulacra et pabula amoris /​absterrere sibi, 4.1063–​1064). Thus Lucretius’ description of the powerful mechanics of vision shocks the implied reader and arms the would-​be lover against unhealthy desire. Epicurus’ lost work On Erotic Love may have offered similar advice, but Lucretius’ vehement denunciation and his descriptions of the debilitated and reckless lover are particularly Roman (Brown 1987, 122–​127; Gordon 2002). It is difficult to reconcile Lucretius’ attack on erotic love with Philodemus’ love poetry (for poems see Sider 1997). Nor is Epicurean theory univocal elsewhere, as is clear from the radical differences between Philodemus’ and Lucretius’ treatments of mourning and the fear of death, and from Philodemus’ polemics against Epicureans who disagree with his theories about rage.

Epicureanism in Rome, the Bay of Naples, and Beyond    625 Epicureans in general agreed, however, that human beings can learn to correct faulty behavior if their errors are openly censured, a position grounded on the theory of the random swerve of the atom (see below), which somehow accounted for free will and responsibility. When Diogenes of Oenoanda mentions the swerve, he draws an explicit connection between free atomic movement and the ability to choose appropriate behavior: “Belief in fate makes admonition and censure irrelevant” (fr. 54, col. 3 Smith). Insight into how an Epicurean conceptualized the spoken word as a form of therapy is afforded by the fragments of Philodemus’ On Frank Criticism, which describe how Epicurean teachers must shape their therapeutic counsel—​and reprimands—​to fit the challenges presented by particular types of errant students and fellow Epicureans. Stark candor is appropriate for some students, but others require extreme care, according to such variables as gender, age, and social stature (see Konstan et al. 1998). Thus Epicurean medicine was therapy for the soul within the body, rather than for the body in isolation. Medical arts that treat the body alone are barely mentioned in Lucretius’ description of the rise of civilization (5.1011–​1457), and Epicurean remedies take precedence over traditional medicine in Lucretius’ famous description of the plague at Athens (6.1138–​1286). But Galen claims that the physiological theory of Asclepiades of Bithynia (late 2nd to early 1st century bce) was derived from Epicurean theories of particles and void, a connection he draws four times (for citations see Leith 2012). Galen asserts disparagingly that Asclepiades “altered only the names, speaking of onkoi [masses] instead of atoms, and pores instead of void” (Theriac, To Piso 11 [Kühn 14.250]). In Asclepiades’ system, the free motion of particles through equally imperceptible pores in body tissues resulted in good health, while blockage or abnormal flow resulted in disease. Galen’s references to his predecessors are not unassailable, and his point may be to disparage Asclepiades by linking him with the oft-​reviled Epicurus. Although many scholars, including Vallance (1990 and 1993), see no connection between Asclepiades and Epicurean theory, an opposing view has been articulated most recently by Leith, who argues, “Asclepiades’ physiology, pathology and psychology cannot be fully understood without a proper appreciation of their fundamentally Epicurean roots” (Leith 2012, 190). Leith adds that Lucretius’ account of the movement of atoms through imperceptible passages in the body (Lucretius 4.649–​657) “precisely parallels” Asclepiades’ description of the pores (2012, 186). Whether Asclepiades’ system was informed by Epicurean theory or not, Asclepiades may have influenced Philodemus’ investigation of the question of whether the moment of death involves pain (Pearcy 2012).

6. Scientific Method Epicurean science underwent a major change during the late Roman Republic. This is apparent from the well-​preserved Papyri Herculanenses 1065, a lengthy fragment of a work usually identified as De signis (On Methods of Inference, or On Phenomena and

626   Greco-Roman Science Inferences), which “offers an extraordinary modernity in comparison with our own era of logic and semiotics” (Gigante 1995, 42). In this work, Philodemus presents a reformulation of Epicurean scientific method that modifies Epicurus’ own approach significantly. According to this later revision—​which Philodemus received from his much admired teacher Zeno and his associates—​Epicurus’ method was wholly inductive, always moving from concrete and specific observations of the physical world to broader theories. For example, when Philodemus describes how the Epicureans infer from their own experience of human mortality that all people are mortal, he records the Epicurean argument that “we do not presuppose that the men about whom we infer are like those in our experience in respect to mortality . . . but from the fact that all men in our experience are similar even in respect to mortality, we infer that all men universally are liable to death, since nothing opposes the inference or draws us a step toward the view that men do not admit of death” (De signis 16.5–​25 DeLacy and DeLacy, 60–​61). Here as elsewhere, Philodemus and his sources make assertions in the first-​person plural, presenting the Epicurean position on inductive method as unified, to be traced back to Epicurus himself. But as Asmis has shown, it was most likely Zeno and his associates—​and not Epicurus—​who first reduced all scientific inference to induction (Asmis 1990, 2380–​ 2381; and 1999). In her view, Epicurus adopted two methods: deduction about what is unobserved on the basis of observations; and inductive inferences, based on similarities among observed things. Both kinds of arguments are based on a distinction between what is observed and what cannot be observed. The later Epicureans accepted this distinction. However, “very differently from Epicurus, they built a transition from the one kind to the other by allowing sufficiently tested empirical judgements to become, in the end, judgements about what is unobserved” (Asmis 1999, 294). The argument in De signis takes the form of a series of responses to Stoic and other objections to Epicurean epistemology, which demonstrates that Zeno and his associates were responding to critiques that were formulated well after the first generation of the Garden. It is significant that Philodemus’ acceptance of Zeno’s interpretation was not unique among Epicureans. In addition to recording Zeno’s defense of Epicurean method as he had heard it himself, Philodemus records recollections of objections and responses as understood by Zeno’s student Bromius, and another set that Philodemus’ older contemporary Demetrius Lacon had presented in his own lectures on “inference by similarities.” This development in Epicurean scientific method demonstrates how Epicureans might iron out and strengthen Epicurus’ own positions as they responded to negative appraisals.

7.  The Size of the Sun As the philosophy that identified pleasure as the telos (the end, or the purpose of life), Epicureanism attracted an array of unsympathetic observers. Although derision of

Epicureanism in Rome, the Bay of Naples, and Beyond    627 Epicurean philosophical language and the theory of pleasure were commonplace as early as New Comedy (some plays being roughly contemporary with Epicurus), Epicurean philosophy was also lambasted on scientific and theological grounds. Ridicule of Epicurus’ estimation of the size of the sun may be a special case, as it is possible that polemical distortion in antiquity has influenced modern understandings of Epicurus’ position. Epicureans claimed—​notoriously—​that the sun is the same size “as it appears to our senses” (Lucretius 5.564–​565; cf. Letter to Pythocles 91). According to Cicero (Academica 2.82, and On Duties 1.20) and the Stoic astronomy lecturer Cleomedes (Caelestia 2.1, with 2.76), Epicurus asserted the sun was thus approximately one-​foot wide, but this specific measurement does not appear in any Epicurean text and may be a reductio ad absurdum (Algra 2000). Cleomedes asserts that Epicureans—​unlike the Stoics—​are intellectually blind: “And no wonder: the discovery of scientific truth is not possible for pleasure-​loving people, but only for men whose natural inclination is toward virtue and who value nothing before virtue” (Caelestia 158). Accusations of effeminacy are typical in anti-​Epicurean discourse, but Cleomedes’ bald assertion that transgressive gender leads to bad science is unique. In the same passage, Cleomedes misrepresents Epicurus’ suggestion that the sun is kindled at sunrise and extinguished at sunset. Epicurus presents that notion merely as a possibility, his other suggestion being that the sun remains fiery when it travels below the earth (Letter to Pythocles 94). Multiple scientific explanations were essential to Epicurean method (but see Hankinson 2013 for the suggestion that Lucretius’ position does not coincide perfectly with Epicurus’). Cleomedes suggests that the Epicureans did not unanimously agree on the size of the sun: “Epicurus and the majority of his sect maintained that the sun is as large as it appears to be” (Caelestia 2.1.1–​2). Diogenes of Oenoanda attests to some flexibility where he argues that most people “suppose the sun to be as low as it appears; whereas it is not as low; for if it were, the earth and everything on it would catch on fire.” Instead, the image of the sun is low, not the sun itself (fr. 13, col. 1–​2 Smith). Sedley has offered a sympathetic contextualization that points out the earlier Greek philosopher Heraclitus was also credited with claiming the sun is a foot wide and reminds us that Epicurus offered an alternative to Plato’s astral theology (Sedley 1976). But Barnes suggests that one may need to accept Epicurean teachings about the sun as “a wart on the fair face of their philosophy” (1989, 35).

8.  The Swerve of the Atom As Tieleman made clear in chapter C2, Epicurus ascribed to a theory of atoms and void that has affinities with the earlier atomic theory of the Greek philosophers Leucippus and Democritus. From Lucretius, Philodemus, Cicero, Diogenes of Oenoanda, and other late sources, we learn of a uniquely Epicurean innovation. This is the theory of the atomic swerve (clinamen in Latin; parenklisis in Greek), described most fully by Lucretius (2.216–​293). According to the theory, atoms—​as they fall vertically downward

628   Greco-Roman Science through the void—​occasionally take a random, unpredictable swerve. Lucretius tells us that the swerve is required to account for the coming together of the atoms to form compounds (2.216–​250) and for uoluntas, the voluntary action of living beings (2.251–​ 293). But scholars disagree about the connection between the swerve and free will, and there is no scholarly agreement about how the swerve was meant to work, or whether any atom could swerve, and how often. Did the swerve operate “like a car changing lanes,” or did the swerving atom travel at an oblique angle to its previous path (Furley1999, 494)? More importantly: Did every act of volition require a new atomic swerve in the soul? Is volition itself the swerve? Or does Lucretius’ claim that the swerve “breaks the bounds of fate lest cause follow cause from infinity” (2.254–​255) mean that the swerve simply accounted somehow for one’s ability to follow a path not preordained by one’s atomic history? In his study of the swerve’s role in the preservation of human freedom, O’Keefe (2005, 26–​47) suggests that Lucretius’ treatment does not adequately explain the connection between volition and the swerve. Although the theory of the swerve of the atoms is not attested in the surviving texts of Epicurus, Cicero—​who called it a “puerile invention” (On Duties 1.6.18–​20: res ficta pueriliter)—​credits Epicurus (Nature of the Gods 1.69), as does Diogenes of Oenoanda (fr. 54 Smith). Most scholars accept that attribution. Nonetheless, it is possible that Lucretius does not present the view of Epicurus in its entirety (see O’Keefe 2005, 226–​247).

9.  The Gods as Atomic Compounds It is possible that the later Epicureans’ understandings of the divine were less subtle and more conventional than those of Epicurus, whose views we have in mere outline form. The former describe the gods as material, immortal beings who dwell in a place unlike our world. For Lucretius, the gods are made of exceptionally fine compounds that make them difficult to perceive: “For the fine (tenuis) nature of the gods, far sundered from our senses, is scarcely seen by the understanding of the mind; and since it lies far beneath all touch or blow from our hands, it cannot indeed touch anything which can be touched by us” (5.148–​151 Bailey). Similarly, Cicero’s Epicurean spokesman Velleius claims the gods have quasi-​body and quasi-​blood (Nature of the Gods 1.49), an idea that Cicero ridicules (1.71). Also according to Cicero, the Epicureans claimed that the gods live in a separate world called the intermundia (Nature of the Gods 1.18), but the term itself does not appear in Epicurean sources. Diogenes of Oenoanda criticizes the traditional iconography of the armed divinity, but tacitly affirms the gods’ anthropomorphic form: “we ought to make statues of the gods genial and smiling, so that we may smile back at them rather than be afraid of them” (fr. 119 Smith). Philodemus’ essays On Piety, On the Gods, and On the Way of the Life of the Gods provide more detailed information on the gods’ corporality and Epicurean piety. Most significant are his descriptions of the gods’ eating, drinking, breathing, and enjoying conversation (in Greek, or something like Greek);

Epicureanism in Rome, the Bay of Naples, and Beyond    629 and his consideration of the question of whether the gods ever sleep. Philodemus may have inspired Cicero’s complaint (voiced by his skeptical spokesman Cotta) that the Epicurean gods are excessively anthropomorphic (Nature of the Gods 1.94–​102). The materiality of these Epicurean gods is not incompatible with the Letter to Menoeceus, where Epicurus writes categorically: “Gods do exist, for knowledge of them is self-​evident” (123–​124). It is possible that Epicurus defended this view elsewhere by reminding his readers that the mind itself is a sense organ that receives effluences from atoms, no matter how rarified. But some scholars think that literal interpretations of Epicurus’ assertion in the Letter to Menoeceus contradict the fundamentals of Epicurean science: if compounds in general are perishable (as Lucretius claims), how could there be indestructible, eternal atomic compounds; and how can something unseen be known—​in the absence of proof—​with such certainty? These scholars propose that Epicurus conceived of gods as psychological projections or constructs, to be visualized by Epicureans as they focused their minds on the blessed life. Thus Sedley has suggested that “[t]‌he first-​generation Epicureans’ carefully coded style of religious discourse was chosen . . . to serve an agenda of theological idealism, while being cast in the existential terms agreeable to a culture that never came to trust atheism” (2011, 52; cf. Konstan 2011; see also Obbink 1989). For Sedley, this may explain why Lucretius never delivers the full treatment of the gods he promises (5.155): Lucretius was unable to find a clear, atomic explanation of the gods in any text by Epicurus himself. Cicero suggests a hostile interpretation (expressed in the voice of Cotta and elsewhere attributed to Posidonius): “I see that some people think that Epicurus—​in order not to offend the Athenians—​kept the gods in word, but in actuality eliminated them” (Nature of the Gods 1.85).

10.  The Epicurean Alternative to Intelligent Design Arguments for creationism are widespread in the scientific and philosophical texts of Greek and Roman antiquity and were expressed most eloquently in Plato’s Timaeus (probably 350s bce), “the ultimate creationist manifesto” (Sedley 2007, 132). For an atomist like Democritus (ca 400 bce), no intelligence could preexist the atoms and void, but it was left to the Epicureans to develop passionate arguments against divine creation. The tradition likely began with Epicurus, but our evidence is primarily Roman, the main sources being Lucretius’ De rerum natura and Cicero’s De natura deorum (The Nature of the Gods; 45 bce). Lucretius describes how the early, more fertile earth spontaneously generated an abundance of diverse organisms. But Lucretius does not present a theory of evolution in which one species develops from another. Rather, all known species, including humankind, are simply those randomly-​produced organisms that were capable of reproduction and the fittest to survive (Lucretius 5.837–​877). Lucretius vehemently denies that anatomical details were created for any purpose: the eyes, the hands, and

630   Greco-Roman Science the ears happened to exist before they were used for sight, touch, and hearing (4.823–​ 857). From Cicero, we learn that Epicurean theory drew a connection between the accidental emergence of every aspect the physical world—​and indeed an infinite number of worlds—​with “the power of infinity” (uis infinitatis; Nature of the Gods 1.50).

11.  Conclusion: “A Sinuous, Evolving Entity” The stereotype of the doctrinaire, anti-​intellectual Epicurean was prevalent in Greek and Roman antiquity, but even the ancient purveyors of the clichés acknowledge overstatement, distortion, and the Epicureans’ tendency to attribute others’ teachings to Epicurus himself. In his invective against Piso, a masterpiece of anti-​Epicurean polemic delivered in 55 bce, Cicero forestalls any objection that his characterization of the philosophers of the Garden might be unjust by conceding that Piso, as an Epicurean, comes “from the pigsty, not the school” (ex hara producte, non ex schola: Against Piso 37). According to Cicero, Piso’s strict adherence to particular words of Epicurus caused that student to want to “seal the tablets,” shutting out his teacher Philodemus’ scholarly explanations of the subtleties (Against Piso 69). Plutarch claimed that Epicurus’ younger contemporary Colotes (ca 310–​260 bce) followed Epicurus so slavishly that he could not comprehend his teaching in new contexts: “Colotes seems to have suffered the same thing that children suffer when they first learn their letters: accustomed to reciting the characters on their tablets, they become perplexed and confused when they see them elsewhere” (Reply to Colotes 1120). In a letter to Lucilius, Seneca contrasts the intellectual autonomy of the Stoics, who are “not controlled by a despot,” to the servility of the Epicureans (Letter 33.4). The latters’ admiration for Epicurus leads them—​ironically—​ to attribute the words of his immediate followers to the master himself: “Among those people, whatever Hermarchus said, whatever Metrodorus said, is ascribed to one man; everything anyone in that brotherhood says is spoken under his authority and control alone” (Letter 33.4). Epicureans clearly idealized Epicurus. And yet, across the centuries, later Greek and Roman Epicurean philosophers and scholars worked in diverse contexts that required new emphases and innovative ways to reactivate and extrapolate from basic Epicurean science. Rather than devoting themselves exclusively to the textual restoration or literal translation of Epicurus’ writings, or to the production of methodical commentaries on the foundational Greek texts, Philodemus, Diogenes of Oenoanda, and even Lucretius focused on new expositions. As Snyder (2000, 53) has written, the school’s texts were thus “not simply a static body of documents to be restored, but a sinuous, evolving entity.” Its relevance to the daily lives of its adherents was the most fundamental aspect of Epicureanism, so attention to context was perforce essential. Thus innovation coexisted with the reverence for tradition.

Epicureanism in Rome, the Bay of Naples, and Beyond    631

Abbreviations SVF = Hans von Arnim, Stoicorum Veterum Fragmenta, 3 vols. (Leizig: Teubner, 1903–​1905).

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chapter D3

Roman M edica l Se c ts The Asclepiadeans, the Methodists, and the Pneumatists Lauren Caldwell

This chapter focuses on three medical sects, or schools—​ Asclepiadeanism, Methodism, and Pneumatism—​ in the Roman Empire of the 1st through 3rd centuries ce. Sects, which were loosely affiliated schools of thought (haeresis, the Greek word for sect or school, means “choice”) rather than formal institutions, furnished theoretical and practical guidance for practitioners and supplied material for lively debates among intellectuals, including non-​ physicians, about the causes and treatment of disease. While this chapter addresses the main theoretical features that defined the Asclepiadeans, the Methodists, and the Pneumatists, it also explores how sectarian affiliation influenced the interactions among practitioners and between practitioners and patients. For example, the evidence for physicians’ participation in debates suggests how sectarian membership may have advanced the careers of the physicians who offered their services in an unregulated and rather chaotic market and hoped to attract the patronage of aristocrats. Similarly, considering how the experience of patients might have been shaped by the availability of these differing “scientific” approaches to health by the Asclepiadeans, Methodists, and Pneumatists deepens our understanding of how the inhabitants of the Roman Empire pursued treatment for medical concerns. The lack of consensus among sects had implications for participants in the world of Roman medicine, including students, practicing physicians, and patients.

1.  Sectarian Theories Although Roman medical sects might have been noteworthy for their theoretical differences and disagreements, the 2nd-​century physician and polymath Galen

638   Greco-Roman Science nevertheless confirms that they found common ground in their emphasis on the concept of equilibrium. “For all the sects,” he notes, “health is a matter of balance. For us, it is the balance of wet and dry, and hot and cold, while for others it is a balance of particles and pores, for others a balance of atoms, or of indivisible bodies, or of similar parts” (On Healthfulness, Kühn 6.15). Galen is our major source of information about Roman medical sects, and while this offers advantages, in that Galen was a keen observer of his profession, it also has its limits. Most notably, Galen often mentions particular sects only to criticize their errors. This is in line with his overall approach to the acquisition of knowledge, a search for “truth” which Galen says he learned from his father. Galen states that he did not adhere to the tenets of any single sect in any aspect of his education and instead learned about them to examine and judge them (On Diagnosing and Curing the Affections and Errors of the Soul, Kühn 5.42–​43). Galen provides enough information for us to sketch a basic outline of the sectarian groups. In On the Sects for Beginners, an introductory text for medical students, and On My Own Books, an overview of his works, Galen refers to three main sects in Roman medicine, the Rationalists, Empiricists, and the Methodists, who differed both in their efforts to advance medicine as a field and in their approaches to patient care. The Rationalists had inherited and adapted the Greek tradition of medical knowledge, most prominently the Hippocratic theory of the four humors, and emphasized the search for causes of disease in the treatment of patients. By contrast, the Empiricists put more emphasis on practice than on theory; they stressed the value of the physician’s past experience and the close observation of symptoms in patient care, and saw little advantage in seeking the cause of disease. The Asclepiadeans and the Pneumatists, too, are identifiable as intellectual groups that make an appearance throughout Galen’s texts—​in On My Own Books, Galen states he wrote two works on Asclepiadean theory, which today do not survive—​but by the 2nd century ce, these groups may have been smaller in their membership than in previous centuries. Galen has more to say, and we have more evidence in general, for the Methodists. Overall, it is difficult to date the beginnings of sectarian groups, and we know little about the men who started them. However, it is clear that by the early Roman Empire, the Asclepiadeans were those who had chosen to follow the medical ideas of Asclepiades of Bithynia, a Greek physician who had developed his theories at Rome in the late 2nd century bce. Asclepiades’ ability to attract students from across the Mediterranean appears to have played a large part in the establishment of the medical profession at Rome (Nutton 2004, 168). Asclepiades’ writings do not survive intact, but references to Asclepiades in the works of other authors provide a sense of his approach. According to his physiological theory, the body was made up of individual particles whose moderate and unimpeded movement through channels or passages in the body was necessary for health (Vallance 1990, 131–​143). Obstruction of the channels caused illness. This illness, in turn, could be treated by a wide variety of inexpensive therapies, including dietary changes and mild exercise. By the 1st century ce, Asclepiadeanism was sufficiently well-​ known among a Roman audience and identified with this conceptual model of particles, passages, and flow that the layman Celsus included it in the introduction to his eight-​ book work On Medicine (1.pref.14–​15).

Medical Sects: Asclepiadeans, Methodists, Pneumatists    639 Pliny the Elder, a writer of the late 1st century ce, who expressed skepticism about the importation of the Greek medical tradition to Rome, disapproves of Asclepiades’ shift from a career in rhetoric to the practice of medicine at Rome. In Pliny’s portrayal, Asclepiades is an opportunist who chose to remain uninformed about medical remedies that required observation and experience, relying instead on his previously honed persuasive speaking skills to sway an audience. Similarly, Pliny notes, Asclepiades failed to properly engage with drug therapy and favored the study of causes and speculations about illness. Pliny (26.7–​8) notes that Asclepiades’ approach grew in popularity not because of his brilliant skill as an experienced clinician but because he prescribed treatment for “all diseases in common” through a regimen of food, wine, water, massage, and exercise, which appealed to a wide clientele. In On Medical Experience, Galen attacks Asclepiades in a similar way, for his neglect of the physician’s experience as adding value to the practice of medicine (On Medical Experience, Walzer, p. 85). Galen also disapproved of physicians, including Asclepiades, who favored a model in which the human body was composed of anything other than the four espoused by the Hippocratics. In the Hippocratic theoretical model, the body was composed of blood, phlegm, black bile, and yellow bile, whose balance was held to be essential for health (On Hippocrates’ the Nature of Man, Kühn 15.34). For Galen, who revered both humoral theory and Hippocrates, the man as “our guide for all that is good” (On Prognosis, Kühn 14.602) and who wrote extensive commentaries on treatises in the Hippocratic Corpus, the Asclepiadean approach did not show sufficient respect for the traditional authority of Hippocratic theory. To be sure, Galen does cite the Asclepiadeans as a group, as when he discusses their views of venesection and purging and, again criticizing their lack of practical skills, invites them to engage in a public contest with him “as though in a stadium” to demonstrate that they can compete not simply with “words” but with “deeds” (On the Effectiveness of Purging Drugs, Kühn 11.327–​330). As Galen presents it, interactions among physicians were often not neutral; instead, they were battles in which there were winners and losers, sometimes with the reputation of a sect at stake. Yet it remains unclear how many followers of Asclepiades’ theory would have called themselves Asclepiadeans by Galen’s day, or how they defined their circle of membership. How to draw a clear line between the Asclepiadeans and other groups is an additional challenge since the Methodist sect, which had appropriated and adapted the basic theoretical framework of Asclepiadeanism, was also flourishing in the 1st and 2nd centuries ce. Distinguishing between the Asclepiadeans and the Methodists in the early empire is made more difficult, too, because few texts written by Methodist authors are extant. As with the Asclepiadeans, our view is distorted by the judgments of Galen, who was not reluctant to disparage the theories and practices of this group. The sole Methodist text that survives intact is the Gynecology of Soranus of Ephesus from the early 2nd century ce. From this text and Pliny’s Natural History we learn that the founder of Methodism was Themison, who was listed as a student of Asclepiades in the genealogy of teachers and students of Methodism. Next in line was Thessalus, whom Galen cites as bringing Methodism to the attention of Emperor Nero as a new sect that would offer a better way to maintain health and cure illness, although Thessalus comes in for a lengthy attack by

640   Greco-Roman Science Galen for founding Methodism and lowering the standards for medical practice (On the Method of Healing, Kühn 10.1–​30). To what extent Galen’s views were shared by others is difficult to say, although there is no doubt that Methodism grew in popularity in the Roman Empire in the 1st through 3rd centuries (Nutton 2004, 191–​206). By Soranus’ day, it is clear that, at least as far as women’s medicine was concerned, a separation had been established between Asclepiadeanism and Methodism. Soranus criticized Asclepiades’ model of particles and channels as oversimplified, and he took particular issue with Asclepiades for contending “the female is composed of the same elementary particles as the male” and for failing to take into account that there were diseases specific to women (Gynecology 3.3, Budé 3.4, Corpus Medicorum Graecorum 4.95 Ilberg). Methodism’s distinctive features are shown most clearly, perhaps, by way of contrast with Empiricism. Empiricist theory held that a physician needed to consider the traits of the individual, including age and gender and environment; to observe the individual over time and record observations; and to refer to specific precedent for guidance on how to treat a patient’s condition. For precedent, the Empiricist could refer to the past treatment, course of illness, and timing of recovery in a patient with the same symptoms, using case notes and histories either from his own experience or from the records of fellow physicians. In contrast, the Methodists held that the physician needed to know only about the general causes of disease and health since all diseases had shared features, or commonalities. In the Methodist model, disease was caused by constriction or flooding of the channels of the body through which particles flowed. The ill patient’s body could be entirely in a state of constriction or in a state of flux; or, if one part of the body was experiencing constriction, while another was suffering from excess fluidity, this was deemed a “mixed” state (Hanson and Green 1994, 988–​990). Health was restored by a treatment that could restore balance to the flow throughout the body. In this model of understanding, external factors, such as climate to which the patient was exposed, mattered less for the prescription of a particular therapy than did the diagnosis of the body’s state. Methodists might recommend a range of treatments, from diet and exercise to drugs to surgery, to restore and then maintain health. Galen vigorously criticizes the three-​day period of fasting prescribed by the Methodists as a treatment for fevers (On the Method of Healing, Kühn 10.559–​563 and 10.580–​583), and tends to cast the entire project of Methodist treatment as a sham by Sophists rather than doctors. However, other texts, such as Soranus’ Gynecology, offer Methodist prescriptions that accord with traditional approaches in Greek medicine. For a woman suffering from an acute uterine problem, for example, Soranus recommends some interventionist therapies that sound similar to Hippocratic therapies, including cupping, leeches, suppositories, and sitz baths. The woman who has recovered, he says, should take part in “passive exercises, walks, baths, vocal exercises, a little wine, and suitable and varied foods” (Gynecology 3.38, Budé 3.41, Corpus Medicorum Graecorum 4.117 Ilberg). Galen, for his part, approved of Soranus’ recommendations. Incidentally, Soranus sets his therapies against what he sees as potentially harmful interventions prescribed by Asclepiades for uterine problems, including making the patient sneeze, wrapping the patient’s abdomen in tight bandages,

Medical Sects: Asclepiadeans, Methodists, Pneumatists    641 and having the patient drink water and engage in sexual intercourse (Gynecology 3.29, Budé 3.31; Corpus Medicorum Graecorum 4.112–​113 Ilberg). While the Methodists traced their origins to the 2nd century bce, the Pneumatists could cite the theories of Athenaeus of Attalia in the 1st century bce as foundational. As a sect with its own discrete identity, Pneumatism appears to have been less coherent than Methodism. After surveying the writings attributed to Pneumatism, Nutton (2004, 206) notes, “one may have considerable doubts about its very existence as a sect in any strong sense of the word.” As in so many other instances, Galen here too influences our understanding of how the sect was constituted. It is possible that when he refers to the group of physicians as Pneumatists, he suggests that they were more united in their views than was the case. However, even if our evidence for the membership of the Pneumatist sect is scant, it is possible to sketch an outline of Pneumatist doctrine that shows how it departs from or aligns with those of other sects. Most notably, the Pneumatists did not subscribe to the model of particles and channels espoused by the Asclepiadeans and the Methodists; they instead embraced, with some modification, the Hippocratic humoral model. To the traditional system of the four humors and the bodily qualities of hot, cold, wet, and dry, the Pneumatists added the element of pneuma, air or breath, carried in the arteries along with blood, whose imbalance in the body was thought to cause illness. Pneuma had long been conceived as a physiologically important substance, especially after Erasistratus, in the 3rd century bce at Alexandria, had theorized that pneuma was a substance carried in the arteries (Nutton 2004, 134–​137). From Galen, we learn that the later adherents to this doctrine, the “followers of Athenaeus,” believed that the healthy individual maintained a balance of heat and moisture in the body. External factors, such as the seasons, influenced health; so did the age of the individual, with childhood the most balanced and vigorous life stage (On Mixtures, Kühn 1.522). Pneuma acted as a kind of life-​force driving the body. From the works of Aretaeus, from the 1st century ce (the date advocated by Oberhelman 1994), we can get some sense of how the Pneumatists envisioned this pneuma as conferring life by allowing the organs to function. As Aretaeus explains, the lungs are not the origin of respiration but rather the heart, which is a hot organ capable of drawing in cold air and then providing pneuma, the most important basis of life (On Causes and Symptoms of Acute Diseases, 2.1.1; Corpus Medicorum Graecorum 2.15, Hude). Aretaeus therefore hypothesizes two kinds of angina, one an “illness of the pneuma,” caused by the body becoming hotter and drier, but with no inflammation, whereas the second is characterized by inflammation of the organs (On Causes and Symptoms of Acute Diseases, 1.7.1–​2, Corpus Medicorum Graecorum 2.7, Hude). Too much hotness and dryness in the body causes the patient suffering from angina to present with a feeling of suffocation. Meanwhile, an imbalance of pneuma could be cured by a variety of therapies: an excess of pneuma in the blood, for example, might be remedied by bleeding and cupping for a period of days and the application of a compounded ointment (On the Causes and Symptoms of Acute Diseases, 1.7.2; Corpus Medicorum Graecorum 2.7, Hude). Aretaeus mentions a variety of drinks and compounds to balance the pneuma; he notes, “animals live by two principal things: food and pneuma,” and, weighing the two, he calls pneuma

642   Greco-Roman Science more important. Such a statement about the vital importance of breath—​with which it was not easy to disagree—​also brings out the potential appeal of Pneumatism to a wide audience. Aretaeus may have engaged in subtle or complex technical arguments with fellow experts about the role of pneuma in physiological functioning, but his exposition of the symptoms and causes of respiratory diseases and his description of pneuma as a material substance are both accessible to a lay reader. Moreover, Galen, although not going so far to endorse Pneumatist doctrine, conceded that Athenaeus had created a well worked out theory. He records that part of his medical education, with a teacher who was a follower of Athenaeus, had involved lively debate about how the Pneumatists incorporated an understanding of hot, cold, wet, and dry qualities into their theories of the body, with Galen questioning ambiguities in the theory (On the Elements According to Hippocrates, Kühn 1.457–​473). Galen does not so much aim in this vignette to present his Pneumatist teacher as inept—​since to do so might invite questions about the quality of Galen’s own training—​as wish to make clear that early in his medical career he had mastered the ability to evaluate and criticize any one sect’s ideas. Such an effort to write a history of his training that distinguishes him as an independent thinker reminds us, in turn, of the diverse and crowded field in which Galen operated as a practitioner:  the Asclepiadean, Methodist, and Pneumatist theories coexisted with those of other sects, including the influential Rationalists and Empiricists. No account of medicine in the Roman Empire can ignore the intense controversy within and among these groups, and no single theory or approach to healing prevailed (Flemming 2000, 124). Thus what we gain from this overview of the theories of the Asclepiadeans, Methodists, and Pneumatists is less an understanding of what Roman imperial doctors actually believed about the body’s mechanisms than a sense of the highly contested state of medical knowledge in this period and the prominence of disputes in the practice of medicine. Yet sects did more than create intellectual noise or distraction: the act of dividing into groups or schools of thought was a way to give some order to the plethora of medical data that had been passed down over the centuries since the Hippocratics (Flemming 2003).

2.  Sects and the Training of Students in Medicine In reflecting on the path of his medical education, Galen writes that he learned the theory and practice of medicine “not from treatises, as some did, but in the presence of the chief teachers of each sect” (On the Affected Parts, Kühn 8.143–​144). His comment singles out his own education as special. But it conveys, too, that some students of medicine may have received their information from treatises rather than from leaders themselves. It also highlights that individual teachers, not formal institutions, served as the guardians of the knowledge associated with sects. No overarching structure along

Medical Sects: Asclepiadeans, Methodists, Pneumatists    643 the lines of the modern university existed in the early empire to finance the study of medicine—​or any other high-​level scholastic pursuit, such as rhetoric or philosophy. The theories surveyed above show that the lack of institutional support did not prevent Roman medical knowledge and practice from developing in a sophisticated way. However, lacking such an institutional context, medical knowledge and practice were sustained and transmitted in less formally organized ways. In the case of philosophy, “the fortunes of the ancient schools depended on the abilities, intellectual influence, and the means of particular individuals” (Mitsis 2003, 464). Without the benefit of continuity and support such as that provided to faculty through the structures of modern universities, the development or survival of intellectual ideas and debate in the Roman Empire depended on individual teacher-​student relationships and personal connections. Although social bonds did not necessarily stand in the way of thought-​ provoking debate and rigorous training, Galen did suggest a potential downside, that the system’s reliance on individuals could do a disservice to the advancement of ideas by prioritizing personal loyalties over intellectual rigor. “Doctors and philosophers,” Galen observes, “admire other doctors or philosophers in ignorance of their teachings . . . because someone influential—​a father, teacher, friend, or other important person in the city—​is an Empiricist, Dogmatist, or Methodist” (On the Order of My Own Books, Kühn 19.50). Galen states that he was driven to write his book On the Best Sect in response to the need to train physicians in logical argument so that they may properly judge the sects for themselves. Armed with logic, they will not be in danger of allying with a sect in the same casual way they might choose to support a particular team at the races (On the Order of My Own Books, Kühn 19.53). In an intellectual climate in which practitioners tended to ally themselves with individuals as much as with theories, it is no coincidence that Galen, in On Medical Experience, continually represents Asclepiadeanism by the person of Asclepiades, and not just by the ideas of the sect he founded. To the extent that there were societies of physicians associated with education, they were “loose groups of practitioners associated with particular theories, teachers, and places, not well-​organized teaching establishments” (Nutton 1992, 19). In nonmedical sources, these are not always identified with a particular sect: a satiric epigram of the poet Martial from the late 1st century ce, written from the perspective of a fictional patient, describes the crowd of “one hundred” students who trailed a doctor as he made his rounds (Epigram 5.9). In the late 2nd century ce, Galen complained that this arrangement was ripe for abuse. He notes that some unscrupulous practitioners recruited students by promising to “teach the arts in the least amount of time,” abandoning their responsibility to train students in technical competence and instead focusing on their own reputation and wealth (On Prognosis, Kühn 14.600). Elsewhere, Galen criticizes students of his day for being focused on earning money rather than on properly understanding diseases and treatment. He stresses that a doctor must have a grounding in philosophy, not only to assist in learning about the nature of the body and about the differences and treatments of disease, but also in order to acquire a temperate character that disdains money (That the Best Physician Is Also a Philosopher, Kühn 1.60–​61).

644   Greco-Roman Science From time to time we hear claims about sects’ approach to medical training from Galen, but often they are colored by his prejudice against medical training that was not as thorough as his decade-​long education: he disapprovingly comments, for example, that the Methodists “notoriously” advertised a six-​month training period for medical students (On the Sects for Beginners, Kühn 1.83). Such training, however, offered the advantage of accessibility to a broader group of students rather than to a narrow elite. Moreover, from Galen we do not hear about those aspiring doctors who lacked the financial resources or social connections necessary to receive training from a well-​ known, learned teacher—​an undertaking that might have called for travel to a city such as Rome or Alexandria—​who must have sought doctors in the local community who could provide basic training in hands-​on skills with little emphasis on Methodist or other theory.

3.  Sects and the Community of Physicians For wealthy and educated physicians, sectarian theories found in medical texts and teachings would have underpinned practice, guiding diagnoses, therapeutics, and prognostic methods. However, as we have seen, the extent to which physicians relied on the formal classification of Asclepiadean, Methodist, Pneumatist, or other sects to identify themselves to one another is not clear from the surviving evidence. Did physicians ever see themselves as banded together to present a united front—​for example, by advertising their membership in a sect—​to a potentially doubting public? Based on Galen’s accounts, sectarian membership seems more like a badge to wield to get ahead or simply to defend oneself as an individual practitioner in a highly competitive atmosphere. Regrettably, there is no text that sheds light on the community-​formation activities of Roman imperial medical sects as does Philostratus’ Lives of the Sophists, a 3rd-​century biographical work that depicts imperial sophists as a “community constituted entirely from within, by the consensus of insiders” who assign outsider or insider status to particular individuals (Eshleman 2008, 396). Yet Galen seems to perceive sectarian affiliation as a central part of many physicians’ professional identity. He emphasizes that he takes the best features and elements from each and combines them to create his own superior method (On the Affected Parts Kühn 3.3). Moreover, even if sectarian affiliation contributed to a spirit of community for some physicians, the very existence of rival sects points to the challenge of credentialing and credibility that was constantly being confronted by individual physicians in the early Roman Empire. Even elite physicians fought for recognition in a culture that had traditionally considered the study of rhetoric and philosophy, not medicine, to be the culmination of elite literate education. Theories put forward by sects, beyond providing detailed descriptions of the body and its mechanisms, helped substantiate the claim that

Medical Sects: Asclepiadeans, Methodists, Pneumatists    645 medicine operated on a high intellectual plane. This eagerness to be authorized as an intellectual is on display in Galen’s treatise That the Best Physician Is Also a Philosopher, which contends that philosophy could make medical students better doctors. There is little reason to doubt the sincerity of his belief that “doctors need philosophy in order to employ their art in the right way,” with study of the “logical, the physical, and the ethical” parts of philosophy helping to guide them toward an understanding of the nature of the body and away from the temptation of financial gain. Yet, by highlighting that training in logic helped doctors be better practitioners and theoreticians, Galen also wished to eliminate any lingering doubt among his 2nd-​century readers that medicine and philosophy were intellectual pursuits that could go hand in hand. Although sectarian membership is not discussed in That the Best Physician Is Also a Philosopher, it is clear that such affiliation could be part of a physician’s effort to be recognized as an intellectual with specialized rather than amateur-​level knowledge, and to identify himself as a practitioner who was not isolated in his views. Such an approach might appeal to Roman aristocratic patients who were able to provide patronage and social connections to physicians in return for their services (Mattern 1999, 2). Competition for the resources offered by aristocrats, understandably, was fierce, as Galen makes clear in his treatise On Prognosis (Kühn 14.600–​601). Ideally, in advertising to his patrons, his peers, and his patients that he had a track record of success treating patients and that he was an insider who was accepted within a group of specialists, the physician would be able to move up the professional ladder. The potential for doctors to use sectarian affiliation to enhance their reputations and status opens the question of how sectarian affiliation, and the deep knowledge of medical subjects that this affiliation suggested, might have functioned to advance physicians’ careers. An educated layman who addresses this issue, albeit indirectly, is Plutarch, who was active in the late 1st century ce. His miscellaneous text Sympotic Questions, a large collection of dinner-​party conversations, includes physicians among the speakers who engage in debate and discussion as part of socializing. In one example, a physician guest, Philo, starts a lively conversation about the origin of the disease elephantiasis, which he claims is new, and refers to Asclepiades. Another guest, Diogenianus, argues to the contrary that there are no new diseases, only differences in intensity of the same diseases. Plutarch offers the final speech, as a nonphysician, contending that the emergence of new diseases is indeed possible and that changes to the body, even those induced by diet and exercise and baths, can create new diseases (Sympotic Questions 731b–​734d). In this depiction, the medical question up for debate—​can new diseases arise or not?—​is not so much brought to a conclusion as left open for further consideration by the reader. This lack of resolution in the partygoers’ conversation reflects, in turn, the unresolved nature of medical sectarian debates among specialists of Plutarch’s day. At the same time, Plutarch’s depiction suggests that the relatively light conversation of the dinner party could provide physicians with the opportunity to employ sectarian knowledge in a way that enhanced their professional reputation while being removed from the day-​to-​ day treatment of patients, with whom interactions could be more high-​stakes and less predictable.

646   Greco-Roman Science In addition, by inviting rigorous but good-​natured questioning and argument, the symposium may have provided learned physicians in the Roman Empire with a way to take sectarian ideas—​many of which overlapped with those of philosophy—​outside the “bubble” of their fellow medical experts and to test them on guests who were highly educated in rhetoric and philosophy. The private and controlled atmosphere of a dinner party also allowed a physician to make social connections, if that was desired, in a way that did not require public advertising of his services. The public demonstrations of medical skills, such as dissections, in which physicians could be expected to participate, were especially competitive, even hostile, environments, as Galen discovered in his experience (Nutton 2012, 224); and a symposium was certainly a kinder, gentler, alternative forum. Plutarch, in particular, seems interested in the ability of the dinner party to encourage guests to offer their imaginative solutions to various problems, with a variety of professional perspectives, including medicine, represented in the conversation (König 2007, 52–​54). A forum for nonthreatening rivalry among the educated, including physicians, might have provided some relief from professional anxiety such as that expressed by Galen in On My Own Books, when he worries about the circulation of his texts in the medical marketplace, and more generally about what might happen to medical ideas if they are taken up outside the respectable sectarian groups by irresponsible readers or authors. It also might have eased fears among physicians about the threats their rivals posed, as Galen suggests in his mention of Quintus, a capable physician who fled Rome after his enemies accused him of murdering his patients (On Prognosis, Kühn 14.600). In this passage, Galen compares himself to Quintus and to another doctor who was murdered; Galen also cites his hostility against him as his reason for leaving Rome in 166 ce (Nutton 2012, 224). Given the competitive professional setting in which physicians regularly identified with or against each other’s views, one might also expect to find professional associations or guilds (collegia) for particular sects that served to create regulations or affirm members’ professional qualifications. There is some evidence of a medical collegium at Ephesus in the 2nd century ce, where the group made dedications to the Greco-​Roman healing god Asclepius and possibly organized contests in which physicians competed in various medical skills—​including, it seems, diagnosis, drug treatment, and surgery—​as part of the festival of Asclepius at Ephesus. No doubt some physicians employed a particular sectarian approach in such contests. However, if the emphasis was on which physician could use his practical skills to reach the best patient outcome, then theories may not have played a large part in such contests (Nutton 1992, 8–​10). Although it would be reasonable to expect the record of inscriptions from the eastern and western empire to enlighten us about how physicians identified with sectarian groups, the surviving inscriptions suggest that the formal clubs or associations to which doctors belonged were often unrelated to their medical activities. For example, physicians (iatroi and medici) appear alongside nonphysicians as members of funerary collegia, the traditional Roman societies or guilds that promised to provide burial services to their members (Nutton 1992, 6). Doctors’ groups were not as organized as those

Medical Sects: Asclepiadeans, Methodists, Pneumatists    647 of athletes, for example, in the early Roman Empire. The inscriptional record shows that by the time of the Emperor Antoninus Pius, in Galen’s lifetime, the club or society of professional athletes had been given a central administrative headquarters in a building near the Baths of Trajan in Rome (Inscriptiones Graecae 14.1055b; Kyle 2014, 321); no similar record suggests the existence of similar institutional support for physicians in the pre-​Christian empire. An examination of imperial medical sects would be incomplete without a consideration of how gender-​based norms influenced the sects’ membership. The texts considered so far have implied, if not explicitly stated, that the members of sectarian groups are men. Men are the authors of almost all surviving medical texts from the Roman Empire, including those that describe the theories of sects such as Methodism, for example, Soranus’ Gynecology. That text, however, also makes clear that women were part of the community of medical practitioners. Physicians and patients alike had a reliance on midwives, whom Soranus portrays as taking the lead in caring for women giving birth and for newborns. Given the importance of these female caregivers, is there a way to determine whether these women were also active members in sects? Soranus is some help on this front; he describes the best midwife as one who goes beyond the performance of her practical medical duties to become educated in theory (Gynecology 1.4, Budé 1.5; Corpus Medicorum Graecorum 4.4, Ilberg). Recent scholarship has investigated the role of women as contributors to the world of medical writing in the early empire and has concluded that while the evidence is not plentiful, it does show that some women moved beyond the practical aspects of caregiving in areas we would expect, such as obstetrics, to have “some engagement with literary culture” (Flemming 2007, 262). Of the few medical treatises from the early empire that have been even loosely attributed to female authors, such as those of Cleopatra and Metrodora (Flemming 2007, 276), none is aligned with the tenets of a particular sect, although Metrodora’s text on pathologies of the womb aligns with the Hippocratic Diseases of Women (Parker 1997, 138–​140). This leaves open the question of whether women’s intellectual projects could have extended to sectarian activities such as lectures, debates, and discussions. Given the traditional Roman concern with respectable women’s appearance in public, and the entrenched cultural view that training in rhetoric could compromise or damage feminine modesty, it seems likely that female medical practitioners did not engage in open-​air public debates in the amphitheater with their male peers, no matter their level of acquaintance with medical theory. Finally, any overview of physicians’ claims to erudition and specialization in the early Roman Empire must acknowledge that most doctors were generalists, and the physicians who attained the highest level of theoretical training were few and far between. Many doctors, including those trained less formally, as discussed above, had a working knowledge of the human body but were more involved with hands-​on practice than with theoretical debates. Given the diversity of the community of physicians, it is not possible to say that sectarian debates and developments pervaded their day-​ to-​day experience. Those physicians who occupied a lower rung of the social ladder, for example, were perceived as figures who shared more qualities with craftsmen than

648   Greco-Roman Science with philosophers. A  document on papyrus from the 1st century ce discovered in Tebtunis, a village in the Fayum region of Egypt, includes doctor on a list alongside craft professions including those of baker, dyer, fuller, tailor, locksmith, and mason (Tebtunis Papyri 2. 278).

4.  Sects and Practice: Patients When we turn to ask how the presence of medical sects affected wider imperial society, another set of questions arises about how relations between doctor and patient were shaped by the existence of Methodists, Asclepiadeans, Pneumatists, and sectarians of other stripes. Did the ideas propounded by these sects mostly serve to drive esoteric debates among rival professionals, with patients barely aware of their physicians’ theories and professional rivalries? Or was the influence of sectarian ideas and allegiances felt broadly, and if so, did this serve to shore up or undermine patient confidence in their physicians? The sources that address these questions either directly or obliquely provide a variety of answers. Martial, in Epigram 5.9, mentioned above, suggests that the cult of personality around a particular physician could create a chaotic atmosphere at the patient’s bedside that detracted from the physician-​patient relationship. While doctors may not have been followed by a hundred students, Martial at least highlights that they were often simultaneously engaged in two professional dynamics at the patient’s bedside—​one with their apprentices, and one with their patients. In On Prognosis, Galen presents a third dynamic, between rival doctors who offer competing diagnoses or prognoses at the patient’s bedside while the ill patient waits expectantly for a cure. The story of Eudemus, the aristocrat whose illness was misdiagnosed by Galen’s rivals, is a case in point. Eudemus summons the most prominent doctors in Rome as he seeks treatment for his febrile illness, only to find that the doctors’ recommendation for doses of theriac proves ineffective (On Prognosis, Kühn 14.606–​612). Effective treatment is offered only by Galen, who relies on his measurement of Eudemus’ pulse and examination of his urine. Galen makes a point that his rivals, including Antigenes and Martianus, were overcome by his expertise in using the pulse to diagnose and treat illness, a technique possibly taken from the Empiricist part of his education (On the Diagnosis of Pulses, Kühn 8.711–​773). While On Prognosis offers several engaging patient case histories, Galen tells their stories from the practitioner’s point of view, crafting a promotional narrative—​Galen’s patients, notably, never die under his care—​that conveys a message about his status and preeminence and would, ideally, build the confidence of prospective patients in his abilities. The extent to which such promotional materials were effective, however, is called into question by the perspective of a lay author like Pliny the Elder, according to whom sectarian posturing and competition adversely affected patients. His Natural History, written at Rome around 75 ce, is well known for its generally unflattering portrayal of physicians, whom Pliny viewed as interfering with the traditional Roman model

Medical Sects: Asclepiadeans, Methodists, Pneumatists    649 in which the paterfamilias, or head of household, was considered able to manage the health of his family and slaves without formal study or abstract theory. Pliny points to the problems created for the patient by the constantly changing landscape of medicine at Rome, and he singles out the sects, or factiones, of physicians for particular criticism. In his account, the crowd of doctors are driven by pride, with their “wretched controversies of opinion” at the patient’s bedside (29.11) compromising their obligation to do no harm to the sick. Likewise, the establishment at Rome of new sects was nothing more than a cynical ploy manufactured by physicians to gain advantage in a competitive market. Practitioners including Vettius Valens, who founded a new sect to gain “followers and power”; the “superstitious” Crinas of Massilia, who similarly created a system to unite medicine with astrology to impress patients by using the stars to create dietary regimens; and Thessalus, founder of Methodism and self-​proclaimed “champion of physicians,” stand out for Pliny as unscrupulous manipulators of the public (29.8–​9). The prescribed therapies, meanwhile, could be as harmful to the patient as the physicians’ endless disputes. Charmis of Massilia entered Rome “condemning earlier physicians” and prescribing harmful cold baths in wintertime—​and to Pliny’s dismay, the Roman elite are only too happy to oblige (29.10). On this view, the accessibility of medical knowledge provided by sects to the patient is a defect, not an advantage, with patients from the upper classes potentially faring worse than those of the lower classes, since they have more resources to spend on harmful treatments. With such a burden placed on patients to choose from a variety of options, some might have preferred the profile of one particular sect over another for basic practical reasons of cost and efficiency and availability, or for other patient-​centered reasons, such as the reputation of a particular sect’s physicians for providing carefully tailored attention and treatment. The approach of an Empiricist physician, for example, that emphasized observation and recording case histories, offered the advantage of careful attention to the individual patient and referral to the authority of precedent for diagnosis and treatment, thereby reassuring the patient that the physician had studied all possible ways this disease had been treated successfully before, particularly with drugs (Nutton 2004, 148–​150). The approach of a Methodist physician, on the other hand, could draw in patients with a less expensive and less time-​consuming diagnosis and treatment plan. Efficiency was emphasized in the Methodist diagnostic process that was largely limited to the initial examination of the patient, where the physician quickly determined which “commonality” was present in the illness and which course of therapy was appropriate. Of course, the constraints of premodern medicine make it likely that there was not a great deal of difference in success rates and patient outcomes for the Empiricist and Methodist clinical approaches. This may have contributed to an overall impression among laypersons that one could expect more or less the same kind of results from physicians no matter the choice one made. In an effort to separate himself from the crowd, Galen may well have been responding to the pressure patients could place on physicians to provide the right approach to clinical care. He seems to take an ambivalent position on whether sects were good or bad for this purpose. In On My Own Books, a friend of Galen responds to a popular anatomist, who had asked about Galen’s

650   Greco-Roman Science sectarian adherence, that Galen calls people who identify themselves as Hippocrateans or Praxagoreans, among others, as “slaves,” while he took what was best from each sect (On My Own Books, Kühn 19.13). Yet Galen also notes that wealthy Roman patients should not be uninterested in the training of their prospective physicians but should investigate and test their skills (On Examinations by Which the Best Physicians are Recognized, Iskandar, p. 43) and confirm that physicians have studied Hippocratic theory so they are able to gain the most from clinical experience (On Examinations by Which the Best Physicians are Recognized, Iskandar, p. 59). The best physician will be able to take theoretical knowl­ edge and innovate as well. As we might expect, in On Prognosis, Galen represents himself as a practitioner who introduced clinical methods he developed, such as using the pulse for diagnosis, in a way that built on earlier Empiricist theory but did not rely entirely on it.

5.  Sects and Other Options for Treatment of Health and Illness The approaches of philosophically based medicine were not the only option for the sick, nor were doctors universally admired, as Pliny the Elder and Martial demonstrate. Many patients—​whether they believed the treatments offered by Methodist or Empiricist doctors to be newfangled or overly abstract, or could not afford or find them in the less urban communities of the empire—​took other routes when seeking treatment. Possible alternatives were numerous, and included folk remedies, magic, and traditional religion, including the cult of the Greco-​Roman healing god Asclepius. While an extended discussion of magico-​religious medicine is outside the scope of this essay, there is one text, the Sacred Tales of Aelius Aristides, written during Galen’s lifetime, that provides some commentary on physicians from the patient’s point of view. The Sacred Tales sheds some light on how the lack of consensus among doctors, which was sustained at least in part by sectarian debate, may have impeded the development of patient trust in the medical profession. The Sacred Tales, a set of five extended speeches, records Aelius’ efforts to seek cures for his ailments, sometimes from prescriptions of physicians but more often from dreams sent by Asclepius. From Aelius’ narrative, we gain a quite different picture from that presented in the Sympotic Questions, where aristocrats took part in medical debate and widened the circle of those “in the know” about sectarian theory beyond physicians themselves. The Sacred Tales make it possible to sketch a picture of an educated patient who maintains a high degree of respect for physicians but nevertheless views them as figures who rarely manage to be decisive and effective caregivers. In the accounts provided in the Sacred Tales, physicians appear technically competent but also uncertain or wrong about the cause of a disease or its treatment: a persistent theme throughout the work is how doctors sometimes serve to exacerbate rather than alleviate Aelius’ pain. Only Asclepius, the medical god, provides sure guidance toward a cure.

Medical Sects: Asclepiadeans, Methodists, Pneumatists    651 Recent scholarship on the Sacred Tales has shown that the text is complex and highly self-​conscious, a literary work which Aelius designed for publication as a testament to his journey of suffering and his special relationship with Asclepius (Holmes 2008). Consequently, the ability of the Sacred Tales to reflect the lived reality of patients and practitioners in the Roman Empire is limited, but Aelius suggests that taking charge of one’s own medical situation and treatment, possibly out of frustration with conflicting advice received from different parties, was not unheard of (Petridou 2016). Indeed, it is possible to detect in some of Aelius’ anecdotes both a resonance with Galen’s On Prognosis and a level of frustration experienced by Aelius that seems to result, in part, from physicians’ lack of consensus about cures. Indeed, when one reads through the narrative with special attention to its portrayal of physicians, one detects the qualities that sectarian training and affiliation could inculcate in its members, most notably a liking for debate for its own sake, in a way reminiscent of Galen’s On Prognosis. Yet, of course, in actual interactions with the patient, a lack of straightforward recommendations could prove problematic for engendering patient trust and confidence. Aelius’ various consultations with physicians, although not necessarily unpleasant or harmful, are often less than satisfying for him and fail to provide him with peace of mind. For example, in one of the more detailed accounts in the Sacred Tales, Aelius is afflicted with a tumor of unknown origin accompanied by pain and fever. The physicians examine Aelius, who notes, “at this point the physicians shouted all kinds of things—​ some said surgery; some said cauterization with drugs, or that an infection would occur and that I would die” (Sacred Tales, Behr 47.62–​63). Amid the disagreement, only the god Asclepius provides Aelius with authoritative, if elaborate, instructions: through a dream, he instructs Aelius to allow the tumor to grow and to undertake various strenuous exercises including horseback riding and sailing; he then prescribes vomiting and a salt-​containing drug to destroy the tumor, and directs Aelius to rub egg on his thigh to eliminate any remaining portion. “From here on,” Aelius notes, “the doctors stopped their criticisms” and “expressed extraordinary admiration for the providence of the god” (47.67; Israelowich 2012). At another point, Aelius also gains little from his interaction with a physician, who quickly runs out of ideas about treatment for Aelius’ illness and concedes that Aelius should do as Asclepius, the “true and proper doctor,” recommends (47.57). When Aelius experiences an illness of the lower respiratory tract, “the doctors were completely at a loss not only as to how to help, but even to recognize what the whole thing was” (48.5; cf. 48.69), while the god directed him confidently. Aelius places confidence in two physicians—​and yet neither one earns special regard from Aelius based on sectarian affiliation, nor does the doctor’s allegiance to a sect appear to register with Aelius as an important credential for gaining his trust as a patient. Satyrus, the teacher of Galen, who examines Aelius at Pergamum, is an example. Aelius agrees to use the plaster Satyrus has prescribed for his abdominal ailment, but stops short of following Satyrus’ direction that he stop the purging of blood recommended by Asclepius (49.9). In another anecdote, the doctor Theodotus is presented as adopting and reusing Asclepius’ therapies when, after seeing the efficacy

652   Greco-Roman Science of Asclepius’ prescription for vocal exercise—​in particular song and lyric poetry—​and the performance of a chorus of boys for curing Aelius’ throat and stomach ailments, he subsequently recommends that Aelius seek out the chorus for “a feeling of comfort” when ill (50.38). Theodotus’ responsiveness to his patient’s need for reassurance that he is in good hands is, in the end, much of what Aelius appears to be seeking in the Sacred Tales. The patient’s relationship with his physician is an aspect of Roman imperial medicine with which we may conclude our consideration of sectarian affiliation and its potential impact on patients. Aelius’ narrative, like Galen’s work, shows educated Roman physicians struggling with their two distinct roles. On one hand, they were men of ideas, as portrayed in Plutarch’s Sympotic Questions or Galen’s On the Sects for Beginners or On Medical Experience, who could expect to be rewarded socially and professionally for taking part in ongoing debates about the nature and causes of disease, which were essential for the advancement of medical ideas. On the other hand, in their day-​ to-​day practice, physicians needed to be clinicians who offered clear and unambiguous recommendations to patients. These very different parts of professional life were left to doctors to reconcile. Amid the disputes of sects and the competition for reputation, the challenge for some Roman physicians, no doubt, was to maintain a focus on their duty to their patients.

Bibliography Entries in EANS:  Aretaios of Kappadokia, 129–​130 (Touwaide); Athenaios of Attaleia, 176–​ 177 (Touwaide); Kharmēs of Massalia, 471–​472 (Keyser); Kleopatra of Alexandria, 482 (de Nardis); Krinas of Massalia, 492 (Jones); Metrōdōra, 552–​553 (Parker); Quintus, 717 (Keyser); Saturos of Smurna, 728 (Keyser); Sōranos of Ephesos, 749–​751 (Scarborough); Themisōn of Laodikeia (Syria), 782–​783 (Scarborough); Thessalos of Tralleis, 804–​805 (Scarborough); and Vettius Valens (Med.), 827 (Keyser). Behr, Charles A. P. Aelius Aristides: The Complete Works. 2 vols. Leiden: Brill, 1981. Burguière, Paul, Danielle Gourevitch, and Yves Malinas, eds. Soranos d’Éphèse Maladies des Femmes. 4 vols. Paris: Les Belles Lettres, 1988–​2000. Erskine, Andrew, ed. A Companion to the Hellenistic World. Malden, MA: Blackwell, 2003. Eshleman, Kendra. “Defining the Circle of Sophists: Philostratus and the Construction of the Second Sophistic.” Classical Philology 103.4 (2008): 395–​413. Flemming, Rebecca. Medicine and the Making of Roman Women. Oxford: Oxford University Press, 2000. —​—​—​. “Empires of Knowledge: Medicine and Health in the Hellenistic World.” In Erskine 2003, 447–​463. —​—​—​. “Women, Writing, and Medicine in the Classical World.” Classical Quarterly 57 (2007): 257–​279. Frede, Michael, and Richard Walzer. Galen:  Three Treatises on the Nature of Science. Indianapolis: Hackett, 1985. Gill, Christopher, Tim Whitmarsh, and John Wilkins, eds. Galen and the World of Knowledge. Cambridge: Cambridge University Press, 2009.

Medical Sects: Asclepiadeans, Methodists, Pneumatists    653 Grenfell, B. P., A. S. Hunt, and E. J. Goodspeed, eds. The Tebtunis Papyri. Vol. 2. London: Henry Frowde, 1907. Hankinson, R. J., ed. The Cambridge Companion to Galen. Cambridge: Cambridge University Press, 2008. Hanson, Ann Ellis, and Monica Green. “Soranus of Ephesus: Methodicorum Princeps.” Aufstieg und Niedergang der Römischen Welt 2.37.2: 967–​1075. Berlin: de Gruyter, 1994. Harris, W. V., and Brooke Holmes. Aelius Aristides Between Greece, Rome, and the Gods. Leiden: Brill, 2008. Holmes, Brooke. “Aelius Aristides’ Illegible Body.” In Harris and Holmes, 2008, 81–​114. Horstmanshoff, Manfred, ed. Hippocrates and Medical Education. Leiden: Brill, 2010. Iskandar, Albert Z. On Examinations by Which the Best Physicians Are Recognized. Corpus Medicorum Graecorum Supplementum Orientale, 4. Berlin: Akademie Verlag, 1988. Israelowich, Ido. Society, Medicine and Religion in the Sacred Tales of Aelius Aristides. Leiden: Brill, 2012. —​—​—​. Patients and Healers in the High Roman Empire. Baltimore, MD:  Johns Hopkins University Press, 2015. König, Jason. “Fragmentation and Coherence in Plutarch’s Sympotic Questions.” In Organizing Knowledge in the Roman Empire, ed. Jason König and Tim Whitmarsh, 43–​68. Cambridge: Cambridge University Press, 2007. Kyle, Donald G. Sport and Spectacle in the Ancient World. Malden, MA: Wiley-​Blackwell, 2014. Lloyd, G. E. R. “Galen and His Contemporaries.” In Hankinson 2008, 34–​48. Mattern, Susan P. “Physicians and the Roman Imperial Aristocracy:  The Patronage of Therapeutics.” Bulletin of the History of Medicine 73.1 (1999): 1–​18. —​—​—​. Galen and the Rhetoric of Healing. Baltimore, MD:  Johns Hopkins University Press, 2008. —​—​—​. The Prince of Medicine:  Galen in the Roman Empire. Oxford:  Oxford University Press, 2013. May, Margaret T. Galen On the Usefulness of the Parts of the Body. 2 vols. Ithaca, NY: Cornell University Press. Mitsis, Philip. “The Institutions of Hellenistic Philosophy.” In Erskine 2003, 464–​476. Nutton, Vivian. “Murders and Miracles:  Lay Attitudes Towards Medicine in Classical Antiquity.” In Porter 1985, 23–​54. —​—​—​. “Healers in the Medical Market Place:  Towards a Social History of Graeco-​Roman Medicine.” In Wear 1992, 15–​58. —​—​—​. “The Medical Meeting Place.” In van der Eijk, Horstmanshoff, and Schrijvers 1995, 3–​25. —​—​—​. Ancient Medicine. London: Routledge, 2004. Oberhelman, Steven M. “On the Chronology and Pneumatism of Aretaios of Cappadocia.” Aufstieg und Niedergang der Römischen Welt 2.37.2: 941–​966. Berlin: Walter de Gruyter, 1994. Parker, Holt. “Women Doctors in Greece, Rome, and the Byzantine Empire.” In Women Physicians and Healers: Climbing a Long Hill, ed. Lillian Furst, 131–​150. Lexington: University of Kentucky Press, 1997. Petridou, Georgia. “Aelius Aristides as Informed Patient and Physician.” In Homo Patiens: Approaches to the Patient in the Ancient World, ed. Georgia Petridou and Chiara Thumiger, 451–​470. Leiden: Brill, 2016. Porter, Roy. Patients and Practitioners: Lay Perceptions of Medicine in Pre-​Industrial Society. Cambridge: Cambridge University Press, 1985. Siegel, Rudolph E. Galen: On the Affected Parts. Basel: S. Karger, 1976.

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Chapter D4

Sci ence and Me di c i ne in the Roma n Encycl ope di sts Patronage for Praxis Mary Beagon

The encyclopedic literature of the late Republic and early Roman Empire is a valuable repository of much ancient scientific knowledge. It illustrates the different conceptualizations and preoccupations of antiquity, and it also foreshadows some of the developments to come. We start by considering what encyclopedic literature was since its general characteristics, and indeed specific variations within those characteristics, directly influence the nature of the areas of knowledge they treat and the manner in which these are presented. We shall then turn to more detailed consideration of a number of authors and their works, before concluding with a glance ahead to the continuation of a tradition that became a vital conduit of scientific knowledge for the next 1,500 years.

1.  Ancient Encyclopedic Literature: Definitions and Delimitations None of the works included in this chapter would be recognizable as an encyclopedia according to modern criteria. All are sole authored, by writers whose use of the authorial “I” is, in many cases, a prominent feature of their treatment, whereas modern encyclopedias are typically composed by a multiple, often-​anonymous contributors. Some, like Varro’s Disciplinae and Celsus’ Artes, were divided into discrete subjects;

656   Greco-Roman Science others, however, like Pliny’s Natural History, were not. The term “encyclopedia” dates from the 16th century, and it is arguable whether the genre existed in antiquity (Doody 2010, 42–​58), as opposed to literature with encyclopedic characteristics. The Greek encyclios paideia, referring to a broadly based but nonspecialist education, is essentially Aristotle’s idea of studies for the properly educated free man (eleutherai epistemai, Politics 8.2, 1337b15, cf. Parts of Animals 1.1, 639a), and Quintilian uses the phrase to denote an education preliminary to more specialized studies (1.10.1). The derivation of our term “encyclopedia” from the ancient phrase may not be straightforward; however, what all the works in this chapter have in common is a desire for comprehensiveness, organization, and utility. All these qualities were to varying degrees linked to a fourth: encyclopedic literature that was essentially a Roman invention. The works under consideration all date from the late Roman Republic and early Empire. As we shall see (sec. 3), they are the product of a people for whom utility was an integral part of the rhetoric of self-​ identity and whose extensive conquests were being organized and rationalized into a world empire; a mass of discrete political and geographical entities marshaled into a coherent unity. If the works themselves match in certain respects the comprehensive political unity being created by the Romans, their authors, too, frequently mirrored the leaders on whose shoulders the burden of making and sustaining an empire fell. Vitruvius suggests that his work is a literary corollary of Augustus’ sole labors for the Romans (1.pref.1–​3), and Pliny likewise aligns his work with that of the Emperor Titus (pref.14–​17, 2.17, 37.205). Additionally, emphasizing the comprehensive nature of their works enhances their authorial reputation as controllers of an empire of knowledge (cf. Columella pref.21, 5.1–​4; Vitruvius 1.11–​16; Pliny pref.15, 37.202; and sec. 2 this chapter). Their readership, however, is debatable; the extent and nature of literacy in antiquity is a vexed issue. Varro seems to assume that the farm’s slave bailiff and chief herdsman have basic reading and writing skills (De re rustica 1.17.4, 2.5.18; Rawson 1985, 65). Despite Pliny’s declared intention to introduce rustics to astronomy, however difficult this might be (18.206), the humilis uulgus, composed of craftsmen and farmers, seems an unlikely beneficiary of his often dense and occasionally rhetorical (pref.6) prose. A more likely audience may be sought among the Roman elite: well-​educated individuals who were not intellectual specialists, rather like the busy man of affairs, to whom Aulus Gellius addressed his Noctes atticae (pref.12). A large miscellany of bite-​sized, self-​contained chapters, its scale and utilitarian principle mirrored those of encyclopedic works: Pliny and Vitruvius, too, suggest that their works are labor-​saving for their readers (Vitruvius 5.pref.5; Pliny pref.33). A number of encyclopedic writers, including Pliny, were of the equestrian class, the second-​highest order in Rome’s social elite. Lacking the prejudices against more practical activities often exhibited by the highest, that is, the senatorial, class, in the early empire, they began to serve as financial procurators and in other governmental posts. Agriculture, however, was of interest to the senatorial class as well (Varro was a leading statesman and supporter of Pompey); their wealth was traditionally associated, at least in theory, with investment in land. Vitruvius’ comments may also reflect a practical interest in building projects among the elite: this was the era of

Science and Medicine in the Roman Encyclopedists    657 increasingly extravagant private villas (discussed in sec. 4). In any case, the Flavian era saw an increase in the number of senators filling administrative posts at the expense of the freedmen discredited by misuse of power particularly under the last two Julio-​ Claudian emperors. With their increased involvement, their antipathies to applied knowledge may also have begun to weaken (König and Whitmarsh 2007, 24).

2.  Roman Knowledge, Roman Power In the preface to his fourth book, Vitruvius says that, unlike many previous commentators whose work was arranged in a haphazard and disconnected fashion (“like atoms”), he thought it appropriate and “most useful” to reduce his material to a perfect order (4.pref.1). The first of our writers, Varro, displayed an obsession for organization, classification, and subdivision in his works: in the preface to De re rustica, prior writers are criticized for imprecision (Rawson 1985, 179). Varro and Vitruvius were writing when the work of consolidating and organizing Rome’s conquests was under way. Like its territorial acquisitions, knowledge, too, was in a way booty (Murphy 2004, 49–​51), and encyclopedic works were a means of consolidating and classifying the earlier, more fluid, Greek traditions of knowledge into something more concrete and essentially Roman. Pliny boasts that the Greeks had never brought all the topics of encyclios paideia into one volume (pref.14). Intellectually, the process mirrored not only the unification of Rome’s conquests into a single empire but also the various ways in which those conquests were brought, literally, into the city as booty to be displayed in triumphal processions or as exotic animals to provide excitement in public displays and the arena. Some of these “encyclopedias” related directly to the (re)construction of Rome as a fitting center to that empire: Vitruvius’ De architectura is offered to Octavian/​Augustus as he begins to restructure Rome physically and politically (1.pref.3; cf. Suetonius, Augustus 18.3). Within their works, these sole writers, as noted, assume the overall control of their empires of knowledge as their imperial dedicatees did the political empire (König and Whitmarsh 2007, 191–​197). In addition, the knowledge was often geared toward specifically Roman needs and concerns. Vitruvius’ reference to the building efforts of the Roman elite meant not only the money and effort being expended on private houses but also the continuing tradition of public munificence in shows and games, even under emperors who increasingly monopolized such displays of power. Thus, he mentions the need for instruction in the seating and machinery for these occasions. Agriculture was and remained a traditional occupation for the elite, both practically and ideologically. Thus, Columella (1.1.7–​11) stresses not only the need to regenerate the agricultural land of Italy but recounts at some length the traditional elements of the agrarian moral discourse and its integral relationship with the Roman past and the elite ethos (more briefly, Varro 2.pref.1–​3). The basic ingredients can be found in the earliest extant prose work in Latin, the Elder Cato’s handbook on agriculture, and appear to a greater or lesser degree in the other

658   Greco-Roman Science Latin writers dealing with the topic. Great leaders of the past were called from their ploughs to the consulship. Old-​world frugality and simplicity produced a tough, uncorrupted breed of peasant soldiers, while their commanders’ strategic and organizational skills were honed by the need to run an estate efficiently—​and vice versa (e.g., Pliny 18.33). These ostensibly utilitarian texts are multilayered, and themes such as traditional values and even utility itself become part of a self-​consciously literary self-​presentation (Doody, Föllinger, and Taub 2012). However, they are more than literary devices and are frequently integral to the choice and presentation of the subject matter and to its cultural context (see sec. 7 on Columella). Indeed, it is not just the desire to formulate and organize knowledge but also to pay tribute to tradition in the broadest sense, which infuses this encyclopedic literature. Roman reverence for the past gave a particular impetus to the more general ancient intellectual preoccupation with giving recognition to and gaining additional auctoritas from earlier writers. Thus Pliny (pref.17) and Columella (1.1.7–​14) stress the number of their sources, even if many of these are Greek. A relative paucity of Latin predecessors can in itself enhance the status of the author in question (cf. Vitruvius 7.pref.15; Pliny pref.14, 25.4–​9). Comprehensive compilations tend to depend largely on other writers. This can make them particularly significant for gauging the general state of knowledge on a given subject, albeit distortion is possible, for example if contemporary developments are ignored in favor of the established canon. It also means that encyclopedic authors are not naturally intellectual pioneers. Not all compilations include consistent and precise attributions. Nevertheless, Pliny places himself in a position of moral superiority based on his lists of sources that comprise the entire first book of the Natural History, and Vitruvius emphasizes the deceitfulness of plagiarism, with a moralizing anecdote (7.pref.1‒18). Emphasizing the number of their sources enhances their own stature, as well as integrating them into the wider tradition (see especially Vitruvius 7.pref.17). Likewise, writers of encyclopedic works claimed to serve the public by preserving knowledge. Vitruvius advocates continuing the intellectual tradition and inveighs against those who keep a “jealous silence” (7.pref.1). Pliny excoriates those who believe that to teach no one increases their own auctoritas (25.1–​2). It is blameworthy even in the unsophisticated illiterates whom he later portrays as refusing to transmit knowledge of herbal remedies, in the magically based belief that they will somehow lose what they have imparted to others: a too-​literal exposition of the notion that knowledge is power (25.16).

3.  Encyclopedic Knowledge: The Arts of Life It is time to consider more precisely how the encyclopedic tradition contributed to ancient scientific thought. The treatment of science and medicine in encyclopedic literature

Science and Medicine in the Roman Encyclopedists    659 highlights the difficulty of dividing ancient ideas up into the discrete scientific fields recognizable today. The ancient encyclopedic tradition almost certainly evolved into the medieval system of the seven liberal arts, most probably from Varro’s lost Disciplinae, through Augustine and Martianus Capella (Shanzer 2005, 69–​112, contra Hadot 1984, 156–​190; sec. 4 this chapter). Medicine and agriculture, the two most obviously practical of Varro’s nine, were eventually shed to leave the canonical seven: grammar, rhetoric, and dialectic (the medieval trivium), plus arithmetic, geometry, astronomy, and musical theory (the quadrivium). However, this apparent continuity obscures the ancients’ outlook and their strategies of knowledge. Moreover, at least one significant encyclopedic work, Pliny’s Natural History, was not divided into artes or disciplinae (cf. sec. 8). Taken on its own terms, however, encyclopedic literature offers some valuable insights into how the ancients viewed their world and devised strategies to evaluate and disseminate such knowledge in a rational and transmittable form. The writers of sole-​ authored works are, almost by definition, polymaths equipped to take an “interdisciplinary” and a “multidisciplinary” view of learning. The apparent dichotomy between those disciplinae, such as rhetoric and dialectic, that now seem less scientific, and those, such as geometry and arithmetic, that better fit our preconceptions, did not exist in the encyclopedic rationale. Common approaches or modes of thought underlay all of them. Moreover, boundaries between the disciplines were not watertight. There was frequent cross-​fertilization, both in terms of content and especially in terms of the methods and outlook used to articulate them. Also, and linked to the foregoing, was the conception in encyclopedic literature that all these subjects had a practical application and/​or a practical inspiration. First, then, each of the artes or disciplinae was stated by its exponents to require a broadly based background education that covered a number of the others. Vitruvius says that the would-​be architect must have a basic grounding in numerous other subjects, including astronomy, medicine, and music, for assistance in the construction of clocks, healthy siting of habitations, and acoustic considerations respectively: a gen­ eral education is put together like a body with its different limbs (1.1.10–​13). This is how encyclios paideia is most closely associated with the ancient encyclopedic tradition. So, too, Cicero’s orator was expected to have a wide-​ranging education (de Oratore 3.72). Such claims seek in part to enhance the importance of the particular discipline, and hence, once more, authorial auctoritas, but the works themselves frequently illustrate the methodological common ground between disciplines. The rules of grammar, rhetoric, and dialectic enabled rational exposition and expression of ideas, required for the exposition of any other subject: definition and order lay at the heart of the tradition. In linguistic debate, anomalists, who emphasized exceptions in etymology (Varro, On the Latin Language 8.23; 9.1, 3, 113; 10.1–​2), may have been influenced by the medical theories of the Empiricists, who stressed observation of particularities above generalized theorizing (Rawson 1985, 127). Moreover, material from one subject can wander into the treatment of another. Varro’s interest in etymology, for example, is frequently revealed in his De re rustica (1.9.1, 1.49.2, 1.50.1–​3, 2.11.10–​12, 3.1.5–​7). In other instances, the inclusion may be more calculated.

660   Greco-Roman Science Columella objects that land measurement is properly the province of the surveyor, but he yields and treats it in his agricultural treatise “on request” and in accordance with his attempts to be as comprehensive as possible (5.1–​4): breadth of knowledge is another promoter of authorial auctoritas. Finally, the practical utility of the knowledge is a running theme. Celsus opens his De medicina by referring back to his (lost) work on agriculture: it gives nourishment to healthy bodies, while medicine gives health to the sick. Vitruvius declares that authors who benefit humanity though the ages are more worthy of honors than athletes who benefit only themselves (9.pref.1–​2). Moreover, he goes back to original scientific discoveries (9.pref.3–​14), including the famous story of Archimedes’ bath, to show their practical importance. The encyclopedic writers are especially concerned to transmit the practice of applied science from which the arts of life are born. Astronomy and meteorology are of assistance to farmers and seafarers. Medicine assists architects in siting a house in a healthy position. It was also tied up with the ethos of Roman self-​sufficiency and agrarian morality: traditionally, the paterfamilias had been responsible for the health of his household and doctoring had been a home-​grown affair using remedies derived from the farm and garden (see sec. 6). These arts of living in turn become part of the broader human environment. Thus, Vitruvius’ architecture offers insights into techniques and raw materials that have a recognizably scientific aspect to modern eyes, but it is also integral both to a particular political situation and to the broader social fabric of society. Of all the works in this chapter, however, the one in which the theme of utilitas uitae is most prominent is Pliny’s Natural History. But the Natural History is not at all arranged according to separate disciplinae. Instead, there is one, all-​embracing, theme: nature. “My subject is nature, that is, life,” he says in the preface. The entire work is shaped by humanity’s life in nature; nature is nature as viewed and used by the human race. Despite the lack of dedicated treatments of the disciplines, there is a strongly defined structure, as he starts with the cosmos in book 2 and works his way down the Aristotelian divisions of nature: animal, vegetable, and mineral. The arts of living are embedded in this ordered division: medicine and agriculture from animals and plants; architecture, sculpture, and the plastic arts from minerals, and so forth. The nature theme allows for the inclusion of many others, including astronomy, cosmology, meteorology, geography, and ethnography. Above all, it encapsulates the ancient answer to the definition of science in the broadest sense: how the world works, not just theoretically but also in relation to the needs and interests of humanity. Thus, the Natural History is the most inclusive and comprehensive of the encyclopedic works of antiquity to survive. In one sense, it illustrates the differences between ancient and modern science: teasing out individual areas of learning from the Natural History is in a sense artificial and misleading, so integrated are they into the overall theme of divine nature and human life. Yet in another sense, perhaps, this very fact of a single, unifying, theme takes Pliny beyond the medieval development of trivium and quadrivium to look toward the Renaissance and beyond, when unifying keys to, and principles within, the world were sought. These ultimately gave way to approaches self-​consciously antithetical to Pliny’s, but even such

Science and Medicine in the Roman Encyclopedists    661 projects such as Bacon’s Novum organum (1620) postulated all-​embracing strategies for studying the natural world in a manner not entirely at odds with the ancient investigator of nature.

4.  Varro: Ordering Knowledge M. Terentius Varro (116–​27 bce) is, in terms of breadth of knowledge and quantity of output, the most encyclopedic of our authors. Born at Reate, northeast of Rome, his early studies followed an increasingly common pattern among the Roman elite in the 1st century bc, including a period abroad absorbing Greek scholarship. Philosophical study, in Varro’s case under the Academic philosopher Antiochus of Ascalon, was as significant for providing a framework for logical and ordered thinking (Griffin 1989) as for teaching specific doctrines. These studies, and those with L. Aelius Praeconinus, Rome’s first significant scholar and an expert in Latin literature, antiquarianism, and etymology among other things, are reflected in Varro’s methodical and analytical approach and some of the recurrent themes in his vast output. A major frustration, however, is that most of this output is lost. We retain a part of the 25-​volume On the Latin Language, written in the 40s bc, and the De re rustica (On Farming) in three volumes. The contents of the rest, including the encyclopedic Disciplinae, must be pieced together from other sources. The subject matter of the De re rustica, and especially the On the Latin Language, might not now seem a likely repository of scientific thought. Both, however, incorporate important methodological principles of considerable relevance. We have seen Varro’s propensity for ordering his subject matter and categorizing it into divisions and subdivisions: a clear precursor of the scientist’s need to classify and define. In De re rustica, for example, the main divisions and subdivisions are presented in 1.5.3–​4 and in 2.1.11–​12; he talks of “at least 81 subdivisions” in cattle farming. Another notable feature of De re rustica is its combination of theoretical and practical knowledge: Varro tells us he will use what he has observed by practice on his land, as well as what he has read and what he has observed from experts (1.1.11). He offers instruction drawn from his experience owning sheep and horses (2.intro.6). He furthermore recognizes the possibility of new technological developments (1.52.1), a feature found in other agricultural writers such as Columella and Pliny (18.172–​173, 261, 296). The increasing market for luxury food items produces some interesting examples of applied science, in such contraptions as the jars fitted with mist simulators for the breeding of edible snails (3.14). On a larger scale were the engineering feats accomplished by those wishing to create salt-​water ponds with tidal basins to prevent stagnation. L. Lucullus was notorious in this respect (3.17.9), and Varro’s slightly critical tone reflects their extreme expense and that their owners’ prime motivation was pleasure and ostentation rather than practical profit. Thus, the scientific mentality, at least, is revealed in this openness to experimentation and innovation.

662   Greco-Roman Science Practicality is the primary motive for the discussion; as a large landowner, Varro, like the other major extant agricultural writers (cf. Columella, sec. 7), is anxious to balance profit against labor costs (1.2.8), and he discusses practicalities such as what should be brought in and what should be produced or kept on the estate, both in terms of produce and staff (1.16.3–​4). The injunction to use hirelings on unhealthy ground, not your own slaves (1.17.3), harks back to the harsh, unsentimental attitudes of the elder Cato, who advocated selling old slaves (Plutarch, Cato Maior 4.4–​5.1). Profit is a major preoccupation of book 3, which deals with the pastio uillatica, the suburban villa producing luxury foods for an increasingly affluent urban elite. That Varro is writing primarily for his fellow landowners, rather than humbler individuals (see sec.1), is also indicated by another consideration: farming as pleasure and profit. The former, it is true, is tied in with profit, for, as he says, land that is visually well presented will be more saleable (1.4.1). More surprising, however, is the element of aesthetics in this practical, teachable “scientific” discipline (1.3.1). In 1.59.2, he notes a fashion for using the fruit store as a dining room, replacing expensive art works with a decorative display of fruit (uenustate disposita pomorum). Nature as art was a concept increasingly exploited in the development of, for example, elite villa gardens from the late Republic onward, where man-​made objects, formal plantations, and cunningly disposed areas of “wild” countryside were juxtaposed (cf. Pliny the Younger, Epistles 5.6; Beagon 1992, 85–​89). Nature was not just creative in a strictly biological sense; her activities also made her an artist (artifex). Indeed, Pliny’s portrayal of his Stoic-​inspired Natura in the Natural History enhances the bond between humanity and nature and the identity of natural science with the art of living. Here, it would seem that the idea of “artful nature” was fashionable enough for Varro to warn against the temptation to cheat and thus undermine the whole agrarian ethos: don’t go to Rome and buy fruit to bring back to the country for this purpose. Varro’s propensity to see things in terms of their components also leads him to link farming with basic building blocks in nature. The elements of agriculture are the same as those of the universe: earth, air, fire, and water (1.3.1) More generally, he seems to have been much influenced by Pythagorean arithmology, which saw numbers and sequences as keys to the understanding of the universe (Latin Language 5.11, cf. Gellius 3.10 for other, lost, numerological works). Language could also be viewed in the light of this scientific structure and order: in the On the Latin Language, Varro had considered the debate over the extent to which etymology adhered to rules and regularities. Of the lost Disciplinorum libri, little can be said for certain. As a putative precursor and inspiration for treatments of the seven liberal arts in later antiquity and the medieval period, it has been the subject of some controversy (sec. 3). Vitruvius mentions a work of Varro’s in nine disciplinae, of which architecture is one (7.pref.14). References in other sources suggest that the others consisted of what became the later trivium and quadrivium (sec. 3), together with medicine. The order of the books remains uncertain and some sources do not specifically say that their references to, for instance, elements of Varronian geometry are taken from the Disciplinae rather than from another of his works.

Science and Medicine in the Roman Encyclopedists    663 More fruitful than trying to reconstruct the Disciplinae is to investigate extant sources for Varro’s attitude to the various areas of knowledge they probably covered. For astronomy, whose practical application to the political and agricultural calendars made it relevant to his class, Varro exhibits personal interest and expertise in De re rustica. Here he describes at some length an elaborate astronomical clock, together with a “compass of the eight winds” modeled on the Tower of the Winds at Athens (3.5.17). On medicine, a little can be gleaned from De re rustica. Best known is his exposition of a connection between stagnant water and malaria: a miasma from such water contains tiny creatures that cause the disease if inhaled (1.12.2); a notion of uncertain, possibly Greek, origin, which, if not entirely accurate, had the salutary effect of warning prospective farmhouse builders to site their dwellings with care. The wholesomeness of farmland and its water supply was of prime importance in the agrarian writers; scientia can alleviate natural defects of environment and careful assessment of the prevailing winds, temperatures, and the aforementioned miasmas can ensure that the windows and doors of buildings are arranged to minimize ill-​effects (1.4.4–​6). At this point, Varro again recounts his own action in blocking up the windows and doors and cutting new ones in the houses sheltering the Roman wounded at Corcyra during the civil war with Caesar, in order to exclude bad winds and let in good ones. The overall picture to emerge from these and many other references is of a crucial contribution to Roman intellectual history, for which the range and frequently the depth of Varro’s scholarship formed the basis of future developments. Greek knowledge was introduced to a Latinate audience and the principles of systematic categorization and ordered analysis in exposition were placed on a firm footing. At the same time as the examination of discrete disciplines, however, the holistic attitude towards learning, epitomized by the polymathic approach, remained discernable. Practicality, profit, and aesthetics all find a niche in the ancient sciences.

5. Vitruvius The generation following Varro produced the writer of the only detailed extant treatment of ancient architecture. M. Vitruvius Pollio (b. 85 bce) may have come from Campania. It is likely that he saw service under both Caesar and Octavian (later the Emperor Augustus) as artillery engineer and staff architect. His work, the De architectura, was in many ways the product of its age. Vitruvius displays not only that desire for ordering knowledge (cf. book 4’s preface), which was a noted feature of the politico-​intellectual ambience of his era, there is also evidence he sought comprehensiveness and inclusivity, that is, the encyclopedic approach to knowl­ edge, whereby Vitruvius stresses the interconnectivity of the arts and the similarity of the principles underlying them (1.1.12; see sec. 3 this volume). The broadly based knowl­ edge of other arts that optimizes the development of his own and enhances its auctoritas (sec. 2) also displays the inherent flexibility and richness of his treatment of his subject,

664   Greco-Roman Science which has sometimes been criticized for its apparent emphasis on rules. Order and uarietas are not necessarily incompatible. Some controversy surrounds the nature and extent of Vitruvius’ learning. As with many of the works we are dealing with, emphasis is placed on a number of authorities apparently consulted, but the extent to which Vitruvius actually read some of his Greek authors is unclear (7.pref.11–​18). Again, his career suggests plenty of practical experience, but this is not directly referred to as much as we might expect: military engineering is treated briefly, though he does refer to Caesar’s siege of Massilia at which he was probably present. Nor is it easy to pin down a definition of “the architect.” Cicero (On Duties 1.151) described architecture, together with medicine, as a respectable occupation “for those to whose order it is suited”: a qualification that probably denied it to the topmost echelons of the elite. Certainly, quite a wide variety of practitioners emerges in Vitruvius’ book, from highly distinguished Greeks like Hermodorus of Salamis, down to trained slaves, as well as the technical experts on senatorial and equestrian officials’ staffs (Rowland, Howe, and Dewar 1999, 13–​14). Something similar emerges in medicine, where learned Greek practitioners such as Galen contrasted with trained slaves and even the quack doctor who is little more than a peddler of dubious potions (cf. Cicero’s pharmocopola circumforaneus in Pro Cluentio 40). Doctors’ reputation at Rome was notoriously mixed, and occasional similar comments impugn the professionalism of architects (Seneca, Epistles 90.8.43) The unscrupulous could make use of essentially unregulated professions to deceive the unwary, and Vitruvius makes angry references to cowboy builders (10.pref.1–​3; cf. 6.pref.5–​6), whose irresponsible estimates could ruin the private landowner who employed them. Public games contracts are similarly vulnerable: in a situation where the provision of awnings, seating, and stage machinery must be kept within a strict time frame, there is a need for “careful foresight and the resources of a highly-​trained intelligence.” Thus, if the liberal arts educated professional of his book seems an impossibility in real life, this may be Vitruvius’ way of instilling counsels of perfection, implicitly warning his reader to think twice about whom they employ. This reader was most likely a member of the educated Roman elite (sec. 1), probably involved in both domestic and public-​building programs. Vitruvius’ work would give him an outline of the principles and some idea of the practicalities to organize and oversee projects in an informed and responsible manner. About a generation before Vitruvius wrote, we see such general knowledge being activated by an elite individual in a letter of Cicero to his brother Quintus in the 50s BCE, on acquisitions and improvements to their respective property portfolios. His architectural knowledge provokes him to forthright condemnation of one hapless architect’s misaligned pillars (Letters to his Brother Quintus 3.1.2). Baths are rearranged to prevent steampipes running directly under some bedrooms; ceilings are altered. Practicalities (the siting of some bedrooms) and overall aesthetic impact (the general effect of a colonnade) alike receive confident assessment. Water supply, whether for the house, ornamental garden features, or the irrigation of farmland, was crucial. Cicero mentions the figures quoted by his architect for irrigation, whilst affecting to understand only the more frivolous of the villa’s water-​fed amenities, such as the fishponds

Science and Medicine in the Roman Encyclopedists    665 and fountains (3.1.3). Nonetheless, Vitruvius’ pronounced interest in engineering, including water-​raising devices, such as the Archimedean screw and the force-​pump of Ctesibius, may have given landowners some idea of the practical devices (10.6–​7) that could assist in irrigation. Moreover, his entire book 8 is devoted to water, including the mechanics of finding it and two chapters on the mechanics of creating a water supply. He also mentions the water-​wheel and its use for milling (10.5.2). Rather surprisingly, there are few specific references to country villas (as opposed to the more general building interests of the elite), and comments on engineering features such as road building are not prominent. The latter, besides their crucial role in the communications infrastructure of the empire, could be of more personal interest to the landed elite: Cicero talks of ensuring that his neighbors keep their private roads in good order (Letters to his Brother Quintus 3.1.3). Otherwise, the emphasis on public works and on the mechanical devices connected with the public games reflects the political priorities of the new regime. This was an area of continuing relevance to the elite, although, as mentioned, the initiative for such projects increasingly passed to Vitruvius’ imperial dedicatee. In 5.pref.3, he says he will write briefly as the state is burdened with public and private business and the reader has little leisure. While the obvious target of this comment is Augustus, and sparing an important dedicatee’s valuable time is a literary topos (cf. also Pliny pref.33), the conviction/​fiction that the entire ruling class was involved in the process of political and material regeneration might partially account for the relative lack of specific material on their private country dwellings, venues of leisure (otium) rather than public duty (negotium). While Vitruvius’ expectations for the training of the ideal architect in the arts and sciences were ambitious (besides the seven liberal arts, he mentions draftsmanship, law, philosophy, and knowledge of painting and sculpture), we have seen that he kept this to a general rather than a specialist level of competence. When discussing the philosophical element, he specifically emphasizes knowledge of “the nature of things” because that will aid understanding not only of the natural processes and principles involved in key areas, such as water supply, but will also facilitate the understanding of engineering manuals such as those of Ctesibius and Archimedes; in other words, the “science” that has been applied in their technology (1.1.7). This knowledge is not profound or complex: building materials must be understood against a backdrop of knowledge of the elements and how they can be blended together (2.1.8–​9). Comments on the physical causation of winds (1.6.2) and climate’s relationship to disease (1.6.3) when siting and orienting buildings to avoid disease are familiar from the agrarian writers’ preoccupations about the healthiness of farms (sec. 4). Elemental properties come into play once again in the treatment of water: the large section 3 of book 8 is given over to the remarkable qualities of waters. This was a topic familiar from paradoxography, which sought to thrill rather than explain (see chap. C10, this volume). Vitruvius, however, more in keeping with modern scientific expectations, attempts to provide explanations:  thus, acidic springs which dissolve gall-​stones gain their quality from acidic soils, but he goes further and offers a simple experiment to illustrate the process: eggshells and pearls can be dissolved in

666   Greco-Roman Science vinegar (8.3.17–​19). Elsewhere, a general, if not very clear or exact, knowledge of ancient theories emerges. At the beginning of book 6.1.1–​11, traditional ideas on climate, latitude, and racial characteristics dating back to Hippocratic writings are voiced in a discussion on the need for geographical variations in types of buildings. Discussion of optical adjustments and illusions in architecture suggests some acquaintance with Epicurean optics (6.2.2–​3; cf. 3.3.13). Most characteristic of Vitruvius’ scientific thinking, however, is the symbiotic relationship between theory and practice. Like medicine, architecture was an overtly practical scientia and particularly pertinent to the notion of human utility promoted in encyclopedic literature. Utilitas uitae underlies Vitruvius’ philosophy of architecture (9.pref.3–​15), and the relationship between nature and architecture is close. The building materials deployed in architecture are derived from the elemental building blocks of nature; their effective fabrication and deployment rests on an understanding of the scientific theories about their relationship but also on the actual variety in their manifestations according to individual localities, and so forth. Architectural rules may form the backbone of his book, as laws of science do to nature. However, nature is also an agglomeration of specifics, and architecture must be willing to adapt according to the nature of the site, climate, and other particular circumstances (5.6.7, 10.16.1–​2). By building, humanity is becoming part of the natural environment: understanding of and harmony with it is vital. For the Romans, the man-​made was not necessarily the antithesis of the natural: each might enhance the other. “The sea-​front gains much from the pleasing variety of the houses built either in groups or far apart; from the sea or shore these look like a number of cities” (Pliny the Younger, Epistles 2.17.27 Radice). For Pliny, this development is an asset not an eyesore, the enthusiastic comparison to an urban environment suggesting that even the most intensive human intrusion into a natural landscape enriches the latter. The practicality of architecture once again epitomizes that Roman holistic attitude to learning, whereby human need, utility, and aesthetics make the study of nature more than the literal sum of its elemental parts.

6. Celsus From architecture we move to the earliest major Latin exponent of the other practical discipline ultimately dropped from the canonical list. A. Cornelius Celsus is an elusive figure. His date is uncertain but is usually placed in the reign of the Emperor Tiberius (14–​37 ce), largely on analysis of references, or lack of them, in his work to other dateable medical figures. Possibly from Gaul or northern Spain, he settled in Rome, and early influences on his thought included the philosopher Q. Sextius Niger, whose son and successor, Sextius Niger, wrote on botany and medicine. The De medicina is divided into eight books: 1–​4 deal with dietetics, 5–​6 with pharmacology, and 7–​8 with surgery. A lengthy and important proemium deals with the history

Science and Medicine in the Roman Encyclopedists    667 of Greek medicine and considers the contribution of precept and experience to the optimum practice of medicine. Celsus reviews the opinions of medical schools and prominent authorities, adjudicating confidently and advocating his own interpretation of best practice. References in other writers and in the De medicina suggest he wrote works on other disciplines, including philosophy (Quintilian 10.1.124), oratory (Quintilian 3.1.21), and agriculture (Columella 1.1, 2.2.15 and 2.11.6, with references in De medicina, proem.1, and 5.28.16). Quintilian (12.11.24) also mentions military matters. Celsus’ output lies within the broader category defined earlier as encyclopedic and the De medicina, with its detailed and ordered analysis and care to cover variations within the broader context of particular conditions, exhibits characteristics in common with the works examined in sec. 4–​5. Both Celsus and his work raise interesting questions about the practice of medicine in early Imperial Rome. He shows considerable knowledge of the development and deployment of Greek medicine from the Hippocratic Corpus through the Alexandrian anatomists and more recent practitioners such as Asclepiades of Bithynia. His expertise, accurate knowledge of authorities old and new, frequent use of the first person, and indications of personal attendance to individual cases and surgical procedures suggest professional experience. Against this, it has been argued that the social status of medical professionals was not necessarily of the highest level (see above, sec. 5 on Cicero, On Duties 1.151). In addition, Celsus never says he is a doctor, and his level of expertise might instead indicate the high level of attainment achievable by the educated and enthusiastic layperson at Rome, returning us once again to the encyclopedic liberal education of the well-​born citizen. If the latter is the case, Celsus may be placed in the context of a broader interest discernable in the late Republic and early Empire. A lost work of Rufus of Ephesus (ca 100 ce) had been entitled For Laymen, while Dioscorides and Galen are both credited with works on remedies easily discernable by laymen. The head of the Pneumatist school, Athenaeus of Attalia (ca 50 ce) promoted lay interest and attendance at medical lectures and, later, Galen gave anatomical demonstrations before members of the elite (Anatomical Procedures 1.218 K.). In the generation after Celsus, Pliny was to devote a large part of his Natural History to medical remedies (see sec. 8). By its very nature, however, medicine was, with agriculture, as Celsus had said, the preeminent art of living, and a medical tradition predating familiarity with Greek science existed. This laid considerable stress on an independent self-​help approach, family-​ based, and reliant on remedies from plants, animal derivatives, and some minerals. Farm and garden produce provided, appropriately, many of the basic ingredients (cf. Pliny 29.29). Professional, Greek-​educated doctors were objects of considerable suspicion, as the famous comments of the Elder Cato suggest (Pliny 29.13–​15). That these were repeated and endorsed a generation after Celsus suggests an underlying prejudice endured, despite the overall entrenchment of Greek medicine at Rome by the 2nd century bce. For the most part, the prejudice was directed not against medicine itself but against its practitioners (Pliny 29.11, 15–​16), whose predominantly low status

668   Greco-Roman Science and non-​Roman origin enhanced fears they would use their life-​and-​death powers to fleece or even murder their helpless Roman patients (Pliny 29.14, quoting Cato). Hence, perhaps, a particular incentive for the educated to pursue a personal quest for medical knowledge, shoring up Roman ideals of liberty and self-​sufficiency against possible undermining by unscrupulous foreigners. Was Celsus, then, a Roman polymath, appropriating Greek medicine for himself and his compatriots and ordering it within the empire of Roman knowledge? He indulges in no diatribes against Greek practitioners, but he presents a learned and judicious assessment of Greek medicine. Pliny expressed dislike of the seemingly overtheoretical nature of the latter (26.11, 29.11). Celsus advocates a middle way: experience of individual cases is important, but he opines that the greatest practitioners did not just busy themselves over fevers and ulcers but also researched “the nature of things,” becoming superior doctors thereby (proem.47). Yet, even in Celsus’ work, residual tensions remain: it was a decline in traditional Roman morals from a plain-​ living, active ideal (see sec. 3)  to a self-​indulgent passivity (desidia, laziness) and luxuria (indulgence), which gave rise to the need for complex (multiplex) Greek medicine (proem.4). Even the sedentary habits of the scholar had a bad effect on health and precipitated a learned pursuit of the art; a more creditable and useful stimulus (proem.6–​7), but one nonetheless that reflects early Roman prejudice against overemphasis on private studia at the expense of public exertion in the military and political sphere. The “complexity” of Greek medicine is also an echo of a Roman tendency to see Greek learning as too subtle as opposed to the Romans’ more direct simplicity. Once again, there is a moral dimension:  deception as opposed to honesty. Pliny criticized overcomplicated treatments and potions (24.4, 29.24–​25), contrasting them with simple, and cheap, Roman herbal remedies; and occasionally even Celsus will point to a simple, single-​herb remedy used by poor Roman rustici in place of the complex treatments prescribed by the Greeks (e.g., 4.13.3–​4). The issue of money and monetary gain raised further sensitivities. Many forms of the latter were socially suspect at Rome. Celsus’ preference for practicing on those known to the practitioner (proem.73), and not on large numbers (proem.65), may owe something to the desire to avoid sordid gain by exercising medicina in accordance with the paterfamilias tradition. For Pliny, the prices of medications were a prime means of distorting the Roman moral outlook. He picks up on the psychological tendency to misvalue the expensive as more effective than the cheap (29.28). That outlook encouraged the loss of knowledge of traditional and effective remedies attainable by even the poorest; and, ironically a cultural enslavement to unscrupulous individuals from a conquered race (24.5). Of course, simple medicaments formed the basis of much Greek medicine, and large numbers of Pliny’s treatments derive from Greek sources. But knowledge, as we have seen, is power. The power of a Greek doctor over the body of his Roman patient was too close to that of a master over a slave (24.5): the conquest and conversion to Roman mores of medicina was vital to Roman liberty.

Science and Medicine in the Roman Encyclopedists    669

7. Columella The most detailed treatment of agriculture to come down to us is that of L.  Iunius Moderatus Columella (ca 50 ce) a contemporary of the younger Seneca and, like him, of Spanish origin; he came from Gades. In addition to the extant De re rustica, he mentions two other works, either written or projected, the themes of which were also related to agriculture: one, attacking astrologers, with a bearing on the agricultural calendar (11.1.31), and another on religion in agriculture (2.21.5). A shorter extant work, De arboribus may be a brief, earlier attempt at the topic covered in his main work. This latter consisted of 12 books, covering the villa and workforce (1); arable crops (2); vines and trees (3–​5); animals (6–​7); pastio uillatica (8–​9); and horticulture (10): in hexameter verse). The last two books dealt with the duties of the slave farm-​manager (uilicus) and his partner, including wine and oil production. So far as we can tell, then, Columella’s output was largely related to the topic of agriculture, and his claim to inclusion in a survey of encyclopedic writers rests not on his coverage of a number of different subjects but on the large scale and comprehensiveness of the De re rustica, which in turn provided material for encyclopedic works from Pliny to Cassiodorus and Isidore of Seville. His work exhibits some of the hallmarks of encyclopedism; there is a parade of bookish learning, including Greek, Latin, and even Carthaginian authors: Mago’s 28-​volume work on agriculture (1.1.13; cf. Varro 1.1.10) had been translated into Latin on the orders of the Senate, probably another instance of intellectual war booty. Another familiar theme is the declaration that learning is needed for farming, and a range of learning at that. Columella implies that too often farmers did not see training as a necessity (2.pref.1–​3). Yet agriculture, he argues, is a discipline and one more vital than those for which training is taken for granted. As Vitruvius’ architect uses the very elements of nature, so too the close reliance of the farmer on nature is emphasized. He who would be an agricultural expert must become well-​versed in nature (rerum naturae sagacissimus, 1.pref.22). Astronomy, meteorology, and knowledge of landscape and soil types are all emphasized (1.pref.23–​25). This is not the department of intellectual specialists but neither can idiots achieve success (1.pref.32). The key, as we saw, is once again the notion of a broad, commonsense instruction realistically attainable by the well-​educated, elite landowners at whom the treatise is aimed. The philosophical expertise of a Democritus or Pythagoras is specifically rejected in favor of the more literally down-​to-​earth examples of Tremelius, Stolo, or Saserna, Roman writers, unfortunately no longer extant, who offered pragmatic instruction to their compatriots (1.pref.29–​33). Real-​life knowledge for real-​life Romans was another facet of the practical Roman ethos: Cicero, in his On Friendship 21, had already used the concept as a device to Romanize the overtheoretical Greekness of philosophy, dismissing some Stoic philosophers’ unrealistic models of the wise and virtuous man in favor of Paulus, Cato,

670   Greco-Roman Science or Scipio, historical Romans renowned for their practical wisdom and virtue. Such an appeal is equally appropriate in a field whose subject matter embodies core values of the same elite ethos. Columella enlarges on the traditional agrarian themes: the statesmen-​ farmers of old, morality, and healthy hard work, contrasted with the effete, unhealthy lifestyle of the contemporary city dweller (1.pref.3–​13). More interesting, however, is his take on the usual association between peace and agrarian plenty (e.g., on the Augustan Ara pacis), whereby the value and effort the Romans of old bestowed on agriculture ensured that their productivity was better, despite the greater incidence of warfare, than contemporary desidia can manage in a time of peace (1.pref.17–​19). Indeed, the self-​sufficiency once maintained in wine and grain has disappeared and imports are necessary. This morally tinged explanation ignores significant economic factors, including population growth, which preoccupy modern historians, but it serves to remind us once again that the “science” of antiquity operated in areas to which considerations and criteria foreign to modern preconceptions were applied: an impression enhanced by religio-​philosophical comments on the divinity and perpetual fertility of the earth. (Columella does not subscribe to the Epicurean view that earth will eventually wear out). However, Columella also has robustly practical explanations and remedies: manuring and allowing land to lie fallow is an essential part of maintaining fertility (2.1.1–​7). Moral considerations in Columella and also in his younger contemporary, Pliny, do not skew rational assessment so much as render the situation more complex. Columella’s work was aimed at the owners of large, slave-​run estates, but to maximize profit the owner must oversee the slaves (1.1.8), who, having no vested interest in the property, may try to cheat him (1.1.20, 1.7.6–​7). The owner must supply cura and diligentia. Even here, however, moral overtones suffuse the hard-​headed business criteria, as Pliny, too, shows: the farming of the land by honorable hands (honestis manibus), at least in a figurative sense, ensures a high moral standard more appropriate and therefore more pleasing to divine earth, and therefore more likely to enhance profits (16.21, 18.9, 18.36). Even making a profit is more than pragmatic, as the “enlarging and passing on of an inheritance” (1.pref.7) was another central part of the elite ethos. Diminution, or even accretion by “dishonorable” means, was to be avoided, and agriculture was regarded as the most honorable source of profit. It involved self-​reliance and honest gain for honest input, and avoided the taint of deceit and misrepresentation endemic to trade or the lack of freedom associated with employment by another (Cicero, On Duties 1.150–​151). That said, the practical principles of Columella’s approach are clearly discernable. He takes a considerable interest in outlay and labor costs and in long-​and short-​term considerations (e.g., 2.2.12). This is seen in his detailed evaluation of the complexities of viticulture, which he suggests contemporaries were shying away from (3.3.1–​15). Pasture, the profitability of which had been advocated by the elder Cato, was evidently still popular and viewed as a simpler option (3.3.1). Owning more than you can farm properly is both morally (wasteful/​greedy) and practically (wasteful/​inefficient) wrong. His scathing judgment of those who own vast tracts of lands they cannot easily travel round, but leave them to be trampled over by animals (1.3.12–​13), may be taken in

Science and Medicine in the Roman Encyclopedists    671 conjunction with Pliny’s famous condemnation of latifundia, which occurs in a similar context of waste and inefficient farming (18.35). Pliny, like Columella, combines moral considerations, for instance, about slave and free labor, with practical cost-​cutting advice (18.38). It is Columella, however, who produces a scientific attempt to calculate labor requirements in terms of man-​days, type of crop, terrain, and so on (2.12). As can be seen, however, creating such a formula illustrates the need to take account of variables, and this is a feature of Columella’s treatment of his subject as a whole. He owned several properties (2.3.3; 7.9.2) and uses specific knowledge from other areas (7.2.3), including his uncle’s estates in Spain (2.15.4). This variety, whether in soil, weather, animal breeds, or crop varieties and their different characteristics (1.1.23–​28) cannot be mastered in its entirety. Yet, as with our other encyclopedic works, the presentation of as much of this variation as is practicable within the carefully ordered subdivisions of a multivolume work represents a scientific effort to render knowledge comprehensible. Principles and particularities intermingle. They are underpinned not only by ethics but also by the elegance of Columella’s prose. Book 10, on gardens, is actually a poem. Yet, even in this hexameter homage to Virgil, an interplay of general rules and particular conditions reflects the same “scientific” principles as the rest of the work.

8.  Pliny the Elder The final author in this survey, Pliny the Elder (23–​79 ce), wrote his 37-​book Historia naturalis (Natural History) in the 70s CE, while simultaneously employed by Emperor Vespasian in a series of important equestrian administrative posts (see sec. 1). Other works covered equestrian javelin-​throwing, grammar, rhetorical training, Rome’s wars with Germany, and a general history up to his time in 31 volumes (Pliny the Younger, Epistles 3.5; cf. Pliny pref.20). However, only the Natural History is extant, “a learned and comprehensive work as full of variety as nature herself ” according to his nephew (Epistles 3.5.6), who portrays his uncle as the epitome of the encyclopedic Roman, the comprehensiveness and variety of his output complemented by his political duties. “Life is being awake,” Pliny tells his dedicatee, Titus, in the preface, explaining that he devoted his days to his imperial masters and the nights to studia (pref.18). The Natural History itself, the largest of the extant works we are dealing with, is also uniquely constructed. It is not divided into separate disciplines (see sec. 3), nor is it a detailed and comprehensive study of one topic only. It does, however, have a unifying theme, and, as indicated, an order that replicated the Aristotelian scala naturae. The broadest subdivisions—​cosmology (book 2), earth and its constituent lands and seas, with their human geography, (3–​6)—​give way to animal life, starting with nature’s highest creation, humanity (7)  and move down the scale to other land animals (8), sea creatures and other aquatic life (9), birds (10), and insects (11). Plant life follows, including medicinal uses of both plants and animals (12–​32), and the work concludes with minerals and their uses (33–​37). Pliny thus places “inquiries into nature” (the literal

672   Greco-Roman Science meaning of historia naturalis), rather than particular disciplines, at the core of his work. However, this was a difference of emphasis rather fundamental conception: rather than a study of medicine triggering a discussion of plants, Pliny’s discussion of plants triggers a discussion of medicine. “My subject is nature, that is, life” (pref.13). His natural science is essentially applied science: the “life” referred to is the life of the human race and his topic is not so much nature as man in nature. Pliny’s particular outlook derived from the Hellenistic Stoa, which portrayed nature as a creative deity suffused throughout the universe. Humanity was viewed as nature’s highest creation that, through the possession of reason, had a share in nature’s divine spark, and nature existed largely to serve humanity’s needs. Thus, while on the one hand his “applied” science has a modern ring, it originated in a worldview of a very different type and era. Pliny’s zoology, for instance, drew on the scientific works of Aristotle but also included much anecdotal material about animals’ behavior and interaction with humanity. Language often borders on the anthropomorphic (Fögen 2007), though importantly it never literally equates animals to nature’s highest creation (Beagon 1992, 133–​144). Rather than categorizing this approach as unscientific, we should instead see it as an excellent example of the way that, for Pliny, nature is life: the breadth and variety of his approach show that science was inseparable from culture generally. Similarly, the practical humanitarian emphasis on the knowledge disseminated, the principle of utilitas uitae noted in a number of our previous authors, is particularly prevalent in Pliny (cf. 25.25, 28.2) but is thoroughly steeped in a distinctively Roman ethos. Both medicine and agriculture, the arts of life par excellence according to Celsus (1.pref.1), receive detailed treatment in Pliny in consequence of his books devoted to plants. His treatment of agriculture, like Columella’s, stresses practical profit and labor-​saving methods against the traditional backdrop of the Roman agrarian ethos (sec. 3). His overtly patriotic resistance to Greek scientific medicine has also been mentioned. Here, unlike Celsus, he made specific and scathing attacks on Greek practitioners (29.1–​28), condemning foreign medicine for its unnecessary complexity and for the expense that was consequent either upon this complexity or else upon the exotic provenance of the ingredients (24.4–​5, 29.23–​25). However, he went further, and made a pronounced attempt to identify and champion a traditional Roman form of herbal medicine, despite the fact that this was not necessarily separable from specifically Greek recipes. Nor was it possible to draw clear distinctions between native herbal remedies and the “magical” recipes of the eastern Magi, which he professed to dislike for their patent absurdity and that the magician was not committed to utilitas uitae, but might even set out to harm. Pliny’s attempt, though, is interesting for several reasons. First, it is the one area covered in his book that offers evidence of authorial firsthand investigation. Pliny tells us that he examined herbs in the garden of an aged herbalist, Antonius Castor (25.9), and has had others sent to him (25.27, 27.99, 25.18). As mentioned, much ancient writing on scientific and technical subject matter tended to rely heavily on other scholarship, and this is particularly the case for encyclopedic works, with their broad, comprehensive remits. Celsus evidently had medical expertise, and firsthand experience acquired incidentally might be utilized: landowners

Science and Medicine in the Roman Encyclopedists    673 like Varro and Columella draw on firsthand agricultural knowledge, as did Pliny, who also describes a mining technique (33.70–​73), possibly witnessed when he was procurator in Spain. But his botanical efforts are unusual, and we have to acknowledge that their impetus was connected more with patriotic motives and authorial auctoritas than a spirit of scientific curiosity per se. Secondly, the inclusion of magical material, despite his protestations, is interesting precisely because it illustrates the difficulties of drawing distinctions between magic, religion, and what would be regarded today as the science of medicine. Pliny himself declares that the three are interlinked, contending that magic was an inferior offshoot of medicine, which subversively accrued elements of religion and astronomy (30.2). What is well illustrated by the work as a whole, however, is the breadth and complexity of the medico-​magico-​religious synthesis. At times, Pliny seems conscious of the difficulties inherent in his attempts to compartmentalize a “Roman” medicine, as when he voices embarrassment at some very magical-​sounding “remedies” found in the work of that icon of Roman tradition, the elder Cato (28.21, 29). Elsewhere, however, he appears oblivious to the nature of his material: a snail’s head amulet prepared at full moon (29.114) as a headache cure seems little different, though perhaps less ambitious in its intended effect, than an amulet of a snake tail in deer-​skin for epilepsy, which is condemned as magical (30.91). However, his overriding theme, we might say the working hypothesis, of his natural science, is nature’s power (7.7), which can assert itself anywhere (2.208). He recounts without comment its manifestations in humans: snake-​charmers, fire-​walkers, and possessors of the evil eye, or body parts with curative properties (7.13–​19). If nature can implant poisons in certain human bodies (7.18), even the possibility that human speech in prayers and incantations possesses real power cannot be discounted (28.10–​29). This overarching hypothesis contextualizes the natural wonders in Pliny, providing them with an explicit rationale that is absent from their use in paradoxography, where their impact is heightened by a technique of isolation from background data and explanations. In 9.178, for instance, a series of examples of a remarkable phenomenon (fish which can apparently survive without water) is given, with the comment that “there is in these accounts, however marvelous (mirabilibus) they may be, a certain principle (ratio).” In nature, Pliny has chosen the ultimate encyclopedic theme for his work. More than any other, it mirrored the world empire controlled by Rome. His proud declaration of 20,000 facts from 2,000 volumes by 100 authors (pref.17) is preceded by a reference to a need for storehouses rather than books to contain them all, recalling ancient theories of memory but also suggesting parallels with the collections of the Imperial capital. Pliny’s ambition to be as inclusive and totalizing as possible also precipitates attacks on the intellectual slackness that can create gaps in the preservation of the intellectual tradition (14.3) and on the superstitious refusal to share and transmit knowledge (25.1, 16; sec. 2 this chapter). His inclusive principle also leads him to record material he may dislike or dispute (e.g., 29.61, 29.140, 30.98). The dubious nature of some of the facts recorded led to increasing criticism in later centuries of the unreliability of its author. This is to ignore Pliny’s language, which frequently shows that he distanced himself from personal endorsement of much of his material. Rather, this principle of inclusivity brings

674   Greco-Roman Science Pliny closer to modern principles of data collecting and preservation than was normal in antiquity. Finally, parallels between the empires of Rome and nature are made explicit in several well-​known passages. The world trade in healing plants, facilitated by the pax Romana, leads to a comparison of Rome to the sun, the ruling principle of nature (27.3, cf. 2.13). At the end of the work, Italy is called ruler and second parent of the world (rectrix parensque mundi altera, 37.201), language evocative once again of the sun as ruling principle and of nature herself, frequently referred to as mother of all. The totalizing aim of Pliny’s work has sometimes been interpreted as signaling an attitude that regarded scientific investigation and discovery as inherently finite. However, Pliny’s attempt to compress nature into 37 books should not be seen as implying that further inquiry was redundant or that a state of completion heralded stasis in scientific endeavor. “The more I observe nature, the more do I consider no statement about her to be impossible” (11.6) is suggestive of an ongoing process. He suggests that nature’s uarietas is seemingly infinite (7.7–​8, 32) and repeats the saying that Africa is always producing something new (8.42; cf. Aristotle, History of Animals 8.28, 606b20). The expansion of Rome’s empire brought increasing contact with the strange and new. Pliny’s official duties ensured he was well-​travelled for his age, and a natural disposition to inquiry may have been fostered by Stoic thought, according to which the wise man schooled himself to expect the unexpected (Strabo 1.3.21). It is therefore unsurprising that, on the afternoon of August 24, 79 ce, when Pliny, now admiral of the fleet at Misenum, saw something new and unexpected in the form of a strange cloud issuing from Mt. Vesuvius, he decided it was worthy of personal investigation. Pliny the Younger’s account (Epistles 6.16) presents a picture now familiar to us, in which scientific interest is exercised against a backdrop of Roman values, as his uncle converted the initial voyage of inquiry into a heroic military rescue mission. Despite, or perhaps because of this, he has succeeded in capturing the imagination of generations of later readers for whom his uncle’s death bridges the conceptual gap between ancient and modern inquiry into nature.

9. Epilogue In the centuries immediately following Pliny’s demise, further works of an encyclopedic nature were produced, in most of which the influence of Pliny (direct or indirect) and some of our other authors is clearly discernable. Augustine had direct access to at least book 7 of the Natural History and knew other parts of the work, possibly indirectly (Beagon 2005, 35–​36). Martianus’ treatment of the seven liberal arts is indebted to Pliny among others. Varro’s Disciplinae probably influenced both (sec. 4). A number of other scholarly and compilatory works continued to transmit ancient scientific ideas (see chap. E7, this volume). They included a little anonymous treatise attached to the manuscripts of Censorinus (3rd century ce), with short sections

Science and Medicine in the Roman Encyclopedists    675 on cosmology, geometry, music, and the first extant discussion on Latin meter; the Commentarii and Saturnalia of Macrobius (5th century ce); and the second book of Cassiodorus’ Institutes (ca 562 ce). Most significant in terms of transmission of previous scholarship and circulation was the Etymologiae of Isidore of Seville, in which the influence of all the authors discussed in this survey can be discerned, at least secondhand. Besides disseminating the scholarship of antiquity into later ages (the Roman Catholic Church declared him patron saint of the Internet in 1997), Isidore, like some of his ancient predecessors, was marshalling knowledge in the wake of political upheaval. When Braulio, bishop of Saragossa, produced a list of Isidore’s works (the Renotatio librorum Isidori), he compared him to the first of our authors, Varro, quoting Cicero’s encomium (Academica Posteriora 1.3) of the latter as the restorer of his country’s intellectual heritage, covering all things human and divine, “that we might understand who and where we are.” In the Roman encyclopedic tradition, this link between life and learning was strong and enduring. The scientific enterprise encapsulated by our encyclopedic authors differed in many ways from our current practice. However, we have seen, to varying degrees, a concern for classification and ordering and a stress on a comprehensiveness that must also be comprehensible. These are scientific principles that have not changed over two millennia. Most remarkably, perhaps, the Roman encyclopedic authors encapsulate a facet of scientific learning in which their society was arguably more advanced than ours. Familiarity with scientific knowledge was regarded as appropriate to a broader section of the educated population than is generally the case in the modern era of scientific specialism, and these authors played a crucial role in disseminating such knowledge in a form comprehensible to an educated public. Since “science” was an intrinsic part of knowledge (scientia), Cicero’s verdict on Varro, reapplied to Isidore nearly 700 years later, endorses Pliny’s dictum that nature is life.

Bibliography Beagon, Mary. Roman Nature:  The Thought of Pliny the Elder. Oxford:  Oxford University Press, 1992. —​—​—. The Elder Pliny on the Human Animal. Oxford: Clarendon Press, 2005. Doody, Aude. Pliny’s Encyclopaedia:  The Reception of the Natural History. Cambridge: Cambridge University Press, 2010. Doody, Aude, Sabine Föllinger, and Liba Taub, eds. Structures and Strategies in Ancient Greek and Roman Technical Writing: An Introduction. Amsterdam: Elsevier, 2012. Fögen, Thorsten. “Pliny the Elder’s Animals: Some Remarks on the Narrative Structure of Nat. Hist. 8‒11.” Hermes 135 (2007): 184–​198. French, Roger. Ancient Natural History: Histories of Nature. London: Routledge, 1994. French, Roger, and Frank Greenaway, eds. Sciences in the Early Roman Empire: Pliny the Elder, His Sources and Influence. London, Sydney: Croom Helm, 1986. Griffin, Miriam. “Philosophy, Politics, and Politicians at Rome.” In Philosophia Togata: Essays on Philosophy and Roman Society, ed. Miriam Griffin and Jonathan Barnes, 1–​ 37. Oxford: Clarendon Press, 1989.

676   Greco-Roman Science Gros, Pierre, ed. Le projet de Vitruve:  Objets, destinataires et réception du de Architectura. Roma: École Française de Rome, 1994. Hadot, Ilsetraut. Arts libéraux et philosophie dans la pensée antique. Paris: Centre National de la Recherche Scientifique, 1984. Healy, John. F. Pliny the Elder on Science and Technology. Oxford: Oxford University Press, 1999. König, Jason, and Tim Whitmarsh, eds. Ordering Knowledge in the Roman Empire. Cambridge: Cambridge University Press, 2007. McEwen, I. K. Vitruvius: Writing the Body of Architecture. Cambridge, MA: MIT Press, 2004. Murphy, Trevor. Pliny the Elder’s Natural History: The Empire in the Encyclopaedia. Oxford: Oxford University Press, 2004. Rawson, Elizabeth. Intellectual Life in the Late Roman Republic. London: Duckworth, 1985. Rowland, Ingrid D., Thomas Noble Howe, and Michael J. Dewar. Vitruvius:  Ten Books on Architecture. Cambridge: Cambridge University Press, 1999. Sabbah, G., and P. Mudry, eds. La médecine de Celse:  Aspects historiques, scientifiques et littéraires. Saint-​Étienne: Université de Saint-​Étienne, 1994. Shanzer, Danuta. “Augustine’s Disciplines: Silent diutius Musae Varronis?” In Augustine and the Disciplines: From Cassiciacum to Confessions, ed. Karla Pollman and Mark Vessey, 69–​112. Oxford: Oxford University Press, 2005. White, K. D. “Roman Agricultural Writers I:  Varro and His Predecessors.” In Aufstieg und Niedergang der Römischen Welt, vol. 1.4, ed. H. Temporini, 439–​497. Berlin: de Gruyter, 1973.

chapter D5

Stoicism a nd t h e Natu ral Worl d Philosophy and Science Teun Tieleman

1.  The History of the Stoic School: An Outline Around 300 bce Zeno of Citium (ca 334–​261 bce), after studying with philosophers of various schools, did not join any of them, becoming an independent teacher of philosophy instead. The followers he acquired were first named “Zenonians” (Gr. Zēnōneioi) but later on “Stoics” (Gr. Stōikoi) after the Stoa Poikilē (Painted Colonnade), the place bordering the Athenian agora where they met (Diogenes Laërtius 7.4–​5 = SVF 1.1). By founding his own school, Zeno entered a philosophical marketplace marked by intense competition. The Academy, the Lyceum, the Garden (founded by Epicurus only a few years before), the Cynics, and others vied for adherents; each attentive to what the others said or did. There was a lively exchange of viewpoints and arguments, which led to important philosophical innovations. Modern historical scholarship has been slow in recognizing this period as a rewarding field of study. This was due not only to the fragmentary and complex state of textual evidence but equally to a distinct bias against philosophy of the Hellenistic period (traditionally 323–​30 bce). For a long time, the attention of historians and philosophers remained focused on the 4th-​century bce philosophers Plato and Aristotle and, to a somewhat lesser extent, the 6th-​to 5th-​ century bce pre-​Socratics, and the much later Neoplatonists. Over the past 40 years, however, the balance has been redressed in favor of the Stoics, Epicureans, Academic Skeptics, and other Hellenistic philosophers. The early Hellenistic context in which Stoicism arose is crucial to understanding some of its basic features. The 3rd-​century bce saw the blossoming of the

678   Greco-Roman Science phenomenon of the philosophical school, or “sect” (Greek:  hairesis, lit. “choice”), which promised its adherents a road toward happiness as the ultimate human end and highest good (telos) (see Dorandi 1999; Natali 2003). The philosophies taught by the schools offered moral and existential guidance to this end. Becoming an earnest student of any of them had clear consequences for one’s daily conduct: philosophy was life transforming. Thus the Stoics defined philosophy as “the art with respect to life,” adding that it is aimed at a “useful end” (SVF 1.73; 3.111, 526; Cicero, On Moral Ends 3.4; Seneca, Moral Epistles 95.7, 117.2; Epictetus, Discourses 1.15.2). The schools, then, were not places to obtain knowledge for knowledge’s sake but were more similar to an association or, as in the case of Epicurus’ Garden, a community. Here doctrine and demeanor were supposed to be in harmony. Each school had a head, or “scholarch,”—​the founder himself or one of his successors, the keepers and exegetes of its doctrinal legacy. The scholarch taught not only by lecturing but also through admonition and personal example. An inner circle of the most loyal and advanced pupils would form around the scholarch. In addition, there were other, less advanced pupils who had made the consequential step of joining the school. Commitment was considered necessary for making progress and to avoid going astray. The degree of coherence varied from school to school, however, ranging from the Garden with its emphasis on close ties of friendship to the more loosely organized Lyceum. At least initially, the Stoa appears to have been closer to Epicurus’ more radical approach. In the 3rd and 2nd centuries bce, Athens remained the undisputed headquarters of each of the main schools (which did not preclude the founding of minor centers elsewhere). Those who wanted and could afford to study philosophy came to Athens. The three first heads of the Stoa, like many of their pupils, came from various Greek and, indeed, sometimes half-​Greek cities, like Zeno’s native town Citium on Cyprus. What has traditionally come to be called Early Stoicism, or the Old Stoa—​the phase in which Stoic philosophy was developed and further refined and strengthened—​is the period stretching from its founder Zeno to Chrysippus and his immediate pupils (roughly 300–​150 bce). After that the school organization became looser, and at some point the succession of school-​heads was interrupted, which meant that there was no longer a single authority who determined official school doctrine. This development also involved a change of location: an important watershed is the sack of Athens by the Roman army in 86 bce, bringing about what Sedley has aptly termed a philosophical diaspora as well as a dispersion of the libraries of the schools (see Sedley 2003, 24–​25). Athens soon regained its role as a center for the study of philosophy—​but without its former predominance. Leading Stoics such as Panaetius of Rhodes (active ca 150–​105 bce) and Posidonius of Apamea (130–​50 bce) studied in Athens, but in their subsequent careers they were more itinerant than the Stoics of the first generations. After extensive travels, Posidonius set up his own Stoic school in Rhodes (Posidonius T 29–​39 E.-​K.). But the schools of Rhodes, Athens, Rome, Tarsus, and other towns were by no means the only places where philosophy was taught. Moreover, the new Roman world brought certain changes in the way teaching was organized. Already Panaetius belonged to what

Stoicism and the Natural World    679 Cicero has portrayed as the circle of Scipio Africanus, a Roman statesman with strong intellectual interests (Tieleman 2007). Roman noblemen with a taste for Greek culture developed the practice of having Greek philosophers stay in their homes to provide education and moral guidance for themselves and their relatives. This diaspora of philosophers further led to an increased importance being attached to the writings of the founders and their successors. When face-​to-​face conversation and inspiration were no longer available, other, written means such as the philosophical letter or biography were needed. It has long been assumed that the advent of Rome and these concomitant sociological changes must have impacted the content of philosophical teaching as well. Panaetius, Posidonius, and their direct pupils have been taken to represent “Middle Stoicism,” a modern term of periodization introduced by Schmekel (1892). This phase is supposedly marked by an increased receptiveness to Platonic and Aristotelian thought, after a first more dogmatic phase, “Early” or “Old” Stoicism. The two leading lights of Middle Stoicism were taken to represent a less radical and more humane version of Stoicism than their predecessors. Panaetius’ agenda of making philosophy more Roman-​friendly was, and often still is, believed to involve an almost exclusive emphasis on practical morality (but cf. Tieleman 2007, 105, on T 140 A). Posidonius, by contrast, was perceived as extensively engaged with the study of the natural world and the “special sciences” (discussed in sec. 5) from the outset—​and this picture finds overwhelming support in our documented evidence. However, he was also credited with major divergences from the teaching of Chrysippus and the Early Stoics, for example, in the area of moral psychology. Today historians handle this periodization more carefully, especially because we know more about the Early Stoics; for instance, it is recognized that they too creatively used Platonic and Aristotelian thought (albeit less openly than Panaetius and Posidonius). This reappraisal was made possible in large part by an increased understanding of the nature of our sources on whom we depend for the data from which we reconstruct Stoic philosophy, whether Early or Middle. Panaetius and Posidonius appear to have stayed within the Stoic framework formulated by the founders and made further refinements to the doctrines and arguments they inherited, and sometimes made their own choices within their inherited framework (see, e.g., Kidd 1999, 10–​11; Sedley 2003, 23–​24; Tieleman 2007). In fact, some of the reports suggest that far from importing non-​ Stoic elements into the Stoic system, these philosophers were in the business of pressing Plato and Aristotle into its service by presenting them as authorities who had anticipated certain Stoic positions (Tieleman 2003, chap. 5; and 2007, 114). The Stoics traditionally dubbed “Late” or “Imperial” have undergone a similar re-​appraisal. The traditional storyline depicted them as late moralizers in a trend in Stoicism instigated by Panaetius when he made Stoicism ready for consumption by the Roman upper class, stereotypically taken to be a more practically minded lot than the Greeks. The main representatives of this phase are Seneca (ca 1–​65 ce), Epictetus (ca 50–​130 ce), and Emperor Marcus Aurelius (121–​180 ce). However, the surviving works of Seneca and Epictetus do give a prominent place to physics. Among other things, this is illustrated by Seneca’s surviving extensive Natural Questions (that this does not offer

680   Greco-Roman Science science in a modern sense is a different matter; see further Wildberger 2006; Hine 2010; Williams 2012). Logic was so fashionable that Seneca and Epictetus warned against excessive concentration on it (see Barnes 1997, esp. 12–​42). Moreover, what struck modern academics as superficial moralizing came, under the influence of scholars such as Pierre Hadot, to be seen in a different light: Stoic philosophy (as well as other schools) viewed itself as a life-​transforming art of life involving the management of daily actions, emotions, and needs. Thus, the letters of Seneca and the discourses of Epictetus may be more representative of what Hellenistic philosophy had stood for from the beginning, instead of being products of a late age, which had sadly lost its capacity for profundity and abstract thought. This also means that we should stop thinking in terms of “popular philosophy” (German Populärphilosophie) as opposed to the real thing. Throughout the history of their school, Stoics were in a position to make certain choices of their own within the framework of fundamental and distinctive doctrines that determined the Stoic identity. Thus Seneca favorably contrasts Stoic freedom with Epicurean slavishness vis-​à-​vis their founder (see the contribution by Gordon, chap. D2, this volume). Although he and other Stoics may exaggerate the difference, the point is borne out by concrete examples: compare, for instance, Seneca’s critical stance regarding traditional religion with the far more accommodating attitude taken by his contemporary Cornutus. Stoics also differed in the degree to which they adopted ideas from the school known as the Cynics. Musonius Rufus did so more than Seneca did, and this made him adopt a more radical stance toward certain moral and societal issues, such as wealth and the position of women, than we find in Seneca. In the next generation, Epictetus dismisses people who pose as Cynics, but only to present an alternative ideal of true Cynicism as embodied by Diogenes of Sinope. The 2nd-​century ce Stoic Euphrates on the other hand was hostile to Cynicism. The teachings of Epictetus as recorded by his pupil Arrianus also point to a strong Socratic orientation, alongside a continued use of the works of Chrysippus and other early Stoics (to a far greater extent than the so-​called Middle Stoics). The anti-​Stoic writings of Plutarch (ca 45–​125 CE) and Galen (129–​ca 216 CE) attest to the status of Chrysippus as the main authority representing the Stoic school doctrine. These polemicists attack their Stoic contemporaries, thus bearing witness to the fact that Stoicism was a living force well into the 2nd century ce. A century later, however, Stoicism disappeared from the stage rather abruptly, giving way to Platonism, or the particular version which today is called Neoplatonism, which dominated later antiquity.

2.  The Place of Natural Philosophy in Stoic Thought From the beginning, the Stoa modeled itself on the life and thought of Socrates, the memory of which lived on in the works of Xenophon, Plato, and others. More schools

Stoicism and the Natural World    681 (though not Epicureanism) saw themselves as Socratic, but the interpretations of what Socrates had stood for varied widely. For the Stoics, the Socratic model involved a radical stance based on the idea that virtue alone is sufficient for happiness or the good life (eudaimonia). The term translated “virtue” (aretē) bears a wide sense, viz. excellence or perfection. For Stoics, it stood for the perfection of our human nature, which was taken to be our rationality, which sets us apart from the other mortal animals, representing a divine spark within us. The successful life consists in improving and, ideally, perfecting reason. The final, perfected state is embodied by the figure of the “Sage,” or wise person. This was a distant and rarely attained ideal, for which the Stoic scholarchs cited Socrates as an example rather than themselves. It functioned as a way of expressing particular doctrines, understandably since Stoic ontology recognizes only individuals as existents. Thus the Sage features in the provocative Stoic “paradoxes,” according to which only the Sage is “happy” (even under torture), “free,” “king,” “rich,” “noble,” and so on, which underline his “self–​sufficiency” while at the same time introducing a new and morally purged meaning for these terms. The Stoics, then, wish to concentrate on rational human nature as the material for philosophy, which they defined as the “art of life” (sec. 1)—​another Socratic legacy. Even so, they do not treat human nature in isolation without regard for the world in which we live. On the contrary, they set morality firmly in a cosmic context: to act rationally, we need to know the fundamental facts about the world in which we live, most notably that it is ruled by Logos (Reason), which is to be identified with the World-​ Soul and God (see sec. 3). We live in a providentially determined world, in which morality makes sense, that is to say, where our life’s goal (telos) is to reflect this perfect cosmic order through our attitude and actions. Thus, the Stoic summary of life’s end, “following nature” (or, alternatively, “living in agreement with nature”) was explained by the important third head of the school, Chrysippus of Soli (ca 280–​204 bc), as bringing our individual nature into harmony with universal Nature (Diogenes Laërtius 7.87 = SVF 3.4). This ideal suits the “holistic” view of individual humans as parts of the greater whole. More specifically, our intellects are rooted in the divine Logos. It is up to us to reject or conform to God’s divine plan, of which we are parts nonetheless (SVF 1.179, 3.16; Diogenes Laërtius 7.87–​89 = SVF 1.179, 3.4; the view of the cosmos as a living being is relevant here: see Lapidge 1978, 163; cf. Long and Sedley 1987, 1.267). Hence Zeno’s other formula for the happy or successful life as the “easy flow of life” (SVF 1.184; cf. 3.16, Diogenes Laërtius7.88). To “go with the flow” does not mean passive resignation but also involves making an active contribution to God’s grand scheme (Posidonius F 186 E.-​K.). Obviously, individual humans do not know the future or what lies in store for them personally—​though most Stoics believed that God in his providential care offers signs through which humans can glimpse the future and act accordingly; hence the controversial acceptance of astrology by most Stoics. But insofar as we do not know the future, we may follow nature by developing our capacity for rational behavior implanted by god within us—​an idea developed by the Stoics in their theory of oikeiōsis (appropriation, familiarization), that is, the process of moral and psychological development whereby we recognize other beings as “our own” (oikeion), that is,

682   Greco-Roman Science belonging to us (Diogenes Laërtius 7.85 = SVF 3.178). This process can be described in terms of ever-​widening circles: the widest circle (or, in Long’s apt expression, community of reason) makes up all rational beings including God. Clearly, then, Stoic moral thought is firmly grafted onto a particular view of nature, both human and universal, which accordingly should be studied and understood. The meaningful cosmological context the Stoics posited for morality is indebted to the Platonic Timaeus in particular. Here a divine Craftsmancraftsman creates the world in the best possible way—​a creation story pervaded by a strong cosmic optimism according to which our world displays rational design, order, beauty, and purposefulness, all of which are also found in our bodies. Clearly, this is not a physical theory driven by a purely intellectual curiosity, but a sense that the study of nature improves our psychic and, thus, moral condition. This is especially clear from what Plato says about the value of observing the movements of the heavenly bodies (Timaeus 90a–​c). Plato gives this account to an otherwise unknown expert in cosmological matters from southern Italy, Timaeus, rather than Socrates, in line with the latter’s abandonment of natural philosophy as suggested by a well-​known passage from the Phaedo (95a–​99d). It would, however, be rash to conclude that the idea of a cosmic context of morality represents a non-​or un-​Socratic element, at least from the Stoic point of view. A version of what may be called the “cosmic intelligence argument” (but is perhaps better known as the “argument from design”) is attributed to Socrates by Xenophon in his Memorabilia (1.4; cf. Sextus, Against the Physicists 1 [= Against the Mathematicians  9] 92–​110, no doubt based upon a Stoic source; see Sedley 2007, 210–​225; on the influence of Xenophon’s Memorabilia cf. Diogenes Laërtius 7.7). Nonetheless, the role and value of the study of nature were not undisputed. Among the earliest Stoics there was a tendency to reject physics and logic in accordance with how the school of the Cynics understood philosophy. The first Stoic scholarchs, however, decided in favor of the inclusion of natural philosophy. Zeno laid its foundation, the second head, Cleanthes, made substantial contributions, and his immediate successor, Chrysippus, gave it the form in which Stoic natural philosophy became known and was debated in Late Antiquity. What appears typical of the first generations of Stoics is that they did not allow the study of nature to ramify into specialized areas and levels of detail where they would lose sight of central philosophical issues. For the principal existential and moral questions, it is essential to know that we live in a providentially determined world. This commits the Stoic philosopher to an interest in the causes manifested in natural processes, and he may study them by using the data furnished by sciences such as astronomy and medicine. Thus, Chrysippus took account of medical insights (see sec. 5). But he appears to have been sensitive to the limits of knowledge or explanation: if the cause of something is concealed and so cannot be grasped, it is incumbent on the wise person to withhold assent. In this context he cited a particular mistake in Plato’s Timaeus concerning an anatomical point, which had been exposed as such by later advances in medical research (SVF 2.763; cf. Tieleman 1996, 189–​196). Caution,

Stoicism and the Natural World    683 therefore, befits the philosopher when confronted with particular scientific ideas. It would, however, be wrong to see here a basic pessimism or even skepticism when it comes to the potential of human reason. We are in principle capable of recognizing the unclear as such and hence avoiding error, even in scientific matters. Moreover, what is most important to know we can know, another sign of divine providence. Plato’s mistake (about the exact route followed by a drink) concerned a minor point and could have been avoided without weakening his argument. The later Stoic Posidonius (see sec. 1) pronounces a division of labor between philosophy and science in a long fragment (fr. 18 E.-​K.), specifically contrasting the philosopher with the astronomer:  the former is concerned with establishing the causes, whereas the latter conducts his proofs on the basis of hypotheses. Clearly, this enables the philosopher to make use of the astronomer’s findings, including his mathematical calculations concerning the movements of the heavenly bodies. But Posidonius was clearly more optimistic than Chrysippus about how far the recesses of nature could and should be explored and further refined Stoic causal theory with a view to more specialized inquiries. This is no doubt why the geographer Strabo (who presents himself as a Stoic) perceives an “Aristotelizing quality” about Posidonius, which sets him apart from the rest of the Stoics including Strabo himself. The other Stoics do not go as far as Posidonius “because of the concealment of causes”—​a phrase that echoes Chrysippus’ position in these matters (Strabo 2.3.8 = Posidonius T 85 E.-​K.; see also sec. 5). Given these ideas on the relation between natural philosophy and the “subservient” special sciences, the Stoics (following an old Academic division) took natural philosophy to be one of philosophy’s parts alongside the moral and logical parts. This tripartition is related to the organic conception of philosophy, which the Stoics were the first promulgate, viz. the formal presentation of philosophy as a coherent system. It is this conception that is also expressed in the images used to explain philosophy’s parts, such as that of the garden (with physics as the land or trees, logic as the fence, and ethics as the fruits) or Posidonius’ image of the body (in which the soul stands for ethics, the flesh for physics, and the bones for logic) (Sextus, Against the Mathematicians 7.16–​19 = SVF 2.38, Posidonius fr. 88 E.-​K.). According to Stoic corporealism (sec. 3), only bodies exist, or “are.” Thus the part of philosophy that studies the notion of “being” belongs to natural philosophy or, more strictly, philosophy’s natural part (Diogenes Laërtius 7.135; ps. Galen, The qualities are incorporeal 19.483.13–​16 K.  =  SVF 3, Apollodorus fr. 6, 2.381). Moreover, since both the soul and God are pneuma and hence corporeal, theology is a part of physics as well. Indeed, theology is described as the crowning part of physics and as an “initiation,” viz. into such things as are appropriate only for advanced students to know and should not be divulged among the uninitiated (see SVF 1.538, 2.42, 2.1008). Likewise the study of the soul, which is pneuma and so corporeal, is part of physics (and, at least originally, psychology even included epistemology, which deals with mental representation [phantasia], which, being a qualitative alteration of the soul, is corporeal too).

684   Greco-Roman Science

3. The Natural World: Universal Nature The Stoics limit being to the corporeal, which they defined as that which is three–​ dimensional and resistant, the test for which is that it is capable of acting or being acted upon (SVF 1.90, 2.363, 2.300). Only bodies exist, and this means that the Stoics reject the notion of form or essence, whether transcendent (Plato) or immanent (Aristotle). In taking this position, the Stoics deliberately stand Platonic ontology on its head: their limitation of being to body as capable of acting or being acted upon derives from Plato’s Sophist (247d8–​c4), where it features as the materialist position. Plato argues that this position is untenable since soul, too, satisfies the criterion of being capable of acting or being acted upon. The Stoics however use this criterion precisely for extending the realm of the corporeal as far as possible. Not only does it include soul but also every quality of soul: thoughts and dispositions, such as virtue. Moreover, God, being identified with the World-​Soul (another concept from the Timaeus), is corporeal too, since its substance is said to be pneuma, or “breath,” a composite of air and fire, which is tenuous and all-​pervasive yet capable of lending cohesion and form to existing things (a point that elicited criticism from opponents: SVF 2.441). As such, God is not one body among the others but rather the active principle or cause (archē), which working on matter (the passive principle) forms all bodies. God and matter are distinguishable though not actually separable. It is however potentially misleading to describe them as (mere) aspects of the cosmic bodily substance. The principles are corporeal themselves: they satisfy the criterion of being capable either to act or be acted upon (SVF 2.300; Long and Sedley 1987, 1.270–​272). The designation of the active principle as the “cause,” as the “World-​Soul,” as “God,” and as the “pneuma” does not exhaust its appellations. “Providence,” “Reason” (Logos), “Nature” and “Fate” are all used to indicate further aspects: the Stoic cosmos is one of providential determinism: everything is causally determined for the best. Even so, the Stoic God, too, needs material for its creative and sustaining activity. For the Stoics, as for Plato and Aristotle, matter is the indispensable substrate of natural change, which sets certain constraints to God’s rule. This too recalls the Platonic Timaeus where the divine craftsman (Demiurge) has to impose order on the “straying cause” or “necessity” (alongside other appellations), which is full of chaotic motions of its own and resists God’s well-​intentioned efforts. The early Peripatetics and Stoics adopted the view of nature as artistic and were quick to identify the errant cause with their notion of matter. But both schools diverged from Plato in seeing matter as entirely passive. Clearly, Plato’s Demiurge and his Model—​none other than the transcendent Forms—​could be seen as anticipating the efficient and formal and final causes of the Aristotelian fourfold schema. The Stoics, however, simplify and condense the Platonic causal distinction by limiting themselves to two principles or causes only: matter vs. the active cause, which combines the functions of the Demiurge, his Model and the World-​Soul. Yet the view of the world

Stoicism and the Natural World    685 as a piece of artisanship remains in place (as it had in fact for Aristotle). But now God the maker is no longer external to it. Thus the doxographer Aëtius summarizes the Stoic account of God as follows: The Stoics made God out to be intelligent, an artistic fire [pur technikon] which methodically proceeds toward creation of the world, and encompasses all the seminal principles according to which everything comes about according to fate, and a breath [pneuma] pervading the whole world, which takes on different names owing to the alterations of the matter through which is passes. (SVF 2.1027; trans. Long and Sedley, modified; on “artistic fire” see also SVF 1.171, 2.1133–​34)

Plato had also described the cosmos as a living being, a compound of body and soul; it is this conception that is continued by the Stoics. In describing and explaining the natural world they are engaging in what David Hahm (1977, 136)  has aptly termed “cosmobiology.” This becomes clear from the account given by the Stoic spokesman Balbus, in Cicero, On the Nature of Gods 2.23–​25, who following Cleanthes argues from the vital heat (said to sustain every living thing, whether animal or vegetable), to the fiery power sustaining the whole world. Clearly this fire is not the element fire from ordinary experience but the all-​pervasive dynamic force, which steers and sustains the cosmos (cf. Tieleman 2018). Apart from more recent biological ideas, Cleanthes and other Stoics found support in the sayings of the pre-​Socratic philosopher Heraclitus, who had also designated fire as the principle of the cosmos while being careful to differentiate it from the destructive fire of ordinary experience (B31 DK; cf. SVF 1.120). Cleanthes devoted an exegetical work of four books to Heraclitus, also lost (Diogenes Laërtius 7.174 = SVF 1.481; cf. Long 1975/​1976). The impact of Heraclitus also emerges from Cleanthes’ preserved Hymn to Zeus (Stobaeus, Eclogai 1.1.12, 25.3–​27.4 Wachsmuth = SVF 1.537; see also the edition, with translation and commentary, by Thom 2005). Heraclitus too had been prepared to call his principle Zeus, the divine ruler of the world, provided he was not identified with the anthropomorphic Zeus of popular religion or the Homeric epics (B32 DK). But certain elements in the traditional representation could be interpreted to suit Heraclitus’ doctrine. Thus he takes Zeus’ characteristic attribute, the thunderbolt, to symbolize God’s fiery nature (B64 DK). Borrowing this Heraclitean idea, Cleanthes gives prominence to Zeus’ thunderbolt in his famous Hymn: All this cosmos, as it spins around the earth, obeys you, whichever way you lead, and willingly submits to your sway. Such is the double-​edged fiery ever-​living thunderbolt, which you hold at the ready in your unvanquished hands. For under its strokes all the works of nature are accomplished. With it you direct the universal Reason (logos), which runs through all things and intermingles with the lights of heaven both great and small. (SVF 1.537 = Thom, lines 7–​13, 35–​36; cf. line 32)

In other Stoic texts the active principle is referred to as the pneuma (breath). Sometimes both fire and pneuma are used, as in the passage from Aëtius quoted earlier (cf. also SVF 1.127). To specify god’s physical substance as pneuma rather than fire or heat was a

686   Greco-Roman Science later development emphasized by Cleanthes’ immediate successor, Chrysippus. Medical authors and Aristotle had given the pneuma a role in human physiology, often in conjunction with vital heat. Zeno had made it the substance of the soul (though he also referred to the soul as fire). Chrysippus may have been the first to apply the concept of pneuma on the macrocosmic level, as that of which God consists. But this step may already have been taken by Cleanthes (Tieleman, forthcoming 1). Chrysippus analyzed the pneuma as a tenuous blend of fire and air, the active elements, as opposed to the passive ones, earth and water. Thus pneuma is the stuff appropriate for the active principle. The quartet of physical elements had been introduced by the pre-​Socratic philosopher Empedocles (active in the middle part of the 5th century bce) and accepted by Plato and Aristotle. Unlike Aristotle, Chrysippus assigned only one quality to each of the four elements: fire is hot and air cold (water wet and earth dry). Brought together in the pneuma, the hot and the cold effect opposing tendencies, with the hot expanding and the cold contracting, and hence tension (tonos). Through this “tensional movement” the pneuma guarantees both the coherence of each thing and its specific character. In other words, a thing’s characteristics are an expression of the fiery element in the pneuma. At this level of analysis one can see why the Stoics could feel that Chrysippean pneuma-​physics was a specification rather than a substitute for seeing the active principle as fire. As we have noticed, the pneuma blends with and pervades passive matter. Since these two principles are corporeal (even if the former is of a particularly tenuous kind), the Stoics had to offer an explanation how this is possible. They introduced the concept of “through–​and-​through blending,” that is, the complete interpenetration of substances while each preserves its own qualities. That is to say, they postulated this as a possible form of mixture alongside fusions in which the constituents do lose their qualities and mixtures that are really juxtapositions, as when one mixes peas with grains of wheat. Diogenes Laërtius reports on this doctrine as expounded by Chrysippus: According to Chrysippus in his Physics book 3, blendings [kraseis] occur through and through, and not by surface contact and juxtaposition. For a little wine cast into the sea will coextend with it for a while, and will then be blended with it. (7.151 = SVF 2.479 Long and Sedley #48A; trans. Long and Sedley).

Chrysippus’ counter-​intuitive example of the drop of wine (which remains a drop of wine, contrary to what Aristotle had said, On generation and corruption 1.10, 328a26–​ 28) made quite an impression. It recurs in a passage from Plutarch, On common notions against the Stoics: Chrysippus says: “Nothing stops a single drop of wine from blending with the sea”; and to stop us being amazed at this, he says that in the blending “the drop will extend through the whole world.” (1078E = SVF 2.480 Long and Sedley #48B; trans. Long and Sedley, slightly modified)

Stoicism and the Natural World    687 The Stoics sought empirical support from the fact that water and wine after having been blended can be separated again by dipping an oiled sponge into the mixture (Stobaeus, Eclogai 1.155.5–​11 = SVF 2.471 Long and Sedley #48D). This example failed to decide the debate in favor of the Stoics: their adversaries could simply dispute that it refers to through–​and–​through blending according to the Stoic definition. Its paradoxical character rested on the assumption that it entailed two bodies occupying the same place (cf. Aristotle, Physics 4.1). But it is useful to recall that the concept of complete interblending was designed to apply to pairs of rather different corporeal substances, most notably the pneuma as pervading passive matter and the soul blending with the body (see Long and Sedley 1987, 294). As the active cause, the pneuma pervades matter, but it does not do so with the same intensity everywhere in the cosmos: the Stoics distinguish between different levels corresponding to three main configurations of the pneuma. At the most basic level pneuma lends coherence to things (apart from determining their specific characteristics); this is the mode of existence of lifeless objects characterized by cohesion (hexis), or cohesive pneuma (pneuma hektikon). Next in the hierarchical series comes physical pneuma (pneuma phusikon, from phusis, “nature”) as defining vegetative life, which is marked by the faculties of growth and reproduction. Animals represent the level of psychic pneuma (pneuma psuchikon) or soul (psuchē) marked by the possession of perception (aisthēsis) and desire or impulse (hormē) in addition to the characteristics of the other levels of pneuma. (On the relation between the kinds of pneuma within the animal see sec. 4.) But this highest general level of the Stoic scale of nature admits of a crucial further differentiation: the soul of human animals in addition possesses the faculty of reason, the gift of divine providence (SVF 2.634, 458). This enables us to develop an orderly and social way of life, which ideally mirrors the rational patterns and processes of the divine cosmos: the Stoic goal (telos) of “following Nature” (sec. 2). From a historical point of view, we are once again reminded of the Timaeus, with its confidence in the moral benefits of studying Nature, and in particular the orderly movements of the heavenly bodies. At the same time there is an important difference related to the fact that the Stoics conflate God and World-​Soul, making God an immanent and all-​pervasive force within the cosmos. This makes individual intellect literally part of the greater and divine whole, whereas for Plato the incorporeal soul really has the transcendent world of Forms as its origin, for which it nourishes a deep-​seated though often latent longing. Seen in this light, the contemplation of the heavens is at best preparatory to a more abstract type of studies. The Stoics, then, forge a closer, physically based connection between human and divine nature—​a connection turning on Logos, or Reason. Even so, this closeness of the divine is counterbalanced by the fact that the Stoics combine it with a localization of the purest pneuma and hence of the divine that is more remote and in line with both traditional and Platonic notions related to the realm of the heavenly bodies, in other words, with, the sense of God being “high up there” (cf. Algra 2003, 167). Physically speaking, this is the realm of the purest kind of fire, the ether (aithēr: note this is not a fifth element as for Aristotle). Here the Stoics also locate the “leading part” (hēgemonikon) or intellect (dianoia) of the World-​Soul (even if Cleanthes diverged in opting for the sun;

688   Greco-Roman Science Diogenes Laërtius 7.138; Arius Didymus fr. phys. 29 Diels = SVF 634, 642; for Cleanthes see Plutarch, On common notions against the Stoics 1075D = SVF 1.510). Furthermore, communion with the divine is often not realized. The Stoics’ cosmic optimism does not blind them to the problem of cosmic evil, which they causally relate to the material principle. This imposes certain constraints on God’s providential activity. Obviously, humans as rational animals are also expressions of divine reason in matter. In their special case, rationality comes with the responsibility of choosing rightly or wrongly if not with the possibility of altering the fated course of events. This introduces moral evil into the world, that is, the perversion of souls so that they respond wrongly and emotionally to what presents itself to them. Thus Cleanthes in his Hymn writes that God determines everything “except what bad men do in their follies” (line 17 Thom; cf. SVF 1.537). This is the pessimistic side of Stoicism, which involves a negative estimation of the moral condition in which individuals and human society at large actually find themselves. In practice, then, many people have “turned their back” on correct reason and, it takes a lot of philosophical guidance to reorient them toward and keep them on the road of rationality leading to wisdom-​plus-​happiness. The study of nature is part of that effort. In the context of their macrocosm-​microcosm analogy, the Stoics invested the World-​ Soul or God also with psychic functions such as desire (hormē) and perception (we already found them specifying a cosmic seat of the divine intellect). Moreover, their view of the cosmos as a living being with both body and soul, combined with a cyclical view of history tied to the revolutions of the planets, led them to develop a theory concerning the life-​cycle of the world itself. Their line of reasoning was the following. Death is the separation of soul from the body, but this does not occur in the case of the world. Thus the World-​Soul continues to grow until it has completely used up its matter on itself (cf. Chrysippus in Plutarch, On Stoic Self-​Contradictions 1052CD = SVF 2.604 = Long and Sedley #46E). It is then that the conflagration occurs, that is, the point where the World-​ Soul becomes completely self-​absorbed and, given its fiery nature, the present world order ends in flames. The cosmos set thus ablaze expands into the empty space by which it is surrounded (cf. Algra 1993; cf. Tieleman 2014b). But a new world is created when the cosmic substance turns from fire through air into water. The moisture contains the logoi spermatikoi, the “seminal reasons” or “spermatic principles” of the world, just as in animal semen these principles (i.e., the blueprint, or, to put it even more anachronistically, genetic code, of the new animal) are enveloped by moisture. From then onward the other elements are produced through processes of condensation (earth) and rarefaction (air, ordinary fire). Together these constitute a new world-​order and a new scale of nature. This is identical to the one of the previous cycle: God is perfect and there is but a single way of making something perfect. In consequence, the same history is replayed down to the smallest details (even though some Stoics allowed small differences, such as a mole on the cheek, given the Stoic principle of non-​identity, according to which no two individuals are alike). In a later age this striking idea was to be taken up, though with a particular twist, by Friedrich Nietzsche as that of “eternal recurrence” (“ewige Wiederkehr des Gleichen”).

Stoicism and the Natural World    689 The Stoic doctrine of conflagration and everything it entails may strike one as fanciful or at any rate as sitting uncomfortably with the Stoic view of a good and providentially governed world (on which problem see Mansfeld 1979). Still, it was part of Stoic philosophy from Zeno onward and it can be shown to follow from a few premises fundamental to it. Even so, a few later Stoics such as Panaetius of Rhodes are on record as having doubted or outright denied it, thus returning Stoicism to a position more in line with the Aristotelian position according to which this world-​order is eternal (Philo, On the Indestructibility of the World, 76–​77 = Long and Sedley #46P). However, it is not necessary to think of the conflagration in terms of a catastrophe (in fact the biggest one imaginable). As the otherwise unsympathetic Plutarch reports, “Whenever they [the Stoics] subject the world to conflagration, no evil at all remains, but the whole is then prudent and wise” (On common notions against the Stoics 1067A = SVF 2.606). All matter has been used up and the divine intellect, no longer restricted by it, comes fully into its own. In other words, the conflagration marks the high point in the life of God or the cosmos, which given the macrocosm-​microcosm analogy is to be seen as a giant cosmic orgasm, followed by the releasing of seed and the growth of a new organism.

4.  The Natural World: Human Nature Stoic corporealism, as we have seen, also extends to the human soul, which is pneuma. The animal organism thus consists of two intimately interwoven corporeal substances—​ soul and body—​which nonetheless form a whole because of their complete interpenetration (sec. 3). Being corporeal, the soul is mortal; it has a beginning and an end. Its beginning goes back to the mingling of the male and female seed (which is itself pneumatic) in the womb. The embryo’s mode of existence is like that of plants: it has pneuma phusikon but not psuchikon; or put differently, it has no soul. The soul comes into being when the pneuma phusikon is exposed to the cold air as the child draws its first breath right after birth. It is then that the pneuma assumes the right tension (tonos), which, as we have seen, is based on a particular proportion of the hot and the cold (Hierocles 1.5–​33  =  SVF 2.806; cf. Tieleman 1991). It then acquires the qualities or powers that make it a soul and thus an animal: perception (aisthēsis)-​plus-​mental representation (phantasia) and desire or impulse (hormē). One may wonder whether there remains a separate portion of natural pneuma accounting for the functions of digestion and growth, which, strictly, are not part of soul or a different explanation was followed (Long 1982, 45; Tieleman 1996, 99). The soul is nourished from respiration and the exhalation of the blood in the heart (Galen, On the doctrines of Hippocrates and Plato 2.8 = SVF 3, Diogenes of Babylon, p. 216, fr. 30), which is the seat of the soul’s central organ according to most Stoics (see further below). So having been plant-​like as an embryo, the human offspring from birth is a nonrational animal. It achieves rationality and so full humanity later on (at the age of seven, or as other Stoics held, fourteen: see the texts assembled as SVF 1.149). A later, much

690   Greco-Roman Science further removed turning point may come (in admittedly rare cases) when human rationality turns perfect—​at the moment of attaining wisdom. Before this, a human is not wise but ordinary or even foolish. The Stoics, then, view psycho-​moral development as punctuated by sudden turning points with concomitant divisions that are rather absolute. Of course they were aware of the gradualness involved in psychological development: children develop their rationality—​marked by the linguistic ability—​gradually in the course of time. The Stoic system includes “progress” (prokopē) from ordinary rationality to wisdom (indeed, the whole mission of philosophy depends on it). Still, the boundaries they drew fulfilled specific functions and were well considered. If nonrational animals (including little children) displayed purposeful behavior, the Stoics could explain it in terms of their theory of oikeiōsis (sec. 2), according to which God has providentially implanted in animals a particular pattern of behavior starting from the first impulse toward self-​preservation. Here cosmic rationality is on display. If we take a closer look at the structure of the soul of the adult human, we find the Stoics breaking away from the faculty approach to the soul taken by illustrious predecessors such as Plato and Aristotle. The Stoics do not operate with a set of permanent and mutually irreducible powers or parts needed to explain human behavior, for instance, mental conflict. Rather they posit one central psychic organ, which is called the command center (to hēgemonikon), that is, the human intellect, located in the heart (according to most Stoics). Given the soul’s pneumatic substance, the intellect controls the body through a tensional, pneumatic continuum: from it seven rays of pneuma project throughout the body to operate the senses, the vocal and reproductive organs (Chrysippus in Galen, On the Doctrines of Hippocrates and Plato 3.1.10–​15 = SVF 2.885). These, then, are the eight soul parts, but the scheme is crucially different from the competing theories of Plato as well as Aristotle: the Stoics assign all the powers or parts of these to the intellect. This difference merits closer examination. The intellect is able to perceive, think, and desire but in doing so acts as a whole, that is to say, human action is not the outcome of different powers co-​operating more, as the case might be, less harmoniously. The Stoics follow the Socratic model according to which the soul acts as a unity. Thus action is produced not by the interplay of reason and desire (hormē) as two different factors: as Chrysippus defined it, desire is reason commanding a person to act (Plutarch, On Stoic Self-​Contradictions 1037F = SVF 3.175). Thus desire in humans involves a judgment and a motion of the intellect toward or away from something. Perception involves rationality in that it comes with propositional content. This has significant and interesting consequences for how the Stoics conceived of the cause of emotion and mental conflict. Drawing a comparison with Plato may again be helpful. Plato, in the Republic IV, the Phaedrus, and the Timaeus, assigned reason and emotion to different sources, or parts of the soul, arriving at his well-​known tripartition of the soul (supplemented with a trilocation in the Timaeus): reason in the head, spirit in the heart, appetite in the belly (Timaeus 69c5–​7 1e2). Spirit and appetite are the nonrational soul-parts and the cause of particular emotions such as anger and sexual passion. In positing his influential scheme, Plato was able to do justice to the widespread intuition

Stoicism and the Natural World    691 that reason and emotion are two irreducibly different factors within us and explain phenomena such as acting against one’s better judgment, that is, weakness of will. For the Stoics, emotions are the symptoms of a weakened and diseased intellect, an intellect that lacks the right physical tension to withstand the impact of mental presentations that may trigger an emotional response. Without denying the physical effects and expressions that accompany emotion, they designate a mistaken value judgment about our situation as its core part. Plato and Aristotle too did not see emotion as blind, irrational forces but as part of our conscious experience. The Stoics, however, come up with the most radical cognitivist theory, according to which emotion monopolizes our entire intellect. In the case of emotion, the intellect produces a conation that is irrational, unnatural, and excessive (On the Doctrines of Hippocrates and Plato 4.2.8–​12; the Galenic context should be taken into account as well; cf. SVF 3.462); that is to say, emotion is not part of our sound mental functioning and should be removed not moderated. Our mental health is further weakened every time we give in to an emotional response. Stoic corporealism allows not only cognitive therapy (given their view of emotions as wrong ideas) but also attention to the physical side of mental health, which, as we have seen, resides in the soul’s tension. Given the close interweaving of body and soul, care for the body through regimen and diet becomes important and justifies an interest in medicine on the part of the Stoics. At face value we seem to be dealing with another of the Stoic paradoxes (sec. 2): strictly speaking the body is an indifferent (i.e., something which is neither good nor evil, although it belongs to the class of “preferred” indifferents), and the soul’s virtue is sufficient for happiness. Yet the soul is part of continuous physical reality as well and cannot avoid interacting with its environment. One may wonder what made the Stoics adopt the Socratic model of mind, which flies in the face of a few widely shared intuitions such as the experience of mental conflict. The Stoics have to deny this phenomenon, saying that it really is a rapid succession of alternative options of the intellect conversing with itself. The value they attached to human responsibility had a great weight: an emotion is not an external event arising outside your “true self.” Instead, it results from reason and your own decision. This makes it all the more urgent to improve your mental and moral health. For the Stoics as for other philosophers death is the separation of soul from body. One would expect them to side with their materialist opponent Epicurus in holding that this brings the dispersal of the psychic pneuma and removes the prospect of a personal afterlife. In most cases this is exactly what happens. Even so, there are souls whose tension is good enough to make them last for some time. Some sources even specify that the souls of the wise may survive until the next conflagration (SVF 2.809–​821; see §3). This idea is not just an insignificant consequence of their ideas on physical coherence and tension, but seems to be related to the early Stoics’ acceptance of the external demons, or semi-​ divine beings, of popular religion, who play their part in “natural” forms of divination, most notably forecasting through dreams (SVF 2.1101–​1105; cf. Algra 2009). Later Stoics tended to suppress this idea in favor of seeing our intellect as our internal demon and guide through life (SVF 3.4; cf. Plato, Timaeus 90a). But Posidonius still took an interest in it (Posidonius F 24 E.-​K.; see further Algra 2009; Tieleman 2014b).

692   Greco-Roman Science

5.  Stoicism and the Special Sciences The Stoics saw special or applied sciences, that is, “arts” (technai), such as medicine, mathematics, astronomy, geography, and history as useful pursuits on which philosophy draws for underpinning the Stoic view of the natural world as providentially determined (see sec. 2). Indeed, philosophy needs these other sciences even if they remain subordinate to it, the “master art” (see sec. 1). We have also pointed to Posidonius’ view of the division of labor between the philosopher and the astronomer as being concerned with causes and hypotheses respectively (sec. §2). It is now time to have a closer look at the interactions between Stoicism and the sciences. First of all, it may be noted that the Stoic response to branches based on applied mathematics, such as astronomy, is conditioned by their view about the ontological status of mathematical objects. Rejecting the Platonic postulate of real mathematical entities, they subsumed geometrical objects such as the line and the surface under the class of incorporeals, that is, aspects of corporeal reality which may be considered separately by the mind (Plutarch, On common notions against the Stoics 1080e; cf. 1081ab; Aëtius 1.16.4; Diogenes Laërtius 7.135 = Posidonius F 16 E.-​K.; see Long and Sedley 1987, 301; Dumont 1978, 129; Algra, forthcoming; but cf. Ju 2009). Being incorporeal, mathematical objects cannot be causes of anything, since it is only bodies that, as we have seen, have the capacity to act (sec. 3). Thus mathematics could never provide a proper causal explanation of the kind sought by the philosopher, in particular an explanation showing why things are for the best. Nonetheless, our evidence suggests that the Stoic philosopher may still take an interest in mathematical models in order to understand how, if not why, natural processes occur. In fact, Stoicism arose at a time of considerable advances in astronomy. Consider the following early testimony about Cleanthes’ response to the heliocentric hypothesis put forward by the astronomer Aristarchos of Samos: [Cleanthes] thought that the Greeks ought to prosecute Aristarchus of Samos for impiety, on the grounds that he was moving the hearth of the cosmos, because the man tried to save the phenomena by hypothesizing that the heavens stand still, while the earth winds about along an inclined circle and at the same time spins on its own axis. (Plutarch, On the Face in the Moon 923a = SVF 1.500)

As Algra suggests, Cleanthes should not be taken to charge Aristarchus with impiety in any traditional sense but as going against Stoic cosmo-​theology in which the earth’s central position made most sense from the Stoic teleological viewpoint (Cambiano 1999, 596–​597; Algra, forthcoming). Given this attitude it may seem surprising that Stoicism could ever influence astronomy. But it was possible to write on it in the Stoic mode. An early example is the celebrated Phainomena by Aratus of Soli in Cilicia, a work from the early Hellenistic period (early 3rd century bce). But it should be noted that the motivation behind the whole work is also Stoic, or Stoicizing, in that it seeks to promulgate a general worldview rather than engage in a disinterested pursuit of detailed astronomical

Stoicism and the Natural World    693 knowledge. Thus Aratus’ Zeus is really the Stoic God, and as such he invites comparison with the Zeus we encountered in Cleanthes’ Hymn (see esp. the preface, Phaenomena, 1–​18; cf. Kidd 1997, 10; cf. sec. 3 above). A second area where we can study the Stoic response to scientific insights and possibly instances of interaction is medicine (cf. Hankinson 2003). The Stoics took an interest in medicine as providing a model for moral philosophy, as concerns both medical theories of human nature and the therapies justified in term of such theories, for example, the restoration of an imbalance between the elementary qualities. This is for instance clear from the fragments Chrysippus’ Therapeutics, where he drew an explicit analogy between moral philosophy and medicine in the conventional, body-​oriented sense: each is concerned with treating its own kind of diseases and involves knowledge of their causes (Galen, On the doctrines of Hippocrates and Plato 5.2.22–​24 = SVF 3.471). This analogy is not merely a device for explaining or clarifying the nature of the moral philosopher’s job by pointing to certain formal similarities with the doctor’s. Zeno and Chrysippus posit an actual correspondence between body and soul: since both are corporeal, then medical ideas about the mixture (i.e., balance or otherwise) of physical elements as determining health and disease are applicable to the soul as well (Galen, On the Doctrines of Hippocrates and Plato 5.2.31–​33 = SVF 3.471, where Chrysippus appeals to Zeno). The corporeal soul is exposed both to external influences, most notably the air through respiration, and to internal ones through its being closely interwoven with the body. Insights of this sort invite comparison with parts of the Hippocratic Corpus in particular (Tieleman 1999). In addition, we find Chrysippus responding to anatomical insights advanced by such medical authorities as Praxagoras of Kos (later 4th century bce), and Herophilus and Erasistratus (even if they are not named in our evidence), who had been active in Alexandria in the first half of the 3rd century bce and so were Chrysippus’ older contemporaries (cf. Cambiano 1999, 599–​602). We find him enlisting Praxagoras’ anatomy and physiology in support of the Stoic cardiocentric view of the human organism, viz. in the discussion on the seat of the intellect or hēgemonikon (sec. 4) to which he contributed in his On the Soul (evidence collected as SVF 2.879–​911; see Tieleman 1996, pt. 2; for Praxagoras see Galen, On the doctrines of Hippocrates and Plato 1.7.1 = SVF 2.897). Here his main opponents were Plato and medical defenders of the encephalocentric view. In another fragment from the same work, Chrysippus points out that even if the brain is the starting point of the nerves (an unmistakable reference to the discoveries of the Alexandrian scientists), that does not preclude that the heart is the main control center (Galen, On the doctrines of Hippocrates and Plato 2.5.69–​70 = SVF 2.898). In other words, no cogent inference can be drawn from their discovery. Presumably we are to see this as a case where the issue still is unclear and undecided, in line with Chrysippus’ stance in SVF 2.763 (see sec. 2). This is supported by Chrysippus’ reference to the disagreement among philosophers and doctors alike (On the Doctrines of Hippocrates and Plato 3.1.15 = SVF 2.885). So what he seems effectively to be doing here is opposing medical authorities rather than opting for one of them. Four centuries later, the doctor and philosopher Galen of Pergamum still saw the need to refute Chrysippus

694   Greco-Roman Science extensively in the light of his own anatomical researches including experiments (see On the Doctrines of Hippocrates and Plato, bks. 2 and 3; cf. Tieleman 1996). In doing so Galen quotes extensively from Chrysippus’ On the soul besides including material from other Stoics. Of these, Diogenes of Seleucia (or Babylon; active in the middle part of the 2nd century bce) appears to have continued Chrysippus’ bid to keep Stoic anthropology scientifically up to date without altering its main elements. But Diogenes’ interests extended to other parts of natural philosophy as well as musicology and linguistics (cf. Tieleman 1991). A broad array of sciences is associated with the name of the Stoic Posidonius of Apamea (on whom see sec. 1):  astronomy, meteorology, mathematics, mathematical geography, hydrology, seismology, zoology, botany, anthropology, and history (cf. Kidd 1999, 6; and White 2007, also for what follows). According to Galen, Posidonius was “the most scientific of the Stoics because of his training in geometry” (On the Doctrines of Hippocrates and Plato 8.1.14 = T 84; cf. PHP 4.4.38 = T 83 E.-​K.). Posidonius also wrote on all aspects of philosophy. But it is particularly with respect to special sciences such as astronomy that he was remembered and influential in later antiquity. To this fact we owe a great number of surviving fragments and testimonies informing us about Posidonius’ scientific work. A surviving example from the Imperial period is The Heavens of Cleomedes (see Bowen and Todd 2004). Cleomedes invokes Posidonius as one of his main sources (2.7.126 = Posidonius T 57 E.-​K.). Stoic interest in astronomy was inspired in large part from the belief that it could be used to foretell the future, that is, with respect to their notorious acceptance of astrology (though there are important exceptions, most notably Panaetius of Rhodes). It was one of the consequences of their deterministic and holistic worldview. Posidonius subscribed to Stoic determinism: the whole universe is permeated by a rational law, that is, a chain of cause and effect. It is therefore rationally intelligible and explicable in causal terms (on Posidonius’ confidence in this regard see above p. 683). The unraveling of causal relations starts from the observation of the phenomena: the pattern of movement of the heavens astronomy, that of the lower sphere by meteorology, that of terrestrial phenomena by geology, biology, geography, and so forth (Kidd 1999, 13). From a logical point of view, however, causality works top-​down. Here the role played by Posidonius’ geometrical-​deductive model of scientific knowledge becomes evident. This was not just a theoretical position without consequences for actual research. Posidonius stands out among his fellow Stoics who on the whole found far less use for mathematical methods (cf. Jones 2003). Posidonius’ remarkable work On Ocean included a study of geographical zones in relation to the celestial one and a famous attempt at measuring the circumference of the earth (F 202 E.-​K.). Another major—​and successful—​feat was his strikingly complete theory of the lunar periodicity of tides, which held sway until Newton. The diurnal and monthly cycles were confirmed through his own observations at Gadeira (mod. Cadiz; F 219–​219 E.-​K., with Kidd ad loc; see also the summary at Kidd 1999, 13). His project of explaining the natural pattern of celestial influence on terrestrial phenomena was based on the Stoic view of the single material cosmic continuum and of the cosmos as an organic whole whose parts are interrelated.

Stoicism and the Natural World    695 According to Galen (On Containing Causes sec. 2 = Lyons 1969, 54–​57) the founder of the Pneumatist school of medicine, Athenaeus of Attalia, studied with Posidonius and took over from him Stoic pneumatology and etiology. Elsewhere Galen also refers to the large debt owed by the Pneumatist doctors to Stoicism and to Chrysippus in particular (Differences of Pulses, 8.631, 642 K.). Here Galen treats Posidonius as representative of a common Stoic background against which to explain essential features of Pneumatist medicine, most notably the balance or imbalance of the pneuma as determining health and illness and its causal theory involving a triple distinction between initiatory, preceding and sustaining causes (cf. Tieleman, forthcoming 2). There are no good reasons to reject Galen’s testimony. Athenaeus, then, learned Stoicism from Posidonius (who over a long period led his own school at Rhodes, but we do not know where and for how long Athenaeus studied with him). The Pneumatist school founded by Athenaeus in turn influenced medical history mainly through its reception by Galen of Pergamum, whose codification of ancient medicine became the basis of Western medicine well into the modern period.

6. Epilogue As emerged from our brief survey of the history of the Stoic school, the Stoics, in common with  other Hellenistic schools, offered a philosophy of life. For them philosophy was the art (technē) of living. Moreover, they designed their philosophy as a system, a whole with interrelated parts. Thus moral life entailed knowledge of the natural world as a providentially determined order, which is actually the source of all morality. Conversely, natural philosophy should be oriented to the needs of those seeking existential and moral guidance. This conception of philosophy and its physical part also conditioned the view taken by the Stoics on the contribution to be sought from the so-​ called special sciences. The latter produce the evidence from which the rationally determined structure of the world may be illustrated. A special role was played by the most scientific among Stoics, Posidonius of Apamea, who went further than the others in pursuing the study of the causal structure of reality. Given this overall framework and orientation, the Stoics developed a theory of the natural world that is marked by an astonishing degree of philosophical economy, starting as it does from two principles or causes, active and passive, God and matter, and remaining consistently corporealist. This is all the more remarkable since the later course taken by intellectual history leads us to expect that materialism excludes theism. In the case of Stoicism, we do not only find them combined but also combined in such a way as to exert a powerful moral appeal.

Abbreviations SVF = Hans von Arnim, Stoicorum Veterum Fragmenta, 3 vols. (Leizig: Teubner, 1903–​1905).

696   Greco-Roman Science

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698   Greco-Roman Science —​—​—​. “The Spirit of Stoicism.” In Holy Spirit:  The Historical Roots of Early Christian Pneumatology, Ekstasis: Religious Experience from Antiquity to the Middle Ages, ed. J. R. Levison and J. Frey, 39–​62. Berlin: de Gruyter 2014b. —​—​—​, Forthcoming 1. “Cleanthes on the Pneuma. The Spirit of Stoicism II.”In The Concept of Pneuma after Aristotle, ed. L. Orly, S. Coughlin, and D. Leith. Berlin Studies of the Ancient World: Edition Topoi, forthcoming. —​—​—​. Forthcoming 2. “The Stoic Philosopher Posidonius and Greco-​Roman Medicine: The Aetiology of Emotions and Diseases.” In Medical Understanding of Emotions in Antiquity, ed. G. Kazantzidis and D. Spatharas. Trends in Classics-​Ancient Emotions series. Berlin: W. De Gruyter, forthcoming. White, Michael J. “Stoic Natural Philosophy (Physics and Cosmology).” In Inwood 2003, 124–​152. White, Stephen. “Posidonius and Stoic physics.” In Greek and Roman Philosophy 100 BC-200 AD, ed. R. Sorabji and R.W. Sharples, Bulletin of the Institute of Classical Studies Supplement 94 (2007): 35–76. Wildberger, Jula. Seneca und die Stoa. Der Platz des Menschen in der Welt. Untersuchungen zur antiken Literatur 84. Berlin: de Gruyter 2006. Williams, Gareth D. The Cosmic Viewpoint:  A Study of Seneca’s Natural Questions: Oxford: Oxford University Press, 2012.

chapter D6

Scrib oniu s L a rg u s and Frie nd s John Scarborough

When Scribonius Largus (ca 25 bce to ca 55 ce) writes that earlier physicians had de­signated medicamenta as the “hands of the gods” (Compositiones, Epistula dedicatoria, the Letter to Callistus: Herophilus . . . fertur dixesse medicamenta diuum manus esse), he echoes sentiments expressed by Herophilus and Erasistratus of Alexandria sometime in the mid-​3rd century bce, an opinion shared by many in classical antiquity, including Plutarch and Galen (Plutarch, Table-​Talk 4.1 663c, of Erasistratus; Galen, Compounding Drugs According to Place, 6.8  =  Kühn 12.966; von Staden 1989, 418). The extant Compositiones (Recipes, or simply Pharmaceutical Formulas, or Prescriptions), however, incorporates not merely the “simples” of a pharmacology in the 1st century ce but also contains numerous complex, multi-​ingredient recipes—​organized a capite ad calcem viz. “by diseases” from head to heel (chap. 1–​162), then antidotes against poisons and bites from venomous animals (chap. 163–​200, of note is 178–​200, mala medicamenta, poisons concocted with an evil purpose), concluding with surgical therapeutics (chap. 201–​271), plasters to help heal fractures, wounds, ulcers, prolapses, and similar problems. Many are replete with a precision in weights and measures accompanied by painstaking instructions to be followed by a competent physician, so that he could prepare these compounds on-​the-​spot as “fresh.” On occasion, this pharmacological technology is so detailed that “explaining” these compounds involves a multilayered analysis incorporating medicinal botany, mineralogy, and aspects of a medical zoology, all suggesting Scribonius’ experienced expertise in the gathering, preparation, and dispensing of compound medicaments: in combination, these constituents give results frequently at variance with the individual ingredients used alone, as “simples.” That complexity renders Scribonius’ Latin prose into an exceedingly intricate accounting of pharmaceuticals, combining his own native Greek with a variant of “common” Latin vocabulary, indicating why some classicists call the Compositiones “vulgar Latin,” which it is, compared with the periodic phrases of a Cicero (Buecheler 1882, 324; but cf. Baldwin 1992, 81). It is little wonder that Nutton titles his short 1995 essay on Scribonius Largus,

700   Greco-Roman Science “The Unknown Pharmacologist,” although Edelstein had reckoned Scribonius a direct heir to Cicero’s evocation of medical humanity in the On Duties (Edelstein [1956] 1967, 340). Even the most perceptive of previous scholars struggled with a sometimes lacunose and corrupted text of the Compositiones (e.g., Deichgräber 1950), but once the Codex Toletanus surfaced (in 1974) to fill in various gaps and guide corrections to the then-​standard Latin text (Helmreich 1877, entitled Conpositiones, with deliberate archaism), a much improved freshly edited Compositiones soon emerged (Sconocchia 1983). Galen seems to know of some works in Greek written by Scribonius Largus (Kind 1921, cols. 879–​880), but there is uncertainty whether Galen quotes directly from a Greek original, or whether he lifts such passages from circulating compendia of compound drugs (Fabricius 1972, 222; Langslow 2000, 51–​52; Guardasole 2014, 327–​328). The Compositiones has affinities with the near-​contemporary works of Cornelius Celsus and Pliny the Elder (Sconocchia 1993, 2014), but recent scholarship has clarified and expanded sections of the revised text, especially in relation to the direct borrowings by Marcellus of Bordeaux “Empiricus” (active ca 400 ce), apparently the only later writer who valued the Compositiones enough to plagiarize large chunks of it in the Gallic-​ enriched De medicamentis (Stok 2008; Fischer 2010).

1. The Letter to Caius Julius Callistus: What It Says, What It Does Not “[F]‌ew classicists have heard of, let alone read, Scribonius Largus, the first, or, depending on the boat in which he arrived, the second named doctor to reach Britain in the Claudian invasion of ad 43” (Nutton 2010, 2–​3), but the Letter to Callistus has received an unusual amount of attention, since it supposedly espouses a presumptive Hippocratic standard in the practice of medicine among the Romans in the 1st century. There are two translations into English of the Epistula (Hamilton 1986, 212–​216; Pellegrino and Pellegrino 1988, 25–​29), and there exist three into German (Helmreich 1887, 1–​6; Rinne [1896] 1968, 1–​5; Schonack 1913, 1–​9); and Deichgräber (1950, 875–​879) provides a laboriously re-​edited text. The Latin is not easy, so that there are varying interpretations of given sentences and phrases, but assertions that Scribonius was “Hippocratic” downplay his delicate finesse in a qualified modulation of the famous Oath and its admonition not to prescribe contraceptives and abortifacients. Scribonius, Epistula, 5, addresses Callistus (and through him, Claudius, who had well-​known interests in medicine: Levick 1990, 30; Osgood 2011, 243–​244): Hippocrates, the founder of our vocation (professio), handed down the beginnings of the discipline in an oath. In it is the injunction that an abortifacient not be provided or displayed to a pregnant woman by a physician, thus inculcating the minds of his students well in advance for humane treatment. How much more evil would this man [Hippocrates] consider the harm to an adult human being, when he believed it

Scribonius Largus and Friends    701 wrong to destroy even the faint hope of a person? Therefore Hippocrates believed it to be extraordinarily important that each practitioner conduct himself in agreement with his stated principles, to preserve the [good] reputation of medicine, and do so with devotion and solemn purpose. Our science is one of healing, and the practice of the art is not about inflicting harm. Unless [medicine] uses absolutely all of the allied specialties, into which it is divided, [medicine] cannot manifest the compassion it promises to humankind. (Cf. trans. Pellegrino and Pellegrino 1988, 26)

This is not an explicit condemnation of contraceptives and abortifacients, to be sure, perhaps reflective of the ongoing debate among physicians regarding these drugs, most vividly summarized not quite a century later by Soranus, Gynecology 1.60–​65 (Ilberg 1927, 45–​49; trans. Temkin 1956, 62–​68). And if one recalls the implications of the Oath, there were many iatroi (doctors) who would give such drugs to a woman, if she requested them (Riddle 1987; Totelin 2009, 221–​224, 261; cf. King 1998), but the “Hippocrates” in the Compositiones does not appear an authority on pharmacognostic plants. Scribonius then proceeds to give his ringing endorsement to pharmaceuticals, in a rather sly contravention and extension of the presumed ideals of a Hippocrates (Epistula 6): Therefore, let those individuals who cannot, or will not, desire to bring help to the ill, cease in their obstruction of others who choose to come to the aid of the sick. Such help is frequently given by means of the power of drugs (uim medicamentorum), since the art (medicina) sometimes offers comfort according to stages in the [course of] illnesses. [The physician] initially attempts to bring health to his feeble patients by means of foods in an appropriate amount over a suitable span of time. Then, if the patient does not become well [from the dietetic regimen], the physician should take up potent drugs, since they are more powerful than foods, and thus more efficacious [than foods].

Only as a last resort does one advocate surgery, and—​so the text says—​the cautery iron (ad ustionem). The Letter to Callistus also has a peculiarly fascinating snapshot of Asclepiades of Bithynia (active in Rome ca 110–​55 bce: Nutton 2013, 171–​173; cf. Rawson 1985, 170–​184). Scribonius declares that Asclepiades is the “greatest authority on the art of medicine” (maximus auctor medicinae:  Epistula 7), who some say, forbade the employment of drugs (medicamenta) in the curing of the sick, and this falsehood is purveyed by those persons (not named) using such a position to buttress the forbidding of drugs (the biting phrase here is “for some individuals employ this lie as evidence”: quidam enim hoc mendacio etiam pro argumento utuntur). Debate and counter-​debate among Greek-​ speaking physicians was typical of the medical practitioners in the late Roman Republic, and such sophistic arguments would continue to be characteristic of physicians in the long centuries to come (Epistula 7–​9): What more can I  say thereby about these men who so shamelessly pander such opinions [against the use of drugs] but that they commit a crime equivalent to the murder of one’s own kin, or sacrilege? (8) To be sure, Asclepiades did say that drugs

702   Greco-Roman Science should not be provided to patients displaying fevers, or for the ailments called by the Greeks “sharp afflictions” (oxea pathe); he thought that food and wine provided at proper intervals of time would more safely render cures in the sick. Moreover, in his book titled Parasceuastikon, i.e., Prepared Drugstuffs, he asserts that only a doctor of the most meager [medical] abilities would lack at least two or three multi-​ ingredient drugs of proven [and tested] results, at the ready to treat most kinds of illness. You [Callistus] do observe, then, that Asclepiades would not approve of the use of drugs by those whose knowledge did not include at least some preparations to treat a number of diseases, and such persons are unworthy of the vocation of the medical arts (non . . . dignus professione medicinae). (9) The ignorance, however, of persons who are physicians in name only, has engendered a widespread impunity [in the practice of medicine], and thereby no man should trust himself or his family to a doctor whom he has not carefully judged [for his abilities].

Galen, Best Physicians, provides similar advice on judging a doctor before employing him (e.g., sec. 12, Iskandar 1988, 122–​129). Scribonius’ analogy to an activity, known to the increasingly wealthy ruling elite of Rome in the early 1st century, mirrors the ordinary desire for a kind of immortality (Epistula 9): Assuredly, then, he [the man who has selected a doctor for his family] would not commission an artist to paint his portrait, unless that artist had been pronounced [as a good one] on the basis of previous works.

As the artist, who uses carefully chosen mixtures of substances, to produce the finest paintings, so too does the skilled doctor have firm control of the amounts of simple drugs that would make up his effective prescriptions (Epistula 9–​10): Everyone [artists, doctors, and other skilled occupations], therefore, possesses precise weights and measures, so that they do not commit mistakes, even in the more minor aspects: of course, there are those who value such knowledge more than life itself. Thus, anyone who aspires to become a doctor does not by necessity require deep investigation [into the art], in fact none at all: such persons remain ignorant not only about the ancient authorities, who formulated the art (professio), and who brought it to perfection, but they brazenly dare to tell lies about their doctrines.

An attentive reading shows how the irony displayed in the Latin uidelicet quia sunt quidam, qui pluris omnia quam se ipsos aestimant (of course, there are those who value such knowledge more than life itself) leads immediately into Scribonius’ further sarcasm regarding these less-​than-​talented physicians. Sconocchia (2014) may be right in thinking that Scribonius targets those physicians who follow Asclepiades’ medical doctrines (the Methodici, as recorded by Cornelius Celsus), and the remainder of the Letter goes on to bewail again and again the lack of standards in the vocation of medicine, then descends (or ascends, if one is taking the view of flattery to one of Claudius’ important freedmen) into a number of paragraphs, evoking Callistus’ many kindnesses.

Scribonius Largus and Friends    703 Scribonius’ snapshot of Asclepiades, however, would be incomplete without the curious discussion of tourniquets at Compositiones 84. At issue here is the extremely common problem of what to do to staunch bleeding from a limb. The chapter begins sensibly enough: “One ought to position a sponge, soaked in fresh water or pungent vinegar, frequently changed, so that it [the sponge] is seen to be just beyond the wound itself, so that it is not further harmed by the heating properties [of the vinegar],” but “to constrict the limbs is forbidden” (uetare artus constringere). As Majno (1975, 404–​405) points out, this admonition against tourniquets is an “obvious” result of physiological reasoning about the vascular system, an assumption drawn from a lack of understanding of what we have called the “closed circulation of blood” since the 17th century. Scribonius details his argument, against those who follow Asclepiades (cum uero Asclepiades etiam pluribus usus sit argumentis in hac re, neque ei quisquam contradixerit (quis enim aduersus ueritatem hiscere potest?), tanto magis sunt custodiendi), citing the observation that fluids spurt from both ends of a bag, if one puts a cord over its middle, then tightens it (Comp. 84): Many practitioners of medicine do this, since they are ignorant of the spurting of blood which is increased by squeezing together the muscles, since any pressure will expel underlying [or adjacent] matter equally into each of the two parts. For example, when someone compresses a limb midway with a tourniquet (laqueus), he will observe that he expels into each part the underlying [or adjacent] fluid; if, by chance, the limb happens to be punctured, what is in it will be ejected through the wound. Likewise, when there is bleeding [from a wound], those who constrict the limbs with a great deal of pressure engender even more hemorrhage through the wound by squeezing out the blood that rests under [or adjacent] in the [nearby] blood vessels.

Some hints occur of possible vivisection of animals: The evidence (argumentum) for these things [is the following]: if someone were to cut into the vein, above the tourniquet (laqueus) which is in the forearm (brachium) of the animal, he will notice that blood rushes out equally from that part as it does from the lower [limb] when the vein is severed. And for this, in itself, if medici do not perceive it [as such], they should rightfully be held culpable, since they would be doubly at fault for a man’s state of health (casus) [being put at risk]. To be sure, Asclepiades has had much to say on this subject, and nobody has contradicted him (who, after all, can yawn at the truth!), all the more reason to be vigilant against those who promise to protect the health of each individual. They are so inept and careless as not to strive to know the essentials of preserving human life that have been discovered through the efforts of others. Thereby, those who cause the spurting of blood in their human patients, with this kind of ignorance (imprudentia) are convicted rightly [of murder]—​and good lord! (o bone deus)—​these are very men who ascribe their faulty [results] to the drugs (culpam in medicamentis), as if they have no [beneficial] effects. But let us return to the subject.

Something similar to Asclepiades’ tourniquets occur in Galen’s Compounding Drugs According to Kind 4.5 (Kühn 13.684–​686), but such devices are superseded by the

704   Greco-Roman Science elaborate, multi-​ingredient plasters, which Galen says he has copied from the drug books of Andromachus. And here, again, the revered name of Hippocrates is invoked (Kühn 13.686) to indicate the use of those sponges, of which he also says that traveling has procured him a supply. Asclepiades’ insight was buried in the later invective reserved for the mechanistic theories of bodily functions, and the works of this very influential Bithynian physician have largely disappeared (Vallance 1990). “Asclepiadean” doctors were prominent fixtures in the courts of the Julio-​Claudians: Antonius Musa, physician to Augustus (Scarborough 2008b), was renowned for his cold-​water cure of the princeps, and although another of Augustus’ known physicians, a Marcianus (Comp. 177) is not attested elsewhere, it is probable that he, too, was a “follower” of this very popular medical philosophy. Several other Asclepiadeans are known in fragments (Tecusan 2004, 61–​62: Thessalus, 65–​66 and Themison, among many), and it is not a great stretch to connect these proto-​Methodist doctors with the flourishing late Republican Epicurean school at Herculaneum, where Philodemus taught the well-​known pseudo-​atomistic philosophy, employing trenchant medical models (Konstan et al. 1998, 20–​23, “Medical Imagery”). Galen invests considerable intellectual energy to refute the long-​lasting influence of these “atheistic” physicians (e.g. Against Julian:  Tecusan 2004, 291–​331), who—​as Scribonius also complains—​boast that they can learn medicine without effort and in a very short time, a charge repeated by Galen (against Thessalus) in the famous passages from the Method of Medicine 1.1.5–​8, 1.2.1–​6 (translated in Hankinson 1991, 4–​ 8; edited and translated in Johnston and Horsley 2011, 1.8–​21).

2.  “Life and Times,” Contexts, and Some Medical Networking In his Compositiones, Scribonius Largus mentions individuals, locales, topographical features, and cities that identify him as Sicilian (Baldwin 1992, 77, prefers North Africa), and he is quite likely one of the Greco-​Roman agricultural intelligentsia characteristic of the smaller towns of southern Italy and Sicily. Bilingualism (Greek and Latin) was certainly common among the intellectual elite, surrounding the new imperial family (Vergil’s Georgics is a masterful evocation of this propagandistic revival of an ancient Roman farmer ideal), and for persons whose native tongue was Greek, it was frequently possible to get along speaking Greek, with a moderate control of spoken Latin (Sconocchia 2014, 332, “as I like to call it, Latin-​Greek, with a high level of integration”). Scribonius writes that Apuleius Celsus of Centuripae (active ca 20 ce: Scarborough 2008a) was one of his (first?) teachers (Comp. 94 and 171), and this places Scribonius as a young man in Sicily, learning the basics of medicine and pharmacology, a drug lore founded on the medicinal plants native to the southwestern Mediterranean littoral and adjacent territories and provinces. Centuripae was a city on a hill facing Mount

Scribonius Largus and Friends    705 Etna southwest across a valley, and Apuleius was famous for his complicated, multi-​ ingredient drug for the presumably successful treatment of rabies. A bit of toxicological folklore appears, when Scribonius notes that Sicilian hunters insert into their belts peucedanum (probably a sulfurwort, Peucedanum officinale L., and related species) and stag horns (presumably powdered, even though the Latin is cerui, perhaps here deer skins) as snake repellants (Comp. 163). Then he adds idem praestat et hierobotane et trifolium acutum, quod oxytriphyllon Graeci appellant:  nascitur et hoc Siciliae plurimum (“it [viz. the Sicilian snake repellant] and the pitch trefoil [prob. Psoralea bituminosa L.], called by the Greeks oxytriphyllon, are [both] superior [as snake repellants] and the pitch trefoil grows in abundance throughout Sicily”). At first glance, it would seem that Scribonius has set his seal of approval on the natives’ snake repellants, but then he proceeds to describe the pitch trefoil in some detail (first having mentioned that it also flourishes in the mountains near Luna, a harbor on north coastal Etruria, where he was posted on the way to England in 43 ce): [The northern Italian pitch trefoil] has a number of leaves quite similar to the [Sicilian] trefoil, except that those from northern Italy are thicker, possessing a woolly part at their ends, terminating in spikes. The pitch trefoil’s bush (frutex) can extend to two feet or more, and exudes an oppressive odor, in contrast to the trefoils that grow in a meadow.

His observations in northwestern Etruria were brief and hurried, although the pitch trefoil’s leaves do emit an odor of tar, when squeezed (Polunin 1969, 193, #537; Polunin and Smythies 1973, 235, #537), and the terse description of the bush does match—​albeit vaguely—​what is given in modern reference books on field botany. But Scribonius’ account of “harvesting the latex” (if that is what it is) reverts to folklore. Compared to the sophistication characteristic of much of the Compositiones, this short snatch of data likely emerges from Scribonius’ attempts at a medical botany beyond Sicily, fused with his sources’ statements about what might be the properties of pharmacognostic plants, as they grew in the wild. Perhaps, since he is traveling while assembling his drug manual (sumus enim, ut scis, peregre: Epistula 14), and without access to books, he may well be quoting both local traditions and from memory—​which is prodigious. The Compositiones is far more than a mere cookbook of drugs (Hamilton 1986, 211), in spite of a superficial resemblance to this genre, represented by the famous De re coquinaria, descending from the 1st-​century gourmand’s handbook by M. Gauius Apicius (Dalby 2003, 16–​17). Another teacher (praeceptor) is Valens (Comp. 94), a doctor of some fame, if he is the same as Marcus Terentius Valens, also recorded by Galen through Andromachus and Asclepiades Pharmakion, where Valens is also named as a student of Apuleius Celsus, thus Sicilian (Scarborough 2008c and 2008e). In spite of the opinion that this “Valens” is the same as the notorious Vettius Valens, linked inexorably in our sources as a paramour of Messalina, there is little evidence that Scribonius’ teacher and fellow student is the same man (Sconocchia 1985, 157; and Keyser 2008b contra Baldwin 1992, 76).

706   Greco-Roman Science Apuleius Celsus’ formula for a cough syrup—​also apparently used by Valens—​was simple and effective: a Roman pound of skimmed Attic honey, two black peppercorns, ground carefully and selected from the finest variety, a denarius of Sudanese myrrh; one is to grind with care the pepper, then put the powder through a sieve, and the myrrh likewise is triturated in a mortar, then the two dry ingredients are mixed together, then these are added to a quantity of honey, sufficient for this medicine, to be administered in five or six spoonful’s, or a few more, depending on the condition of the patient. Soon the patient coughs up the phlegm blocking his breathing, and the cough ceases (Comp. 93). Another friend is the physician Ambrosius of Puteoli: or perhaps he is a professional rival, because Ambrosius’ bladder stone diuretic is condemned as nonsense, since one is to use a wooden pestle for grinding up the ingredients, and not to wear a ring of iron (Comp. 152: pilum ligneum sit, qui contundit, annulum ferreum non habeat. hanc enim superstitionem adiecit Ambrosius medicus Puteolanus). Yet, Scribonius does conclude “it is said” (dixit) that Ambrosius’ stone-​smasher reduced the calculi to grains of sand in seven days, and thereby were easily eliminated in the urine. A “mixed review,” at best, but Scribonius may well be making sure he lets us know he is aware of a multi-​ingredient compound that presumably relieved the sometimes excruciating pains of bladder stones. Elsewhere, Ambrosius is called “Rusticus” and knows the narcotic properties of the latex of the opium poppy (Wellmann 1894, col. 1812; Keyser 2008a). Scribonius names Tryphon of Gortyn (Crete) as a third mentor or teacher (praeceptor: Comp. 175). Galen supplies his city of origin, and Tryphon is most often attested in our sources as “the surgeon,” famed for his healing plasters to treat skull fractures and similar injuries, frequently sustained by gladiators (texts and references collected in Scarborough 2008d). Tryphon was apparently also a drug vendor dealing in exotic simples from all over the empire. Scribonius ascribes to Tryphon a 12-​ingredient “plaster-​as-​antidote” (emplastrus antidota [sic]:  Comp. 175), deemed effective against bites of animals, especially dogs (the text intriguingly reads quod Augusta propter eiusmodi casus habuit compositum et multis profuit, hinting at the compound’s use by members of an unspecified court): Five denarii [by weight] of the [ground-​up] rhizome of the Illyrian iris; five denarii [by weight] of Pontic beaver castor; five denarii [by weight] of the dried juices of the wild fig; eight denarii [by weight] of fat, taken from a black dog; ten denarii [by weight] of blood from the same animal; eight denarii [by weight] of the resin from the Chian mastic; four denarii [by weight] of curdled rennet taken from a rabbit; two denarii [by weight] of Ammoniac salt; two denarii [by weight] of Libyan silphium (laseris Cyrenaici), or that from Syria four denarii [by weight]; thirty-​six denarii [by weight] of Pontic beeswax; two cyathoi of old olive oil; and three cyathoi of vinegar mixed with squills. The dry ingredients are to be triturated in the vinegar: these are able to become fluid-​like, liquefied in the oil over a flame, as they are mixed in a mortar, ground and blended into a consistency like honey. This antidote is to be put up in storage in a glass vessel.

Scribonius Largus and Friends    707 Glass containers (uitrea) suggest a commerce in drugs, since transport would be more assured, especially in terms of the retention of pharmaceutical properties, as contrasted to the usual earthenware pots (blown glass jars appear eight times in the Compositiones, 106, 108, 111, 122, 125, 170, 173, and 175: analyzed by Taborelli 1996, 148–​156). Crete was a thriving pharmaceutical marketplace, exemplified by Scribonius’ attribution of an exotic remedy—​hyena hide—​to a Zopyrus of Gortyn, who had turned up one day as an agent (legatus) and spent awhile as a guest of Scribonius (ab hospite meo: Kollesch 1972 suggests die Gastfreundschaft; Nutton 2013, 176, calls Zopyrus a “friend” of Scribonius), attempting to sell hyena pelts at a high price (pro magno munere), since this particular animal’s skin had an especially excellent “binding quality” (esse panno inligatam). Scribonius put Zopyrus off, writing suspiciously that he was not an expert on the utility of hyena hides, although if such patches of hide had the miraculous properties retailed by Zopyrus, the purchase would likely be contracted; but instances where such an exotic remedy might be useful, were not yet experienced by Scribonius, even though one could argue that the remedy could be produced, if such a patient were to appear at some future date (Comp. 172). One could relegate this rather odd account of hyena pelts as a cure all, to the pages of a purely folkloristic pharmacy, were it not for the jumbling of at least two recipes in a compound to treat rabies in Galen’s Antidotes 2.11 (Kühn 14.174–​175). Here the drug is called a basilike, and as for Tryphon’s plaster, an unspecified “Augusta always had this compound at hand.” The first listing of ingredients closely parallels those in Compositiones 175 (ammoniac salt, Libyan silphium in preference to that from Syria, rabbit’s rennet curdled, iris rhizome, Pontic beaver castor, with dry constituents to be turned into a liquid), but then comes hyena fat, mastic, apparently the fat of that black dog, and again hyena blood [?]‌, Pontic beeswax, and the vinegar with the additive of squills. The Greek text, adapted by Galen, sometime in the late 2nd century, thus likely had its origins in an earlier Greek compilation of rabies treatments, first obliquely mentioned by Scribonius Largus (the hyena here is the sole reference in the Compositiones), and then picked up by Galen as a “tried-​and-​true” remedy since an “Augusta” used it. One can speculate, then, that Tryphon’s hyena hides made their way into Roman pharmacology, even though Scribonius (rightly) offers his skepticism about the efficacy of this particular substance. And yet, hyena parts had widespread applications in medicine, in spite of the animal’s nasty reputation (digging up and eating corpses, for example:  Kitchell 2014, 92–​93). Then, too, Scribonius may well be expressing his doubts about the renowned magical properties of the hyena and its various parts, many attributed to the magi by Pliny the Elder, whose catalogue of uses range from the pharmaceutical to the amuletic (Pliny, Natural History 28.92–​106, with Ogden 2014, 296–​299). Pharmacologists and surgeons mixed their skills, as is apparent from both Cornelius Celsus and Scribonius Largus: Tryphon pater, Euelpistus, and Meges of Sidon (Celsus, De medicina 7.prooemium.3) not only were notable surgeons who practiced in Rome likely late in the reign of Tiberius and extending into the rule of Caligula (thus ca 30–​ 41 ce), but they were also distinguished compounders of multi-​ingredient plasters, ointments, and salves, usually of a “styptic” nature, designed to rapidly clot bleeding

708   Greco-Roman Science wounds. Tryphon is cited by Celsus 6.5.3 (for masking cosmetics), and by Scribonius, Compositiones 175 (above), 201 (plaster for skull fractures), 203 (plaster for wounds, especially on gladiators), 205 (likewise), 210 (similar), 240 (caustic ointment against “protuberance[s]‌of the flesh”), and 241(scarifying ointment). This Tryphon is likely Celsus’ Tryphon pater, and since he is nuper (recent), this suggests he was advanced in years when Scribonius was his student. As often as Scribonius cites Tryphon “the Elder” as an honored source for pharmaceutical recipes, the student was not completely in awe of his teacher. Scribonius records Tryphon’s misuse of blister beetle solutions to remove slave brands, when treating Sabinus Caluisius, who had been shipwrecked, enslaved, and freed—​and was then apparently harmed by the potion, based on a poorly written prescription (Comp. 231; Diller 1939, col. 745). Here the 20 cantharides are labeled “Alexandrian,” and the heads of these beetles are to be triturated in a mortar and used in combination with raw sulfur, copper-​ flakes, beeswax, and olive oil. The two types of blister beetles were quite toxic in solution (Comp. 139–​140), and at Compositiones 231, Scribonius has described them as “variably oblongated in shape,” rather close to the actual species, often used as aphrodisiacs, still around as “Spanish fly.” Blister beetles remain common in Greco-​Roman pharmacology (Scarborough 1977; Scarborough [1979] 2010, 73–​80: “Remedies: The Blister Beetles”; Beavis 1988, 167–​175: kantharis and bouprestis, genera Lytta and Mylabris) and are listed in the later Roman law codes among the amatoria (Scarborough 2013, 761–​ 762: “Appendix: Drugs and the Law”).

3.  A Court Physician? The Life of a Doctor as One of Many Although Scribonius Largus was a physician in service to royalty in the reigns of Caligula and Claudius (thus 37–​54 ce), uncertainty emerges regarding which Julio-​Claudians are mentioned since there are various “branches” of the regal family to whom he provided his medical and pharmacological skills. He writes that he had gone to England in 43 ce to attend to needs of the traveling court, as Claudius went across the Channel to celebrate the presumptive conquest of Britannia (Comp. 163: cum Britanniam peteremus cum deo nostro Caesare). But in the “dedicatory epistle” addressed to his patron, C. Iulius Callistus (i.e., the Epistula), Scribonius documents that this powerful and wealthy freedman (Pliny, Natural History 36.60) was still influential, putting the date of Scribonius’ Prescriptions before 48 ce, when Callistus’ patron Messalina was forced to commit suicide (Levick 1990, 66–​70; Osgood 2011, 209–​210; Romm 2014, 30). The same date is indicated by Scribonius’ record of a dentifrice used by Messalina (Comp. 60), where she is called “[the wife] of our deified Caesar” (nam Messalina dei nostri Caesaris hoc utitur). Tracking the particular Imperial houses shows how he “borrows” recipes from an earlier generation, since Scribonius sometimes causally mentions an Augusta:

Scribonius Largus and Friends    709 Compositiones 60, Augustam constat hoc usam; 70, hoc Augusta semper compositum habuit (here likely Antonia Minor, the mother of Claudius); 175, mentioning that this formula for an emplastrus antidota was invented by one of his mentors, Tryphon of Gortyn on Crete (above), and that quod Augusta propter eiusmodi casus habuit compositum et multis profuit, again suggesting the recent past; 268, a recipe for an acopum, an anodyne plaster or ointment for the relief of pain or fatigue, hoc Augusta utebatur; and 271, another acopum, this time quo fere Augusta et Antonia usae sunt (Antonia Major, the daughter of Marc Antony, so Kokkinos 1992, 33). Then there are three other mentions of the Imperial family, again casually noted, almost in passing: Compositiones 59, another tooth powder that the sister of Augustus used (hoc Octavia Augusti soror usa est); 110, a recipe from the books of Antonius Musa, physician to Augustus, for abdominal pain and bloatedness (Ad stomachi dolorem et inflationem); and 97, Tiberius deposits in the public libraries a recipe for a compound drug, invented by a Paccius Antiochus, deemed very effective against gout and pains in the flanks. One also notes an Anterus, freedman (libertus) of Tiberius, whose gout was cured with the “living black, electric ray” (torpedinem nigram uiuam), placed under his feet in the shallows of the sea, until the pain was numbed up to the knee (Comp. 162; Thompson 1947, 169–​171 cites Pliny the Elder, but not Scribonius; Finger and Piccolino 2011, 46); and another recipe for intestinal colic, successfully administered to Tiberius by his physician Cassius (the formula itself, however, is gained from Cassius’ slave, Atimetus: Comp. 120). Perhaps, as Nutton suggests (1995, 8), this “name-​dropping” reflects professional rivalries, and Comp. 97 certainly displays a grumpiness against Paccius Antiochus, student of Philo of Catina, whose supposedly wonderful drug was manufactured in secret, behind closed and locked doors (quamuis omnia fecerimus, ut sciremus quae esset, ipse enim clusus componebat nec ulli suorum committebat). After Paccius died, his recipe was made known to all by Tiberius’ deposition of it in the public libraries. It is curious, indeed, that after expressing his anger at the unseemly selfish behavior of Paccius Antiochus, Scribonius does not provide the heretofore “secret” formula (maybe something has dropped out of the text). In fact, Compositiones 98 goes on to claim that he, Scribonius Largus, has become the expert in its compounding, but never reveals its exact formulation: This drug is truly efficacious not only for pain in one’s flanks, but also to treat many illnesses, and therefore I always have it prepared and ready to be dispensed (quamobrem semper habeo id compositum). Nonetheless, I  shall quickly relate in brief [the details] about those illnesses for which one ought to prescribe [this drug], since it is also set down in [Paccius Antiochus’] little book, and I, for the most part, am already experienced with its compounding.

Compositiones 98 closes with an extraordinary claim: “Thus, this compound is remedial for cases of comitialis morbus, which the Greeks call epileptici, and also for uncontrollable frenzies, which they call maenomeni.” Compositiones 99 continues with even more lavish claims for the usefulness of this yet-​to-​be-​specified compound:  it

710   Greco-Roman Science now cures dizziness, headaches, and one’s eyes that are suddenly darkened. Possibly the medication is so “ordinary” that Scribonius is somewhat chagrined after having made such a fuss over it: “One ought to give two denarii of it [mixed] in four cyathi of honeyed wine, [and] then [the patients] would gain relief,” and if this did not provide an improvement, especially if seizures continued, then one should administer an antidote, called by various names, including picra and diacolocynthides. The picra is extremely bitter (amara), and if Pliny, Natural History 21.105, is any sort of guide, this is some kind of succory or a wild chicory, identified by André (1985, 199) as Cichoria intybus L. If what is recorded here as diacolocynthides is accurate, then this is a salve or ointment, prepared from the common gourd, Citrullus colocynthis L. Paccius’ wonder drug is quite ordinary, indeed, secret or not. Paccius’ anodyne recipe for lower back pain (Ad lumbrorum dolorem:  Comp. 156)  is likewise vegetable laden (cucumbers, walnuts, spiced with black pepper, chamomile, and old oils and Pontic beeswax), but—​perhaps—​the missing wonder drug is the mineral-​rich white plaster recorded at Compositiones 220, prescribed for breast cancers (cum in mammis mulierum . . . quam Graeci carcinoma . . . uocant). There are true narcotics in this formula, attributed to Paccius Antiochus, including henbane seeds, mandrake “apples” (if the terrae mali are meant to designate the “fruits” of the Mandragora spp.), and the rinds of wild opium poppies. Some kind of transdermal pain relief might benefit the patient, but this multi-​ ingredient “white plaster” is no way curative. One can describe Scribonius Largus’ “life at court” as very competitive, and his frequent mentions of “royal” recipes delineate a continuous struggle for recognition, mirrored in the blatant flattery of Callistus that colors the last sections of the Epistula. Scribonius, in effect, offers a better approach to an often imprecise drug lore, and his insistence on exact weights and measures in the composition of his numerous formulas sets him apart from most other known figures in the medical circles around the families of the Imperial houses. The Compositiones allows sharply defined glimpses into imperial medicine chests, at the ready no matter who might be the “Augusta” stated to have used this or that carefully prepared and administered compound drug. Some ingredients are, indeed, “exotic,” but the great majority are minerals, plants, and animal products of local origins, “local,” that is, if one considers Sicily, Italy, and Spain to be “in the neighborhood.”

4.  The Pharmaceutical Recipes The demands for exact weights and measures, as well as the complicated multi-​ ingredient compounding—​in turn requiring the would-​be physician/​pharmacologist to exercise extreme care in the “timing” of these preparations—​all of these facets of the Compositiones doomed it to obscurity. To be sure, Galen records numerous multi-​ingredient drugs in his massive compilations that have survived in the four works Properties and Blendings of Simples, Drugs According to Kind, Drugs According

Scribonius Largus and Friends    711 to Place, and Antidotes (a total of 2,274 pages in Kühn 1821–​1833, vols. 11–​14), plus the Theriac to Piso, whose 84 pages are deemed genuine by Nutton 1997. But these, however, are almost all secondhand copies of earlier texts in Greek (Andromachus Junior and Senior, Asclepiades Pharmakion, Criton the physician to Trajan, and a number of others, as documented by Fabricius 1972; cf. Totelin 2012 for Galen’s attempts to quote accurately). Scribonius figures prominently in the poison lore, set out by Galen (Ihm 1997). Scribonius thus is not the only physician/​pharmacologist active in Rome, touting complicated medicines, during the first half of the 1st century. Antonius Musa, the renowned physician to Augustus also set down a multi-​ingredient trachea-​loosening medicine (Comp. 140: here subsumed under those medicines suggested for abdominal pains and bloatedness). Marcianus’ extraordinarily complex 40-​ingredient antidote against poisons illuminates the fear exhibited by the Julio-​Claudians (Comp. 177; Keyser 2008b; Osgood 2011, 243, “Scribonius boasts that he, too, has made this preparation—​ perhaps for Claudius”). Florus, a personal physician to Antonia Major (b. 39 bce, d. 37 ce), contributes a complex multi-​ingredient recipe (13 substances, not counting the preparation technologies) for the preparation of an ointment (here a kollyrion) to treat chemical burns around the eyes, injuries that resulted from another doctor’s formula (Lucius in Galen, Compounding Drugs According to Place 4.8 = Kühn 12.768–​769; roughly translated by Kokkinos 1992, 33). Notable is Galen’s great preference and respect for Dioscorides of Anazarbus, whose Materia medica retailed some 700 “simples,” which made Dioscorides much easier to follow, since the gathering of fresh constituents was frequently the most important element in the Materia medica. And throughout the Middle Ages, Dioscorides’ book survived, most often in an alphabetical rearrangement of the simples, an impossible task when faced with the inordinately complex multi-​ ingredient formulas characteristic of Scribonius’ Compositiones. Neither of the two renditions of the Epistula into English (Hamilton 1986; Pellegrino and Pellegrino 1988) makes any attempt to deal with the pharmacological technology, and the translation of the whole into German (Schonack 1913) is founded on the necessarily defective edition published by Helmreich in 1887, and identifies the plants with German “common names,” with an occasional stab at what might be termed a “scientific name,” certainly not very useful even to German speakers. Rinne’s partial translation ([1896 ] 1968: through ­chapter 79) does better with the Linnaean nomenclatures as current in the late 19th century, but it too is based on the Helmreich edition, and much of the complexity in the Latin text is lost when Rinne separates his translation from his tabulation of substances, and of weights and measures. Deichgräber’s admirable 1950 study lets us know about the multiple pre-​Roman Imperial influences that contributed to Scribonius’ outlook, as a kind of “medical humanist,” but—​again—​there is no attempt to untangle the pharmaceutical complexities that festoon the Compositiones, and Deichgräber’s re-​editing of the Epistula is based on necessarily defective texts ranging from the Renaissance to the Teubner edition by Helmreich in 1887. To illustrate the intricately complicated multistage, multisubstance prescriptions in the Compositiones, one is selected and translated (below) as the text itself indicates it should be, a continuous, multipronged set of ingredients infused with weights and

712   Greco-Roman Science measures and equally precise instructions for preparations of the compound, “on the spot,” so that an “Augusta” could have these at hand, a variety of drug preparation that remained typical of pharmacists and apothecaries well into the early 20th century. To comprehend how and why Scribonius did what he did, one needs to offer identifications of the plants, keeping in mind that our notions of phytochemistry are distant from those of classical antiquity. Perhaps Scribonius understood, in an empirical way, what modern pharmacognocists term “synergies,” that is the multiconstituent actions of several active principles simultaneously producing observed results (Pengelly 2004, 12; Wichtl 2004, 631). Thereby the combination of several natural substances will engender different actions, than if one used the “simples” alone, so prominent in Dioscorides’ Materia medica. The Compositiones, in contrast, requires a translation, accompanied by a commentary, encompassing both the Roman notions of drug action and the variable precisions represented in modern pharmacognosy. Compositiones 153 (Sconocchia 1983, 75–​76)

[A remedy for those who suffer] from bladder stones, swollen spleens, and those who are affected by dropsy [edema]: this compound draws down the urine [viz. is a diuretic] and diminishes a stone. Ten denarii [by weight] each of sea holly, pellitory, Celtic spikenard, and black caraway [root], five denarii [by weight] each of dwarf elder [berries] and birthwort. All these ingredients are to be pounded together with a wood [pestle] in the juice of butcher’s broom (which is sometimes called goosefoot), [and these combined ingredients] are then fashioned into lozenges of one denarius [by weight]; the medicament is to be administered with three cyathi of vinegar mixed with honey. [Those who suffer] from stones should gather a handful of wall pepper, or the same amount of alsine-​plant or the same amount of betony [leaves]. It does not matter which one of the herbs you use, and [this] is to be mixed into three heminae of water, and then boiled down to one-​third [of its volume]; then three cyathi of this [decocted part] are to be taken [and] are to be [additionally] mixed with two cyathi of wine and ½ denarius [by weight] of sodium nitrate, and thus [making] from these ingredients a dissolved [i.e., liquid] medicinal; it is given as one denarius [by weight] per day for forty-​five days. It breaks down a stone into grains of sand. And those who suffer from dropsy [edema] should be given [this medicine] mixed with three cyathi of honeyed wine.

Sea holly (Latin eryngium from Greek ἠρύγγιον): thistle-​like in appearance, identified as Eryngium viride Link = E. planum Matth. by André 1985, 97–​98. The leaves are fashioned into a salad in modern Greece and Italy, much as they were in ancient times. Usher 1974, 234, offers E. maritimum L., so-​called the proper sea holly; cf. Polunin 1969, 277, #853. The roots can function as a vegetable, but the plant has fallen out of fashion in current herbal medicine, although earlier 20th-​century herbal manuals continued to list it, but see van Wyk and Wink 2004, 409 (revived use as a diuretic, expectorant, and treatment of inflammation of the urinary tract: tannins and saponins distilled from the roots), and the Schönfelders 2004, 182–​183 (a short entry under “Feld-​Mannstreu”).

Scribonius Largus and Friends    713 Pellitory (Latin pyrethrum): with the OLD, s.v., suggesting “apparently the camomile Anacyclus pyrethrum.” André 1985, 212, agrees, but adds = Anthemis pyrethrum L., with comparison to Dioscorides, Materia medica 3.73, who describes the pharmacological properties of what we would call a “pellitory.” Still cultivated in North Africa, the pellitory gives folk medicine an oil used for toothaches in the form of a mouthwash and also is employed as a flavoring for liqueurs. The active principle in the root is pyrethrin, which gives it insecticidal properties, and Algerians use the root to stimulate the flow of saliva and as a rubifacient. Boulos 1983, 52–​54, lists a dozen or so more uses. Celtic spikenard (Latin saliunca): translated as “Celtic spikenard,” following the etymological suggestion of André 1985, 224. This is Valeriana celtica L., sometimes called the “garden heliotrope,” or “common valerian.” It is prominent in European alternative medicine as a sedative, antispasmodic, carminative, and in treatment of intestinal colic, a broad range of “nervous” disorders, and even for insomnia and migraine headaches (and some would advocate its use in hypertension). An essential oil (1%) contains a mix of constituents, including monoterpene valepotriates, which combined promote the sedation and antispasmodic action noted in the literature. Duke 1985, 503–​504, #357, lists the active compound α-​methylpyrryl ketone as a narcotic, and also notes its approval for use in food by the FDA, see US Code of Federal Regulations §172.510. Detailed phytochemistry by Wichtl 2004, 630–​634. See also Stuart 1979, 277–​278. Black caraway [root] (Latin saxifraga):  André 1985, 45, identifies as Pimpinella saxifraga L., the black caraway, identified as “root” since European folk medicine and alternative medicine use the oil, extracted from the root, in treatment of upper respiratory infections (as a gargle), and it is said to promote secretion of gastric acids, as well as being a weak galactogogue. The oil (up to 0.4% by weight) has coumarinic constituents including isopimpinellin and pimpinellin, as well as some saponisides, the bitter principles, a resin, and tannin. Closely related is P. anisum L., the common anise, which has hundreds of uses, from being a major ingredient in “Anisette” (two spoons each of anise, coriander, and fennel seeds in a quart of vodka) to being recommended as an abortifacient. André 1985 bases his reading on Scribonius Largus 150, where the plant is also called σκολοπένδριον (lit. a centipede), but this morphology is most often linked to what is called “harts’ tongue.” Cf. Duke 1985, 374–​375 (anise); Boulos 1983, 187 (anise); Stuart 1979, 240 (caraway or what is called “burnet saxifrage”); Willuhn 2004a; and Tucker and DeBaggio 2009, 398–​399 (anise). Dwarf elder [berries] (Latin ebulum):  OLD s.v. identifies as Sambucus ebulus L., sometimes in Britain called “Danewort.” André 1985, 97, tentatively agrees, and here it is identified as “berries,” since European medieval folk medicine used the berries as an extreme cathartic, and the odd, local name comes from the Saxon word danes (diarrhea), which is what happened when anyone consumed the bluish-​black berries; these yield a blue dye, argued to be the war paint observed by Julius Caesar and later Tacitus in descriptions of those fierce warriors opposing the Roman conquest of Britain after 43 ce. There is a blue dye produced today from the berries for the coloring of textiles. Alternative medicine in Europe simply designates dwarf elder berries as “poisonous,” noting that one should avoid the constituent anthocyanins: Stuart 1979, 258; Polunin

714   Greco-Roman Science 1969, 401 with plate 133. The Cannons 1994, 50, however, strongly assert that this is not the blue war paint of the ancient Celtic warriors. Birthwort (Latin aristolochia from Greek ἀριστολόχεια):  lit. “best birthing,” long used as a parturifacient in childbirth (cf. the Hippocratic Nature of Women 62: Potter 2012, 240), one of three varieties of Aristolochia, as recognized by Dioscorides, Materia medica 3.4, viz. A. rotunda L., A. longa L., and A. clematatis L. (Scribonius, Comp. 206, quoting Glycon the surgeon’s green plaster, has two kinds, aristolochia strongyle and aristolochia clematatis). Over the centuries, birthwort came to be used in stimulant tonics, as a recommended treatment of joint pains, and the more severe agonies of gout. By the late 20th century, the toxic properties of aristolochic acid, especially harmful to the kidneys causing interstitial nephritis and kidney failure, had been documented in Belgium, Croatia, and elsewhere, so that any “weight-​loss” drug containing birthwort is now banned (except in China). Wink and van Wyk 2008, 55; Scarborough 2011. Butcher’s broom/​goosefoot: the Latin is difficult, reflective of technical details in both Greek and Latin, and specific production mechanics are carefully worded: Oxymyrsinae, quae scopa regia uocantur, suco haec omnia contusa ligno colliguntur. “Oxymyrsina” is a transliteration of the Greek ὀξυμυρσίνη, identified by André 1985, 183, as Ruscus aculeatus L., the common butcher’s broom (OLD s.v. scopa, def. c, scopa regia, says “perhaps Achillea nobilis”), or kneeholm, sometimes called the box holly or Jew’s myrtle. Folk medicine and alternative medical circles in Europe employ butcher’s broom as a sudorific, as a treatment for jaundice, and for uterine complaints. Constituents include an essential oil, a saponiside, a resin, and some potassium salts. Cf. Boulos 1983, 155; Stuart 1979, 256; and Willuhn 2004b. “Scopa regia” refers to the common use of the plant as a “broom,” thus a “goosefoot” to the Romans; in the 1st century ce and later, it was much used by butchers to scrub chopping blocks of the blood and residues of accumulated fat, and one could assume equivalence to a small wire brush or a small rake. Wall pepper (Latin illecebra): OLD s.v. def. 3 identifies as “a species of stonecrop” citing this passage in Scribonius Largus; identified by André 1985, 131, as Sedum album L., the wall pepper, or white stonecrop. The leaves are occasionally eaten in salads, and the Sedum spp. (leaves) are used in European alternative medicine as a skin irritant and as an external liniment to dissolve warts and corns. The leaves have some alkaloids, including sedamine, a few glycosides, and mucilage (likely the property observed by the Romans). Cf. Usher, 533; Dalby 2003, 272 (variety of purslane); and the Schönfelders 2004, 406–​407 (brief entry “Scharfer Mauerpfeffer”). The Latin word usually means “enticement by magic,” or “allurement,” so that one is initially tempted to translate it as “a charm,” with no botanical or pharmaceutical specification. Betony (here Sconocchia has emended the text on the basis of his reading in the Codex Toletanus, his MS T, to Vectonica, a form that appears neither in André 1985 nor the OLD): André 1985, 271, provides vettonica or betonica as his choices from passages in Vegetius and another veterinary medical tract we know as the Mulomedicinae Chironis, explaining, along the way, that the name is derived from the “plant of Vettones,” a tribe in Roman Lusitania (modern Portugal), according to Pliny the Elder. André thus identifies it as Stachys officinalis L., the common betony, sometimes labeled S. offinialis

Scribonius Largus and Friends    715 [L.] Trevisan. Betony has a long history as a folk medical substance used as a sedative and applied on wounds as an astringent; powdered it functions as a sternutatory, emetic, and powerful laxative. Phytochemical constituents include tannins (up to 15% by weight), bitter principles, some saponisides and glucosides, and two alkaloids appropriately named betonicine and stachydrine. Cf. Stuart 1979, 266; Usher 1974, 552. Alsine (Latin auricula murina, lit. ear of a mouse): identified by André 1985, 31, as Thelygonum cynocrambe L. (fourth of six Latin names for plants, called by their shapes after the ears of various animals: rabbit ear, donkey ear, sheep’s ear, etc.). The young shoots have been used as a powerful laxative: Usher 1974, 573. OLD, s.v. auricula, def. 3, offers “alsine,” citing this passage in Scribonius Largus. It does not matter:  Latin’s quilibet (here quaelibet) usually means “which ever or whatever you please,” but what Scribonius is saying is “it does not matter which of the herbs you use.” Sodium nitrate (Latin nitrum, transliterated from the Greek νίτρον): a sodium or potassium nitrate found not only in Egypt but also anywhere shallow lakes formed from rainstorms that evaporated during hot weather, here translated as the generic “sodium nitrate” (NaNO3), suggesting its common chemical properties, similar to what is often known as saltpeter. As Scribonius is dissolving the nitrum in water, the translation is accurate, since sodium nitrate dissolves in three parts of water at 60°F: Dana 1949, 739.

5.  Weights and Measures (Adapted in Part from Berendes [1902] 1983, 13–​15, and Beck 2011, xi, also OLD s.vv.) cyathus (Greek κύαθος), taken to be 10 drachmae (Pliny, Natural History 21.185), thus = approximately 40 to 45 milliliters hemina = ½ sextarius = 6 cyathi denarius and one-​half denarius (here uictoriatus). In Scribonius’ day, the silver denarius was tariffed as equal to one drachma, about four grams, thus the unit labeled a uictoriatus would be half this weight. The coin called the uictoriatus (from the image of Victory on its obverse) had long circulated by weight (“item of commerce” in Pliny 33.46), and in the early Roman Empire its value was half that of the denarius (Howgego 1995, 112; Woytek 2012, 318). Thus Scribonius could easily assume the uictoriatus had a weight that was half that of the denarius. If one dates the Compositiones to 48 ce or slightly earlier, it means that Scribonius’ “weights and measures” would fluctuate, especially after the debasement of the coinage by Nero (before 68 ce). Thereby the presumptive exactitude in the Compositiones may well

716   Greco-Roman Science have baffled fellow pharmacologists, who might have encountered the work later in the century (Richardson 2005, 39). Then, too, when weighing with beam balances, the Roman pharmacologist probably tolerated a small percentage of error, unless he used balances for unequal weights, equipped with carefully calibrated yards. (Wikander 2008, 765)

6.  Results/​E ffects of Scribonius’ Remedies for Bladder Stones Remedies for bladder stones are to be made “in bulk,” with some 50 denarii in the first recipe, with the combination to be fashioned into lozenges, and given in three cyathi of vinegar mixed with honey. No period of time is specified over which to take this six-​ingredient recipe (not counting the butcher’s broom, no quantity included, and the honey and vinegar), but the second part of the recipe (“handfuls” of betony, or wall pepper, or alsine) adds a uictoriatus of sodium nitrate, and then the patient is given presumably this full eight-​ingredient medicine in dosages of one denarius per day for 45 days. Among the physiological effects of this compound drug are notably an increased volume of urine, likely long-​term diarrhea, some muscle weakness, digestive side effects, and the improbable passage of stones, unless they were small enough to pass out in the urine, given the amount of fluids consumed in the one-​and-​a-​half months. Kidney poisoning seems likely, given the quantity of birthwort consumed (some 10% of the lozenges), reduced to about 5% in the 45-​day administration period. Adding the sodium nitrate would increase the alkalinity of fluids in the patient, quite the opposite of what modern urologists recommend for the prevention of kidney stones, that is, goodly quantities of lemon juice, freshly squeezed each day. Birthwort, combined with the sea holly, pellitory, and valerian, would be felt as a mild narcotic, but such a patient—​especially those who suffered from frequent stones—​would have likely sought surcease with mandrake, or henbane, or large doses of the opium poppy latex, dissolved in hot wine or water.

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Scribonius Largus and Friends    719 Rawson, Elizabeth. “The Life and Death of Asclepiades of Bithynia.” Classical Quarterly 32 (1982): 358–​370; repr. in Elizabeth Rawson, Roman Culture and Society: Collected Papers. Oxford and New York: Clarendon Press, 1991, 427–​443. —​—​—​. Intellectual Life in the Late Roman Republic. London, Duckworth, and Baltimore, MD: Johns Hopkins University Press, 1985. Richardson, W. F. Numbering and Measuring in the Ancient World. Rev. ed. Exeter:  Bristol Phoenix, University of Exeter Press, 2005. Riddle, John M. “Folk Tradition and Folk Medicine:  Recognition of Drugs in Classical Antiquity.” In Folklore and Folk Medicines, ed. John Scarborough, 33–​ 81. Madison, WI: American Institute of the History of Pharmacy, 1987. Rinne, Felix. “Das Receptbuch des Scribonius Largus, zum ersten Male theilweise ins Deutsche übersetzt und mit pharmakologischem Commentar.” Historische Studien aus dem Pharmakologischen Institute der Kaiserlichen Universität Dorpat 5 (1896):  1–​ 99; repr. as Historische Studien zur Pharmakologie der Griechen, Römer und Araber: Kobert’s «Historische Studien aus dem Pharmakologischen Institute der Universität Dorpat» Teil I. Leipzig: Zentralantiquariat der Deutschen Demokratischen Republik, 1968. Romm, James. Dying Every Day: Seneca at the Court of Nero. New York: Alfred A. Knopf, 2014. Scarborough, John. “Some Beetles in Pliny’s Natural History.” Coleopterists’ Bulletin 31 (1977): 293–​296. —​—​—​. “Nicander’s Toxicology, II: Spiders, Scorpions, Insects and Myriapods.” Pharmacy in History 21 (1979): 3–​34 and 73–​92; repr. in Pharmacy and Drug Lore in Antiquity: Greece, Rome, Byzantium, chap. 11. Farnham, Burlington: Ashgate, 2010. —​—​—​. “Antiokhos, Paccius (20 bce‒14 ce).” In Keyser and Irby-​Massie 2008a, 95. —​—​—​ “Antonius Musa (40‒20 bce).” In Keyser and Irby-​Massie 2008b, 101. —​—​—​. “Apuleius Celsus of Centuripae (ca 20‒40 ce).” In Keyser and Irby-​Massie 2008c, 119. —​—​—​. “Truphon of Gortun (ca 15 bce‒20 ce).” In Keyser and Irby-​Massie 2008d, 817. —​—​—​. “M. Terentius Valens (25‒40 ce).” In Keyser and Irby-​Massie 2008e, 773–​774. —​—​—​. “Ancient Medicinal Use of Aristolochia: Birthwort’s Tradition and Toxicity.” Pharmacy in History 53 (2011): 3–​21. —​—​—​. “Theodora, Aetius of Amida, and Procopius:  Some Possible Connections.” Greek, Roman, and Byzantine Studies 53 (2013): 742–​762. Schonack, Wilhelm. Die Rezeptsammlung der Scribonius Largus:  Eine kritische Studie. Jena: Gustav Fischer, 1912. —​—​—​. Die Rezepte des Scribonius Largus. Zum ersten Male ins Deutsche übersetzt und mit ausführlichen Arzneimittelregister versehen. Jena: Gustav Fischer, 1913. Schönfelder, Ingrid and Peter. Das neue Handbuch der Heilpflanzen. Stuttgart: Franckh-​Kosmos, 2004. Sconocchia, Sergio, ed. Scribonii Largi Compositiones. Leipzig: Teubner, 1983. —​—​—​. “Le fonti e la fortuna di Scribonio Largo.” In I Testi di Medicina Latini antichi. Problemi Storici e Filologici. Atti del I Convegno internazionale (Macerata . . . 1984), ed. Innocenzo Mazzini and Franca Fusco, 153–​213. Rome: Bretschneider, 1985. —​—​—​. “L’opera di Scribonio Largo e la letteratura medica latina del 1 sec. d.C.” In Aufstieg und Niedergang der Römischen Welt II.37.1, 843–​922. Berlin, New York: de Gruyter, 1993. —​—​—​. “Greek Medicine in Scribonius Largus’ Compositiones.” In Maire 2014, 330–​349. Stok, Fabio. “Marcellus of Bordeaux ‘Empiricus’ (375‒425 ce).” In Keyser and Irby-​Massie 2008, 527–​530. Stuart, Malcolm, ed. The Encyclopedia of Herbs and Herbalism. London: Orbis and Novara: Istituto Geografico de Agostini, 1979.

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chapter D7

Di stilling Nat u re ’ s Secrets The Sacred Art of Alchemy Kyle Fraser

Recent studies in the history of early modern science have done much to rehabilitate the poor reputation of alchemy, long associated with pseudo-​science, superstition, and even fraud. The central role played by the “sacred art” in the researches of Boyle, Newton, and other luminaries of the scientific revolution is now generally acknowledged, if still not fully understood (Principe 2011). Regrettably, this new wave of scholarly enthusiasm has not yet had an appreciable impact on the neglected study of Greco-​Egyptian alchemy. In part, this neglect reflects the lack of reliable scholarly editions of the Greek alchemical texts, whose scant remains are preserved in several medieval Byzantine manuscripts (Mertens 1995, xxii–​xliii; 2006). The standard modern edition, despite its flaws and eccentricities, remains that of Berthelot and Ruelle (1888/​1967), though new and superior editions are slowly emerging (see Halleux 1981; Mertens 1995; Martelli 2011). The fragmentary state of the manuscript tradition makes the work of reconstruction especially daunting; and the relative dating and contextualization of the surviving texts is further complicated because alchemists often concealed their identities under pseudonyms. Though important studies have appeared on specialized topics, we have yet to see a major reappraisal of the historiography of Greco-​Egyptian alchemy comparable to the recent scholarship on the early modern tradition. A. J. Festugière’s classic periodization of the surviving texts into three distinct typological phases has become standard and now stands in serious need of reassessment: it is highly probable that alchemy was nothing other than a technique before Bolus the Democritean, in the second century before our era; and that once Bolus provided its philosophical form, alchemy became both an art and a philosophy (already mixed with mysticism) until the second or third centuries of our era, after which, without

722   Greco-Roman Science ceasing to operate as an art and a philosophy, it increasingly assumed the appearance of a mystical religion. (Festugière [1950] 2006, 219; translation mine)

On the face of it, this typology may appear uncontroversial; indeed, I suspect that it continues to be followed with insufficient attention to its underlying historiographic assumptions (see, e.g., Mertens 2002, 168). Festugière characterizes the technical, philosophical, and mystical dimensions of alchemy as separable diachronic layers, rather than interdependent aspects of a unified worldview. Indeed, he judges that alchemy is a derivative syncretism (“un mélange”) of Greek philosophical concepts and “mystical daydreams” (Festugière [1950] 2006, 218–​219; cf. Halleux 1981, 26; Mertens 2006, 206; 1998, 5 note 9). On his view, the mystical dimension, which is already “mixed” with the philosophical theories of Bolus of Mendes, increasingly predominates, gradually eroding the rational foundations of the art. The final phase of this mystification is typified by Zosimus (circa 300 ce), in whose writings the techniques of alchemy have become little more than ritualized expressions of a quest for Gnostic realization (Festugière, [1950] 2006, 260–​261; cf. Sheppard 1957, 96; Fowden 1986, 123). Like his friend E. R. Dodds, Festugière was guided by the assumption that the Roman Imperial age was a period of decline, characterized by a flight from the ideals of Greek rationality into the irrational vagaries of mysticism (Festugière [1950] 2006, 1–​18). The rise of alchemy and the other “occult sciences” was symptomatic of this age of anxiety. But if we take this assessment as our starting point, we have decided in advance that alchemy does not properly belong to the history of science—​that the spirit of discovery and innovation is foreign to the alchemical “mentality.” The argument of this paper proceeds by way of a critical reexamination of two key aspects of this prevailing historiography: (1) In the first section, the question of the origins of alchemy is revisited. Whereas alchemy has typically been characterized as derivative and “syncretic,” I approach the art as a unique cultural synthesis of Greco-​Egyptian provenance. In their single-​ minded focus on the Greek inheritance of alchemy, scholars have overlooked the continuing influence of native Egyptian religious ideas, which were deeply interwoven with the craft technologies of the temples. They have also badly underestimated the originality of the alchemists, who were by no means passive imitators of the older Greek philosophical systems (here I follow the lead of Viano, 1996; 2005). In framing the idea of transmutation, the alchemists drew creatively (even provocatively) on Aristotelian concepts of mixture and substantial change, adapting Greek ideas and arguments to their own theoretical perspective. (2) In the second section, I  challenge the claim that the alchemy of the Roman Imperial period is characterized by a decline into irrationalism. The esotericism of alchemy, far from undermining the rational development of its theories and practices, served to stimulate independent research, since the secrets of the ancient masters could only be decoded in the light of practical laboratory experience. I reject the standard image of Zosimus as an “otherworldly” mystic, arguing he remains committed to a natural alchemy modeled on cosmic processes.

The Sacred Art of Alchemy    723

1.  Assimilation and Transformation: Greco-​E gyptian Alchemy in Cultural Context Festugière famously described alchemy as originating from the encounter of Egyptian craft technologies and Greek philosophical concepts (Festugière [1950] 2006, 218–​219). In the light of Platonic and Aristotelian ideas about matter and its transformations, traditional techniques of imitation acquired a more profound significance and were reinterpreted as methods of transmutation. Whereas the Egyptian artisan aimed to create a convincing facsimile, the alchemist claimed to replicate gold and silver—​to transform copper or lead into gold—​by altering the fundamental structure of the base metal. From Egypt, the alchemists took their techniques and from Greece, their rational methodology and the central concept of transmutation. How should we understand this encounter of Egyptian technology and Greek philosophy? Are we really to suppose that the Egyptian contribution to alchemy was merely technical, while its intellectual content derived from the rational “Greek spirit” (Festugière [1950] 2006, 238)? The Hellenocentrism of this formula is readily apparent. The question of the origins of alchemy cannot be resolved at the level of ideal abstractions but must be approached as a cultural phenomenon. Like the Hermetic tractates and the magical papyri, the literature of alchemy points to the existence of a living tradition, which arose out of the complex processes of Hellenization operative in Egypt since Ptolemaic times. The alchemical worldview is not reducible to its cultural components; it is an original synthesis in which Greek and Egyptian ideas were mutually transformed. This point can be illustrated with respect to the central idea of alchemy, that of transmutation. This is not a Greek idea, but an alchemical idea, which drew creatively on older Greek concepts (see Viano 1996; 2005, 91). Moreover, the idea seems to have been inspired not only by Greek philosophical speculations but also by traditional Egyptian religious beliefs, albeit often filtered through a Hellenistic conceptual framework. In what follows, we shall explore the Egyptian and Greek contributions, with a view to highlighting not only the assimilation of pre-​existing ideas and practices but also their adaptation to the alchemical worldview.

1.1 Egyptian Contributions to Alchemy The temple workshops of Egypt, from very ancient times, enlisted artisans for the gilding and decoration of sacred icons. These craftsmen were renowned for their expertise in the creation of gold leaf, the fabrication of glass and imitation gems, and the dyeing of fabrics. Typically, gilded objects were created by fastening gold leaf to an underlying structure with glue or small nails (Ogden 2000, 160, 164). However, from at

724   Greco-Roman Science least the Eighteenth Dynasty, we find evidence of attempts to alter the surface color of metals through chemical means. Pink-​tinted gold artifacts unearthed in the tomb of Tutankhamun seem to have been created by treating gold with iron salts or pyrites (Lucas-​Harris 1962, 233–​234). Pliny (33.131) attests that silver and copper artifacts, consecrated to Anubis, were stained black by treatment with sulfur (on these “niello” effects, Lucas-​Harris 1962, 249–​251; Ogden 2000, 160; and, more recently, Martelli 2014, 15). This claim is confirmed by an inscription from the temple workshop of Dendara, the so-​called House of Gold: “If it says of a god that the material is copper, this means black bronze” (Derchain 1990, 235; translation mine). The ingredients and procedures employed by these craftsmen were secrets, and so were concealed under elliptical formulae: for example, “copper” really means black bronze, “electrum” means juniper gilded with fine gold (Derchain 1990, 222–​223, 235). In Hellenistic times, these techniques were disseminated beyond their original cultic context and came to form the basis of an industry aimed at the production of imitation jewelry and dyed fabrics. The Leiden and Stockholm papyri, which date to the 3rd or 4th century ce, are precious survivals of this industry (Halleux 1981, 22–​30). The recipes of the papyri employ procedures of cementation, which are obviously an inheritance (though greatly elaborated) of the methods employed by the temple artisans to create purple-​tinted gold or blackened silver. Artificial silver is created by treating the surface of copper with arsenical compounds (P. Leid. 22) or mordants, such as vinegar and alum (P. Leid. 12, 18). Imitation gold is fabricated by treating the surface of a gold alloy with a cement of sulfates and salts, thus creating the appearance of pure gold (P. Leid. 14). The use of metallic mercury, beginning in Ptolemaic times (Ogden 2000, 169), inspired an important innovation to the traditional methods of gilding: now rather than attaching gold leaf with adhesives, it was possible to create a fixed golden hue, by varnishing the surface of an object with a gold amalgam and then evaporating the mercury (P. Leid. 55). Recently, compelling parallels have also been drawn between the recipes of the papyri and much older Mesopotamian dyeing techniques for the coloring of metals, stones, and wool (Martelli and Rumor 2014). These recipes probably filtered into Egypt in the Persian period, which may partly explain the prestige afforded to the Persian magus Ostanes (who is further discussed below). If we compare the techniques of these papyri with our earliest alchemical recipes—​ those contained in the surviving writings of pseudo-​Democritus—​the similarities are beyond question. Though there are no exact correspondences that would permit us to postulate a direct borrowing from one to the other, the operations are certainly identical in kind (Halleux 1981, 74). The chief methods of pseudo-​Democritus are those of debasement (creating alloys that look like the real thing) or techniques of cementation involving the application of corrosive varnishes to the surface of a base metal. As in the papyri, compounds of arsenic and sulfur are employed to whiten copper, or to purify the surface of a gold alloy (on these techniques, see Taylor 1930, 125, 130). We recognize the same basic range of ingredients, including such staples as alum (styptēria), arsenic sulfide (sandarachē), and iron sulfate (misy). The difference lies in the interpretation of the techniques: whereas the papyri envision only the creation of facsimiles,

The Sacred Art of Alchemy    725 pseudo-​Democritus holds that his methods can yield genuine transmutations. Despite this fundamental difference of perspective, it seems that a common source lies in the background. The papyri follow the same fourfold classification of operations that is attributed to Democritus by later commentators, and which is partially preserved in the extant fragments of his Natural and Mystical Topics (Physika kai Mystika): viz. imitations of gold, silver, precious stones, and purple dyes (Halleux 1981, 72–​73; Martelli 2014, 6). Moreover, one of the Stockholm recipes is actually attributed to Democritus (Papyrus Holmiensis 2). It appears that the compiler of the papyri had access to some “Democritean” source closely related, in structure and content, to the pseudo-​ Democritean alchemical texts. This common source may be the elusive Bolus of Mendes, a Hellenized Egyptian and Pythagorean, with a keen interest in occult properties and natural marvels. He was probably active between 200 and 100 bce: the earliest authors who discuss his writings belong to the 1st century ce, and he is presumably later than Hermippus of Smyrna (fl. ca 200 bce), who seems to have initiated the Hellenistic vogue for magian lore, a theme that was prominent in the works of Bolus (Halleux 1981, 66–​67). Columella tells us that Bolus wrote a work called the Cheirokmēta under the “false name” of Democritus (De re rustica 7.5.17). This work was fairly well-​known. Pliny drew from it in his discussions of the plant lore of the Persian magi (Dickie 1999, 174–​192). In the Byzantine Suda (Β–​482), we learn further that Bolus composed a catalogue of the sympathies and antipathies of natural substances, arranged in alphabetical order (kata stoicheion). According to Tatian (Oratio ad Graecos. 17), “Democritus” boasted in this work about his tutelage under the Persian mage, Ostanes. The relationship between the treatise on sympathies and the Cheirokmēta is unknown, but a comparison of the various testimonia suggests that the two works were similar in kind. Both purported to contain magian lore, transmitted through Democritus. A likely hypothesis is that the Cheirokmēta—​ which means something like “manual operations”— contained practical techniques for harnessing natural sympathies. In my view, the evidence for thinking that Bolus lies (however remotely) behind the pseudo-​Democritus of the alchemical tradition comes to the following: 1. The Natural and Mystical Topics were framed around the legend of Democritus’ initiation by Ostanes in a Memphite temple. Judging from the testimony of Tatian, Bolus was among the first—​perhaps he was the first—​to associate Democritus and Ostanes as student and master (Beck 1991, 560–​561). 2. Zosimus composed an alchemical compendium called the Cheirokmēta, arranged in alphabetical order (Suda, Z.168). The alchemical appropriation of this strange title, with its established links to the magical lore of “Democritus” and the magi, is surely not accidental. If, as seems likely, Zosimus was inspired by the well-​ known Cheirokmēta of Bolus-​Democritus, then the Democritean exemplar must have discussed matters germane to alchemy (Kingsley 1994, 6–​7, with n. 36; pace Hershbell 1987). This influence appears even more probable in light of the fact that Zosimus structured his encyclopedia according to the letters of the alphabet, the same arrangement employed by Bolus in his work on sympathies (Suda Β–​482).

726   Greco-Roman Science The evidence linking Bolus to alchemy, though not extensive, is persuasive. We are justified in supposing that the 1st-​century ce author of the pseudo-​Democritean alchemical writings drew upon the earlier research of Bolus. (For the dating of the pseudo-​Democritean alchemical texts, see Martelli 2011, 90–​92: in addition to the lexical evidence of Festugière [1950/​2006, 225], Martelli notes the reference to Pammenēs [CAAG 2.49.8], an Egyptian astrologer contemporary with Nero.) How much of the pseudo-​Democritean alchemy is a direct borrowing from Bolus, and how much elaboration, we cannot ascertain. It is tempting to suppose that the standard fourfold division of the art (gold, silver, stones, and purple dyes) originated with Bolus and was subsequently adopted both by the alchemists and the artisans of the papyri. With respect to the framing narrative of the Natural and Mystical Topics, the influence is more certain, since it was Bolus who shaped the lore concerning Democritus and his Persian master, Ostanes. An essential element of that narrative frame is the mise-​en-​scène of an Egyptian temple in Memphis. The secrets of alchemy are represented as an inheritance of the sacred lore of the Egyptian priesthood. This claim pervades the corpus. Zosimus says that the Egyptian prophets engraved the secrets of alchemical tincturing on temple stelae, concealing them in the enigmas of the hieroglyphs (The Final Quittance, 365.23–​26, edition of Festugière [1950] 2006, cited by page and line). He calls the art Chēmeia (CAAG 2.213.15), that is, the “art of the black earth” (from kmt, the indigenous name of Egypt; in Coptic, khme), a title that alludes both to the Egyptian provenance of alchemy and to the centrality of the black lead or prime matter of transmutation (Fraser 2007, 35, 41; Bain 1999, 217–​219). Now, of course, we cannot believe that Egyptian priests were conducting alchemical experiments in the temples with apparatus of distillation and sublimation. Nor is there any evidence that the traditional techniques of gilding were ever conducted with a view to transforming materials into gold. However, it is important to consider why Bolus and his alchemical heirs discerned a deeper connection to the religious ideals of Egypt than the merely “technical” contribution conceded by modern scholars. Before dismissing such appeals as “Orientalizing” conceits (Festugière [1950] 2006, 20), we should consider the possibility that something of the original religious meaning of these techniques may have been carried forward into alchemy, albeit in a Hellenistic guise. Recent scholarship on the Hermetic corpus and the magical papyri has shown that beneath the Hellenistic stereotypes of Egyptian priests and their esoteric wisdom there are genuine points of continuity with traditional religious belief (Fowden 1986, 155–​195; Frankfurter 1998, 221–​224). The challenge lies in disentangling the elements of cultural continuity from their often-​exaggerated Hellenistic reinterpretation. At the level of technique there are obvious continuities between the early experiments with cementation in the temples—​the purple-​tinted gold of Tutankhamun or the black bronzes produced at Dendara—​and the methods employed by the early alchemists. But can we discern, beyond this technical continuity, any analogies of an ideological nature? How were the techniques of the “House of Gold” understood in the religious context of the temple cult? We know that the temple artisans at Dendara, a group including gilders, sculptors, engravers, lapidaries, and jewelers, worked under the supervision of priests (Derchain

The Sacred Art of Alchemy    727 1990, 233–​234). Their role was the fabrication of the bodies of the gods:  “They are those who cast all the jewels of gold, silver, and true stone, which must touch the divine body” (Derchain 1990, 234; translation mine). The gold that covered the statues was conceived as the flesh of the gods, a reification of the life-​giving energies of the sun god. Once crafted by the artisans, the statues were animated by the priests through the ritual of “uniting with the sun,” a late elaboration of the “opening of the mouth” ceremony, which was traditionally employed for the enlivening of mummies and cult statues (Assmann 2005, 312, 322–​323). The golden statues of Hathor and her entourage were brought to the roof of the temple to bathe in the life-​giving rays of Ra (Derchain 1990, 233). The goal of transforming inert matter into an incorruptible, “golden” matter is central to Egyptian religious belief and symbolism. The same pattern can be discerned in the funerary cult, where the preserved flesh of the mummy was assimilated to the imperishable stars or the luminous substance of Ra: “Ho, Neith! Raise yourself on your metal bones and your golden limbs. This body of yours belongs to a god: it cannot molder, it cannot end, it cannot decay” (Pyramid Texts of Neith [Dynasty 7], Spell 249, in Allen 2005: cf. Teti, Spell 225; Pepi I, Spells 318, 337). This transformation of decaying matter into divine matter was accomplished through ritual and technical operations; indeed, mummification involved the chemical alteration of the corpse, through the application of dehydrating agents and solvents. To Zosimus it is self-​evident that alchemy is based upon mummification: “This is the place of the practice called embalming (taricheia). Those wishing to attain virtue enter here and become spirits, once they have fled the body” (The “Visions” of Zosimus, Mém. auth. 10.54–​57; on this passage and the allusion to embalming, see Quispel 2000, 307 with n. 8). Taricheia can simply mean “salting,” but it is also the standard word for mummification (Keyser 1990, 362), and this is the sense that fits the context of the “Visions,” with its allusions to rites of sacrifice and resurrection. We need not suppose that Zosimus has any privileged understanding of the rite of mummification. It is clear that he is reinterpreting the process in terms of Hermetic mysteries of spiritual rebirth. The Egyptian influence is apparent, but it has been transformed in the light of Hellenistic religious ideas. Another striking illustration of this process of cultural translation is Olympiodorus’ (6th century ce) appropriation of the Osirian myth as an allegory for the treatment of the black lead: Here too the oracles of Apollo bear witness, for they speak of the tomb of Osiris . . .[Osiris] is the principle of every humid substance, that which undergoes fixation (katochos hyparchōn) in the “spheres” [i.e., vessels] of fire. Thus he has bound together the All of lead. (CAAG 2.94.22–​95.7).

Olympiodorus may be following a suggestion in Plutarch, who claims that Seth sealed the tomb of Osiris with lead (Isis and Osiris, 356c–​d). Whatever his source, he is clearly reading the myth through some kind of Hellenized presentation. Nonetheless, the comparison of Osiris with the prime matter of alchemy (the “all of lead”) makes a certain sense in Egyptian religious terms. Osiris was linked with the power of rebirth latent in

728   Greco-Roman Science the soil of the Nile valley (Cauville 1988), the very black earth that some alchemists took as the prototype of their prime matter: thus the name Chēmeia. The techniques that Bolus appropriated from the Egyptian temples had acquired, over many centuries, a deep religious significance, which continued to inform the ideal of transmutation as a sacred activity. But, it must be stressed, these cult practices were not equivalent to the alchemical concept of transmutation. The rite of the opening of the mouth, whether it was performed on a gilded statue or a mummy, involved the transformation of an ordinary object into an icon, imbued with sacred qualities (Assmann 2005, 312–​317). An icon is an object that is more than it appears to be: its divine aspect is not directly visible but is notional or symbolic. By contrast, the alchemists believed that they could produce a transmutation that was verifiable in empirical terms and that could be explained according to a philosophical conception of nature. The idea of transmutation retained its spiritual significance—​gold was still associated with divine incorruptibility—​but the process also admitted of a naturalistic interpretation. The materials that formed the basis of this alchemical philosophy of nature were derived from the Greek tradition, in particular from Aristotle, but this derivation was by no means uncritical (see Viano 2005, 91–​92). The Greek elements, like the Egyptian, were creatively adapted and transformed in this new alchemical synthesis.

1.2  Transmutation in Theory, or, Aristotle Transformed The physical theory of transmutation assumes a fundamental distinction between the metallic bodies (sōmata), on the one hand, and the incorporeals (asōmata), or sublimed vapors (aithalē), on the other. The four fixed bodies—​tin, copper, lead, and iron—​are the substrates (hypostata) of transmutation. The vapors are the active and transformative principles. These are sublimates of reactive minerals—​notably, of sulfur, mercury, and arsenic ores—​especially characterized by their volatility and their power to transform the colors of the metallic bodies. For this reason, they are typically called “tinctures” (baphai). The metallic bodies share a common material substrate, the precise nature of which we shall consider in due course. The operative assumption of the art is that the essential distinctions between the metals derive from the modes by which this generic matter has been differentiated by the active properties of the vapors. Thus, to transform lead into gold, one would need to transform the underlying matter by applying the appropriate reagents. Though these transformations were thought to be signaled by color changes, the goal was by no means a superficial alteration. The change in color was the sign of a more fundamental transformation occurring in the depths of the metal. In other words, the intention was not merely to make copper look like silver, as in the case of the techniques preserved in the Leiden and Stockholm papyri, but actually to

The Sacred Art of Alchemy    729 turn copper into silver. This transmutation is described as a synthesis of opposites, in which the reactive vapors penetrate the fixed bodies of the metals: “that which is volatile has penetrated that which is not volatile . . . and they have been united to one another (allēlois hēnōthēsan)” (CAAG 2.298.5–​7). It was thus crucial to employ reagents that were “sympathetic” to the nature of the metal to generate a substantial unity of opposites. In the background we detect the influence of Aristotle, who distinguishes a mechanical synthesis, in which the components are externally juxtaposed, from a true mixis, in which the ingredients are mutually transformed, yielding a new substance (Generation and Corruption 1.10, 328a5–​17). The mixture is conceived as an “intermediate” entity (metaxu), in which the opposing powers of the components have been brought to a balanced state. Such mixtures are uniform or, as Aristotle says, “homoiomerous.” The components do not actually subsist in the mixture but are present in it only in a virtual way, inasmuch as they impart qualities to the final product—​as, for instance, fire imparts a fiery digestive power to bile. Aristotle’s privileged examples of homoiomerous mixtures are organic substances, like flesh and bone. But metals are also mixtures. In the Meteorology, he describes how the metals form underground when moist vapors are dried and compressed by a smoky exhalation, which derives from the heating of the earth and its ores (3.6, 378a13–​b6). He notes that, in one sense, the metals are water while, in another sense, they are not. The vapor from which the metals originated was water in potentiality (it could have condensed back into water), but the metals themselves are not water, nor can they easily be converted back into water. While a metal can be melted, its nature persists in this molten state: we can say that it is watery, but not that it is water. Thus metals are different from “savors,” which arise from a merely qualitative alteration of water (dia ti pathos, 3.6, 378a35). In short, the metals satisfy Aristotle’s stringent conception of a homoiomerous mixture. The essential differences between the metals are functions of the proportions in which their components are blended. Of all the metals, gold is the purest, containing the least admixture of the earthy smoke, and thus it is not affected by fire (3.6, 378b4)—​ in modern terms, it does not oxidize. The alchemists seem to have identified their reactive vapors with the exhalations described by Aristotle (e.g., CAAG 2.84.16–​85.5). They imagined they were replicating, in their vessels, the natural processes by which metals came into being. Aristotle’s account provided a theoretical model for making sense of transmutation: it was a question of synthesizing the underlying matter of the metals with the right kinds of exhalation and in the right proportions. However, it is crucial to recognize that the idea of transmutation does not follow obviously from Aristotle’s theory. From the fact that we can understand, in principle, how lead differs in composition from gold, it does not follow that we can replicate these differences of composition artificially. For one thing, we would need to know the exact proportions of the mixture and no such quantitative analysis is ever attempted by Aristotle (on this point, see Viano 1996, 210–​213). For another thing, Aristotle is adamant that the metals are fixed natures and, of course, one species cannot be converted into another (Viano 1996, 202–​203). In order for lead to be transformed into gold, we would first have to decompose the lead into the

730   Greco-Roman Science common substratum of the metals. As he explains elsewhere: “all things that change into one another in this way must revert to their matter . . . vinegar first goes back to water, and only then becomes wine” (Metaphysics 8.5, 1045a3–​6). If the metals can no longer become water on Aristotle’s view (Meteorology 3.6, 378a35), it is difficult to see how this precondition might be met. Clearly, the elaboration of Aristotle’s theory into an operative alchemical technique faced significant obstacles. Indeed, Aristotle often seems to hold, as a matter of principle, that art (technē) is incapable of replicating natural processes. He draws a rigid ontological distinction between natural entities and artifacts. In natural substances, form and matter are indissolubly connected: the parts of an organism cannot exist apart from the form that imparts their functionality (Parts of Animals 1.1, 641a4–​6, 18–​21). By contrast, the matter of an artifact, like the bronze of a statue, pre-​exists the form imposed on it by the artisan. While an artifact must be generated out of appropriate materials (Metaphysics 8.4, 1044a27–​29), there is a degree of “compositional plasticity”: a house could be built of wood or stone indifferently (see Lloyd 2010, 61–​62). In other words, the relation of artificial forms to their underlying matter is largely incidental (kata sumbebēkos, Physics 2.1, 193a14–​17). While technology can modify the external properties of matter, or impose structures onto pre-​existing materials, apparently it cannot cause substantial transformations. On this rather narrow understanding of technē, it seems that the alchemists would be limited to the imitation of precious metals through the alteration of superficial qualities. Granted, this demarcation between substance and artifact tends to break down precisely in Aristotle’s discussions of chemical mixture, where the kinds of artifact under consideration become more subtle (synthesized medicines, rather than houses) and harder to distinguish from their natural counterparts. This leveling of distinctions is evident in Aristotle’s treatment of “concoction” (pepsis) in book 4 of the Meteorology. Concoction, in the strict sense, is the process by which vital heat transforms an indeterminate moist substratum into an organic mixture; for instance, the transformation of nutriment into blood. However, in illustrating the varieties of his biological process, Aristotle deploys culinary analogies: one mode of concoction is a “boiling” (hepsēsis), effected by moist heat, the other is a “roasting” (optēsis), effected through dry heat. Though he notes that these terms are employed metaphorically when applied to biological phenomena, like the “boiling” of food in the stomach, he finds it hard to maintain this distinction. He vacillates between the similarity and the identity of the artificial and natural varieties: Roasting and boiling are certainly artificial processes, but, as we have said, in nature too there are generally the same forms (ta eidē katholou tauta kai physei). The affections produced are similar (homoia), but we lack distinct names for them. For art imitates nature. (4.3, 381b4–​7)

Are the artificial varieties of concoction just similar to the natural, or are they, at least in some cases, the same? At the level of inorganic mixtures, like metals, it is difficult to draw a meaningful distinction between natural and artificial products. The metals, as

The Sacred Art of Alchemy    731 homoiomera, are closer to organic mixtures, like flesh, than they are to crude artifacts like houses. But since they are not ensouled, it is not clear on what grounds Aristotle could distinguish an artificially generated metal from a natural specimen. Does a metal become less natural when it is smelted? Is bronze less natural than copper? As we have considered, the metals are generated through the drying of their inherent moisture—​ that is, through the type of process described in Meteorology 4 as a “roasting.” An alchemist who was keen to seek the backing of Aristotle could appeal to his statement that the processes of boiling and roasting have the same cause (dia tēn autēn gar aitian) whether they are carried out naturally or in artificial vessels (en organikois technikois kai physikois, 4.3, 381a9–​12). Indeed, later European alchemists appealed to this very discussion (Newman 2001, 148–150; Martin 2004). It should be noted, however, that these alchemical attempts to marshal the authority of Aristotle involve a selective and strategic reading of his texts, which downplays the uncertainties in his position. While support of a certain kind can be derived from Aristotle’s discussions of chemical mixture, this evidence must be weighed against other statements, of a more metaphysical character, which suggest that artifacts are ontologically deficient. In general, Aristotle is less confident than the alchemists in the power of technology to replicate natural substances and processes. He regards technē as imitative (e.g., sculpture), or at best as a handmaiden, like the medical arts, which assist nature in realizing her innate goals (Physics 2.8, 199a15–​17). No doubt the alchemists appropriated elements of Aristotle’s doctrines of mixture and substantial change, but they did so in a creative manner, adapting his theories to their own belief in the possibility of artificial transmutation. Even if Aristotle were to concede that there is no substantive difference between natural and artificial mixtures, the practical realization of the alchemical project would face serious obstacles, two of which were signaled earlier: (a) the problem of determining the correct proportions of the metallic mixture, and (b) the problem of reducing the base metal to its generic matter so it can be reconstituted. Regarding the first problem, it must be conceded that the alchemical tradition was never especially attentive to the quantitative analysis of chemical mixtures. With some notable exceptions, the decisive turn toward quantitative models occurs only with the corpuscularian alchemy of the early modern period. However, the second problem, arising from Aristotle’s doctrine of substantial change, does seem to have preoccupied the heirs of pseudo-​Democritus. Faced with the limitations of the Democritean techniques, these alchemists did not continue stubbornly to adhere to the old ways but introduced striking innovations. At the center of these developments was a Jewish alchemist named Maria.

1.3  The Innovations of Maria Maria lived in the intervening period between pseudo-​Democritus (the 1st century ce author of the Natural and Mystical Topics) and Zosimus (fl. ca 300 ce). Though

732   Greco-Roman Science her writings do not survive, the extent of her contributions to the art can be gauged through the testimony of Zosimus, who regards her as a chief authority in matters of technique. It appears she perfected the apparatus of distillation, adapting the primitive ambix described by Dioscorides and Pliny to the demands of alchemical practice (Mertens 1995, cxvi–​cxxx). This involved: (a) the elongation of the main body of the still by the addition of a column separating the base of the vessel from the still head; (b) the addition of condensing tubes, soldered to the still head, through which the divine waters descended into receiving vessels. On the older approach of pseudo-​ Democritus, divine waters were prepared by boiling mixtures of sulfur, lime and various organic substances, like vinegar or urine (Martelli 2009, 11–​16). The Democritean recipes instruct the alchemist to immerse the base metal directly in these sulfurous waters, which must have varied considerably in their effects depending on their composition. There is no indication yet of any technique for improving the purity and concentration of the solution, apart perhaps from filtering it to eliminate sediment (P. Leid. 87: “Use it pure, once you have filtered out the sediment”). The still of Maria eliminated the need for filtering altogether and enabled the production of a more potent reagent. Maria must also be credited with the invention of the kerotakis, a circulatory vessel in which base metals were subjected to a prolonged treatment with vapors of sulfur and mercury. The metal, typically an alloy of lead and copper, was situated in the upper regions of the vessel, suspended on an iron palette, while the reagents were deposited in the base, which was heated below by a furnace (Mertens 1995, cxxx–​clii). In the initial phase of the operation, the lead-​copper alloy was exposed to sublimed vapors of sulfur, which gradually disintegrated the metal and converted it (in modern terms) into its sulfide (Taylor 1930, 135–​137). According to Zosimus and Olympiodorus, the objective of this process was to reduce the metallic bodies to their prime matter, a “black lead copper” (molybdochalkos), which Maria called the “body of Magnesia” (CAAG 2.192–​ 198). She insisted that this was not common lead, which is black from the start—​that is, galena, an ore of lead—​but a lead that is artificially blackened (CAAG 2.93.10–​13). The product is described sometimes as a divine water (a “black juice,” CAAG 2.94.5; cf. 92.10–​ 12), but there are indications that its ultimate form was that of a powder—​the scoria or ashes of Maria (skōridia kai tephrai Marias, CAAG 2.91.14). In Aristotelian terms, this black lead was the ultimate substrate, formless in itself, but possessing in potentia the forms of the various metals (CAAG 2.192.16–​18). Now, Zosimus contends that the “Philosopher,” Democritus, held the same doctrines as Maria with respect to the black lead (CAAG 2.192.19–​21). Synesius (4th century ce), likewise, ascribes to Democritus the view that the metals must be subjected to a decomposition, in the course of which they are blackened and liquefied (CAAG 2.58.3–​4, 23–​24). No doubt these commentators had access to “Democritean” writings no longer extant; and amongst the various works circulating under the name of the “Philosopher” there may well have been some that adhered to the doctrine of Maria. But it is impossible to believe, based on our surviving fragments, that the 1st-​century ce author of the Natural and Mystical Topics already had such a doctrine in mind. He does refer to “our

The Sacred Art of Alchemy    733 lead” (CAAG 2.49.1), which may indicate that this metal was already regarded as the most basic. But his recipes do not recommend any kind of decomposition or blackening of lead as an essential preliminary to the processes of whitening and yellowing. (Dufault 2015, 219, likewise notes that the recipes of pseudo-​Democritus do not presuppose a prime matter. However, he understates the importance of the “blackening” phase in the later tradition. If transmutation is modeled, in part, on Aristotle’s ideas of mixture and substantial change, then an initial reduction to a common matter is by no means “superfluous” [224]. As I explain above, this reduction is a theoretical requirement, since there can be no immediate conversion of one substance into another.) Rather than being decomposed, the base metal is directly treated with varnishes, leaving its underlying nature unchanged. As we have considered, the methods of pseudo-​Democritus are essentially those of the papyri—​techniques of debasement, cementation, and amalgamation. These processes would have generated only superficial alloys from which the nature of the original metal was easily recoverable. The goal of pseudo-​Democritus was certainly to cause the “medicine” to penetrate the depths of the metal (e.g., CAAG 2.53.6: hina diadynēi to pharmakon entos), but it is obvious that his techniques were inadequate to this theoretical objective. The insistence of the commentators that Maria and “Democritus” agree on all essential doctrines arises from their conviction that alchemy is a timeless science, revealed in its fullness to the ancient prophets. This esoteric perspective, which we shall explore in the next section, tends to conceal precisely what is of interest to the historian of science—​the development of the art over time. That Greco-​Egyptian alchemy did indeed undergo a dramatic development in the early centuries ce becomes evident upon careful comparison of the pseudo-​Democritean fragments with the alchemical practices of Maria. We must credit Maria with introducing the idea—​foundational for the subsequent history of alchemy—​that transmutation requires the total destruction of the base metals. In order for lead to become gold, it must first be stripped of its own properties, its characteristic color, density, fusibility, and reduced to a generic state. Again, this requirement should be understood against the background of Aristotle’s doctrine of substantial change, which taught that one substance could only transform into another through the mediation of their common material substrate (see Keyser 1990, 366). In this way, Maria brought the doctrines of alchemy in line with the stringent demands of Aristotelian natural philosophy. Even more remarkable is that Maria invented an apparatus specially designed for this objective. The kerotakis made possible a continuous exposure to the transformative vapors of sulfur and mercury. Restrained within the hermetically sealed vessel, these volatile spirits could now be effectively harnessed by the alchemist and forced to penetrate the depths of the metals. Only in this way could a true synthesis of opposites be realized: “If the bodies are not rendered bodiless, and if the incorporeals are not embodied—​and you do not make the two into one—​none of the objectives (prosdokōmenōn) will be achieved” (CAAG 2.93.14–​15). So long as the essential nature of the base metal persisted, the result was not a transmutation—​a genuine mixture in Aristotle’s sense—​but an accidental change.

734   Greco-Roman Science In the Natural and Mystical Topics, the ideal of transmutation is already present in germ. The goal of the art, pseudo-​Democritus says, is to harmonize the natures (CAAG 2.43.1), to synthesize the fixed and the volatile. But it was Maria who explained the actual conditions under which such a mixture of opposites was possible, and who set about to invent an apparatus and methodology appropriate to this task.

2.  Esotericism and Innovation in Alchemy 2.1 Revelation and Concealment: The Obscurity of the Ancients Greco-​Egyptian alchemy is represented by its practitioners as a sacred and divine art. Its doctrines are mysteries, protected by oaths of secrecy, and are thus accessible only through initiation (Mertens 1988). This esotericism is reflected in the frequent use of pseudonyms: the earliest texts (1st–​3rd centuries ce), many of them mere fragments, are attributed to sacred authorities, real or mythical, like Hermes Trismegistus, Ostanes, Isis, or Moses. This convention functions as a kind of prestige-​building device, but its motivation can hardly be accounted for in terms of the modern concept of forgery. It may well be that later authors were sometimes deceived and took these attributions at face value; but the intention behind attributing one’s works to Hermes or Ostanes—​ while concealing one’s own identity—​was surely to underscore the traditional character of the knowledge conveyed (see Kingsley 1993, 22–​23). Veneration of the ancient authorities and their books was an essential aspect of the alchemical ethos. On the face of it, the esotericism of alchemy may appear unfavorable to any kind of genuine scientific curiosity. One may be tempted to suppose, with Festugière, that the history of alchemy is marked by a decline into irrationalism. But the conclusions of the preceding section show otherwise. The idea of transmutation involved a subtle and creative appropriation of Aristotelian ideas, which were not obviously congenial to the alchemical project. Moreover, the effort to realize this theoretical goal inspired complex technical innovations. How, then, can we square the esotericism of alchemy—​its conservative and traditional dimension—​with the clear evidence of its theoretical and technical development over time? In truth, the alchemical attitude toward revelation and authority is a conflicted one. Though the alchemists regard their art as a divine wisdom, a persistent theme in the literature is the inaccessibility of this esoteric knowledge. For one thing, the ancients speak obscurely; they conceal the doctrines of the art under the veil of allegory and symbol. It is noteworthy that the three primary Byzantine manuscripts all preserve versions of an alchemical lexicon, which claims to present authoritative decodings of the various Decknamen, or cover names, employed by the ancient masters (CAAG 2.4–​17).

The Sacred Art of Alchemy    735 Why did the ancients speak so obscurely? For one thing—​and most obviously—​they were bound by oaths, which prevented them from revealing the art. While conceding this fact, Zosimus complains that some adepts take this secrecy to extremes. They are motivated less by sacred mandate than base human jealousy; a point stressed especially in the Syriac fragments (Fraser 2007, 37–​38). The alchemist Synesius (4th century) introduces a more strategic and edifying rationale for alchemical secrecy: the ancients have concealed the art to weed out lazy alchemists! In his commentary on pseudo-​ Democritus, he addresses the concept of the “divine water,” a mysterious reagent that has the power to dissolve metals into a primal liquid state. Sulfur is one of the ingredients—​ as reflected in double entendre of the Greek expression hydōr tou theiou (divine water or sulfur water). But so is mercury. Indeed, the divine water, like all the ingredients and operations of the art, has many names, reflecting subtle distinctions of use and composition (CAAG 2.58.24–​59.4). The intention behind this perplexing use of language is not merely to conceal, but “to exercise (gymnasēi) us and test our intelligence” (CAAG 2.59.4–​6). One begins to see that the alchemical understanding of initiation is not that of a passive transmission of doctrine. The secrets of the art can only be accessed by those who struggle with the work of transmutation, those with the right combination of exegetical skill and hard-​won experience. The exegetical and experimental dimensions are not opposed, but complementary (see Mandioso 2000, 481–​483; and Viano 2000, 458, who notes parallels with the Neoplatonic commentary tradition). The paradoxes confronted in exegesis motivate independent research; in turn, personal discoveries in the laboratory lead to the resolution of those paradoxes, affording a deeper insight into the secrets of the ancients. This point is illustrated in the oft-​discussed—​and, in my view, misunderstood—​ account of Democritus’ evocation of the shade of Ostanes. Festugière, in his classic analysis, drew attention to a number of Hellenistic topoi: (1) the frustrated and ultimately vain search for truth; (2) the realization that human reason is inadequate, and must be aided by revelation; (3) the use of magical operations to access divine secrets; (4) the discovery of a secret book in a temple. These elements seemed to confirm his guiding thesis that alchemy, like the other “occult sciences,” exemplified the decline of rationalism characteristic of the Imperial age (Festugière [1950] 2006, 229–​230). However, in dissecting the tale for evidence of this thesis, Festugière missed its message entirely. In the surviving excerpts of the story, we learn that Ostanes died before the initiation of Democritus was complete. Democritus summons the shade of his master to learn how to “harmonize the natures” (hopōs harmosō tas physeis, CAAG 2.43.1). But Ostanes tells him, “the daimōn will not permit it,” divulging only that his books are somewhere in the temple (43.2–​3). Now, note well that this is a failed attempt to secure supernatural guidance. Though the nature of the interfering daimōn is not explained, there is clearly some kind of barrier between this world and the spiritual realms. Nor is Democritus able to seek guidance in the books of Ostanes; for it turns out that these have been concealed in the temple until the son of Ostanes comes of age (43.7–​11). Democritus is left to his own devices. But, despite these obstacles, he and his fellow initiates succeed in “perfecting the synthesis of matter” (eteleiōsamen tas synthesis tēs hylēs, 43.12). It is

736   Greco-Roman Science only after succeeding through his own labors that the books of Ostanes are revealed to Democritus, and he is amazed to discover that they contain no instructions that he has not already discovered through his own experimentation. The only revelation is a cryptic formula, the famous maxim of Ostanes, which resounds throughout the alchemical corpus: “Nature delights in nature, and nature conquers nature, and nature rules over nature” (43.17–​21). Democritus notes admiringly how Ostanes drew together all his teachings in this simple formula (43.21–​22). Presumably it is only in the light of his own experience that Democritus can now appreciate how neatly the formula of Ostanes encapsulates the processes of the alchemical opus. The moral of this story confirms the interpretation of Synesius: the obscure formulae of the ancients are designed to motivate and test the initiate, and their inner meaning only becomes apparent in the light of independent research. The story does not illustrate a decline into irrationalism: it illustrates the complex and subtle interdependence of the esoteric and scientific dimensions of the alchemical worldview. In a later fragment from this pseudo-​Democritean text, the philosopher complains about the current crop of alchemists—​the “young” (neoi)—​and their disdain for the ancient writings. His explanation of their lack of reverence is telling: they refuse to put their faith in the writings due to their ignorance of matter (CAAG 2.47.4–​6). In their incomprehension, they conclude that the cryptic sayings of the ancients are mere fables (mythikon), rather than mysteries (mystikon, 47.14–​15). Whereas the true adept perseveres in the face of this obscurity, these irreverent moderns become careless in their work. They do not conduct a close examination (exetasis) of the different species of tincture, distinguishing between those that are volatile (pheukton), and those that penetrate and cleanse the inner depths (ta entos) of a metal (47.15–​23). In other words, they are lousy alchemists, unable to distinguish between imitation and transmutation. Alchemists who mock the books of the ancients will be equally reckless in their laboratory work. The same point is stressed by Zosimus in On the Letter Omega, his introduction to a now lost treatise on alchemical instruments (Mertens 1995, l). In the opening section, Zosimus complains to Theosebeia about a school of alchemists who have ridiculed a certain book “on furnaces and apparatus,” which he evidently holds in high esteem. Their disdain for this book and its technical complexities is tied to their misguided belief in the efficacy of “opportune tinctures” (kairikai katabaphai), reagents whose effects depend on astrological conditions (Mém. Auth. 1.11–​24). These lazy alchemists put all their trust in daimones, the ministering spirits of fate, which convey the influences of the stars and planets into the sub-​lunar realm. Following the lead of his Gnostic sources, Zosimus takes a very sinister view of these daimones, regarding them as malicious agents of the planetary archons, who seek to imprison the divine soul in the material body (Fraser 2004). He suggests that alchemists who rely on astrology, at the expense of proper technique, are enslaving themselves to these daimones, in exchange for vain material rewards. Here we encounter again—​and now in a more extreme form—​the idea that supernatural revelation is unreliable. The alchemist who puts his faith in the oracles of the daimones, at the expense of independent work, has no hope of success.

The Sacred Art of Alchemy    737 In the Final Quittance, Zosimus distinguishes opportune tinctures and “genuine and natural” (gnēsiai kai physikai) tinctures (366.12, 368.1: edition of Festugière [1950] 2006, citations by page and line). Whereas opportune tinctures depend on daimonic causes, natural tinctures are self-​regulating (automata, 366.21–​22). He claims that “in the time of Hermes” the secrets of the natural tinctures were well-​known; but the daimones become jealous and suppressed this knowledge, so that humans would be subjugated to their will (365.15–​21). Hermes managed to carve some information concerning these tinctures on stelae (366.11–​15), but he veiled them in a mystifying language (mystikōs). Indeed, even if one dared to descend into depths of the temples, he would have no chance of unlocking the secrets of these “symbolic characters” (symbolikois charaktērsin) without the correct key (365.22–​26). Zosimus imagines that the hieroglyphs on the old temples contain fragments of a forgotten alchemical wisdom. There is an imagined rupture between the mythical time of Hermes and the Egypt of Zosimus, now plagued by predatory daimones, which seek to subvert the work of alchemy. This nostalgia for the lost wisdom of the ancients reflects a historical reality: under Roman occupation the temples were in steady decline, and knowledge of the hieroglyphic script was almost extinguished (Frankfurter 1998, 27–​ 30, 248–​249). For Zosimus, alchemy is part of this decaying heritage, and it falls to the modern adepts to reconstruct its surviving traces. The following anecdote—​ironically, itself a mere fragment—​seems to illustrate this situation: “At the ancient sanctuary of Memphis, I saw a furnace lying in pieces, which not even the initiates of the sacred rites (hoi mystai tōn hierōn) could figure out how to assemble” (Mém. Auth. 7.8–​10). Even the priests have forgotten the art, just as they have forgotten the true meaning of the hieroglyphs. While, in an ideal sense, alchemy is a timeless and unalterable wisdom, that wisdom is no longer immediately accessible to the aspiring alchemist. The only way forward is to struggle with the work against all obstacles, as Olympiodorus states in a comment on Zosimus: “Wise men are sought and the writings lack true knowledge. The multiplicity of matter confounds us. Such a work is accomplished only with great toil” (CAAG 2.86.2–​4). In order to crack the code of the ancients, the adept must master the disciplines of laboratory work. On both levels—​exegetical and experimental—​the alchemist is trying to bring about a synthesis of disparate materials: in the laboratory, he seeks to synthesize the bodies and the vapors; in his exegesis, he seeks to reconstruct the fragments of the ancient wisdom. In this work, he is motivated by the conviction that there is a unified doctrine concealed behind the paradoxical and often conflicting maxims of the old masters, a single art mirroring the unity of the divine: “the Art is one, even as God is one” (CAAG 2.83.22).

2.2 Rethinking Zosimus In the historiography of Festugière, the alchemy of Zosimus exemplifies the decline of the art into a “mystical religion.” This view has become commonplace: Zosimus is

738   Greco-Roman Science regarded as a mystic, for whom the techniques of alchemy are symbols of an inner process of spiritual transformation (e.g., Fowden 1995, 123). Admittedly, there are aspects of Zosimus’ spiritual orientation that are hard to reconcile with the practical aims of alchemy. His appropriation of Gnostic sources leads him, at times, to express a very negative view of embodiment. In a frequently cited passage, he exhorts Theosebeia to “spit on matter” (tēs hylēs kataptyson) and hasten back to God once she has realized the natural tinctures (367.27–​368.4:  edition of Festugière [1950] 2006, cited by page and line). He suggests that the practice of natural alchemy culminates in spiritual purification: “Operate in this way until you have perfected your soul” (heōs an teleiōthēs tēn psychēn, 368.1–​2). In his enigmatic “Visions,” the alchemical vessel becomes a kind of baptismal font (“a bowl-​shaped altar,” Mém. Auth. 10.18) in which metal-​men are decomposed and regenerated. The immersion of metals into divine waters (baptein, to dye) is likened to the baptism of a neophyte (baptizein). Just as the alchemist sought to bring about a permanent transformation of the base metals, so baptism was understood as a spiritual regeneration of the initiate (Fraser 2007, 41–​43; cf. Charron 2005, 442). The Sethian Gnostics, whose texts Zosimus has clearly studied, transformed the rite of baptism into a visionary rite of ascent, culminating in enlightenment (gnōsis) and union with the divine (Fraser 2007, 45–​49). The Gnostic initiate was divested of the “garments” of embodiment as he ascended into the cleansing “waters” of the intelligible world or “divine fullness” (plērōma). Likewise, Zosimus compares the decomposition of the base metals to the crucifixion of the “outer man,” which liberates the pneumatic essence or divine spark of the initiate (Mém. Auth. 1.121–​132). Taken at face value, such passages suggest that Zosimus has abandoned the quest to perfect nature and has adopted an anticosmic spirituality, in which alchemical concepts serve merely as illustrative metaphors. The objective now, it seems, is to escape from the material world and the clutches of the oppressive archons. However, the situation is not so straightforward. Of all the works of Zosimus, it is Omega that contains the most evident appropriations of Gnostic materials. Yet, as we have seen, this work is intended as an introduction to a technical treatise on apparatus. How does an otherworldly quest for gnosis lead to a preoccupation with the correct operation of furnaces? The paradox is only apparent. We must recall that the Gnostic materials are deployed in the context of a polemical critique of a competing school of alchemists, who rely on astrology at the expense of proper technique. In order to rebut this astrological alchemy, Zosimus paints a thoroughly Gnostic picture of the cosmos and its malefic ruling archons. He sets the groundwork for a purely natural alchemy by undermining all forms of supernatural mediation—​ astrological or daimonic—​and forcing the alchemist to fall back on his own resources. Though I would not go so far as to claim (with Letrouit 2002, 88) that Zosimus’ appropriation of Gnostic ideas is merely polemical, it does serve a strategic function in Omega. His Gnostic presentation appeals to anxieties about astral determinism prevalent in the late ancient world.

The Sacred Art of Alchemy    739 Zosimus is not always so dismissive of the role of astral influences in alchemy. In the “Visions” he proclaims, “as nature is influenced by the moon according to the measure of time, [the art] takes account of the diminution and increase through which nature swiftly passes” (Mém. Auth. 10.11–​16). Inasmuch as alchemy imitates the processes of nature, it must observe lunar phases, which govern the processes of generation and decay in the sub-​lunar world. Just as the moon undergoes a cycle of waxing and waning, so the lead of the alchemist must first be decomposed before it is transformed into silver, the lunar metal. The alchemist must understand the relations of cosmic sympathy through which earthly beings, including the metals, are connected with celestial phenomena. Zosimus here endorses the Hermetic and Neoplatonic idea that terrestrial processes mirror the motions and juxtapositions of the stars and planets:  “Heaven gives and the earth receives” (Mém. Auth. 10.84). The cosmos is envisioned as a living entity, bound together by invisible webs of sympathy and antipathy. The alchemist must follow the method (methodos) of nature if he is to succeed in the work: “Without method, the connection and disconnection of all things and the continuity (syndesmos) of the whole do not arise” (10.91–​93). There is no hint in the “Visions” of the demonized cosmos of the Sethian Gnostics—​no rupture between heaven and earth. Zosimus’ attempts to integrate Gnostic conceptions into his essentially Hermetic worldview are not entirely successful, chiefly because the idea of a fallen material cosmos is alien to the teachings of Hermes, which are premised on the fundamental unity of the cosmos (see Fraser 2007, 50–​51). It is this latter conception that forms the proper basis of the alchemical project, which aims not merely at the destruction of matter, but its regeneration. The image of Zosimus as a mystic, no longer preoccupied with the technical development of alchemy, must be rejected. Such a view only appears plausible if one exaggerates the significance of the “anticosmic” elements in his philosophical system and fails to appreciate their polemical function: in Omega, as we have seen, Gnostic arguments are deployed (somewhat ironically) in defense of a purely natural alchemy. Moreover, the Gnostic and “other-​worldly” tendencies of Zosimus must be balanced with other statements, in the “Visions” and elsewhere, more in line with Hermetism and its cosmic spirituality, and more congenial to alchemical practice as traditionally conceived. If we approach the alchemical texts with rigid distinctions between science and mysticism, or rationality and irrationality, we have little hope of grasping what the art meant to its practitioners. We end up with the hazy and unhelpful category of pseudo-​ science—​or, as Festugière calls it, “occult science.” Alchemy thus appears, from the start, as an incoherent amalgam of mystical and scientific goals. The label of “occult science” glosses over the subtle and quite fascinating interrelations of esotericism and science that define the alchemical worldview and which, it is hoped, this chapter has brought into clearer focus.

740   Greco-Roman Science

Abbreviations CAAG 2 = Berthelot and Ruelle. Collection des anciens alchimistes Grecs II: Texte Grec (cited by page and line). Mém. Auth. = Zosimus, Mémoires Authentiques. Greek text and translation in Mertens 1995 (cited by tractate and line). P. Leid. = Leiden papyrus X, Greek text and translation in Halleux 1981. Papyrus Holmiensis = Stockholm papyrus, Greek text and translation in Halleux 1981.

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The Sacred Art of Alchemy    741 Keyser, Paul T. “Alchemy in the Ancient World:  From Science to Magic.” Illinois Classical Studies 25.2 (1990): 353–​372, plus plates, figures 1–7. Kingsley, Peter. “Poimandres: The Etymology of the Name and the Origins of the Hermetica.” Journal of the Warburg and Courtauld Institutes 56 (1993): 1–​24. —​—​—​. “From Pythagoras to the Turba Philosophorum: Egypt and Pythagorean Tradition.” Journal of the Warburg and Courtauld Institutes 57 (1994): 1–​13. Letrouit, Jean. “Chronologie des alchimistes grecs.” In Alchimie:  art, histoire et mythes, ed. Didier Kahn and Sylvain Matton, 11–​93. Paris: Société d’étude de l’histoire de l’alchimie, 1995. —​—​—​. “Hermetism and Alchemy:  Contribution to the Study of Marcianus Graecus 299.” In Magia, alchimia, scienza dal ‘400 al ‘700, ed. Carlos Gilly and Cis van Heertem. Florence: Centro Di, 2002. Lloyd, G. E. R. Aristotelian Explorations. Cambridge: Cambridge University Press, 1996. Lucas A., and J. R. Harris. Ancient Egyptian Materials and Industries. 1962. Mandioso, Jean-​Marc. “Commentaire Alchimique et Commentaire Philosophique.” In Le commentaire entre tradition et innovation, ed. M. O. Goulet-​Cazé and T. Dorandi, 481–​491. Paris: Vrin, 2000. Martelli, Matteo. “‘Divine Water’ in the Alchemical Writings of Pseudo-​Democritus.” Ambix 56.1 (March 2009): 5–​22. —​—​—​. Pseudo-​Democrito. Scritti alchemici con il commentario di Sinesio. Textes et Travaux de Chrysopeia 12. Milan: Archè, 2011. —​—​—​. “The Alchemical Art of Dyeing: The Fourfold Division of Alchemy and the Enochian Tradition.” In Laboratories of Art: Alchemy and Art Technology from Antiquity to the 18th Century, ed. Sven Dupré, 1–​22. New York: Springer, 2014. Martelli, Matteo, and Maddalena Rumor. “Near Eastern Origins of Graeco-​Egyptian Alchemy.” In Esoteric Knowledge in Antiquity, ed. Klaus Geus and M. Geller. Berlin:  Max Planck Institute, 2014, 37–​62. Martin, Craig. “Alchemy and the Renaissance Commentary Tradition on Meteorologica IV.” Ambix 51.3 (Nov. 2004): 245–​262. Mertens, Michèle. “Une scène d’initiation alchimique:  La lettre d’Isis à Horus.” Revue de l’Histoire des Religions 205.1 (1988): 3–​24. —​—​—​. Les alchimistes Grecs. Tome IV, 1re partie: Zosime de Panopolis, Mémoires Authentiques. Paris: Belles Lettres, 1995. —​ —​ —​ . “Alchemy, Hermetism and Gnosticism at Panopolis c.300 ad:  The Evidence of Zosimus.” In Perspectives on Panopolis—​an Egyptian Town from Alexander the Great to the Arab Conquest, ed. M. Egberts et al., 165–​175. Leiden: Brill, 2002. —​—​—​. “Graeco-​Egyptian Alchemy in Byzantium.” In The Occult Sciences in Byzantium, ed. Paul Magdalino and Maria Mavroudi, 205–​230. Geneva: La Pomme d’Or, 2006. Newman, William R. “Corpuscular Alchemy and the Tradition of Aristotle’s Meteorology, with Special Reference to Daniel Sennert.” International Studies in the Philosophy of Science 15.2 (2001): 145–​153. Ogden, Jack. “Metals.” In Ancient Egyptian Materials and Technology, ed. Paul T. Nicholson and Ian Shaw, 148–​176. Cambridge: Cambridge University Press, 2000. Principe, Lawrence M. “Alchemy Restored.” Isis 102.2 (June 2011): 305–​312. Quispel, Gilles. “Gnosis and Alchemy: The Tabula Smaragdina.” In From Poimandres to Jacob Böhme: Gnosis, Hermetism and the Christian Tradition, ed. R. van den Brock and Cis van Heertem, 303–​333. Amsterdam: In de Pelikaan, 2000. Sheppard, H. J. “Gnosticism and Alchemy.” Ambix 6 (1957): 86–​101. Taylor, F. Sherwood. “A Survey of Greek Alchemy.” Journal of Hellenic Studies 50.11 (1930): 109–​139.

742   Greco-Roman Science Viano, Cristina. “Aristote et l’alchimie Greque.” Revue d’Histoire des Sciences 49 (1996): 189–​213. —​—​—​. “Quelques aspects théorétiques et méthodologiques des commentaires alchimiques Gréco-​Alexandrins.” In Le Commentaire entre tradition et innovation, ed. M. O. Goulet-​Cazé and T. Dorandi, 455–​464. Paris: Vrin, 2000. —​—​—​. “Les alchimistes Gréco-​Alexandrins et le Timée de Platon.” In L’alchimie et ses racines philosophiques: La tradition greque et la tradition arabe, ed. C. Viano, 91–​107. Paris: Vrin, 2005.

chapter D8

Physio gnomy Mariska Leunissen

1. Introduction Physiognomy (from the later Greek physiognōmia, which is a contraction of the classical form physiognōmonia) refers to the ancient science of determining someone’s innate character on the basis of their outward, and hence observable, bodily features. For instance, Socrates’ famous snub nose was universally interpreted by ancient physiognomists as a physiognomical sign of his innate lustfulness, which he overcame through philosophical training. The discipline in its technical form with its own specialized practitioners first surfaces in Greece in the 5th century bce, possibly through connections with the Near East, where bodily signs were taken as indicators of someone’s future rather than his character. The shift to character perhaps arises from the widespread cultural practice in the ancient Greek and Roman world of treating someone’s outward appearance as indicative for his personality, which is already visible in Homer (8th century bce). In the Iliad, for instance, a description of Thersites’ quarrelsome and repulsive character is followed by a description of his equally ugly body (see Iliad 2.211–​219), suggesting that this correspondence between body and character is no accident. Thersites is thus the perfect foil for the Greek ideal of the kaloskagathos—​the man who is both beautiful and good. The same holds for the practice of attributing character traits associated with a particular animal species to a person based on similarities in their physique: it is first formalized in physiognomy but was already widely used in a nontechnical way in ancient literature. The most famous example of the latter is perhaps Semonides of Amorgos’ satire of women (fr. 7 On Women; 7th century bce), which profiles 10 different women types, mostly by reference to their similarities to animal species: thus, one woman type is filthy and fat as the sow; another is charmless, sex crazed, and criminal as the weasel; and yet another is deformed and shameless as the ape. Only the bee woman stands out positively for her modesty and industriousness.

744   Greco-Roman Science The encompassing nature of physiognomical thought in antiquity, both crystallized in the form of technical handbooks and in its informal uses in literature, historiography, philosophy, medicine, and rhetoric can be gleaned from Förster’s two-​volume edition Scriptores physiognomonici Graeci et Latini ([1893] 1994), which is still the most comprehensive collection of ancient physiognomical material available (for an updated edition and translation of the physiognomical handbooks in English, see Swain 2007a). This chapter focuses more narrowly on physiognomy as a formalized, technical discipline (for an overview of physiognomical practices in Greek and Roman literature, see Evans 1969; Sassi 2001), but it should be noted from the outset, physiognomy never operated in a scientific or cultural vacuum. In the extant source material, the most thorough theoretical discussions of physiognomy are provided either by philosophers, who worried about the validity of physiognomical inferences or the identification of signs, and whose theories about the relation between body and soul allowed physiognomy to be used as a diagnostic tool for the prediction of the moral potential of prospective students, or by physicians, who found in physiognomy a cognate way of reading the human body, and integrated medical diagnoses and prognoses with moral ones. Similarly, the handbooks we have are written by men who were primarily philosophers, physicians, or even rhetors, who appropriated physiognomy for improving the delivery of their speeches but also for being more effective in the (negative) characterization of others as part of a political strategy. In the sections below, I first provide an overview of the most important physiognomical sources (sect. 2), followed by a discussion (in sec. 3) of the assumptions and methods of reasoning used in physiognomical science. The close relationship between physiognomy and philosophy, medicine, and rhetoric is the topic of sections 4–​5.

2.  Physiognomical Sources and Handbooks According to our sources, physiognomy first became a topic of theoretical reflection toward the end of the 5th century bce. Antisthenes, a follower of Socrates and head of the Cynics, is reported to have written a Physiognomical Treatise on the Sophists (mentioned by Diogenes Laërtius 6.16), which unfortunately is lost, and we know almost nothing of its contents (perhaps it offered an attack of physiognomical diagnoses offered by the sophist: see Tsouna 1998). The oldest extant material roughly consists of two categories: discussions focusing on the methods of physiognomy stemming from the 4th and 3rd centuries bce, written by Aristotle and his students; and handbooks focusing on the collection of physiognomical signs from the 4th century ce, preserving—​ in various forms—​a treatise by the physician Loxus from probably the 3d century bce (although see Misener 1923 for an earlier date) and a rhetorical treatise by the rhetor Polemon of Laodicea from the Second Sophistic (2nd century ce).

Physiognomy   745 The oldest theoretical discussion of physiognomy can be found in ­chapter 2.27.70b7–​ 38 of Aristotle’s Prior Analytics, dating from the 4th century bce. In the last five chapters of this treatise, Aristotle explains how the validity of nondeductive types of reasoning, such as inductions or inferences from signs or probabilities (the so-​called enthymemes, which are often used in rhetorical contexts and yield persuasion rather than truth), can be tested. According to Aristotle, these nondeductive inferences are logically valid if they can be resolved into the syllogistic figures he had previously established. Physiognomical inferences are discussed at the very end (Prior Analytics 2.27.70b7–​38), and although there is no explicit link between the preceding discussion of sign inferences and this section (it has been suggested that the physiognomical section is unrelated or a later appendix: see Burnyeat 1982 and Smith 1989), it expresses the same interest in showing the potential validity of a nondeductive type of reasoning that is apparently prevalent in Aristotle’s time. By using an example of a physiognomical inference that takes its signs from animals, Aristotle lays out the conditions under which “it is possible to physiognomize” (see sec. 3) and argues that physiognomical inferences are valid as long as the proof is in the first figure (i.e., all premises must consist of universal affirmative propositions and the syllogism must have the form “A belongs to all B, B belongs to all C, therefore A belongs to all C”), just as he had argued earlier in the chapter with regard to other types of sign inferences. Aristotle’s treatment of physiognomy in the Prior Analytics opens the door to a scientific use of the discipline, but it is not clear whether he endorses it himself: Aristotle’s use of conditional language—​it is possible to physiognomize if certain conditions are met—​warrants caution. However, given his inclusion of physiognomical material in the biological treatises (in the History of Animals 1.8.491b9–​11.492b4, Aristotle lists physiognomical signs along with functional descriptions of parts on the human head; see sec. 3 below), it looks like Aristotle incorporated physiognomy as a valid way of reasoning into his own philosophy. The oldest physiognomical handbook that has been preserved is the Physiognomy, falsely attributed to Aristotle (see pseudo-​Aristotle Physiognomy, 1.805a1–​6.814b9). The handbook, which consists of two parts, stems most likely from the 3rd century bce, and it was written by two Peripatetic authors who were each responsible for their own text (see Boys-​Stones 2007, pace Vogt 1999 who believes that the handbook was written by one author at two different stages in his life). Treatise A (so labeled in Förster’s [1893] 1994 collection) runs from 1.805a1 to 3.808b10. It opens by stating that mind and body are mutually affected by each other, offers examples of these mutual affections, criticizes the three existing physiognomical methods for identifying signs (from animals, human ethnicities, and expressions of emotion: on these methods, see further in sec. 3), and argues for a modified form of animal physiognomy. It also provides a detailed list of those aspects of the body that can constitute physiognomical signs, and lists 22 characters traits and the signs by which they can be recognized. Treatise B runs from 4.808b11 to 6.814b9 and similarly opens with a preface confirming the “sympathetic” (sumpathein) relationship between body and soul and a list of examples illustrating their causal dependency. It continues by discussing the problems and difficulties in

746   Greco-Roman Science using the method of animal physiognomy; introduces the idea that for doing this type of animal physiognomy appropriately, the animal kingdom should be divided into two classes, that is, the male and the female; and offers a list of body parts and the characters they signify (moving from foot to head, and then on to gait, voice, and stature). The methodology put forward in both treatises, as we will see in sec. 3, is quite sophisticated and roughly Aristotelian in nature. The attribution of the treatises to Aristotle is therefore quite understandable: both treatises open by responding to the condition formulated by Aristotle in the Prior Analytics that the body and soul must change simultaneously for physiognomy to be possible, and they make use of similar technical terms borrowed from Aristotle in their methodological sections (see Boys-​Stones 2007 on the convergences between the three authors). In addition, both Pliny (Natural History 11.273–​274) and Diogenes Laërtius (5.25) believed that Aristotle had written a physiognomical treatise, so that already in antiquity the oldest extant handbook was simply attributed to him. The handbooks from the 4th century ce preserve older sections of handbooks originally written by two different authors, Loxus and Polemon. From the handbook on physiognomy by the physician Loxus from the 3rd century bce, we only possess a couple of fragments, translated from its original Greek into Latin and scattered through various chapters of the eclectic Book of Physiognomy, or Liber Phisiognomoniae, from the 4th century ce (for the Latin text of this handbook with translations, see André 1981 and Repath 2007b, who both rely heavily on Förster 1893; see also Origen, Against Celsus 1.33). The author of the Book of Physiognomy—​who was once falsely identified as Apuleius—​is unknown and is henceforth referred to as “Anonymus Latinus.” The handbook opens with a reference to the three sources the author drew his material from: “I had at hand the books of three authors who have written on physiognomy, Loxus the physician, Aristotle the philosopher [the reference is to the pseudo-​Aristotelian handbook], and Palemon [sic; the author appears not to have known Polemon’s real name:  see Repath 2007b] the rhetor.” However, few sections are derived from the pseudo-​Aristotelian handbook or from Loxus, leaving us with relatively little information about Loxus for whom this treatise is our only source (Anonymous Latinus 1, 2, 12, 48, 80–​81, 89, 117–​131, and 133 uses Loxus; Boys-​Stones 2007 argues for the additional inclusion of ­chapters 13–​15). As with Loxus’ handbook, the original Greek handbook that constitutes perhaps the greatest masterpiece in ancient physiognomy, so also Polemon’s Physiognomy from the 2nd century ce is lost. However, due to its continued importance and usefulness for physiognomical practice both in the Second Sophistic society and in Arabic physiognomy, its contents have survived in a variety of independent sources and translations (see the appendix at the end of the chapter for the five most important source materials on Polemon’s Physiognomy). From these sources it appears that Polemon was uninterested in the logical form of physiognomical inferences or in the relation between body and soul, both of which preoccupied the Aristotelian treatments of physiognomy (on the contents and methods of Polemon’s Physiognomy, see Barton 1994; Swain 2007b). Instead, his handbook is mostly a collection of physiognomical signs, accompanied

Physiognomy   747 with ethnic and psychological portraits of his contemporaries drawn from his personal observations of them. Unusual attention is paid to the physiognomical signs of the eye (Polemon’s Physiognomy probably consisted of two books, the first of which was entirely devoted to the eye), which Polemon claims are the most important among signs and which require his expertise to be clearly distinguished. On the surface, the handbook appears to be have been written for the sake of the rhetorical training of students in how to recognize physiognomical signs, but the mostly negative characterization of his contemporaries in it suggest that Polemon may also have used physiognomy for the purpose of invective and the betterment of his status. In addition to these extended theoretical discussions of physiognomy in handbooks, there are many other relevant passages and remarks preserved in the ancient corpus about the science of physiognomy; the most interesting of these will be discussed in the sections 4–​6 below, but let me first present the scientific assumptions and the methods of reasoning used in physiognomy according to the sources discussed above.

3.  The Scientific Assumptions and Methods of Physiognomy The main method of reasoning used in physiognomy is that of induction: once the physiognomical signs of the human body have been identified, the corresponding character traits can simply be inferred, while knowledge about the significance of bodily signs for character is derived by analogy from one or more of the following three domains. First, in what is purportedly the oldest physiognomical method, practitioners of animal physiognomy rely on parallels between the human body and that of animals (for instance, lions have distinctively long extremities and are courageous in character; a person with exceptionally long extremities must therefore also possess the corresponding character trait, which is courage). Second, physiognomists of the ethnologist kind rely on parallels between the person being physiognomized and the physical characteristics of human ethnic groups (thus, a person who possesses red hair like the Scythians must also be rash and quick to anger like the Scythians). And third, physiognomists of the pathological kind rely on parallels between that person and the physical characteristics of people undergoing strong emotions or passions (e.g., a person with a permanent snarling grin on his face must have a surly character). This type of reasoning raises many methodological questions, such as which (combination) of these domains one is supposed to use, how each of the individual signs is to be identified, and what forms of physiognomical inferences are actually valid, all of which come up in the oldest extant theoretical discussions of physiognomy. As mentioned, Aristotle is interested in the logical validity of physiognomical inferences in the Prior Analytics, but he also formulates conditions for the possibility of physiognomy that express other—​ontological and epistemological—​concerns, all

748   Greco-Roman Science of which are also addressed by the later Peripatetic authors of the Physiognomy. The first condition Aristotle imposes for physiognomy to be possible is that the body and soul must be changed simultaneously by natural affections. This is an ontological condition: for physiognomical signs to be true, certain parts of reality, namely body and soul, must be structured in a certain “sympathetic” way. Aristotle does not expand on the details of this kind of theory of body and soul that underlies physiognomy—​or whether he endorses it: certainly his hylomorphic psychology makes physiognomy a practicable scientific enterprise (see Boys-​Stones 2007). The Peripatetic authors, however, explain that this sympatheia between body and soul entails not only an ontological interdependence of the two, which explains why natural affections of the one simultaneously cause alterations of the other, but also some kind of natural unity between the two, which explains why specific body types always go together with their own appropriate character types and vice versa. Neither of the two Peripatetic authors specify their own causal theory about this sympathetic relation: given their examples, the author of Treatise A may have been what we now call an epiphenomenalist, that is, someone who considered the physiological conditions of the body to be the cause of psychological character traits, whereas the author of Treatise B seemed to have held the opposite view (see again Boys-​Stones 2007). Nevertheless, both start out by affirming that there indeed exists such a relation, which is all that is needed to make physiognomy possible. Aristotle combines his formulations of the second and third requirements: he states there must exist one distinctive or proper (idion) sign for each affection (again an ontological requirement) and it must be possible to grasp these distinctive signs for each affection (an epistemological requirement). Assuming there is one distinctive bodily sign for each affection of the soul or character trait, we need a method for getting to know the relevant signs and for being able to tell with which affection or trait they correlate. Aristotle clarifies this method with an example from animal physiognomy, with which he must have been familiar from contemporary practices (in his Generation of Animals 4.3.769b20–​21, Aristotle provides one of the earliest references to physiognomical activity in Athens when he mentions “a certain physiognomist” who “reduced all faces to those of two or three animals”). Let us suppose that the distinctive sign for courage in lions is having large extremities, where the sign is distinctive because it only belongs to the species of lions as a whole. However, the bodily feature of having large extremities may also belong to individuals of other animal kinds, such as a man (as long as it does not belong to that animal kind as a whole, otherwise the sign would no longer be distinctive), in which case the corresponding character trait, courage, will also be present in those individuals. Thus, for physiognomy to be possible, one first needs to be able to collect all distinctive signs from animals that have a particular, distinctive character trait. The case gets more complicated when an animal kind as a whole has two distinctive affections, such as lions being both courageous and generous. For, as Aristotle points out, how can we know which bodily feature is the sign for which character trait? The answer for this problem is to search for other individual

Physiognomy   749 animals to which one of the two character traits—​but not the other—​belongs, and to see what distinctive bodily feature they have: for instance, if a man is brave but not generous, and he has long extremities, long extremities must be a sign of braveness, but if he has some other distinctive bodily feature, long extremities must be a sign of generosity. Compared to the methodological discussions of how to select signs in the pseudo-​ Aristotelian Physiognomy, Aristotle’s discussion here seems much less sophisticated:  although all three authors share a common concern for the identification of signs proper to one animal species as opposed to common ones, the Peripatetic authors exhibit knowledge of other (possibly later) physiognomical methods of selecting signs besides that of using animals, and even their use of the animal method is more critical and refined. The first author criticizes the selection of signs by animal physiognomists who search for signs that are distinctive for one animal species only. As he points out, human features are never completely like those found in one kind of animal, but form a resemblance to several of them, and only very few signs are distinctive for individual animal kinds to start with—​most signs are common to many animals. He therefore proposes, “instead, it is necessary to select [signs] from as many animals as possible, and from those that do not have any affection in common in their mindset except for the one of which we search the signs” (Physiognomy 1.806a4–​6). The author of the second treatise adds the condition that one must first divide the animal world into males and females and then collect the physical and mental attributes fitting with these two. He also introduces the idea—​absent from both Aristotle and Treatise A—​of “congruity” or “fittingness” (epiprepeia) between the sign and the character trait it signifies as a criterion for judging how to interpret a certain physiognomical sign in a person (for instance, the pale skin that indicates fear is only slightly different from pale skin that indicates bodily fatigue, so that only those experienced with the congruity between signs and signified will be able to tell the difference and determine quickly and correctly whether a person is scared or fatigued) and in collecting signs (signs must stand out as being congruous with the character traits they signify, for instance, hair falling onto foreheads and reaching down to one’s nose signifies servility, as “this kind of appearance is fitting to a slave”; Physiognomy 6.812b36–​813a2). Note that the deeper epistemological question about whether we can in fact know the characterological contents of the souls or minds of others is raised by none of these authors: it is simply taken for granted that one can, as is the related ontological presupposition that souls/​ minds have content or exist at all (see Tsouna 1998:  apparently the ancients rarely expressed doubts about other minds). The fourth condition pertains to the logical validity of physiognomical inferences. According to Aristotle, “it is possible to physiognomize in the first figure when the middle term [B]‌converts with the first extreme [A], but extends wider than and does not convert with the third extreme [C]” (Prior Analytics 2.27.70b32–​34). Aristotle had already explained why the inference has to be drawn in the first figure: only the use of the first figure gives rise to valid inferences from signs and to arguments that count as

750   Greco-Roman Science evidence in those cases in which the signs are in fact universally true. The lion example, in its formalized form, is used to illustrate the further requirements: A belongs to all B

[and: B belongs to all A]

B belongs to all C

[and: B belongs to some D]

A belongs to all C

courage belongs to all that has large extremities [and: vice versa] having large extremities belongs to all lions [and: to some men] courage belongs to all lions [and: to some men]

First, in the minor premise of the form “B belongs to all C,” where B picks out the physiognomical sign and C picks out the animal species from which the sign is taken, the sign picked out must belong to the whole animal species, but its scope must also extend to some other animals, although not to that other animal species as a whole. If the terms were to be convertible (for instance, if all animals with large extremities were lions), the sign would be a unique sign for that species and could not be used to draw inferences about the presence of its concomitant affection in other animals. Second, regarding the major premise of the form “A belongs to all B,” where A picks out the character trait for which the sign (B) is indicative, Aristotle explains that the sign must belong to all animals that are courageous, and conversely, that all animals that are courageous must have the concomitant sign, otherwise, there would not be one sign for one character trait. If, then, the sign is true, one can infer from the presence of long extremities in a person that he is courageous. The two Peripatetic authors do not discuss the details of physiognomical syllogisms in the way Aristotle does, but they do affirm the usefulness of syllogisms in physiognomy. The author of Treatise A points to the unique capacity of philosophers to understand “that when certain premises are given, something else necessarily follows,” which is exactly how Aristotle defines syllogistic reasoning. This author claims we should rely on this method of reasoning in his alternative, “never been tried” method of physiognomy according to which one infers a character trait indirectly from the observation of the presence of the sign of a second character trait with which the presence of the first is necessarily connected (e.g., one can infer that a person is envious from seeing that he has the physiognomical sign for irascibility, since the disposition for irascibility presupposes the existence of envy in that person; Physiognomy 2.807a3–​10). The method is also endorsed by the author of Treatise B, who similarly refers to the use of syllogisms in the selection of signs (4.809a19–​25). The handbooks of Polemon and Loxus are first and foremost practical manuals, influenced by the rhetorical practices of the time, and show much less concern for the epistemological, ontological, and logical issues raised in the Peripatetic treatises (on the absences of philosophical themes in Polemon, see Ghersetti 2007). However, the handbooks of the Second Sophistic make use of the same forms of inferential reasoning (reflected in the enthymeme-​like structure of the descriptions of signs and their significances) and similarly emphasize the need for collecting and combining

Physiognomy   751 signs carefully (on methods used by Polemon, see Barton 1994 and Swain 2007b). For instance, when addressing the interpretative question of how to deal with multiple, opposing signs in one person, Polemon’s advice is to memorize his version of the hierarchy of parts (according to which eyes come first, then the other parts on the face, then the neck, chest area etc. until one reaches the feet) and assign more value to the signs from the more important parts and most to the eyes. (Note that Polemon’s ordering of the parts from head to foot here follows the standard practice in ancient medicine, but that this was not necessarily also the standard in physiognomy: pseudo-​Aristotle B and Adamantius, for instance, use the foot-​to-​head ordering of bodily parts. Why these latter authors deviate from the medical ordering of parts, and why physiognomy uses two distinct orders, is unclear.) For the eyes are “the gateway to the soul” (see Adamantius A4), “sum of all physiognomy,” and the basis of the physiognomists’ “whole authority” (see Anonymus Latinus 20). Other methodological remarks pertain to techniques that will be of practical use: one must not warn the person whom one is about to physiognomize beforehand (he may deliberately change his signs: Adamantius A4) and be careful about using signs from physical attributes like color, movement, voice, and hair (making “correct judgment” of a person by using these signs only works in combination with other, more significant signs: see Leiden B31). Polemon also adds a new practice to the repertoire of the Greek physiognomist: providing predictions of the future. In the last three chapters of his Physiognomy, Polemon describes among others how he was able to foretell a great evil was about to happen to a woman he saw in a temple (moments after predicting her impending evil, the woman was told that her daughter had drowned) and how he predicted abductions at weddings (Leiden B53). His methods in forming these prognoses involve not only the trusted physiognomical method of interpreting bodily signs but also assessing other, situational indications and reading people’s intentions (cf. Anonymus Latinus 133): physiognomy practiced in this way thus shares close affiliations to the contemporary, prognostic disciplines of astrology and medicine. The connections between physiognomy and ancient medicine will be explored further in section 5, but let me first say more about the philosophical interest in physiognomy beyond its particular method of reasoning.

4.  Diagnostic Uses of Physiognomy in Ancient Philosophy As I suggested in the introduction, the practice of reading the body for signs probably arrived in Greece via the Near East, where bodily signs were treated as having prophetic significance (on the Mesopotamian sources, see Barton 1994 and Bottéro 1974.) The earliest historic practitioners of physiognomy in Greece appear to have been of Near Eastern origin, and, interestingly, the person who is being physiognomized by these foreign physiognomists is the most famous Greek philosopher—​and the notoriously ugly—​Socrates.

752   Greco-Roman Science According to one story, an anonymous Syrian magus traveled to Athens, where he used physiognomy—​in accordance with the Near Eastern practice—​to predict Socrates’ future violent death (Aristotle, F 32 Rose3). In a different story, the physiognomist Zopyrus (who might have been Persian, but it is also possible that Zopyrus and the Syrian magus were actually the same person), used physiognomy—​perhaps in a manner already reflecting the Greek obsession with character rather than with future—​ to diagnose Socrates as a man of many vices, low intelligence, and as being addicted to womanizing (or pederasty, in the version of Cassian, Conferences 13.5). The latter story is preserved in fragments of a Socratic dialogue called Zopyrus by Phaedo of Elis (see fr. 6–​11 Rosetti), which present an unexpected twist on the scene familiar from Plato’s dialogues in which Socrates reveals the ignorance of a sophist. Here, instead of joining his friends in laughter or ridiculing Zopyrus’ sophistic art (Socrates was known to be a model of virtue and a seeker of wisdom: surely Zopyrus’ physiognomical diagnosis must have been wrong), the fictional Socrates states that Zopyrus was right about his natural character traits. He then points to the power of philosophy, which helped him overcome those bad innate characteristics in one way or another. According to most sources, it was to be able to act virtuously: the idea seems to be that a well-​trained reason can overrule bad inclinations and desires grounded in our innate nature and thereby steer our actions toward the good. But according to Cicero’s version (fr. 6 Rosetti), it was rather to transform his nature to become a virtuous man, by habituating and thereby permanently changing his innate character traits. This anecdote about Zopyrus and the seeming paradox about Socrates’ outward ugliness and inward beauty remained a famous test case in the debates about the validity of physiognomy well beyond antiquity and especially among the Renaissance physiognomists and their skeptics (see McLean 2007). Whatever its exact historical origins, physiognomy appears to have made its first entry into Greek culture through philosophy, and this explains perhaps why, according to one tradition, it was a Greek philosopher—​Pythagoras of Samos from the 6th century bce—​who first invented the discipline. Supposedly, Pythagoras applied physiognomy to his prospective students as a means to assess their character traits and intelligence before admitting them to his school (the story is related in Late Antique Platonist sources: see especially Aulus Gellius, Attic Nights 1.9.2; Hippolytus, Refutation of all Heresies 1.2; and Porphyry, Life of Pythagoras 13.2–​14.1 and 54). In both this anecdote about Pythagoras and the story about the encounter between Socrates and Zopyrus, physiognomy is portrayed as a discipline that apparently provides a reliable means for diagnosing innate character based on outward appearance, while philosophy is what provides the means for the moral development of this natural character (and of reason). The two disciplines complement each other in this way, and the Greek philosophical source material is full of passages expressing the diagnostic value of reading someone’s outward appearances, even if not all of those passages endorse physiognomical thinking in the technical sense. For instance, in his narration of Prodicus’ myth about Hercules at the crossroads, who has to choose between a life of virtue or of vice, Xenophon depicts the woman embodying Virtue as fair and beautiful with modest eyes, whereas the body of Vice is plump and soft with open eyes—​the physiognomical sign for immodesty (Memoirs of

Physiognomy   753 Socrates 2.1.22). Xenophon also has Socrates explain to the painter Parrhasius and the sculptor Cleiton that the beauty of the soul and not just that of the body can be captured by their art: since the soul uses the body as a tool, a person’s inner character will manifest itself through his physical expression and posture and can thus be represented (Memoirs of Socrates 3.10.3). Even Plato, who seems to treat Socrates’ ugliness as evidence that outward appearance is not a reliable guide for the qualities of one’s soul (see especially Symposium 215b–​222b and Boys-​Stones 2007, who argues that the majority of bodily descriptions in Plato resist any physiognomical conclusions) and whose own theory of the soul fits ill with the ontological presuppositions of physiognomy, suggests—​in a manner familiar from animal physiognomy—​that there is a correspondence between the kinds of virtues or vices present in one’s soul and the kind of animal body in which one reincarnates (see Phaedo 81d–​82b; Timaeus 42b–​c and 90f–​92c; and Republic 620a–​ d). And in Theophrastus’ Characters, which generally focuses more on the behaviors exhibited by people representing a certain vice (thereby codifying the so-​called ethical types that played a role in the pathological method of physiognomy), the Backbiter (­chapter 27) claims to be able to read bad character from someone’s face. Serious interest in physiognomy among Greek philosophers was, however, limited to those who had already accepted, for independent reasons, a theory based on the sumpatheia of the body and soul. Physiognomy thus did not so much influence developments in philosophy as that it was accepted and discussed by philosophers who were already hospitable to the kind of correspondence between body and soul presupposed by physiognomy (see again Boys-​Stones 2007). Traces of such serious interest can be found in Aristotle, the Stoic philosopher Posidonius, and, to some extent, in the later Platonists. Aristotle clearly had a theoretical interest in physiognomy (see Prior Analytics 2.27, 70b7–​38 discussed above), but he may also have had a practical interest in the discipline as suggested by the inclusion of physiognomical signs in his treatment of the parts on the human head in the History of Animals (1.8.491b9–​11.492b4). One of the most salient features in his description of the physiognomical signs is that they all constitute facial parts that hold an exact middle between two extremes in position, size, or color. For instance, eyes recede, protrude, or are in a position in between, and Aristotle says that while the ones that are most receding are sharpest and thus functionally best, “the middle ones are a sign of the best character.” This language, of course, is strongly reminiscent of Aristotle’s doctrine of the mean as presented in his ethical treatises, according to which virtues of character are conditions that hit the mean—​appropriate to the agent—​between two other states, the one involving an excess, the other a deficiency (see Nicomachean Ethics 2.2.1103b26–​6.1107a27). Aristotle explains the preservation of virtue, which is a disposition of the soul, by analogy to how health—​a physiological condition—​in the body is preserved: people are healthy who exercise and eat in the amounts that are appropriate for them and preserve a mean between exercising and eating too much or too little. Aristotle’s identification of intermediate facial features as signs of the best character also suggests that there is an underlying physiological condition, functioning as an intermediary, that is responsible for both those facial features and the character traits of the soul. For, according to Aristotle, the natural (prehabituated)

754   Greco-Roman Science character traits animals or humans possess are determined by the four material elements that make up the mixture of their blood, which is the nutriment and matter for their body (see Parts of Animals II 2.647b10–​4.651a19). Humans reportedly have the best quality of blood: it is well-​mixed and is therefore hot, thin, and pure, making humans prone to natural courage and intelligence. It is possible that Aristotle thought that those people in which the blood was optimally well-​mixed (hot, but not too hot, etc.) would not only have the best possible natural character traits (such as courage, rather than spiritedness that is caused by too much hotness) but also the best possible realization of their physical traits (where “best” is holding a mathematical mean between two extremes). People in which the blood is slightly off balance—​for instance, due to climate, diet, or age—​would also have facial features that are slightly off from their ideal intermediate position, size, or color. Aristotle never explores this possibility explicitly, but if natural character traits can be read from someone’s facial features, and if a “well-​mixed” natural character makes it easier to make men virtuous (as Aristotle thinks it does: see Politics 7.7.1327b18–​38), lawgivers ought to use physiognomy in their selection of future citizens, just as Pythagoras physiognomized his future students. In the Hellenistic period, we find several philosophers who are associated with the practice of physiognomy. For instance, Zeno of Citium (333–​263 bce), the founder of the Stoa, is reported to have provided a physiognomical image of a young man (see Clement of Alexandria, The Teacher 3.11.74). An anecdote about his student Cleanthes of Assos (331–​232 bce) narrates how he had claimed, “character could be grasped from appearance” but had trouble diagnosing the sexual deviancy of the man brought before him (as his skin had toughened from working on the land)—​until he sneezed (see Diogenes Laërtius 7.173). And Chrysippus (280–​207 bce), said, “goods and evil are perceptible,” including the passions, vices, and virtues (see Plutarch, On Stoic Self-​ Contradictions, 19). It has even been argued that the Epicureans created physiognomically coded statues of Epicurus to be sent out of the Garden as a means to recruit new students through his image (see Frischer 1982), although the supporting evidence for this hypothesis is fairly thin. It is not clear, however, whether any of these philosophers actually considered themselves physiognomists or can be thought of as being physiognomists in the technical sense (see Boys-​Stones 2007). The case may be different for the late Stoic philosopher Posidonius (ca 135–​51 bce), who “rightly reminds us of what physiognomical considerations can show,” which is that the quality and heat of the blood—​influenced by the mixture characterizing the environment in which animals and humans live—​determine bodily features, which in their turn determine emotions and character traits (see Posidonius, fr. 416 Edelstein-​Kidd; Galen, On the Doctrines of Hippocrates and Plato 5.5.22 [De Lacy 1978, 320–​322 = Kühn 5.463–​464]). If this report is right, Posidonius might have been a true physiognomist who believed there exists an innate character grounded in the material properties of the body. Although Plato’s psychology and treatment of outward appearance was mostly anti-​ physiognomical in outlook, later Platonists (3rd to 5th century ce) largely appear to have accepted physiognomy as true: the story about Pythagoras using physiognomy to select his future students appears to originate in them, and they also add a story

Physiognomy   755 about Socrates physiognomizing a very young Plato (Apuleius, On Plato and His Teachings 1.1) and Alcibiades before taking them on as students (Plutarch, Alcibiades 4.1; Proclus, Commentary on Plato’s First Alcibiades 94.4–​15; Olympiodorus, On the Alcibiades 13.19). According to Proclus, Socrates “saw many wonderful indications in Alcibiades that he was capable of virtue” and had learned this custom of judging characters from the Pythagoreans. However, in order to make physiognomy possible, Plato’s psychology had to undergo some transformations (see Boys-​Stones 2007): while the Platonists preserve the ontological independence and separability of body and soul, the process of reincarnation is now described as souls finding bodies that carry a “resemblance” or “image” of the soul’s disposition. Outward appearance can be used as a reliable indicator for the innate qualities of the soul, because the soul selected that body because of its fittingness to itself (see, e.g., Plotinus, Enneads 4.3.12). One Platonist, Aristides Quintilianus (probably late 3rd century ce), goes so far to claim that souls that do not find a fitting body remodel the body they receive in accordance with their own characteristics and make it like themselves, thus explaining, for instance, why some men come to have feminine features while some women come to have masculine features (On Music 2.8, 66.25–​67.14). The power of physiognomy for these philosophers was limited, however:  since a person’s innate characteristics do not determine his present behavior or moral character, physiognomy can only reveal a person’s innate potentials—​potentials that, as in the case of Alcibiades, may well go unfulfilled. Physiognomy can diagnose, but philosophy is required to realize someone’s potential to the fullest or to provide a moral cure for the naturally base.

5.  Physiognomy and Medical Prognosis According to a different tradition, it was not the philosopher Pythagoras but Hippocrates—​the late 5th-​century physician from Kos and proclaimed author of a wide-​ranging corpus of medical treatises (dating from the 5th to 3rd century bce)—​ who invented the science of physiognomy. This is at least what Galen of Pergamum, the philosopher-​physician from the 2nd century ce, says in his own treatise about physiognomy (The Soul’s Dependence on the Body 8 [Müller 2.57–​58 = Kühn 4.798–​799]). In a work falsely attributed to Galen, Hippocrates is supposedly quoted as saying, “the judgment of those who practice medicine but have no share in physiognomy rambles in the dark, getting old and sluggish” (pseudo-​Galen, Prognostica de Decubitu, Kühn 19.530.5–​10; the author of this treatise—​whose real name was possibly Imbrasios of Ephesus—​uses the quote, however, as evidence of Hippocrates’ interest in astrology). And in the Arabic physiognomical tradition, in which Polemon is hailed as the discipline’s founder, the classic anecdote about Socrates’ encounter with Zopyrus is repeated, but now with Polemon taking the role of Zopyrus and Hippocrates that of Socrates. Although Hippocrates was likely not the actual inventor of the discipline and certainly not a physiognomist in the technical sense, there are indeed a number

756   Greco-Roman Science of quasi-​physiognomical observations scattered through the Hippocratic corpus. In the Epidemics, for instance, the Hippocratic author mentions several bodily signs from which character can be inferred: according to 2.6.1 (5.132 Littré), a big head with small eyes indicates quickness to anger; for other signs, see 2.5.1, 16, and 23 (5.128, 130, and 132 Littré), 2.6.14 and 19 (5.136 Littré), and 6.4.19 (5.312 Littré). The chapter titles of Epidemics 2.5 (5.128 Littré) and 2.6 (5.132 Littré) also include references to the science of physiognomy, but these are likely later additions and not original. And certainly ancient medicine and physiognomy share very similar approaches to the human body and rely equally on prediction and inductive reasoning in their respective methods (on physiognomy and ancient medicine, see Boys-​Stones 2007). For where the physiognomist draws inferences from external bodily signs (sēmeia) to determine the underlying character of a person, the physician relies on external bodily symptoms (symptōmata) to diagnose diseases in his patients and—​perhaps more importantly—​to provide a prognosis for their development. And to the extent that physiognomists and physicians express any commitment to underlying physiological theories about character or health and disease, they both identify as causes the mixtures (kraseis) of blood and/​ or other bodily humors (such as phlegm, black bile, and yellow bile). Thus, both health and good character traits are due to a balance and well-​mixedness of the material constituents of the body, whereas disturbances in this balance produce diseases and bad character traits. It should come as no surprise that one of the few physiognomists of antiquity we know by name, Loxus, was a physician, and that it was one of the most famous physicians of antiquity, Galen, who developed the causal connection between the mixture of bodily elements, health, and character most fully. About the first we know rather little: based on the fragmented and often disorganized material in Anonymous Latinus, Loxus appears to have defended a strikingly Aristotelian account of how differences in the heat of the blood, which he identifies as the seat of the soul, are responsible for bodily differences and for differences in the intelligence and character of people (on Loxus’ Peripatetic affiliation, see Boys-​Stones 2007). He probably practiced a physiognomy of the animal method (each of the ­chapters 117–​131 describes the characteristics of one particular animal species, identifies the physical features by which humans of this animal type can be recognized, and explains what it means for their character), and, according to the opening of ­chapter 133, may even have used physiognomy for predicting the future. Unfortunately the remainder of the chapter and the rest of the treatise are not preserved, so the exact nature of these predictions—​whether they are medical prognoses or general predictions about what would happen to a person in the future—​remains unknown. About Galen’s theoretical views about physiognomy we are much better informed, even if we do not know whether he actually relied much on physiognomy in his medical practice. According to him, every part of a living being’s body consists of its own mixture or temperament of the four humors, blood, phlegm, black and yellow bile (see especially his On Temperaments). Each humor contributes its own material properties to the mixture (blood, for instance, is hot and wet, and accordingly heats and wets the body,

Physiognomy   757 whereas black bile is cold and dry, etc.), and the particular mixture and balance of these properties in the resulting body determine an individual’s bodily features, health, and also his character traits. For, as Galen states at the beginning of his most important physiognomical treatise (The Soul’s Dependence on the Body 1 [Müller 2.32 = Kühn 4.767]), “the faculties of the soul follow the mixtures of the body,” thereby explicitly endorsing the kind of sympathetic relationship between body and soul required for physiognomy (cf. the opening line of pseudo-​Aristotle’s Physiognomics, “that the minds follow the bodies,” to which Galen is likely responding). The exact details of Galen’s psychology remain unclear (Galen himself claims agnosticism about the nature of the soul and its relation to the body, and shifts positions even within a single treatise), but the correspondence between bodily mixture and psychological faculties allows Galen—​mostly by reflecting directly on quotes drawn from Hippocrates, Plato, and Aristotle—​to develop an extensive physiognomical theory. First, because each species is constituted of roughly the same mixture of humors (they all follow the same recipe, so to speak), Galen can explain why all members of that species, if their mixture is appropriately balanced, will have relatively similar bodily features and the same corresponding character traits. For instance, because all lions have a relative large amount of blood in their mixture and especially around their heart, they all have much hair on their chests and are spirited in character (and a lot of chest hair on a man will be a sign of his spiritedness). Second, because the mixtures of the whole body and of its parts can be affected by other physiological factors, such as climate or diet, or even aging and disease, individual variations in those mixtures can explain why individuals within one species look different (Galen spends a lot of time discussing ethnic differences in humans, such as differences in the color and structure of hair and skin) and have slightly different character traits. The phlegmatic person (typically, a woman), for instance, has a bodily mixture in which phlegm dominates (relative to the human ideal or standard recipe, as it were): the excess wetness and coldness results in soft, white, hairless bodies and in cowardly and spiritless characters. The person with the healthiest condition and the best character traits is according to Galen—​and following Aristotle’s lead—​the well-​mixed person, who in every respect takes up a mean between two extremes: his character is between rash and cowardly, his skin between smooth and hairy, and so forth. By thus making a balanced mixture of the body both the cause of health and of good character, Galen also allows physicians, like himself, to take over some of the tasks of philosophy and to contribute to the development of virtue: physical exercise and diets should not only be prescribed to people with illnesses but also to those who need moral improvement (cf. Galen’s advice on studying the eyes of the healthy for determining the character of the soul and of the sick for prognosis in To Glaucon on Medical Method 1.2 [Kühn 11.11]): physiognomy and medical diagnosis go hand in hand according to this passage). Galen claims that his theory about the temperaments has practical value, and claims that “it would be wise of my opponents—​those men who are unhappy at the idea that nourishment has this power to make men more or less temperate, more or less continent, brave or cowardly, soft and gentle or violent and quarrelsome—​to come to me even now and receive instruction on their diet; they would derive enormous

758   Greco-Roman Science benefit from this in their command of ethics” (see The Soul’s Dependence on the Body 1, 9 [Müller 2.32, 66–​67 = Kühn 4.767, 807–​808]). In the later Arabic tradition, in which physiognomy and medical science were also closely connected, Galen’s thoroughly medicalized physiognomy with its grounding in a humoral psychology would become a major influence.

6.  The Political Use of Physiognomy in the Rhetoric of the Second Sophistic Although Galen traces his interest in physiognomy to its roots in Hippocratic medicine and the philosophy of Plato and Aristotle, it is likely that he first encountered the discipline during his years as a student with the physician Pelops in Smyrna. The city of Smyrna, which was part of the province of Asia under the High Roman Empire, formed the main center for the education in rhetoric during the period of the Second Sophistic. It was also full of practitioners of physiognomy, whose art had been appropriated by the rhetors for the practical purposes of describing the characters of others (the images and analogies used in these character sketches or ethologiae often drew from physiognomical clichés) and of enhancing the delivery (or hypokrisis) of their speech, which involves the representation of the character of the speaker himself through his body language, voice, gait, gestures, and facial expressions. One of the most famous of these rhetors who had incorporated physiognomy in his art, Polemon of Laodicea (also known under his Roman name, Marcus Antonius Polemo), had just died when Galen arrived in Smyrna, but Galen must have been familiar with Polemon’s physiognomical handbook. As the son of a very wealthy family with close ties to the Roman emperors, Polemon grew up to be a well-​rounded intellectual and political leader of Smyrna, the city he settled in during his teens: there he taught rhetorical skills to students (hence his name, Polemon the Sophist), was famous for his display speeches and improvisatory style as a rhetor, acted as a diplomat and administrator of his city, and received various special honors and privileges from Hadrian, the Roman emperor (Polemon’s life is described by Philostratus, in his Lives of the Sophists; see also Barton 1994 and Swain 2007b). Ostensibly, Polemon had written the physiognomical handbook for instructional purposes for his students in rhetoric, and certainly the treatise is full of pedagogical remarks (see, e.g., the opening of Leiden B2: “So when you look at a man, compare him and think about him: do you see that he is masculine or feminine?”), while his long and minute discussion of the physiognomical signs of the eye fits with the rhetorical practice that had made the eye the primary indicator of the rhetor’s feelings (as Cicero says in On Rhetoric 3.221 “all delivery comes from the soul, and facial expression is the mirror of the soul, the eyes the indicators of what it feels”; see Gleason 1995). However, the rather disorderly discussion of physiognomical signs and their illustration

Physiognomy   759 by a range of examples drawn from his own—​mostly, male—​contemporaries and especially his adversaries reveal the underlying political nature of the treatise. Physiognomy, combined with rhetoric, became for Polemon an effective tool for attacking opponents and destroying their moral persona, and, to a lesser extent, for making allies with those in power. One recipient of this form of invective was Favorinus of Arles, a fellow rhetor and ambassador for Ephesus, who had also won favors with the Roman emperors and was a bitter rival of Polemon. Polemon mentions him as person in whom “the eye is open with a shimmer like marble and a sharp gaze,” which indicates immodesty and is often found among “eunuchs born without testicles” (the passage preserved in Leiden A20 is one of the most well-​known in the Physiognomy). “The Celt,” as Polemon refers to him (the name Favorinus is supplied by Anonymous Latinus), was “greedy and immoral beyond all measure,” had many feminine features (such as soft cheeks and limbs, abundant hair, and a woman’s voice, neck, and walk), and was a “deceitful magician” and “a leader in evil and a teacher of it.” Polemon’s depiction of Favorinus as effeminate and as a monster of nature ended up being successful: Favorinus lost his Imperial favors and was temporarily exiled from Rome, while Polemon’s influence—​and with him, that of Smyrna—​grew. And Favorinus’ example does not stand alone. By depicting the physical features of his contemporaries (not all of which were necessarily also his enemies) as being proper to women, exotic animals, or foreigners, Polemon turned many other men into objects of scorn and laughter. Even Emperor Hadrian, whose eyes are clear and shining and “full of beautiful light” and indicate good character, does not receive unambiguous praise (see Leiden A16; Swain 2007b argues that Hadrian may have been dead at the time the Physiognomy was published). For Polemon, the ideal human is an intelligent, manly, great-​minded man (see Leiden B24, 26, and 40), a “pure Greek” (Leiden B32; Rome does not feature explicitly in the Physiognomy) with bodily features that maintain a mean and that resemble those of the lion (Leiden B2), and that, of course, are very hard to find. With his rather negative and polemical use of examples from his contemporaries in the handbook, Polemon offers us also a glimpse into the turbulence of his political life and that of the Greek world of the Second Sophistic. The picture that emerges is of a highly regulated and morally sensitive society, where the elite continually compete for patronage of the Roman emperors and for status among their peers, and fear nothing more than to lose face and reputation. The handbook might also have served a more positive purpose: the negative moral exempla with all their flaws could have been used as a starting point for moral self-​ improvement, the study of others as a means to acquire knowledge about oneself. As Polemon says, “if you have any memory of that [i.e., the previously described physiognomical signs of the eye], you can learn of the matter of your soul and of others” (see Leiden A20; emphasis mine). The implicit suggestion being perhaps that knowledge of the principles of physiognomy and of how not to be or act can help one not just to avoid dealing with the moral failures of others (as expressed in Adamantius A2) but also to avoid vice and wrongdoings in one’s own life and thus become a better person. The success of physiognomy in antiquity appears to have lain in its versatility:  scientists in other disciplines used and adapted its methods and suppositions

760   Greco-Roman Science about the body and soul to make it fit their own theories and purposes. For philosophers, the discipline sparked epistemological questions, but for those who already endorsed a sympathetic relationship of body and soul, it also raised a practical interest, in that physiognomy could disclose the persons needing or deserving philosophical training. For physicians, physiognomy expanded their diagnostic field from symptoms of health and disease to also include signs of character, and both could be used as a basis for medical prognoses and for advice for cures. Moral improvement could be achieved through medical regimen, not (just) by philosophical training. For rhetors, physiognomy proved to be a fruitful resource for improving their rhetorical skills and the effectiveness of their speeches on the audiences familiar with physiognomical thoughts and clichés. And, since physiognomy itself was morally neutral, it could be used to teach others how to become a better person while at the same time destroying your enemies and aggrandize yourself.

Appendix: The Five Most Important Source Materials on Polemon’s Physiognomy The contents of Polemon’s Physiognomy have survived in a variety of independent sources and translations, among which the following five are the most important: (1) The 4th-​century handbook by Anonymus Latinus contains—​in addition to the materials from the pseudo-​Aristotelian handbook and Loxus—​large sections from Polemon’s treatise translated into Latin. (2) The Greek author Adamantius of Alexandria (also referred to as Adamantius the Sophist) from the 4th century ce more or less rewrote Polemon’s handbook and excised all of Polemon’s personal observations, preserving a shorter, but otherwise faithful, version of the original (for the Greek text with translation, see Repath 2007a). (3) Sometime during the late 8th to the early 10th century ce, Polemon’s handbook was translated in its entirety into Arabic. The original translation is now lost, but it formed the source for all the surviving Arabic reworkings of Polemon. The text that is closest to Polemon’s original text in Arabic translation is probably that of MS Leiden Or. 198.1, referred to as “the Leiden Polemon” (Kitāb Aflīmūn fī l-​firāsa, folios 2b–​50a, dated Damascus 1356 ce; Hoyland 2007). Both Adamantius and the Leiden Polemon order their discussion of physiognomical signs from bottom to top, thereby reflecting the order of the physiognomical signs in Treatise B of the pseudo-​ Aristotelian Physiognomy and the order followed by Polemon himself. (4) From this lost Arabic translation of Polemon, we also possess an Arabic epitome from Istanbul. It is preserved in two closely related manuscripts kept in the Topkapı Sarayı Museum in Instanbul, and henceforth often referred to as the “Istanbul Polemon” or the “Topkapı (TK) Recension” (Kitāb Aflīmūn fī l-​firāsa wa-​l-​tawassum, Ahmet III 3207 folios 33a–​ 75a, dated 1281 ce, and Kitāb Aflīmūn fī ‘ilm al-​firāsa, Ahmet III 3245, not dated; Ahmet III 3207, 33a–​42b is translated by Ghersetti 2007). The first of these manuscripts also

Physiognomy   761 contains an Arabic translation of the pseudo-​Aristotelian Physiognomy and of a treatise on the physiognomy of women falsely attributed to Polemon. The TK Recension, which best preserves the original lost Arabic translation, is more Islamicized than the Leiden Polemon: the ordering of physiognomical signs is from top to bottom, which is the order typical of the great medical treatises of the Arabic tradition of that period, and it substitutes anecdotes and references to the Greek contemporaries and culture of Polemon with elements from the Islamic world (for a comparison of the Arabic sources for Polemon, see Ghersetti and Swain 2007). (5) Finally, Polemon’s treatise was also translated into Syriac (either in the 5th or in the 6th century ce), and citations from this now-​lost translation are preserved in a 13th-​century encyclopedia called The Cream of Wisdom, by bishop Bar Hebraeus.

Bibliography Agrimi, J. Ingeniosa scientia nature: Studi sulla fisiognomica medievale. Florence: Edizioni del Galluzzo-​SISMEL, 2002. Amberger-​Lahrmann, M. Anatomie und physiognomie in der hellenistischen Plastik. Dargestellt am Pergamonaltar. Stuttgart: Franz Steiner Verlag, 1996. André, J., ed. Anonyme Latin: Traité de physiognomonie. Paris: Belles Lettres, 1981. Armstrong, A. M. “The Methods of the Greek Physiognomists.” Greece and Rome, new series 5 (1958): 52–​56. Barton, T. S. Power and Knowledge, Astrology, Physiognomics, and Medicine Under the Roman Empire. Ann Arbor: University of Michigan Press, 1994. Bost-​Pouderon, C. “Dion de Pruse et la physiognomie dans le Discours XXXIII.” Revue des Études Anciennes 105 (2003): 157–​174. Boys-​Stones, G. “Physiognomy and Ancient Psychological Theory.” In Seeing the Face, Seeing the Soul, Polemon’s Physiognomy from Classical Antiquity to Medieval Islam, ed. S. Swain, 19–​124. Oxford: Oxford University Press, 2007. Burnyeat, M. “The Origins of Non-​deductive Inference.” In Science and Speculation: Studies in Hellenistic Theory and Practice, ed. J. Barnes, J. Brunschwig, M. Burnyeat, and M. Schofield, 193–​238. Cambridge: Cambridge University Press, 1982. Crawford, J. S. “Physiognomy in Classical and American Portrait Busts.” American Art Journal 9.1 (1977): 49–​60. Currie, H. M. “Aristotle and Quintilian: Physiognomical Reflections.” In Aristotle on Nature and Living Things, ed. A. Gotthelf, 359–​366. Pittsburgh: Mathesis, 1985. Dagron, G. “Image du bête ou image de Dieu:  La physiognomonie animale dans la tradition grecque et ses avatars byzantins.” In Poikilia: Études offertes à Jean-​Pierre Vernant, ed. Centres de Recherches Comparées sur les Sociétés Anciennes, 69–​80. Paris:  Éditions de l’EHESS, 1987. De Lacy, P., ed. Galen:  On the Doctrines of Hippocrates and Plato. Corpus Medicorum Graecorum, part 5.4.1.2. 3 vols. Berlin: Akademie-​Verlag, 1978–​1988. Evans, E. C. “Roman Descriptions of Personal Appearance in History and Biography.” Harvard Studies in Classical Philology 46 (1935): 43–​84. —​—​—​. “The Study of Physiognomy in the Second Century B.C.” Transactions and Proceedings of the American Philological Association 72 (1941): 96–​108.

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Physiognomy   763 Singer, P. N. Galen: Selected Works. Oxford: Oxford University Press, 1997. Steel, C. “The Moral Purpose of the Human Body: A Reading of Timaeus 69–​72.” Phronesis 46 (2001): 105–​128. Stok, F. “Il prologo del De Physiognomonia.” In Prefazioni, prologhi, proemi di opera tecnico-​ scientifiche latine, ed. C. Santini and N. Scivoletto, vol. 2, 499–​517. Rome: Herder, 1992. Swain, S., ed. Seeing the Face, Seeing the Soul, Polemon’s Physiognomy from Classical Antiquity to Medieval Islam. Oxford: Oxford University Press, 2007a. —​—​—​. “Polemon’s Physiognomy.” In Seeing the Face, Seeing the Soul, Polemon’s Physiognomy from Classical Antiquity to Medieval Islam, ed. S. Swain, 125–​201. Oxford: Oxford University Press, 2007b. Tsouna, V. “Doubts About Other Minds and the Science of Physiognomics.” The Classical Quarterly 48.1 (1998): 175–​186. Vogt, S. Aristoteles: Physiognomonica. Aristoteles, Werke in Deutscher Übersetzung. Vol. 18.6. Berlin: Akademie Verlag, 1999. —​—​——​. “The Istanbul Polemon (TK Recension):  Edition and Translation of the Introduction.” In Seeing the Face, Seeing the Soul, Polemon’s Physiognomy from Classical Antiquity to Medieval Islam, ed. S. Swain, 465–​485. Oxford: Oxford University Press, 2007. Weiler, I. “Physiognomische Überlegungen zu mens sana in corpore sano.” In Satura Lanx: Festschrift Werner A. Krenkel zum 70. Geburtstag (Spudasmata 62), ed. C. Klodt, 153–​ 168. Hildesheim: Georg Olms, 1996. Zanker, P. The Mask of Socrates: The Image of the Intellectual in Antiquity. Berkeley: University of California Press, 1995.

chapter D9

Galen and H i s Syst e m of M edi c i ne Ian Johnston

Galen (b. 129–d. ca 215 ce) is undoubtedly one of the major figures in the history of medicine, not only in Latin-​speaking lands but also throughout the Greek-​, Syriac-​, and Arabic-​speaking countries. His enormous influence, transmitted through his 50 years of practice in Rome and Pergamum and his massive written output, persisted until the early 19th century. Through critical analysis and synthesis of the considerable body of medical and philosophical materials available to him, supplemented by his own experience, both clinical and experimental, he established a comprehensive system of medical practice based on a secure theoretical foundation, which included all the basic medical sciences and relevant areas of philosophy. Apart from this, however, he made important anatomical discoveries (although he was limited by his need to rely on animal dissection only) and carried out illuminating physiological experiments. He often stressed the need for a doctor to have a solid grounding in philosophy. In addition, he seems to have intervened decisively in the debate between the several contending medical sects. Finally, his œuvre provides an unparalleled source of information on the lost writings of many important doctors and philosophers who preceded him. Galen has attracted criticism for his arrogance and self-​aggrandizement, for his intemperate attacks on his opponents, and for his prolixity (which he acknowledged). Some scholars have criticized him for having a stultifying effect on progress in medicine—​although this would surely be a fault more appropriately attributed to his successors, bowed down by the weight of his considerable authority. However, these perceived faults do little to detract from the magnitude of his achievement. No doctor, with the possible exception of his revered predecessor Hippocrates, has had an influence so enduring in time and so extensive in place. In this article, after brief accounts of his life, his predecessors and their influence on him, and his prodigious body of written work (much of which survives), the theoretical foundation of his method of practice will be outlined, followed by a concluding summary of how his theory translated into practice.

766   Greco-Roman Science

1. Galen’s Life Galen’s life is relatively well documented. Much of the information comes from his writings in which numerous anecdotes provide factual information and insights into the writer’s character. The abbreviated account that follows is divided into seven relatively well-​defined periods. (i) Early Years (129–​146 ce): Galen was born at Pergamum in Asia Minor—​a place renowned for its shrine to Asclepius, and for its library that acted as a considerable attraction to scholars. Nikon, his father, was a wealthy architect of the city and played a very active role in his son’s early education, personally instructing him in the basic disciplines of geometry, mathematics and arithmetic, as well as in logic and architecture. Then, from the age of 14, Galen was exposed to the teachings of the major philosophical schools, his father arranging for him a series of teachers of philosophy including a Stoic, a Platonist, a Peripatetic, and an Epicurean. Galen’s mother, remembered through her son’s unflattering portrayal, seems to have been notable for her intemperate and somewhat violent conduct. Galen himself gives the following contrasting descriptions of his two parents and of his attitude towards the behavior of each: I was extremely fortunate in having a father who was not in the least irascible, very civilized, very kindly and very courteous, whereas my mother was so irascible that she sometimes bit the female servants, always bawling at, and fighting with, my father to an increasing extent—​a Xanthippē to Socrates. For myself, seeing set side by side the virtues of my father’s actions with the disgraceful affections of my mother, there was an eager following and love of the former but avoidance and hatred of the latter. (On the Affections of the Soul, 5.40–​41 K.—​cited from the edition of Kühn [1821–​1833] 1997, as throughout)

(ii) Medical Training (147–​157 ce): The course of his education, and indeed of his life, was changed significantly in his 17th year as a result of his father’s dreams. In On the Order of My Own Books, Galen writes:  “Then, persuaded by clear dreams, he made me, in my seventeenth year, train in medicine at the same time as philosophy” (19.59 K.). The initial years of Galen’s medical education were spent in Pergamum. His first known teacher was the renowned anatomist Satyrus who had come to the city and was apparently lodging with the Roman architect Rufinus, who was in charge of restoring the shrine to Asclepius. Among his other teachers in Pergamum were Stratonicus, an otherwise unknown Pneumatist, and two other men: Aeficianus, a Rationalist, and Aeschrion, an Empiricist, During this period, probably in 149, two things happened that altered the course of his life. First, his father died, depriving him of his assiduous

Galen and His System of Medicine    767 educational guide and supervisor. Second, his main teacher Satyrus returned to Smyrna. To further his medical education, Galen then began his travels, which lasted until 157. His first port of call was Smyrna, where he spent about a year, studying under Pelops, a noted commentator on Hippocrates. He may also have attended lectures by the Platonist philosopher Albinus, himself a pupil of Gaius. He then left Smyrna in search of instruction from Pelops’ teacher, Numisianus, possibly after a brief return to Pergamum for family reasons. Subsequently he stayed in Alexandria over the five years from 152–​ 157 ce. This was the culminating period of his extended medical training that saw the refinement of his knowledge of anatomy—​general, comparative, and surgical—​and of pharmacology. Among Galen’s teachers was Numisianus’ son, Heraclianus, and possibly also the Methodists, Julian and Lycus the Macedonian, against both of whom Galen subsequently wrote short treatises (Against Julian, 18A.246–​ 299 K.  and Against Lycus, 18A.196–​ 245 K.; cf. Hankinson 2008, 396). Finally, it is thought he traveled widely while in Egypt, furthering his knowledge of medications.

(iii) Initial Practice at Pergamum (157–​162 ce): Galen returned to Pergamum from Alexandria in his 28th year. Shortly thereafter he was appointed doctor to the city’s gladiators and began the practice of medicine as his occupation, combining his work among the gladiators with other aspects of practice, and with continuing study and research. Thus, by the time he entered medical practice, he had undergone a period of training roughly equivalent to that required for specialist training in modern English-​speaking countries (i.e., around 10 years). His credentials were impressive. Impressive, too, was his work in Pergamum. He records how he came to the notice of the Pontifex through demonstrations of his method of treating tendon injuries, hence his appointment as doctor to the gladiator school, which he retained for at least five periods of seven months. This appointment afforded him a singular opportunity for the study of surgical anatomy and the management of all kinds of wounds and fractures, and may have contributed to the prominence he was subsequently to give “dissolution of continuity” in his system of disease classification. Precisely why Galen left his apparently flourishing practice in Pergamum remains uncertain. Perhaps it was because of ambition, as Nutton suggests (in Conrad et al. 1995, 62), or because of unrest, either personal or general, or possibly other, unknown factors were involved. Whatever the explanation, Galen left Pergamum around 161 and spent the next four years in Rome. (iv) First Period in Rome (162–​166 ce): Galen’s journey to Rome was relatively rapid, although it may have involved some study of medicinal plants en route, perhaps in Lemnos and Cyprus (for Cyprus, see: On the Powers of Foods, 1.11, 6.507 K., and 2.34, 6.615 K.). The precise date of his arrival in Rome is also uncertain but was probably either late 162 or early 163. Although his first stay in Rome was comparatively brief, lasting only until 166, it was eventful in three ways. First, he established himself as a student of the highly regarded Peripatetic philosopher

768   Greco-Roman Science Eudemus, who was in turn to benefit from his pupil’s medical expertise, which was recorded in detail in Galen’s On Prognosis for Epigenes sec. 2 (14.608 K.). As Nutton remarks, “His cure of his old philosophy teacher Eudemus in the winter of 162–​163 was crucial in establishing him as a fashionable healer” (Conrad et al. 1995, 62). Second, there was his association with Boethus, flatteringly described in the opening sentences of his On Anatomical Procedures 1.1 (2.215–​216 K.). This was an association that encouraged and facilitated the continuation of Galen’s own anatomical researches. The first part of one of his greatest works, On the Use of the Parts, was completed during this period and sent to Boethus, who had been appointed governor of Palestine in 165. Third, as part of an active practice of medicine, he engaged in public demonstrations and debates with members of other sects and schools. While this must have furthered his reputation, it most certainly also made him some enemies. (v) Return to Pergamum (166–​168 ce): In 166, he left Rome and returned to Pergamum, visiting various parts of Greece during his journey. Why he did this is not clear. In different works written at quite different times, Galen cites two distinct reasons: (1) difficulty with his rivals in Rome coupled with improved conditions in Pergamum; and (2)  the advent of plague in Rome (see his On Prognosis to Epigenes sec. 4, 14.623, 648 K., and On My Own Books, sec. 1, 19.15 K.) (vi) Second Period in Rome (168–​200 ce): His stay in Pergamum this time was very short. In 168, he was summoned by Marcus Aurelius to join the Imperial army on a campaign in northern Italy, although abandonment of the immediate military objectives resulted in the army’s return to Rome in 169, Galen with it. He was to remain in Rome for most or all of his remaining life. The years immediately after his return (169–​176) were most productive in terms of his literary output, seeing the completion of a number of his major works, including the first six books of his Method of Medicine. During this time, Marcus Aurelius entrusted him with the medical care of his ill-​fated son, Commodus, while the emperor was away from the capital. When Marcus Aurelius returned to Rome in 176, Galen was made Imperial physician, his crowning achievement in terms of gaining powerful patronage. He continued his writing throughout the last decades of the century, producing among other works the second part of the Method of Medicine and his major works on pharmacology. Also from late in the century are the two short works that provide valuable information about his writings, On My Own Books and On the Order of My Own Books, and his On My Own Opinions in which he makes the significant observation that his core ideas changed little over the 50 or more years of his writings. (vii) Final Years (200–​216/​7? ce): The details of the final part of Galen’s life become increasingly obscure, in no small part because they are not chronicled by Galen himself with the same completeness as the earlier years. Until recently, scholars speculated that he left Rome somewhere around his 70th year and returned to his native Pergamum for the remainder of his life (Sarton 1954, 24). The Byzantine lexicon Suda claims that he died at the age of 70 or 71 (i.e., 199–​200).

Galen and His System of Medicine    769 The thinking now is that he lived well into the 3rd century. The latest date for any of his writings is that for his On Theriac, to Piso, which, according to Nutton, could not have been earlier than 204 and may have been as late as 207 (Nutton 2004, 226). Where he died is also unknown. He may have remained in Rome or returned to Pergamum for his last years. Nutton gives no credence to the theory that he died at Perama in Egypt while on a pilgrimage to Jerusalem—​indeed, why would he make such a journey? He probably died in either 216 or 217 at the age of 87, but how and where he died remains unknown.

2.  Galen’s Predecessors There is no doubt as to Galen’s most respected authorities—​Hippocrates in medicine and Plato in philosophy. He refers frequently to Hippocrates throughout his writings, and always favorably, although he is aware that his revered predecessor left work to be done. In his Method of Medicine 9.8 (10.632 K.), in relation to the treatment of duskrasias, he writes: But, because he was the first to discover them, he neither established the proper order for all of them, nor determined the worth of each of the indicators precisely. And he left out some distinctions between them, and explained the majority without clarity due to the ancient [predilection for] brevity of speech. Moreover, all in all, he taught very little about combined conditions.

Three principles of primary importance to Galen were taken from Hippocrates. First, the humoral theory of the composition of the body, as expressed in Hippocrates’ Nature of Man, which rejects claims of a single basic substance. Second, the view that each dis­ ease had a causal explanation that should be sought and if identified, would be relevant to treatment. Third, the allopathic principle underlying treatment—​opposites cure opposites. Of more general importance were Hippocrates’ perceived emphasis on ethics and his methodology, both of which prefigure Galen’s own belief in the essential nexus between medicine and philosophy. Concepts developed by Plato important to Galen include the following: the concept of the body as composed of the four elemental qualities (hot, cold, dry, and moist), as propounded in the Timaeus; the recognition of design in nature, involving the concept of the Demiurge; the tripartite division of the soul, involving consideration of the physical correlates of the psychical; and Plato’s ideas on causation in general and in medicine in particular, as expounded primarily in the Timaeus and the Phaedo. On a somewhat more minor but nonetheless important issue, Galen’s agreement and identification with Plato on the need to give primary attention to matters themselves rather than to terminology is revealed in the following statement from the former’s On Anatomical Procedures: “But if you are at least persuaded by Plato and myself you will always think

770   Greco-Roman Science little of names, whereas you will be attentive primarily and particularly to the knowledge of matters” (6.13, 2.581 K.). Galen is more reserved in his praise of Aristotle, but a number of the latter’s ideas do figure prominently in his writings. For example, in Galen’s teleological views, which especially inform his major work On the Use of the Parts, Aristotle’s immanent teleology plays a stronger role than the Platonic Demiurge. In his methodology, Galen is clearly and profoundly influenced by Aristotle, particularly by the works of the Organon. In his conception of the structure of the body, he was committed to the theory of four elemental qualities, which, while not originated by Aristotle, was held and developed by him. Further, in his formulations of structural levels, which are of considerable importance to the classifications of diseases and symptoms advanced in the four treatises on these subjects, and restated in the Method of Medicine, Galen followed Aristotelian concepts, especially the idea of homoiomeres. On causation, he is also influenced by Aristotle, both in the assumption of the validity of the search for causal explanations and in the specific theory of causation. In his attention to taxonomy, Galen is following Aristotelian principles. He was influenced by the psychology of De anima, as indeed were almost all who came after Aristotle and grappled with the same subject matter. Finally, the empirical component of his studies and the use of observation of biological phenomena as the basis for theoretical formulation reveal an Aristotelian imprint. As mentioned at the outset, Galen was clearly very conversant with the substantial body of medical and philosophical writing that preceded him; his references to predecessors are numerous, although by no means always flattering! In one of his major works, The Method of Medicine, he refers to more than 50 doctors and philosophers individually. Others, apart from the three main influences already considered, who were important to Galen include the following five: 1. Diocles of Carystus (4th century bce) is classed by Galen among the Dogmatics and cited on a variety of topics; he espoused the concepts of pneuma and the four humors (blood, phlegm, yellow and black bile). On the matter of treatment, he held the Hippocratic view on the importance of opposites. Particular remedies associated with his name include diet, exercise, bathing, emetics, fomentations, phlebotomy, and medications. 2. Praxagoras of Kos (ca 300 bce) has been identified as a follower of Diocles of Carystus and perhaps a teacher of Herophilus; Galen classified him as a Rationalist. He espoused theories that attracted Galen’s criticism; for example, the cardiocentric view of mental and emotional function, shared by other notables including Aristotle, and also his belief that the arteries carried pneuma, a concept developed by Erasistratus in his theories of disease causation. On the positive side, however, he is credited with having made the structural distinction between arteries and veins. Galen follows him on the importance of seeking a causal explanation for disease. Indeed, he is said to have written a book on the subject. In addition, he studied the pulse and its abnormalities, another subject substantially developed by Galen, and he incorporated pneuma into theories of physiology and

Galen and His System of Medicine    771 pathology. Praxagoras also expanded on the concept of humors, subdividing the basic four on the grounds of color, taste, and other aspects to make 10. He particularly associated disease with alteration of the humors and specifically fever with putrefaction of humors. 3. Herophilus of Chalcedon (ca 270 bce) made a major contribution to anatomy, especially of the nervous system, liver, and heart. He subscribed to the same physiology based on the four elemental qualities with a significant role for pneuma, especially in neurological function. He also played a major part in establishing “pulse theory,” a subject enthusiastically and extensively taken up by Galen. In terms of methodology, Herophilus argued for attention to be directed to phenomena but did, it is thought, accept the importance of causal explanation. 4. Erasistratus (ca 250 bce) had both a positive and a negative effect on Galen. Positively, Galen admired his significant contribution to anatomy, mainly in the cardiovascular system and peripheral nerves. Negatively, Galen strongly criticized a number of his theoretical formulations. First, in his physiology and pathology he moved away from the concept of four elemental qualities, basing his physiology on a corpuscular theory following, it is said, Straton of Lampsacus. In his explanation of disease, he gave particular importance to blood and pneuma, invoking the concepts of plethora and paremptosis. In short, what was involved in these presumed pathological processes was an increase in blood in the veins to an abnormal level causing a spillover into the arteries with a resultant displacement of pneuma. Other aspects of Erasistratus’ theorizing to which Galen took exception were his concept of horror vacui ( following toward what is emptied), his theory of digestion, his departure from the idea of “complete” teleology, and some of his attitudes to therapy. Also, on the issue of causation, there were substantial differences, although Erasistratus did clearly accept the need for causal explanation. 5. Asclepiades of Bithynia (ca 105 bce) was also influential in a negative way, basing his physiology and pathology on the concept of fragile corpuscles (anarmoi onkoi) which traveled through channels (poroi) distributed throughout the body but not anatomically definable. Diseases occurred when this process was interfered with, in particular when there was impaction (emphraxis). He was the first to apply the atomic theory to medicine and hence the forerunner of the Methodist school further developed by Themison and Thessalus in particular. This was a theory that Galen opposed in no uncertain terms, although he does include it without criticism in his treatises on disease classification and causation.

3.  Galen and the Sects or Schools One feature of Roman medicine in the centuries immediately prior to Galen was the development of sects or schools—​Empiricists, Rationalists, Methodists and Pneumatists. How important these recognized divisions were is hard to assess accurately, given that

772   Greco-Roman Science surviving evidence is limited to very few contemporary sources; the two notable ones being Celsus (1st century ce) and Galen himself. The latter certainly attached considerable significance to these sects, writing two works specifically on the subject—​On Sects for Beginners and On the Best Sect—​and mentioning them frequently in other works. Moreover, in his late work On My Own Books he writes, regarding his On Sects for Beginners, that this “should be the first book to be read by students of the art of medicine” (19.12 K.). The essential features of the four sects mentioned above may be summarized as follows.

(i) Rationalism: • A theory of the basic structure of matter that is applicable to the human body. • Based on that theory, a theory of the nature of health and disease in terms of concepts of structure and function. • A detailed knowledge of human anatomy. • Acceptance of the idea of causation—​all events have a cause or causes that are at least potentially identifiable. • Acceptance of the view that measures to maintain health and cure disease can be determined theoretically (at least in part) on the basis of this theoretical foundation. Galen followed Rationalist principles insofar as his method of medicine was based on a theoretical foundation formulated by reason. He was, however, also aware of some of the pitfalls of Rationalism as a dogma, writing in his Method of Medicine 1.4 (10.32 K.): On the other hand, for those who make reason (logos) the principle of discovery and order, who propose that this is the one road leading to the goal, there is the necessity to begin from something primary, agreed upon by all men, and in this way then proceed to the rest. They do not in fact do this, but rather the majority take up disputed starting-​points, not demonstrating them, and proceed to the rest in the same way, legislating rather than demonstrating.

(ii) Empiricism • There is no need for a foundational theory of structure and function or a detailed knowledge of anatomy. • There is no need to search for causal explanations—​indeed, this is not only unnecessary but also fruitless. • Recognition of diseases and their treatment is based on experience (peira), observation (teresis), history or inquiry (historia—​or in medicine collected case histories), and inference from analogy (metabasis). Galen was aware of the importance of experience. In the opening paragraph of his work On Medical Experience, he writes:

Galen and His System of Medicine    773 When I take as my standard the opinion held by the most skillful and wisest doctors and the best philosophers of the past, I say: The art of healing was originally invented and discovered by logos (reason) in conjunction with experience. And today also it can be practiced excellently and done well by one who employs both of these methods. (Walzer and Frede 1985, 49)

(iii) Methodism • A  theory of basic structure that involved identical atoms/​corpuscles (anarmoi onkoi) and channels/​pores (poroi) inaccessible to observation through which the corpuscles moved. • The view that disease was due to disturbance of this normal movement—​either constriction of the channels obstructing flow or dilatation of the channels allowing excessive flow, or a third possibility, coexistence of constriction and dilatation giving a mixed condition. • The view that these states were readily recognizable and were the basis for treatment. • The claim that all parts of the body were similarly affected by these processes and that there was no need for a detailed knowledge of anatomy. Galen objected to Methodism because it was based on the wrong theoretical foundation. Further, according to Galen, Asclepiades despised experience. The later developments of Methodism, culminating in the work of Themison and later Thessalus, were even more of an anathema to him. In essence the problem was that the later Methodists had no method, as he often states in his Method of Medicine. Somewhat curiously, given the virulence of his criticism of the Methodist sect and Thessalus as its self-​styled champion, Galen seems to have had no quarrel with the Methodist Soranus (ca 110 ce).

(iv) Pneumatism • Acceptance of the same four element/​four quality theory of basic structure as in Rationalism. • Postulation of a particularly important role for the pneuma in health and disease. Galen had no major difficulty with the Pneumatists—​those differences that are recorded are largely with specific individuals (e.g., Athenaeus) and on specific points. (The same applies to his differences with the Erasistrateans, although here the points of difference are more fundamental.) Galen did not have any hardline allegiance to one school or another. He was, he claimed, aware of the advantages and disadvantages of each. Galen repeatedly refers to the two ways of gaining knowledge: through reason and through experience. Moreover, theoretical formulations, if they are not verified by and in accord with experience, must be rejected while experience that is not “organized” by reason risks being unsystematic and irrational. Galen might, then, be best categorized as an eclectic with strong

774   Greco-Roman Science Rationalist tendencies, drawing what he saw as relevant from all the schools and molding it into his method of medicine.

4.  Galen’s Writings Galen’s writings are remarkable for their sheer volume alone. However, they are arguably no less notable for their range of subject matter and their enduring influence. No other ancient writer of any genre comes close to matching Galen’s prodigious output, although, of course, as much ancient writing has been lost, a true comparison is impossible. However, Galen was not immune to such loss; some of his writings were destroyed in the fire near the Temple of Peace in 192 ce (Sarton 1954, 23). In quantitative terms, Galen’s preserved writings account for about 10% of all surviving literature in Greek prior to 350 ce; assuming a writing life of a little over 50 years, he must have averaged two to three pages per day—​a quite extraordinary output! The following three sources provide very useful information on the number and nature of his works. (i) Galen’s two short works written late in his career; On My Own Books and On the Order of My Own Books. In the former there are 187 separate treatises. It is, however, not always clear what constitutes a separate treatise and not all Galen’s writings are included anyway. There are also those works written after Galen wrote On My Own Books and works he might have omitted for some reason. (ii) Ackermann’s introduction to Kühn’s edition of the Galeni opera omnia (volumes 17 and 18 are divided into parts A and B, and volume 20 is a Latin index). In this edition there are 124 titles. A current listing of these titles marks 23 as spurious and a further three as questionable. The genuine works range in length from 3 to 4 pages only, for example, On the Causes of Respiration, to those in excess of 1,000 pages, for example, On the Use of the Parts and the Method of Medicine. Ackermann lists 100 genuine works, 44 “libri manifeste spurii,” 19 fragmenta, and 18 commentaries on works by Hippocrates. (iii) Appendices I & II of Hankinson 2008. These list, respectively, “the editions and abbreviations of the Galenic corpus” (128 works of which about two dozen are spurious) and “English titles and modern translations” (see below). The range of subjects covered is extraordinary. From his first work, some notes on the writings of the Stoic Chrysippus to the very late, and possibly last, work On Theriac—​to Piso, he covered all aspects of practical medicine and its basic sciences. He wrote on the medical schools or sects; he produced detailed commentaries on earlier works, particularly those of Hippocrates; and he wrote on theoretical and nonclinical aspects of medicine. On philosophical topics his range was also very wide. Although he was particularly preoccupied with the works and ideas of Plato and Aristotle, he also wrote a number of

Galen and His System of Medicine    775 works on Stoic and Epicurean philosophy, as well on other general philosophical topics. Finally, there is a miscellaneous group of writings that includes works on lexicography, linguistic matters, politics, comedy, education, and writing. In tracing the preservation of his works after Galen’s death, the concepts and methods they expounded were extensively covered in the writings of the medical encyclopedists of the immediately following centuries—​for example, in the extant works of Oribasius (ca 350–​400 ce), Aëtius of Amida (ca 500–​550 ce), and Paul of Aegina (ca 630–​670 ce). By the 6th century, Galen’s core treatises on the theory and practice of medicine had been gathered together in what became known as the Galenic or Alexandrian Canon comprising the following works: 1. On Sects (1.64–​105 K.); cf. Hankinson 2008, 391. 2. The Art of Medicine (1.305–​412 K.); cf. Hankinson 2008, 391. 3. Synopsis on Pulses (9.431–​549 K.). 4. The Method of Medicine for Glaucon (11.1–​146 K.). 5. Collection 1 (on anatomy)—​On Bones for Beginners (2.732–​778 K.); On the Anatomy of Arteries and Veins (2.779–​830 K.); On the Anatomy of Nerves (2.831–​ 856 K.); and On the Anatomy of Muscles (18B.926–​1026 K.). 6. On the Elements According to Hippocrates (1.413–​508 K.); cf. Hankinson 2008, 391. 7. On Mixtures (Kraseis) (1.509–​694 K.). 8. On the Physical Powers (Natural Faculties) (2.1–​204 K.); cf. Hankinson 2008, 391. 9. Collection 2 (on diseases and symptoms)—​ On the Differentiae of Diseases (6.836–​ 880 K.); On the Causes of Diseases (7.1–​41 K.); On the Differentiae of Symptoms (7.42–​84 K.); and On the Causes of Symptoms (7.85–​272 K.). 10. On the Affected Parts (8.1–​452 K.). 11. Collection 3 (on pulses)—​On the Differentiae of Pulses (8.493–​ 765 K.); On Diagnosis by the Pulses (8.766–​961 K.); On the Causes in Pulses (9.1–​204 K.); and On Prognosis from the Pulses (9.205–​430 K.). 12. On the Differentiae of Fevers (7.273–​405 K.). 13. On Crises (9.550–​760 K.); cf. Hankinson 2008, 394. 14. On Critical Days (9.761–​941 K.). 15. The Method of Medicine (10.1–​1021 K.). 16. On the Preservation of Health (6.1–​452 K.); cf. Hankinson 2008, 393. Continued dissemination then depended on translation from the Greek into a number of other languages. The following is an outline of the chronology of an ongoing translation project. 1. Translation of the components of the Alexandrian Canon into Syriac by Sergius of Resaena in the 6th century ce. 2. The major program, particularly attributed to the Christian doctor Hunain ibn Ishaq (d. 873 ce), which resulted in the translation of 129 works into Syriac and Arabic during the 9th century ce.

776   Greco-Roman Science 3. The translation of the majority of Galen’s extant works from Greek, Syriac, and Arabic into Latin that began in the 11th century ce with men such as Constantine the African (fl. ca 1080), Gerard of Cremona (d. 1187)  and Burgundio of Pisa (d. 1193). This culminated in the veritable explosion of Latin translation that marked the period from the 14th to the 16th centuries, and involved such notable translators as Niccolò de Reggio (active 1304–​1350), Niccolò Leoniceno (1428–​1524), and Thomas Linacre (ca 1460–​1524). This period also saw the publication of the Giunta edition of the Latin Galen in 1541–​1542 with Giovanni Battista as the gen­eral editor. Bylebyl (1991, 173) described this as “perhaps the greatest landmark in the whole movement by Renaissance physicians to bring about a rebirth of ancient Greek medicine in their own time.” 4. Preparation of the collected versions of the complete works with both Greek and Latin texts, the first by René Chartier in 1679 in Paris and the second by Carl-​ Gottlob Kühn in Leipzig from 1821 to 1833. 5. Preparation of critical editions of individual treatises and the translation of a goodly number into modern European languages, the latter starting particularly with Daremberg’s French translations of 1854 and the former with the beginning of the Corpus medicorum Graecorum (Galen appears in the many parts of vol. 5) at the start of the 20th century. This movement has gathered considerable pace in the last generation such that Hankinson (2008, 391–​403) lists 60 works translated (some more than once) into English, French, German, Italian, and Spanish from 1978–​2008.

5.  Galen’s System of Medical Practice Although Galen wrote prolifically on a wide range of subjects within and beyond medicine, he was first and foremost a doctor, actively engaged in the practice of medicine and the teaching of his method of practice. It is this method or system of medical practice distilled from his detailed knowledge of the work of his predecessors, both medical and philosophical, and refined through his own research and clinical practice that I attempt to summarize in the present section. He set out his theoretical foundation (5.1 below) in a number of major works—​on the basic structure of matter, on anatomy, on physiology, on pharmacology, on logic and demonstration, on classification and on causation, and on the opinions of earlier writers. These were supplemented by a number of shorter works on various more specific matters. Details of the practical application of his methods are found, particularly, in two very influential works; the one devoted to treatment in all its aspects (The Method of Medicine, Canon #15), and the other devoted to the preservation of health (his On the Preservation of Health (Hygiene), Canon #16), again supplemented by many shorter works (see 5.2 ).

Galen and His System of Medicine    777

5.1 The Theoretical Foundation 5.1.1 Structure The keystone of Galen’s theoretical foundation is an understanding of the structure of the human body. There are two quite distinct aspects to this. First, there is the knowledge of the fundamental components of matter generally, which is the province of physics and philosophy. Second, there is the specific and detailed knowledge of how these fundamental components are organized to form the recognizable structures of living organisms, and of the human body in particular, which is the province of anatomy, both macro-​and microscopic, although, of course, only the former was available to Galen. On the first issue, Galen espoused a continuum theory of matter. According to this, matter is composed of the four elements—​fire, water, air, and earth—​and the four elemental qualities associated with them (hotness, wetness, coldness, and dryness) in varying combinations. Related to these are the four humors: blood, phlegm, yellow bile and black bile. It is a theory that can be traced back to Empedocles, but Galen particularly identifies Hippocrates, Plato, and Aristotle as his forerunners in embracing this concept. Galen’s own articulation of the continuum theory and its application to the human body, as well as his objections to the main rival theory, are to be found chiefly in two works: his commentary On Hippocrates’ Nature of Man and in his own On the Elements According to Hippocrates, which elaborates on the same Hippocratic work. The main rival theory was the theory first applied specifically to medicine by Asclepiades of Bithynia (ca 120–​90 bce), an atomic theory. The Hippocratic writings firmly adhere to a quality-​based model, and thus Galen repudiated Asclepiades’ atomic theory. According to the atomic theory, which originated with Leucippus (460–​420 bce) and Democritus of Abdera (440–​380 bce), matter in general is composed of minute, discrete particles, all similar, existing and moving in an empty space or void. These primary entities, the elements, were taken to be indestructible, immutable, and impassible in themselves, forming the identifiable structures of the world by their unending associations and disassociations. Second, for the specific and detailed knowledge of how these fundamental components are organized to form the recognizable structures of living organisms, Galen recognized three levels of organization: (i) Homoiomerous structures: structures of uniform composition, exemplified by muscle, bone, cartilage, and so on. (ii) Organic structures: structures compounded from simple structures to form discrete organs serving a particular function, such as heart, liver, lung, and so on. (iii) The whole body: the sum total of the all the structures in the first two groups. All these structures are seen as ultimately being combinations of the four elemental qualities, the actual balance of which may differ between different structures in the same

778   Greco-Roman Science body. What the doctor must know is the norm for each of the specific structures, how they are normally arranged in themselves and in relation to other structures, and what their function is. Much of this knowledge comes from anatomy, both by simple observation and by dissection. Knowledge of function also derives from observation but is, in addition, also dependent on physiological experimentation and reason. Galen wrote a number of treatises on anatomy, notable among which are his On Anatomical Procedures and On the Use of the Parts (neither in the Canon).

5.1.2 Function Two general aspects pertaining to function that are of considerable importance in Galen’s theory are as follows: (i) Function is dependent on structure. Thus to function satisfactorily a part must be in eukrasia (balance, or literally, good mixture). On this point it should be recognized, first, that the eukrasia as a “normal” balance to the four elemental qualities is not a single, specific state but allows a range outside of which it shades into duskrasia (imbalance, or literally, bad mixture); and second, that what constitutes eukrasia in terms of elemental qualities varies in different tissues/​ parts (e.g., the balance of qualities necessary for eukrasia in skin is different than that required in bone). In the case of organic structures, function also depends on normal morphology and the relationship to other structures (in Galenic terms, normal conformation, number, size, and relative position). (ii) Psychical function is determined by the same factors that determine physical function; that is, dependent on a satisfactory krasis (mixture) of the structures responsible for mental function and also their structural integrity. In the case of krasis one might assume that there are homeostatic (to borrow a modern term) mechanisms operative in the body, where necessary supplemented or aided by regimen or medications, that maintain all the parts, whether homoiomerous or organic, within a satisfactory range of krasis that allows normal functions/​actions. Next, Galen considered that the animal body is divided into three major functional systems or “principles” as follows: (i) The brain, spinal cord, and nerves, both cranial and spinal: these are responsible for motor and sensory functions. (ii) The heart and arteries: these are responsible for the vital force and preservation of the innate heat (vide infra). (iii) The liver and veins: these are responsible for the nutrition of all the bodily parts. (In his Art of Medicine, Canon #2, he includes a fourth—​the testes and the spermatic ducts.) Other structures are subsidiary to, and dependent on, these main systems and their components. Further, the working of such a system is dependent on its dunamis (capacity, faculty, power) and there may be more than one dunamis per system. Galen

Galen and His System of Medicine    779 recognizes the imprecision of his fundamental concept of dunamis, writing in his On the Physical Powers (Natural Faculties): The so-​called haematopoietic (blood-​making) faculty in the veins, then, as well as all the other faculties, fall[s]‌within the category of relative concepts; primarily because the faculty is the cause of the activity, but also, accidentally, because it is the cause of the effect. But if the cause is relative to something—​for it is the cause of what results from it, and of nothing else—​it is obvious that the faculty also falls into the category of the relative; and so long as we are ignorant of the true essence of the cause that is operating, we call it a faculty. (1.4, 2.9–​10 K, trans. Brock [1916] 1963)

Nonetheless, the concept of dunamis is critical to Galen’s physiology. Initiated by their capacities, the various structures carry out their functions (energeiai), which become manifest in their actions (erga). For example, the stomach, which Galen often uses to exemplify a mechanism or concept and which is a component in the third (vegetative, nutritive) system, attracts the ingested food through its attractive capacity, retains it through its retentive capacity while it is being processed, alters it through its alterative capacity in this process and then passes it on through its expulsive capacity. The nutriment, so processed in the stomach, then moves on to the liver (the headquarters, as it were, of the nutritive system) and the process of transformation into blood is set in motion. This allows the food to provide nutrition for the other structures of the body. This triad of dunamis (capacity, faculty, power), energeia (function) and ergon (action) is, then, one critical component of Galen’s physiology. Two other factors that are also of major importance are pneuma (or really pneumas) and innate heat. In The Method of Medicine Galen states that there are three pneumas; one associated with each of the three major systems identified above. In order, there is a psychic pneuma, a vital pneuma, and a physical pneuma. Ultimately these pneumas are derived from the external air, either taken into the lungs via the upper airways and bronchial tree or, in the case of the psychic pneuma, into the olfactory tract via the nose and cribriform plate, and are distributed by the arterial system but may undergo modification within their respective systems. Thus the psychic pneuma is formed by a modification of the vital pneuma in the rete mirabile at the base of the brain (a structure that Galen did not know was absent in the human) and in the choroid plexus tissue of the lateral and third ventricles plus the addition of air passing directly to the brain via the nose, cribriform plate, and olfactory tracts before entering the brain to be distributed by the nerves. For health, the system of pneumas needs to be functioning in a normal way. “Innate heat” is another key concept that Galen inherited from his ancient authorities, on this occasion, Hippocrates and particularly Aristotle. He considered this innate heat to have its seat in the heart and arteries and to be supplied in the formation of the fetus, as the following statement indicates: We do not posit masses and pores as elements in the body, nor do we declare that heat comes from motion or friction or some other cause. Rather, we suppose the whole body breathes and flows together, the heat not acquired or subsequent to

780   Greco-Roman Science the generation of the animal, but itself first, original and innate. This is nothing other than the nature and soul of life so that you would not be wrong in thinking heat to be a self-​moving and constantly moving substance. (De tremor, palpitatione, convulsione et rigore, sec. 6, 7.616 K.)

Thus, the innate heat is located centrally in the heart, its maintenance is aided by respiration, and its distribution to the rest of the body takes place through the arteries. Physiology of the respiratory and cardiovascular systems was also a subject that Galen both wrote about and experimented on extensively; there are three works specifically on respiration (On the Causes of Breathing, On the Use of Breathing, and Difficulties in Breathing) and eight on the arteries and arterial pulse (On the Anatomy of Veins and Arteries, Whether Blood Is Naturally Contained in the Arteries, On the Pulse for Beginners, On the Differentiae of Pulses, Diagnosis by the Pulses, The Causes in the Pulses, Prognosis from the Pulses, and Synopsis on Pulses: see Canons, #3, 5, and 11 for some of these works). Galen’s main predecessor on these matters was undoubtedly Erasistratus, whose concepts he both criticized and modified, but whose fundamental ideas were, in a number of instances, incorporated into Galen’s thinking. Both men accepted the idea of a separation of the arterial and venous systems, failing to realize they were part of a single, continuous circulatory system. In short, Galen believed that the cardiovascular and respiratory systems largely served the same functions—​they maintained the balance of the innate heat and provided for the creation of the psychic pneuma.

5.1.3 Philosophical Issues Philosophy occupies an important place in the theoretical foundation of Galen’s medical practice. In the short work The Best Doctor Is also a Philosopher (not in the Canon), he writes: What, then, still remains for a doctor who wishes to practice the craft in a manner worthy of Hippocrates not to be a philosopher? For if, in order to discover the nature of the body, the differentiae of diseases and the indications for cures, it is appropriate that he is practiced in logic, and that he stays diligent in the practice of these things, despises money and exercises self-​control, he already has all the components of philosophy—​the logical, the physical and the ethical. (1.60 K.)

Three aspects of his application of philosophy to medicine may be briefly summarized as follows: (i) In terms of the acquisition of knowledge, he stresses the separate but complementary roles of reason (logos) and experience (peira). (ii) He attaches great importance to the need for the doctor to be conversant with the methods of logic and demonstration. This allows him to reason soundly from the theoretical foundation to the practical application of the system of medicine and to evaluate critically the claims of others.

Galen and His System of Medicine    781 (iii) The premise that every event has a causal explanation is central to Galen’s system. That is to say, he believed that potentially one or more causes can be identified for every affection, symptom, and disease and that to initiate effective treatment of disease the causal factors must, if possible, be established. Further, it must also be determined which causal factors have acted but are no longer acting and which are still operative. Galen’s use of the terms pertaining to causation is somewhat variable, but two recurring terms are prokatarktic and proegoumenic. The former seems to indicate external factors, many of which may be readily recognized, like excessive heat or cold in the surroundings—​ such causes may be termed external antecedent causes. The latter seems to indicate internal factors, for example movement of substances such as humors or fluxes that may alter the krasis of the part affected—​such causes may be termed internal antecedent causes. Also, in refuting Erasistratus’ objection to causal explanation—​that two people subject to the same putative cause are quite likely to be affected differently—​Galen claims that it is not only what acts but also what is acted upon (i.e., the person’s body) in the causal nexus that determines the outcome.

5.1.4 Terminology and Definitions Despite his repeated protestations that names are unimportant and that it is only matters that matter, Galen devotes considerable attention to the definition of a group of key terms in a number of his works, both the theoretical (e.g., On the Differentiae of Symptoms, Canon, #9) and the practical (e.g., The Method of Medicine, Canon, #15). There is also his work on nomenclature specifically (On Medical Names, translated into German from the Arabic by Meyerhof and Schacht, 1931). It is essential for the doctor to have a clear concept of what actually constitutes health and disease and their concomitants if he is to perform his prophylactic and therapeutic tasks adequately. What follows is a brief summary of the definitions most central to Galen’s formulations; these are gathered into five groups. (i) “In accord with nature” (kata phusin), “not in accord with nature” (ou kata phusin), and “contrary to nature” (para phusin). The first and third of these are central to Galen’s concepts and definitions of health, disease, and related terms—​ see (iii) below. The second term is considered particularly in his Art of Medicine (Canon, #2). It is applicable to a condition in which the person is not “in accord with nature,” having gone beyond a proper balance, but is not yet “contrary to nature,” in that function is not yet impaired. Examples include obesity and warts. “In accord with nature” (kata phusin—​which might also be rendered normal or natural) applies when the body or one of its parts has a krasis and morphology, as well as a relation with other parts, which allows it to serve its particular function or functions satisfactorily. “Contrary to nature” (para phusin) applies when this is not the case.

782   Greco-Roman Science (ii) Condition (diathesis), constitution (kataskeue), state (hexis), and state (schesis). To a significant degree these terms are interchangeable. Galen certainly uses the first two interchangeably, writing, “If health is some condition or constitution in accord with nature, so disease will be some condition or constitution contrary to nature” (Method of Medicine 1.7, 10.52 K.). In his various definitions and in gen­ eral Galen uses condition more frequently than constitution. In some respects diathesis and schesis refer to less stable or permanent states while kataskeue and hexis refer to more stable or permanent states. (iii) Health (hugieia), disease (nosos/​nosema), symptom (sumptoma), affection (pathos/​ pathema), epiphenomenon (epigennema), and syndrome (sundrome). The first point to make is that for Galen, health is something that positively exists; it is not just the absence of disease. He attacks the Methodist Olympicus in Method of Medicine 2.7 (10.137 K.) because he takes the latter position. The key elements of the definition of health are that it is a balanced state (presumably a proper balance of the elemental qualities, at least in part), and that it is a stable state that allows the body and its component parts to function normally. Galen offers two definitions of health in his On the Differentiae of Diseases 1.2 (6.836–​837 K.), one functional and the other structural, as follows:

(a) Health exists when the functions (energeiai) of the body are in accord with nature (kata phusin). (b) Health exists when the constitution (kataskeue) of the organs by which the body functions is in accord with nature (kata phusin).



Disease, then, is a state of imbalance of sufficient degree to impair a function or functions. (iv) Power/​capacity/​faculty (dunamis), function (energeia), and action (ergon). This triad of terms has been briefly considered in sec. 5.1.2, and the imprecision in the first, recognized by Galen, was noted. In his On the Physical Powers (Natural Faculties) his usage of the three terms may be summarized as follows: a structure has a certain power or capacity to carry out a particular function; the function is what the power or capacity is capable of doing; the action is the doing of it. Thus the stomach has a power to digest food; its function is to apply this power and digest food; its action is actually digesting food. Dunamis is a particularly important term in Galen’s Method of Medicine where it is found in three distinct contexts; in the “physiological” sense as above, in relation to a patient’s ability to tolerate a particular treatment (i.e. his “strength”), and in relation to the strength, power, or potency of medications. (v) Indication/​indicator (endeixis/​ skopos). Endeixis is an important term in Galen’s method and has been a particular point of discussion in recent times. Galen describes it in the Method of Medicine 2.7 (10.126 K.) as “a reflection of the consequence” and gives detailed consideration to the term in the opening section

Galen and His System of Medicine    783 of book 3 (10.157–​160 K.). In essence, his use of “indication” appears close to the present usage as defined in Stedman’s Medical Dictionary: “The basis for initiation of a treatment for a disease . . . may be furnished by a knowledge of the cause (causal indication), by the symptoms present (symptomatic indication) or by the nature of the disease (specific indication).” It is the last that Galen is particularly concerned with. The term “indicator,” which is sometimes used to translate skopos rather than the more usual “aim” or “objective,” is taken to apply to what furnishes the basis for the indication and/​or is the target of the indicated treatment.

5.1.5 Classification Galen, as far as we know, was the first to propose a comprehensive classification of diseases and symptoms. Although there are undoubtedly problems in his classification pertaining to the basic definitions of disease and symptom and to the “naturalness” of his divisions, among other things, his system did have unquestioned usefulness. The classification is set out in the two works, On the Differentiae of Diseases and On the Differentiae of Symptoms (Canon, #9), and is used as the basis for his major work The Method of Medicine (Canon, #15). In summary, he divided diseases into three primary classes. (i) Duskrasias: applicable to homoiomerous structures. (ii) Abnormalities of morphology, composition and position : applicable to organs. (iii) Dissolution of continuity:  applicable to both homoiomerous structures and organs. Duskrasias were further subdivided into four simple duskrasias (an imbalance involving one of the four elemental qualities—​hot, cold, wet, dry), four regular compound duskrasias (an imbalance involving two of the four elemental qualities that are “compatible”—​hot and wet, hot and dry, cold and wet, cold and dry), and two irregular compound duskrasias (an imbalance involving two of the four elemental qualities that are “incompatible”—​hot and cold, wet and dry), although details of the last subgroup are not altogether clear. Abnormalities of morphology and composition were subdivided into disorders of conformation, disorders of number, disorders of size, and disorders of position in relation to other structures. A person or a part of the body could be simultaneously affected by more than one of the major classes of disease—​for example, an infected wound in a homoiomerous part could be simultaneously affected by a duskrasia and dissolution of continuity. Symptoms were more simply classified into loss of function, reduction of function and disorder of function—​an example is the stomach, which may manifest apepsia (absence of digestion), bradupepsia (slow digestion), or dyspepsia (disordered digestion). The details of Galen’s classification of diseases and symptoms and some of the problems involved in his nosological endeavors are discussed in Johnston 2006 (chap. 1.5, 65–​80).

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5.1.6 Pharmacology There are three major works on pharmacology by Galen that still survive: On the Powers and Mixtures of Simple Drugs (11.369–​892, 12.1–​377), On the Composition of Drugs According to Places (12.378–​1007, 13.1–​361), and On the Composition of Drugs According to Kind (13.362–​1052). In addition, there are several other, lesser treatises such as On the Powers of Purgative Medications (11.323–​342) and On Antidotes (14.1–​209). From the theoretical standpoint it is the first that is of particular relevance. The definition of a pharmakon (medication, drug) is that it is a substance or agent that acts on the body to produce an effect in contrast to a food or drink which the body acts on to produce an effect. Galen’s concept of drug action rests ultimately on the same theoretical foundation as does his theory of the structure of the body—​the four elements (or elemental qualities) as the fundamental components of matter. A drug then acts on the krasis of the body or body part of the patient being treated according to the allopathic principle articulated by Hippocrates—​opposites cure opposites. Each drug has specific properties and powers (dunameis), and in Galen’s scheme, four degrees of intensity. In treatment, attention must be given to the issue of matching the intensity of the drug or medication with the severity of the duskrasia. With compound as opposed to simple drugs it is more difficult to determine what the overall effect will be inasmuch as mixture itself may alter the powers of the individual components. Galen also makes a distinction between the basic and the derivative properties of a drug, the latter being its effect on the body. The science of pharmacology is then about the investigation of the basic and derivative properties of simple and compound drugs so they can be applied to the diagnosed disorder in a systematic and rational manner.

5.2 The Practical Application For the doctor with a thorough grounding in the theoretical foundation outlined above, the four main components in the practical application of Galen’s system of medicine—​ diagnosis, prognosis, prophylaxis and therapeutics—​are considered in brief. (i) Diagnosis. Galen has no general work devoted to diagnosis as he does for prognosis, prophylaxis, and therapeutics. However, the subject features prominently in works such as the Art of Medicine (Canon, #2) and On Affected Parts (Canon, #10). It is also an important part of his Method of Medicine (Canon, #15), and the subject of specific works such as Diagnosis from the Pulse. The essential components—​distinguishing normal from abnormal and identifying sites and types of disorder—​depend on Galen’s definitions and on his classification of diseases and symptoms. The measures available in his time were those that are still the foundation of diagnosis today: an accurate history of the presenting illness, background details such as the patient’s previous health and circumstances, and a thorough physical examination utilizing all

Galen and His System of Medicine    785 five senses and including all available secretions and excretions. The ultimate aim was, as it is now, to arrive at the indication (endeixis) or indications for treatment. (ii) Prognosis. Galen wrote several works devoted to prognosis: his On Prognosis, and his two lengthy commentaries on Hippocrates’ Prognostic and Prorrhetic. There are also the specific works such as Prognosis from the Pulses (Canon, #11), On Crises and Critical Days (Canon, #13–​14). Galen clearly subscribed to Hippocrates’ ideas on the importance of prognosis, as set out in the opening sentences of the latter’s Prognostic. In acquiring expertise in prognosis, the combination of reason and experience is of particular importance. (iii) Prophylaxis. Galen’s major work on this subject was his Hygiene (Canon, #16). In this, he deals systematically with such essential components of prophylaxis as diet, exercise, massage, and bathing. The sixth (and final) book of the work is devoted to the prophylaxis of specific diseases. Aspects of prophylaxis are also dealt with in other specific works such as Thrasybulus. A key element of prophylaxis in Galen’s theory is the preservation of krasis within the normal range in all parts of the body. (iv) Treatment. Galen’s major work on this is his Method of Medicine (Canon, #15), supplemented by On the Method of Medicine for Glaucon (Canon, #4), and The Art of Medicine (Canon, #2). In addition there are works on specific measures (such as his several works on venesection) and on specific conditions, as well as his works on foods and medications, especially the three major works on pharmacology referred to earlier. In summary, and following Galen’s disease classification, the aims of treatment may be enumerated as follows: (1) Restoration of a normal krasis in the simple or compound duskrasias, usually through the exhibition of opposites, either as foods or medications. (2)  Restoration of an accord with nature in organic parts that are contrary to nature in terms of size, number, conformation or position—​at least if the change is sufficient to interfere with function. This may involve surgery or other measures depending on circumstances. (3) Restoration of continuity or union where there is dissolution of continuity or union. This may involve direct surgical measures with appropriate postoperative care (e.g., immobilization in a fracture) or treatment by medications and other measures in cases such as infected wounds or chronic ulcers. In addition, symptoms consequent upon the primary disease can be treated with symptomatic measures. The means available to achieve these aims include foods, drinks, and medications to restore eukrasia, surgical measures to deal with dissolution of continuity (for example, in the Method of Medicine he gives detailed accounts of the surgical treatment of full-​thickness wounds of the abdominal wall and of various kinds of skull fractures), measures to deal with inflammation and pain, and ways of correcting organic diseases that often involve surgery but also may include other measures, such as exercise in the case of obesity (an organic disease of size in Galen’s classification).

786   Greco-Roman Science

6. Conclusion I conclude by attempting to briefly answer the question, “What relevance does the study of Galen have today?” 1. Above all, knowledge of Galen’s work is critical to an understanding of the history and development of medicine in the West and the Near East—​he and Hippocrates are the two key figures from 500 bce to the 16th century ce. 2. His more purely philosophical writings are also relevant in the same way, albeit to a much lesser degree, to the history of philosophy. 3. His writings are an unparalleled source of information on the writings of his predecessors that are partly or completely lost—​many apparently direct quotations from these works are included in Galen’s writings. 4. His writings are also valuable to social historians, with anecdotes and digressions often giving vivid portrayals of the conditions of his time. 5. Finally, and by no means least, his writings are of considerable interest to doctors generally. His detailed formulation of a system of practice, founded on a comprehensive theoretical basis, is an enduring blueprint for the science and art of medicine regardless of how elements of the theoretical foundation may change and how new and improved methods of investigation and treatment may become available. Moreover, his emphasis on philosophy, and particularly its ethical component, should never be lost sight of.

Bibliography Boudon(-​Millot), V. Galien, Tome II:  Exhortation à l’étude de la médecine. Art médical. Paris: Les Belles Lettres, 2002. —​—​—​. Galien, Tome I: Introduction général, Sur l’ordre de ses propres livres, Sur ses propres livres, Que l’excellent médecin est aussi philosophe. Paris: Les Belles Lettres, 2007. Boudon-​Millot, V., and Jacques Jouanna, with Antoine Pietrobelli. Galien, Tome IV: Ne pas se chagriner. Paris: Les Belles Lettres, 2010. Boulogne, J. Méthode de traitement. Paris: Gallimard, 2009. Brain, P. Galen On Bloodletting. Cambridge: Cambridge University Press, 1986. Brock, A. J. Galen On the Natural Faculties. Cambridge, MA: Harvard University Press, 1916. Reprint 1963. Bylebyl, Jerome J. “Teaching Methodus Medendi in the Renaissance.” In Galen’s Method of Healing. Proceedings of the 1982 Galen Symposium, ed. Fridolf Kudlien and Richard J. Durling, 157–​189. Leiden: Brill. Conrad, L. I., M. Neve, V. Nutton, R. Porter, and A. Wear. The Western Medical Tradition (800 BC to AD 1800). Cambridge: Cambridge University Press, 1995. Daremberg, C. Œuvres anatomiques, physiologiques et médicales de Galien. Paris: J-​P Baillière, 1854–​1856.

Galen and His System of Medicine    787 De Lacy, P. H. Galen On the Doctrines of Hippocrates and Plato. Corpus Medicorum Graecorum, V.4.1.2. Berlin: Akademie-​Verlag, 1978. —​—​—​. Galen On the Elements According to Hippocrates. Corpus Medicorum Graecorum, V.5.1.2. Berlin: Akademie-​Verlag, 1996. Duckworth, W. H. L., M. C. Lyons, and B. Towers. Galen On Anatomical Procedures. The Later Books: IX.6‒XV. Cambridge: Cambridge University Press, 1962. Edlow, R. B. Galen On Language and Ambiguity. Leiden: Brill, 1977. Garofalo, Ivan, and Armelle Debru. Galien, Tome VII: Les os pour les débutantes. L’anatomie des muscles. Paris: Les Belles Lettres, 2005. —​—​—​. Galien, Tome VIII: L’anatomie des nerfs. L’anatomie des veines et des artères. Paris: Les Belles Lettres, 2008. Hankinson, R. J. Galen on the Therapeutic Method: Books 1 and 2. Oxford: Oxford University Press, 1991. —​—​—​. Galen On Antecedent Causes. Cambridge University Press, Cambridge, 1998. —​—​—​, ed. The Cambridge Companion to Galen. Cambridge: Cambridge University Press, 2008. Johnston, I. Galen: On Diseases and Symptoms. Cambridge: Cambridge University Press, 2006. —​—​—. Galen. Hygiene, Thrasybulus, On Exercise with a Small Ball. Cambridge, MA: Harvard University Press, 2018. Johnston, I. and G. H.  R. Horsley. Galen’s Method of Medicine. Cambridge, MA:  Harvard University Press, 2011. Kudlien, F. and R. J. Durling, eds. Galen’s Method of Healing. Leiden: Brill, 1991. Kühn, C.-​G. Claudii Galeni Opera Omnia. 20  vols. Leipzig:  Cnobloch, 1821–​1833. Reprint, Hildesheim: Georg Olms Verlag, 1997. Mattern, Susan P. The Prince of Medicine: Galen in the Roman Empire. New York: Oxford University Press, 2013. May, M. T. Galen On the Usefulness of the Parts of the Body. Ithaca, NY: Cornell University Press, 1968. Meyerhof, M., and J. Schacht. Galen über die medizinische Namen. Berlin: Abhandlungen der Preußischen Akademie der Wissenschaften, 1931. Nutton, V. Galen On Prognosis. CMG, V.8.1. Berlin: Akademie-​Verlag, 1979. —​—​—​. Galen On My Own Opinions. CMG, V.3.2. Berlin: Akademie-​Verlag, 1999. —​—​—​, ed. The Unknown Galen. London: Bulletin of the Institute of Classical Studies, suppl. 77, 2002. —​—​—​. Ancient Medicine. London: Routledge, 2004. Nutton, V., and Gerrit Bos. Galen On Problematical Movements. Cambridge, New  York: Cambridge University Press, 2012). Petit, Caroline. Galien, Tome III: Le médecin. Introduction. Paris: Les Belles Lettres, 2009. Sarton, G. Galen of Pergamon. Lawrence: University of Kansas Press, 1954. Siegel, R.E. Galen On the Affected Parts. Basel: S. Karger, 1976. Singer, C. Galen On Anatomical Procedures. Oxford: Clarendon Press, 1956. Singer, P. N. Galen: Selected Works. Oxford: Oxford University Press, 1997. Singer, P. N. ed., with Daniel Davies and Vivian Nutton, trans. Galen: Psychological Writings. Cambridge, New York: Cambridge University Press, 2013. Thomas L. Stedman. Stedman’s Medical Dictionary. 27th ed. Baltimore, MD:  Lippincott, Williams and Wilkins, 2000. Walzer, R., and M. Frede. Three Treatises on the Nature of Science. Indianapolis: Hackett, 1985. Wilkins, John. Galien, Tome V: Sur les facultés des aliments. Paris: Les Belles Lettres, 2013.

chapter D10

P tole my James Evans

1. Introduction Claudius Ptolemaeus (Κλαύδιος Πτολεμαῖος) (2nd century ce) or Ptolemy, as he is usually known in English-​speaking lands, was a polymath who lived in Alexandria. He is one of the most significant of all ancient scientific writers and many of his works are extant. There are disputes about what is original in these works and what represents summary or development of the works of his predecessors. Coming as he did in the closing period of creative scientific work among the Greeks, he managed to place several fields of study into forms that long remained definitive—​in some cases until the Renaissance. Much of his surviving work involves the application of mathematics to the natural sciences. As Owen Gingerich expressed it, Ptolemy attempted to do for applied mathematics what Euclid had done for pure mathematics. This was a vast program. It involved (surviving) works of astronomy, cosmology, astrology, optics, geography, harmonics, and philosophy. Proclus (EANS 698–​699) gives details of Ptolemy’s attempt to prove Euclid’s parallel postulate, in a lost work of pure geometry (Friedlein 1873, 365–​368; Morrow 1970, 285–​289; Heath 1921, 2.295–​297). Simplicius mentions a work On Dimension in which Ptolemy attempted to prove that no more than three dimensions are possible (Heiberg 1894, 9.21–​29; Hankinson 2002, 27–​28). According to the Ptolemy entry in the Suda (a Byzantine biographical encyclopedia of about the 10th century; www.stoa.org/​sol/​), Ptolemy wrote a work in three books on mechanics, but this has not come down to us. Ptolemy is also known to have written a separate work on an astronomical instrument, the meteoroskopeion, which was somewhat more complex than the armillary sphere (astrolabon) that he described in the Almagest (Rome 1927). Simplicius mentions a book of Ptolemy On the Elements, as well as a work On Weights (Peri rhopōn), which seem to have been closely related to one another (perhaps

790   Greco-Roman Science parts of a single work), and which addressed such questions of natural philosophy as whether air is heavy in its own place (Heiberg 1894, 20.10–​25 and 710.14–​7 11.25; Mueller 2011, 52–​53; 2009, 106–​107). Of the works commonly attributed to him, only the Karpos (Centiloquium in its Latin title) is definitely not his; it consists of a hundred astrological aphorisms. Little is known of Ptolemy’s life. The ancient and medieval testimony has been collected in Boll 1894, 53–​66. The dates of astronomical observations reported in the Almagest that are certainly Ptolemy’s range from 127 to 141 ce, and another that may be his was made in 125 (Pedersen 2011, 408–​422). Since some of his other writings refer to it, the Almagest was one of Ptolemy’s earlier works (though not his very earliest). Moreover, the Almagest is a work of considerable sophistication and must have required some time for its development. If we suppose that Ptolemy began to make his own observations at around the age of 20, we may put his birth in 105 or 107. Ptolemy’s Canobic Inscription (Heiberg 1907, 144–​155; superseded by Jones 2005) was set up in the 10th year of the Roman Emperor Antonius (146/​147 ce). Since the Almagest in its final form was later (Hamilton, Swerdlow, and Toomer 1987), it seems that Ptolemy was in his early 40s when he completed it. The entry on Ptolemy in the Suda says that Ptolemy lived into the reign of Marcus Aurelius (r. 161–​180 ce, though in joint rule with Lucius Verus until 169). Thus, we may take Ptolemy’s life to have been from about 105 or 107 ce until some year between 161 and 180. (According to a medieval tradition attributed to Abu’l-​Wafa, he died in his 78th year (Boll 1894, 58); but there is no reason to put any faith in this report.) Many of Ptolemy’s works are addressed to a certain Syrus. Whether this was a friend, a fellow mathematician, or a patron we do not know. A number of scholars both before and after Ptolemy’s time were associated with the Alexandria Museum, but no such connection is attested for Ptolemy. Nevertheless, he must have had nearly complete freedom to devote himself to his scientific work. And he seems to have spent his entire professional life in Alexandria or nearby Canobus.

2. Astronomy Ptolemy’s single most important work was the Almagest, an astronomical treatise devoted mostly to the theories of the motions of the sun, moon, and planets (Heiberg 1898–​1903; Toomer 1984). The original title was something like The 13 Books of the Mathematical Treatise (Syntaxis) of Klaudios Ptolemaios. In later Greek sources, this was sometimes referred to as the big or great syntaxis (Tihon 2014, 74). It is surmised that Arabic writers of the early Middle Ages appended the definite article al to the superlative form of the Greek adjective (megistē = greatest), which would account for the Arabic title al-​Majistī. Medieval Latin writers smoothed this into Almagestum, and then Almagest. The history of the Western astronomical tradition, with its Greek, Arabic, and Latin contributions, is embodied in this one book title.

Ptolemy   791

2.1 Epistemological and Moral Value of Astronomy In the introduction to the Almagest, Ptolemy attempts to justify the art of astronomy. He begins by distinguishing the theoretical part of philosophy from the practical. Practical philosophy is concerned with such things as ethical behavior, but this can often be acquired by practice, without close study. Following Aristotle (Metaphysics 6.1.1026a18–​20), Ptolemy divides theoretical philosophy into theology, physics, and mathematics (by which, in this context, he means mathematical astronomy). Ptolemy argues that only in mathematics is certainty of knowledge possible. The subject matter of theology is an invisible and changeless deity located at the periphery of the universe. This god clearly has nothing to do with the traditional Greek pantheon; rather it is an austere god of philosophers—​ the god of Aristotle. The subject matter of theology has the advantage of being eternal, but it is imperceptible to the senses. And thus, it will be impossible for philosophers to agree about it. Physics deals with the hot, the white, the soft, and such, located in the realm below the sphere of the moon. Its subject matter is perceptible to the senses but unstable and always changing. So, again, certainty of knowledge is impossible. But mathematical astronomy deals with eternal, divine objects (the planets, sun, and moon), which are always what they are, but which can also be perceived. So only in mathematical astronomy may we aspire to certainty of knowledge. Moreover, astronomy is a good road to start on even if one’s ultimate goal is physics or theology. For in physics, the essential natures of bodies are best disclosed by their motions. (Here Ptolemy is alluding to Aristotle’s theory connecting natural motions with elemental natures.) Thus, a good way to prepare to do terrestrial physics is to study the motions of celestial objects. As for theology, the best entryway is the study of eternal divine things that can still be seen. So here Ptolemy has given epistemological arguments for placing astronomy first in a hierarchy. But he goes on to make a claim for its moral significance—​ that is, its benefit for the practical side of philosophy. By meditating on things that are constant, orderly, and calm, we become lovers of divine beauty and gradually produce in ourselves a similar spiritual state. Was this was mostly intended to fortify the reader of the Almagest for the hard work ahead, or did Ptolemy sincerely feel it? Ptolemy displayed the numerical parameters of his astronomical theories on a stela he set up in Canobus, which could still be seen in the 6th century (Jones 2005, 53). The text was copied in Late Antiquity and is known as the Canobic Inscription. Ptolemy began this display of the secrets of the cosmos with a dedication “to the savior god.” In Ptolemy’s time and place, this may well have meant Sarapis, which seems to acknowledge a god less impersonal than the austere divinity mentioned in the introduction to the Almagest.

2.2 Physical and Philosophical Foundations of Astronomy In Almagest 1.3–​9, Ptolemy sets out his physical premises: the heaven is a sphere and rotates on its axis, the earth is also a sphere, the earth is in the middle of the heaven

792   Greco-Roman Science and has no motion from place to place, and the earth is so small it can be considered a point in relation to the heaven. These propositions and proofs were conventional by Ptolemy’s time and were common in the elementary writers (Evans 1998, 76–​77). Most interesting is Ptolemy’s admission that, as far as appearances are concerned, it would make no difference whether the sky turns to the west once a day or the earth turns to the east. Indeed, sky and earth could both be in motion, as long as the relative speeds allowed for one overtaking per day (Almagest 1.7). Here Ptolemy must fall back on physical arguments, in conformity with the view expressed by Aristotle, Posidonius (EANS 691–​692), Geminus (EANS 344–​345), and others that astronomy must take its first principles from physics (philosophy of nature) (Evans and Berggren 2006, 250–​255). Ptolemy argues that if the earth turned, this would be the most violent of all motions (since the natural motion of elemental earth is not circular, according to Aristotle, but radial). Consequently, clouds and things thrown up into the air would be left behind.

2.3 Solar Theory In the remainder of book 1 and book 2, Ptolemy deals with trigonometrical and spherical trigonometrical preliminaries. These include a table of chords, a table of the sun’s declination (its angular distance above the plane of the equator), and a table of ascensions (rising times for each of the zodiac signs in 11 klimata). In book 3, he turns to his main subject, the quantitative description of the motions of the sun, moon, and planets. Of all these bodies, the sun has the simplest theory. The equinoctial and solstitial points divide the zodiac into four equal 90º arcs. If the sun moved a constant speed on a circle centered on the earth, the four seasons would be equal in length. But already by the time of Callippus (EANS 464–​465), the Greek astronomers realized that the seasons are slightly unequal. Probably by around 200 bce, Greek astronomers began to treat the theory of the sun by means of an eccentric (off-​center) circle. See figure D10.1. The outer circle represents the sphere of stars, with its zodiac belt. The sphere of stars is centered at the earth, O (for observer). But the sun travels at uniform speed on a circle that is centered at point C, somewhat displaced from O. Because of the eccentricity, it is possible to “save,” or account for, the inequality in the length of the seasons. When the sun reaches a, we see it against VE, the vernal equinoctial point (or beginning of the sign of Aries). When the sun reaches b, we see it against SS, the summer solstitial point (beginning of Cancer). Thus, the sun appears to run through the equal quadrants of the zodiac (VE to SS, SS to AE, and so on) in unequal times, because the arcs that the sun traverses (ab, bc, and so on) are of unequal lengths. The season lengths shown in the figure are those given by Ptolemy in the Almagest and due originally to Hipparchus (EANS 397–​399). They are reasonably accurate for their epoch. It follows from the model that when the sun is at A (the apogee), it is at its greatest distance from us. At Π (perigee) it is closest. The eccentricity OC of the sun’s circle is most conveniently expressed in terms of the radius of the circle. As far as we know, Hipparchus was the first to show how to calculate the eccentricity from the lengths of the seasons. Angle A is the longitude of the apogee.

Ptolemy   793 SS 94 1/2

b

C AE

c

94 1/2 days A

A a

O

VE

Sun’s circle

Π d 88 1/8

90 1/8 Sphere of stars WS

Figure D10.1  Ptolemy’s solar theory (eccentric circle). Drawing by author.

Hipparchus obtained an eccentricity of 0.0417 (or, as Ptolemy put it, 2½ parts if the radius of the sun’s circle is taken as 60) and placed the apogee at 65½º (5½º of Gemini). Ptolemy retained these values. Astonishingly, it happened that there were two different geometrical models that could account for the apparently nonuniform motion of the sun while still retaining the uniformity of movement that was believed to be appropriate for divine, celestial things. See figure D10.2. Now we assume that point K moves at uniform speed on a circle that is centered on the earth O. This circle is called the deferent (from the medieval Latin: deferre = to carry). Meanwhile the sun S revolves in the opposite direction around a small epicycle (a Greek word: epi = on, kuklos = circle). These two motions are at the same rate, so we always have angle β = angle α. Thus, when the sun is in the direction of Z, it will appear to be moving more slowly than average, since the motion of S on the epicycle will subtract from the forward motion of K. And when the sun is in the direction of Y, it will appear to be moving more rapidly than average, since the motion of S will be in the same direction as the motion of K. Thus the sun apparently speeds up and slows down, while it is really simultaneously executing two uniform circular motions. This may be called the concentric-​plus-​epicycle model. The concentric-​plus-​epicycle model is rigorously equivalent to the eccentric-​circle model, as shown by Fig. D10.3. We begin with the concentric-​plus-​epicycle, as in figure D10.2. Since always β = α, it follows that as K moves around the deferent, KS remains parallel to OC. Thus the path traced by the moving point S, shown in dashed line, is an off-​center circle. If we choose the epicycle radius KS to be equal to the eccentricity

794   Greco-Roman Science β

Z S α

K epicycle

O

deferent Y

Figure D10.2  Concentric-​deferent-​with-​epicycle version of the solar theory. Angles α and β increase at the same rate. Drawing by author.

β

S K

α C O

Figure D10.3 Equivalence of the eccentric circle model for the sun to the concentric​plus-​epicycle model. Drawing by author.

OC of the eccentric, then the two models are geometrically equivalent. The proof of the equivalence of an eccentric circle to a concentric-​plus-​epicycle is usually attributed to Apollonius of Perga (ca 190 bce) (EANS 114–​115), based on some remarks of Ptolemy. Proofs of the equivalence survive in Theon of Smyrna (EANS 796) and in Ptolemy. Nevertheless, there arose a debate in antiquity over which model represents the nature of things. According to Theon of Smyrna (3.34; Dupuis [1892] 1966, 305), Hipparchus preferred the concentric-​plus-​epicycle model because it seemed more likely that things were placed concentrically with the earth. Ptolemy, however, in Almagest 3.4, expresses a preference for the eccentric circle model because it requires only one motion rather than two. Here we can see that both Hipparchus and Ptolemy were making choices based on nonastronomical criteria that may be described as physical or philosophical. A crucial parameter of the theory is the length of the tropical year, defined as the time that the sun requires to travel from spring equinox, all the way around its circle,

Ptolemy   795 and return to the same equinox. The rough value of 365¼ days was already well-​known in Hipparchus’s time. But Hipparchus had shown that this is slightly too high and had adopted 365 + 1/4 – ​1/​300 days, followed by Ptolemy (Almagest 3.1)

2.4 Ptolemy’s Astronomical Instruments Ptolemy describes his astronomical instruments and, although most were not original with him, he is the oldest detailed source for most of them. Later writers, such as Theon of Alexandria and Proclus supply some other details, but are strongly influenced by him. For observing a solstice, the easiest thing to use was a quadrant, made of stone or wood (Almagest 1.12). See figure D10.4. One face of a block is smoothly finished and set in the plane of the meridian. Peg A, at right angles to the surface, casts a shadow over the inscribed quadrant CDE of a circle. A plumb line hanging from A and a second peg B can be used for leveling the instrument. Summer solstice is indicated when the noon altitude is the greatest for the year; winter solstice, when the noon altitude is the smallest for the year. The equinox is indicated when the noon altitude is halfway between the minimum and maximum values. A second instrument for taking altitudes is the closely related meridian circle. It consists of a vertical metal ring (figure D10.5), divided into 360º. A smaller ring fits inside the first ring in such a way that their faces are in the same plane and the smaller ring may turn freely within the larger one. Fixed on a diameter of the movable ring are two small plates and, at their middles, two pointers for indicating degrees on the divided scale. To use this instrument, one aligns it in the plane of the meridian. When the sun comes to the meridian, one turns the movable ring until the shadow of the upper

A

C

D

E

B

Figure D10.4  Ptolemy’s meridian quadrant. Drawing by author.

796   Greco-Roman Science

Figure D10.5  Ptolemy’s meridian circle. Drawing by author.

small plate falls upon the lower one. Then one can read the altitude of the sun on the graduated scale. Both the meridian quadrant and the meridian circle have the disadvantage that they are used for taking only noon altitudes. There is no reason, of course, why the moment of solstice has to come precisely at noon. For solstices occurring at some other time of day (or even at night), one would interpolate among a series of noon observations. For the obliquity of the ecliptic (half the difference between the noontime solar altitudes at summer and winter solstice), Ptolemy (Almagest 1.12, 1.14) adopted 23º51′20″, in close agreement with Eratosthenes (EANS, 297–​300). The equatorial ring is a simple instrument specially designed for observing equinoxes (Almagest 3.1). This consists of a ring fixed to the pavement and oriented in the plane of the celestial equator. This requires that the ring face toward the north and that it make an angle with the horizontal that is equal to the co-​latitude (90º minus the latitude) of the place of observation. In the spring and summer, the sun is perpetually north of the celestial equator. In the fall and winter, it is perpetually south of the equator. Only at the moment of equinox does the sun come into the plane of the celestial equator. If this happens in the daylight, one would see the shadow of the upper part of the equatorial ring fall on the lower part of the ring. In principle, the equatorial ring has an advantage over the meridian instruments, in that it can be used to observe an equinox at any time of day—​not just at noon. In practice, this advantage was undermined by the difficulty of accurately orienting the ring. Ptolemy mentions that one of the equatorial rings in the Palaestra in Alexandria sometimes falsely indicated a double equinox (two equinoxes on the same day). This might occur if the ring were out of the correct plane or if it were warped. For observations made shortly after sunrise or shortly before sunset, atmospheric refraction could also derange the observed time of equinox (Britton 1992).

Ptolemy   797 The most sophisticated astronomical instrument described by Ptolemy is his astrolabon—​ the “star-​taking” instrument (Almagest 5.1). Often it is called an armillary sphere. (It should not be confused with the plane astrolabe, the emblematic astronomical instrument of the Middle Ages.) See the reconstruction by Adolphe and Paul Rome in figure D10.6. The astrolabon was the instrument that Ptolemy regularly used for measuring the celestial longitudes and latitudes of stars and plants. The outer ring 7 is fixed in the plane of the meridian. Inside it, ring 6 may be turned to adjust for the geographical latitude of the place of observation. (The altitude of the north celestial pole above the horizontal must be equal to the geographical latitude.) The inner nest of rings, consisting of rings 1–​5, may be turned as a unit about the celestial poles. Ring 3, the ecliptic, is divided into signs of the zodiac, and each sign is divided into 30º. Rings 2 and 5 may be turned about the poles of the ecliptic. Inside ring 2 is ring 1 (equipped with two sights), which may be slipped around inside ring 2. These sights are used for measuring the celestial latitude of an object—​ the angular distance of the object above or below the plane of the ecliptic. Rings 5 and 2 are used for measuring the difference in celestial longitude between two objects. (On observing with a replica of Ptolemy’s astrolabon, see Włodarczyk 1987.)

Figure D10.6  Ptolemy’s armillary sphere as reconstructed by Paul and Adolphe Rome (from Rome 1927). Scan of book published in 1927.

798   Greco-Roman Science Ptolemy also describes an instrument he designed expressly for taking zenith distances of the moon (Almagest 5.12; Dicks 1953–​1954; Price 1957, 589–​590). Modern writers sometime call this “Ptolemy’s rulers,” or “parallactic rulers,” since Ptolemy used it in an investigation of the moon’s parallax. In the Renaissance it was called the triquetrum. The Renaissance illustration in figure D10.7, which shows Ptolemy using the instrument, depicts him with a crown on his head, owing to the common medieval confusion linking him to the Ptolemaic dynasty, which ruled Egypt from the death of Alexander to the death of Cleopatra. Ptolemy also mentioned a dioptra four cubits long (Almagest 5.14; Price 1957, 591) that he used for measuring angular sizes of the sun and moon. It involves a small cylinder

Figure D10.7  Ptolemy’s rulers, or the parallactic instrument (the medieval triquetrum). From Cuningham 1559. Houghton Library, Harvard.

Ptolemy   799 that may be slid back and forth along a long rod. At one end of the rod is a plate with a small hole, though which the observer looks. The cylinder is slid along until it is seen to just barely cover the moon. Archimedes (EANS 122–​128) had described a similar instrument in the Sand Reckoner (1.4; Mugler 2002, 137–​138) and, according to Ptolemy, Hipparchus had also used one.

2.5 Lunar Theory The moon, like the sun, appears to speed up and slow down as it travels around the ecliptic. Naturally, there is again a choice between an eccentric-​circle theory and an epicycle theory, both of which were investigated by Hipparchus. Figure D10.8 illustrates the epicyclic version. O is the earth and ♈ indicates the fixed direction of the spring equinoctial point. The moon M travels backward on its epicycle, while the center K of the epicycle travels around the earth on the deferent circle. So far, this is similar to the epicycle version of the solar theory. If angles α and β increased at the same rate, KM would remain parallel to OA and the lunar apogee would be fixed at A. But, in fact, the location in the zodiac at which the moon moves most slowly itself moves eastward, completing a circuit of the zodiac in about nine years. Thus, if this year the moon moves most slowly in (say) Cancer, then in about 2¼ years it will move most slowly in Libra, and in 4½ years it will move most slowly in Capricorn. So, in figure D10.8 we must let β increase a little more slowly than α. Thus, when α has gone through 360º (after one tropical month), we will have to wait a little while for β to complete its 360º (and so complete one anomalistic month). Thus the lunar apogee will slowly move eastward (counterclockwise). (From the modern point of view, the advance of the apogee is a perturbation of the moon’s motion around the earth, due to the gravitational action of the sun.) Hipparchus’s lunar theory worked well for the prediction of eclipses—​but eclipses only test the model at the times of new or full moon.

β M

a

A

K α

O

Π

Figure D10.8  The simple lunar theory that Ptolemy inherited from Hipparchus. Drawing by author.

800   Greco-Roman Science Ptolemy found, however, that at the time of the quarter moons (when the angle between the sun and moon is about 90º), the epicycle of the moon seemed to be too small to give accurate positions. So he introduced an ingenious crank mechanism to pull the moon closer to the earth at quarter moon, and thus make its epicycle appear larger. (From the modern point of view, Ptolemy was grappling with a second perturbation of the moon’s motion, called “evection,” also due to the gravitational action of the sun.) For Ptolemy’s modification of Hipparchus’s theory, see figure D10.9. The motion of M on the epicycle is as before. But now the position of the deferent circle is constantly changing. The deferent has a constant radius DK, but its center D moves around the earth O on a small circle. The business of this crank mechanism is to push the epicycle farthest from the earth at new and full moon and to bring the epicycle closest to the earth at the quarter moon. Let Ŝ be the direction of the mean sun (so ♈OŜ goes through 360º in a tropical year). Angle ♈OK gives the direction of the mean moon, which goes through 360º in one tropical month. Thus, θ1 is the mean elongation of the moon (the angular distance between the mean moon and the mean sun). The motion of D on its small circle is governed by the stipulation that θ2 = θ1. Thus DOK is equal to twice the mean elongation. Now, when we have mean new moon (and DOK is zero), then the distance from O to K takes on its maximum value, DK + OD. But at quadrature (mean elongation θ1 = 90º) DOK becomes equal to 180º and so the distance from O to K takes on its minimum value, DK—​OD. In a final touch to his lunar theory (figure D10.10), Ptolemy modified the way he defined the position of M on the epicycle. In the earlier versions of the theory, angle β was measured from the apogee a of the epicycle (along the extension of OK). But now Ptolemy introduces point F, diametrically opposite D on the small circle, and uses this to define a new effective apogee a′ along the extension of FK. Thus angle β, which is assumed to increase uniformly with time, is to be measured from a′ rather than a. Ptolemy’s lunar theory is reasonably good at predicting angular positions—​the direction of M as seen from O. But it results in an unsatisfactory treatment of the distances. In Ptolemy’s final theory, the moon’s maximum distance from the earth exceeds its Sˆ

β a K

M

θ2

θ1

D O

Figure D10.9  Ptolemy’s second lunar theory. Drawing by author.

Ptolemy   801 Sˆ

β a a' M K

θ2

θ1

D O F

Figure D10.10  Ptolemy’s third and final lunar theory. Drawing by author.

minimum distance by nearly 2 to 1. In reality, the moon’s greatest distance is only about 12% greater than its least distance. Thus, according to the theory, the moon’s apparent size should vary much more than is seen. However, Ptolemy passes over this defect of the theory in silence. Note also what a savage rupture of accepted physical principles is involved in postulating the effective apogee a′. The mean motion of the moon on its epicycle is now measured with respect to a point that is accelerating back and forth. What sort of uniformity of motion is this, when β is measured with respect to a point that is moving nonuniformly? Ptolemy was to be criticized for both of these shortcomings—​ one a matter of an objective contrast between theory and reality, and the other a matter of philosophical preference.

2.6 Planetary Theory By the time of Apollonius of Perga (active ca 190 bce), Greek astronomers had turned to deferent and epicycle theory for explaining the retrograde motion of the planets. In figure D10.11, O represents the earth and ♈ indicates the fixed direction of the spring equinoctial point. Let point K move uniformly about the deferent circle (which is centered on O), completing one revolution in the planet’s tropical period. (The tropical period is the average time required for the planet to go all the way around the zodiac.) Meanwhile, the planet P moves uniformly in the same direction around the epicycle (which is centered on the moving point K), competing one revolution in the planet’s synodic period. (The synodic period is the average time required for the planet to go from the middle of one retrograde motion to the middle of the next.) This model can explain in a general way how the planet could make forward progress around the zodiac and still appear to move backward from time to time. The planet will be in the middle of its retrograde motion at the perigee π of the epicycle; the planet will have the fastest

802   Greco-Roman Science

O Π K a

deferent epicycle

P

Figure D10.11  Simple concentric-​and-​epicycle model for the motion of a planet due to Apollonius. Drawing by author.

forward motion at the apogee a of the epicycle. Note the flexibility of the epicycle as an explanatory tool. In planetary theory, the motion on the epicycle is in the same direction as the motion of the epicycle’s center; moreover, the epicycles are rather large; and the epicycle is responsible for producing retrograde motion. In the solar theory, the motion on the epicycle is in the opposite direction to the motion of the epicycle’s center; the epicycle is small; and the epicycle produces a variation in speed without a reversal in direction. Apollonius even proved a theorem concerning the locations on the epicycle where retrograde motion would begin and end. Nevertheless, this first version of the planetary theory was not capable of predicting the times and zodiacal positions of the regressions with quantitative accuracy. For some planets, and notably Mars, the actual retrograde arcs are spaced very nonuniformly around the zodiac, while Apollonius’s simple version of the theory requires uniformly sized and spaced retrograde arcs. By the middle of the 2nd century bce, astronomers had also experimented with a version of the theory in which the center of the deferent circle is placed off-​center from the earth. Placing the deferent off-​center from the earth will cause the retrograde arcs to be seen as unequally spaced around the zodiac. This borrows an idea from the ancient solar theory. But the theory is not able to simultaneously account for the unequal spacing of the retrogradations and the unequal widths of the retrograde arcs themselves (Evans 1998, 342–​343). This perhaps explains why Hipparchus did not offer a theory of the planets, even though he had produced good theories of the sun and the moon. The theory of planet longitudes that Ptolemy used for Venus, Mars, Jupiter, and Saturn is shown in figure D10.12. (The Mercury theory has some extra complications.) The epicycle’s center K moves on a circle whose center C is eccentric to the earth O. But Ptolemy has introduced a third center E, which in the Middle Ages came to be called the equant point. E serves as a center of uniform motion. That is, K moves at constant angular speed as viewed from E—​and thus angle α increases uniformly with time. Thus it results that the linear speed (in miles per hour, say) of K is greater at perigee Π and smaller at apogee A. The introduction of the equant point made it possible, for the

Ptolemy   803 A

α

E C

O

K

β

Π P

Figure D10.12  Ptolemy’s theory of longitudes for Venus, Mars, Jupiter, and Saturn. Drawing by author.

first time, to predict planetary phenomena accurately from a geometrical theory. Thus the theory predicts with good accuracy the direction of P as viewed from O. Ptolemy’s theory of Mars, for example, can satisfactorily match both the unequal spacing and the unequal widths of the retrograde arcs. (Evans 1984; for alternative views of how the Greek astronomers arrived at the equant see Jones 2004; Swerdlow 2004; Duke 2005a). Greek astronomers had long been aware of, and creatively using, Babylonian arithmetical theories based on nonuniform motion. A  good example is provided by Geminus’s Introduction to the Phenomena (1.18–​22; Evans and Berggren 117–​118), which endorses the principle of uniform circular motion for celestial things, but goes on to discuss a Babylonian lunar theory in which the moon’s speed changes from day to day in a regular sawtooth pattern (18.4–​19). Greek astronomy could be opportunistic. Greek planetary theories, most likely from the time between Hipparchus and Ptolemy, turn up in later Indian material and show some experimentation with nonuniform planetary motions (van der Waerden 1961; Duke 2005b). However, the first clear setting out and use of the equant is in Ptolemy’s Almagest. To account for the planets’ latitudes (their departures from the plane of the ecliptic), Ptolemy allowed the planet’s deferent and the planet’s epicycle to lie outside the plane of the ecliptic. This is the most complex part of his theory, which we do not have space to discuss here. Ptolemy changed his latitude theories as he matured, making them simpler and more accurate as he moved from the Almagest to the Handy Tables to the Planetary Hypotheses (Swerdlow 2006). Ptolemy’s plan in the Almagest for each celestial body is to explain his model and to describe the observations that will be used to derive numerical values for the elements or parameters (radius of the epicycle, eccentricity, and so on). Once he has derived the elements, he calculates tables for each celestial body. The tables allow a user to rapidly work out (following Ptolemy’s directions) the position (celestial longitude and latitude) of a body for any desired date. The advantage of the tables is that Ptolemy has already done the trigonometry. Thus, the user merely needs to perform additions, subtraction,

804   Greco-Roman Science and interpolations. The Almagest also contains a catalogue of about 1,000 stars, with their longitudes, longitudes, and magnitudes. Most scholars believe it is substantially based on an earlier catalogue by Hipparchus (Grasshoff 1990).

2.7 Applied Astronomy After completing the Almagest, Ptolemy wrote a more user-​friendly book, suited for practical calculation. This is the Handy Tables (Tihon 2011; Halma 1822). Here the tables of the Almagest are expanded in size, so that entries occur at smaller intervals of the arguments. Moreover, the tables are stripped of their theoretical justification, the observations on which the elements were based, the methods of deriving the elements, as well as the methods of calculating the tables themselves. What remains is the tables and directions for using them. The Greek title is Procheiroi kanones, “tables for the hand,” from which the modern English rendering. In the Handy Tables Ptolemy introduced a few changes in theory, especially for the latitudes of the planets (Pedersen 2011, 398–​400; Swerdlow 2006), and also provided a table for the equation of time. Because of the obliquity of the ecliptic, as well as the nonuniformity of the sun’s motion, the sun is not a uniform keeper of time. That is, the length of a solar day varies slightly, and in a complex way, over the course of the year. Ptolemy had discussed this effect in the Almagest but had not reduced it to a table. According to Ptolemy’s numerical values, the true time interval between two observations made at just the right times of year could be off by as much as 5/​9 of an hour from the time apparently elapsed based on direct sun observations. As Ptolemy remarks (Almagest 3.9), for the planets, the motion on the ecliptic in such a short time is negligible. But, for the quickly moving moon, this is not the case; thus, in calculations involving eclipses, it is necessary to take the equation of time (to use the modern expression) into account. Although Geminus (6.2–​4; Evans and Berggren 2006, 161–​162) had stated that the solar day is not constant, Ptolemy’s mathematical treatment of the subject in the Almagest and the Handy Tables is the oldest we have. Ptolemy’s introduction to the Handy Tables survives (Heiberg et al. 1907, 156–​185). The tables themselves exist in the form given them in the edition of Theon of Alexandria (EANS 793–​795). But Theon’s tables, when compared with Ptolemy’s directions, show that Theon could not have changed the tables very much. Papyrus fragments of the Handy Tables (Jones 1999) from before Theon’s time confirm this. Theon also wrote two commentaries on the Handy Tables—​the second, or “Little Commentary,” after his after his students complained that the “Big” one was too hard to understand. (For the Little Commentary see Tihon 1978; for the Big Commentary see Tihon 1985, 1991, 1999.) The Handy Tables served as the prototype for many of the collections of astronomical tables, with directions for their use, created by Pahlavi and Arabic writers and known as zīg (Pahlavi) or zīj (Arabic). (See EANS 819 and Mercier 1997, 1057–​1058.) Ptolemy wrote several much shorter works on specialized astronomical topics. The Phaseis (Heiberg 1907, 1–​67) deals with phases of the fixed stars, that is, heliacal risings

Ptolemy   805 and settings. A central problem of early Greek astronomy was to tell the time of year by the behavior of the stars. For example, in the Works and Days of Hesiod, the morning setting of the Pleiades (when the Pleiades are seen setting in the west just before the sun comes up in the east) signaled the onset of the rainy weather of late fall. This was the sign to plow the ground and sow the wheat. The morning rising of the Pleiades (roughly May) was the sign of the grain harvest. The study of heliacal risings and settlings was motivated by the complexity of the Greek civil calendars. These luni-​solar calendars had the duty of approximately tracking both the sun and the moon. Months alternate between 29 and 30 days; and there are either 12 months or 13 months in a civil year. Thus, events in the astronomical year—​such as the summer solstice or the morning rising of the Pleiades—​do not occur always on the same date (or even in the same month). Moreover, each major city had its own calendar with different month names and different conventions for the beginning of the year. In the 5th century bce, Greek astronomers compiled parapegmata, which we might call star calendars (Lehoux 2007). They allowed one to know the time in the annual cycle and perhaps also to predict annual recurring weather events. Autolycus of Pitane (ca 300 bce) initiated the mathematical study of the subject with his On Risings and Settings (Aujac 1979). Ptolemy’s Phaseis gives an overview of the subject but is more systematic in its handling of the technical vocabulary than were the works of his predecessors (Evans 1998, 197). The Phaseis concludes with a parapegma, or star calendar. In his parapegma, Ptolemy gives the dates of the heliacal risings and settings of 15 stars of the first magnitude and 15 of the second, in each of five different klimata (latitudes). It seems that Ptolemy observed the dates of these stars’ phases in Alexandria then calculated (perhaps with the aid of a celestial globe) the dates on which they would occur in the other klimata. An unusual feature of Ptolemy’s parapegma is its use of the Alexandrian calendar (which has a leap day once every four years, and so stays in track with the Julian calendar), rather than the old Egyptian calendar (in which every year is 365 days) that he used in the Almagest, as the simplest choice for chronological calculations. For the weather predictions in the Phaseis, Ptolemy relied on the usual set of traditional authorities: Euctemon (EANS 317), Eudoxus (EANS 310–​313), Callippus, Hipparchus, among others, whom he cites for the predictions. Julius Caesar is included as a weather authority (since he issued a revised parapegma in conjunction with his reform of the Roman calendar.) At the end of the work, Ptolemy also lists the places at which these authorities made their observations of the weather, so that the user of his parapegma can choose those most applicable to the user’s own location. On the Analemma is concerned with the solution of problems of spherical trigonometry by means of geometrical projections, methods that might be useful, for example, in the making of sundials (Heiberg et al. 1907, 187–​223; Neugebauer 1975, 839–​840, 848–​ 856). Some Greek fragments exist, but the treatise is best preserved by the Latin translation made by William of Moerbecke in the 13th century. The end of the work is missing. The Planisphere deals with a particular way of projecting the celestial sphere onto a plane surface (Heiberg et al. 1907, 225–​259; Neugebauer 1975, 857–​868; Sidoli and Berggren 2007). This is the form of projection (stereographic projection) that underlies the plane

806   Greco-Roman Science astrolabe and related instruments, such as the anaphoric clock. Although stereographic projection was known before Ptolemy’s time, his is the oldest surviving mathematical treatment. The work survives in Arabic and in a Latin translation from the Arabic.

3. Cosmology In the Almagest, Ptolemy confined himself to straightforward mathematical astronomy, which largely meant the theories of the motions of the sun, moon, and planets, and necessary supporting apparatus. Applied astronomical arts, such as sundial making and astro-​meteorology, did not feature; nor was there any place for the more speculative fields of astrology and cosmology. All these sciences Ptolemy relegated to separate works. His cosmological speculations were developed in the Planetary Hypotheses (Heiberg et  al., 1907; Goldstein 1967; Morelon 1993). In this work, Ptolemy had two aims—​first to describe physically realizable models for the abstract theories of the Almagest and, second, to work out the actual distances of the planets and therefore the size of the cosmos itself. The idea of nested planetary spheres goes back to the homocentric spheres of Plato, Eudoxus, Callippus, and Aristotle. These spherical models were abandoned for planetary theory within a century of the death of Aristotle, but they continued to dominate cosmological thought until the 16th century. Starting around 200 bce, two-​dimensional theories using epicycles and deferent circles emerged as a better way to do planetary theory. But it was still necessary to ask how these could be made consistent with a three-​ dimensional, spherical cosmos. As Theon of Smyrna (3.31. Dupuis [1892] 1966, 288–​389) asked, how could the bodies of planets be carried on incorporeal circles? Ptolemy was not the first to attempt to incorporate the epicycles and deferents of Hellenistic planetary theory into cosmology, for Theon, basing himself on Adrastos, had explained how this is done. It is even possible that the first discussions of deferent-​and-​epicycle theory (as by Apollonius of Perga) were also based on three-​dimensional versions. The basic idea in Ptolemy’s three-​dimensional cosmology is to regard a deferent circle as an “equator circle” of a three-​dimensional spherical shell. See figure D10.13, taken from a 16th-​century edition of Georg Peurbach’s Theoricae novae planetarum, written in the 1470s and first published by his student Regiomontanus (Aiton 1987). Peurbach called his book New Theories of the Planets, not because it contained any new theories, but because it was intended as a replacement for the unsatisfactory, anonymous Theoricae planetarum, a 13th-​century introduction to Ptolemy’s planetary theory widely used in the medieval universities. Peurbach had probably drawn on Ibn al-​Haytham’s On the Configuruation of the Sphere or some work dependent on it (available in Langermann, 1990). It is remarkable that we can use a print from a 16th-​century textbook to illustrate Ptolemy’s cosmology in the Planetary Hypotheses. In figureD10.13, B is the earth, the center of the universe. The sun revolves around a point A that is slightly eccentric to B. The spherical shell D (shown in white), in which

Ptolemy   807

Figure D10.13  Ptolemy’s physical theory of the motion of the sun. From Georg Peurbach, Theoricae novae planetarum (Paris, 1553). Photo by author.

the body of the sun is embedded, carries the sun around. This is accomplished with the aid of the stationary spacer orb C (shown in black). This orb has its inner surface centered on B, but its outer surface centered on A. Finally, the outer spacer orb E has its inner surface centered on A, but its outer surface centered on B. This restores concentrality with the earth. The mechanisms for the inner planets (Venus, Mercury, and the moon) may be inserted into the hollow inside C; the mechanisms for the outer planets (Mars, Jupiter, and Saturn) may be stacked outside E. Figure D10.14 shows the mechanisms for the sun and Venus in one diagram. The three solar orbs (all labeled A) are as before. Three orbs labeled B account for the zodiacal motion of Venus: the revolving deferent (white), and the two stationary spacer orbs (black). The epicycle of Venus is like a small bowling ball carried in a spherical cavity in the deferent sphere. Venus is the star shown on the surface of the epicycle sphere. (For a more detailed discussion, including the treatment of planetary latitudes, see Murschel 1995.) Now let us consider the cosmological distance ladder. Only for the moon did Ptolemy know the real distance (its mean distance from the earth is about 60 earth radii). But he thought he also knew the distance of the sun, obtained from calculations based on methods introduced by Aristarchus of Samos (EANS 131–​133). For the planets,

808   Greco-Roman Science

Figure D10.14  The three-​dimensional systems for the sun and Venus. From Georg Peurbach, Theoricae novae planetarum (Paris, 1553). Photo by author.

the parallaxes are so small that they simply are not susceptible of measurement by techniques of naked-​eye astronomy. In the Almagest, Ptolemy always just takes the radius of a planet’s deferent to be 60 units. To obtain real planetary distances, something more than astronomy is required—​an additional assumption. There is yet a further complication. One cannot begin to address the problem of planetary distances without first making an assumption about the order of the planets. Everyone agreed that the moon is closet to us, since it eclipses the sun and sometimes occults the other planets. Almost everyone agreed that distances are correlated with periods—​that the planets that are farthest from us are those that take the longest to go around the zodiac, a principle endorsed by Aristotle. Thus Saturn is farthest from us (zodiacal period of 30 years), Jupiter next (12), and Mars after that (a bit less than 2 years). The issue was what to do with the sun, Mercury, and Venus since all three take one year to go around the zodiac, on average. Different ordering schemes had been adopted in earlier astronomy. Plato, for example, influenced by Pythagorean speculation, had favored the order Moon, Sun, Venus, Mercury, Mars, Jupiter, Saturn. But already by Geminus’ time (1st century bce), the standard order of later antiquity had fallen into place: Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn. Ptolemy adopts this order but takes some pains to justify it. Ptolemy mentions (Almagest 9.1) that some people place Mercury and Venus above the sun, since the sun has never been seen eclipsed by them. But in the Planetary Hypotheses (Goldstein 1967,

Ptolemy   809 6), he points out that a blocking by such a small body might not be visible to the eye, just as a small grazing eclipse by the moon is not perceived. In the Almagest, he says it is reasonable to place the sun in the middle (Mercury and Venus below it, Mars, Jupiter, and Saturn above it), so that it can separate the planets with limited elongations from the planets that can be at any elongation from the sun. And in the Planetary Hypotheses (Goldstein 1967, 7), he remarks it makes sense for the moon and Mercury to be closest to the elemental air, for their theories involve more motions than do the theories of the other planets—​and so they resemble the turbulent air. For the cosmological distance scale, Ptolemy assumes, consistent with the lunar theory of the Almagest, that the least distance of the moon from the earth’s center is 33 earth radii and the greatest is 64. To proceed further, he takes the deferent and epicycle theories of the Almagest as physically meaningful, as a way of deducing, for the each planet, the ratio of greatest to least distance. A final physical assumption is that there is no empty, wasted space in the cosmos, which was consistent with both Aristotelian and Stoic opinion. He can then stack up the mechanisms for the planets and the sun above that of the moon, with no gaps between the various systems, and with the distance of the moon providing the overall scale (Swerdlow 1968). For the distance of the sun, he had two ways to proceed. One was by starting from the known distance of the moon and stacking the mechanisms of Mercury and Venus above, as just described, which led to a maximum distance for Venus of 1,079 earth radii. The other way of finding the distance of the sun was though a calculation based on methods introduced by Aristarchus of Samos, which led to a minimum distance of the sun of 1,160 earth radii. These results did not agree perfectly—​ but they were close, which must have seemed to Ptolemy a confirmation of his approach (including the ordering of Moon, Mercury, and Venus). This is the explanation of the gap between the greatest distance of Venus and the least distance of the sun listed in Table D10.1. Ptolemy probably did not believe in the existence of a gap, but he did not cover up the minor discrepancy in his figures. Ptolemy was led finally to a radius for the sphere of fixed stars of about 20,000 earth radii. Although the earth is at the center of the system, it is tiny compared to the cosmos. Ptolemy remarks that distances he has found depend on the assumption that there are no gaps between the systems for the various planets, but if there are gaps the universe must be even larger (Goldstein 1961, 6). Table D10.1 Greatest and least distances of the planets in Ptolemy’s Planetary Hypotheses Moon Mercury Venus Sun Mars Jupiter Saturn

Least Distance (earth radii)

Greatest Distance (earth radii)

33 64 166 1,160 1,260 8,820 14,187

64 166 1,079 1,260 8,820 14,187 19,865

810   Greco-Roman Science

4. Astrology Ptolemy’s astrological work is commonly known under the title Tetrabiblos (though its original title may have been Apotelesmatika, ἀποτελεσματικά), or, in its Latin translations, Quadripartitum (see Robbins 1940; Heiberg et al. 1998). Babylonian astrology entered the Greek world by the 2nd century bce. Especially in Greek Egypt, it was adapted and richly developed, with attempts made to rationalize it by connecting it with philosophy. Signs of its popularity in Egypt include the zodiacs that began to appear in Egyptian temples around 200 bce (Clagett 1995, 474–​479). We know a lot about astrological doctrine from the half-​dozen Greek and Latin treatises that have survived. We have also hundreds of Greek horoscopes preserved on papyrus or as examples in the astrological treatises. In the 19th century, attempts were made to protect Ptolemy’s scientific reputation by denying that he had really written the Tetrabiblos. But few contemporary scholars doubt that the work is really his. The Tetrabiblos is addressed to the same Syrus who is mentioned in the opening lines of the Almagest. Moreover, the Tetrabiblos refers to topics treated in the Almagest. Finally, the writing is stylistically similar to Almagest. That there were a few ancient critics of astrology, such as Cicero and Sextus Empricus (EANS 739–​740), should not blind us to the fact that in Ptolemy’s time it was very widely believed in. Of all the surviving ancient treatises on astrology, Ptolemy’s is the most rationalized and orderly. He begins by offering a justification for this art. Ptolemy notes that there are two different methods of prediction in astronomy. The first, which involves the study of the movements of the celestial bodies (as in the Almagest), is naturally first in order and force. The second (what we would call astrology) is by its nature somewhat less sure but worthy of investigation. Ptolemy points out that there are critics of astrology. There are those who argue that astrology is useless whether it is effective or not: if it is not effective, it most obviously is useless; but if it is effective, it tells us of a fate we cannot possibly avoid. Thus it is useless in either case. But Ptolemy remarks that if even if we were unable to avoid a foreknown fate, foreknowledge could at least help us prevent excessive elation when good fortune arrived or severe dejection when the opposite occurred. Moreover, for Ptolemy, the configuration of the planets is not necessarily forcing. He makes an analogy to medical practice: a good physician can make a diagnosis and then offer a view of what the course of the illness will be if there is no intervention. Also, it is sometimes the case that local circumstances can overwhelm the propensity of the stars. For example, in the case of a shipwreck in which many are drowned, we need not think that all were subject to the same celestial influences. Ptolemy also admits that there are bad practitioners and outright fakes who give astrology a bad name. But we would not throw out the whole art of medicine because of a few bad practitioners.

Ptolemy   811 Table D10.2 Qualities of the planets according to Ptolemy in the Tetrabiblos Heating

☉☾♀♂♃

Cooling

♄

Changeable

☿

Humidifying

☾♀♃

Drying

☉♂♄

Changeable

☿

Beneficent

☾☿

Maleficent

♂♄

Changeable

☉☿

Masculine

☉♂♃♄

Feminine

☾♀

Androgynous

☿

Diurnal

☉♃♄

Nocturnal

☾♀♂

Common

☿

Note: ☉Sun  ☾Moon  ☿Mercury  ♀Venus  ♂Mars  ♃Jupiter  ♄Saturn

The planets have powers that are particular to their individual natures. See table D10.2. For example, the sun, the moon, Venus, Mars, and Jupiter are warming, while Saturn is cooling. Mercury—​ the astrologer’s wild card—​ may act in either way. The humidifying planets are moon, Venus, and Jupiter; the drying ones are sun, Mars, and Saturn; Mercury may be either. Here Ptolemy is at pains to tie the planets’ powers to the familiar principles of heating/​cooling and humidifying/​drying that play a role in Aristotle’s element theory, as well as in Hippocratic medicine. From these he is then able to deduce which planets are beneficent and which are maleficent. A planet with both the life-​giving properties of warmth and moisture will be beneficent, and these are clearly the moon, Venus, and Jupiter. Maleficent are Mars and Saturn. Changeable are the sun and Mercury, which makes good sense—​ some sun is required for life but too much can kill. The categories of beneficent and maleficent planets come from Babylonian astrology, with exactly the same lists. Thus the feeble powers of Aristotelian physics have only been used to provide support for a commonplace. And as we go further into the art, the doctrines become even less impressive. For example, the sexes of the planets correspond to what would be expected from mythology. The planets’ powers also wax and wane as they move around the zodiac, and this in several ways. Each planet has a solar house and a lunar house, in which it becomes stronger. Each planet has another sign that is its exaltation, and a diametrically opposed sign which is its depression. The planets also interact with one another, especially when they are in particular aspects to (at particular angular distances from) one another. Finally—​and this is, as far as we know, a purely Greek contribution, for nothing comparable has yet been found in the Babylonian material—​each planet waxes and wanes in the course of a single day and night. Planets are stronger at the horoscopic point (when rising in the east) and at the midheaven (when crossing the meridian). They are weakest when at the descendant (setting) or at the anti-​midheaven (below the earth). These four cardinal points are called the “centers.” Ptolemy also provides advice about which features of a nativity are most important to consider when particular questions are being investigated. See table D10.3 for some of them.

812   Greco-Roman Science Table D10.3 Starting points for some investigations according to Ptolemy Sex of native

☉☾ Horoscope

Bodily temperament

☾ Eastern horizon

Rational qualities of soul

☿

Irrational qualities of soul

☾

Diseases of soul

☿☾ Centers, maleficents

Occupations

☉ Midheaven

Children

Good demon, midheaven

Material fortune

Lot of fortune

5. Geography Ptolemy’s Geography (Nobbe 1843–​1845; Berggren and Jones 2000)  contains an introduction to the methods and problems of world geography, a detailed criticism of his immediate predecessor, Marinus of Tyre (EANS 533)  (otherwise unknown), and instructions for making a map of the whole oikoumenē (the known inhabited world), as well as smaller regional maps. A great part of the book is taken up by a gazetteer, giving the longitudes and latitudes of some 8,000 places, most of the underlying data being drawn from Marinus, although Ptolemy systematically reduced some of Marinus’ distances, especially for faraway places. Ptolemy measured latitudes as we do: north or south of the equator in degrees. He measured longitudes in degrees from the meridian through the Islands of the Blest (Geography 7.5). These may be the Cape Verde Islands plus the Canary Islands. Ptolemy was probably the first to systematically give a pair of geographical coordinates for each place tabulated. He complains (Geography 1.18) that Marinus gave latitudes of some places in his descriptions of particular parallels and longitudes of some places in his account of particular meridians, so it was not easy to ferret out the needed information from Marinus’s book. Some basic information for the construction of a world map came from travelers’ itineraries (EANS 447) and sailing times. The itineraries might give distances in stades or Roman miles, measured along well-​traveled roads, or merely days of travel. The working out of east-​west and north-​south distances from such material involved a lot of patchwork and second guessing. For example, it was sometimes necessary to reduce the road distances by a factor of one-​half to account for twists and turns (Geography 1.12). Travel data could be supplemented by a small number of known geographical latitudes. The Greeks expressed the latitude of a place in three different ways. First, one could give the length of the noon shadow of a vertical gnomon on the day of equinox. Second, one could give the length, in equinoctial hours, of the summer solstitial day.

Ptolemy   813 (This defined a so-​called klima, a latitude belt on the earth narrow enough that the day length was everywhere the same.) Third, one could give the altitude of the north celestial pole in degrees above the horizon. (This is equal to the angular distance of the place above the earth’s equator—​and thus is equivalent to the measure we use today). These three methods of expressing latitude are interconvertible. In everyday life, by far the most common method was in terms of the klima. But a number of equinoctial shadow lengths are preserved in writers such as Strabo, Pliny, and Vitruvius. For an educated traveler, the measurement of a shadow would be by far the easiest because it did not require special instruments, such as a water clock or a meridian circle. Of course, the casual observer could easily go wrong by mistaking the day of the equinox—​and the sun’s declination changes by 4/​10º per day around the equinox. Nevertheless, the preserved shadow lengths usually give latitudes that are correct within two degrees, although larger errors do occur. When it comes to longitudes, the situation was dire. Ptolemy included a chapter (Geography 1.4) arguing that a geographer should give priority to astronomical methods over travelers’ reports, which was only endorsing something underway since the time of Eratosthenes and Hipparchus. But the only possible way to get accurate longitudinal differences was through simultaneous observations of lunar eclipses. For example, there was an eclipse of the moon shortly before the battle of Arbela in 331 bce, when Alexander defeated Darius III, the king of Persia. According to the historians of Alexander’s campaign, this eclipse was seen there at the fifth hour of the night. But the same eclipse happened to be observed in Carthage at the second hour. Thus, Ptolemy deduced a difference between Arbela and Carthage of three hours, or 45º (Geography 1.4). (In the gazetteer, he adopts 45º 10′.) This considerably overstated the longitudinal difference (which is about 34º). But simultaneously observed eclipses were so rare that Ptolemy had no way to correct this error. As a result, he overestimated the angular width of the Eurasian continent. Ptolemy follows Marinus by adopting the value of 500 stades per degree, saying that this is generally agreed on (Geography 1.11). This results in 180,000 stades for the circumference of the earth (Geography 7.5), a value that Ptolemy retained in his later Planetary Hypotheses (Goldstein 1967, 7). It is possible that when he wrote the earlier Almagest Ptolemy accepted an equivalence closer to 700 stades per degree, in accord with Erathosthenes’ circumference of 252,000 stades. This is suggested by the fact that the longitude difference between Alexandria and Babylon is larger in the Geography than in the Almagest, in the ratio of about 3:2, which is not far from 700:500. In Almagest 6.6 (Toomer 1984, 191), Ptolemy says that Babylon is 5/​6 of an hour east of Alexandria, but in the Geography (Nobbe 1843‒1845, 8.20.27), he says the time difference is one and one-​quarter hour. If Ptolemy had retained the same overland distance, as being well established, but had adopted a smaller earth, this would have increased the time difference between the two cities. Strabo (Geography 2.2.2) attributes to Posidonius, the Stoic philosopher of the 1st century bce, an earth circumference of 180,000 stades, so it is sometimes assumed that this was Ptolemy’s source. However, Cleomedes, the only ancient source to give details of Posidonius’s method, put his circumference at 240,000 stades (Bowen and Todd 2004, 78–​81).

814   Greco-Roman Science Although the issue is controversial, most historians of ancient geography believe that Eratosthenes and Ptolemy (and indeed most ancient geographical writers) used the Attic stade, reckoned at one-​eighth of a Roman mile or about 185 m (Berggren and Jones 2000, 14; Pothecary 1995; Engels 1985). Thus Ptolemy’s earth turns out to be about 17% too small and Eratosthenes’ about 16% too big. As we have seen, Ptolemy overestimated the longitudinal extent of the Mediterranean, but because his earth was undersized, it turns out that his east‒west distances are better than his longitudes. A key problem for making a world map is finding a method of projection so that the curved surface of the sphere can be represented in a systematic way on a flat surface. Eratosthenes had probably laid out his world map on a rectangular grid, and Strabo (Geography 2.5.10) tells us that in his day this was still a general practice, although some people tilted the meridians inward slightly at the north. In his book, Ptolemy describes not one, but two more sophisticated ways of projecting a world map, so that the parallels and meridians represented on the plane would give an impression of a spherical surface. It was also important to design the projection to preserve a roughly correct relationship among distances. See figure D10.15 for the grid of parallels and meridians for Ptolemy’s first projection (Geography 1.24). The portion of the globe to be represented is only the oikoumenē. It runs from west to east through roughly 180º of longitude, from the islands of the Blest in the Atlantic to Sērikē, the silk country in China. And it runs north‒south from the parallel through the island of Thule (latitude 63º north) to a latitude as far south of the equator as Meroe (Egypt) is north of it (thus latitude 16-​5/​12º south). In Ptolemy’s projection, the meridians are treated as straight lines, all intersecting at a point (which can be thought of as the north pole). The parallels are segments of circles centered on this same point. To represent distances reasonably consistently, Ptolemy stipulates that the included arcs of the equator and the parallel of Thule should have lengths in the correct parallel of Thule parallel of Rhodes parallel of Soene equator

12 h

0h

parallel of “anti-Meroe”

Figure D10.15  Ptolemy’s first projection of a world map. Drawing courtesy of Alexander Jones.

Ptolemy   815 proportion. Effectively, this means that the radius of the circle for the Thule parallel should be cos 63º (about 0.45) times the radius of the circle representing the equator. The other parallels are to be at placed at even intervals according to their latitudes between the equator and the parallel of Thule. Furthermore, Ptolemy stipulates that the ratio of north‒south distances to east‒west distances should be correctly represented on the parallel of Rhodes, which runs through the heart of the Greek world. Now, the latitude of Rhodes is 36º. Thus, on the parallel through Rhodes, one degree of longitude is only cos 36º (≅ 4/​5) times as long in actual distance as one degree measured along the equator or the meridian. This is what determines how long an arc needs to be included for the parallel of Rhodes. If we treat the distance along the central meridian from the equator to the parallel through Thule as 63 units (for the 63º), then the arc length of the Rhodes parallel from its midpoint to its end should be 63 units × (90º/​63º) × (4/​5) = 72 units. This distance may be stepped off along the Rhodes parallel using dividers and determines where the map ends. For the parallel of “anti-​Meroe” (the southern boundary of the map), Ptolemy suggests it can be drawn just as long as the segment of the parallel of Meroe north of the equator. And thus it will be necessary to have kinks in the meridian lines at the equator. While somewhat spoiling the simplicity of the projection, this would have two desirable effects: it would suggest to the eye the curvature of the surface, and it would prevent distances south of the equator from being grossly exaggerated. Ptolemy’s second projection (figure D10.16) offers an even more suggestive representation of the curvature. In this case, the meridians are represented as arcs of circles. This also allowed Ptolemy to preserve the correct relation between arcs along the parallels for three different parallels (rather than only for two as in his first projection). In Geography 7.6, Ptolemy provides yet a third projection of the oikoumenē, for a drawing in which the earth is to be seen from outside the cosmic sphere, peeking out from among the surrounding celestial circles.

parallel of Thule parallel of Rhodes parallel of Soene

equator

12 h

0h

parallel of “anti-Meroe”

Figure D10.16  Ptolemy’s second projection of a world map. Drawing courtesy of Alexander Jones.

816   Greco-Roman Science Ptolemy provides an extensive caption for his world map (Geography 7.5), as well as (in bk. 8) captions for 26 smaller regional maps, in which the parallels and meridians were to be represented merely as families of orthogonal lines (8.1). The oldest manuscripts of the Geography are from around 1300 ce; some contain maps and some do not. Of those that do include maps, some provide 26 regional maps, in accordance with Ptolemy’s captions, while others include 64 maps that display smaller regions than Ptolemy’s classical 26. Scholars are divided over whether Ptolemy’s original publication contained maps. Did Ptolemy include the world map (which would have been very large) along with the regional maps, or just the regional maps, or no maps at all? The Greek title of Ptolemy’s book, Geōgraphikē Hyphēgēsis, can be rendered Geographical Guidance, or, more suggestively, as by Bergreen and Jones (2000, 55), Guide to Drawing a Map of the World. This does correspond to the plan of the work: a description of the projections, the extensive list of data to be represented, and captions for the maps. Why would the map itself be necessary, especially since Ptolemy remarks (Geography 1.18) that successive copying of maps from earlier examples gradually leads to great distortions? The purpose of the book was to allow other people to draw accurate maps (Berggren and Jones 2000, 45–​50.) However, Mittenhuber (2009) presents a convincing case for a map tradition going all the back to antiquity. This scholarly dispute has a parallel in the argument over whether the ancient botanists, such as Pedanius Dioscorides, included drawings of plants in their manuals.

6. Optics Ptolemy’s Optics survives only in a 12th-​century Latin translation by Eugene of Sicily (a highly placed official in the Norman Kingdom of Sicily), made from a now-​lost Arabic version. The Arabic manuscript from which Eugene worked was missing the first book and the end of the fifth, as Eugene acknowledges in his translation (Lejeune 1989; Smith 1996). Ptolemy adopts the more widely held, “extramissionist,” theory of his day, that the visual ray propagates from the eye to the object that is perceived. Thus vision is an active process, a sort of laying-​hold analogous to touch. The visual faculty can apprehend such properties as size, color, shape, motion, or rest. But this cannot happen without illumination. And, also, there must be some sort of opaqueness in the body to block the visual flux. This is why, for example, we do not perceive the shape of the air near us (Optics 2.2–​9). This theory was developed in the missing book 1 and summarized at the beginning of book 2. In the remainder of book 2, Ptolemy uses simple geometrical demonstrations to explain a number of phenomena that depend only on the straight-​line propagation of the ray. For example, suppose two pegs C and D are placed at different distances from the face. If we look with both eyes at C, we will see one peg C but two pegs D. (Optics 2.30–​35). Book 3 deals with reflection from and image formation in plane and convex mirrors, and book 4 deals with concave mirrors. The technical constructions are in the tradition of Euclid’s Optics,

Ptolemy   817 the pseudo-​Euclidian Catoptrics, and the Catoptrics commonly attributed to Hero of Alexandria (EANS 384–​387). The most original aspects are found in the final book (Optics 5.3–​24), where Ptolemy takes up the quantitative study of refraction and describes experiments made with special apparatus. See figure D10.17. A  bronze disk is divided by two perpendicular diameters BD and AG, which cross at the center E of the disk. The four quadrants are each divided into 90º intervals. (This divided circle is therefore similar to one made for his meridian circle, shown in figure D10.5.) The disk is stood in a half-​cylindrical container of water that lies on its back. Put a small, colored peg at E. Let the eye be placed at Z. If there no refraction (that is, no water in the container), the visual ray would be the straight line ZET. But let the water come up to level DB. Let another colored peg be moved along arc DG until it comes to H, and the two pegs are seen to lie apparently in a line. The visual ray is therefore the broken line ZEH. Ptolemy tabulates the angles AEZ and GEH, with the results shown in table D10.4. Of course, the correct law of refraction was not discovered until the 17th century; but Ptolemy’s table is a tolerably good approximation to it, as we can see in figure D10.18. Ptolemy’s table was not determined merely by measurements, however but was based on a pattern of constant second differences. The successive refraction angles form the sequence 0 (understood), 8, 15½, 22½, 29, 35, and so on. The differences between successive pairs values are 8, 7½, 7, 6½, 6, . . . this is an arithmetic progression with constant differences of one-​half. That is, in Ptolemy’s list of refraction angles, the differences between the differences (second differences) are constant: ½, ½, ½, . . . The tool of the arithmetic progression was widely used in Babylonian astronomy and in early Greek astronomy. A number sequence of constant second differences is a fine way to interpolate between points on a smoothly varying curve with a single maximum or minimum. Although the ancients did not draw graphs, we might describe this sequence as the rough equivalent of drawing a smooth line through a set of data points. Ptolemy also describes an experiment in which the visual ray goes from air to glass. For this he uses a clear glass half-​cylinder, a flat face of which he attaches to his bronze disk. Finally, he puts his glass half-​cylinder into the water tank and describes A Z

E

D

B

T H

G

Figure D10.17  Ptolemy’s investigation of refraction. Drawing by author.

818   Greco-Roman Science Table D10.4 Ptolemy’s values for angles that the visual ray makes with the normal to the boundary in refraction between air and in water Angle in Air AEZ

Angle in Water GEH

10 20 30 40 50 60 70 80

8 15½ 22½ 29 35 40½ 45½ 50

60

Angle in Water

50 40 30

Ptolemy Modern

20 10 0

0

10

20

30

40

50

60

70

80

Angle in Air

Figure D10.18  Ptolemy’s refraction for air and water compared with modern theory. For the modern, the index of refraction of water is taken as 1.33. Drawing by author.

an experiment in which the ray goes from water to glass. For each of these experiments Ptolemy again tabulates the refraction angles as arithmetic progressions with constant second differences of one-​half, but the starting values for the angles (as also for the first differences) are different.

7.  Epistemology and Psychology In Peri kritēriou kai hēgemonikou (Heiberg et al. 1961; Huby and Neal 1989, 179–​230), whose title may be rendered approximately as On the Standard of Judgment and the

Ptolemy   819 Commanding Faculty, Ptolemy provides an epistemology suitable for a practicing scientist, as A. A. Long has aptly expressed it (in Huby and Neal 1989, 151–​178). Ptolemy begins by analyzing the process of judgment in a court of law. See table D10.5. There the subject under investigation is the act that is in dispute. The agent of judgment is the presiding magistrate, and the goal aimed at is social harmony. These are the most important terms in Ptolemy’s system. The two intermediate terms are the instrument to be used in reaching a judgment (the presentation of the case in court) and the means for passing judgment (the law). Ptolemy then constructs parallels for such processes as weighing or measuring the length of an object. He then expresses a more general situation, as in the right column of table D10.5. Since this immediately follows his discussion of weighing and measuring, we may take it as the general case applicable to scientific investigations. The subject under judgment is “what is” (to on), the agent of judgment is the mind (nous), and the goal is truth (alētheia). The instrument is sense perception (aisthēsis) and the means of judgment is reason (logos). So here he adopts a sensible middle-​of-​the road epistemology: sense evidence is crucial, but cannot be employed without rational analysis. The criterion of truth was a standard philosophical topic in Ptolemy’s day, but he shows no interest in the current state of the argument and mentions no other writers. Sextus Empiricus, who was a younger contemporary of Ptolemy, gives a detailed history of the positions on the kritērion taken by various schools, and even discusses some of the same examples as does Ptolemy (Bury 1935, 18–​19). The last parts of Peri kritēriou kai hēgemonikou address the nature of the human soul and, in particular, its hēgemonikon, or commanding faculty. Ptolemy notes that, of the elements that make up compound bodies, earth and water are considered more material and are passive, while air and fire are more capable of causing movement and are therefore both active and passive. But the changeless ether is always active. The division of the four elements into active and passive pairs is a Stoic doctrine; but Ptolemy retains the Aristotelian ether and endows it with activity, which is perhaps an original twist. Now, a human being also is a compound, composed of body (sōma) and soul (psychē). “Body” denotes what is more material and less active, and “soul” what is capable of moving both itself and the body. Thus, body is naturally associated with earth and water, while soul is associated with air, fire, and ether. Moreover, heat and moisture (the life-​giving qualities

Table D10.5 One of Ptolemy’s epistemological analogies, using a court case as a model for the scientific investigation of nature Law Court Analogy

General Case

Subject under judgement

Act in dispute

What is

Instrument to be used

Presentation of case

Sense perception

Agent of judgement

Presiding magistrate

Mind

Means by which it is judged

The law

Reason

Goal

Social harmony

Truth

820   Greco-Roman Science from Greek medicine and from Ptolemy’s astrology) indicate the greatest admixture of soul, while coldness and dryness go with the smallest admixture of soul. Thus tendons and bones (which are cold and earthy) have no psychic function; but flesh and blood (with more moisture and heat) do. Thus, for Ptolemy, soul is an actual substance whose nature reflects the elements of which it is composed—​air, fire, and ether. The materiality of soul is an old position in Greek philosophy, as Anaximenes had made it of air. Like Plato, Ptolemy accepts a three-​part soul: a sensitive part (responsible for sense perception), an impulsive part (responsible for appetites and emotions), and a thinking part. Here Ptolemy is in opposition to the Stoics, who stressed the indivisibility of soul. The three aspects of soul are distributed differently through the body. For example, of the senses, touch is distributed over the whole body, while sight and hearing, being more excellent, are located higher up and near the faculty of thought. The appetitive part of the soul is located around the stomach and abdomen, while the emotive part is located around the liver and heart. The part of soul that is responsible for thought is made of pure ether and is located around the brain. To make the commanding faculty of the soul of ether is another original twist—​ a Stoic would have made it of pneuma. Ptolemy does not work out in detail the connections between his psychology and his discussion of the criterion of truth. But the parts of soul connected with the senses and with reason could be worked into a scheme similar to table D10.5. Finally Ptolemy asks just where the hēgemonikon of the soul is located, and he concludes it must be located in the hēgemonikon of the body, that is, in the brain. For Ptolemy, it is natural that the most excellent parts should be in the highest place—​in the universe, as in man. However, he makes a concession to Aristotle and the Stoics by confessing that the most important part of the soul as far as mere life is concerned is located about the heart; but the most important part as far as both life and living well are concerned is located around the brain.

8. Harmonics The bulk of Ptolemy’s Harmonics (Düring 1930; Barker 1989, 270–​391; Solomon 2000) is a technical discussion of Greek music theory, especially the theory of the division of the scale. Three concords were accepted by all theoreticians, the octave (2:1), the perfect fifth (3:2), and the perfect fourth (4:3). (Each ratio may be taken to represent the relative lengths of two strings that will sound the concord.) Now the octave may be expressed as a fifth plus a fourth (in a modern example, based on the key of C, the interval from C to G plus the interval from G to the next higher C). Or, we may express the octave as a fourth (C to F) plus a tone (F to G) plus another fourth (G to C). These notes are considered fixed. The question is how to divide the two tetrachords (the intervals of the fourth). Thus, where should two notes be placed between C and F, and where should two notes be placed between G and C? These notes are considered movable. There were at least six different ways of doing this, for different genera of Greek music, though three

Ptolemy   821 genera were considered fundamental and called enharmonic, chromatic, and diatonic. (A simple modern analogy would be the scales of C major and C minor, both of which include the fixed notes C, F, G, and C, but which differ in some other notes.) In Greek music, notes may be placed at finer intervals than we are used to. There was, moreover, a division into two main camps—​the Pythagoreans and the Aristoxeneans. The Pythagoreans championed the construction of the various scales from abstract arithmetical principles, but, according to Ptolemy, could get tangled up in absurdities from too strict application of their rules (Barker 2000, 59–​72). The followers of Aristoxenus (while still insisting on the use of reason along with perception: EANS, 153–​155) argued that music theory should be based on principles of its own, not constructs borrowed from mathematics or physics (Barker 1989, 119–125). Thus the surviving parts of Aristoxenus’ Elements of Harmonics make no use of ratios. Ptolemy is in the Pythagorean camp, in that he wishes to show that scales can be constructed by consistent application of mathematical hypotheses; but he also insists that the results of the theory must be tested by perception. Ptolemy gives unusually detailed descriptions of his instruments—​the kanōn, or monochord, and its multistringed generalizations—​ including the forms of the bridges, and so on. He provides numerical tables of the attunements of the various genera, constructed according to his hypotheses, but also describes sophisticated experiments to verify that they conform well to actual practice. Book 3 (which is incomplete) considers the relation of music theory with psychology and astronomy. Ptolemy claims that harmonics applies to anything that is of a more perfect nature and gives as his prime examples the human soul and the heavens. For example, the three concords (octave, fifth, and fourth) correspond to the three parts of the soul (thinking, perceptive, and animating, respectively). And the three branches of theoretical philosophy (physics, mathematics, and theology) that Ptolemy considered in the introduction to the Almagest, combined with Aristotle’s three subdivisions of applied philosophy (ethical, domestic, and political) are divided up to correspond to the three musical genera: the enharmonic corresponds to physics and ethics, the diatonic to theology and politics, and the chromatic to mathematics and the domestic (Harmonics 3.4–​6; Baker 1989, 374–​378). It was a commonplace that different kinds of music could excite different emotions and could strengthen particular virtues, and Ptolemy works out the correspondences in considerable detail. The final sections of the Harmonics deal with relations between music and the motions of the planets. The motions in longitude, in depth, and from north to south are all assigned musical meanings (Harmonics 3.8–​16; Baker 1989, 380–​391; Neugebauer 1975, 931–​934). This is a way of thinking that had ancient roots in Pythagoreanism but was still current in Ptolemy’s time and pushed by some of Ptolemy’s immediate predecessors, including the neo-​Pythagorean Nicomachus of Gerasa (Baker 1989, 245‒269; EANS 579). These chapters of the Harmonics were, 1,400 years later, an inspiration to Kepler. Finally, there is a notable philosophical consistency between the Almagest, On the Criterion, and the Harmonics (Feke and Jones 2010; Feke 2012).

822   Greco-Roman Science

9.  Toward an Assessment There is a long-​running debate about whether Ptolemy believed in the celestial models he proposed or regarded them merely as tools for calculating positions. In the philosophy of science, the question may be put this way: Was Ptolemy a realist or an instrumentalist? These are, of course, modern and not ancient categories. But a realist believes that when a theory is found that successfully accounts for the phenomena, the elements of the theory may well correspond to things actually existing in nature. An instrumentalist, by contrast, may renounce the very possibility of knowing the reality of things and be content with a theory that “works.” In 1908, Pierre Duhem published his influential study To Save the Phenomena, in which he drew on such ancient writers as Geminus, Theon of Smyrna, Ptolemy, and Proclus to argue for an instrumentalist interpretation of ancient Greek astronomy (Duhem 1908). This has proved a popular interpretation, for it provides an excuse for the Greeks: it explains how they could have been so wrong-​ headed about the motion of the earth and many other things. It makes them heroes of positivism. However, Lloyd (1978) has shown in detail that Duhem misinterpreted much of the evidence. Certainly, thoughtful writers such as Geminus and Ptolemy are careful to distinguish what can be determined by astronomical methods and what cannot. Astronomy cannot determine whether the earth spins on its axis or the heaven rotates. It cannot determine whether the sun moves on an eccentric circle or on a concentric plus epicycle. But this did not mean that Geminus and Ptolemy were indifferent to the answers. As we have seen, when a question is undecidable by astronomical methods, Ptolemy will use physical or philosophical arguments to settle it so that he may carry on. The question is complicated because two forms of planetary theory existed side by side in Ptolemy’s day. There was an astronomy of the high road, practiced by people like Theon of Smyrna and Ptolemy, who used geometrical methods and were well versed in the philosophy of nature. (These are the only sorts of people who figure in the discussions of Duhem and Lloyd). But there was also an astronomy of the low road—​practiced by astrologers who wanted quick and reliable methods for finding planetary positions and were happy to use Babylonian methods based on arithmetical procedures. Papyri recovered from Oxyrhynchus show Greeks in Egypt happily using Babylonian methods right up to the time of Ptolemy, and even afterward (Jones 1999). And astronomers could be opportunistic. We have seen Geminus asserting in one chapter that celestial things move uniformly and, in another, giving the rudiments of a Babylonian theory in which the moon moves nonuniformly. There are ample signs that Ptolemy’s regarded his theories as having something to do with the physical world. For example, Ptolemy tells us that he tried to measure the angular diameter of the sun with a dioptra to confirm the variation in size predicted by his eccentric theory. He discovered that this was not possible, because of the brightness of the sun and the distortion it suffers near the horizon, when it is safe to look at it. The fact that Ptolemy tries to determine the size of the universe by taking the

Ptolemy   823 deferent-​and-​epicycle models seriously and stacking them up with no empty space between them is only consistent with being a realist. Perhaps the best evidence one could point to for the contrary position is Ptolemy’s willingness to accept an exaggerated variation in the moon’s distance as the price of a theory that predicted the longitudes well. When all the evidence is weighed, it is clear that he was seeking the real nature of things, but sometimes he made unsatisfactory compromises. There are serious issues involving Ptolemy’s reliability as a witness, especially as concerns his astronomical observations. Delambre ([1817] 1965) already asked whether these were all real observations or rather, in many cases, examples Ptolemy made up to illustrate his theories. The issue was brought to the fore by Robert R. Newton’s The Crime of Claudius Ptolemy (1977). Historians of science have gradually become accustomed to the idea that scientists do not always tell what they really did and do not always faithfully reproduce data—​witness famous 20th-​century debates over data handling by Mendel, Pasteur, Millikan, and Eddington, to name but a few. But Newton made a searching investigation of Ptolemy’s observations and argued that every one of them for which it is possible to make a test is fabricated. Newton concluded that Ptolemy was a liar, a plagiarist, and a thief, and that astronomy would have been better off if he had never lived. While few historians of science have accepted Newton’s conclusions in their entirety, let alone his moralizing and indignation, his book did start a wide-​reaching re-​ examination of Ptolemy’s observations. The literature is very large, but a good overview of the problem is available in Jones 2006. Historians of ancient astronomy no longer accept Ptolemy’s report of an observation as simple raw data without a more careful examination. A good example of the problem is provided by Ptolemy’s observations of equinoxes, which he uses in combination with his reports of Hipparchus’ equinox observations to establish the length of the year and other features of the solar theory. His key equinox is a day too late (as checked against modern theory), and yet it agrees exactly with the Hipparchean solar theory he adopted. Some of Ptolemy’s works serve as comprehensive treatments summarizing whole fields of knowledge. Three good examples are the Almagest, Optics, and Geography. Other works are specialized treatments that attack a particular problem, such as On the Analemma and the Planisphere. In either case, questions can arise about Ptolemy’s originality. Certainly he was brilliant at mastering a field of knowledge and presenting it as a coherent and well-​ordered discipline. But several lines of evidence give amply convincing proofs of his originality, of his own intellectual development, and of his influence on those who followed. In optics, we may note Ptolemy’s treatment of the refraction of star light. In the Almagest, Ptolemy makes a few vague remarks about atmospheric refraction. He mentions the supposed fact that the moon looks larger when it is near the horizon (which is not really true), and he makes an analogy to the change in the apparent size of objects immersed in water. When he wrote the Almagest, it seems that Ptolemy had no clear understanding of atmospheric refraction and its effect on the apparent places of celestial bodies. But in the later Optics (5.23–​31), Ptolemy makes a cogent analysis of atmospheric refraction, apparently based on careful observations. He says a celestial body

824   Greco-Roman Science when rising or setting is seen on a more northerly circle of declination than when it is higher in the sky and adds that this is seen with the aid of an instrument for measuring stars. This almost certainly refers to the use of his armillary sphere (the astrolabon). And, of course, his quantitative study of refraction using three media is unparalleled. The thoughtfully improved projections for the world maps in the Geography are similarly without any known precedent. In the matter of the latitudes of the planets (their departures north or south of the plane of the ecliptic), Ptolemy modified his theory between the time of the Almagest and the time of his Handy Tables. He changed the latitude theory again before writing the Planetary Hypotheses. In this final version, the latitude theory is greatly improved—​ it is not only simpler but also in better agreement with the actual phenomena. So, in the case of some subjects, we can actually watch him grow and mature as a theoretical astronomer.

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826   Greco-Roman Science Huby, Pamela, and Gordon Neal, eds. The Criterion of Truth:  Essays Written in Honour of George Kerferd, Together with a Text and Translation (With Annotations) of Ptolemy’s On the Kriterion and Hegemonikon. Liverpool: Liverpool University Press, 1989. Jones, Alexander. Astronomical Papyri from Oxyrhynchus. Memoirs of the American Philosophical Society 233. Philadelphia: American Philosophical Society, 1999. —​—​—​. “A Route to the Discovery of Non-​Uniform Planetary Motion.” Journal for the History of Astronomy 35 (2004): 375–​386. —​—​—​. “Ptolemy’s Canobic Inscription and Heliodorus’ Observation Reports.” SCIAMVS 6 (2005): 53–​97. —​—​—​. “‘In Order That We Should Not Ourselves Appear to Be Adjusting Our Estimates . . . To Make Them Fit Some Predetermined Amount’.” In Wrong for the Right Reasons, ed. Jed Z. Buchwald and Allan Franklin, 17–​39. Dordrecht: Springer, 2006. Langermann, Y. Tzvi. Ibn al-​ Haytham’s On the Configuration of the World. New  York, London: Garland, 1990. Lehoux, Daryn. Astronomy, Weather and Calendars in the Ancient Word: Parapegmata and Related Texts in Classical and Near-​Eastern Societies. New  York:  Cambridge University Press, 2007. Lejeune, Albert. L’Optique de Claude Ptolémée dans la version latine d’après l’arabe de l’émir Eugene de Sicile. Leiden: Brill, 1989. Lloyd, G. E. R. “Saving the Appearances.” Classical Quarterly 28 (1978): 202–​222. Mercier, Raymond. “Zīj.” In Encyclopedia of the History of Science, Technology, and Medicine in Non-​Western Cultures, ed. Helaine Selin, 1057–​1058. Dordrecht: Kluwer Academic, 1997. Mittenhuber, Florian. “The Tradition of Texts and Maps in Ptolemy’s Geography.” In Ptolemy in Perspective: Use and Criticism of his Work from Antiquity to the Nineteenth Century, ed. A. Jones, 95–​119. Dordrecht: Springer, 2009. Morelon, Régis. “La version arabe du livre des Hypothèses de Ptolémée.” Mélanges de l’Institut Dominicain d’Études Orientales du Caire 21 (1993): 7–​85. Morrow, Glenn R., trans. Proclus:  A Commentary on the First Book of Euclid’s Elements. Princeton, NJ: Princeton University Press, 1970. Mueller, Ian. Simplicius: On Aristotle, On the Heavens 3.7‒4.6. London: Duckworth, 2009. —​—​—​. Simplicius: On Aristotle, On the Heavens 1.2‒3. London: Bristol Classical Press, 2011. Mugler, Charles. Archimède. Œuvres, Tome II. Des spirales, De l’équilibre des figures planes, L’arénaire, La quadrature de la parabole. Paris: Les Belles Lettres, 2002. Murschel, Andrea. “The Structure and Function of Ptolemy’s Physical Hypotheses of Planetary Motion.” Journal for the History of Astronomy 26 (1995): 33–​61. Neugebauer, Otto. A History of Ancient Mathematical Astronomy. 3  vols. Berlin: Springer-​Verlag, 1975. Newton, Robert R. The Crime of Claudius Ptolemy. Baltimore, MD: Johns Hopkins University Press, 1977. Nobbe, C. F. A., ed. Claudii Ptolemaei Geographia. 3vols. Leipzig: Sumptibus et Typis Caroli Tauchnitii, 1843–​1845. Pedersen, Olaf. A Survey of the Almagest. With Annotation and Commentary by Alexander Jones. 2nd ed. New York: Springer, 2011. Pothecary, S. “Strabo, Polybios and the Stade.” Phoenix 49 (1995): 49–​67. Price, D. J. “Precision Instruments: To 1500.” In A History of Technology, ed. Charles Singer et al., vol. 3, 582–​619. New York, London: Oxford University Press, 1957.

Ptolemy   827 Robbins, F. E. Ptolemy. Tetrabiblos. London: W. Heinemann; Cambridge: Harvard University Press, 1940. Rome, Adolphe Marie. “L’astrolabe et le météoroscope d’après le Commentaire de Pappus sur le 5e livre de l’Almageste.” Annales de la Société scientifique de Bruxelles, série A, Sciences mathématiques 47 (1927): 77–​102. Sidoli, N., and J. L. Berggren. “The Arabic Version of Ptolemy’s Planisphere or Flattening the Surface of the Sphere: Text, Translation and Commentary.” SCIAMVS 8 (2007): 37–​139. Smith, A. Mark. Ptolemy’s Theory of Visual Perception: An English Translation of the Optics with Introduction and Commentary. Transactions of the American Philosophical Society, vol. 86.2. Philadelphia: American Philosophical Society, 1996. Solomon, Jon. Ptolemy Harmonics: Translation and Commentary. Leiden: Brill, 2000. Swerdlow, Noel M. Ptolemy’s Theory of the Distances and Sizes of the Planets: A Study in the Scientific Foundations of Medieval Cosmology. PhD diss., Yale University, 1968. —​—​—​. “Ptolemy’s Theories of the Latitude of the Planets in the Almagest, Handy Tables, and Planetary Hypotheses.” In Wrong for the Right Reasons, ed. Jed Z. Buchwald and Allan Franklin, 41–​7 1. Dordrecht: Springer, 2006. Tihon, Anne. Le “Petit Commentaire” de Théon d’Alexandrie aux Tables Faciles de Ptolémée. Studi e Testi 282. Città del Vaticano: Biblioteca Apostolica Vaticana, 1978. —​—​—​ (with Joseph Mogenet). Le “Grand Commentaire” de Théon d’Alexandrie aux Tables Faciles de Ptolémée, Livre I. Studi e Testi 315. Città del Vaticano:  Biblioteca Apostolica Vaticana, 1985. —​—​—​. Le “Grand Commentaire” de Théon d’Alexandrie aux Tables Faciles de Ptolémée, Livres II et III. Studi e Testi 340. Città del Vaticano: Biblioteca Apostolica Vaticana, 1991. —​—​—​. Le “Grand Commentaire” de Théon d’Alexandrie aux Tables Faciles de Ptolémée, Livre IV. Studi e Testi 340. Città del Vaticano: Biblioteca Apostolica Vaticana, 1999. —​—​—​. Ptolemaiou Procheiroi kanones. Les Tables Faciles de Ptolemée, Vol. 1a:  Tables A1‒A2: Introduction, Édition critique par A. Tihon. Ptolemaiou Procheiroi Kanones. Ptolemy’s Handy Tables, Vol. 1b: Tables A1‒A2: Transcription and Commentary par Raymond Mercier. Publications de l’Institut Orientaliste de Louvain, 59A, 59B. Leuven: Peeters, 2011. —​—​—​. “Alexandrian Astronomy in the Second Century ad: Ptolemy and His Times.” In The Alexandrian Tradition:  Interactions Between Science, Religion, and Literature, ed. L. A. Guichard, J. L. García Alfonso, and M. Paz de Hoz, 73–​91. Bern: Peter Lang, 2014. Toomer, George J. Ptolemy’s Almagest. London: Duckworth, 1984. van der Waerden, B. L. “Ausgleichspunkt, ‘Methode der Perser’ und indische Planetenrechnung.” Archive for History of Exact Sciences 1 (1961): 107–​121. Włodarczyk, Jarosław. “Examining the Armillary Sphere.” Journal for the History of Astronomy 18 (1987): 173–​195.

chapter D11

Science in th e 2 nd a nd 3 rd Centu ri e s  ce An Aporetic Age Paul T. Keyser

Every age is transitional between its past and its future, but some ages are more transitional than others. So it was in the years around the 10th century of the city of Rome—​ that label for the period dodges the seductive pull of round figures like “100 ce” and “200 ce,” which mark transitions in our count of years, but not in the long evolution of ancient Greek and Roman science. Looking back through the compound lenses formed by the Renaissance, the Middle Ages, and the Byzantine (i.e., late Roman) Empire, we see refracted fragments, and standing out huge amid them the extant works of Ptolemy and Galen. Dazzled by their dominance, itself only established by the later evolution of their respective traditions, scholars have discerned a partial and distorted view of the period. This chapter attempts to synthesize a more synoptic, and less telescoped, view of the science of those decades. It begins by eliciting three apparent trends in the works of the period, which can be seen in literature both scientific and not; then turns to a survey of some works that display the range and the troubles of the scientific writing of the period. This also is selective, but a broader selection, admitting many works rarely considered. As will be seen, the trends of the time doomed most works of the age. First among these trends is that Roman culture valorized founders and authoritative leaders, both on the whole and in scientific works (Keyser 2010, 860–​863). That promoted a turn to archaism in literature, in which the early authors became canonical and indeed “classical” (Vessey 1994; Sandy 1997, 50–​7 1). Similar moves can be seen in other cultures, for example, in ancient China (Lloyd 1996, 20–​46), and Romans in the age of the empire often wrote about their own literature being in decline (Williams 1978, 6–​51; Fantham 1978, 111–​116; Barnes 1986, 232–​238). This “cult of the past” operated also in scientific writing, with writers turning more and more to earlier and earlier authorities, especially Pythagoras (see Thibodeau, chap. D1, this volume). Galen, for

830   Greco-Roman Science example, argued in his long work On the Opinions of Plato and Hippocrates that medical science was mainly established by authoritative early sages, namely Hippocrates and Plato, who were in essential concord despite appearances (de Lacy 1978, 48–​50). Writers attributed great scientific accomplishment to cultures far more ancient than the Greeks. Two examples, from the beginning of this period, are Ofellius Laetus who “translated” the ancient Phoenician sage Mōchos of Sidon (Keyser 2016), and Philo of Byblos who “translated” the ancient Phoenician sage Sanchuniathon of Byblos (Edwards 1991). Second, Roman assimilation of foreign wisdom and promotion of native wisdom valorized “usefulness” (Keyser 2010, 863–​866), and among the works produced to meet that need were “encyclopedias” (see Beagon, chap. D4, this volume) and compendia of various kinds. This can already be seen in the works of Varro (in the 1st century bce) and Pliny (in the late 1st century ce), as well as in works of this period: Philo of Byblos’ book on the collecting of books (ca 125 ce), or the miscellany of Gellius (ca 177 ce), or the works of Aelian, Nature of Animals and Various Tales (ca 200 ce), or the massive Dinner-​ table Philosophers by Athenaeus (ca 230 ce; compare Sandy 1997, 71–​84). Thirdly, Roman discourse valorized authoritative masters, and so in scientific writing the preferred source was the master of wisdom (Keyser 2010, 870–​874). That preference is visible already in Cicero, On the Orator 1.16–​23 (the orator must know all history and law, and all arts: “omnium rerum magnarum atque artium scientiam”) and 2.5–​6 (to speak well the orator must know all subjects), as well as in Quintilian (a contemporary of Ofellius Laetus), Instruction of an Orator 1.10, who lists every known science as a requirement for the education of an orator. Within this period, Galen claims that he never needed to revise, thus presenting himself as master of medicine (Gurd 2011, 176–​180). Likewise, Philostratus in his Lives of the Sophists praises those who mastered all arts, both ancient masters (e.g., Hippias of Elis, 1.11) and recent ones (e.g., Dion of Prusa, 1.7). Those sophists who successfully sold themselves as omni-​competent public intellectuals were often rewarded with lucrative posts or exemptions from civic burdens (Millar 1983, 78). As Keyser (2013) argued, the decline in numbers of practicing scientists in (and after) this period can be traced to a reconfiguration of Greco-​Roman society into a more homogenous and hierarchical whole. Furthermore, as will be seen, the type of writing, the subjects treated, and the approach to those subjects, all manifest a turn toward compendia claiming wide competence and based on older sources. The turn to authority and compendia in science may be understood as attempts to deal with the aporia of scientific debate about questions beyond the capacity of the science of the era to resolve, which the Romans saw as endless debate.

1.  Epitomic Encyclopedism The market for encyclopedic works seems to have been robust, and compendia of many kinds were produced, all seeking to contain the world within their text. Three examples

Science in the 2nd and 3rd Centuries CE    831 display the nature of these works, none of which reproduced the kind of book that Pliny had written: Ampelius, Apuleius, and Censorinus. The little Liber memorialis (aide-​mémoire) of Ampelius is rarely read and survived antiquity in a single manuscript. It is a small encyclopedia or epitome on cosmology, geography, theology, and history, addressed to his student “Macrinus.” (This man may be the future emperor Macrinus, in power 217–​218 ce, although some scholars dispute that and date the book to the end of our period: see the essay by Paniagua, chap. E7, this volume.) It attempts to survey all that is known about the world in which the student lives. Working upward from the foundations, Ampelius describes the four elements and five zones of the earth (sec. 1); then proceeds through the element fire, that is, the stars (sec. 2–​3); the element air, that is, the winds (sec. 4–​5); the element earth (sec. 6); and the element water (sec. 7). After that, about three-​fifths of the work is a Romano-​centric “world” history: Florus (ca 125 ce) had earlier written a similar epitome of Roman history. The brevity of Ampelius’ treatment and the range of his material conform to the teacher’s goal of mastering all subjects and to the student’s need to demonstrate himself a master. Ampelius ostensibly wrote to answer the queries posed in the book’s second sentence, “What is the world, what are its elements, what the globe bears, and what the human race has wrought?” For his presentation on the constellations of the zodiac (sec. 2), Ampelius used an early Roman source, namely the Pythagorean scholar Nigidius Figulus (ca 60 bce), who offered etiologies from Mesopotamia and Syria for the constellations, including the Phoenician sage Mōchos of Sidon whom Ofellius Laetus “translated” (sec. 2.7). Although best known for his magic-​infused novel (Golden Ass), in the decades around 160 ce, Apuleius of Madaurus wrote on a wide variety of topics in natural science (Harrison 2000, 36–​38). Each of those short works constitutes a didactic compilation on some topic, so that Apuleius presents himself as a polymathic master of scientific learning. Some he wrote in Greek, such as a now-​lost Natural Questions (Harrison 2000, 29–​30). Others were translations from Greek into Latin, such as the extant On the World (based on the work falsely attributed to Aristotle, On the Kosmos, also extant), and lost translations of Plato’s Phaedo (Harrison 2000, 23) and of Nicomachus’ Arithmetic (Harrison 2000, 32). He also published extensively in Latin, which was probably his primary language of teaching. His Latin compositions include an extant summary of Platonic doctrine, On Plato and His Teaching, plus various lost works: (1) on drugs (Harrison 2000, 25–​26), which led later writers to credit him with the Herbarius; (2) on fish (Harrison 2000, 29–​ 30); (3) on trees and agriculture (Harrison 2000, 26–​28), a work known to have been used by later writers; (4) on astronomy and meteorology, that is, on heavenly marvels such as comets (Keyser 1994, 643–​645; Harrison 2000, 29), and (5) on music (Harrison 2000, 31–​32). Out of all that, only two works survive: On the World and On Plato and His Teaching (Harrison 2000, 174–​209). They imply that Apuleius was a follower of Plato, and indeed the later ancient tradition presents him as a Platonist. In his summary of Plato’s doctrine, Apuleius creates his own version of Plato (Dillon [1977] 1996, 311–​336; Gersh 1986, 318–​328). Matter is defined experientially as the object of sense and of thought, and although matter is perpetual and infinite, Apuleius doesn’t use Plato’s model of matter

832   Greco-Roman Science as a “receptacle” (1.5, contrast Plato, Timaeus 52b). Moreover, the creator god ordered the kosmos by imposing number and geometry—​ the “geometrical” atoms upon chaotic formless matter (1.7, compare Plato, Timaeus 52e–​57d). The resultant world-​being is composed of the four elements and extends through all space and time (1.8, compare Plato, Timaeus 31b–​34a). Apuleius is here interpreting the Timaeus, just as had Aristotle, Heaven 1.10 (279b–​280a), to say that the cosmos began but nonetheless is eternal. Apuleius’ presentation culminates in a description of the “perfect sage” (2.20–​23) and how that man would rule (2.24–​28)—​ it is easy to imagine that Apuleius was thinking of the Emperor Marcus Aurelius, in power 161–​180 ce. All that we know of Censorinus is that he wrote a book about the concept of the birthday, and gave it as a birthday gift to his friend in the year 238 ce. In the small set of manuscripts that contain the birthday book, it is immediately followed by an encyclopedia or epitome on natural science that has lost its preface, and so it is anonymous but was often attributed to Censorinus. The epitome in its extant portion very briefly covers all the usual topics of ancient cosmology. The elements are described; then the nomenclature and geometry of the geocentric cosmos; the fixed and wandering stars, together with the basic geometry of astrology (oppositions, trines, quartiles, etc.); the shape and central position of the earth; the nomenclature and postulates of geometry; and, finally, music (the nomenclature of the various modes and meters). Censorinus’ birthday book displays cosmic and curious learning based heavily on Varro, perhaps in imitation of his scholarship, and flits or bounces from one topic to the next through metonymic association, following the thread of “birthday” and time. He glissades from birth through human generation to astrology, thence with a glance at Pythagoras into harmonics, especially as applied to human lifespans, and next, after an encomium of the dedicatee (the middle-​aged lawyer Caerellius, known only from this book), the author turns to time itself, eternity and centuries, the Roman secular games, and the Great Year of the planets, then the Roman calendar leading to a survey of the history of the world, and returning via months, days, and hours, to the abrupt and probably fragmentary ending.

2.  Mathematics in Service to Meaning The Greek scientific tradition largely treated mathematics as a kind of royal road to certainty and true knowledge. Thus the geometrical works of the Hellenistic era, such as those by Euclid, or Archimedes, or Apollonius of Perge, presented proofs considered rigorous, of propositions considered abstractly (see Acerbi, chap. C3, this volume). Other scientists exploited mathematics as they sought the guaranteed certainty it was seen to provide: those who studied the heavens and the earth, as well as those who studied how music or machines worked. Although Ptolemy’s works of astronomy dominate the standard narrative of this period, many others composed mathematical treatises with various goals. We will briefly consider six of those, beginning with the Nicomachus whom Apuleius translated; in each case, the works of the author seem to

Science in the 2nd and 3rd Centuries CE    833 display a desire to master and promote the works of earlier writers or an older tradition, and innovation seems to consist of exploring the ramifications of what has already been discovered. Nicomachus of Gerasa (ca 125 ce) wrote an introduction to Pythagorean science, in the form of a series of books on arithmetic, on music, on geometry, and an introduction to Pythagoras, presented as the founder of science (Dillon [1977] 1996, 352–​361; O’Meara 1989, 14–​23). Nicomachus’ presentation of mathematics is discursive not demonstrative: he is interested in results and theorems, and he assumes that others have provided the proofs. His Introduction to Arithmetic became a school text and is his sole work to have survived (and was commented on by several later scholars), although his lost Theology of Arithmetic was extensively extracted. The works consider such things as evenness and oddness, the number 1 as the origin of “sameness,” the number 2 as the origin of “otherness,” the “sieve” of Eratosthenes, perfect numbers (6, 28, 496, 8128, etc.), various ratios, the square numbers, the triangle numbers (1, 3, 6, 10, etc.), the cube numbers, and so on. It was what arithmetic (and geometry) could suggest about the structure and meaning of the cosmos that interested Nicomachus. Anatolius was born in Alexandria, and late in life he became a bishop of Laodicea in Syria, which led the church historian Eusebius to compose a brief biography (History of the Church 7.32.6–​21; O’Meara 1990, 23–​25). Eusebius recounts how Anatolius was solicited to become professor of Aristotelian philosophy in Alexandria, how he aided citizens during a siege of Alexandria (probably in 264 ce), and how he was coopted as bishop of Laodicea in 268 ce. He composed a simplified method of computing the date of Easter and is credited with a work on the significance of the numbers from 1 to 10, which digests and streamlines what Nicomachus and others had provided (Keyser 2006). His complex career emphasizes the fluidity of intellectual categories in this period, and although he was solicited for the post of Aristotelian philosophy, Eusebius names the areas of his mastery as arithmetic, geometry, and astronomy—​so far, typical of a Pythagorean, not an Aristotelian—​plus dialectics, physics, and rhetoric, which are simply the typical “parts” of philosophy. The compendious work of Diophantus (ca 250 ce) treats what we now call by its Arabic name, “algebra,” that is, the mathematics of numbers and their equations. The works of Greek mathematics that survive mainly valorize geometry, which was seen as embodying an elitist perspective (cf. Keyser 1992), and thus recommended itself to the Neoplatonists (see Bernard, chap. E2, this volume). The Elements of Euclid, for example, reconfigure number theory in terms of geometrical entities (bks. 2 and 7–​9). It seems likely, however, that the work of Diophantus is an outstanding relic of a rich tradition, rather than an isolated effort, for we also have the “algebraic” work by Heron of Alexandria, the Metrica (ca 60 ce; compare Acerbi, chap. C3, this volume). The origins of this form of mathematics are much older than Euclid, and go back to Mesopotamian methods (compare Høyrup, chap. A1a, this volume). Most of his “problems in numbers” (as Diophantus calls them in his first sentence) are systems of equations for which a solution in positive rational numbers is desired; they are solved by a variety of clever assumptions.

834   Greco-Roman Science By the end of our period, Ptolemy was canon, but that was not undisputed during our period. The earliest known commentator on Ptolemy, preserved in one brief quotation, was the mathematical astronomer Artemidorus, writing apparently ca 200 ce (Jones 1990, esp.  10–​12), who criticized his lunar model. The same damaged manuscript that preserves the comment of Artemidoros apparently contained a portion of a commentary on Ptolemy’s Handy Tables, and contains a lengthy extract from the astronomer Apollinarius (perhaps ca 120 ce), whose lunar model was more elaborated than Hipparchus’ but less exact than Ptolemy’s (Jones 1990, esp.  12–​17, and 38–​45). Apollinarius may have contributed to transforming the Babylonian arithmetical system for computing planetary positions into the 248-​day scheme found in several Greek papyri and is attested to have written about solar eclipses. That is, in the early 3rd century ce, astronomical writers still considered alternatives to Ptolemy worth quoting (Apollinarius) and were still willing to engage critically (if perhaps ineffectively) with Ptolemy’s system (Artemidorus). Serenus of Antinoeia (ca 215 ce), like his near-​contemporary Artemidorus, composed commentaries on earlier works, notably a lost one on the Conics of Apollonius of Perge, as well as treatises of his own, one of the Section of the Cylinder, and the other on the Section of the Cone (Decorps-​Foulquier 2000, 33–​41). The treatises imitate the form of Apollonius’ work but present more elementary mathematics, as if Serenus sought to fill out the work of the earlier mathematician. The practice of filling out earlier works is well attested for philosophers and scientists of this era, compare Bernard, chap. E2, this volume. Greek writing on mechanics is represented by a diverse collection of texts, all offering some degree of mathematical argument and presentation. Around 100 ce, Apollodorus composed a treatise on war machines, which he says in his preface was for a campaign that would involve sieges (probably Trajan’s war in Dacia), that needed to be constructed with εὐπόριστα (handy materials), that needed to be small and light, and that could be built by any old engineer (Whitehead 2010). The emphasis here is not on mathematical exactitude or artisanal precision, but instead on practical efficiency on a battlefield expected to involve rapid shifts in the nature of the conflict. Among the items Apollodorus provides are defenses (trenches and mobile wedges) against objects rolled down from hill forts; devices for undermining walls at the top of hills; rams against gates and towers; siege towers built in situ, that is, at the defensive wall (rather than being rolled up from a distance); and ladders to scale the walls. The book is organized around the likely progress of the attacks and allows for the need to make do with the materials at hand.

3.  The Earth, So Rich and Strange Greek exploration of the world slowly accumulated geographical knowledge, both particular (concerning specific bodies of water, specific mountains, and so on) and general (the shape of the earth, the effects on climate of the spherical earth and the motion of

Science in the 2nd and 3rd Centuries CE    835 the sun, and so on): see Kaplan, chap. B3, this volume. The conquests of Alexander the Great, king of Macedon, stretching from Greece to Egypt, Persia, and beyond, provided a wealth of data, mainly through explorers who accompanied or followed his advances. Hellenistic geographers, especially Eratosthenes and Hipparchus, sought to create a complete model that built upon that data (see Roller, chap. C5, this volume). For Roman audiences, descriptive geography was a more successful product, and the colossal work of Strabo (ca 20 ce) surveyed the entire inhabited world (oikoumenē), centered on the Roman Empire ruled by Augustus and Tiberius. Once the floods of new data ebbed, after the Roman Empire reached its maximum extent, writers focused more and more on synthesis and overview. Moreover, from the time of Herodotus and the earliest Greek geographers, works of geography regularly reported marvels from remote regions of the earth—​such reports now played a leading and increasing role in geographical writing. We will briefly survey five writers, whose works display these features:  Dionysius of Alexandria, Iulius Solinus, Iulius Africanus, the anonymous work Rivers and Mountains and What Is Found in Them, and the anonymous work Physiologus. Dionysius of Alexandria (ca 135 ce) was employed as a scholar (director of the Imperial libraries) and bureaucrat (secretary in charge of correspondence and embassies), under the Emperor Hadrian. His sole surviving work is a single book of verse (1186 lines) describing the entire inhabited world (oikoumenē), written in the meter typically used for didactic poetry, hexameters, and based mainly on Eratosthenes. That is, he aims at concision and pleasure and uses an authority over three centuries old. The sites are described very briefly and allusively, and his most prominent interest lies in the marvels of the botanical and mineral world (Lightfoot 2014, esp. 141–​143, 150–​156). Most of the individual marvels are well-​known items, found also in Pliny or Strabo. The precious stones of the remoter regions are exotic, colorful, and brilliant, and are often “carried down” by rivers. In the fragments of another work, on stones, he says the earth “gives birth” to stones, thus melding the botanical and mineral worlds. In his Description of the World, the region Mesopotamia (lines 992–​1013) offers the date palm (as in Herodotus 1.193.4) and the beryl (as in Strabo 15.1.69 and Pliny 37.76–​79). Further afield, Arabia (lines 936–​939, 945, 950–​951) supplies the botanicals citron, myrrh, reed, frankincense, cassia, and “leaf ” (i.e., cinnamon-​tree leaves, as in the pharmacist Kosmos (“Cosmus”), ca 90 ce), as well as gold. Most exotic and remote of all, India (lines 1114–​1122) produces gold, linen, and ivory, plus the stones beryl, adamant (Pliny 37.56), green iaspis (Pliny 37.115), topaz (Strabo 16.4.6), and purple amethyst (Pliny 37.121). Iulius Solinus (ca 235 ce?), like Ampelius (above), includes a précis of the history of Rome (1.1–​52) in his book of geographical marvels (praef.4) that explicitly prefers archaic sources (praef.5), yet was apparently extracted primarily from Pliny. Spiraling outward from Rome (praef.7–​8), he describes the regions ruled from Rome, and those beyond Roman rule all the way to the Outer Ocean. His “compendium” (praef.2) was extensively exploited for a thousand years. He concludes most of the geographical sections with natural marvels of the region, often stones (Brodersen 2014, 196–​200). Solinus uses that pattern even with Rome and adds to his précis an account of human marvels (1.53–​127),

836   Greco-Roman Science many of which also appear in Pliny book 7, and asserts, “in a degenerate succession, the corrupt offspring of our age have lost the ornament of archaic beauty” (1.87). Solinus then turns to the marvels of the homeland Italy, which include its wise wolves (2.35–​36), its urine-​hiding lynxes (2.38–​39), and the maritime red coral that becomes a gemstone on land (2.41–​43). The rivers of Greece produce the “galactite” stone that exudes milk (7.3–​4: known to the pharmacist Dioscorides 5.132, found in Pliny 37.162, and repeated by Iulius Africanus, below). Macedonia grows the fecund “paeanite” stone that aids conception and birth (9.22, cf. Pliny 37.180), whereas the cranes of Thrace ballast themselves with sand for better flight (10.12–​16, cf. Pliny 10.59–​60). Further from Rome, but still within reach, the Black Sea region spawns the marvelous almost-​ human dolphin, a swift sea-​beast that can leap over the sails of ships, that bears and cares for its young like humans, that has a human-​like voice, and has often become friends and lovers of men (12.3–​12, cf. Pliny 9.20–​33). Beyond Roman rule, Scythia spawns the best of all the gems, the green emerald most pleasant to view (15.23–​28, cf. Pliny 37.62–​ 65), and quartz “crystal” most resistant to cold (15.29–​31, cf. Pliny 37.23–​28). From far Taprobane (Ceylon), at the very ends of the earth, comes the pearl, a stone born by lunar powers from a sea-​animal (53.23–​27; found also in Pliny 9.106–​116 and in the Latin of the Physiologus sec. 24, below). Iulius Africanus, who also wrote on chronology and biblical exegesis, composed his Kestoi ca 230 ce (the title means “embroideries,” or perhaps “embroidered and decorated girdle,” as in Souda κ–​1428, διακεκεντημένος καὶ διαπεποικιλμένος ἱμάς; see Wallraff and Adler 2012, T5, and 17–​18). Based on surviving evidence, the 18 or more books of the work varied greatly in content, including, for example, metrological data (Wallraff and Adler 2012, 27–​32). The book appears to be a kind of miscellany, like Gellius’ Attic Nights, but focused on technē and intended to entertain readers and celebrate the universal learning of the author. It is informed by ideas about secret properties of natural substances (like the Physiologus, below), and, for example, repeats the information in Solinus 7.3–​4 about the “galactite” stone (Wallraff and Adler 2012, D33). Two long fragments display the wide range of Africanus’ topics. First, an extract, possibly the whole of book 7 (Wallraff and Adler 2012, F12), concerns primarily military matters: armor, tactics, poisoning the enemy’s food and water, improving battlefield surgery, training horses for battle, surveying a wall or river using geometry, mixing potions of wakefulness, dealing with elephants, making wine from fruits other than grapes, and an experiment on the speed of arrows. Then, a fragment on papyrus, from the very end of book 18 (Wallraff and Adler 2012, F10), an interpretation of the “Nekyia” (descent into Hades) recounted in Odyssey 11, augmented with a long spell spoken by Odysseus, and commented by Africanus in a kind of sphragis attesting his inspiration to restore the spell to the text of the Odyssey, and his authorship of the Kestoi and architectural service to the emperor, especially building the library in the Pantheon. Africanus also provides two alchemical recipes (cf. Wallraff and Adler 2012, 76–​78), for (a) a paste that is “self-​igniting” (αὐτόματον πῦρ) when exposed to the sun (Wallraff and Adler 2012, D25: sulfur, pyrite, bitumen, quicklime, etc.); and (b) a mordant for dyeing (cited from bk. 3) and an imitation purple dye (Wallraff and Adler 2012, F69, F70), both preserved in

Science in the 2nd and 3rd Centuries CE    837 the alchemical Papyrus Holmiensis (the Stockholm Papyrus), written only a few generations after Africanus published his Kestoi. The book Rivers and Mountains and What Is Found in Them (ed. Bernardakis 1896) is attributed to Plutarch in the manuscripts, but scholars usually suppose that it was written ca 300 ce, that is, about two centuries after Plutarch’s death. The work resembles many works in the genre of paradoxography, that is, writings about marvels, in which they are detached from their original authorial context and presented as freestanding marvels (usually with citation of the author from whom they were drawn). This work records marvels about 25 rivers, almost half (11) of them remote and fabulous, flowing in India (sec. 1 Hydaspes, sec. 4 Ganges, and sec. 25 Indos), or into the Black Sea (sec. 5 Phasis, sec. 14 Tanais, and sec. 15 Thermodon), or the Caspian (sec. 23 Araxes), plus the Gallic Arar (sec. 6), the Nile (sec. 16), and the Mesopotamian Euphrates (sec. 20) and Tigris (sec. 24)—​the others are rivers of Greece (eight: sec. 2 Ismenos, sec. 3 Hebros, sec. 8 Lycormus, sec. 11 Strymon, sec. 17 Eurotas, sec. 18 Inachos, sec. 19 Alpheus, sec. 22 Achelous) or western Asia Minor (six: sec. 7 Pactolus, sec. 9 Meander, sec. 10 Marsyas, sec. 12 Sagaris, sec. 13 Scamander, sec. 21 Kaïkos). So the only river located to the west of Greece is the Arar, and the geographical range is more typical of the Hellenistic than Roman era (cf. Keyser 2011). For each river, a mountain is described as “near” it (thus the title), and both river and mountain are provided with brief etiological myths. Reflecting the third part of the title, “what is found in” most of these rivers and mountains are stones and plants with marvelous powers. In a few cases, however, either the river or the mountain lacks any special product: sec. 2: both the Ismenos, in Boiotia, and its mountain, Cithaeron, lack any special product (the section on the Thermodon, sec. 15, seems to have been truncated in transmission). The lone western river, the Arar (sec. 6, in Gaul, the modern Saône) produces a fish whose head produces the stone attributed to the Arar. The products and the authorities cited are mostly unparalleled, so that some scholars have interpreted the work as a kind of scholarly forgery or perhaps joke. The anonymous work known as Physiologus seems to have been composed ca 200 ce and is preserved in an extraordinary number of ancient versions and translations, with the chapters presented in different orders (Offermanns 1966). The earliest version may have been a Christian work seeking allegorical meaning from tales about animals, similar to those preserved in the (pagan) work by Aelian, Nature of Animals. The practice of eliciting such meanings goes back to Aristotle’s History of Animals, especially book 9, and can also be seen in Apion of Alexandria (ca 50 ce, as preserved in Aelian, Nature of Animals 10.29), on the ibis: “it is beloved of Hermes [Thoth] the father of words, since its form is like the nature of speech: for the black wing-​feathers might be compared to speech silenced and turned inward, and the white ones to speech brought forth and heard,” and it is also “an eater of bad food,” that is, feeding on whatever it finds in the mud (Keyser 2015). Plutarch, Isis and Osiris 381b, 382b–​c, writes similarly on Egyptian animal symbolism, according to which the crocodile and other animals manifest divine qualities (Curley [1979] 2009, xi–​xiii). The Physiologus itself offers allegorical interpretations of about 40 marvelous animals, plus a few plants and stones. On the ibis (in the Latin, sec. 17), Physiologus records only

838   Greco-Roman Science that it eats unclean food from muddy water, so that the bird becomes a symbol of the spiritually shallow (in contrast to what Apion said). On the elephant, Physiologus (in the Latin, sec. 20) records its family values style of mating (performed after consuming the drug mandrake) and giving birth (immersed in a pond, guarded by dad), and the myth that it cannot bend its legs, known already to Aristotle (History of Animals 2.1, 498 a3–​13, and Progression of Animals 9, 709 a8–​10), and transferred to the northern elk by Caesar (Gallic War 6.27: see Keyser 2011, 52 and 64). The Physiologus contains the earliest record of the myth that a unicorn (monokeras) can be mastered only by a virgin girl (in the Latin, sec. 36), in contrast to earlier tales of the beast that seem to refer to the rhinoceros, long ago described by Ctesias (see Photius, Library 72, p. 48b, and Aelian, Nature of Animals 4.52), and Pliny 8.76; again, Caesar transfers a fabulous unicorn to the northern forests (Gallic War 6.26: see Keyser 2011, 52 and 64).

4.  The Sublimation of the Schools For centuries after the deaths of the founders of the Athenian schools of philosophy, their arguments and doctrines determined the shape of what was considered philosophy. The schools in time variously transformed the teachings of their founders and responded variously to the Roman conquest. By the beginning of our period (ca the 10th century of the city of Rome), the doctrines of the school of Epicurus seem mostly rejected, those of the school of Zeno seem partly assumed or partly rejected, whereas the actual debates mostly concern Aristotle and Plato. By the end of our period, the new direction consisted of an attempt to synthesize philosophy by interpreting Aristotle, when “correctly” understood, as having agreed with Plato about all essentials, and Plato as having taught a doctrine that modern scholars label “Neoplatonism” (see Siorvanes, chap. E1, and Griffin, chap. E3, this volume). That later synthesis dominated thinking and writing for centuries, and most of the transformative works of the long tenth century of Rome have been lost because their manuscripts were no longer of interest to later scribes, who focused on copying works that cohered with the developed system. But some works did survive, and from Plutarch, Alexander, Plotinus, and Porphyry, we can trace some aspects of the evolution. Plutarch, a priest at Delphi, the son of a wealthy family, and a proponent primarily of Platonism, lived most of his life in the small town of Chaeronia in Boiotia (active ca 80‒ca 120 ce). He often wrote as if the Athenian schools of philosophy founded by Plato, by Aristotle, by Zeno, and by Epicurus were all still in operation. In two long works (plus other works now lost), he opposed Zeno’s school (Cherniss 1976). One is the work entitled Stoic Self-​Contradictions, which concerns mostly ethics and theology, and the other is the Against the Stoics on Common Conceptions, where Plutarch attempts to refute their foundational principles, especially sec. 30–​50 (1073d–​1086b) on natural philosophy. He likewise opposes Epicurus, in three works concerned with ethics and theology (plus other works now lost): the Reply to Colotes (an early Epicurean), with

Science in the 2nd and 3rd Centuries CE    839 its pendant work, That Epicurus Actually Makes a Pleasant Life Impossible, plus the Is “Live Unknown” a Wise Precept? (Einarson and De Lacy 1967). In contrast to those two schools, Plutarch appears never to have directed a work against the school of Aristotle, and its followers appear as speakers in his dialogues. Two works especially show how Plutarch approached science:  On the Face in the Moon, and On the Principle of Cold, although his works on animals, for example, Whether Land or Sea Animals Are Cleverer, and Irrational Animals Employ Reason, also display engagement with science (all four in Cherniss and Helmbold, 1957). His rejection of Stoic and Epicurean ideas, coupled with his advocacy of Plato’s ideas, and his assumption of Aristotelian interpretations of Plato, show Plutarch participating in the gradual evolution of the eventual “Neoplatonist” synthesis. In the Face in the Moon, sec. 8 (924d–​f ), Plutarch argues in various ways that the moon is “earthy.” The element earth is a substance that attracts like to like, and there could be many bodies made of earth, in the same way that the multiple fiery stars show that fire also attracts like to like. Moreover, infinite space allows for multiple “centers” in addition to the earth itself, sec. 11 (925f–​926b). He compares the fire under the volcanic Mount Aetna, that is, located in an unnatural place for fire, and argues that matter composed of the element earth could also be located for a long while in an “unnatural” place, sec. 12 (926c–​f ). Having thus argued that nothing prevents the moon being made of the element earth, he introduces observations to show that it actually is made of the element earth. First, the rough surface of the spherical moon does not reflect the sun like a mirror would, because if it did we would always see only an image of the sun, that is, a small bright dot: sec. 17 (929f–​930e). The moon must be “solid” (i.e., earthy), in order to reflect in the way that it does, sec. 18 (930e–​931c), and likewise in order to eclipse the sun, the moon must be “solid,” sec. 19 (931d–​932c). The properties and powers of the moon show that it is not only fiery: for example, she has a moistening power that acts on earthly things, sec. 26 (939f–​940b). The moon, he concludes, is a blend of earth and star, sec. 29 (943e–​944a), in which the sun provides the mind, the moon provides the soul, and the earth provides the body, sec. 30 (945c), so that the moon is a mean between sun and earth, sec. 30 (945d). In his work On the Principle of Cold, Plutarch appears to call into question the standard four-​element model, as enunciated by Aristotle, in which the four elements are composed of pairs of opposites, hot and cold plus wet and dry. Plutarch considers whether cold could be merely an absence or privation, in the way that darkness is merely the absence of light. But in the end, he concludes that the cold is actually a principle, like the hot. He then considers whether the cold element could be the air, as according to the Stoics, or could be the water, as according to Empedocles and others (unnamed), or could be the earth—​this last suggestion is not attributed to anyone and was perhaps an original contribution by Plutarch. Alexander of Aphrodisias was appointed by Emperor Septimius Severus as professor and head of the school of Aristotle in Athens, probably by 209 ce. He also became a Roman citizen, perhaps through the universal grant of citizenship by Emperor Caracalla in 212 ce, as recorded by the historian Dio Cassius (77/​78.9, Ῥωμαίους πάντας

840   Greco-Roman Science τοὺς ἐν τῇ ἀρχῇ αὐτοῦ . . . ἀπέδειξεν: “he made everyone in his realm into Romans”) and by the jurist Ulpian (in Justinian, Digest 1.5.17, In orbe Romano qui sunt ex constitutione imperatoris Antonini ciues Romani effecti sunt:  “Those who are in the Roman world were made Roman citizens by the constitution of the emperor Antoninus”); see Sasse (1958) and Ando (2012, 1–​2, 51–​57, and 93–​99). Alexander wrote sentence-​by-​sentence commentaries on Aristotle’s “esoteric” works—​that is, extant lecture notes. The commentaries are focused on explaining Aristotle, and Alexander created from Aristotle’s texts a coherent and consistent philosophical system, suitable for teaching, but which allows for unresolved problems (as in his extant work Questions). These commentaries later became the basis for the Neoplatonist commentaries that dominated philosophy in the Late Antique and early Byzantine era. Among the commentaries on scientific works, the one on the Meteorology survives, and fragments of those on Heaven, and on Generation and Destruction. Alexander’s move, an attempt to elicit a coherent system from Aristotle’s lecture notes, marks a departure from what we know of prior commentators: the move was fruitful and came in time to form the basis of the new synthesis, Neoplatonism. Alexander also wrote monographs on special topics that appear to be more pedagogical, particularly the work On Mixture (Todd 1976). There, Alexander attacks a Stoic doctrine of “total blending” (sec. 5–​12), itself advanced as an analogy to explain how the Stoic pneuma (a body, albeit rarefied) could pervade matter (also body, but dense: Todd 1976, 29–​73). Alexander discusses the long-​standing problem of how a small amount of wine could pervade a large quantity of water, or how the element fire could pervade the material iron. Having also rejected the Epicurean account based on mixtures of atoms (sec. 2), Alexander states the Peripatetic position (sec. 13–​15), already in Aristotle’s Generation and Destruction, that during blending none of the constituents is entirely destroyed, and instead, their properties partially persist, that is, blending is the unification of juxtaposed bodies that are altered not destroyed, and that can, in principle, be separated and recovered. Although Alexander nowhere says so, this problem is intimately related to the processes and theory of alchemy (see Fraser, chap. D7, this volume), as well as to the relation between body and soul (below). The philosopher often credited with having “founded” the school of Neoplatonism is Plotinus (active 254–​280 ce), who thought he was merely interpreting what Plato actually said: but—​just as all history is in some way current history—​all philosophical interpretation is in some way current philosophy. That is, Plotinus’ interpretation is very much a product of his era, and not a timeless, much less “true,” reading of Plato. Moreover, the works of Plotinus were published by his student Porphyry (below), who rearranged, and even divided, them, on principles that are unclear to us—​so we must work through an extra layer of mediation. (Other students of Plotinus also published editions of his works, but those are lost:  on what principles were they organized?) Plotinus seems to have been primarily concerned to elucidate what he saw as Plato’s concept of the relation between the sensible (i.e., physical and mutable) world on the one hand, in contrast to the intelligible (i.e., immaterial and eternal) world, on the other (O’Meara 1993). For example, he taught that number is the foundation of the intelligible

Science in the 2nd and 3rd Centuries CE    841 realm (see especially Ennead 6.6  =  #34, in the order of composition according to Porphyry’s Life of Plotinos), and he used “number” in an intellectual flight of abstraction, describing it as undergirding the entire existence of the intelligible world, so that multiplicity is the manifestation of number in the composition of the physical universe (Slaveva-​Griffin 2009, 3–​23, and 141–​145). Plotinus saw the physical world as a good creation (for example, Ennead II.9  =  #33, sec. 4–​5, 17–​18) and taught that biological generation, even among animals and plants, was a manifestation of θεωρία (contemplation), that is, apparently some kind of consciousness was present in all living beings (Ennead III.8 = #30). Note that Ennead 30–​33 form one continuous treatise, dispersed by Porphyry into, respectively, Enneads III.8, V.8, V.5, and II.9 (Harder 1936). Moreover, in Ennead II.7 = #37, Plotinus considers the problem of “total mixture,” in response to Alexander, and concludes that what penetrates throughout in a mixture are the qualities, not the bodies (e.g., when water perfuses papyrus). Porphyry of Tyre (active ca 260–​305 ce), as mentioned, both edited the works of his teacher Plotinus and also composed commentaries and monographs. It is through his writings that we know about the earliest stages of what modern scholars call Neoplatonism (O’Meara 1989, 25–​29). Porphyry’s commentaries included one on Plato’s Timaeus (fragmentary), one on Aristotle’s Physics (fragmentary), and one on Ptolemy’s Harmonics (extant). The monographs include one arguing in favor of vegetarianism on both physical and ethical grounds (i.e., a Pythagorean outlook; Clark 2000); another arguing that embryos receive their fully formed soul only at the moment when their bodies are fully formed to receive it, that is, at birth (a Stoic outlook; Wilberding 2011); and third, an introduction to the astrological work of Ptolemy (Suda π–​2098; Boer and Weinstock 1940). For him, mathematics served to mediate between the evil material world and the perfect immaterial world (Life of Pythagoras sec. 47 and 58.12–​19). Porphyry was a universalizing Platonist, able to find the doctrines of Plato, as he understood them, in all cultures. He presented his philosophical doctrines as revealed by gods to men, prominent among whom was a reconstructed “Pythagoras” imagined by Porphyry as essentially Platonist; those doctrines were presented within a philosophical system that Porphyry claimed was both consistent and complete, and served as a relief from perplexity (ἀποϱία).

5.  Synthesis Covering Perplexity Two scientists of the 2nd century ce display in full measure how the creation of comprehensive syntheses founded on antique authorities dealt with perplexities. Galen, the philosophical physician (see Johnston, chap. D9, this volume), and Ptolemy, the applied mathematician (see Evans, chap. D10, this volume), each presents himself as an authoritative master. Each composed a set of works intended as a comprehensive compendium of their science. Galen harks back to Hippocrates and Plato and asserts their essential concord and his essential adherence thereto. He presents his medical system as more

842   Greco-Roman Science efficacious than any other. For Ptolemy, the essential authorities appear to have been Aristotle and Hipparchus, although their influence is more latent than explicit. Ptolemy too presents his synthesis of applied mathematics as more complete and comprehensive than any prior work. None of these writers, neither Galen nor Ptolemy, much less the others discussed in this chapter, asserted that science had achieved a perfect finale. But the range and power of the syntheses offered by Galen and Ptolemy were such that their systems held the field for a millennium or more. They manifest in their work the turn toward compendia claiming wide competence and based on older sources. The turns to authority and to compendia may be understood as attempts to deal with the aporia or perplexity of ongoing scientific debate about questions beyond the capacity of the science of the era to resolve. The resolution chosen was to suspend debate. The desire to decide rather than debate is displayed in the Sacred Tales written by Aelius Aristides, who was faced with quarreling physicians and an unendurable disease. With the doctors offering opposing prescriptions, he concluded they were completely perplexed as to how to heal (Sacred Tales 2, p. 292 Jebb). In the face of what seemed to be irresolvable perplexities, scientific activity slowed to trickle, and the practice of science reoriented toward synthesis and authority. Reverence for antique traditions risks stifling debate and innovation.

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E

L AT E A N T IQU E A N D E A R LY B Y Z A N T I N E SCIENCE

chapter E1

Pl otinus a nd Neopl atoni sm The Creation of a New Synthesis Lucas Siorvanes

1.  Introducing the Period and the Philosophers The philosophy we call Neoplatonism informed the intellectual life of Late Antiquity. Plotinus (3rd century ce) was its acknowledged genius, however, research has shone light on antecedents and on the significant contributions of Porphyry (3rd century ce) and Iamblichus (4th century ce). By the 5th century ce, it had spread to the philosophy schools of Athens (Proclus) and Alexandria (Ammonius), where it lasted until the 6th or 7th centuries ce. As we shall see, the Neoplatonists used earlier philosophical sources in a nuanced, selective manner, which they called “harmony.” Plotinus (ca 204–​270 ce) was born in Egypt. At 28, he attended the renowned professors of Alexandria, but “he came away from their lectures depressed and full of sadness.” So he found “the one I sought,” the free philosopher Ammonius Saccas, with whom he stayed for 11 years (Porphyry, Life of Plotinus 3). He joined the campaign of Emperor Gordian III against the Persians, and, following the emperor’s assassination, he escaped with difficulty, eventually settling in Rome in his 40th year. He befriended Emperor Gallienus, who promised to fund a “Platonopolis” so that Plotinus and his followers could live according to their ethics. Powerful senators opposed it, and it was never built. Plotinus’ “seminars were like conversations” that raised problems sourced from a variety of philosophical authors. From the mid-​250s, he wrote extensive notes on his philosophy. In the last years of his life his followers dispersed, probably due to his failing health (according to one reading, he succumbed to leprosy). His notes were edited and compiled in a thematic form, the Enneads, by his student Porphyry.

848   Late Antique and Early Byzantine Science Porphyry (ca 232/​234‒ca 305/​309 ce) was born in Phoenicia of Syrian parents. He studied in Athens under the eminent academic Longinus, a “living library and walking museum.” At the age of 30 he joined Plotinus in Rome, whose seminars he found highly original but unclear in expression and logical coherence (Life of Plotinus, chap.  18). Porphyry discerned that Plotinus’ philosophy differed from the traditional views on the Platonic Forms, and that it was “full of concealed Stoic and Peripatetic doctrines, particularly Aristotle’s treatise the Metaphysics is condensed in them” (chap. 14). Helpfully, he identified the kinds of philosophical works they studied:  Platonic, Aristotelian (especially Alexander of Aphrodisias), and Pythagorean-​Platonist. Five or so years later he moved to Sicily, apparently because he fell into a depression (or because of disagreements in Plotinus’ circle?). In this period away from Plotinus, Porphyry formulated the “Harmony of Aristotle and Plato,” wrote clarifications of Plotinus’ philosophy, composed an Introduction to logic, and revived the commentaries on Aristotle in a form designed for teaching. These kindled the study of Aristotle in Late Antiquity and the medieval period. He wrote a major treatise On Abstinence from Animal Food, which is a pioneering work on ecological living, and he established the Neoplatonic literary theory, through the allegorical reading of Homer. He returned to Rome about 12 years after Plotinus’ death and completed editing the Enneads around 301–​305 ce. Porphyry publicized Plotinus’ Platonism to audiences in the Greek east and the Latin west of the late Roman Empire, but changed it to a more scholarly philosophy, in which Aristotle’s theory of logic and language was indispensable. Iamblichus (ca 245‒ca 325/​327 ce) was born in Syria. He studied in Caesarea (modern-​day Kayseri), Cappadocia, under Anatolius, probably a student of Porphyry. Sometime during 280–​300, Iamblichus may have studied with Porphyry himself, but this connection rests on scant evidence. He disagreed strongly with Porphyry on transcendence in the relation of soul with matter. By 305 Iamblichus had established a school of philosophy at Apamea, in Syria, which became extremely popular. He extended the “Harmony” to Pythagoras, mathematized philosophy, and made acts of transcendence (theourgia = god-​working) essential to unification. He set out the Neoplatonic order of reading the Platonic Dialogues, which remained the standard way of education at the philosophy schools until the end of antiquity. His many commentaries discussed both Plato and Aristotle. His followers converted Emperor Julian from Christianity to Neoplatonic Hellenism, and spread their Neoplatonism to the centers of learning of the eastern Roman Empire. (See also Bernard, chap. E2, this volume.) The Neoplatonists’ corpus makes up about 58% of the total Greek philosophical writing of 11 million words (6th century bce to 7th century ce) (Goulet 2007; Adamson 2009). We can now recognize this extent thanks to the word counts provided by the Thesaurus Linguae Graecae, University of California at Irvine. Yet, the major share of their writing travels under the label Greek Commentaries on Aristotle (English translations project ed. R.  Sorabji). (On the harmonizing of Plato and Aristotle, see Griffin, chap. E3, this volume.) The term Neoplatonism, invented in the 18th century, is inadequate, but it may be kept for the sake of convention, or re-​appropriated from

Plotinus and Neoplatonism    849 its pejorative sense. Gerson, editor of the new Cambridge History of Philosophy in Late Antiquity (2010) has opted to ban the term in favor of plain Platonism. Indeed, they named themselves Platonists. Yet, they assimilated other schools of thought, especially Aristotelianism, Pythagoreanism, and Stoicism (they excluded Epicureanism). Did the Neoplatonists take philosophy as one whole and assign within it a different place for each mode of philosophical inquiry according to its perceived truth-​ value? The origin and evolution of the “harmonization” are subjects of current research internationally. Rarely, they called themselves “new,” meaning “recent” or “after”—​“of the more recent (neōteroi) commentators, all the Platonists from Plotinus” (Proclus, Commentary on Plato’s Timaeus 2.88.12); “the philosophers after (neōteroi) Plato” (Proclus, Platonic Theology 1.28.9–​10); “among the more recent ones, Plotinus” (Simplicius, Commentary on Aristotle’s Physics 9, 790.30); “the more recent of the Platonic philosophers” (Simplicius, Commentary on Aristotle’s On the Heavens 7, 564.11–​14). They liked to consider their ideas, not as novel, but as a return to the original Plato and his sources, particularly Pythagoreanism. Still, we must not take this unoriginality at face value, either. In their context, “innovation” almost amounted to being newfangled, which they shunned as something transient or superficial. So their original contributions tend to be couched as owed to some old or master authority. They lived through the period when Christianity suffered its greatest persecution by Emperor Diocletian (290s–​304), then became the state religion and in turn persecuted pagans. Neoplatonists also viewed the increasing impact of Christianity and Gnosticism with alarm. Plotinus rejected comprehensively the Gnostics (Enneads II.9, also in III.8, V.5, V.8). In the 290s Porphyry wrote fiercely “Against the Christians” (the title is a later attribution), exposing the inconsistencies in Christian doctrines and works (condemned for destruction in the 5th century), while Proclus’ treatise On the Eternity of the World was called the “Eighteen Arguments Against the Christians” (Suda Π–​2473). The late ancient philosophers were urban, highly educated, well versed in the classics and rhetoric. Typically they were immersed in the traditional polytheistic values, which had become known as “Hellenic.” This ancient title of the Greeks in Late Antiquity took on a new, cultural identity, which was more universal: many Neoplatonists were ethnically non-​Greeks. For Christians it denoted the pagans. But the philosophers were not “pagan” in the sense of its Latin root for a rural illiterate (as in the French and English derivations, peasant). After Porphyry, Neplatonism was no longer one family of ideas among many, but became, in effect, the voice of philosophy. By the 5th century it offered the higher education of the period. This paideia was taught in a systematic curriculum that aimed to elevate the soul with logic, ethics and politics, mathematics and astronomy, philosophy of knowledge and being, physics and theology. In this way the Neoplatonists profoundly influenced Christian thinkers, and later, Jewish and Muslim thinkers, too. Neoplatonism as a professional teaching practice followed the fate of the ancient philosophy schools, of which the two main ones ended in different, instructive ways. The Athenian school was exceptionally rich with endowments from patrons. The

850   Late Antique and Early Byzantine Science Alexandrian depended on local city grants and student fees. During a period of persecution (487–​489 ce) that affected “Hellenes,” Ammonius (former student of Proclus), head of the Alexandrian school of philosophy, is reported to have negotiated with the local Christian authority. At any rate, the Alexandrian school continued for at least another generation, headed by Olympiodorus in the 6th century and subsequently by Christians, until the coming of the Arabs in the 7th century. Damascius, who became head of philosophy in Athens around 515 ce, scorned Ammonius. In 529 and more permanently in 531 ce, the Athenian school had been closed down by the local application of Emperor Justinian’s ban on public teaching of philosophy and astronomy by pagans. After a disillusioned attempt to take up residence at the Persian court, the last representatives of the Athenian school (e.g., Damascius, Simplicius) were allowed to return to the Roman Empire. We do not really know where they settled, although Simplicius’ substantial writings testify to a wealth of recorded knowledge, which covers the whole of ancient philosophy, from the 6th century bce pre-​Socratics to his own era. From the pre-​Socratics, through the Stoics and Epicureans, Greek philosophers had their own ways of valuing the divine. The Neoplatonists were not simple polytheists, either. On the one hand, they admitted both devotion and reason, since both address what is permanent: the divine, and the principles of reality, respectively. Being pious was esteemed by Hellenes and Christians alike. On the other hand, the Neoplatonists made polytheism conform to their philosophy by interpreting the gods of the former as personifications of principles of the latter. This philosophical adaptation of polytheism appears conspicuously in Proclus’ Platonic Theology, whose detailed account has more principles than gods of the Greek pantheon, and so he fills the vacancies with more grades of the same gods. At the Alexandrian school, Olympiodorus showed how Neoplatonism could be translated for Christian audiences (e.g., in the Commentary on Plato’s Gorgias). Above all, the Neoplatonists postulated that the many kinds of being, mortal and divine, originate in a supreme unity. Philosophy provides the “way of life” that trains the soul for unification. They did not set philosophy against faith. Instead, they distinguished (a) having an unreliable, irrational faith, from (b) a higher faith that relies on reason as a sound foothold but extends beyond it to the ineffable “root” of existence, which Plotinus called “the One”: Beings have their foundation in it, and their source and root and principle. For the One is the principle of being, and being depends on it. (Plotinus, Enneads VI.6.9.38–​41)

2.  Conceiving of the One The Neoplatonists arrived at the concept of “the One” via every route of their philosophical inquiry. Asking questions, such as what is to be, what is good, why we desire,

Plotinus and Neoplatonism    851 what is god, what is to learn, all led to a discernment of an ultimate unity. Because this endeavor was often “theological,” Neoplatonism is often judged to be a religious system. In the classic Encyclopaedia Britannica (1957) article on Plotinus, W. R. Inge, Dean of St Paul’s Cathedral, London, described it as a philosophy whose special task was to isolate religion in its purity and bring it to the realm of spiritual existence where values are fully realized. In the Greek philosophical tradition, Aristotle considered “theology” to be the “first philosophy,” because it is the most fundamental “science” addressing the nature of being per se, that which is “everlasting and unchanging” (Metaphysics bk. 6). Proclus’ The Elements of Theology alluded to Aristotle (Dodds 1963, 187) and showed that every being “participates in some way” in unity, which characterizes divinity. Starting with Plotinus, the Neoplatonists identified states of being with states of thought. Their ontology and epistemology supported ethics of corresponding virtues. The biographies of Plotinus and Proclus were written as accounts of the Neoplatonic theory of virtues. To be a good person and a good citizen (O’Meara 2003) entailed understanding the nature of one’s true being. In trying to establish the grounds of knowledge, the Neoplatonists inquired about what can we know for certain and what are the principles of things. In Greek philosophy, “science” (epistēmē) meant precise or certain knowledge. Plato’s theory of Forms had shown that precise knowledge is only possible for things with a permanent identity. The Neoplatonists believed that to maintain a stable integrity, the objects of true knowledge must possess a self-​cohesion that has its “root” in an ultimate unity. This choice of what constitutes knowledge remains alive in modern physics, among those for whom science is about formulating properties with beautiful, precise mathematics (e.g., fluid mechanics, string theory). Plato counted the mutable, transient events of the world as “phenomena,” that is, appearances, which are “sense-​perceived,” known as opinion (doxa) not epistēmē. True, rational knowledge was reserved for the “intelligible” Forms. They are the objects of Platonic reality, whose patterns we can behold in theōria, contemplation. Some of Plato’s early successors identified the Forms with the mathematical objects. The Neoplatonists upheld mathematics as the “bridge” between our sense-​perception and the Forms. Proclus’ seminal work on mathematics, the Commentary on Euclid’s Elements, was valued by the pioneers of modern astronomy: it was quoted by Kepler, and it was read by Copernicus and in Galileo’s circle. First the soul (psychē) will climb to Intellect (nous) and there will know that the Forms are beautiful, and affirm that this is beauty, the Ideas. For all things are beautiful by these, by the products and essence of Intellect. That which lies ‘beyond’ (epekeina) this we call the nature of the Good, which has beauty draped in front of it . . . the intelligible beauty is the place of the Forms, and the Good is what lies “beyond,” which is both “the source (pēgē) and principle” of Beauty. (Plotinus, Enneads I.6.9.34–​43) The beauty and ordered arrangement of mathematics, and the stable, steadfast character of this study, bring us into contact with the intelligibles and establish us fully in things that are both always steadfast, and always endowed with divine

852   Late Antique and Early Byzantine Science beauty . . . order, symmetry and capacity for definition, we find most certainly in mathematical science (mathēmatikē epistēmē). (Proclus, Commentary on the first book of Euclid’s Elements 20.27–​21.3, 26.22–​23)

The underlying question might be, in our terms, does the world consist of a collection of facts or can it be explained rationally? According to the Timaeus, Plato’s “physical” treatise, the natural world is mutable but not random because it is a kosmos, namely, Greek for being orderly and beautiful (hence our term, cosmetics). For Plato, it has an ordered and lasting existence derivatively, owed to principles that are permanent by themselves. Besides the Forms, there are Nous (intellect, the principle of rational order), and Psychē (life/​soul, the principle of self-​motion). The former was personified as the divine Demiurge, the universal Craftsman responsible for the world’s organization, who fashioned the cosmos using the Forms as “paradigms” (Plato, Timaeus 28–​29, 39e). Platonists expanded on this scheme by analyzing its main elements. How can psychē fulfill different roles: To provide integrity to composite physical things, which would fall apart without it? To self-​initiate movement? In human beings, how can our personal psychē as soul be enmattered in a mortal, particular body, but, being incorporeal, not belong to any location and be capable of living transcendently? How can nous be occupied with different domains: To turn toward the natural world, toward the Forms, toward itself? Such problems indicated that even these permanent principles are to a degree composite, which presupposes a fundamental simplicity, the “simply One” (Proclus, Commentary on Plato’s Parmenides 74 K.). The Neoplatonists’ conception of the One dovetailed with their response to the problem of what and where are the Forms? From Porphyry’s academic training, we know that traditional Platonists took the Forms to be “intelligible” in the sense of being “objects of thought” (noēta) existing outside Nous. Porphyry tells us vividly how difficult he found Plotinus’ idea that the Forms are the internal contents of Nous, and that Nous identifies with the Forms as the objects of its self-​thinking. It took three arduous attempts before he understood it (Porphyry, Life of Plotinus 18). Yet it offers us a way of making sense of the Neoplatonic synthesis. The doctrine that the Forms are Nous’ thoughts fits in a network of ideas about the world’s organization, which were discussed in Plotinus’ circle. The Stoics believed that rational divine order is immanent in the world. Aristotelians argued that there is a divine nous separate from the world, which supplies the permanent activity that actualizes the world’s potentialities. In this pure intellect, “the thinking will be the same with the object of its thinking” (Aristotle, Metaphysics 12.9, 1075a1–​5). Another example of Nous acting separably from material affairs was Aristotle’s description of our human thinking process. In De anima 3.4–​5 (429a10–​430a25), Aristotle said that when we are thinking our human mind (nous) is identically the form of what we are thinking. He called the actualization of thinking, the “active intellect,” and he compared it to light actualizing the sense-​perception of colors. Enigmatically, he described it as separate and immortal.

Plotinus and Neoplatonism    853 Was it because, like light, the active intellect is neither a perceived material quality nor a physical instrument? Alexander of Aphrodisias (around 200 ce), speculated that the “active intellect” must originate externally to human beings in a perfect, divine Nous that has itself as object of thinking. As Aristotle left open to interpretation the problem of the active intellect, so Plato had left open the problem of the Forms. A 2nd-​century Platonist, Alcinous, summarized the post-​Aristotelian Platonic developments in a useful handbook. In relation to material things, the forms are their measure, but in relation to the divine Nous, the Forms are its thoughts (Alcinous, Handbook of Platonism 9). With Aristotle’s Metaphysics 12.9 in mind, Alcinous stated explicitly that “the primary Intellect” has as objects of thinking always its own thoughts, and “this activity is Form” (10.3). The Pythagorizing Platonist Numenius (2nd century ce) identified Plato’s Forms with the contents of Nous, which is contemplative in the capacity of reflecting on the thinking “single” “first god,” but is demiurgic in the capacity of turning to the material world. In short, we encounter a hierarchical system of thinking principles similar to that of Neoplatonism. Interestingly, Porphyry reports that some scholars accused Plotinus of plagiarizing Numenius. In the light of such antecedents, compare the Neoplatonic theory that Nous’ ordered thoughts delineate the patterns of reality: The contemplation must be the same as the contemplated, and Intellect the same as the intelligible; and if not the same, there will not be truth; for someone who would possess real-​beings will possess an impression different from the real-​beings, which is not truth . . . therefore, in this way the Intellect and the intelligible are one, and real-​ being and the first reality, and the first Intellect that has the real beings, or better, it is the same as the real beings. (Plotinus, Enneads V.3.5.23–​29)

Nevertheless, for Plotinus, the identity of Nous with the Forms suggested a composite whole that contains coexistent distinct entities: Nous and the thoughts/​Forms. What sustains them all must be a pure, undifferentiated unity. By generalizing this argument, the Neoplatonists concluded that everything exists by being “more-​or-​less” a unity, with the One being absolute. This constructs the basic Neoplatonic schema in an “ascending” direction, that is, from the least unified to the most unified: Nature organized by forms in matter; Psychē and the world-​soul; Nous with the Forms; the One. Having arrived at the terminus of their journey to unity, the Neoplatonists faced the problem of how can absolute simplicity be described? A  thing is usually defined by differentiating it from others within a more general class or by assigning it characteristic properties. But the One is absolutely unique (Gerson 1994, 11–​17), and more fundamental than anything that could define it. The core of science lies beyond any scientific description. Arguably this became the most controversial aspect of Neoplatonism. In the 19th and 20th centuries, English philosophers often condemned it as the fall of Greek thought into mystical nonsense. We can refer some of the problem to the philosophical topic

854   Late Antique and Early Byzantine Science of nondiscursive and nonpropositional thought. However, such a cerebral approach would leave out the ways by which Neoplatonists attended to the One with personal experience and emotion. The One is the object of the philosopher’s desire (erōs), truth (alētheia), faith (pistis) (the three in Porphyry and Proclus), and hope (elpis) (in Porphyry): Four elements must be kept fast most of all about God—​faith, truth, yearning (erōs), hope. We must have faith so that the only salvation is the reversion to God, and having faith, we must with all our capacity earnestly pursue to know the truth about Him. And in knowing this, we must yearn for what we know of Him. For when we yearn for Him we nourish the soul on good hopes throughout life, for it is by good hopes that good men hold themselves above the superficial ones. (Porphyry, Letter to Marcella 24.5–​11)

For Plotinus, erōs is not simply love for a dear person, but rather an intense yearning for what will fulfill our sense of lack. Having “descended” into body, our particular psychē desires to complete herself again. Borrowing from Plato’s Symposium, Phaedrus, and from Aristotle on appetite, Plotinus evoked the many kinds of desire that reflect yearning on the many levels of being. At the physical level, desire is often expressed in sex and need for procreation. At the intellectual level, desire is directed at the “intelligible Beauty” as an aspect of the One, where our psychē can “behold” (theōria) its source (reversion of the soul, e.g., Enneads IV.8.4). Desirous love drives the philosopher’s motivation for the One. The act of unification was called indeed “mystical.” It is open to personal experience (Porphyry, Life of Plotinus 23), not to learning from books (Lloyd 1990, 126). The Neoplatonists resorted to the language of the traditional Greek religious festivals, the “mysteries,” because these provided a familiar means of describing the indescribable. Still, they distinguished at least two ways of approaching the “ineffable” One, which had already been cited in Alcinous’ Handbook of Platonism (10.4–​6): the path of analogy, and the path of negation. The path of analogy tells us what the One is like, by comparing it to known affirmative qualities: for example, the One is “beautiful,” the “most-​beautiful,” “beauty itself.” Another compelling analogy is the numerical (Plotinus, Enneads V.5.5; Proclus, Elements of Theology prop. 21; and a precedent in Eudorus, the 1st-​century bce Pythagorizing Platonist). The One relates to the universe like the “monad,” number one, which yields the multitude of other numbers from itself, while keeping itself undivided. Nonetheless, the most famous analogy was the One as the sun: How did things come to be, and what are we to think of those about the One, while itself remains as it is? It is a surrounding radiation from It, while It remains unchanged, just like the bright light of the sun, which, so to speak, revolves around it and emanates perpetually from it, while it remains unchanged . . . produced like the image of archetypes; as fire produces heat from itself; as snow does not keep cold only to itself. (Plotinus, Enneads V.1.6.27–​36)

Plotinus and Neoplatonism    855 Like the radiating sunlight, the One extends without diminishing itself. It “illuminates” everything else (the universe) without being affected by them. Darkness is the absence of light: by analogy, disorder and all sorts of bad things do not exist independently, but as absence of light, “privation” of unity. Each thing receives the appropriate degree of light, thus accounting for the variety of order and disorder, good and bad, in the world. Best of all, the analogical way reminds us that, although the One itself is not known, it can be inferred from its knowable effects. As Proclus observed, inquirers do not address the One itself, but rather the “one” projected in each principle of reality (Proclus, Commentary on Plato’s Parmenides 54.11–​15 K.). So we can know about it via philosophy and science. On the other hand, the path of negation calls attention to the stark truth that the One is not like anything we know. So, each time we try to approach it with something known, we need to take this away (abstract, subtract), add a negative prefix, or negate the statement. The Neoplatonists deployed a host of negative terms about the One. It is “unknown” (agnōston), “ineffable” (arrhēton), “unlimited” (apeiron), “imparticipable” (amethekton), “not to be entered” sanctum (adyton), “negated” (apophatikon), and many more. The negative way appealed both to followers of faith and of reason: to the former, because of its freedom from definitions; to the latter, through its resemblance to Skepticism. For romantics, the sublime cannot be captured by word, thought, or art. For mystics, the apophatic way to God is superior to the positive articulations elaborated by theologians. Later Neoplatonists distinguished a superior faith guided by reason but transcending it appropriately for that which their philosophy inferred to be “incomprehensible” (akatalēpton) (e.g., Proclus, Elements of Theology prop. 93.10). But negation is one of our conceptions (Proclus, Commentary on Plato’s Parmenides 70.4–​9 K.). We cannot just keep silent in word and thought about it, because this would mean that silence applies to the One. The One lies “beyond activity, silence and stillness” (Proclus, Commentary on Plato’s Parmenides 1171.1–​15). Damascius wrote an entire treatise titled Doubts and Solutions of First Principles, mostly against Proclus’ conciliation of unity with knowledge. He used Skeptical-​style arguments to reinforce that we remain in “hyper-​ignorance” (hyperagnōsia) about the fully transcendent. Careful consideration of what is the One raised many philosophical problems. An important question was how can the One be the cause of other things, the universe, when it is absolutely self-​contained? Plotinus likened the One’s causal action to that of light emanating from an unceasing source (see above). Still, for Plotinus, the absolute One must stay distinct from the imparting of oneness, or henad, that characterizes a Form because the latter belongs to substance (Gerson 1994, 230 n. 20). To account for these different ways of thinking about the One, Iamblichus proposed two Ones:  the fully transcendent (compare Damascius above), and the causal that relates to the universe. Proclus rejected this separation and worked on an approach that drew on theories of being, causation, and knowledge, and the logic about attributes (for developments see Lloyd 1990, 76–​97; Siorvanes 1996, 71–​86). He applied Neoplatonic

856   Late Antique and Early Byzantine Science synthesis to Plato’s conception of form in itself, and Aristotle’s immanent in a thing. A  principle is self-​contained but “superabundant.” It is the “first,” which relates to things as an archetype does to the distributed members of its class (Proclus, Elements of Theology prop. 21, 123). Let us attempt a modern illustration. A prototype product in itself stays “exempt” from, and “prior to,” general distribution to the marketplace. From another perspective, the prototype is the first that serves as a model for the manufacture of the many units, as they are often called, which will be distributed to market. In Neoplatonic Greek, each “unit” or “an one” (henas) is the measure of unity that sustains the essence of the corresponding being (Proclus, Elements of Theology prop. 117, 136, 137). Both a candle and the sun are defined by radiating light, but candlelight differs from sunlight. Another important problem concerned the One’s opposite terminus. What is the total absence of unity? Platonists had faced a similar question when they tried to interpret Plato’s hints in the Timaeus (52–​53) that chaotic qualities existed before Nous’ action put them into determined order. Plato said that they were contained in a “receptacle.” Aristotle thought it was equivalent to his notion of substrate “matter,” and many post-​ Aristotelian Platonists adopted it. But this left the challenging question, where does disorder originate? Platonists already had a concept of nondetermination, which they identified with “nonbeing,” and more generally with the opposite of limit (peras): unlimitedness (apeiria). Some middle Platonists, especially Plutarch of Chaeronea (ca 80–​ 120 ce), contended that material disorder was caused by a principle of movement that is separate from the principle of ordered determination. Neoplatonists derided Plutarch’s strong dualism. Other Platonists (e.g., Alcinous, Numenius) asserted that the world is put in order in conjunction with indefinite diversity as a principle. Did Plotinus wish to integrate the two different views on matter: As absence of definition? As the substrate of the universe? Controversially, Plotinus identified corporeal matter with “primal” “evil itself ” (Enneads I.8), which echoed dualist Platonism. His argument was that since the unqualified One is the same as the Platonic principal Good, its opposite must be unqualified bad: evil. Yet he had to admit that since his entire system emanates from the One, the Good must have led to bad, as absence, and he attacked those (the Gnostics, middle Platonists) who believed the world was created by an evil agent (Plotinus, Enneads II.9). Other Neoplatonists vigorously disputed Plotinus’ solution. Proclus made a wry joke of the notion of absolute evil: it would have to be “beyond even the total lack of existence . . . further than the nothingness of non-​existence” (Proclus, Commentary on Plato’s Timaeus 1.374.14–​17). Instead, he linked universal Matter to the One’s power to transcend definition: Matter proceeds from the One and the Unlimited, which is prior to Being. . . . For this reason, matter is to a degree good and infinite, as well as the most illegible and formless, because they (the One and Unlimited) exist prior to the Forms and their manifestation. (Proclus, Commentary on Plato’s Timaeus 1.384.27–​385.16)

Plotinus and Neoplatonism    857

3.  Unfolding the Levels of Being and Knowledge Although the Neoplatonic system centered on the One, it did not collapse into it. When the Neoplatonists spoke of different kinds of being, they conceived it as definition in different degrees of coherence. Because things are “more or less” unified, the Neoplatonic view of “one and many” supported the emergence of identity in the richest variety of “more or less” degree. So, the Neoplatonic hierarchy is famous, not only for the One but also for the “unfolded” many levels of being. For example, the hypostaseis of Nous and Psychē (Plotinus, Enneads V.1, etc.) were analyzed by later Neoplatonists into essence (ousia), power (dynamis) and activity (energeia). These distinctions were devised by recasting Aristotle’s concepts of substance in actuality and potentiality within a Platonic framework. By this, they attempted to elucidate Plotinus’ response to the question, How could the abundance of different things derive from the One? He compared it to what living beings do. When they reach maturity, their full substance, they multiply themselves. Their activity can be distinguished into two: (a) activity that is “of the essence,” (b) activity that extends “from the essence.” As cited in the Ennead V.1.6 earlier, the sun radiates heat, and similarly, snow gives off cold. Substances are not “fixed in sterility and isolation” (Proclus, Elements of Theology prop. 23). From this perspective, they “proceed” in a productive manner, so we can say that they have “potency.” However, their products count as different things. To maintain their original identity, they must keep in contact with their cause. So, they “revert” to the “remaining,” that is, essence beheld in the perspective as that which is defined, “limited”: But how does that (the Intellect) come into being from that which remains? In each thing, there is one activity (energeia) that belongs to essence, and there is another activity that extends from it, and the one which belongs to the essence is the activity that defines each thing, but the other derives from it, and being dependent in every way by necessity must be different from it. Just like in fire, there is a heat which is the fulfillment of fire’s essence, and another which comes into being from that heat which is native (symphyton: Aristotle’s term, e.g., Generation of Animals 5.4, 784b7) to the essence of fire as it remains. So it is also “over there” (i.e. the domain of principles) . . . from whose perfection and innate activity is generated an activity which acquires substantiation (hypostasis), which comes from a great power (dynameōs), greatest of all, and arrives into being (einai) and essence (ousian). . . . And if the product is all things, but the One (to hen) is prior to all things, and does not stand equal to all things, in this way too, it must be “beyond being” (epekeina tēs ousias: a loaded phrase in Plato Republic 6, 509b9) . . . Nous is identically the same as Being . . . Nous has itself as its object of thinking. . . . But here is Nous with its objects and the same and one with them; and here is the knowledge (epistēmē) of objects without their matter (see also Aristotle, De anima 3.4, 430a2–​5; 3.7, 431b17–​19). (The

858   Late Antique and Early Byzantine Science quote from Plotinus, Enneads V.4.2.26–​49; for further info see O’Meara 1993, chap. 6; Gerson 1994, 23–​36)

How are the hypostaseis derived? The One’s power is exuberant, “unlimited,” but in a secondary sense it means it is not determined. To activate its definition, it reflects on the One (e.g., Plotinus, Enneads V.1.7.4–​12), holding it as that which offers “limit.” Thus the One’s activity that extends from itself crystalizes as Nous, which Plotinus identified with pure Being. Each level of being thus “proceeds” as an offspring of its antecedent, while it is reflecting, “reverting” on the parent that defines it. However, each “proceeding” level becomes successively weaker in its connection with the first principle. Psychē emerges from Nous, but particular psychēs act by turning, “falling” into the world, into particular things, bodies in matter. They lend them movement, not random but defined, because psychē can “imitate” nous. The world-​soul creates by providing the “law” and “providence” of the corporeal world. At the level of Physis (nature), the transient “phenomena” still have a measure of definition because they abide within the glow of the One’s Nous. So, from the perspective of judging what is defined by whom, a material body does not, and cannot, contain a psychē, but instead, material things dwell “in” their defining principles (further, O’Meara 1993, chap. 2).

4.  Soul and the Levels of Education With this kind of approach the Neoplatonists accommodated the Aristotelian and Platonic philosophies, usually by placing them on different levels. Roughly speaking, Aristotle can be true when things are known by sense-​perception and discursive reasoning, and addressed by ordinary language. Plato prevails when things are conceived in their causes and principles. Still, the “harmonization” was continuously debated. Should the Aristotelian perspective hold sway over worldly aspects as a matter of fact or convention? Or as a subordinate representative of the Platonic reality? To a Neoplatonist, we come to know the many levels with our personal psychē. With the rational function of our human psychē we can devise concepts, with the nonrational we activate our senses and instincts. In its imagination, psychē can bring together images from sense-​perception, from reasoning, and from intuition. With “discursive reasoning” we assess different pieces of information, arguments, theories, and can arrive at an understanding (logos), while with intellection (noēsis) we can grasp a concept as a “whole.” At the level of unity, we lose the capacity of asserting this or that, and thinking becomes not only nondiscursive but also nonpropositional (see earlier, section 2 “Conceiving of the One”). In Plotinus’ famous, moving words, at “the end of the journey” our psychē is set free in a “flight of the alone to the Alone” (Plotinus, Enneads VI.9.11.45–​46, from Plato, Republic 7, 532e3; and Enneads VI.9.11.51).

Plotinus and Neoplatonism    859 For Plotinus, a part of human psychē must remain “undescended” at the “higher” level where it can communicate with the Forms. For Iamblichus and later Neoplatonists, the psychē cannot be split like this but “descends” whole in the respective body and matter. To “ascend” we need the right education and mentoring, but rely on the transcendent element in each soul. The Iamblichean system of education followed the Neoplatonic theory of a soul’s journey. Appropriately, the curriculum consisted of “degrees.” The students prepared with Porphyry’s Introduction and Aristotle’s works on logic and language. They honed their ethical, political virtue through Aristotle’s books, Stoic manuals, and collections of exhortations. Next, they looked at Aristotle’s physical treatises, which included Aristotle’s work On the Psychē. After the mathematics of arithmetic, geometry, music (harmonics), and astronomy (the four became known in the medieval West as the “quadrivium”), they moved to the “science” or “theology” of Aristotle’s Metaphysics, as a pointer to Plato. They studied 12 of Plato’s Dialogues, which were selected thematically, not chronologically, with the aim of elevating the philosopher’s soul. On the Plato course, students first gained a better awareness of self (Alcibiades A) and place in civic life (the Gorgias as standard, and perhaps in a more flexible curriculum topics from the Republic). Then, they were meant to be purified (Phaedo), to prepare for the levels of contemplation (theōria) (Cratylus with Theaetetus, Sophist with Statesman, Phaedrus with Symposium), and an appreciation of the Good (Philebus). Intellectual knowledge culminated in an understanding of the world’s “physics” (Timaeus) and of Platonic “theology” (Parmenides). For revealed knowledge, students were inducted into the allegorical reading of works (e.g., Homer, Orphics, Chaldaean Oracles) about the higher life.

5.  Physics, Astronomy, Space, and Time Did the preoccupation with the One mean that Neoplatonists had no interest in nature (physis)? For a long time in modern scholarship this has been assumed to be the case. Recent research has shown that they did value physical matters. Similarly, O’Meara (2003) has shown how Neoplatonism’s concern for the world of politics had been overlooked. Plotinus discussed specific topics rather than an account of nature. He drew selectively from Aristotle and Plato, combined with a complex reaction to the Stoics. For Plato, the world-​soul supplies a rational, unified principle of movement to the corporeal cosmos, otherwise natural things would only be ruled by blind necessity. For Aristotle, on the other hand, things change by their own “natural” motion. On earth, the lighter elements, fire and air, travel naturally upward, while the heavier ones, water and earth, gravitate downward. The celestial bodies move naturally in a circular way because of their own element, aether. For the Stoics, the physical world is imbued with reason (logos)

860   Late Antique and Early Byzantine Science due to the rational divine principle that inheres in it. Fire is the world’s basic substance, out of which emerges the common four elements. Within a Neoplatonic system, Physis is a downward projected activity of Psychē as a principle. Nature organizes the indefinite matter by being immanent in it and acts with the principle of necessity, weakly directed by reason. It encompasses the lowest level of being, where things are “particular,” dispersed into “dimension” in bodies. While all corporeal things have physical properties, of these some are living (have some particular psychē) but many others are not. We speak of “natural” also of things that do not (have psychē), such as rocks, other minerals (metalla:  orig., quarried), dead bodies and simple bodies. Furthermore all body has a nature, including the material of artifacts such as that of a statue. . . . But not all body has a psychē. Therefore physis would not be the same as psychē. (Simplicius, Commentary on Aristotle's Physics 9, 286.30–​34)

Did the post-​Plotinian doctrine that the soul descends whole into matter spur the study of nature? In later Neoplatonism, the study of the natural world was tied closely to the study of the divine. In the Iamblichean curriculum, the two final readings of Plato’s Dialogues were those of the Timaeus and the Parmenides, the latter interpreted as an account of the paradigms of the cosmos. For Proclus, studying physis can combine our opinions derived from sense-​perception, with scientific knowledge, leading our soul to “revert” toward the domain of Platonic reality and ultimately to God. Plotinus’ views on the cosmos are encapsulated in Ennead II. Most of the Ennead II.1, however, is taken up by arguments set to prove that the world exists in perpetuity, as opposed to being generated and destroyed in cycles, as held by Stoics. His lengthy rebuttal offers a measure of the impact of Stoicism on post-​Aristotelian thought, particularly on Platonists who appropriated Stoic ideas on matters ethical and physical. As a result, his response to Stoic influence on problems of physics is complex. In arguing in favor of an everlasting cosmos, Plotinus differentiated between the individual physical things, which perish, from the forms that define their species, which maintain their identity permanently. From antiquity until the early modern period, thinkers believed in fixed species, which allowed scientific knowledge of the natural world. The concept of changing species, made famous by Darwin’s theory of evolution, marked a revolution in scientific thinking. Plotinus’ choice of terms carefully distinguished what does not change but exists within time, the everlasting (aei) or perpetual (aidion), from that which is altogether atemporal or eternal (aiōnion). The celestial bodies merited their own explanation, because according to ancient observation and theory, they are everlasting, not only as a species but also each individually. Since bodies disintegrate, how do the stars and planets last (Plotinus, Enneads II.1.2)? Plotinus rejected Aristotle’s solution of a special element, aether. He preferred Plato, who had said that their movement is due to an imperishable psychē. Applying this reasoning to the celestial bodies solved at least two problems at once: What causes and sustains their motion? Why do they move consistently in their orbits?

Plotinus and Neoplatonism    861 Plotinus thought each celestial body must be moved, not by some external force that may come and go, but by its own self-​moving agent. As we have seen, psychē fulfilled this requirement. Bringing theory and observation together, this meant that each celestial psychē moves in a well-​defined way, its astronomically observed orbit, because it exercises to the full its rational capacity of “turning” to Nous. Although astronomy is occupied with phenomena, it is a science that shows the rational workings of the cosmos. How do the celestial bodies keep themselves in perpetuity? To respond to the problem, Plotinus revisited the body and soul relation. A celestial body must match its psychē in perfection, and therefore it must be everlasting, too. Celestial bodies must be made from matter in a special condition that does not perish. Utilizing Platonic sources, Plotinus, and later Proclus, proposed fire of a pure, energetic kind. This remarkable conclusion was an application of their philosophy of being to the four-​element theory. It was a not a simple solution, because fire alone could not account for all the physical properties of the celestial bodies. Plotinus and Proclus concluded, in varying ways, that the other three elements must also be present, but not in the gross sense we are familiar with down on earth. Each element contributes something necessary yet in a refined state. Fire provides visibility; the element of earth solidity and opacity (in occultations and eclipses); air adds volume and lightens the mass; while the element of water maintains cohesion. How do the celestial bodies move circularly? To answer this question, Plotinus combined diverse arguments that addressed the different levels of the celestial entity. “So, its movement will be a mixture of body-​movement and soul-​movement” (Enneads II.2.1.17–​18). The celestial moving agent moves circularly “because it imitates Intellect” (Enneads II.2.1.1). But if the celestial bodies consist of fire mixed with the other three elements, how do their physical movements of rectilinear up or down convert into a circular orbit? Plotinus thought that the celestial bodies physically incline to move in a straight line but because they run out of space to move into, they curve within the constraints of celestial place (Plotinus, Enneads II.2.1.21–​28). Later Neoplatonists remained unconvinced by Plotinus’ explanation. Instead, they proposed that the celestial modality of the four elements must supply their native unbroken movement. Because of their stability, the celestial bodies are objects worthy of scientific knowledge, training our minds to consider the unobservable realities. At the Athenian school, Neoplatonists engaged in a more systematic account of nature. In astronomy, Proclus speculated that both planets and stars must circulate, not only in their orbits but also around their own axis, and that the planets ought to be surrounded by satellites. Because the Neoplatonists thought the celestial bodies circulated by themselves, they were able to criticize Ptolemy’s elaborate epicyclic circles that were intended to account for the variations in planetary movement. Proclus even suggested that the sun is the center of power, stationed in the middle of a system composed of the planets’ and the four elements (Siorvanes 1996, chap. 5). Not limited to theorizing, the Neoplatonists at Athens and Alexandria conducted practical astronomy—​contrary to modern perceptions that they did not bother. We have their instructions on how to construct instruments, such as the meteoroscope (spherical

862   Late Antique and Early Byzantine Science armillary astrolabe) and the water clock for measuring the sun’s diameter. They also left practical guides on the composition of astronomical ephemerides. They conducted astronomical observations, including of optical binary stars, the tracking of planets, and occultations and conjunctions:  from Athens, of the moon and Venus (18 November 475 ce); from Alexandria, of Mars and Jupiter (1/​2 May 498), moon and Saturn (21/​22 February 503), Jupiter and α Leo (27 September 508), moon and α Tauri (11/​12 March 509), Mars and Jupiter (13 June 509), Venus and Jupiter (21/​22 August 510) (Neugebauer 1975, 1031–​1050). Once the Neoplatonists applied their theories of being to the questions of space and time, they advanced a wealth of new ideas. These included that quantity is primary, space is a three-​dimensional extension more basic than matter, time has its own reality, and that “when” and “where” are siblings. In Aristotelian discussions on nature, time defined when a thing changes, and place where a thing changes (Simplicius, In Phys. 9, 397.7–​12). So, most of the Neoplatonic theories are summarized in the Corollaries on Place and Time in the Commentary on Aristotle’s Physics (CAG vol.9) written by Simplicius. For Plotinus, the primary property of bodies is their quantity, not some quality. He elevated quantity to a form (Plotinus, Enneads II.4.9.5–​10). Matter as pure potentiality lacks such definition, and therefore it must be conceived like “all bodiless nature as altogether without quantity.” He concluded, “place is posterior to matter and bodies, so that bodies need matter before they need place” (Enneads II.4.12.11–​13), yet he admitted that “place is something encompassing, and encompassing body” (IV.3.20.12). In this, he referred to Aristotle’s view of place, who defined it as the boundary of a body, the two-​ dimensional surface that surrounds it. But this was rejected by later Neoplatonists. Mindful of the criticisms of Aristotle’s main theory of place, the Neoplatonists developed two other conceptions, which they extrapolated in outline from Plato and Aristotle. In the Timaeus, Plato had said that the whole cosmos was created in a universal “receptacle.” It was left open to interpretation that the world has place in “room” or extension. Second, in Physics 4.1 (208b8‒14), Aristotle proposed that place has a power that makes possible the natural movements of the elements. This left open the option that place is not a passive thing but enables the organized placing of objects. According to Simplicius, most Platonists and the Stoics believed that place is a three-​ dimensional extension, that is, space. But, since body is itself a three-​dimensional object, does it mean that place is a body, too? Some Neoplatonists, such as Simplicius, thought not, because it would mean that space could exist by itself without objects in it. John Philoponus (6th century) argued that space could exist by itself even if, notionally, it were void of objects to occupy it. Proclus (5th century), on the other hand, equated three-​dimensional space with a massless body. On the cosmic scale, universal space consists of the most refined kind of light, which is invisible because it contains no opaque element, unlike the material of the celestial bodies (Siorvanes 1996, chap. 4). However, for Iamblichus (4th century) and Damascius (6th century), place is what maintains things in their order. It is a power that extends from the intelligible level to the physical and keeps the members of the cosmos in their assigned locations, that is, their place.

Plotinus and Neoplatonism    863 When Plotinus defined time as the unceasing movement of psychē from one activity to the next (Enneads III.7.11.43–​45), he followed the tradition of Greek philosophy, including Aristotle, that time measures change. In Platonism, the world-​soul gives rise to cosmic time, which according to Plato’s Timaeus (37d) is the “moving image of eternity.” In this respect, time has a metaphysical root in the atemporal, which Plotinus described as “the life proper to that which exists and is in being, fully in every way without dimension” (Enneads III.7.3.35–​39). According to Simplicius (Commentary on Aristotle’s Physics 9, 790.30–​35), he anticipated the next development. Starting with Iamblichus, Neoplatonists broke with past Greek philosophy and gave time its own substantial reality. By applying their theory of the many levels of being to the definition of time, they distinguished primary from passing time, that is, time in principle from time in the world of phenomena. Primary time is “in essence” stationary, if one were to see it from an Aristotelian perspective. But in more Platonic terms, it is the “monad” and “center” of the rotating, “moving” time (Proclus, Commentary on Plato’s Timaeus 3.26.23–​27.10). Primary time contains paradigmatically what manifests in sequential, “flowing” time. In this way, time can be said to be real, thus refuting Aristotle’s paradox that time does not exist, because the past is gone, the future has not happened, and the present is not a part of time. Primary time “exists by itself ” (Simplicius, Commentary on Aristotle’s Physics 9, 794.21; see pages 793–​796). It has the power to keep events and causal chains in a perfect tense. When these “unfold” in the physical domain, they acquire dimension and become manifest in our familiar time and space.

6. Influence As the principal philosophy of Late Antiquity, Neoplatonism became the way by which Greek philosophy was understood in the subsequent periods. Until the 19th century, when the so-​called Neoplatonism was separated from Plato, both Aristotle and Plato were read through the ancient commentators. The Neoplatonists proved highly influential in four ways. With their philosophy, they inspired thinkers, from the medieval Christian and Muslim scholars, through scientists of the early modern era, to philosophers of the 19th century. With their commentaries and interpretations, they informed the study of both Plato and Aristotle, especially in the medieval and humanist periods. With their sources, they furnished textual material on ancient philosophy, from the earliest pre-​Socratics (e.g., Thales 6th century bce), through the Hellenistic and the Roman times, to the last ancient philosophers themselves (e.g., Simplicius 6th century ce). With their system of education, they set an example of higher learning for the medieval Western and Byzantine intellectuals. The 15th-​century Florentine “Academy” was modeled on the Neoplatonic example, and its leading figures Ficino and Mirandola continued the Neoplatonic reading of Plato’s Dialogues.

864   Late Antique and Early Byzantine Science Plotinus’ Enneads were read in the 4th century by the Cappadocian Christian fathers, and in the Latin-​speaking West by Ambrose and Augustine. In 6th-​century Alexandria, John Philoponus wrote voluminous commentaries on Aristotle, and used his Neoplatonic training both to defend monophysitism and articulate a theology of God’s relation to the created universe. In Orthodoxy, Athenian Neoplatonic concepts and terminology entered Christian doctrine with pseudo-​Dionysius the Areopagite (5th century) and Maximus the Confessor (7th century), who was venerated as saint also by the Catholic Church. The Byzantine upsurge of interest in Aristotle (7th century, etc.) flourished within the uncredited influence of Neoplatonic commentaries and curriculum. Psellus (11th century) and Plethon (15th century) not only acknowledged the Neoplatonic sources but were also strongly attracted to the Hellenic aspect. Toward the end of Byzantium, Plethon presented a plan to the emperor to establish a Platonic state to take over the Christian one and save Greek culture (O’Meara 2003, 203–​204). In 1439 at the Council of Florence, he had met Cosimo de Medici, who then decided to form the “Platonic Academy” of the Italian Renaissance. Muslims encountered Greek philosophy when they entered Syria and Egypt (7th century). In the following three centuries, they translated, paraphrased, and commented on most of the philosophical material, often attributing Neoplatonic works to Aristotle’s authority:  Plotinus’ Enneads IV–​ VI, were labeled as the “Theology of Aristotle.” Neoplatonism influenced Islamic philosophy (Al-​ Farabi, Avicenna) and religion (Ismailism). When the Muslims went to Sicily and Spain, translations of the Arabic books became a source of philosophy for western Europeans. In the West, the Neoplatonic curriculum can be discerned in the Latin 5th-​century Neoplatonist, Martianus Capella, who devised an enduring allegory of the seven liberal arts. Neoplatonic ideas influenced both mystics, notably the author of the Cloud of Unknowing (14th century), and scholastics, particularly through Porphyry and the Neoplatonic commentaries on Aristotle: Boethius (6th century), Eriugena (9th century), King Alfred (9th century), Anselm of Canterbury (11–​12th centuries), Abelard (12th century), Robert Grosseteste (13th century), Albertus Magnus (13th century), and Duns Scotus (13th century). Thomas Aquinas benefited from new translations composed by William of Moerbeke (13th century), bishop of Corinth during the Latin reign in Greece. From his Greek sources, Moerbeke brought to the West most of Aristotle and the Neoplatonists. From the Renaissance to early modern times, Neoplatonic writings were read both in their Platonic and Aristotelian form. Ficino (15th century) translated Plotinus’ Enneads and many Neoplatonic works into Latin. Their impact extended to European art, literature, and landscape theories. Neoplatonism gained a place among the Renaissance humanists, especially the idea that individuals have their own means for salvation. Christian mystics (Eckehart, 14th century) and theologians, such as Nicolas Cusanus (15th century), especially valued the Neoplatonic reflections on the divine. The Neoplatonic light-​metaphysics, mathematics, and astronomy appealed to 16th-​and 17th-​century scientists. As mentioned, Proclus was cited by Copernicus, read in Galileo’s circle, and quoted by Kepler, who regarded the Neoplatonic insights as his guide to knowledge of the cosmos.

Plotinus and Neoplatonism    865 In modern literature, Neoplatonic texts or ideas aroused interest in the Cambridge Platonists, such as Ralph Cudworth and Henry More (17th century), and later, the 18th-​ and 19th-​century Romantics, namely Blake, Coleridge, Shelley, and Yeats. The works of Plotinus, Porphyry, Proclus et al., were made available to the London circle with the English translations of Thomas Taylor. These crossed to the United States, influencing the American Transcendentalists, principally Ralph Waldo Emerson (19th century). In modern philosophy, Neoplatonic conceptions attracted the interest of Leibniz (who distinguished them from Plato), Spinoza, and Idealists in Britain (Berkeley, Bradley, McTaggart), France (Bergson, Brehier), and Germany (Hegel, Schelling). In the mid-​to late-​20th century Britain, Neoplatonism found a defender in London University professor F. C. Copleston. In the 19th century, Hegel and Schelling copiously read Plotinus and Proclus and regarded Neoplatonism “a forward advance of the human mind.” In the same period appeared the first complete editions of Neoplatonic texts, by Cousin (France) and Creuzer (Germany), who were friends of Hegel and Schelling. In science, Hegel and Schelling’s Naturphilosophie proposed that nature has a unity of energy, which unfolds into different forces. In London, the chemical science of Naturphilosophie found a ready convert in Humphry Davy at the Royal Institution, and his friend Samuel Coleridge, who had both literary and scientific interests (and read Plotinus and Proclus). The idea of unity in nature informed Naturphilosophie experimental physicists, such as Oersted and Ritter, who opened research in the interconnectedness of electricity, magnetism, and radiation.

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chapter E2

Greek Math e mat i c s an d Astronomy i n L at e Antiqu i t y Alain Bernard

1. Introduction 1.1 General Perspective The term “Late Antiquity” is mainly due to the ground-​breaking work of Peter Brown (1971) and H. I. Marrou (1996) and was meant to criticize, or at least nuance, the traditional view of the period as one of decline and dramatic replacement of the classical political structures and culture of the polytheist Roman Empire by the structures emerging from the Christian empire founded by Constantine. The “multiculturalist” view of Brown and other scholars has now become mainstream and aims at representing the period first and foremost as one of intensive innovation, transformation, and change. These changes consist, on the one hand, of a process of appropriation and assimilation within a literate and educated milieu that for decades shared the same cultural references and worldviews, in spite of their doctrinal and philosophical differences. On the other hand, they also consist of a process of fierce cultural and doctrinal competition between various doctrinal, philosophical, and religious allegiances. The most dramatic outcome was the (almost) complete disappearance, or at least delegitimation, of some of the protagonists, the most famous example being the definitive condemnation of Greek philosophy and traditional religion under Justinian (which did not entirely shut down Platonist teaching, especially in Alexandria where it coexisted with Christian doctrines: see Gerson 2010, 601–​602). From this point of view, the period was one of explicit competition and fighting among Jews, Christians, and late polytheists (pagans), sometimes writing in various languages, often following different doctrines

870   Late Antique and Early Byzantine Science and worldviews, and above all taking different classical texts as their main references. Inglebert (2001) takes several suggestive examples (among them geography and cosmography, which have some relation to mathematics and astronomy) where this phenomenon could be observed from the 2nd to the 6th centuries: the variety of positions and cultural references, as well as the greater or lesser intensity of cultural conflicts are obvious from the wide range of evidence discussed. The underlying historiographical debate has its counterpart in the long-​lasting debates related to late mathematical productions, the idea of a decadent period being widespread and almost common sense to many historians. In this respect, Reviel Netz’s recent introduction (1998) of the notion of “deuteronomic texts” to characterize late mathematical texts as always second to others (like, typically, in commentaries), has raised debates to which I have contributed (Bernard 2003a; Chemla 1999), and I will here deepen my position: not only should we be skeptical about viewing late mathematical or astronomical productions as untalented and “decadent” derivatives of previous knowledge, but also we should try to capture—​as Netz proposed to do—​what is new and original in them. This originality, as I understand it, has to do with the consistent attempt to consolidate mathematical and astronomical practice as a legitimate part of literate and/​or philosophical paideia, therefore changing this practice itself in a significant and influential way (Bernard 2003a, 162–​170). Choosing as chronological limits the end of the 3rd century ce (Pappus and Iamblichus) and the 6th century ce (commentaries by later Platonists like Eutocius, Simplicius, or Philoponus), we discuss a fairly diverse range of mathematical and astronomical productions, which goes beyond the perspectives and styles of mathematical writing developed within Platonist circles. Given the perspective proposed here as a general background, Latin productions in mathematics and astronomy in the same period would in principle belong to the subject, and enlarge the perspective offered here on a very limited set of works written only in Greek, but including them would go well beyond the reasonable scope of this chapter.

1.2 Five Main Characteristics of the Period Taking my point of departure from some key ideas developed by Averil Cameron (2006, 12–​19) or Serafina Cuomo (2000 and 2001) in their apprehension of the complex evolution of education and culture in the same period, I propose to defend the following points, in conscious analogy to the insights provided by the general history of this period (sec. 1.1): (a) First, and parallel to the contemporary fight between competing models of intellectual and religious life and training, the period should be seen as one of (sometimes intense) cultural competition and emulation between various justifications of mathematics and astronomy, in terms of cultural and educational value, even within polytheist circles. It is marked, therefore, by conscious and visible

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attempts to build consistent arguments representing a particular kind of mathematical knowledge, both in terms of its nature and acquisition, as a matter of cultural choice against alternative possibilities. (b) Second, these cultural choices were furthermore justified in the terms of wider domains of knowledge and intellectual activities. Among the domains concerned were astronomy and astrology, mechanics and architecture, philosophy and religious wisdom (see Cuomo 2000, pt. 1, who has a more extensive and different discussion). The main intellectual techniques throughout all these domains were rhetorical practice and training, as well as exegetical techniques. (c) Third, in tight connection to the previous features, the period also displays a deep movement to justify and over-​valorize traditional knowledge, which is taken as an almost unavoidable reference point, very often in relation to key figures of heroes or icons of knowledge. This phenomenon already appears in the Imperial period but often took quasi-​religious overtones in the late antique period. Thus Proclus turned Euclid into an early disciple of Plato, and Theon of Alexandria, or later epigones like Hypatia or Synesius, turned Hipparchus and Ptolemy into (ethical) models for the astronomical pursuit of knowledge. Beyond this valorization of past icons of knowledge, in later developments and particularly with Athenian Platonists like Proclus or Marinus of Neapolis, earlier philosophers soon became the equivalent of holy men (Fowden 1982), like Iamblichus or Syrianus were for Proclus, or like Proclus was for Marinus. This tendency to sanctify the past had important consequences, which parallels the Christian transformation of historiography (Brown 2008, 632–​638; Inglebert 2001, pt. II): namely the development of a history of science and philosophy in terms that gave a significant (if not essential) place to the figures of the past (O’Meara 1989, 119–​128). (d) Fourth, and just as late antique writers, theologians, or philosophers widely innovated in terms of styles of writing, expression, and intellectual techniques, so also mathematics and astronomy in Late Antiquity followed a fairly wide range of stylistic patterns, many of them inherited from the Imperial period, and that must be in turn related to various aims and forms of reasoning. If the Hellenistic period seems dominated by the model of demonstrative geometry (cf. Acerbi’s, chap. C3, and Bowen’s final conclusions in chap. C4, this volume), late antique productions must be situated in the wake of the rich palette of styles afforded by the early Greco-​Roman authors like Ptolemy, Nicomachus, or Hero, corresponding to the “cultural models” previously mentioned. (e) Fifth, the diversity of productions in this period should not be judged in principle only against the variety of better known productions like those of Pappus, Theon, Diophantus, or Proclus, which all have in common that they underwent a process of textual transmission with reliable attribution. We must also take into account corpora that are less known or have a problematic identity, like the pseudo-​ Heronian metrological corpus, the collections of anonymous scholia that can be traced back to our period (not an easy task, in general), school material (tablets, ostraka, papyri) with mathematical contents, astronomical and/​or mechanical

872   Late Antique and Early Byzantine Science instruments (astrolabes, sundials, etc.), calendars, architectural monuments, or the like. Cuomo’s synthesis (2001, pt. 7) proposes a general view of this kind of evidence, and Acerbi in this volume (chap. C3, sec. 7) touches on the role that late antique scholiasts and “editors”—​among others—​took in the transmission and canonization of the ancient corpus. I will not go into the details of these difficult questions but will indicate their importance for understanding the period.

1.3 Structure of the Chapter In accordance with the various points emphasized above, section 2 deals with some of the competing models available for the cultural legitimation of mathematical practice in Late Antiquity. Section 3 delves into the contents by first proposing a classification of the better known texts according to the variety of erudite activities that gave rise to the various genres and styles found in late productions. Section 4 returns to the notion of a “decadent” versus “transitional and multicultural” period and concludes with the relative originality of mathematical and astronomical productions, as well as their influence on later developments.

2.  The Competing Models for the Cultural Legitimation of Mathematics 2.1 Plausible Contexts Although we know very little of the precise social status of Hellenistic mathematicians or astronomers, like Apollonius, Hipparchus, or Archimedes, it seems that many of them could confidently identify themselves as belonging to a group of competent researchers in a delimited field of knowledge, with its own practice, traditions, and (mostly demonstrative) style, with a sense of legitimacy that manifests in their epistolary prefaces (Acerbi, chap. C3, sec. 2, this volume; Vitrac 2008b, pt. III) or through Hipparchus’ criticism of Aratus’ phenomena. As suggested in this volume by Bowen when discussing the latter, the adoption of a deductive “mathematical” style for treatises later known as belonging to the corpus of “Little Astronomy” (see the list in Bowen, chap. C4, sec. 6, this volume), might have contributed to defining a sense of legitimacy for their authors and readers. In Late Antiquity, by contrast, it seems that experts in mathematics or astronomy obviously had to defend their cultural status and activity in (often contentious) terms that would be recognizable to their contemporaries, as Pappus of Alexandria apparently did with contemporary philosophers (Cuomo 2000, pt. 3). More often than not, late antique “mathematicians” defined themselves as being mathematically skilled in

Greek Mathematics and Astronomy in Late Antiquity   873 close association to other legitimate qualities having high social visibility, like being philosophers, astronomers and astrologers, architects, or land surveyors. In any case, most of them presented themselves as being knowledgeable teachers, writers and/​or exegetes, and, in general, educated persons, preserving a sense of the glorious past of Greek culture embodied by the body of classical works they referred to. These literary and erudite aspects are crucial to the self-​representation of mathematicians, astronomers or philosophers in this period, as we shall see (below, 3.2 and 4.3); following Cuomo’s seminal ideas, I think it is also crucial for the understanding of the nature and function of mathematics in this period. In what follows I quickly review some of these aspects.

2.2 Platonist Cultures, in the Background of Astrology There are, first, the philosophical domains that can be seen as varieties of late Platonism and that were usually related to strong educational programs. The better known, and by far the most studied of them, is the so-​called Neoplatonist domain, beginning with Iamblichus’ revision of the Plotinian and Porphyrian program in the 3rd century ce. The fundamental study on this question remains that by O’Meara (1989, 30–​105), see also Siorvanes chap. E1, sec. 4, this volume. In particular, the numerous commentaries left by Proclus give us a fairly good idea of the importance of mathematical, astronomical/​ astrological knowledge and practice for the philosophical context of late Platonism: of special interest are his commentaries on Plato’s Republic and on the Timaeus, on Euclid’s Elements (iE), to which must be added his Exposition of Astronomical Hypotheses (Hyp.). The two prologues of his commentary to the Elements, iE 3–​84 (Morrow 1992, 3–​69) show the importance given to “whole mathematics” (holē mathematikē) in the first prologue and to geometry in the second, within the framework of late Platonist philosophy and educational system. For these philosophers, Pythagoras, Plato, and Nicomachus were highly important icons—​we know for example through Marinus of Neapolis (Life of Proclus sec. 28) that Proclus believed he was the reincarnation of Nicomachus’ soul. The “divine” Plato was, of course, considered a major authority, as was Euclid, who is considered and presented by Proclus as Plato’s follower (Vitrac 1996). A second strand of Platonism in the same period is the “Ptolemist” one. Following the analysis of Feke (2012) and Feke and Jones (2010), or in this volume Evans, chap. D10 (sections on psychology and epistemology, and on Ptolemy’s Harmonics), Ptolemy’s system should not be regarded only as an intelligent compendium of mathematical models but also as a fairly coherent philosophy, in which mathematical technicalities and competence took a central role. This type of “Platonist empiricism” (Feke and Jones 2010, 197, 209) is more radical and less “dialogical” than the Plotinian one, and directly relies on a highly demanding level of mathematical and astronomical practice.  It is therefore less accessible than the contents of Nicomachus’ introductory works or the kind of material found in Theon of Smyrna. Its cultural references are also different from those in the first tradition: much as Hipparchus is the main figure evoked and upheld

874   Late Antique and Early Byzantine Science in the Almagest as the model of rigorous and inspiring astronomical practice (Bernard 2010c, 508–​ 512), Ptolemy became an icon for later commentators and epigones, from Pappus or Theon to late antique astrologers. I have thus speculated that the few testimonies about Hypatia’s engagement could be mainly interpreted in light of a kind of Ptolemist ethics (2010b, 423–​424). Closely related to these two tendencies is the broader cultural ideal of ancient astrology (Barton 1994). Astrology, like rhetoric, was not considered a narrow and technical field of competence, but rather it provided a cultural training desirable in itself and with its own sense of being able to carry the individual, through enduring and hard work, both to a state of personal accomplishment and to an improved knowledge of the divine thought governing the world (Bernard 2010c). It must be recalled that the Latin term mathematici could designate astrologers, probably because the mathematical competence needed to determine the position of the stars—​even if in practice it was the mere use of convenient tables—​gave this training a particular prestige. Ptolemy nevertheless made a strong and significant distinction between the practice and significance of theoretical astronomy and that of apotelesmatica (on which see Evans, chap. D10, section on astrology). Likewise, Plotinus ridiculed astrology—​unlike his followers, Porphyry, Iamblichus, Proclus, or Olympiodoros, who incorporated astrological lore in their system. So the late antique types of Platonism were distinct and also remained close to the astrological background; and conversely late antique astrologers like—​typically—​Firmicus Maternus highly respected the cultivation of mathematical technicalities involved in astrology (Bernard, 2010c, 514–​516; Cuomo, 2000, 10–​13). Finally, there was much contact between the two traditions, as is attested by Porphyry’s early interest in Ptolemy’s tradition, or the obvious knowledge of technical astronomy in late Neoplatonist circles, as attested by Heliodorus’ observations (EANS 363, and Siorvanes, chap. E1, sec. 5). Ptolemy had also contributed in the 2nd century ce to mathematical geography and cosmography (see Evans, chap. D10, section on geography)—​as a complement to his astrology to some extent. But it seems that what is preserved from late antique geographers, like Marcianus of Heraclea’s Periplous of the Outer Sea (EANS 530–​531), does mainly show that Ptolemy was taken as an authority (the “most divine” Ptolemy, GGM 516, 519, 542) and that Marcianus, so to speak, inverted the sense of Ptolemy’s project of a mathematical geography (Berggren and Jones 2000)—​by actually recalculating terrestrial distances according to Ptolemy’s data (Gautier Dalché 2009, 45–​49; Marcotte 2002, cxx–​cxxii). Marcianus’ work is therefore much closer to ancient chorographies (also mentioned in Ptolemy) than to mathematical geography proper; it nevertheless betrays calculating skills and some understanding of Ptolemy’s project. Pappus is known to have paraphrased Ptolemy’s geography, and Theon mentions in his Great Commentary on the Handy Tables (on which more in sec. 3.1(a)) how Ptolemy’s Geography should be used, but none of these works (so far as the little that is left of Pappus) or remarks shows any interest in the discussion of Ptolemy’s project (Gautier Dalché 2009, 24–​35).

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2.3 The Heronian-​like Background of Architecture, Land Surveying, and Metrology The second set of “cultures” forming a legitimate background for the late antique practice of mathematics is well represented in the epistemological position of Hero of Alexandria on the science of mechanics. Recent research again (Feke 2014; Tybjerg 2003; Vitrac 2009) indicates that Hero seems to have developed a coherent view of mechanics not just as a collection of technical devices with practical utility, but as representing a wider encyclopedic and intellectual system with its own coherence. This system, furthermore, was probably conceived as an alternative view to the (by then already) standard Aristotelian view of the relative independence of theoretical philosophy from practical (“productive”) concerns. The eighth book of Pappus’ so-​called mathematical collection (probably derived from Hero’s Introduction to Mechanics, perhaps the same as the first book of his Mechanika—​on which see Rihll, chap. C6, sec. 2, this volume), as well as the late revival of Hero among 6th-​century ce architects like Anthemius of Tralleis (EANS 90–​91), attest to the strong influence of this trend of “mechanistic” philosophy on late antique developments. For this tradition, Archimedes was certainly an important figure—​though not the same Archimedes as the Platonist figure extolled by Plutarch of Chaeronea (Cuomo 2001, 192–​201) and by later Platonists like Proclus (e.g., iE 63–​64). Likewise, Hero himself had become an important reference, as is attested by the generous attribution of metrological problems to his authorship (Acerbi and Vitrac 2014, 22–​26). Connected to the Heronian interests and mechanico-​mathematical epistemology, as well as its growing fame in Late Antiquity, is the wide question of the background of late antique architecture and mechanics. According to Cuomo’s synthetic overview on architecture in Late Antiquity (Cuomo 2007, 131–​168), both the professional status of late antique architects and their cultural importance only grew in importance in this period, culminating in the design of Hagia Sophia by Anthemius of Tralleis and Isidorus of Miletus in the 6th century ce. Another well-​known group of late antique practitioners attributed great importance both to their professional status and to the body of “practical” and metrological geometry useful for their work, namely the ancient land surveyors, or agrimensores (Chouquer and Favory 2001; Dilke 1992). There is no consensus on the thorny question of whether they directly borrowed from Hero’s treatises, like the Metrica, the Dioptra, or even some part of the pseudo-​Heronian metrological corpus (Acerbi and Vitrac 2014, 519–​533). What seems pretty sure, by contrast, is that Roman land surveyors knew and used some Greek material of this kind. What their treatises interestingly show, on the other hand, is that these technical treatises were only part of a much wider culture, similar to what technical astronomy represented to astrologers. For these traditions, both on the Greek and on the Latin side, Euclid and Archimedes represented important icons.

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2.4 Accountants and Traders Late Antiquity was the time when the administration of the empire, legal matters, and accounting skills gained importance in terms of literature, activity, and probably social status (Cuomo 2000, 26–​30, and 2001, 212–​218). One would expect to see, in this particular corner of the late antique world, some kind of cultural legitimation of calculating skills attached to administration or trade, lore similar to what was found much later in the Middle Ages with Fibonacci, or much earlier in ancient Mesopotamia (on which see Høyrup’s discussion about “supra-​utilitarian” problems, chap. A1a, this volume). Given the fairly close resemblance between some of the problems of Diophantus’ Arithmetica (on which more in sec. 3.3.1) and the problems of these later traditions, one might speculate whether a similar background in antiquity existed (but this is, as stated, mainly speculative: the enigmatic problem 30 concluding the “Greek” fifth book of the Arithmetica hints at such connections, but it might be interpolated).

2.5 Two Major “Cultural Techniques” in the Background: Rhetoric and Exegesis Finally, and on a different level than the previous “trends” of cultural contexts, we must take into account the strong prevalence of two underlying sets of ideals and techniques in this period, namely ancient rhetoric on the one hand, and exegetical activities on the other—​both related to teaching activities in all probability. As far as rhetoric is concerned and following the “revival” of Sophistics in the 2nd century ce, historians have stressed the central importance of rhetorical culture and training for late political and religious developments, both on the Christian and “pagan” sides (Cameron 2008, pt. III). The prevalence of sophistic techniques and values, like “invention” or “imitation,” left deep traces in several mathematical works of Late Antiquity, especially Pappus and Diophantus, who both present some of their works in a manner that seems fairly coherent with contemporary rhetorical ideals (Bernard 2003b; 2015). We must note, however, that rhetorical training was not a special field in Late Antiquity, but the common ground that many cultural models with strong identities would use as a basis or would take into account. Thus, the abovementioned authors did not obviously belong to any defined intellectual or philosophical sect, but they still belonged to the more general sphere of ancient culture with its key techniques and ideals, which were still jealously defined by the well-​to-​do elite. Commentary activities, alike on the “pagan,” Christian, or Jewish sides in this period are ubiquitous and strongly depend on earlier traditions: in this volume, Aristotelian commentaries are treated by Griffin, chap. E3, and medical commentaries by Slaveva-​ Griffin, chap. E6; but, of course, other kinds of exegesis existed, on biblical material for Jewish and Christian scholars, and on mathematical and astronomical treatises. The variety of these commentaries will be treated in more detail in sect. 3.1. Recent research,

Greek Mathematics and Astronomy in Late Antiquity   877 based on Greek material and Arabic translations, has plausibly shown the important role played by Hero of Alexandria in the elaboration of a genre of commentary, at least on Euclid’s Elements (see Acerbi and Vitrac 2014, 26–​39; Vitrac 2004, pt. XI for detailed discussions). As for the commentaries on Ptolemy, by Pappus and Theon, although apparently not the earliest (by his own account, Theon could already rely on a rich tradition) are early representatives of a genre of erudite interest in Ptolemy, whose originality appears when compared to the much more ancient procedure texts (of Mesopotamian origin) or with the material afforded by astronomical papyri in the Greco-​Roman world (Jones 1999). For a wider perspective on Ptolemy’s reception in Late Antiquity, see also Pingree (1994). The important point for us here is that commentators “perceived and construed a symmetrical relationship between their own interests and intentions and those of their authoritative source” (Sluiter 1999, 204), an observation well illustrated by the case of Theon’s attitude to Ptolemy, as we shall see. Thus commentators “all enhance the respectability of the tradition and emphasize its value and continuity” (Sluiter 1999, 204). This point cannot be underestimated: commenting was a matter not just of having an erudite activity, but had to be understood, first and foremost, as representing cultural and ethical values. As far as late Platonist commentators, and in particular Proclus, are concerned, this question is all the more crucial in that commenting was conceived by him as a form of theurgy, and this in turn is related to his Pythagoreanism and therefore his views on mathematical activity (Van den Berg 2001, 127–​138): we shall return to this important point (sec. 4.4). Rhetorical and exegetical practice were both intimately related to late antique education; as far as mathematics and astronomy are concerned, though, one has to remain very cautious with the interpretation of the available evidence, which tells us much more about didactic ideals than real practice (Bernard, Proust, and Ross 2014, 38–​53).

3.  The Stylistic Variety of Mathematical and Astronomical Writing in Late Antiquity Given the general environment, one further and difficult discussion is whether it is reflected in the style and contents of late mathematics and astronomy. Bowen’s cautious preliminary remarks (chap. C4, this volume) on the variety of local situations in antiquity at large (and Late Antiquity in particular), as well as the relative dearth of reliable information outside the transmitted texts, should discourage us from taking the risk of proposing coherent narratives. The remark especially applies in a period of intense cultural competition and conflict like Late Antiquity. Moreover, for a period when authors were obsessed with the justification of their cultural status, it is very risky to take

878   Late Antique and Early Byzantine Science at face value the corresponding rhetorical moves as reflecting reality rather than their discourses and values. On the other hand, I suggest that precisely the “messy” atmosphere of dispute and cultural conflict might explain why so many authors of this period insist on meta-​ mathematical arguments bearing on the nature of their interest and intellectual pursuits, their intended audience or readership, and their sense of legitimacy. This phenomenon is already perceived in the early empire (Cuomo 2001, 192–​211) but becomes even more obvious and intensified in Late Antiquity. Vitrac’s overview on the aims and contents of ancient prefaces to mathematical treatises (2008b) thus makes a difference between Hellenistic material and later productions (see also Acerbi, chap. C3, sec. 2, this volume). The later are open toward a wider readership, with more emphasis on erudition, historiography, pedagogical concerns, and self-​justification than before. In this long-​term process, the era of Hero, Ptolemy, or Nicomachus globally marks an important transition. These remarks lead us to a direction of research of growing importance in the last decades, namely the study of stylistic features of ancient mathematics written in Greek. Traditional to the study of Latin literature—​as far as mathematical sciences in Latin Late Antiquity is concerned (see, e.g., Paniagua’s remarks on Martianus Capella’s quadrivium, sec. 6, chap. E7, this volume)—​this approach is the point of departure of Acerbi’s chap. C3, on Hellenistic mathematics and is meant primarily as a tool for the study of such complex texts as Diophantus’ Arithmetica or his On Polygonal Numbers, or Hero’s Metrica (more on this in sec. 3.3), all belonging to the transitional period mentioned above and characterized by stylistic complexity. The stylistic approach can also be seen as part of a larger set of erudite attempts to adapt to the ancient Greek mathematical and astronomical corpus approaches similar to those adopted for literature at large, or more specifically for medicine and science (Asper and Kanthak 2013). These recent works led to new interpretations, often related to renewed editions and translation of the material. To present and interpret these results in some plausible and clear order, I try to give an idea of the variety of styles and composition of late antique products, by proposing a rough and tentative classification of the kind of intellectual activities and operations that are apparently “behind” the texts we have (for a more general discussion on this issue, see Taub 2013). This approach will serve to relate the function of these various activities to the general environment described in the previous section and to better understand in what late antique productions innovated in a substantial way (sec. 4). I first differentiate between commenting activities that are typical of the period and led to various kinds of mathematical commentaries (sec. 3.1); then making various variations on classical material (sec. 3.2), including making pastiches, collecting problems, editing and rewriting; and finally (sec. 3.3) mixing demonstrative and procedural styles, especially in Diophantus, pseudo-​Hero, and astronomical commentaries. These are all possible points of view on these texts rather than strictly separated categories, so that one and the same text might fit various categories.

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3.1 Styles of Mathematical Commentaries Late antique philosophical commentaries have been the subject of many studies in the history of ancient philosophy, on which see the chapters of Griffin E3 and Siorvanes E1, this volume, or Gerson (2010). But not all late mathematical commentaries follow the strong and explicit Platonist orientation given to them by Iamblichus or by his late followers like Syrianus or Proclus. Each mathematical commentary has its own structure and particularities, as well as its specific relation to the primitive text. Here are some notable examples. (a) The styles of Theon’s various commentaries, namely the so-​called Little and Great Commentaries on the Handy Tables, and the commentary on the Almagest, have been characterized and studied by their modern editors, A. Rome and A. Tihon, as well as compared with what is preserved of Pappus’ commentary on the Almagest (Theon’s probably derives in part from Pappus’). First, Theon’s three commentaries differ from each other because they are not addressed to the same audience and readerships, as his prologues make clear (Bernard 2014, 103–​105, 117–​119). His commentary on Ptolemy’s Handy Tables supplies the reader with examples of calculations, with no pretense of proving their validity; his Great Commentary is of much higher level and consists in a critical comparison between the Handy Tables and the tables found in the Almagest; finally, his commentary on the Almagest itself seems devised not only as a clarification of the contents, when needed, but also and perhaps foremost, as an imitation of Ptolemy’s style and overall project (Bernard 2014, 112–​115). Moreover, the commentary provides its author several opportunities to add long digressions that come close to becoming self-​contained discussions, like the famous discussion on isoperimetric figures (iA 355.3–​379.15 Rome) derived from Zenodorus: here the commentary almost verges on separate treatments that could then stand on their own, as is shown in the complex discussion of Pappus’ Collection, book 5 (Cuomo 2000, chap. 2), or by the late compilation known as the prolegomena to the Almagest (Acerbi, Vitrac, and Vinel, 2010). One also finds interesting digressions on calculating techniques (e.g., iA 469.16–​473.8 for the procedure of calculation of approximate square roots justified in geometrical terms): such calculations were not systematically treated in antiquity, whereas they acquired much importance in the Middle Ages. This kind of commentary, for example, became the source for further developments—​they are found again, for example, in the aforementioned prolegomena to Ptolemy. (b) The structure of Proclus’ commentary on Euclid is sophisticated: it is prefaced and introduced by two long prologues, which partly correspond to the introductory genre; this is obvious for the presentation of Euclid’s Elements in Proclus’ commentary (iE 69–​84), but the first prologue, strongly inspired by Iamblichus, about “general” or “whole” mathematics, and the beginning of the second prologue about geometry, look like either introductions or encomia. In any case, they can hardly be separated from the core of the commentary, which illustrates the theories developed in the prologues (Bernard 2010a). The style of this commentary follows the philosophical

880   Late Antique and Early Byzantine Science commentaries in many respects: presence of a large doxographical material, overemphasis on definitions and preliminary matters, to and fro movement between word-​ for-​word linguistic and “overall” semantic explanations. The conceptual apparatus of late Platonist metaphysics is furthermore as heavily employed here as in Proclus’ other commentaries—​which means that the commentary on Euclid must be understood in this wider context (as shown, for example, in Harari 2008). In particular, one central point discussed by Proclus, in the wake of Syrianus’ commentary to Aristotle’s Metaphysics, is the nature of mathematical entities (a good example of the “conciliatory” argumentation discussed in this volume by Griffin, chap. E3). Another crucial point in Proclus relates to the inclusion of the study of mathematics within the philosophical curriculum (a move going back to Iamblichus, as we have seen): thus the text is truly considered as an introduction to mathematics in the sense in which Proclus conceives it: we shall return to this point in sec. 4.4. (c) Standing somewhere in the middle of the two previous authors are the interesting commentaries by Eutocius of Ascalon on Archimedes (AOO 3), on the Sphere and Cylinder, (translated in Mugler 1972; Netz 2004, 243–​368), on the Measurement of a Circle, on the On Plane Equilibria, and on the first four books of Apollonius (Decorps and Federspiel 2014). Their stylistic features have been closely scrutinized in recent studies (Decorps and Federspiel 2014, xix–​lii; Netz 1999). They deserve full attention, let alone because, as far as Apollonius is concerned, this is a rare testimony, stemming from the commentator himself, about a commentary tightly associated with a new edition of the text and explaining the principles and modus operandi of this erudite work (Decorps and Federspiel 2014, 11.26–​31). On the one hand Eutocius, like Theon, stands close to the classical tradition of commentary leading back to the Hellenistic period, with his emphasis on clarity and his care to confront the various versions of the text he has at his disposal. Like in Theon, his commentary also provides opportunities for long digressions that could stand on their own, the most notable one being his lengthy and erudite comparative discussion of solutions of the Delian problem (AOO 3, 66.3–​ 126.3), and to the solution of the geometrical problem of division contained in SC II.4 (AOO 3, 152.3–​208.6)—​the two compendia are of high interest, especially the second, in which Eutocius, as in his commentary on Apollonius, gives some hints about his quest for the best manuscripts available and on the corrections and clarification he made on them. But Eutocius probably also belongs to the tradition of late Platonist commentators, as a direct follower of Ammonius and a commentator on Aristotle’s categories (Decorps and Federspiel, 2014, ix–​xvii; see also EANS 324–​325). Thus some of the features of Proclus’ commentary are also retrieved in Eutocius, although in an attenuated manner: the allusion to classical discussions among Platonists (e.g., Decorps and Federspiel 2014, 55.13–​58.16 on the “community” of arithmetic and geometry), his care to provide a commentary useful for mathematical practice and understanding, or also the special devotion to his task that is expressed in the foreword of his commentary to Archimedes (AOO 3, 2). (d) Close to Eutocius, the commentaries by Philoponus or Asclepius on Nicomachus (Tarán 1969) have the classical aspect of a commentary apo phonēs (i.e., deriving from

Greek Mathematics and Astronomy in Late Antiquity   881 a lecture by Ammonius), and share with many similar commentaries the characteristic structure of detailed explanations of words, balanced with more general interpretation, which reflect the classical divisions of a commentary. These works show, at least, the importance that the reading of Nicomachus had kept until this late period. On the late commentaries on Nicomachus on general, see the recent discussion by Riedlberger (2013, 84–​88) in his commented edition of Domninus’ works. Finally, these famous late commentaries are only the tip of the iceberg, since in the margins of classics like the Elements, or the Almagest, are found many (sometimes highly) interesting scholia, some of them deriving from well-​known commentaries like Theon’s (Tihon 1987). The interest of such material is that it shows again that reading such treatises and using commentaries were closely related activities that went hand in hand (Bernard 2014, 100–​102). They are also of high importance to understand the long-​ lasting process of transformation of our texts, since the latter eventually favored the progressive integration of scholia to the main texts.

3.2 Other Variations on Classical Texts: “Atticist” Attitudes I take up here the expression used by Acerbi to describe the work of Pappus of Alexandria as a “mathematical Atticist,” and in this sense a kind of very late “Hellenistic” mathematician. I will roughly categorize these attitudes through the kind of typical operations made on those classical texts, with some examples for each category: rearrangement (pastiche, imitation); collecting classical problems; introducing classical texts; prefacing; and editing and revising texts.

3.2.1 Pastiche, Imitation, Amplification A typical pastiche of classical treatises, in this case Apollonius’ Conics, is found in Serenus’ two treatises On the Section of a Cylinder and On the Section of a Cone (cf. Acerbi’s Onomasticon in chap. C3, this volume). The style and the kind of problems defined in those treatises strongly recall and follow Apollonius’ approach but can also be seen as a variation on Euclid’s Elements 11 or on his Optics. The two treatises share four main characteristics: (1) they are written in the demonstrative style; (2) their explicit purposes strongly recall those of Apollonius (see Acerbi, chap. C3, sec. 3, this volume); (3) their general scope and purpose differ from the classical treatises since they are not focused on new results or general methods; and (4) they tend to promote mathematical knowledge, either for its usefulness (SO 96.10–​116.12) or for its own sake—​the cultivation of geometry (SO 2.3–​15). All in all, they look like pastiche, a kind of indirect encomium of classical geometry celebrated through a variation on its style and purpose. The various treatises written by Pappus of Alexandria and later grouped in the so-​ called mathematical collection—​ probably compiled much later than the 4th century (Decorps 2000, 47–​51)—​ afford a rich set of variations on classical material, the purpose of which is sometimes identifiable. One of the most interesting of them is the fifth

882   Late Antique and Early Byzantine Science book, about which Cuomo’s detailed analysis (2000, chap. 2) shows that its material is carefully arranged to reach a readership aware of the related philosophical discussions, but not skilled in elaborated mathematics, and to promote a precise image of Pappus’ mathematical competence. Other kinds of variations abound in Pappus’ various treatises composing the collection, and Cuomo (2000, 174–​186) has proposed a tentative categorization of their various types: “arithmetizations” (on which more below), generalizations, or addition of subcases, all of which would be typical of the work of a scholiast. The last example proposed here of such late antique variations is Iamblichus’ alleged “commentary” on Nicomachus’ Arithmetical Introduction. This is actually not a commentary, in spite of a misleading subscription in the manuscript tradition, as has been confirmed by its recent editor and translator Vinel (2014, 14–​15). Better characterized as an orthodox imitation of Nicomachus, the treatise of Iamblichus is self-​contained and imitates Nicomachus’ approach while recognizing his philosophical authority. The paradox is thus that Iamblichus’ introduction substantially diverges from Nicomachus’ at several places, while claiming to be strictly obedient to his model. This is thus an early testimony of the phenomenon of (late) Platonist orthodoxy and results in a text that is heavily loaded with meta-​mathematical remarks oriented toward the defense of the Nicomachean technē as superior to anything else, especially Euclid’s approach to arithmetic. As signaled above, Theon’s commentary technique only partly follows the usual schema of an explanatory text on various lemmata, although most sections do follow this model. But even those explanations should probably be interpreted in light of a coherent project of “distorted imitation” of Ptolemy, on the hypothesis that the latter is understood as some kind of “commentator” and imitator of the ancients. The question of understanding better Theon’s project and technique is thus intimately related to the understanding of Ptolemy’s own project (Bernard 2014, 112–​115).

3.2.2 Collecting Classical Problems and Lemmata One striking practice of some of the authors already mentioned above (especially Eutocius in his commentary to Archimedes’ Sphere and Cylinder) is to organize part of their discussions through the compilation of various solutions to classical problems, as mentioned by Acerbi in this volume (chap. C3, sec. 5). One of the best known examples, besides Eutocius, is Pappus’ discussion of a series of classical problems in Collection, book 3: the whole discussion is structured around original solutions to the Delian problem (56.22–​68.27), including one that Pappus claims as his own, to a classical problem of geometrical construction of various means and to paradoxical problems of geometry (which is more an exercise in problem setting than in problem solving: see EANS 301, Erukinos). There is a similar exposition in Collection, book 4, in relation to the classical problem of trisection of an angle (270–​288.3) We also have the famous case of the locus problem treated by Euclid and Apollonius and presented in Collection, book 7 (pp. 120–​123 Jones). Each of these discussions has its own complexity and deserves a separate treatment: I emphasize here some common features. First, they betray a marked interest in

Greek Mathematics and Astronomy in Late Antiquity   883 the organization of knowledge and methods through the prism of problems and problem-​solving activities. In my study of Pappus’ Collection, book 3 (Bernard 2003b), I  proposed to relate this practice to contemporary discussions of classical culture through the prism of oratorical challenges (in Philostratus or Eunapius). This practice was also understood by Pappus and his followers according to the long-​lasting debates about the nature of mathematical knowledge, illustrated by the classical opposition between Speusippus and Menaechmus’ opposite views about problems and theorems in mathematical activity (Collection, bk. 3, 30.1–​17; the discussion is found again in a more developed manner in Proclus’ iE, second prologue). As shown by the interesting structure of Collection, book 8, which probably follows a lost work of Hero on mechanics, the emphasis on problem-​solving is also related to the attempt to include mathematics in the larger field of mechanical knowledge and methods, especially problem-​solving methods through mechanical devices (Cuomo 2000, 119–​121). Understanding mathematics through problem-​solving activities thus had a cultural and epistemological value and offered the possibility to reconcile the mathematical, astronomical, and mechanical traditions. Second, this understanding was also a means to promote a certain kind of historiography, as explained in Acerbi’s chapter, in this volume, about the deep and long-​ lasting influence that these late antique views have had on modern historiography. This is well illustrated by Pappus’ discussion of the respective merits of Aristaeus, Euclid, and Apollonius on the locus problem discussed in Collection, book 7, or by Eutocius’ reconstitution of the respective merits of various solutions to the problem set in SC 4. This way of writing about problems can also be seen as a means of self-​ promotion for the above mathematicians, who could claim to be both erudite scholars and able practitioners, the two notions being (or becoming) tightly connected to each other: they stood at the end of a long chain of (allegedly) continuous efforts to treat difficult problems. Again, the remarkable examples signaled above are probably only the tip of the iceberg, in the sense that collecting this particular kind of problems that are geometrical lemmata is a favorite way in which late antique mathematicians developed and amplified the classical material by reading problems into the deductive and problematic sequence of classical treatises. A typical example is found in Collection, book 7, which proposes a general classification of the treatises included in the “treasury of analysis” (analuomenos topos) according to the number of lemmata or possible cases discussed in each of them—​many of them being presented and developed at the end of the book. A late and remarkable example, probably no earlier than the 6th century ce, is given by the transformation of Hypsicles’ treatise (about the comparison between the dodecahedron and icosahedron inscribed in the same sphere) into the 14th book of Euclid’s Elements, at the price of stylistic harmonization involving the insertion of key lemmata (Vitrac and Djebbar 2011, 63–​67). For another example, see also my notice on the “Book of Assumptions” known through the Arabic translation (EANS 197).

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3.2.3 Completing Classical Texts with Preliminary or Complementary Material We have seen (sec. 3.) that the writing of prefaces to mathematical treatises, by the authors themselves and dedicated to contemporary mathematicians, is a practice well attested from the Hellenistic period onward and further developed in the Imperial age, as the examples of Hero, Nicomachus, or Ptolemy show. It flourished in Late Antiquity, as Pappus’ and Theon’s carefully written prefaces illustrate. But instead of letters addressed to contemporary mathematicians and discussing advanced problems, they become pieces of rhetorical prooimia directed at real or fictional contemporaries—​ including potential students—​full of erudite references and meta-​ mathematical arguments. They reflect the competitive atmosphere about culture characteristic of this period, as we have seen. Generally different from prefaces and artificially added to classical material are the introductions written at various (not always identified) periods that are meant to prepare the reader regarding aspects of the introduced work. One typical example is the so-​called Prolegomena to the Almagest, compiled in late Platonist circles around the 6th century ce. The term “introduction” is slippery and can be understood in various ways: (a) Self-​ contained “introductions,” like Iamblichus’ imitation of Nicomachus, perhaps also Domninus’ Encheiridion, which might be better considered a free epitome (Riedlberger 2013, 72–​77), or Proclus’ Hypotyposis, which can be considered a critical and synthetic discussion of Ptolemy’s hypotheses (Segonds 1987). (b) Introductory discussions in the precise and standard sense in which Neoplatonists understood it: such are the end of the second prologue to Proclus’ commentary on Euclid, or the first part of the abovementioned Prolegomena to the Almagest (Acerbi et al. 2010, 76–​77). (c) Occasional pieces of discussion on a precise point, appended to classical treatises like the second edition of Euclid’s Optics, or the introduction to Euclid’s Phenomena (Berggren and Thomas 1996, 8–​18). The second and third categories should probably be understood as pedagogical devices meant to facilitate and prepare for the reading the classics. The first one has to be understood in the larger framework of a philosophical and protreptic program, characteristic of late Neoplatonist schools. But this “protreptic” aspect is not alien to other prefaces that partly have this character, like Diophantus’ preface to his Arithmetica, which also introduced the general method followed in all of his problems (Christianidis 2007). Finally, I alluded to the practice of “complementing” classical texts with erudite “post-​ scripta,” for example, the addition of two books to the Elements around the 6th century ce—​in this case part of book 15 is due to a disciple of Isidorus of Miletus (EANS 444). These addenda implied the partial rewriting of some of the propositions in books

Greek Mathematics and Astronomy in Late Antiquity   885 11 or 13 (addition of lemmata, insertion of alternative proofs). The same can be said about Pappus’ writings, such as his commentary on Elements X, in which late Platonist scholars apparently interfered, or with his Collection that was possibly rearranged in this late environment and which bears traces of “complementary” interpolations.

3.2.4 Transmitting, Editing and Transforming Classical Texts These erudite activities should probably be understood against the background of the “silent” operations performed on classical texts like the works of Euclid, Apollonius, Archimedes, or Ptolemy, like those listed by Acerbi in chap. C3. They can be qualified as “silent” in the sense that are often difficult to date precisely and have no specific authors, even in the case when the provenance of scholia is taken from classical commentaries. The remarkable exception we have to this silence is the case of Eutocius’ explanation of his editorial technique, as far as the first four books of the Conics are concerned (see sec. 3.1 (c)). In other cases, like Theon’s “re-​edition” of the Elements to which he briefly alludes in his commentary to the Almagest, or with Hypatia’s contribution to her fathers’ work, we know that there was such an operation but are unable to identify in detail the editorial interventions, because we do not know the precise material with which these scholars worked. As with Eutocius, who had to face a complex manuscript tradition, Theon’s procedure most probably consisted of checking the multiple versions circulating in his time (Vitrac 2004, 22–​23). Most transformations occurred at various stages of the long-​term process, perhaps begun with the first “annotated re-​editions” of such classics as the Elements begun by Hero of Alexandra in the Imperial age (Vitrac 2004, 24–​27). Important for us here is that this “inventive transmission” process affected the texts, and that the texts formed the basic background of the varied erudite activities listed above (and see sec. 4.3).

3.3 Mixing Demonstrative, Algorithmic, and Procedural Styles One striking feature of the mathematical styles elaborated and developed in the Imperial period, whether in Hero (Metrica), Ptolemy (Almagest), or in Nicomachus (Arithmetical Introduction), is the special (and massive) role given to explicit calculations on given values (i.e., algorithms), more abstract operational thinking (procedures), and the use of numerical tables. By “calculation” we mean here a concatenation of numbers, operations, and their results, expressed without justification; by “procedure” a more abstract concatenation of quantities designated by reference to a diagram or by abstract formulas and operations performed on them: for more details on these notions see Acerbi and Vitrac (2014, 416–​428). Given the dependency of late antique commentators and authors on these traditions, it was inevitable that they would “play” on these various stylistic registers in their own productions. I propose here various examples of the resulting productions and kinds of reasoning.

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3.3.1 Diophantus’ Demonstrative Style Based on Procedures It is not certain that Diophantus of Alexandria, from whom we have a collection of arithmetical problems originally in 13 books, as well as an interesting treatise on polygonal numbers (Acerbi 2011), was active in Late Antiquity. He is known to Theon of Alexandria, as has been again confirmed by the recent discovery of a solution using “diophantine numbers” of a problem discussed in Theon’s commentary to book 11 of Ptolemy’s Almagest (Christianidis and Skoura 2013). Tannery’s traditional dating of him to around the end of the 3rd century ce is not certain at all (Acerbi 2011, 9), but even though he might have lived in an earlier period, his two treatises have a late antique flare (see sec. 4.1). Although he most probably borrowed much of his material from previous traditions of arithmetical problems, he rearranged them in a fairly schematic format in a coherent and highly sophisticated treatise. This implies the use of a method or “way” (hodos, DOO 4.10–​11 and 14.25) for problem-​solving based on a range of ad hoc numbers (similar to our algebraic expressions) exposed in his preface, as well as the use of a general scheme for the solution of each problem (Bernard and Christianidis 2012; Christianidis 2007). The subtlety and depth of the treatise lies in the various tricks and partial methods used for the solution of subgroups of problems, including the use of “simulators,” that is, ad hoc procedures introduced used to construct the solution (Bernard and Christianidis 2012, sec. 3.4). There is still much to explore about the structure and progressiveness of these problems (Bernard 2015, 13). One promising direction of research is the comparison with the theoretical technique and language used by the same Diophantus in his second treatise (Acerbi 2011, 49–​113). The two treatises share in particular a stylistic proximity to the classical, demonstrative style, as well as the systematic use of a procedural language—​although in a different way in each case. In the case of the Arithmetica, the procedures are transformed and understood on the background of calculations implicitly performed on the ad hoc numbers introduced in Diophantus’ preface and that behave like common values of numbers (Christianidis 2015). In other words, Diophantus artfully plays on three intermingled stylistic registers: demonstrative, procedural, and algorithmic. The key problem is to understand how and what role repetition and variation on problems play in this sophisticated arrangement.

3.3.2 Justified Calculations in Hero’s or Ptolemy’s Style Diophantus also uses a kind of demonstrative analysis through the language of “givens,” akin to what is found in Hero’s Metrica or in Ptolemy’s Almagest, that give a means to validate or find calculating procedures (for his particular use of “given” language and theory, see Acerbi and Vitrac 2014, 363–​368). Such a concern for the “validation” of a calculation in geometrical terms permeates Pappus and Theon’s commentaries on the Almagest, especially since the ambition to justify geometrically, which Ptolemy presents only as a desideratum for the establishment of chord tables, is actually generalized by Theon (and probably Pappus before him) to the whole of Ptolemy’s treatise (Bernard 2014, 114–​115). This point is hardly secondary, since the same Theon

Greek Mathematics and Astronomy in Late Antiquity   887 strongly contrasts in his Little Commentary the mere capability to calculate with tables and basic procedures—​precisely the kind of skill that was most useful for contemporary astrologers—​with the more elevated ambition to justify and understand astronomical calculations (Bernard 2014, 117–​119). The interest of the abovementioned problem found in Theon’s commentary is that this method of calculation “from geometrical procedures” is clearly contrasted to another method “through diophantine numbers” (Christianidis and Skoura, 2013).

3.3.3 Following the Nicomachean Philosophical and Heuristic Style Lastly, we return to the attention paid, throughout Late Antiquity, to Nicomachus’ Arithmetical Introduction. As we have seen, this text and its particular style, which mixes up the language of categories for numbers and ratios, with the exposition of “generative” procedures for various kinds of numbers, was an object of high interest, if not reverence, by philosophers such as Iamblichus, Domninus, or late commentators like Ammonius and his followers Asclepius and Philoponus. It is doubtful that the only reason for this was reverence for an early icon. Nicomachus was praised, as early as Iamblichus, because studying his book helped one learn heuristic processes (Vinel 2014, 68.31), thanks in particular to the use of numerical tables (Megremi and Christianidis 2015, and 2016). One might inquire, as Vitrac does in his study of the pseudo-​Heronian corpus (part of which might have been known and reworked in Late Antiquity), whether there existed a similar counterpart, for geometrical thinking, to the kind of didactic apparatus represented by Nicomachus’ work (Acerbi and Vitrac 2014, 533). In the aforementioned collections of problems, unlike in Hero’s Metrica, there is no emphasis on geometrical justification. But one wonders how these kinds of problem, characterized by their schematic solutions and repetitiveness, were used in an educational context.

4.  Conclusions: The Development of Mathematics and Astronomy in Late Antiquity One would be tempted to see the previous discussion about late antique mathematical styles as bearing only on form and function, in accordance to the new social, religious, and intellectual context, and not on mathematical or astronomical contents. In an even more radical sense, well in line with the traditional view of Late Antiquity as a period of unfruitful decadence and fossilization, one could argue that the emphasis on form, function, and “second order” writing is only a sign that very few conceptual or theoretical innovations took place in this period. I conclude this chapter by pointing toward a different picture, in continuing the previous discussion.

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4.1 The Puzzling and (Seemingly) Isolated Case of Diophantus As mentioned, Diophantus does not necessarily belong to the late period. Nevertheless, the tone and orientation of his preface, turned toward the definition of a didactic proj­ect; the partial imitation of the classical demonstrative style on well-​known subjects (like polygonal numbers); the complete adoption of a structure of exposition only through problems (like in the pseudo-​Heronian corpus, albeit with more explanations); the fact that, in theoretical terms, there is little that is really proved in Diophantus’ Arithmetica but much that is subtly shown through the progressive deployment of his solving method: all this has the taste of late antique developments. This shows, at least, we can find a treatise having these features, while being highly innovative and inspiring, which squares badly with an image of decadence.

4.2 Writing Through the Arrangement of Problems and Lemmas . . . Diophantus also shares with authors such as Hero, or late antique scholars like Pappus, a clear concern for mathematical “invention,” probably understood in the technical sense it had in ancient rhetoric: a technique to build new discourses on the basis of ancient and well-​known material. The association between what Acerbi (this volume, ch. C03, sec. 5) calls “the ideology of the heuristic value of analysis” with an exposition of a classical collection of treatises on the subject, is precisely what is typically discussed in Pappus’ Collection, book 7. This, of course, goes very well with exposing knowledge through problem setting or solving. Building and discussing a collection of classical problems or solutions to the latter, and developing collections of lemmas inspired by the classics, not only gave them an occasion to make sense of their history and culture, as we have seen (sec. 3.2.2). The shift from an “architectonic” model of mathematical knowledge to a model in which problems were at the center of the stage is a significant one that gave more centrality to invention. How can we reconcile this with the perception that there were few major conceptual innovations in this period? The key to this apparent paradox lies in an aspect of the ancient tradition rightly mentioned in Acerbi, namely the “predominance of rhetorico-​grammatical curriculum . . . entailing a rigid adherence to a canon of texts.” We must never forget that invention (heurēsis or inventio) is one of the key concepts attached to the ancient rhetorical ideal, and that the latter was in turn inseparable from the preservation and “ossification” of a classical treasury.

4.3  . . . Against the Background of Long-​lasting Traditions I have hinted that, in a period of social and political upheaval, the preservation and continuation of traditional knowledge is an important historical fact per se. The mere

Greek Mathematics and Astronomy in Late Antiquity   889 preservation and partial “ossification” of classical knowledge was perhaps an active response to a time of threats when this classical treasury and its specific value was no longer taken for granted. Correlatively, it means that texts were not copied and transmitted in a passive way. The kind of scholarly activities, of which we have proposed a list, helped maintain a general sense of coherency and continuation, even though this was made at the price of important distortion, as in Theon’s reinterpretation of Ptolemy’s project. But clever distortion is principally the gist of a correct and successful imitation—​as seen in the various examples proposed above (sec. 3.2.1). The case of the long-​lasting study of regular and semiregular polyhedra is interesting in this respect (see Acerbi’s discussion of regular polyhedral in chap. C3, sec. 5). The detailed discussion of them in Pappus’ Collection, books 3 and 5, as well as in the supplementary books 14 and 15 of Euclid, the last of which was compiled in the 6th century ce, shows that these questions were still of interest well into Late Antiquity; the same holds true, of course, for the contemporary attention paid by Eutocius to the understanding and edition of Apollonius’ Conica. Dating the most “original” findings in this very long process of research and scholarly activities is perhaps less interesting than becoming aware of this longue durée and for the underlying “canonization” process (see Acerbi’s preliminary remarks in sec. 3 of chap. C3). In a world structured according to traditions that were competing in the Imperial period, this also produced new conceptions of geometry. A typical case is the development of what could be called “erudite” ancient mechanics in the style of Hero’s mechanics. This explains, for example, that some, such as Pappus or the later Eutocius, could conceive geometry as no more disentangled from mechanical and instrumental concerns. Here the innovation comes through both new ways of writing (through problems, again) and through the legitimate use of mechanics into mathematics, a move that was prepared by earlier scholars like Hero and Ptolemy. The same can be said about the highly particular insertion of mathematical practice into a structured philosophical curriculum, operated by orthodox Neoplatonists following Iamblichus, to which we now return.

4.4 Bringing Meta-​Mathematical Concerns into Mathematics: The Neoplatonist Heritage The (too) easy distinction between philosophy and mathematical practice, though it visibly had some significance to some of the ancients (see Cuomo on Pappus, Collection, bk. 5), tends to hide a basic and crucial fact that is well illustrated by the conclusion of the first “prologue” to Proclus’ commentary on Euclid: for Proclus, what he was doing was not a commentary on mathematics, but an introduction to mathematics in a (to him) true and elevated sense: As we begin our examination of details, we warn those who may encounter this book not to expect of us a discussion of matters that have been dealt with over and over by our predecessors, such as lemmas, cases, and the like. We are surfeited with those topics and shall touch on them but sparingly. But whatever matters contain more substantial science and contribute to philosophy as a whole, these we shall make it

890   Late Antique and Early Byzantine Science our chief concern to mention. [For] we must cultivate the science of geometry which with each theorem lays the basis for a step upward and draws the soul to the higher world.” (iE 84.8–​20; Morrow 1992, 69)

This self-​appreciation signals to the historian the important and crucial fact that this period is one in which, in general, meta-​mathematical concerns entered mathematical practice. While this move has early roots in Hellenistic mathematics (see, in this volume, chap. C3, Acerbi’s remarks on Apollonius’ innovations, found again in Pappus), it became even more obvious and prevalent in Late Antiquity, at least in Neoplatonist circles following Iamblichus’ important reform of the mathematical curriculum. What philosophers like him apparently found attractive in Nicomachus’ style, and that he could not find in Euclid, was the particular mixture of mathematical procedure and philosophical categorization. Most probably, this conveyed a sense of being introduced to philosophy through the progressive discovery of mathematical ratios and series. This view of mathematical practice, sustained by the original theory known as “projectionism” (on which see O’Meara 1989, 133–​134, 168), lies behind the philosophical reinterpretation of the classical scheme of the mathematical proposition, presented by Proclus in his important commentary to Euclid’s first problem. In a similar way, Proclus’ commentary is oriented toward a particular understanding of mathematical demonstration that strongly relates it to the notion of physical causality (Harari 2008). This means that, for him, what the mathematician experiences on a small scale within his own soul is the reflection and analogue of causal processes in nature, and therefore mathematical activity is an introduction to physical theory and natural philosophy at large. These philosophers thus introduced notions like holē mathematikē, first in Iamblichus and then reinforced in Proclus through his notion of causality. The new representation of mathematics in Late Antiquity has therefore much to do with the important philosophical shift that took place in this period. The relative dissension among Platonists (the Ptolemists on the one hand, and the orthodox Platonists on the other, as recalled in sec. 2.2), also produced interesting results:  most notably, Proclus criticized the system of astronomical hypotheses as discussed by traditional astronomers and by Ptolemy, in particular, in favor of a deeply different view of the cosmos, in which stars and planets were allotted a certain autonomy and soul (see Siorvanes, chap. E1, sec. 5, this volume). We have also seen that his view of mathematical practice is strongly oriented by its philosophical (protreptic) objective and leads him to criticize the discussion of lemmata and cases, which was the gist of late antique activities on classical texts. In spite of their conciliatory efforts and the de facto acceptance of this traditional baggage, strongly inserting mathematical practice into an orthodox philosophical curriculum had consequences for the definition of this practice and its underlying concepts. These evolutions are quite substantial, although apparently unremarkable at first sight—​with the exception of Diophantus’ treatises and of the spectacular reinterpretation of mathematical practice by late Platonists. They paved the way for the outburst of physical mathematics in the Renaissance period, to a kind of mathematics adapted to

Greek Mathematics and Astronomy in Late Antiquity   891 analytical reasoning (once paired with medieval algebra). First and foremost perhaps, the period paved the way to the notion that mathematics could represent a legitimate field of intellectual and social endeavor, with its own encyclopedic corpus, ranging from arithmetic to instrumental mathematics, a partially self-​contained field.

Bibliography Abbreviations AOO:  Archimedis opera omnia, cum commentariis Eutocii. 3  vol. J. L. Heiberg, ed. Leipzig, 1910–​1915. DOO: Diophanti Alexandrini opera omnia cum graeciis commentariis. 2 vol. P. Tannery, ed. Leipzig, 1893–​1895. iA: Commentaires de Pappus et de Théon d’Alexandrie sur l’Almageste. 3 vol. A. Rome, ed. Roma, 1931–​1943. iE:  Procli Diadochi in primum Euclidis Elementorum librum commentarii. G. Friedlein, ed. Leipzig, 1873. GGM: Geographi Graeci Minores, ed. C. G. Müller. Paris 1855–​1861. Reprint Hildesheim 1990. Hyp.  :  Proclus’ Exposition of Astronomical Hypotheses  =  Procli Diadochi hypotyposis astronomicarum positionum, ed. C. Manitius. Teubner 1909. Reprint de Gruyter 2010. SO: Sereni Antinoensis Opuscula, ed. J. L. Heiberg. Teubner 1896.

Modern Studies Entries in EANS: Anthēmios of Tralleis, 90–​91 (Kourelis and Bernard); “Book of Assumptions,” 197 (Bernard); Erukinos, 301 (Bernard); Eutokios of Askalōn, 324–​325 (Bernard); Hēliodōros of Alexandria, 363 (Keyser); Isidōros of Milētos, 444 (Kourelis); Marcianus of Hērakleia, 530–​532 (Kuelzer). Acerbi, Fabio. Diofanto, De polygonis numeris. Rome, Pisa: Italie, 2011. Acerbi, Fabio, and Bernard Vitrac, eds. Héron d’Alexandrie: Metrica. Pisa: Fabrizio Serra, 2014. Acerbi, Fabio, Bernard Vitrac, and Nicolas Vinel. “Les ‘Prolégomènes à l’Almageste.’ Une édition à partir des manuscrits les plus anciens. Introduction générale—​Parties I‒III.” SCIAMVS 11 (2010): 53–​210. Asper, Markus, and Anna Maria Kanthak, eds. Writing Science:  Medical and Mathematical Authorship in Ancient Greece. Berlin: de Gruyter, 2013. Barton, Tamsyn S. Ancient Astrology. London: Routledge, 1994. Berggren, John Lennart, and Alexander Jones. Ptolemy’s Geography: An Annotated Translation of the Theoretical Chapters. Princeton, NJ: Princeton University Press, 2000. Berggren, John Lennart, and Robert S. D. Thomas. Euclid’s Phaenomena: A Translation and Study of a Hellenistic Treatise in Spherical Astronomy. History of Mathematics 29. New York, London: AMS, 1996. Bernard, Alain. “Comment définir la nature des textes mathématiques de l’Antiquité grecque tardive ? Proposition de réforme de la notion de textes deutéronomiques.” Revue d’Histoire des Mathématiques 9.1 (2003a): 131–​174. —​—​—​“Sophistic Aspects of Pappus’s Collection.” Archive for History of Exact Sciences, 57.2 (2003b): 93–​150.

892   Late Antique and Early Byzantine Science —​—​—​. “L’arrière plan rhétorique de la théorie de l’activité mathématique chez Proclus.” In Études sur le commentaire de Proclus au premier livre des “Éléments” d’Euclide, ed. A. Lernould and Bernard Vitrac, 67–​85. Lille: Presses Universitaires du Septentrion, 2010a. —​—​—​. “Theon of Alexandria and Hypatia.” In Gerson 1 (2010b) 417–​436. —​—​—​. “The Significance of Ptolemy’s Almagest for its Early Readers.” Revue de Synthèse 131.4 (2010c): 495–​521. —​—​—​. “In What Sense Did Theon’s Commentary on the Almagest Have a Didactic Purpose?” In Scientific Sources and Teaching Contexts throughout History: Problems and Perspectives, ed. A. Bernard and C. Proust, 95–​121. Berlin: Springer, 2014. —​—​—​. “Interpréter la sériation des problèmes des Arithmétiques de Diophante : une forme de modélisation ?” SHS Web of Conferences 22 (2015): #00003. http://​doi.org/​10.1051/​shsconf/​ 20152200003 Bernard, Alain, and Jean Christianidis. “A New Analytical Framework For The Understanding of Diophantus’s Arithmetica I–​III.” Archive for History of Exact Sciences 66.1 (2012): 1–​69. Bernard, Alain, Christine Proust, and Micah Ross. “Mathematics Education in Antiquity.” In Handbook on the History of Mathematics Education, ed. A. Karp and G. Schubring, 27–​53. Berlin: Springer, 2014. Brown, Peter. The World of Late Antiquity ad 150-​750. New  York:  Harcourt Brace Jovanovich, 1971. —​—​—​. “Christianisation and religious conflict.” In Cameron and Garnsey (2008) 632–​664. Cameron, Averil. “New Themes and Styles in Greek Literature, A Title Revisited.” In Greek literature in Late Antiquity: dynamism, didacticism, classicism, ed. Scott Fitzgerald Johnson, 11–​28. Aldershot, Hants, England, and Brookfield, Vt., USA: Ashgate, 2006. —​—​—​. “Education and Literary Culture.” In Cameron and Garnsey 2008 665–​707. Cameron, Averil, and Peter Garnsey, ed., The Cambridge Ancient History XIII: The Late Empire ad 337-​425. Cambridge: Cambridge UP, 2008. Chemla, Karine. “Commentaires, éditions et autres textes seconds: Quel enjeu pour l’histoire des mathématiques ? Réflexions inspirées par la note de Reviel Netz.” Revue d’Histoire des Mathématiques 5.1 (1999): 121–​142. Chouquer, Gérard, and Favory, François. L’arpentage romain:  histoire des textes, droit, techniques. Paris: Errance, 2001. Christianidis, Jean. “The Way of Diophantus: Some Clarifications on Diophantus’ Method of Solution.” Historia Mathematica 34.3 (2007): 289–​305. —​—​—​. “The Meaning of Hypostasis in Diophantus’ Arithmetica.” In Relocating the History of Science: Essays in Honor of Kostas Gavroglu, ed. T. Arabatzis, J. Renn, and A. Simões, 315–​327. Berlin: Springer, 2015. Christianidis, Jean, and Ianna Skoura. “Solving problems by algebra in Late Antiquity: New evidence from an unpublished fragment of Theon’s commentary on the Almagest.” SCIAMVS 14 (2013): 41–​57. Cuomo, Serafina. Pappus of Alexandria and the Mathematics of Late Antiquity. Cambridge: Cambridge UP, 2000. —​—​—​. Ancient mathematics. London and New York: Routledge, 2001. —​—​—​. Technology and culture in Greek and Roman antiquity. Cambridge: Cambridge UP, 2007. Decorps, Micheline. Recherches sur les Coniques d’Apollonios de Pergé et leurs commentateurs grecs: histoire de la transmission des livres I-​IV. Paris: Klincksieck, 2000. Decorps, Micheline, and Michel Federspiel, eds. Eutocius:  Commentaire sur le traité des “Coniques” d’Apollonius de Perge (Livres I‒IV). Berlin: de Gruyter, 2014.

Greek Mathematics and Astronomy in Late Antiquity   893 Dilke, Oswald Ashton W. The Roman Land Surveyors: An Introduction to the Agrimensores. Amsterdam: A.M. Hakkert, 1992. Dzielska, Maria. Hypatia of Alexandria. Translated by F. Lyra. Cambridge: Harvard University Press, 1995. Feke, Jacqueline. “Ptolemy’s Defense of Theoretical Philosophy.” Apeiron 45.1 (2012): 61–​90. —​—​—​. “Meta-​mathematical rhetoric: Hero and Ptolemy against the philosophers.” Historia Mathematica 41 (2014): 261–​276. Feke, Jacqueline, and Alexander Jones. “Ptolemy.” In Gerson 2010, 199–​209. Fowden, Garth. “The Pagan Holy Man in Late Antique Society.” Journal of Hellenic Studies 102 (1982): 33–​59. Gautier Dalché, Patrick. La géographie de Ptolémée en Occident, IVe‒XVIe siècle. Turnhout: Brepols, 2009. Gerson, Lloyd P., ed. The Cambridge History of Philosophy in Late Antiquity. Cambridge: Cambridge University Press, 2010. Harari, Orna. “Proclus’ Account of Explanatory Demonstrations in Mathematics and Its Context.” Archiv für Geschichte der Philosophie 90.2 (2008): 137–​164. Inglebert, Hervé. Interpretatio christiana: Les mutations des savoirs (cosmographie, géographie, ethnographie, histoire) dans l’Antiquité Chrétienne, 30‒630 après J.-​C. Paris: Institut d’Etudes Augustiniennes, 2001. Jones, Alexander. “Uses and Users of Astronomical Commentaries in Antiquity.” In Most 1999, 147–​172. Marcotte, Didier, ed. Les géographes grecs: Pseudo-​Scymnos. Paris: Belles Lettres, 2002. Marrou, Henri-​Irénée. Décadence romaine ou antiquité tardive  ?:  IIIe‒VIe siècle. Paris: Seuil, 1996. Megremi, Athanasia, and Jean Christianidis. “Theory of Ratios in Nicomachus’ Arithmetica and Series of Arithmetical Problems in Pachymeres’ Quadrivium :  Reflections About a Possible Relationship.” SHS Web of Conferences 22 (2015): #00006. http://​doi.org/​10.1051/​ shsconf/​20152200006. —​—​—​. “Tables in Nicomachus’ Arithmetical Introduction:  Their Construction and Role in Teaching Arithmetic in Late Antiquity and Byzantium.” In Computations and Computing Devices in Mathematics Education Before the Advent of Electronic Calculators, ed. Alexei Volkov and V. Freiman. Berlin: Springer, forthcoming 2018. Morrow, Glenn R., ed. Proclus: A Commentary on the First Book of Euclid’s Elements. Princeton, NJ: Princeton University Press, 1992. Most, Glenn W., ed. Commentaries—​Kommentare. Göttingen: Vandenhoeck und Ruprecht, 1999. Mugler, Charles, ed. Archimède:  Œuvres. Tome IV, Commentaires d’Eutocius. Fragments. Paris: Belles Lettres, 1972. Netz, Reviel. “Deuteronomic Texts: Late Antiquity and the History of Mathematics.” Revue d’Histoire des Mathématiques 4.2 (1998): 261–​288. —​—​—​. “Archimedes Transformed:  The Case of a Result Stating a Maximum for a Cubic Equation.” Archive for History of Exact Sciences 54.1 (1999): 1–​47. —​—​—​. The Works Of Archimedes: Translated into English, Together with Eutocius’ Commentaries, with Commentary, and Critical Edition of the Diagrams. Cambridge: Cambridge University Press, 2004. O’Meara, Dominic J. Pythagoras Revived:  Mathematics and Philosophy in Late Antiquity. Oxford: Clarendon Press, 1989.

894   Late Antique and Early Byzantine Science Pingree, David. “The Teaching of the Almagest in Late Antiquity.” In The Sciences in Greco-​ Roman Society, ed. T. D. Barnes, 75–​98. Edmonton: Academic, 1994. Riedlberger, Peter. Encheiridion and Spurious Works. Domninus of Larissa. Introduction, Critical Text, English Translation, and Commentary. Pisa: Fabrizio Serra, 2013. Saffrey, H. D., and A.-​P. Segonds, eds. Marinus:  Proclus ou Sur le bonheur. Paris:  Belles Lettres, 2001. Segonds, Alain. “Proclus:  Astronomie et philosophie.” In Proclus lecteur et interprète des anciens, ed. J. Pépin and H. D. Saffrey, 317–​334. Paris:  Centre National de la Recherche Scientifique, 1987. Sluiter, Ineke. “Commentaries and the Didactic Tradition.” In Most 1999, 173–​205. Tarán, Leonardo, ed. Asclepius of Tralleis:  Commentary to Nicomachus’ Introduction to Arithmetic. Philadelphia: American Philosophical Society, 1969. Taub, Liba. “On the Variety of ‘Genres’ of Greek Mathematical Writing:  Thinking About Mathematical Texts and Modes of Mathematical Discourse. In Asper and Kanthak 2013, 333–​365. Tihon, Anne. “Le livre V retrouvé du Commentaire à l’Almageste de Théon d’Alexandrie.” L’antiquité Classique 56.1 (1987): 201–​218. Tybjerg, Karin. “Wonder-​making and Philosophical Wonder in Hero of Alexandria.” Studies in History and Philosophy of Science Part A 34.3 (2003): 443–​466. Van den Berg, Robbert M. Proclus’ Hymns:  Essays, Translations, Commentary. Leiden: Brill, 2001. Vinel, Nicolas, ed. In Nicomachi arithmeticam. Pisa: Fabrizio Serra, 2014. Vitrac, Bernard. “Mythes (et réalités ?) dans l’histoire des mathématiques grecques anciennes. in L’Europe Mathématique, ed. C. Goldstein, J. Ritter, and J. Gray, 32–​51. Paris: MSH, 1996. —​—​—​. “A propos des démonstrations alternatives et autres substitutions de preuve dans les Éléments d’Euclide.” Archive for History of Exact Sciences 59 (2004): 1–​44. —​—​—​. “Les préfaces des textes mathématiques grecs anciens.” In Liber Amicorum Jean Dhombres, ed. P. Radelet-​de-​Grave, 519–​556. Turnhout: Brepols, 2008. —​—​—​. “Mécanique et mathématiques à Alexandrie :  Le cas de Héron.” Oriens-​Occidens 7 (2009): 155–​199. Vitrac, Bernard, and Ahmed Djebbar. “Le Livre XIV des Éléments d’Euclide :  Versions Grecques et Arabes (première partie).” SCIAMVS 12 (2011): 29–​158.

chapter E3

The Greek Neopl atoni st C om mentators on Aristot l e Michael Griffin

1. Introduction: Philosophy as Commentary It is sometimes suggested that in the Aristotelian tradition “genuine philosophy is commentary,” beginning either with Aristotle himself (Nussbaum 1978, xvi) or in the schools of Late Antiquity (Fazzo 2004; Baltussen 2007, 2008). What might a judgment like this mean? The study of natural philosophy among the Neoplatonist commentators on Aristotle affords a vivid example of the practices that give rise to it. To investigate nature (Greek phusis, more literally “growth”) is, for the commentators, to read with understanding Aristotle’s treatise On Nature or Physics (Peri phuseōs), followed by related books in a set curriculum, accompanied by an established commentary and a knowledgeable teacher. Therefore, a mature philosopher would often prove to be a capable commentator, or interpreter (exēgētēs), who could foster the reading of the primary texts with charity plus objectivity, eliciting the author’s meaning through paraphrase, lemmatized discussion, and a critically evaluated doxography of the puzzles (aporiai) presented by the text. Each generation’s outstanding intellectual might be designated with the honorific “philosopher of our time,” as in Marinus, Life of Proclus 1, echoing the opening overture of Porphyry’s Life of Plotinus (Edwards 2000). Arguably, he was expected to be an authoritative and sensitive interpreter, not only of Aristotle but also of all the Greek classics (Tarrant 1997). Simplicius of Cilicia (ca 530 ce) characterizes the competent commentator on Aristotle as follows: [T]‌he worthy exegete of Aristotle’s writings must not fall wholly short of the latter’s greatness of intellect. He must also have an experience of everything the philosopher

896   Late Antique and Early Byzantine Science has written, and must be a connoisseur (epistēmōn) of Aristotle’s stylistic habits. His judgement must be impartial, so that he may neither, out of misplaced zeal, seek to prove something well said to be unsatisfactory, nor, if some point should require attention, should he obstinately persist in trying to demonstrate that [Aristotle] is always and everywhere infallible, as if he had enrolled himself in the philosopher’s school. (On Aristotle’s Categories 7, 23–​29, trans. Chase 2003; throughout, the commentators are cited by comma-​ separated page and line numbers in the Commentaria in Aristotelem Graeca).

Thus the commentary was—​alongside the monograph—​a leading medium of philosophical exposition, training, and investigation in Late Antiquity (Sorabji 2016; Baltussen 2008; Mansfeld 1994; Hadot 1991; Hoffmann 1987); the great texts circumscribe the field on which philosophy is played, and the maneuvers of exegesis, explanation, and criticism are the rules of the game. The tether that bound philosophical activity to a textual canon might encourage us to envisage the literary life of a later Greek philosopher as an uncreative, restrictive, and tralaticious procedure one step removed from a copyist’s dungeon. Such a caricature would undoubtedly break down in the case of individual innovators such as Philoponus, who deployed the commentary medium for the promotion of unapologetically novel and sometimes unfashionable ideas (Sorabji 2010). But the impression of philosophical unoriginality would also be misleading for the Neoplatonic “mainstream” as a whole, in at least one crucial respect: the commentators were induced to execute brilliant exegetical fireworks to demonstrate the synthetic unity of the philosophical systems that they developed from their primary texts. On the Neoplatonist account, for example, the system expounded in Aristotle’s treatises is uniform and consistent and is also harmonious with the philosophy expounded in Plato’s dialogues (Karamanolis 2006) and with other essential texts of Hellenism. So in every case where a discrepancy appears to arise—​say, due to some rhetorical or polemical hyperbole (as described by Syrianus, On Metaphysics M, 80,1–​81,2; Dillon and O’Meara 2006), divergence of technical vocabulary, or curricular emphasis—​it is incumbent on the competent commentator to expound the larger, integrated philosophical picture into which the apparent disagreement can be resolved. Therefore Simplicius, in the passage quoted above, continues that the competent exegete should “not convict the philosophers of discordance by looking only at the letter of what [Aristotle] says against Plato, but he must look toward the spirit (nous), and track down the harmony which reigns between them on the majority of points” (On Aristotle’s ‘Categories’ 7, 29–​32, trans. Chase 2003). In certain respects, the distinctive methodology of the later ancient philosophers as commentators can perhaps be understood as a natural descendent of Aristotle’s dialectical procedure, in which the philosopher lays down various reputable beliefs about some subject (endoxa, phainomena), then settles the inconsistencies or puzzles (aporiai) to which they give rise, for example, Nicomachean Ethics 7.1 (Owen [1961] 1986; Nussbaum 1982; Irwin 1988; against this, see Frede 2012) or Physics 1.1 (de Haas 2002). But whereas Aristotle argues that “no one is able to attain the truth adequately, while  .  .  .  no one fails entirely” (Metaphysics B 1, 993a31–​b19), Neoplatonists since

Greek Neoplatonist Commentators on Aristotle    897 Plotinus (Enneads 3.7.7) were prepared to credit at least some of their predecessors with the discovery of the truth. Standing at the end of a long post-​Hellenistic trend toward respect for the authority of antiquity in philosophy (Boys-​Stones 2002, 99–​122), the Neoplatonists display considerably greater respect for the opinions of past “experts” than does Aristotle himself.

2.  Who Are the Later Ancient Commentators? A Selection of Key Figures, ca 300–​600 ce The monumental Berlin edition of the commentators on Aristotle, the Commentaria in Aristotelem Graeca, totals about 15,000 pages. A significant portion has been translated into English in the Ancient Commentators on Aristotle series edited by Richard Sorabji, and important individual texts have been collected in Sorabji (2005). The current state of the scholarship is helpfully summarized in the introduction to Sorabji (2016). Sellars (2004; 2016) provides a guide to the secondary literature on the commentators, and recent scholarship on the Aristotelian tradition is accessible in Tuominen (2009). Nonetheless, the vast bulk of the material and the number of ancient authors challenge efforts to collect and organize the important ideas. The present survey will be necessarily selective and focuses on the later Neoplatonist commentators:  see also the excellent compilation of articles in Sorabji ([1990] 2016) and Blumenthal and Robinson (1991). A list of the important ancient commentators on Aristotle in later antiquity would include at least the following names: • Alexander of Aphrodisias (fl. ca 200 ce). Writing before the inauguration of “Neoplatonism” by Plotinus, Alexander’s monumental commentaries on the Aristotelian corpus earned him the title of “the commentator” (ho exēgētēs). Alexander may be the source of many of the Neoplatonists’ doxographies of earlier Peripatetic thinkers, and he anticipates the methodological tone of later ancient commentary on Aristotle. His Problems and Solutions (Quaestiones) investigate many problems in natural philosophy; of further relevance to ancient physics, commentaries by Alexander on Aristotle, On Sense Perception, On the Soul, On Heaven, On Generation and Corruption survive, together with his essays On the Soul, On Fate, On Mixture, and other works surviving in Arabic. • Plotinus (ca 204–​270 ce). He is often treated as the founding figure of ancient Neoplatonism. Even where he is not explicitly cited, Plotinus’ system of thought provides the substructure of much later Neoplatonist commentary on Aristotle. • Porphyry of Tyre (ca 233–​309 ce). Plotinus’ pupil and editor, he acted as the “great sifter” of the tradition before him (Ebbesen [1990] 2016), and like Plotinus, was respected, if not always followed, by his successors. Smith (1994) collects

898   Late Antique and Early Byzantine Science the fragments; Smith (1974) treats his role in the Neoplatonist tradition in detail. Barnes (2003) also offers an excellent introduction to Porphyry’s thought and pedagogy, with an emphasis on logic. • Iamblichus (ca 242–​325 ce). A contemporary and possibly a pupil of Porphyry, who debated with him on questions such as the importance of theurgy (On the Mysteries) and applied a symbolic “intellective interpretation” to the harmonization of Aristotle and Plato (Dillon 1997), providing an influential foundation for later commentators. • Themistius (317–​c. 390 ce). A politician and rhetorician, as well as a leading commentator on Aristotle, particularly well-​known for his writing of paraphrases. The introductory discussions in Todd (2008; 2011) are excellent general introductions to his work. • Proclus of Lycia (412–​485 ce). The towering Athenian Platonist of Late Antiquity; his natural philosophy has been surveyed in English by Siorvanes (1997) and Chlup (2012). • Ammonius of Alexandria (ca 435/​45–​517/​26 ce). A disciple of Proclus, Ammonius taught the last great generation of Neoplatonist commentators, including Simplicius, Olympiodorus, and Philoponus, among others. He was an influential holder of a chair in pagan philosophy at Alexandria at a time when such a position was rather controversial (cf. Westerink [1990] 2016). • Simplicius of Cilicia (ca 490–​c. 560 ce). A great bulk of Simplicius’ work survives; nearly a million words of Greek from his commentaries on Aristotle alone. He is well-​known, thanks to his majestic commentary on Aristotle’s Physics, as the preserver of key fragments from many pre-​Socratic philosophers; he also preserves the doxographies of his predecessors on many important questions of Greek philosophy. Simplicius represents the post-​Plotinian, fully Neoplatonic strain of commentary that strives to integrate Aristotle into the framework represented by Plato’s Timaeus, inclusive of a higher model. On Simplicius’ life and thought in general, see Hadot (1997) and Baltussen (2008). • Olympiodorus of Alexandria (ca 495–​ 570 ce). A  student of Ammonius, Olympiodorus the Younger was among the last pagan philosophers to teach at the Alexandrian school in the 6th century ce; indeed, he may have been the last pagan philosopher to hold the chair. Wildberg (2007) and Westerink ([1990] 2016) are both useful introductions to Olympiodorus’ life and times, with bibliography. • John Philoponus (ca 490–​570 ce). Philoponus was also a pupil of Ammonius—​ although, unlike Olympiodorus, he did not succeed Ammonius in a chair. His work and innovative thought is surveyed in Sorabji (2010); as we will find in the following discussion, Philoponus’ attitude to Aristotle often diverges from that adopted by his contemporaries. Philoponus, who was likely born a Christian, developed an intellectual defense of Christian doctrine while his staunchly traditionalist contemporaries operated under growing pressure to attract Christian students and stay on the good side of Christian authorities; Simplicius reveals that (some of) his dialectical opponents treated his criticisms of Aristotle as a function of his new faith (Simplicius, On Aristotle’s ‘On Heaven’ 90, 13–​18).

Greek Neoplatonist Commentators on Aristotle    899

3.  Integrating Plato and Aristotle: Two Worlds The Neoplatonic commentators’ use of Aristotle entails a synthesis of his views with those articulated in Plato’s dialogues. This synthesis is especially apparent in the case of his natural philosophy. For (1) although Aristotle appears to us to develop his philosophy in conscious response to certain principles of Platonism, particularly where the causal framework of nature is concerned (as in Physics 1), nevertheless, (2) the Neoplatonists interpret or “transform” (Sorabji [1990] 2016) the arguments of the Aristotelian texts, in order to restrict the scope of Aristotle’s doctrine and situate it within the broader integrative framework of Platonism—​a move that has partly inspired similar efforts in modern scholarship (notably Gerson 2005). In particular, the later ancient commentator situates Aristotle’s natural treatises within the broader “two-​world” framework that is sometimes understood as a hallmark of ancient Platonism, contending that Aristotle’s terminology and arguments are chiefly useful for describing the world insofar as it is perceptible via the senses, while Plato’s terminology and arguments apply primarily to the world insofar as it is graspable by the mind (nous) (but see Wilberding and Horn 2012 on the importance accorded to natural philosophy in Neoplatonism). It is useful to consider this overarching division of “two worlds”: With the whole of philosophy being divided into study of intelligibles and study of immanent things—​quite rightly too, as the kosmos too is twofold, intelligible kosmos (noētos) and sensible kosmos (aisthētos) as Plato will go on to say (Timaeus 30C). . . . The sensibles exist in the intelligibles as paradigms, and the intelligibles exist in the sensibles as images (eikōnikōs). (Proclus, On Plato’s Timaeus 1.13, 1–​14, 1, slightly adapted from Tarrant 2007 and Siorvanes 1997)

The Neoplatonic commentators, then, regard Aristotle as a specialist, whose systematic philosophy is designed to tackle “encosmic” questions. His apparent divergences from Plato could be said to run along both disciplinary and pedagogical fault lines. On the one hand, an illustrative analogy might be the presumption that a biologist would rely on principles and language different from those employed by a physicist. On the other hand, it would also be illustrative to compare the difference between a basic survey and an advanced graduate seminar on a given topic. The crucial point is that, on the Neoplatonic commentators’ view, Aristotelian natural philosophy focuses on the analysis of the entities that come-​to-​be (as images, eikōnikōs) according to the pattern of higher, timeless paradigms. Today, by contrast, Aristotle is often read as developing a philosophical thrust that is basically opposed to Plato, or at least tracks a gradual but determined evolution away from Plato’s middle-​period thought (compare Jaeger 1934 and Barnes 1995, chap. 1 sec. IV). When Aristotle develops his celebrated analysis of change in terms of four causes or modes of explanation (aition: Johnson 2005), he argues that Plato has omitted the final

900   Late Antique and Early Byzantine Science and efficient causes from analysis (Metaphysics 1.6, 1.9); how, then, could Aristotle really fit into a broader Platonic framework? In response, the Neoplatonists first contend that Aristotle is playing at school polemics, so the remark need not mean Aristotle rejected Platonist causation (for, as they would argue, what is the dēmiourgos (Demiurge) of the Timaeus if not an efficient cause? And what is the idea of the good in the central books of the Republic if not a final cause?) Then, as we will find below, the Neoplatonist commentators turn the tables and suggest that Plato, in addressing himself to the intelligible world, adds two kinds of causation to the four recognized by Aristotle: the paradigmatic and the instrumental. Thus the commentators strive to situate Aristotelian natural philosophy in a wider Platonic framework and construct a curriculum that answers to this structure.

4.  Curriculum and Context Simplicius (On Aristotle’s ‘Physics’ 1, 4–​14) offers a sketch—​which could serve as a gen­ eral outline for the Neoplatonist treatment of natural philosophy in general—​of the large-​scale curricular and philosophical “frame” within which Aristotelian natural philosophy is located: Consider that philosophy completes the soul (psukhē), just as the medical art completes the body. Now one part of the soul is unreasoning, while the other part reasons. Of the reasoning soul, one part joins forces with the unreasoning soul (such as what Aristotle calls the “potential intellect”), whereas the other part is independent (such as what Aristotle calls the “intellect in action”). Moreover, the capacity of the entire soul is twofold, being concerned either with impulse or with understanding (gnōstikē). Now the kind of philosophy that completes the impulsive part of the unreasoning soul, as well as the part of the potential intellect that joins forces with unreasoning impulses—​all of this, the Peripatetics designate “practical” . . . but the kind of philosophy that completes the understanding part of the soul, and has truth for its end, they designate “theoretical,” in general . . . and the part of this which completes the potential intellect’s understanding—​which, along with perception and imagination, deals with enmattered forms that are inseparable from matter—​this they call “natural” (phusikos), because nature (phusis) is proven to be concerned with things like this, and in them.

The passage captures two preliminary questions posed by the Neoplatonist commentators about each work in the Aristotelian œuvre, namely, its position in the integrated sequence of study (Mansfeld 1994, 193) and the philosophical subdiscipline to which it belongs. The two questions are interlocked because the order of texts read reflects the hierarchy of philosophical disciplines adopted, in such a way that one might begin with logic (from the Categories), proceed to physics and then metaphysics before advancing to the study of Plato.

Greek Neoplatonist Commentators on Aristotle    901 Given this scope, we might ask which Aristotelian works are included in this program? The commentators roughly followed the list offered by Aristotle at Meteorology 1.1 for the canon of natural philosophy: the study of primary causes and natural motions (Physics), the pure upper motions (On Heaven), the elements, generation and diminution (Generation and Corruption), the middle realm of the sky and earth (Meteorology), and finally the biosphere of animals and plants upon the earth (the biological corpus), bringing us “almost” to the limit of the subject (trans. Webster in Barnes 1994). Thus the commentators situate the sphere of nature (phusis), and the specific Aristotelian texts through which it is studied, within a wider ontology: physics is about enmattered forms, that is, forms in the process of change and development. The physicist studies forms “just insofar as they are not separate from matter (hulē)” (cf. Aristotle, De Anima 403a15–​23).

5.  The Scientific Method of Aristotle and the Commentators The Neoplatonist commentators also have views on the method appropriate to physics. Their method of inquiry arguably resorts to the style and dialectical approach that characterizes Aristotle’s own Physics. But Aristotle’s approach to natural philosophy is itself a notorious puzzle. As this is discussed in more detail in chapter C01, by Althoff of this volume, I will confine this discussion to a brief overview of the points especially relevant to the general methodology of the commentators. First, we should note that, although Aristotle’s commentators broadly adhere to his views about the nature of scientific demonstration in Posterior Analytics, neither he nor they attempt to produce scientific demonstrations in works like the Physics or Simplicius’ commentary on the Physics (although the commentators do regard syllogistic reasoning as having a place in thinking about nature: cf. Alexander On Aristotle’s ‘Prior Analytics’ 39, 19–​ 40,5, with Sharples 1982). Nor is either party concerned to set down theory-​neutral observations of the physical world—​“hard data”—​and then to construct theories that match those data; rather, Aristotle and his commentators are concerned to lay down and cross-​examine commonly held beliefs or expert views (phainomena, in the dialectical interpretation championed by Nussbaum 1982 and Owen [1961] 1986). Aristotle writes: Here, as in all other cases, we must lay down the appearances (phainomena, from the Greek verb phainesthai, “to appear”), and, first working through the puzzles (diaporēsantas), in this way go on to show, if possible, the truth of all the beliefs we hold (ta endoxa) about these experiences; and, if this is not possible, the truth of the greatest number and the most authoritative. For if the difficulties are resolved and the beliefs (endoxa) are left in place, we will have done enough showing. (Nicomachean Ethics 7.1, 1145b1–​7, trans. Nussbaum)

902   Late Antique and Early Byzantine Science This remark has seemed to some to capture the spirit of Aristotle’s general method of inquiry into both natural and ethical puzzles (Frede 2012 advises caution here). Having determined a subject of inquiry, Aristotle first endeavors to set down the phainomena about it. What are these phainomena? Various translations have been used for the Greek participle in the Aristotelian corpus: “observed facts,” “data of perception,” “observations.” G. E. L. Owen argued forcefully that the word phainomena can also refer to our ordinary beliefs and use of language about some subject, and Nussbaum pressed the point that this might be primarily and consistently what Aristotle means by it; thus the Physics does not begin by recounting hard facts or results of observation, but by recounting a wide range of common views and expert arguments on topics in natural philosophy, which are then subjected to dialectical discussion and confronted with various puzzles. (An exemplary passage follows the above-​quoted excerpt from Nicomachean Ethics 7, where Aristotle promises to lay down the phainomena about weakness of the will, or akrasia, and then proceeds to recount everyday beliefs about this topic.) Something like this is arguably the kind of procedure we find operative, on an even grander scale, among the Neoplatonic commentators. The philosopher takes up some general topic, say, nature. How does one philosophize Peri phuseōs? One should first research and collate the phainomena and endoxa about the subject of phusis—​expert or majority views that have been defended about the subject. Having presented the phainomena, it is time to present and attempt to settle the aporiai or puzzles that have been raised about them. The execution of this procedure in Aristotle’s own Physics and Metaphysics 1 furnishes essential reports of prior philosophy, adapted to the warp and weft of Aristotle’s philosophy; similarly, the Neoplatonic report of the phainomena generates even larger doxographies, casting a synoptic gaze back over a millennium of speculation, incorporating the Aristotelian school itself, as well as Stoicism, “middle” Platonism and Pythagoreanism, early Roman Aristotelianism, and various other strands of the theological and mystical movements sometimes collected under the head of the “Platonic underground” (Dillon 1996, 384–​389). As in Aristotle, the resulting doxographies are not strictly neutral reports but are consciously organized around a central spine, namely, the commentator’s commitment to a synoptic view, portrayed as accommodating the partial positions he reports from the past. Thus, for instance, we might compare the approach of the first books of Aristotle’s Physics, which assume that explanation can be divided into four “modes,” the final, formal, efficient, and material; leveraging this submerged structure, Aristotle presents the earlier schools of philosophy and finesses each to fit into one or another of the relevant pigeonholes, in such a way that Aristotle’s system accommodates aspects of each and explains why they were partially correct (compare Cherniss 1944). When we turn to the commentators, this is the approach owe encounter writ large. For example, in the tradition of commentary on the Aristotelian Categories that includes Porphyry, Dexippus, Ammonius, Simplicius, Philoponus, Olympiodorus, and others, we find previous opinions on the target or subject (skopos) of the Categories slotted into three silos: it is about words (a position ascribed to certain Stoics), or about concepts (a position ascribed variously to Alexander or others), or about real beings as such

Greek Neoplatonist Commentators on Aristotle    903 (a position ascribed to some Peripatetics). The Neoplatonist commentator appears in propria persona to declare that each of the three positions is partially true, but the complete truth lies in their integration: the Categories is actually about words insofar as they signify (sēmainein) real beings via concepts (see, for example, Iamblichus, in Olympiodorus, Prolegomena to Aristotle’s ‘Categories’ 19, 36–​20,12). The essential point to draw from this exegetical similarity is that Neoplatonic commentary as philosophy is not a peculiar late antique innovation, but a practice adopted from a long Peripatetic (Sharples 2010; Sharples and Sorabji 2007) and more broadly Stoic and post-​Hellenistic tradition (Boys-​Stones 2002) that traces some of its roots to Aristotle’s practices.

6.  Subject Matter of Physics: Aristotle and the Commentators Here the focus is on a survey of the Greek Neoplatonic commentators’ reception of Aristotelian phusis and related core concepts, especially hylemorphism, causality, place, and time. This roughly constitutes the first portion of the natural philosophical curriculum studied in late antiquity, typified by the schematic pattern that appears at the head of the Aristotelian Meteorology 1.1 (as above). The commentators’ use of this gen­eral schema to frame the natural philosophy of Aristotle can be found, for example, in Philoponus’ introduction to his commentary on the Physics. An excerpt from the Neoplatonist Proclus also shows how the Neoplatonists locate Aristotle’s focus on “what belongs to all natural things in common” within a broader Platonist framework based around the reading of the Timaeus: The incredible Aristotle was also pursuing Plato’s teaching to the best of his ability when he arranged his whole treatment of physics like this. He saw that there were common factors in all things that have come to exist by nature:  form, substrate, the original source of motion, motion, time and place—​things which Plato too has taught about:  distance [cf. Timaeus 36A], time as image of eternity [cf. 37D] coexisting with the heavens, the various types of motion [40AB, 43BC], and the supplementary causes of natural things—​and that other things were peculiar to things divided in substance [i.e., the world of becoming, the encosmic world] . . . As for what concerns coming-​to-​be, part belongs to things in the skies, whose principles Plato had accounted for, while Aristotle has extended their teaching beyond what was called for. (On Plato’s Timaeus 6, 21‒7, 9)

The following discussion will focus on the basic questions of “what belongs to natural entities in common,” nature (phusis), matter and form (hylemorphism), and the framework of four causes, and sketch the commentators’ adaptation of these three ideas, followed by a briefer discussion of their reception of Aristotle on place and time.

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6.1 Phusis 6.1.1 The Commentators on Aristotle’s Phusis The commentators follow Aristotle in positing the existence of phusis, described along the lines developed in Physics 2.1 (193ab) and in expounding the obviousness or self-​ evidence of its existence. As Themistius suggests, this is a question of no practical importance; every human being is perfectly capable of recognizing and distinguishing nature’s products using only their senses, and without the aid of reasoning (1,1), and in general “it is ridiculous to try to prove that nature exists . . . nothing is more self-​evident than this” (On Aristotle’s ‘Physics’ 37,10). Like Themistius, the commentators generally develop the implications of Aristotle’s passing comments on the self-​evidence of nature into what we might today call a Moorean argument, after G. E. Moore’s famous comment that “here is a hand”: the existence of nature can be posited without argument, because there are no principles more obvious or self-​evident from which a contrary result could conceivably be inferred. Every normal person can distinguish a plant, an animal, and water (1, 2); these are, as Aristotle would say, the most familiar and obvious realities. To prove the existence of nature to someone would be like explaining what colors are to someone who is blind (Simplicius On Aristotle’s Physics 272, 12). Themistius also broadly follows and expands Aristotle’s briefer remarks, in Physics 2.1–​3 and Metaphysics 5.4, in subdividing nature according to the scheme of four causes, beginning with the crucial distinction of nature as matter and as form (On Aristotle’s ‘Physics’ 37,22–​38,1). But the commentators also found some difficulties or puzzles (aporiai) concerning Aristotle’s basic definition of nature as a principle of change and rest, which stood in need of solution. Some of the puzzles are fairly simple; for example, if only natural objects have natural motions and artifacts are not natural, why does a bed fall to earth? As Aristotle said, Physics 2.1 (192b12‒23): it is qua natural (wood) that the bed falls, not qua artifact (so Simplicius On Aristotle’s ‘Physics’ 267). Let us review two of the more serious puzzles about Aristotle’s definition of phusis. First, if natural entities contain an internal source of both change and rest, what should we say about the celestial beings, such as stars and planets, which are evidently constantly in motion? If they possess an intrinsic source of stability, they never use it; conversely, if they do not, they don’t seem to be encompassed in Aristotle’s definition of nature. Second, a more serious puzzle about the knowledge of nature arose for the Neoplatonists, who adopted from Plato’s dialogues, such as Theaetetus and Republic, as well as Aristotle’s thoughts (e.g., Posterior Analytics 1.20–​24), the view that what is changing and indefinite is unknowable: if natural beings are constantly and intrinsically changing (by their very nature, as it were), how can we know about them and their natures? The early commentator Alexander had a straightforward, exegetical answer prepared for the first puzzle:  when Aristotle spoke of nature as “an internal principle of change and rest,” that formula was simply restricted to “animals (zōa) and plants (phuta) and simple bodies [such as elementary earth, water, air, fire]”; the formula

Greek Neoplatonist Commentators on Aristotle    905 should not be taken to apply to all natural beings (phusika), because the celestial element which moves in a circle, though natural, contains no principle of rest (Alexander, in Simplicius On Aristotle’s ‘Physics’ 264,18–​22). This is a good example of a commentator settling the aporiai by arguing for a position that is consistent across different Aristotelian texts. As for the trickier puzzle about knowing what is in constant flux, Alexander appeals to the identity and regular order and regularity throughout change—​that is, we can derive knowledge of the consistent laws of nature that persist through the flux (e.g., On Aristotle’s ‘Metaphysics’ 103, 35–​104, 3). Similarly, Philoponus contends, following the passage cited above from his Physics commentary, that we can get to know what is common across natural entities (matter, form, place, time, and motion), even if the entities themselves are in flux. The commentators are split along party lines regarding a third and more fundamental difficulty in Aristotle’s account of phusis. The reliance of Aristotle’s physical theory on analogies from the crafts is often pointed out, for better and for worse. His presentation in terms of four modes of causation or explanation might lead us to think about nature as operating in all four kinds of causality, the material, efficient, formal, and final. (Aristotle stresses that we might find one and the same natural entity operating in more than one causal category: Physics 2.7, 198a24–​7). Broadly, though, if we ask “why?” about the products of nature, we might answer in the same sort of ways that we would answer the question about the building of a house, (a) to be sheltered from the extremities of the elements (final), (b) because the builder has a model in mind, (c) because of the materials, or (d) because of the builder (so Philoponus, On Aristotle’s ‘Physics’ 241, 10–​16; cf. Tuominen 2009, 127–​129). Now this might seem to imply that there is some higher model or paradigm according to which nature works, as the builder builds according to a blueprint. That sort of notion would seem to allow for a close integration of Aristotle’s natural philosophy with the Timaeus of Plato, where the Demiurge (dēmiourgos) operates like the builder, according to a model, or paradeigma, namely the ‘complete living being’ (Tim. 31B), which can be treated as a Platonic Idea.

6.1.2 Phusis and Biological Reproduction “Purely” Aristotelian commentators such as Alexander reject that comparison, and regard nature as operating alone without any higher model or paradigm. Thus Alexander argues, “none of the things constituted by nature comes to be or has come to be by reference to a model,” following Aristotle (e.g., Metaphysics 1.6, 988a7–​14) in broadly rebutting the causal efficacy of Platonic ideas (Alexander, On Aristotle’s ‘Metaphysics’ 103, 4–​5). Themistius and other later commentators level a number of arguments in reply to Alexander and on behalf of the existence of higher, Platonic models. For example, Themistius in Metaph. 12 (in Averroes, in Metaph. 12 Bouyges 1938–​1948, vol. 3,1492–​ 1494) suggests that animals arise occasionally by a kind of abiogenesis, without a similar creator, as hornets seem to arise from the bodies of dead horses. Simplicius leverages a number of arguments in reply to Alexander, but the essential point is that

906   Late Antique and Early Byzantine Science when a human being produces a human being, it transpires according to a preexisting model (cf. sec. 2 above), even if there is no conscious cognition of that model in the producer. The productive rational principle is twofold, one producing in a cognizant manner, which Alexander sees as reason alone, the other without cognition and turning to itself, but still producing in an ordered and determinate manner for the sake of some prior end . . . just as what comes-​to-​be by nature does so according to a rational principle of this nature, so it does so according to a model which is not established as something known by the producer, but because the producer makes the product like itself by being, not by choosing, just as the signet-​ring makes the impression . . . higher up are the psychic principles of the movements, and even higher than these are the intelligible forms, from which in the first instance the shining forth of the forms is produced in all things according to the suitability of the recipients. (Simplicius On Aristotle’s ‘Physics’ 313, 27–​314, 6, excerpted, trans. Fleet)

The thrust of Simplicius’ reply to Alexander is that, although natural reproduction does not imply any consciousness of a higher model on the part of the active producer (or efficient cause), nevertheless consciousness is involved at a higher level, namely, the level of soul (psukhē), and above that the level of mind (nous) and the intelligibles (noēta) which it contemplates. These ideas, dependent on the broader framework of the Neoplatonic hypostases, depend largely on the accounts of nature found in Plotinus (3.8.3–​4). This way of thinking about nature enables later commentators to treat nature as the nearest, proximate member of a chain of hypostases—​in a sense, a principle that has “descended” here. In a way, this approach broadly opens the door to “supernatural” causation, which can also suit the exegetical needs of commentators such as Philoponus (in Phys. 197, 34–​198,3; cf. Tuominen 2009, 124–​125). Similarly, Simplicius stresses that soul (psukhē) is a higher principle that allows for nature to operate according to Platonic explanatory principles and Aristotelian ones. This opens the way to a new approach to hylemorphism and the framework of four causes. (For the biological implications of this debate, see Henry [2005] with bibliography).

6.2 The Elements, Dynamics, and “Natural Place” 6.2.1 Aristotle When we observe the stars and planets, they appear to move in circles around the earth. On Aristotle’s view, this suggests we need to posit a separate element, which later commentators sometimes called “ether,” from which the heavenly bodies are composed, and whose elementary nature it is to circle. Aristotle develops this point, for example, in On Heaven 1.3 (cf. Meteorology 1.3). There must be a body that moves naturally in a circle; and there are some deductions we can make about this body, for example, that

Greek Neoplatonist Commentators on Aristotle    907 it is eternal (for generation and corruption transpires between contraries, and circular motion has no proper contrary).

6.2.2 The Commentators on the Elements: Five or Four? Aristotle’s notion that every entity, at the level of its constituent elements, possesses an internal source of motion “by nature” may seem strange and rather unintuitive today. We are acclimatized to a different way of thinking about dynamics. On Aristotle’s view, every entity is (at the most basic level) composed of constituent elements. Those constituent elements fall into five kinds: the traditional four elements, earth, water, air, and fire (cf. On Heaven books 3–​4, where Aristotle offers an account of these elements), plus an additional fifth element posited to explain certain unique features of the heavens. So far, perhaps with the exception of the fifth element, the elementary theory seems fairly straightforward and derivable from observable states of matter, such as solid, liquid, and gas. Plato (in the Timaeus, as at 40A) was read by many ancient commentators (e.g., Porphyry, in Philoponus, Against Proclus 521, 25–​522, 23) as constructing the heavens out of just four elements—​fire for visibility, earth for tangibility, and air and water as the mean binding the two extremes—​in contrast to Aristotle’s position that the heavens were formed out of a fifth element whose natural motion was circular. This evaluation of Plato’s position was already familiar, in Taurus (2nd century ce, in Philoponus contra Proclum 520, 23–​521, 6) and Plutarch On the Failure of the Oracles (422f–​423a). Already, on the other side of the Academic-​Peripatetic fence, Aristotelians such as Xenarchus of Cilicia (1st century bce) had rejected the Aristotelian fifth element. Simplicius (On Aristotle’s ‘On Heaven’ 21, 33–​22, 17) sketches for us Xenarchus’ influential arguments. The arguments in the passage are summarized by Sorabji (2005, sec. 23a); see also the exposition in Irby-​Massie and Keyser (2002, 67–​69). Xenarchus concludes that actual earth, water, and air rest, while actual fire rotates. The earlier commentator Alexander, by contrast, had vigorously defended Aristotle’s separate fifth element, by stressing that the immaterial heavens cannot be a mixture of some kind (as Plato’s account might have implied), because mixture requires matter (On Mixture 229,3–​9). Alexander’s argument, based on the immateriality of the heavens, will prove useful in understanding the harmonizing tactics of the later Neoplatonists. The argument about the fifth element appears to represent a major challenge to the Neoplatonist project of harmonizing Aristotle’s views on the natural world into the broader framework of Platonism. In reply, Proclus argues that the fifth Platonic solid (dodecahedron, the shape of the whole world order, or kosmos) maps to the Aristotelian fifth element (On Plato’s ‘Timaeus’ 1.6, 29–​50, 2). Furthermore, there is a “scale” of species of flame (2.8, 20–​5)—​a notion indebted to Iamblichus (cf. Julian, Hymn to Helios 134AB). Proclus believed that even the highest light was bodily, despite being immaterial, and at least had (or even was) extension (cf. Simplicius, On Aristotle’s ‘Physics’ 611, 10–​13), whereas many Neoplatonists (such as Plotinus and Iamblichus) had believed that light was wholly incorporeal as well as immaterial. Through all of this, the notion of a kind of fire that was immaterial at the peak of a “scale of flame” helped harmonize

908   Late Antique and Early Byzantine Science the views of Plato and Aristotle. Immaterial existence was, as we noticed, fundamental to Alexander’s defense of the need for a fifth element; transforming Platonic fire into a spectrum allowed for that view to be compatible with a four-​element scheme. “Perhaps,” as Proclus continues, if someone were to say to [Aristotle] that material (enulon) fire is one thing, while immaterial (aülon) fire is another . . . and in general that there are many species of fire, perhaps he will concede the argument. (On Plato’s ‘Timaeus’ 2.9,8–​18)

Proclus does believe that the scope of Aristotle’s natural philosophy is limited: “for in most cases he stops at the point of matter, and by pinning his explanations of physical things on this he demonstrates to us just how far he falls short of the teaching of his master” (1.7, 14–​16). Proclus is also known to have developed a powerful attack on Aristotle’s disagreements with Plato in the Physics (Steel 2003; 2005). Regardless of these debates, the heavens were treated as divine in both Platonic and Aristotelian circles. But Philoponus strongly rejected the Aristotelian fifth element, deploying arguments similar to those used by Xenarchus (Simplicius, On Aristotle’s ‘On Heaven’ 42, 17–​20 even accused Philoponus of simply plagiarizing Xenarchus). Philoponus also strongly rejected the divinity of the heavens (Simplicius, On Aristotle’s ‘On Heaven’ 88, 28–​34), an important principle of Neoplatonic and Aristotelian thought which appeared to be incompatible with Philoponus’ Christian belief (90,13–​18).

6.2.3 The Commentators on Natural Place Aristotle’s hypothesis of “natural place” stated that each of the elements moves to its natural place when it can, and remains there (Physics 2.1, 4.1, 8.4). Within the framework of Aristotle’s geocentric picture of the world, “down” describes a line toward the center of the world, and “up” is the contrary direction. The intuitive appeal of Aristotle’s theory of natural places is grounded in the observation that a heavy object thrown upward will fall to the center, unless something impedes it, whereas fire or a hot gas will always rise upward toward the heavens. This kind of intentional language helps highlight the appeal of the theory of natural places to common sense. The hierarchy of kinds of fire in Proclus, as a solution to the problem of the fifth element and the natural rotation of the heavens, also shows itself in the Neoplatonic reception of the doctrine of natural place. Proclus adopts a theory of natural place (On Plato’s Timaeus 2.11, 27–​31), and Proclus’ teacher Syrianus held that space itself influenced bodies to their natural places (Simplicius, On Aristotle’s ‘Physics’ 618,27–​ 619,3). But while the mainstream Neoplatonic position favored the doctrine of natural place, Philoponus attacked it. Against the view that elements are naturally attracted to certain places, which on Aristotle’s view are surfaces, he contends that entities try to get into the correct relation to the whole of the world, like parts to a whole. Some passages, such as On Aristotle’s ‘Physics’ 581, 18–​30, might imply a Christian theological motivation.

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6.2.4 A Challenge in Aristotelian Dynamics: Philoponus and the Theory of Impetus In Physics 4.8 and elsewhere (such as Physics 8.4–​5, along the way toward his celebrated argument for the existence of an unmoved mover), Aristotle offers a basic and exhaustive subdivision between (a) motion or change that occurs according to nature, and (b) motion that occurs contrary to nature (para phusin) or by force. Aristotle argues that for either kind of motion, there must be a mover. For (a) a given natural entity, one part of that entity must be causing motion in the rest. But what does Aristotle have to say about (b) artificial or contra-​natural motion? To use a familiar ancient example, what is going on when a soldier or athlete throws a javelin and it hurtles forward through the air? It is not merely demonstrating the influence of nature; if that were so, it would simply fall to earth like a dropped stone, since down is the natural place of the elements in the javelin. Rather, it might look to us as if some kind of force is being impressed into the javelin from an external source. But on Aristotle’s view, we can’t simply suppose that the thrower is the moving cause of the projectile all the way through its flight; the thrower can only influence the javelin so long as his hand is in direct contact with it. On Aristotle’s view, perhaps (so Sorabji 2005, sec. 22(f)(iv) on Physics 8.10 and On Heaven 3.2) the external mover—​ that is, the thrower—​ imparts a certain capacity to the air. This idea raises a number of puzzles, which spur a development in dynamics among the commentators, most famously for Philoponus. He inquires: If the force were really implanted via the air, why not use bellows to drive arrows forward? (Philoponus, On Aristotle’s ‘Physics’ 641, 13–​642, 20, in Sorabji 2005, sec. 22(f)). In reply, Philoponus offers the remarkably original alternative that the thrower is really putting an impetus, an impressed force, into the projectile. This critical response allows for the development of impetus theory: an inner force can be impressed directly into a moving body from an external source. (For further discussion, see Sorabji 1988, chap. 14; Sorabji 2005, sec. 22(f)).

6.3. Hylemorphism and Causality 6.3.1 Aristotle on Hylemorphism in Nature According to the first, materialistic account of nature in Physics 2, a few single, reductive principles—​elements governed by forces—​could be posited to describe the whole diversity of apparent nature. In a deep way, all objects exhibit natural behavior because they are built up out of constituents that are natural. As for these items, it appears to be at the level of their basic material constitution—​such as wood, bronze, gold—​that they have some reliable consistency over time and can properly bear names. This kind of reduction of the “nature” of things to their “matter,” or hulē, had been adopted in various forms, according to Aristotle, by some of his predecessors and contemporaries (cf. Physics 2.1, 193a10–​29). Neoplatonist commentators like Simplicius are careful to note that material elements are relatively lowly compared to other principles (see for example Sorabji in Baltussen 2012, introduction).

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6.3.2 Aristotle on Four Modes of Causation When we pick out some composite entity which is a “natural” whole, such as a given man, we could describe his “nature” in terms of the stuff from which he is composed; but we would do a more complete job of the description if we also described the structuring principle, for example, the species, in virtue of which we call him “man” and not “flesh and bone” or “earth and water” and so on. In general, a description of the nature of something in terms of the form or structure (morphē) would be more informative than a description in terms of the matter alone (hulē). Aristotle argues that nature is shape rather than raw material, drawing on the root etymology of phusis as “growth” Physics 2.1 (193b7–​193b18). But Aristotle takes these notions of matter and form as only part of the story. Matter will tell us the story about what something grows out of “by nature”; form will tell us something of the story about what it grows into. But Aristotle’s story about causation—​ the why—​is richer than this. He posits, not four causes, but four fashions or modes of causation; not strictly four causes, but “four ways in which we cite the cause of a thing” (Lear 1988, 28): with respect to its “out of which” (material causation), its “for the sake of which” (final causation), its structure or definition (formal causation), and its source of change or rest (efficient causation) (cf. Physics 2.3).

6.3.3 The Neoplatonist Commentators on Hylemorphism and Revision of Four Modes of Causation to Six The late ancient commentators broadly accept Aristotle’s scheme of causation for natural change, as it has been described above. However, they strive to situate the four kinds of causation described by Aristotle in a wider framework, represented by Plato’s Timaeus as the commentators understood it, including both the division of causality into cause proper and auxiliary causes (sunaitia). Simplicius’ commentary on the Physics offers a clear statement of how this integration was accomplished and argued, generating (superficially puzzling) language that implies Plato adds to or expands on Aristotle’s scheme through the addition of the paradigmatic cause and the instrumental auxiliary cause (cf. Simplicius, On Aristotle’s ‘Physics’ 3, 13; 6, 31). Platonic philosophy is envisaged as embracing Aristotle’s four-​causal account of change, in which “form” is not a model separate from and transcendent of nature, but a model inherent in nature. But we still need some means of talking about the paradigm of the Timaeus, according to which the Demiurge creates, that arises before natural change, and according to which natural change takes place. For example, as Philoponus points out, the Demiurge knows the paradigms and creates in accordance with them, while natural entities develop toward completion unknowingly (Philoponus, On Aristotle’s ‘Physics’ 5, 7–​6, 7, 244, 14–​245, 2, cf. Tuominen 2009, 129). Thus we need to add the paradigmatic cause alongside the Aristotelian formal cause to accommodate the Platonic framework of the Timaeus. Another important addition, not as a proper paradigmatic cause but as an auxiliary cause, is the instrumental cause. Aristotle does make some distinction, for instance

Greek Neoplatonist Commentators on Aristotle    911 between a craftsman and the craftsman’s tool (Philoponus, On Aristotle’s ‘Physics’ 241,29–​242,3), but we need to draw out that distinction explicitly. These developments from four to six causes are grounded in a much longer history, including Stoic thought, of expanding and connecting Platonic and Aristotelian comments on causation (Seneca, Letter 65.4.14, cf. Karamanolis 2006, 274; Tuominen 2009, 129). The 6th-​century commentator Olympiodorus of Alexandria describes the resulting six-​causal framework: There are six principles of each thing: matter, form, productive cause, paradigm, instrument, end. As matter for a builder there is his wood; as form there is the drawing board or some such thing; the productive cause is the builder himself; the paradigm is what he had derived his mental plan from before building; as an instrument he may have a saw perhaps or an axe; the end is that for which it has been brought into being. (On Plato’s ‘Gorgias’ proem 5, 1–​6, 1, trans. Jackson-​Lycos-​Tarrant)

The official and mature Neoplatonic list of six modes of cause, then, runs as follows: (A) Causes: (Platonic) paradigm, (Aristotelian) efficient cause and final cause; (B) Auxiliary Causes:  (Platonic) instrumental cause, (Aristotelian) form, and matter. The purpose of this causal framework is to explain entities insofar as they appear in “this” world of becoming, that is, the proper subject matter of natural philosophy, and not to explain entities in their pure, separate nature as paradigms, which is Plato’s business. Thus, for instance, Proclus is careful to restrict the scope of this six-​causal analysis—​modified Aristotelianism—​to becoming, precisely because only in this encosmic world are the auxiliary causes of (inseparable) form and matter necessary: It is with good reason that Plato investigated and taught in detail about all these [three: paradigmatic, efficient, and final causes], plus the remaining [auxiliary] two, form and matter, which are dependent on these. For this cosmic order is not the same as intelligible or intellective cosmic orders, which are rooted in pure forms, but there is in it a part that acts as structure (logos) and form, and a part that acts as substrate. (On Plato’s Timaeus 1.3, 14–​19)

6.3.4 Teleology in the Commentators Broadly, all of these reflections on nature tend toward an Aristotelian teleology (for this idea, see the companion chapter on Aristotle chapter C01, by Althoff, in this handbook; and cf. Johnson 2005), according to which every natural entity has a goal or target of its own, namely its own natural completion (teleiōsis), toward which it is tending. Tuominen summarizes Simplicius’ position (2009, 137–​138): Either nature works by chance or for the sake of some end. This dichotomy is understood as exhaustive and mutually exclusive. Therefore, to argue that there is final causation in nature, one needs to argue against nature working at random. These arguments, in turn, are based on the idea that what happens by chance does not and cannot happen randomly. As Simplicius points out (in Phys. 372,30)

912   Late Antique and Early Byzantine Science in nature a man regularly begets man rather than a horse, and this shows that it cannot merely be a lucky coincidence.

6.4. Place and Time 6.4.1 Place While Aristotle recognizes change or motion in a number of categories, such as quality and quantity, locomotion (change in the category of where) is naturally one of the most important categories for understanding his picture of the natural world. Aristotle describes the place (topos) of a body as the immobile, two-​dimensional surface containing that body (Physics 4.4). Simplicius considers the Aristotelian view, among many others, in his Corollary on Place (601, 1–​645, 18; cf. Urmson and Siorvanes 1992, Sorabji 1988, chap. 11), surveying the full history of Greek reflection on locomotion. Indeed, Aristotle’s definition provided a basic starting point for the Neoplatonist commentators, although they challenged it on several fronts. Aristotle’s immediate successor Theophrastus might have already raised puzzles about Aristotle’s thesis that my “place” would be, say, the surface of the air around me, whose place in turn would be the immediately surrounding surface of that air, up to the heaven (ouranos) that surrounds me (in Simplicius, On Aristotle’s ‘Physics’ 604,5–​11 = fr. 146 Fortenbaugh et al. 1992; on Theophrastus’ intent in this fragment, see Sorabji 1988, chap. 11–​12, and Algra 1994, 231–​248; on the context, see Sorabji 2005, 226–​231). The Neoplatonist commentators developed these puzzles, for instance arguing (a) that a two-​dimensional surface could hardly be an “exact fit” for a three-​dimensional body, that is, quantitatively equal to it, or else a point could be equal to a line, a line to a plane, and a plane to a solid, and a point would appear to get indefinitely large (Simplicius, On Aristotle’s ‘Physics’ 604, 33–​605, 2); (b) that the heaven, on Aristotle’s account, seems to move in a circular fashion, yet is supposed to double as an immobile vessel for what is inside of it (603, 28–​607, 9); and (c) that the heaven (ouranos) looks like it is nowhere (in no place) at all (595, 9–​15). The Neoplatonists diverged on their final definition of place. Iamblichus, writing in the later 3rd century ce, described place as a capacity (dunamis) similar to bodies that sustains and organizes bodies, settling them into their natural place (Simplicius, On Aristotle’s ‘Physics’ 639,36–​ 640, 11; On Aristotle’s ‘Categories’ 361,7–​ 362, 33); Proclus (uniquely, according to Simplicius) maintained that place was in fact a three-​ dimensional bodily extension (diastēma), albeit immaterial, which was identical with the finest kind of fire or “light” described in the Myth of Er in Plato’s Republic X, 616B (Simplicius, On Aristotle’s ‘Physics’ 612, 24–​613, 1) and identical with the loftiest, luminous vehicle of soul; Damascius, writing in the later 5th and early 6th centuries, treats place as an organizing principle that keeps an organism’s parts in order relative to the whole (625, 13–​637, 30), in such a way that place is properly “a measure of position” (645, 4–​17); and Simplicius himself regards place, not as a mere extension but as a real being

Greek Neoplatonist Commentators on Aristotle    913 (ousia), which is also an intelligible unit of measurement (634, 11–​31, 623, 18–​20). All of these views are articulated in ongoing dialogue with Aristotle’s definition and the problems raised about it over the history of Greek physics, and offer a strong example of the interaction of commentary and philosophy in the Neoplatonists.

6.4.2 Philoponus, Space, and Prime Matter Philoponus also dissented from Aristotle’s view, maintaining that we should speak of “space” as a three-​dimensional extension (using this language rather than Aristotle’s “place,” topos, to represent the idea that place is not only what surrounds bodies but is also coextensive with them). For Philoponus, space is there regardless of whether there is a body in it; articulated in Aristotle’s framework, this idea would appear incoherent. Philoponus’ account of space is also bound up with his controversial view that “prime matter,” the ultimate subject (in the commentators’ interpretation of Aristotle) of which all properties are predicated, just is three-​dimensional extension. As Sorabji (2010, 58–​59) summarizes Philoponus’ view in relation to Aristotelian hylemorphism: Philoponus in his earlier writings, including the Physics commentary, or its early version of 517, accepted the conventional view of prime matter. But in the De aeternitate mundi contra Proclum of 529 he had a new idea [11.1–​8, pp. 405–​445]: Why not treat length, breadth, and depth, or three-​dimensional extension, as the ultimate subject of properties, and dispense with the lower-​level subject which he found in Aristotle’s passage? The great advantage from our point of view of this man­ oeuvre . . . is that three-​dimensional extension, or expanse, is something perfectly familiar. We are no longer left with a “something, I know not what” [as in Locke, An Essay Concerning Human Understanding, 1690, 2.23.2] as our ultimate subject of properties.

Although Philoponus seems to frame this development as a direct rebuttal of Aristotle, Simplicius suspects that Aristotle had something similar in mind all along (e.g., On Aristotle’s ‘Physics’ 229, 6–​232, 24). While Sorabji had (1984) suggested that Philoponus’ move disrupted Aristotle’s system of categories by prioritizing quantity above substance (ousia), de Haas (1997, 172–​180) compared Philoponus’ account of space with Porphyry’s development of the notion of “substantial quality,” which is intended to protect, not disrupt, Aristotle’s system; for further discussion, see Sorabji 2010, 19–​20 and de Haas 1997. It is also important to distinguish the Neoplatonist concerns that motivate Simplicius, on the one hand, from Philoponus’ interests, on the other (see Golitsis 2008, 127–​139; Sorabji in Baltussen 2012, introduction).

6.4.3 Time Aristotle’s definition of time as the number of change insofar as it is countable in terms of “before” and “after” was influential on the commentators, both in its own right and as a fruitful source of puzzles. The locus classicus for the definition is Physics 4.1:

914   Late Antique and Early Byzantine Science [Time is] not change, but change in so far as it admits of enumeration. An indication of this: we discriminate the more or the less by number, but more or less change by time. Time then is a kind of number. (Physics 4.1, 219b1–​8, trans. adapted from Hardie and Gaye)

No less influential than the plain definition, however, was the collection of paradoxes about time that Aristotle developed in Physics 4.10. These may be briefly summarized as follows: (a) time is nonexistent because it has no existent parts (the future is not yet; the past is no longer; the present is not a part of time, because it has no length and is merely an instant); (b) the present moment must cease to exist, considering that we do not live alongside people of the past; but when we can point to the present going out of existence? It is not ceasing to exist now, nor in the very next moment, since instants have no extension and—​like points on a line—​cannot be seen as directly adjacent. As in the case of place, Simplicius, in his Corollary on Time (On Aristotle’s ‘Physics’ 773, 8–​800, 21) and elsewhere in his commentary on the Physics, provides an invaluable doxography of ancient interpretations of Aristotle’s doctrine of time, leading to his own contemporaries in the 6th century ce. For instance, he tells us about his predecessors’ concerns about the circularity of Aristotle’s definition: Galen, writing around the 2nd century ce, asked, how can the words “before” and “after” be used in the definition of time, when these are temporal concepts in the first place? The commentator Themistius replied with several arguments, including the response that the circularity is not vicious (in Simplicius, On Aristotle’s ‘Physics’ 718, 13–​7 19, 18). In response to Aristotle’s view that time is dependent upon a soul, since it is defined as countable and it needs souls to do the counting (Physics 4.14, 223a21–​9), the commentators diverged: for example, the early 1st-​century bce Peripatetic commentator Boethus of Sidon had argued, seemingly against Aristotle, that “nothing prevents there being the enumerable apart from an enumerator, as there can be the perceptible without a perceiver” (in Simplicius, in Phys. 759,18–​20). By contrast, Alexander agrees that, indeed, “if time were enumerable as the before and after are enumerable, then if there were nothing to enumerate there would be no time. But nothing prevents the substrate of time, which is change, from existing” (excerpted from Alexander, in Simplicius, On Aristotle’s ‘Physics’ 759,20–​760,3 trans. Urmson, in Sorabji 2005, 202). With regard to the major puzzles or paradoxes about how time can exist (Physics 4.10), the Neoplatonists offered a number of original and striking solutions, which are analyzed in detail by Sorabji (1983). In reply to the paradox that none of the parts of time (past, present, future) appear to exist, Iamblichus suggested that time should be divided into a higher and a lower kind. The higher kind of time lies beyond the world of change, and always is (although it is still inferior to eternity, following Plato, Timaeus 37D); this “higher present” does not flow, because it is not subject to change, and so is not subjected to the paradox. The lower kind of time does flow, but the present moment “here” is not sizeless but has extension; thus it can be a part (cf. Sorabji 1983, chap. 3). The later Neoplatonist commentator Damascius stressed that the present moment could have size, a kind of irreducible extension, and therefore could be a part; he proposes that

Greek Neoplatonist Commentators on Aristotle    915 motion and change can occur by a kind of “leap,” where the body concerned vanishes from one part of time and reappears in the next, slightly analogous to a modern motion picture (Damascius, in Simplicius, On Aristotle’s ‘Physics’ 796, 32–​97,13; Damascius, On Plato’s ‘Parmenides’ 2, 241, 29–​242,5; 242, 9–​15, discussed in Sorabji 1983, ch. 5). Damascius also goes further, arguing that the whole of time in reality exists simultaneously (Simplicius 775, 33–​34; 798,4: discussion in Urmson and Siorvanes 1992, 8–​9). In response to Aristotle’s paradox that we cannot say quite when the present moment ceases, Damascius and Simplicius himself propose that an instant, in actuality, is just a division of time in potentiality (798, 9–​10; 799, 34); the divisions are executed in thought, not in reality (798,10–​11, a position also attributed to Alexander at 748, 23–​24). Simplicius suspects that Aristotle himself would have dealt with the paradoxes in this way (800, 21–​24) (cf. Urmson and Siorvanes 1992, 9).

6.5 World Picture 6.5.1 Does the World have a Beginning in Time? Aristotle, in contrast to many of his predecessors, had maintained that the world as a whole has no beginning or end in time. We cannot tell time without change, which is defined as “the actuality of the changeable qua changeable” (Physics 8.1, 251a9); and Aristotle argues at length that there cannot have been a “first change” (251b10) and there can be no final change (251b29–​252a5). By contrast, at least on the face of it, Plato’s Timaeus appears to tell the story of a first moment of creation in time, or rather, a moment in time when order was introduced into disorder by a creator, the Demiurge (e.g., Timaeus 52D). Aristotle already tells us that some contemporary Platonists, such as Xenocrates, understood this account metaphorically (On Heaven 1.10, 279b32–​280a), as a way of describing what is really a process without beginning or end, a continuous creation that would appear more compatible with Aristotle’s own account. Debate continued between proponents of a literal or metaphorical interpretation of Plato’s creation story (in antiquity, as recounted by Plutarch in the first centuries of our era in his On the Generation of the Soul in the Timaeus, and also in modern scholarship between commentators such as Guthrie, Vlastos, and Tarán). In antiquity it was the metaphorical interpretation that prevailed, and this became the position of the Neoplatonists (see, e.g., Proclus’ description of the world as “always arising” at On Plato’s Timaeus 1.294, 10–​12). As such, Aristotle’s account and Plato’s were judged compatible and harmonized, and Aristotle’s arguments against Plato could be treated as exercises in rhetoric or school polemics, not representative of a fundamental disagreement. This consensus in favor of the beginningless and endless world was much more difficult to reconcile with Christian doctrine. Philoponus, motivated at least in part by exegesis of scripture describing the world’s literal creation in time, developed a number of influential arguments against the Neoplatonist consensus (see Sorabji 1983, chap. 14, 17).

916   Late Antique and Early Byzantine Science He argued that if the world had no beginning, then past years were actually infinite in number; but the Neoplatonists accepted Aristotle’s view that this was absurd, for how could an actual infinity be traversed? And more puzzling still, if there had been an infinite number of years until now, then next year how many would there have been? Infinity with one added—​ which appeared to Philoponus prima facie to be an absurd notion. (Philoponus, Against Aristotle, in Simplicius, On Aristotle’s ‘Physics’ 1179, 15–​26; Against Proclus 9,14–​11,17; translated in Sorabji 2005, sec. 9(a)). To this Simplicius replied, drawing on Aristotle’s Physics 3.6–​8, that past years do not actually exist (On Aristotle’s ‘Physics’ 506, 3–​18), except in our imagination. (The debate raised interesting questions about the nature of mathematical infinity, and it has been pointed out that Georg Cantor offered an intuitive proof for several cardinalities of infinity, up to an infinity of infinities, which would raise difficulties for Philoponus’ case, although 14th-​century Latin thinkers, perhaps dependent on Arabic sources, already had articulated the possibility of different sizes of infinity; see Sorabji 2005, 175–​176 for further discussion and bibliography).

6.5.2 The Kosmos, Its Spatial Limits and Contents Together with the position that the world was beginningless in time, Aristotle maintained that it had limits in space, and that the world exhausted what there is. What, then, is in the world? It consists of a series of nested concentric spheres, with the fixed stars rotating steadily at the outside in a transparent sphere, and seven spheres inside it, answering to the five classical planets and the sun and moon (thus: Saturn, Jupiter, Mars, Venus, Mercury, the Sun and the Moon, then the Earth). While some of these bodies seem to rotate in a regular way, the planets seem to wander (whence their name planētes, “wanderers”) on irregular paths. To explain the apparent irregularities and answer the puzzle of how we could “save the phenomena” by explaining how the heavens really do all answer to a regular mathematical pattern of revolution, Aristotle and his predecessors proposed a series of as many as 55 concentric spheres, some counteracting the motions of the others (Metaphysics 12.8). Centuries of astronomical observation made it clear that Aristotle’s system was insufficient to explain the advance and retreat of the planets viewed from the earth (e.g., Simplicius, On Aristotle’s ‘On Heaven’ 504, 17–​506, 3). Later Aristotelians, like philosophers and astronomers from many different schools, tried different methods to save the phenomena and bridge the gap between the world as it presented itself to precise mathematical geometry and the world as it presented itself to the senses, including epicycles (circles on circles) (Simplicius, in Cael. 32.1–​29); the Almagest of Ptolemy in the 2nd century ce was a majestic and tremendously influential systematization of mathematical astronomy. Some also proposed that the earth might turn around the sun rather than vice versa (Aristarchus), a solution against which Simplicius argues in his commentary on Aristotle’s On Heaven (e.g., On Aristotle’s ‘On Heaven’ 444.33–​445.3). Proclus cuts to the core of the challenge, from a Neoplatonist vantage point, when he suggests that these mathematical structures, building on and correcting for Aristotle’s model, represent human constructions of an apparent reality whose true, intelligible nature only Plato grasped (On Plato’s Timaeus 3.95,34–​96,32). Moreover, as Siorvanes

Greek Neoplatonist Commentators on Aristotle    917 (1999, 304) observes, Proclus endorses both the arrangement in Plato’s Timaeus, which locates the sun as second to the earth, and the order of Ptolemy and the Chaldaean Oracles, which locates the sun in the middle of the seven spheres, and regards these two as disclosing reality from two different vantage points, in such a way that the “Chaldaean” view is metaphysically true and the Platonic order is physically true. As Proclus’ approach suggests, the challenge of “saving the phenomena” can be treated very much like Aristotle’s dialectical approach to physics, treating the phainomena as beliefs of the wise (in the commentators’ case, canonical texts to which they are committed) that need to be laid out in such a way that the majority of their puzzles (aporiai) can be solved. At the same time, as Sorabji (2007) has stressed, Proclus—​in allowing the planets to “choose” their paths—​has already diverged from the mechanical explanation attempted by Ptolemy.

7.  Concluding Remarks This chapter has surveyed the Greek Neoplatonic commentators’ reception of Aristotelian phusis and related core concepts, especially hylemorphism, causality, place, and time. I only touched briefly on the late ancient reception of Aristotelian biology, a rapidly growing field in its own right (for an exemplary study of one idea, embryogenesis, as it is developed in Aristotle, Alexander, and Simplicius, see Henry 2005; for the later Neoplatonic reception of Aristotelian psychology, including sub-​sensitive psychology, see Blumenthal 1996; for a survey of Neoplatonic biology in general, see Preus 2002). I  have not touched on ancient mechanism, the subject of an excellent recent survey by Berryman (2009). For other themes in the physics of the commentators, such as determinism and fate, mixture, light and optics, and a much more detailed treatment of dynamics, the reader is encouraged to turn to Sorabji (2005) with bibliography. The results of this survey chapter are be briefly summarized as follows. • The commentators accept Aristotle’s account of phusis as an internal principle of change and rest, but restrict the applicability of Aristotle’s natural philosophy to the visible and “sub-​Platonic” world, that is, from the earth up to the visible heavens (which are phusika, even if they do not possess an internal source of rest). • The commentators maintain that phusis must operate according to a higher Platonic paradigm, or model, as the account of the Timaeus would imply. They make Aristotle’s four modes of causation into six. • The commentators maintain that nature possesses a higher mode of contemplation, even if it is not “conscious” in the cognitive sense to which Alexander objects. • The commentators fuse the Aristotelian (five-​ elemental) and Platonic (four-​ elemental) accounts by suggesting that one of the four elements, fire, contains a kind of spectrum of kinds, of which the highest is immaterial, and for this reason is able to correspond to Aristotle’s heavenly element.

918   Late Antique and Early Byzantine Science • Philoponus argues against “natural place,” posits a theory of impetus or externally impressed force to replace Aristotle’s dynamics, and suggests “space” is really three-​ dimensional extension, which can operate as a kind of “prime matter” in replacement of the more ambiguous, purely propertyless subject that the Neoplatonists found in Aristotle’s account of matter (hulē). In developing each of these positions, the commentators’ methodology is to represent the positions of their predecessors, in greater or lesser detail, typically taking their starting point from the text of Aristotle, and attempt to resolve the puzzles, or aporiai, which arise from those positions, including the puzzle (from the integrative position of the commentators) of Aristotle’s compatibility with Plato. As this procedure reflects a methodology recommended by Aristotle, the commentators can be regarded as descendants of Aristotle, not always with respect to his particular philosophical positions, but certainly in method and approach to philosophical writing.

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920   Late Antique and Early Byzantine Science Sharples, R. W, and R. R.  K. Sorabji. Greek and Roman Philosophy, 100 BC—​200 ad. Supplement to Bulletin of Institute of Classical Studies 83.1 and 2.  London:  Institute of Classical Studies, 2007. Siorvanes, Lucas. Proclus:  Neo-​ Platonic Philosophy and Science. New Haven, CT:  Yale University Press, 1997. Sorabji, R. R. K. Time, Creation and the Continuum. London: Duckworth, 1983. —​—​—​. Matter, Space, and Motion. London: Duckworth, 1988. —​—​—​. Aristotle Transformed. London: Duckworth, 1990. 2nd ed. London: Bloomsbury, 2016. —​—​—​. The Philosophy of the Commentators, 200‒600 ad:  A Sourcebook. Vol. 2:  Physics. London: Duckworth, 2005. —​—​—​. Philoponus and the Rejection of Aristotelian Science. 2nd ed. Bulletin of the Institute of Classical Studies, supp. vol. 103. London: Institute of Classical Studies, 2010. —​—​—​. Aristotle Re-​ Interpreted:  New Findings on Seven Hundred Years of the Ancient Commentators. London: Bloomsbury, 2016. Steel, C. “Why Should We Prefer Plato’s Timaeus to Aristotle’s Physics? Proclus’ Critique of Aristotle’s Causal Explanation of the Physical World.” Bulletin of the Institute of Classical Studies, suppl. 78 (2003): 175–​187. —​—​—​. “Proclus’ Defence of the Timaeus Against Aristotle’s Objections. A  Reconstruction of a Lost Polemical Treatise.” In Plato’s Timaeus and the Foundations of Cosmology, ed. T. Leinkauf and C. Steel, 163–​193. Leuven: Leuven University Press, 2005. Tarrant, H. S. “Cultural and Religious Continuity:  2. Olympiodorus and the Surrender of Paganism.” In Conformity and Non-​conformity in Byzantium, ed. L. Garland, 181–​192. Amsterdam: Hakkert, 1997. Todd, R. B. Themistius on Aristotle’s Physics 1‒3. London: Duckworth, 2011. —​—​—​. Themistius on Aristotle’s Physics 5‒7. London: Duckworth, 2008. Tuominen, Miira. The Ancient Commentators on Plato and Aristotle. Durham: Acumen, 2009. Urmson, J. O., with L. Siorvanes. Simplicius, Corollaries on Place and Time. London: Duckworth, 1992. Wedin, Michael. Aristotle’s Theory of Substance:  The Categories and Metaphysics Zeta. Oxford: Oxford University Press, 2000. Westerink, L. G. “The Alexandrian Commentators and the Introductions to Their Commentaries.” In Sorabji 1990, 325–​348. Reprinted in 2nd ed., 2016, 349–​375. Wilberding, J. and C. Horn, eds. Neoplatonism and the Philosophy of Nature. Oxford: Oxford University Press, 2012. Wildberg, C. “Philosophy in the Age of Justinian.” In The Age of Justinian, ed. M. Maas, 316–​ 340. Cambridge: Cambridge University Press, 2005. —​—​—​. “Olympiodorus.” In Stanford Encyclopedia of Philosophy, ed. E. N. Zalta, 2007. Online. Available http://​plato.stanford.edu/​entries/​olympiodorus/​, January 2012.

chapter E4

Byz antine Geo g ra ph y Andreas Kuelzer

Geographical regions in their wide variety influence human ways of living and settling habits decisively, whether a desert, a harsh mountain range, or a fertile plain. Geographic phenomena such as mountains and volcanic landscapes, river deltas, extensive marshes, lakes, seas and ever-​changing coastlines, impenetrable woods, and deadly deserts governed the actions of Byzantine people, affected their journeys and their way of living, as well as trade and general communication. People were exposed to climatic forces more severely than today; people had to endure droughts and floods, storms, and frost periods. Under these circumstances they toiled, cultivated crops, and held livestock while operating with very modest tools. Therefore, geographic and climatic factors were of great importance: they left their mark on all people, on those who spent their lives in a remote valley in the highlands of Asia Minor or in the wide Thracian plains, as well as on the sailors cruising along the Aegean Sea or the eastern Mediterranean. Even though mobility was less intensive than nowadays, people gained impressions and individual perceptions of the area he (or more seldom, she) was moving around. Certainly, these perceptions can only be reconstructed if they were put into writing at a certain point. That implies that, on the one hand, geographical or climatic observations were preserved in various genres of Byzantine literature, but, on the other hand, the number of such remarks is very limited—​many observations were lost due to an insufficient or altogether nonexistent access to literacy. Other remarks, although written down at some time, were considered of inferior literary value and therefore no longer copied or passed on by the following generations. Problems of literacy and transmission of texts should not be confused with the fundamental question of human perception or the general relevance of geography in the life of Byzantine era people. In principle, the preserved Byzantine geographical literature can be divided into scientific texts that confront and comment on the relevant ancient scriptures, and into more practical texts written for civil or ecclesiastical administration, for guiding travelers over land or over sea, and notices based on travelers’ observations.

922   Late Antique and Early Byzantine Science

1.  The Ancient Heritage and Its Reception Geography in Byzantium means transmission of the ancient Greeks’ knowledge and the more or less critical handling of this material by certain scholars, via copying manuscripts, via making extracts from the old writings, or even via writing separate commentaries on various ideas. Homer (ca 8th century bce), in antiquity highly praised as the spiritual father of Greek geography (Strabo 1.1.1–​2, 1.1.11), had a very limited influence on Byzantine geographic thought, in spite of the high appreciation he enjoyed in other fields of knowledge. His geographic knowledge was essentially limited to the eastern Mediterranean and neglected the Far East and western Europe; even statements on the different climate zones hardly exist. His cosmological model of a flat earth covered with a sky dome in the form of a spherical iron bowl (Iliad 17.425; Odyssey 3.3; 15.329), resting on dark depths (Iliad 8.13–​16; 478–​479; 14.204; 15.188–​192), surrounded by a river Okeanos (Iliad 14.200–​201; 18.607–​609) with the sun and the stars rising from and setting into a stream every morning and every evening (Iliad 5.5–​6; 7.421–​423; 8.485–​486; Odyssey 19.433–​434) did not represent the ideas of the Byzantines, or at least left no perceptible traces. The same happened to the geographical ideas of the Greek pre-​Socratic philosophers, of the philosophers of the so-​called Milesian school, whose most famous representatives were Thales of Miletus (about 600 bce), Anaximenes, and Anaximander (both 6th century bce). Their writings are only fragmentarily preserved today. They regarded the earth as a flat disc, surrounded by an ocean, that floated either on the water or in the air, depending on the theory. Their opinions had just as little influence on Byzantine geographical concepts as the writings of Hecataeus of Miletus (ca 560–​480 bce) who expanded the knowledge of the ancient Greeks as far as India in the Far East and Gibraltar in the West. The same applies to the writings of the erudite Hellenistic geographers who worked in Alexandria, Pergamum and other new centers of learning, and tried to free their discipline from the influence of both history and philosophy and to link it more strongly to mathematics and astronomy. In this context Eratosthenes of Cyrene (ca 275–​ 195 bce) should be mentioned along with Aristarchus of Samos (ca 320–​250 bce). The former in his work Peri anametrēseōs tēs gēs had calculated the circumference of the earth as 252,000 stadia, about 45,460 km, which was astonishingly accurate—​today he is regarded as the founder of mathematical geography. Yet shortly after being published, the geographical concept of Eratosthenes was fiercely criticized because of its alleged imprecision, for example by Hipparchus of Nicaea (2nd century bce) and by Polybius (ca 200–​120 bce). Following their authority, the majority of scholars reverted to a simple description of countries and landscapes, to a more “practical geography.” They limited themselves to a description of the oikoumenē as the well-​known world (the term first in Herodotus 3.106); in ideal cases they traveled around before they wrote about particular regions. The ideas of separate continents in

Byzantine Geography   923 the world ocean, in essential features known already in the 5th century bce and developed on the basis of the theories of the five climatic zones and of the spherical earth, first manifested as oikoumenē and anti-​oikoumenē, later also as peri-​oikoumenē and as the continent of the antichthons, faded gradually into the background. Nevertheless, these theories were reprised in the geographical studies of Posidonius of Apamea (about 135–​ 51 bce), and they were significantly developed by Crates of Mallus (first half of the 2nd century bce). Even if it is unlikely that the older Heraclides Ponticus (about 390–​322 bce) proposed any heliocentric planetary system by the 4th century bce, Heliocentrism was proposed by Aristarchus of Samos around 280 bce. But this idea was rejected in favor of the geocentric theory of Aristotle (384–​322 bce), which manifested itself so obviously and therefore had to be true in the opinion of the majority. So the geocentric model remained the predominant doctrine throughout the whole Byzantine period. Those ancient works that had a formative influence on the geographical ideas of the Byzantines were first, the Geōgraphika written by Strabo of Amasia in Pontus (about 63 bce‒23 ce), a 17–​volume descriptive history, or chorography, of people and places, enriched with numerous digressions and, in many parts, a result of his observations; and second, the 8–​ volume Geōgraphikē huphēgēsis of the Alexandrian Claudius Ptolemaeus (about 100–​178 ce) that comprises methodical discussions and assigned coordinates to about 8,100 topographica and geographical features, based on astronomic data. The work describes the earth as a globe and as the center of the universe; it is the first surviving treatise that gives instructions on map-​making. Besides a world map, 26 local maps of the Roman provinces were drafted, clearly demarcated by latitudes and longitudes. Several Greek manuscripts (inter alia the 15th-​century manuscripts Laurentianus Conventi Soppressi 626, Vaticanus Urbinas Graecus 83, and Vindobonensis Historicus Graecus 1) named one Agathodaemon of Alexandria as painter of the maps; however, the date when the maps were created is still unknown, just as whether he painted only the world map or all the maps. Strabo’s critical analysis of his predecessors simply transmitted numerous ideas from the antecedent geographic works. His Geōgraphika was probably published posthumously, and initially it seems to have had no vast effect. Although the first evidence of this work being applied occurs in the writings of Dionysius Periegetes under Emperor Hadrian’s rule (117–​138 ce), it seems to have been extensively used only from the 6th century on, as far as the available information allows us to determine. In the Middle Byzantine period, scholars intensively studied Strabo’s text: the well-​educated Archbishop Arethas of Caesarea (about 860–​944) must be the author of the famous commentaries on Strabo, renowned for their elaborateness. The geographer’s impact on the writings of contemporary historians is evident, for example, Genesius, Theophanes Continuatus, or related texts from the so-​called Epitome-​group. Claudius Ptolemaeus (Ptolemy) undoubtedly exerted an even stronger influence on the Greek-​speaking world; it was he who so significantly formed the geographic ideas of Late Antiquity and the Byzantine millennium. The texts (Anōnumou) Diagnōsis en epitomē tēs en tēi sphairai geōgraphias (after 150 ce) and the almost 6-​volume Geōgraphia

924   Late Antique and Early Byzantine Science tēs oikoumenēs of Protagoras (3rd century; Photios, Bibliotheca cod. 188) formed already in pre-​Byzantine times two fascinating works that followed the tradition of the famous Alexandrian author. Marcian of Heraclea in Pontus, living in the 4th or the early 5th century, composed, among other writings that are largely lost today, the almost completely preserved Periplous Maris exteri, a coastal description covering the Far East and the Atlantic Ocean. He made explicit use of Ptolemy, even if only to cite an authority. The Geōgraphikē huphēgēsis was translated into Syriac and into Armenian by the early Byzantine period; at least three Arabic adaptations are known from the middle Byzantine period. Moreover, the oldest of the more than 50 surviving Greek manuscripts date to the same period; they witness the continuous preoccupation with Ptolemy’s geographical magnum opus and verify his impact on the Byzantine “view of the world.” Numerous Byzantine authors demonstrate acquaintance with the geographical work of the Alexandrian scholar.

2.  School Editions and Abstracts So the Byzantines were rather familiar with the testimonies of famous ancient geographers like Strabo or Ptolemy concerning the body of the earth, the structure of the oikoumenē, the location of the world oceans, or the accurate position of the high mountain ranges. The ancient geographical writings were often simplified both linguistically and in terms of content, and revised for school editions; furthermore, the adaptations were enlisted to comment on other geographical works. In this context, for example, one should mention Hupotupōsis geōgraphias en epitomē (“Short outline on geography”) by a student of Patriarch Photios (ca 810–​893) and the treatise Didaskalia pantodapnē (“Comprehensive instruction”) written by the prolific courtier Michael Psellus (about 1017–​1078); moreover, certain passages from the erudite textbook Sunopsis tōn phusikōn (“A general view on natural [phenomena]”) by the 11th-​century Antioch physician Symeon Seth. Another interesting work from the 12th century is the commentary on Dionysius Periegetes’ Periēgēsis tēs gēs (“Geographical description of the World”) by Eustathius of Thessalonica, an excellent rendering of the poetic late antique terrestrial description into prose (Geographi graeci minores 2 [1882] 201–​407). Among ancient geographers, Eustathius primarily resorted to Strabo and quoted Ptolemy less frequently. Curiously enough, he emphasized explicitly that the commentary was written for students and thus cannot reach the linguistic level of Dionysius, but rather is broader in scope and simpler in style. Literary works like this were rather popular in Byzantium. Authorless and difficult to date writings, which Armand Delatte published largely from manuscripts from the 15th century, were also meant as teaching material. An interesting text of this genre appears in the late 16th century codex Athen. Eth. Bibl. 1308; definitely older itself, it describes the 12 highest mountain ranges of the earth, the world oceans, the seven climatic zones, and the genesis of earthquakes, explaining all of them except for the one during the crucifixion of Jesus through natural causes.

Byzantine Geography   925

3.  Autonomous Geographic Works from Byzantium Although the majority of Byzantine geographic literature was created in discussion and examination of ancient writings, there are still several autonomous achievements in this field of research to mention. The most famous work is undoubtedly a geographical dictionary entitled Ethnika; originally consisting of 55 to 60 books, it was written by Stephen of Byzantium, a Christian grammarian, about whom little is known except that he lived during the reign of Emperor Justinian I (527–​565) in Constantinople. His work is a detailed catalogue of geographic names and grammatical derivations arranged in alphabetical order; it was probably used for reference by officials and soldiers in the hugely expanded Byzantine Empire. The text was drawn from numerous sources, including the works of Claudius Ptolemaeus, Pausanias, and Marcian of Heraclea; the Ethnika is the first well-​known Byzantine book that shows extensive use of Strabo’s Geōgraphika. The interesting eight-​volume regional history Isaurika by Kapiton of Lycia (also 6th century) is known to us primarily through Stephen’s work; likewise the Arabika, consisting of at least five books and composed by his contemporary Ouranios, who wrote, among other works, about the Arabic Nabataeans. The Ethnika is acknowledged here as an autonomous geographic work, because the author used his sources and references with a considerable portion of criticism. The book was certainly too voluminous with its ample information on etymologies, foundation legends, name alterations, historical anecdotes, and son; therefore, it was reduced to an epitome rather early by one Hermolaus, who dedicated his work to the Emperor Justinian. Whether the first (6th century) or the second emperor of this name (r. 685–​695 and 705–​7 11) is meant, is not clear at all. The complete version of Stephen’s work was still known in the 10th century but apparently lost soon afterward. The geographer Hierocles wrote his Sunekdēmos, a list of 64 eparchies (provinces) and 912 cities under Byzantine rule, already in the beginning of Emperor Justinian’s I  reign. Probably created for civil administration, the Sunekdēmos is arranged geographically: this is in sharp contrast to the Notitiae episcopatuum, which were composed for ecclesiastical administration and listed the hierarchical rank of metropolitans and suffragan bishoprics in every ecclesiastical province; the first of these Notitiae was produced during the reign of Emperor Heraclius (610–​641) and is almost a century younger than the work of Hierocles. His table, very important for our knowledge of the political geography of the 6th century, reflects the status before the imperial reforms in 535—​an important dating clue: Hierocles mentioned only one of the 27 cities that were renamed into either Justinianoupolis or Justiniana during the reign of Justinian I. The Sunekdēmos might be a revised edition of a similar work composed under the reign of Emperor Theodosius II (408–​450). Whereas the table of Hierocles was confined to the eastern part of the Roman Empire, an analogous work, written in the first quarter of the

926   Late Antique and Early Byzantine Science 7th century by a hardly known George of Cyprus, also includes the prefectures in Italy and in northern Africa. This textbook was then connected, in the middle of the 9th century, by the Armenian Basilius of Ialimbana, to a Notitia episcopatuum focused on the diocese of Constantinople. Stephen of Byzantium and Hierocles were the most important sources for the famous manual De thematibus by Constantine VII Porphyrogenitus. This early work of the scholar-​emperor was written in the 30s of the 10th century; it catalogues the individual provinces of the Byzantine Empire and provides explanations of particular terms. The Byzantines deliberately archaized geographical terms and tried to reconcile (not always correctly) the names of contemporary places and people with the expressions of classical authors. This habit constitutes a constant challenge for the modern scholar. Moreover, the Byzantines were not always familiar with these attempted reconciliations: therefore, many manuscripts of De thematibus and many other texts also contain dictionaries of ancient and contemporary names. Another famous manual of the emperor is De administrando imperio, created between 948 and 952. The book was written only for the use of Constantine’s son and successor, Romanus II, not for general publication. The aim was to educate the young emperor in governance issues; hence, it provides numerous ethnographies of peoples and geographic information about their habitats. Whereas all writings addressed so far pertained to the civil administration and state governance, the ecclesiastical administration was served by the abovementioned Notitiae episcopatuum. These are authorless catalogues of ecclesiastical provinces, arranged in hierarchical order—​the patriarch, followed by greater metropolitans (with suffragan sees), autocephalous metropolitans, archbishops, and simple bishops—​for ceremonial procedures, so that every incumbent was properly classified. More than 20 catalogs are known today; the first of these dates to the reign of Emperor Heraclius in the 7th century, the second was compiled between the 8th and the first quarter of the 9th centuries. These writings did not were not always truthful, sometimes listing theoretical claims for episcopal sees that had become titular (their cities lost to enemies and their bishops resident at Constantinople) or that remained vacant for long periods (no bishop appointed). The genre of Patria, a mixture of local history, topography, and urban legends, belongs to the geographical literature of an inferior standard. The genre appears for the first time in the late 3rd century, when a certain Callinicus (of Petrai) wrote a Patria of Rome, which survived only fragmentarily. Patria of many other cities, including Anazarbus in Cilicia, Aphrodisias in Caria, Berytos, Miletus, and Thessalonica are only known by being mentioned in later Byzantine writings. The only more or less complete collection is the Patria of Constantinople, preserved especially in the chronicle of the pagan Hesychius of Miletus (6th century). This one was substantially extended and supplied with similar texts in the late 10th or early 11th centuries, such as the legendary story about the construction of Hagia Sophia or the Parastaseis suntomoi khronikai with their special focus on the antique sculptures of the city.

Byzantine Geography   927

4.  Geographical Notices in Byzantine Literature Naturally, geographical remarks and notices can be found in many passages of Byzantine literature: works of historiography for example mention many place-​names as stages of an imperial military campaign, emphasize peculiar climatic phenomena, or refer to different cities, mountain ranges, and rivers when reporting about a barbarian invasion; encomia and the closely related ekphraseis (“descriptions”) are often dedicated to cities; epistles mention itineraries and particular geographical observations. Following are some interesting notices of individual authors and works. The anonymous school editions treating important rivers and oceans, the catalogues of holy mountains, and the accounts of climatic zones have been mentioned. Some of these works were absorbed into historiography: for example, in the Chronicon Paschale, a 7th-​century Byzantine universal chronicle of the world, one can find, after introductory reflections on Christian chronology and on the calculation of the Paschal cycle, an exhaustive account of climatic zones with 134 cities distributed into the individual zones. Catalogues of holy mountains were included in the 10th-​century chronicle of Joseph (?) Genesius, as well as in the approximately contemporary text collection of Theophanes Continuatus. Encomia and ekphraseis gave descriptions of cities already in the early Byzantine period; Libanius (ca 314‒after 393), for example, described in his famous Antiochikos (Oration 11) the geographical features and the extraordinary beauty of Antioch in great detail. The pagan rhetorician Himerius wrote an encomium paying tribute to the sights and beauties of Constantinople in the 4th century. The Roman historian Ammianus Marcellinus (ca 330–​395), of Greek descent but writing in Latin, wove many digressions into his spacious 31-​volume historical account Res Gestae that provided important information concerning geographical details, for instance in Egypt and in Persia (23.6); he also described the tsunami that devastated Alexandria and the shores of the Eastern Mediterranean in July 365 (26.10.15–​19). The church history of Philostorgius of Borissus (ca 368–​439), which survived in meager fragments because of its radical pro-​Arianism, contains some geographical remarks, inter alia concerning the Antioch suburb Daphne and the sources of the Jordan River, which originate in personal observations. In his voluminous history De bellis libri VIII, dealing with the wars of Emperor Justinian I against the Persian Sassanids, the Vandal kingdom in northern Africa, and the Ostrogoths in Italy, Procopius of Caesarea (ca 500–​562) often touched on geographical themes; among others, a passage concerning the Black Sea (8.1.7–​6.31) is famous. A separate work, the six-​volume De aedificiis, written ca 555–​559, was dedicated to the restoration and building activity of the emperor: volume 1 deals with Constantinople; volumes 2, 3, and 5 with Asia Minor; volume 4 with the Balkan Peninsula; and volume 6 with Africa. Unfortunately, some parts of this book are

928   Late Antique and Early Byzantine Science now lost. Procopius accompanied Justinian’s chief military commander Belisarius on different campaigns and saw personally numerous landscapes and areas of the East Roman Empire; furthermore, he had access to official documents; therefore, his statements are well informed. By characterizing settlements as polis (city), komē and chorion (village), or as proasteion (suburb, suburban house), he gave significant information concerning the dimension and importance of their status in the 6th century. Other contemporary historians also mentioned geographical phenomena: Agathias of Myrina (ca 536–​582/​94), for example, who continued the history of Procopius with his five-​volume Historiai, gave climatic information by describing the cold spell accompanying the earthquake of 557. Agathias’ work is also an important source for Persia before the rise of Islam (2.25–​28 and 4.24–​27; 5.3 on climate). The ambitious work of Theophylact Simokatta, describing in eight books the reign of Emperor Maurice (582–​602), contains numerous data concerning the Balkans; a very interesting digression deals with the Scythians in the extreme north. Very famous is the description of the Dead Sea (pp. 188.10–​189.2 D.) in the world chronicle Eklogē Chronographias (“Extract of Chronography”) of George Syncellus (died after 810), a monk who had lived many years in Palestine before going to Constantinople. The 10th-​century Suda, “fortress (against lack of education),” is a historical encyclopedia with about 31,000 entries; it contains much geographical information, using many ancient sources that are now lost. The earliest praise of Byzantium was written by the rhetorician Themistius already in the 4th century; thenceforth the phenomenon of laudes urbium is consequently documented over the whole Byzantine period.

5.  Geographic Information in the Records of Byzantine Ambassadors As mentioned, mobility in the Byzantine era was less pervasive than today. But one group was compelled to travel: ambassadors—​functionaries or scholars, who served as official representatives of the Byzantine Empire, and who had the authority to negotiate and to deliver the emperor’s messages to foreign peoples. At the same time, they were important informants about the habits and the culture of the “barbarian” world, about exotic cities and landscapes faraway from Constantinople. In Byzantium, political missions and ecclesiastical missions existed side by side; and travelers working in both fields were used as observers and as informants. The Egyptian Olympiodorus of Thebes (ca 370–​430) was sent on a mission to the Huns in the year 412. The record of his journey survived in fragments; but by reading them, one discovers he undertook a further journey to Athens in 415, and he traveled to Upper Egypt in 423. The records of the ambassadors, normally written in an elevated language, were collected in the imperial chancellery in Early and in early Middle Byzantine times; they were used for both information and education.

Byzantine Geography   929 This material served as a basis for Constantine Porphyrogenitus’s diplomatic manual Excerpta de legationibus (“Extracts about Embassies”) in the 10th century. This book is very important for our knowledge of the earlier texts: for example, it is the only source for the record of Priscus of Panion (ca 420–​472) concerning his embassy to the Huns in the year 449. Furthermore, it is the main source for Peter the Patrician’s (ca 500–​after 562) legation to the Persians in the year 562, which resulted in a 50-​year uninterrupted peace between Byzantium and the Sassanids. Nonnosus (first half of the 6th century), member of a Jewish family and therefore probably knowledgeable of Oriental languages, was a Byzantine ambassador, like his father Abram (524 and later) and his grandfather Euphrasius (502) before him; he led a mission to the Arabs and to Ethiopia in 533. His record was known to Patriarch Photios (Bibliotheca cod. 3) in the 9th century but was then lost; only a few fragments survived. Something similar happened to the record of Zemarchus of Cilicia, who was sent on a mission to Sogdiana by Emperor Justin II (565–​ 578); he stayed abroad for several years before returning to Constantinople. Inter alia he recorded interesting details concerning the local customs of Sogdiana; some fragments are preserved in the history of Menander Protector (also 6th century).

6.  Exploration Literature in Byzantium There is an abundant literature written by Byzantine ambassadors, but only a few texts can be assigned to explorers. This is amazing, especially in comparison with the numerous texts written by explorers that came down to us from the Arabic and Western worlds, such as Ibn Battuta (1304–​1369), Marco Polo (ca 1254–​1324), and Pedro Tafur (ca 1410–​1484), the only ones who need be mentioned. In Byzantium however, a certain Manuel Angelos is the only well-​known person who traveled for the simple reasons of curiosity and inquisitiveness. His journey lasted for more than nine years, from March 1342 to the late summer of 1351, and led from Constantinople through the Aegean Sea to Egypt and Syria, afterward to Cilicia, Cypru, and Crete, after that back to Constantinople by visiting different islands of the Aegean Sea. No documents from Early or Middle Byzantine periods are preserved.

7.  Geographical Observations Made by Merchants In Byzantium, and in many other parts of the Byzantine world, merchants were those who traveled most. They were important both as narrators and as messengers; they were mentioned frequently in literature, for example, in juridical texts, in historiography

930   Late Antique and Early Byzantine Science and in hagiography. But unlike their Latin competitors, they had in general neither enough education nor sufficient interest to record their impressions and observations. This means that Byzantine literature includes only a few texts that can be assigned to the merchants definitively. Always mentioned in this context is the Expositio totius mundi et gentium (“Sketch of the Whole World and its Peoples”), a 4th-​century geographical treatise preserved in two distinct Latin versions but probably originally written in Greek. Its anonymous author did write about climate and trade, about political facts, customs, and conventions. The description started in the Far East, touched India and Persia, Mesopotamia and Syria. From Arabia and Egypt it came to Asia Minor, to Thrace and Macedonia, to Greece and the landscapes in the western Mediterranean; the text ended with the reference to some famous islands, including Cyprus and Britannia. Distances were given in mansiones, units of a day’s journey. The Khristianikē topographia (“Christian Topography”), written by Cosmas Indicopleustes (Indian voyager), in the middle of the 6th century, is occasionally classified as a trade report: book 11 describes some landscapes in India and in Sri Lanka; the island is acknowledged as an important trade center, furthermore, local harbors and commodities like ivory were mentioned. But in spite of this, the book had no intention to report about daily life; Cosmas mentioned the facts in passing. The literary conception of his writing is theological. Therefore, firsthand information on trade was rare in Byzantium; for centuries, short notices in so-​called books of account were the most important sources, being little more than simple itineraries. Most of these documents were consumer items, soon becoming worthless and destroyed.

8.  Geographical Notices in Byzantine Pilgrims’ Literature The Byzantine pilgrims’ literature is divided into two different genres: first, travelers’ tales containing strong personal elements and many individual observations and remarks; and second, guidebooks, or proskynetaria, a kind of practical handbook, written to organize visits to the holy places at Constantinople or in Palestine, to guide pilgrims and to describe particular sights in great detail. Therefore the main characteristics of these writings are the form of catalogued lists, a tendency to completeness and the absence of personal elements. Guidebooks were carefully elaborated; the instructions of admired rhetoricians like Hermogenes of Tarsus (ca 160–​225 ce), Aphthonius of Antioch (second half of the 4th century or later) or Nicholas of Myra (5th century), on the right way to describe towns and buildings were diligently observed. Unlike the guidebooks, Byzantine pilgrims’ tales have a strong personal element: they are notes of real travelers, who have written their observations; the descriptions

Byzantine Geography   931 are more diverse, the itineraries are of higher individuality. Sometimes the readership is directly addressed; sometimes the authors distanced themselves from wondrous legends by using the phrase “It is said.” The oldest text of this genre is written by Epiphanius Hagiopolites after 638; it came down to us in four Greek manuscripts from Late Byzantine times and two different Slavonic versions from the 15th and 16th centuries. From these one can recognize three text versions: the first edition described a journey from Cyprus to Jerusalem and other places of the Holy Land. In later times, a copyist added passages concerning Egypt and Mount Sinai; this second version was also translated into Armenian. Furthermore, a third edition added a description of Galilee. Therefore, the original text of the otherwise unknown Epiphanius was reworked and the personal elements reduced; the account was enlarged to complete the picture of the whole Terra Sancta. (The earliest attested use of the term is in Justin Martyr, Dialogue with Trypho 80.)

8.  Missionaries and Saints Missionaries were also among the Byzantine era travelers. Widely known are the Byzantine missions to the Ostrogoths, to the Arabian Peninsula, to Ethiopia, and to the Far East. Very famous is the missionary work among the Slavic peoples of the Balkan Peninsula by Cyril and Methodius, the Greek brothers from Thessalonica, in the 9th century. The Christianization of Kievan Rus’ in 988 was one of the most important successes Byzantine missionaries ever had. Interestingly, no personal report of a Byzantine missionary is preserved today. By contrast, in the Latin world many reports written by missionaries survived, giving numerous details about foreign countries and strange behaviors, about travel conditions and climate. These Latin writings were intended to arouse interest in the individual reader, usually a theologian, to go on a missionary journey himself. But the Byzantine custom was different: missionary work was a political affair and supported by the emperor, not an individual concern. Therefore, there was no need for writings to spark interest in individual missionary work. However, in hagiography there is much information about itineraries, communication routes, guest houses, and other details of travel. The mobility of Byzantine saints was impressive; numerous Lives report about their extensive journeys: for example, St. Chariton in the 4th and St. Gerasimos in the 5th century traveled in the Terra Sancta; St. Theodore of Sykeon traveled around Asia Minor and Judaea in the 7th century. Indeed, the main intention of the Lives’ authors was not the description of geographical details or historical and social facts of life, but emphasis on the marvelous. Landscapes and cities were only mentioned as stages, as scenes for the saints’ action; therefore, in many cases the geographical “reality” described in the accounts is a kind of fiction. But for Byzantine readers it was absolutely trustworthy.

932   Late Antique and Early Byzantine Science

9.  Christian Geography The geographical and cosmological theories of the ancient pagan Greeks could only gain acceptance by the Byzantines after they had received the sanction of the church fathers. But in most cases, the theologians passed over the cosmological theories in silence; for instance, the Christian schools at Rome and at Gaza did not contribute to the development of an autonomous “Christian geography.” Lactantius (ca 250–​325) is the only well-​known author who wrote against the theory of the antipodeans (Divine Institutes 3.24); but most representatives of these two schools had obviously no real idea about it. The oldest representatives of the famous catechetical school of Alexandria acted in a similar way: ancient ideas concerning the shape of the oikoumenē could be found in different early Christian texts: for example, in the Miscellanies (Stromateis 5.6.33.1 or 5.12.80.1) written by Clement of Alexandria (ca 150–​215 ce; his work is not precisely dated), in the Legatio pro Christianis (8.4, 13.2, and 16.1) by Athenagoras of Athens (ca 177 ce), or in the manual Peri arkhōn (2.3.6) by Origen (between 220 and 230 ce). However, although the oikoumenē was mentioned, these texts did not go into detail. Many other theologians combined ideas and concepts concerning the shape of the oikoumenē and those concerning the earth as a whole. Most of these statements were only passing mentions; the writings of the older church fathers require careful reading. But some of the younger representatives of the school of Alexandria expressed their ideas concerning the sphericity of the earth and the universe more: important in this context is the Christian philosopher John Philoponus, also known as John of Alexandria (ca 490–​570). In his refutation of some of Aristotle’s doctrines On the Eternity of the World against Aristotle from 529, but also in his important theological work On the Construction of the World, written between 546 and 549, he tried to combine both the creation story of the Old Testament and the classical cosmological system of the pagans. One of his main preoccupations was the rejection of the classical idea of the eternity of the world promulgated by the philosophers Aristotle and Proclus. Even though numerous Christian theologians were open-​minded about ancient geographical concepts, acceptance was not all-​embracing: most of the church fathers who belonged to the so-​called school of Antioch rejected vehemently the ancient ideas of the sphericity of the earth and the universe. St. Theophilus of Antioch (d. between 183 and 185 ce) developed already in his important Apologia ad Autolycum (2.13, 32) a multitiered model of the universe, which was based on ancient near eastern concepts. In his eyes, the supporters of sphericity were simply ignorant. Diodorus of Tarsus (d. ca 394) refined the concept of a cosmological building; also his famous disciple Theodore of Mopsuestia (ca 350–​428) decisively denied the idea of sphericity of the earth. The latter was of the opinion that Moses’s tabernacle was a model of the world, the different stories represent earthly preparation and heavenly perfection of the human beings.

Byzantine Geography   933 Some other theologians of the Syrian school expressed similar opinions; most popular might be the abovementioned Cosmas Indicopleustes. Although born in Alexandria, he was a supporter of the Syrian ideas that he learned in Nisibis. As a very old man, Cosmas wrote his famous Khristianikē topographia around 550, directed primarily against the writings of John Philoponus. It is impossible to understand this book as an account of a merchant; it is a complex cosmological work of art: its theological intention, the complete rejection of pagan sciences by Christians, is expressed by the introductory phrase: “Pros tous khristianizein men ethelontas, kata tous exōthen de sphairoeidē ton ouranon nomizontas kai doxazontas” (Against those who want to be Christians, but believe in the sphericity of heaven, like the pagans do, and support this doctrine). The text is preserved in three Greek manuscripts today, it was also translated into Slavonic at an early stage; furthermore, some of the miniatures in the Greek manuscripts had a deep influence on miniatures drawn in the Middle Byzantine period. But one ought not to overestimate the significance of the text: Patriarch Photios criticized the Khristianikē topographia intensely in the 9th century (Bibl. cod. 36). The multitiered model of the universe, based on near eastern roots, withered in later periods; it left no traces in Byzantine thinking but was replaced by the geographic and cosmological doctrines of Greek antiquity. In conjunction with Christian Geography, one should remember the so-​called Tables of Nations, commentaries on Genesis 10, where the division of the earth between the three descendants of Noah—​Shem, Ham, Japhet, and their wives—​is reported. This report was taken as historical fact by the Byzantines. The genre was already established in Jewish literature: one can find a Table of Nations in Titus Flavius Josephus’ Antiquities of the Jews (1.6; ca 94 ce). The church father Hippolytus of Rome (ca 170–​236 ce) created the archetype of all Tables of Nations known in the Byzantine world. Its traces can be found in the famous chronicle of Sextus Iulius Africanus (died after 240 ce), in the Chronicon Paschale, in the chronicle of John Skylitzes (11th century), and in numerous anonymous Byzantine manuscripts from different centuries.

10.  Land and Sea Travel Guides: Itineraries, Periploi, and Portolan Charts Besides the mentioned pilgrims’ texts, there are numerous late antique and Byzantine writings with the intention to describe routes and roads and to mention distances between individual settlements. Most important are the itineraria, independent works mainly written in the first centuries of the Christian calendar and preserved in Latin. Greek itineraria were mostly composed in later times; normally they were not independent writings but part of a saint’s Life or a historical text. The only noteworthy

934   Late Antique and Early Byzantine Science exception is a papyrus from the 6th or 7th century that describes an itinerarium from Heliopolis in Egypt to Constantinople. Very important is the Latin Antonine itinerary (Itinerarium Antonini), probably composed in the late 3rd century by an unknown author. It mentions 17 main routes of the Roman Empire, furthermore numerous minor roads; it refers to Africa, Italy, and the Balkans, to parts of Asia Minor and Britain; it reports many settlements along the way. But at many points poor quality, inexactness, and confusion can be detected. Therefore, the Antonine itinerary is more likely a private collection of communication routes usable as a personal manual rather than an official document of the late Roman state. In the manuscripts, the Antonine itinerary usually is connected with an Itinerarium maritimum Antonini Augusti, a catalogue of Mediterranean Sea lanes, reporting distances, not travel time. The Itinerarium Burdigalense, also known as Itinerarium Hierosolymitanum was written by an anonymous author in 333; it described a journey from present-​day Bordeaux by land through northern Italy, the Danube valley to Constantinople, then through Asia Minor, Syria, and Judaea to Jerusalem. From the Terra Sancta the traveler went back to Constantinople, to Macedonia and Milan, where the text ended. The described route is quite unusual; normally travelers used the sea to reach the eastern Mediterranean. The text is more detailed than the Antonine itinerary; it mentions not only distances and important cities (civitates) but also roadhouses (mansiones) and places where one could change horses (mutationes). The author was probably an official or an administration employee using the cursus publicus; but there are also different theories, even a lady traveling because of religious affairs was suggested. There is no common scholarly opinion yet. But some passages in the text, for example forms of address to the reader, may be used as circumstantial evidence that the Itinerarium Burdigalense was written as a manual for travelers and not as a simple rec­ ord. Sometimes amazing is the author’s choice of the sights to mention: the famous Christian sights in Bethlehem and in Nazareth were omitted, and this despite that locations in the Terra Sancta were described in much greater detail than places in Europe or in Asia Minor. A Milanese manuscript of the 9th or 10th century contains the Itinerarium Alexandri, composed about 340 and dedicated to the Emperor Constantius II (337–​361); the work describes the route of Alexander the Great to Persia, against the background of current Byzantine problems with the Sassanids. Finally, in the late 4th century, an itinerary was written by a French or Spanish (monastic?) woman named Egeria or Aetheria. The text came down to us in one fragmentary manuscript, Codex Arretinus (11th century); it describes a pilgrimage to the Holy Land about 381 to 384. Egeria mentioned inter alia her travels through Egypt and the Sinai Peninsula, Syria, and Asia Minor to Constantinople. The second part of the account contains important information about contemporary liturgical worship in Jerusalem and about Christian customs in the Terra Sancta. Admittedly, the importance of the last-​mentioned writings to the Byzantines was minute; but for modern historians they are significant and deserve to be noted. A maritime correlate of the itinerary is the periplous, a list of ports, coastlines. and landmarks and of the intervening distances. The genre was developed in early

Byzantine Geography   935 antiquity; a famous representation is from the 6th century bce. The importance of the periploi grew during the time of Hellenism with its numerous expeditions to distant destinations. Most of the coastal itineraries concentrated on the Mediterranean Sea, on some coastal sections of the Atlantic Ocean, and on the Red Sea; but in the time of the Roman emperors, the Black Sea became a focus of attention. Already in the 3rd century, an anonymous author wrote the Anōnumou stadiasmos ētoi periplous tēs Megalēs Thalassēs, a fragmentarily preserved work covering the coastlines of Africa and Asia Minor, with the islands of Crete and Cyprus (Geographi graeci minores 1 [1882] 427–​514). Also in the late 6th century, the Anōnumou periplous Euxeinou Pontou was written. Perhaps the text was based on earlier models; but more than 40 references to current situations of the 6th century, to Alans and Ostrogoths, to the Turkish invasion of the Crimea, and so on, show its high topicality (Geographi graeci minores 1 [1882] 402–​423). It is not yet clear whether there is a connection between the ancient periploi and the Byzantine era portolans. Portolans are also descriptions of coastlines and harbors, either written or pictorial. The oldest portolans in Latin known to us are from the 13th century; portolans in Greek date mostly from the early post-​Byzantine period, even if the existence of older models from Byzantine times is unquestionable. The “Byzantine” portolans are always written:  not a single pictorial portolan chart with Greek inscriptions is preserved. Portolans were not used for education or reading pleasure; they were based on personal experiences of sailors and were composed to be used. Therefore, they are among the abovementioned practical handbooks. By this fact also the genre’s sparse manuscript tradition can be explained. Portolans noticed coves and bays, coastal features, cliffs, and sandbanks if they were important for shipping. This means the genre noticed many place-​names undocumented anywhere else; therefore reading portolans is of high importance to modern historians. Most of the portolans relevant to our context are dedicated to the Mediterranean Sea, the Sea of Marmara, and the Black Sea.

10. Geographic Maps The portolans lead to the subject of geographic maps, even if Byzantine portolans are preserved in writing (scriptura) without pictures. In contrast, the portolans from the western Latin world, in most cases, combine scriptura and pictura, written descriptions and visual representations of individual areas, often of larger parts of the Byzantine Empire. Nevertheless, properly Byzantine geographic maps containing Greek legends are rarely encountered. The problem of the maps of Ptolemy, their dating, and the question of their original affiliation to the text was mentioned above; from the 13th century onward one can find manuscripts of the Geōgraphikē huphēgēsis with maps and their Greek inscriptions. The oldest one known that has a world map and all 26 local maps is the severely damaged codex Seragliensis GI 57 from Istanbul

936   Late Antique and Early Byzantine Science from the late 13th century. Other impressive illustrated manuscripts with maps, maybe all of them, maybe some of them, are preserved in the libraries of Florence, Paris, the Vatican, and some other cities. The illustrations are sometimes marvelous, sometimes sketchy; but all are important representatives of the seldom-​preserved Byzantine geographic maps. When talking about Byzantine geographic maps, one must consider the so-​called Tabula Peutingeriana or Peutinger map, an itinerarium showing the communication roads of the Roman Empire (see figure E4.1). The map is preserved in a copy from the late 12th or early 13th century; it originally dates ca 435 ce (Weber 2012). It is a parchment scroll, about 6.75 meters long and only 34 centimeters high, and it currently shows in 11 sections the road system from Britain over the Mediterranean region as far as India and China. A lost 12th section may have presented the Iberian Peninsula. The map is named after a former owner, the humanist Konrad Peutinger (1465–​1547) from Augsburg. The Tabula Peutingeriana is one of the long Roman road maps that were drawn since the days of the Emperor Augustus (27 bce‒14 ce) but are today almost totally lost, but in all probability some of these maps were kept in the great libraries of the Byzantine Empire. Not only roads and traffic routes were depicted but also mountains and rivers, cities and villages, roadhouses, and mutationes. The three most important

Figure E4.1  Peutinger Table, section showing Constantinople. Wien Staatsbibliothek. Geography and fictional journeys.

Byzantine Geography   937 cities of the empire, Rome, Constantinople, and Antioch, were exceptionally dec­ orated; Constantinople presented as an imperial city is an important dating indicator for the original map. Further Byzantine world maps may be ignored here; but I  mention one important local map: in the church of St. George in Madaba, Jordan, there is a floor mosaic depicting the Terra Sancta (see. It dates to the time of the Emperor Justinian I (6th century). Originally, it measured 21 m x 7 m, today it is fragmentary, measuring 15.7 m x 5.6 m. The mosaic shows the Holy Land from Lebanon in the north to the Nile delta in the south, from the desert beyond the Dead Sea in the east to the Mediterranean shore in the west; Jerusalem is at the center of the composition. Most probably the map was composed by an unknown artist by using the Onomastikon written by Eusebius of Caesarea (ca 260/​264–​337/​340). It is very detailed and presents many Greek legends; its elaborateness makes it important for the historical geography of the region. The depiction of the Church Nea Anastasis in Jerusalem, which was dedicated in November 542, is important for dating the mosaic; buildings erected after the year 570 are not shown, so the time of its creation is clearly delimited. Finally, a genre of Byzantine literature should be mentioned that lies between reality and fiction: the so-​called Paradise journeys. While the literary genre of Byzantine afterlife journeys provides important information concerning historical events and public figures but nothing significant concerning geography, the case is quite different for Paradise journeys. The former texts were read either satirically (e.g., the Apocolocyntosis by Seneca, 1st century ce) or, more seldom, contemplatively; but the latter texts were understood as reality. Starting from Genesis 2:8 “And the LORD God planted a garden eastward in Eden,” the early Christians thought Paradise was a real place on earth, lying east of the oikoumenē, somewhere beyond India and China. An interesting source for this conviction is the Hodoiporia apo Edem tou paradeisou arkhi tōn Rōmaiōn, written in the 5th century by using the 4th-​century Expositio totius mundi et gentium (above) as a source. The text is an itinerary starting in Paradise and leading from India and Ethiopia through Persia and Arabia, Syria and Constantinople to Rome and to France; also the territory of the Huns is mentioned. The short text is preserved in several Greek manuscripts; an Iberian (Georgian) translation also exists. Paradise and its rivers are described in great detail; this can be understood as an indicator of importance. The distances between particular locations were mentioned; the numbers are not correct, indeed, but this is unimportant. Nevertheless, one can understand the idea of the anonymous author: Paradise is a real place on earth, and one can reach it by covering the distance. The text reflects the common understanding of the masses in the Byzantine world; possibly it was written against pagan ideas of afterlife that were still alive at the time of its composition. In any case, one can feel the theological aim of the text by reading its notices regarding whether Christians or pagans lived at particular places. It should be emphasized that Paradise as a real place on earth appears not only in the Hodoiporia apo Edem but also in numerous Latin writings, in western medieval cartography and in the Khristianikē topographia of Cosmas Indicopleustes.

938   Late Antique and Early Byzantine Science

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940   Late Antique and Early Byzantine Science Haury, Jacob. ed. Procopii Caesariensis opera omnia I–​II. De bellis libri VIII. Leipzig: Teubner, 1905. Reprint 1963. —​—​—​, ed. Procopii Caesariensis opera omnia IV. De aedificiis libri VI. Leipzig: Teubner, 1913. Reprint 1964. Hösch, E. “Gesandte. Byzanz und Abendland.” Lexikon des Mittelalters 4 (1989): 1364–​1365. Honigmann, Ernst. Die sieben Klimata und die πόλεις ἐπίσημοι:  Eine Untersuchung zur Geschichte der Geographie und Astrologie im Altertum und Mittelalter. Heidelberg: Winter, 1929. —​—​—​. “Stephanos Byzantios,” RE 3A.2 (1929): 2369–​2399. —​—​—​. “Die Notitia des Basileios von Ialimbana.” Byzantion 9 (1934): 205–​222. —​—​—​. “Un itinéraire à travers l’Empire Byzantin.” Byzantion 14 (1939): 645–​649. —​—​—​. Le Synekdémos d’Hiéroklès et l’opuscule géographique de Georges de Chypre. Brussels: Éditions de l’Institut de Philologie et d’Histoire Orientales et Slaves, 1939. Hunger, Herbert. Die hochsprachliche profane Literatur der Byzantiner. Vol. 1. Munich: Beck, 1978. Jones, A. H. M. The Cities of the Eastern Roman Provinces. 2nd ed. Oxford: Oxford University Press, 1971. Kaplony, Andreas. Konstantinopel und Damaskus. Gesandtschaften und Verträge zwischen Kaisern und Kalifen 639–​750. Berlin: Schwarz, 1996. Kelly, Gavin. “Ammianus and the Great Tsunami.” Journal of Roman Studies 94 (2004): 141–​167. —​—​—​. Ammianus Marcellinus:  The Allusive Historian. Cambridge:  Cambridge University Press, 2008. Kordosis, M. “The Limits of the Known Land (Ecumene) in the East According to Cosmas Indicopleutes. Tzinista (China) and the Ocean.” Byzantion 69 (1999): 99–​106. Kretschmer, Konrad. Die italienischen Portolane des Mittelalters. Ein Beitrag zur Geschichte der Kartographie und Nautik. Berlin: Olms, 1909. Krumbacher, Karl. Geschichte der byzantinischen Literatur von Justinian bis zum Ende des Oströmischen Reiches (527–​1453). Vol 1. 2nd ed. Munich 1897. Kubitschek, W. “Itinerarium Alexandri,” RE 18 (1916): 2363–​2366. Külzer, Andreas. Peregrinatio graeca in Terram Sanctam. Studien zu Pilgerführern und Reisebeschreibungen über Syrien, Palästina und den Sinai aus byzantinischer und metabyzantinischer Zeit. Frankfurt am Main: Lang, 1994. —​—​—​. “Die byzantinische Reiseliteratur. Anmerkungen zu ihrer literarischen Gestaltung.” Medium Aevum Quotidianum 40 (Krems/​Donau 1999): 35–​51. —​—​—​. “Reisende und Reiseliteratur im Byzantinischen Reich.” Symmeikta. Annual of the Institute for Byzantine Research 14 (2001): 77–​93. Laurent, V. “La “Notitia” de Basile l’Arménien.” Échos d’Orient 34 (1935): 439–​472. Lee, A. D. Information and Frontiers:  Roman Foreign Relations in Late Antiquity. Cambridge: Cambridge University Press, 1993. Lemerle, Paul. Le premier humanisme byzantin. Notes et remarques sur enseignement et culture à Byzance des origines au Xe siècle. Paris: Presses universitaires de France, 1971. Leppin, H. “Heretical Historiography: Philostorgius.” Studia Patristica 34 (2001): 111–​124. Lesmueller-​Werner, A., and I. Thurn, eds. Iosephi Genesii Regum libri quattor = Corpus Fontium Historiae Byzantinae 14. Berlin, New York: de Gruyter, 1978. Löhberg, Bernd. Das“ Itinerarium provincarium Antonini Augusti.” Ein kaiserzeitliches Straßenverzeichnis des Römischen Reiches. Berlin: Frank & Timme, 2006.

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chapter E5

B y z antine A l c h e my, or the E ra of System ati z at i on Cristina Viano

1.  Introduction: Byzantine Egypt and the Period of the Commentators The Byzantine period of Egypt begins at the death of emperor Theodosius I in 395 ce, when the province of Aegyptus came under the Eastern Roman Empire. It ends under the reign of Heraclius, with the Arab conquest in 640 ce. Byzantine Egypt experienced a period of peace, which extends from the 5th to the beginning of the 7th century, during which Alexandria is at the center of intense intellectual and spiritual activity. Philosophical and scientific debates continue to flourish, and lively doctrinal disputes arise around the tenets of Christianity, which intersect with the doctrines of Gnosticism and Hermetism. In this bustling atmosphere, Greek alchemy experiences a crucial moment in its development, because at that period doctrines and operations and the conceptual tools for thinking are developed and defined that will be the basis for all subsequent periods. This period is characterized indeed by a generation of “commentators” tied to the Neoplatonic milieu, like Synesius (4th century ce), Olympiodorus (6th century ce) and Stephanus (7th century ce). The writings of these commentators, designed primarily to clarify the thinking of the great figures of previous generations, including Democritus and Zosimos, represent the most advanced stage of ancient alchemical theory. We are witnessing a genuine process of defining and systematizing alchemical doctrine through the intellectual tools of philosophy available to these authors. This process, already begun by previous authors, now finds its full realization. From this perspective, through the systematic search for causes, historia of the recipes is integrated

944   Late Antique and Early Byzantine Science through theōria. Indeed, these authors, seeking to develop the links between theory and practice, between nature and technē (art), between the doctrine of transmutation, philosophical theories of matter on one hand, and technical processes on the other, laid the basis for a reflection on the possibility and on the nature of alchemy as an autonomous knowledge. It was also at that period, around the 7th century, that the corpus of alchemical texts began to be assembled under its very particular form of an anthology, essentially of extracts, as found in a large number of manuscripts, among which these three are the most important: (1) the oldest and most beautiful, the Marcianus Graecus 299 (M) (10th–11th century), brought back from Byzantium by Cardinal Bessarion in the 15th century and currently kept at the Library of St. Mark in Venice; (2) the Parisinus Graecus 2325 (B), of the 13th century; and (3) the Parisinus Graecus 2327 (A), copied in 1478. Finally, it is in the 5th century that authors external to alchemy explicitly speak of alchemy as a contemporary practice to produce gold starting from other metals. Proclus (5th century ce) compares astronomers who make astronomical tables to “those who claim to produce gold by the mixture of certain species (of metals)” (On Plato’s ‘Republic’ 2.234.14–​25 Kroll). Aeneas of Gaza (5th–​6th centuries ce), Christian philosopher and orator, pupil of the Neoplatonist Hierocles, talks about the possibility of improving the material of bodies by changing their form, and offers the example of those who produce gold by melting together and dyeing silver and tin (Theophrastus, 71 Barth). Here it is proposed to develop a picture of the most characteristic aspects of the alchemy of that period starting from the specific contributions of its most representative protagonists. This presentation seeks to answer two closely related questions, which are essential for identifying and understanding this complex and paradoxical knowl­ edge, which will not even receive a proper name until a relatively late period. Indeed, the Greek term chēmeia is found in Stephanus in the 7th century, and the Latin term alchimia, an Arabic derivation, appears only in the Western world in the 12th century. The first question is essentially internal to the texts: How did the alchemical authors view their knowledge? We seek to understand, through the methodological reflections of the authors, how they defined, and what epistemological status they attributed to, their field. The second question is external and concerns our epistemological approach to this knowledge: How should we study the alchemical texts? Can one sketch the rules of a proper approach that can take account at once of the multiple facets and also of the unique specificity of this cultural phenomenon we call Greco-​Alexandrian alchemy?

2.  The Protagonists and the Question of Pseudepigraphy To locate the generation of the commentators and show their position in the core of Greek alchemy, we must draw a brief sketch of its historical development. Greek alchemical literature is usually divided into three parts.

Byzantine Alchemy   945 The first part is located between the 1st and 3rd centuries ce. It includes the chemical recipes of the Physika and mystika attributed to “Democritus” (1st–2nd centuries ce) and the anonymous papyri of Leiden and Stockholm (3rd century ce). These recipes focus on imitation of gold, silver, precious stones, and purple. One finds there the idea of the fundamental unity of matter and that of the relations of sympathy between substances, expressed by the famous “small” formula revealed by mage Ostanes, which can be considered as the zero degree of alchemical theorizing, in the essentially technical context of the recipes: “Nature is delighted with nature, nature conquers nature, nature dominates nature” (Hē phusis tē phusei terpetai, kai hē phusis tēn phusin nika, kai hē phusis tēn phusin kratei). In these recipes the model of production of gold seems to be that of an imitation (mimesis) through coloring that acts on the external properties of bodies. This notion of imitation is the crux of the old conception of the art, and contains, as we shall see, in embryo the idea of transmutation. At this stage we also see reported a series of short quotes or treatises of the mythical “old authors” such as Hermes, Agathodaimon, Isis, Cleopatra, Mary the Jewess, Ostanes, Pammenes, and Pibechius (between the 1st and 3rd century ce). The second period is that of authors properly so-​called:  Zosimos of Panopolis, Pelagios, and Iamblichus (3rd–4th century). Zosimos appears as the greatest figure of the Greco-​Egyptian alchemy. Coming from Panopolis of Egypt, he perhaps lived in Alexandria around 300 ce. From his work, we have fragments gathered in four groups in the manuscripts:  the Authentic Memoirs, the Chapters to Eusebia, the Chapters to Theodore, and the Final Account with two excerpts from the Book of Sophē. One of the major problems is to identify the “28 books kata stoicheion” (in alphabetical order) mentioned by the Byzantine lexicon Suda, which seem to comprehend the entirety of the work of Zosimos and to relate them to the titles transmitted by direct and indirect traditions. Among the most famous pieces should be mentioned: On the Letter Omega and the three Visions, which are part of the Authentic Memoirs; the Visions describe dreams that unveiled to Zosimos the properties of metals. Metal-​processing operations are accompanied by a ritualization of the symbols of death and of resurrection, and of purifying the mind of matter. Indeed, the concept of metals is often paralleled in Zosimos with the concept, inspired by Gnostic and hermetic thought, of the double nature of humans, composed of body and spirit, of soma and pneuma. Finally, the third and final period is precisely the one that interests us:  that of the commentators. The most important are Synesius (4th century), Olympiodorus (6th century), and Stephanus (7th century). Close to Stephanus are four poems transmitted under the names of Heliodorus, Theophrastus, Hierotheus, and Archelaus (7th century). Later, perhaps between the 6th and 8th centuries, two anonymous commentators, commonly called the Christian Philosopher and the Anonymous Philosopher, lead directly to the period of the most extensive compilation of the main manuscript of the collection, the Marcianus Graecus 299. Indeed, it is assumed that this anthology was compiled in Byzantium in the 7th century, at the period of Heraclius, by a certain Theodore, who wrote the verse preface, which is found at the beginning of this manuscript (folio 5v), and who was probably a pupil of Stephanus. Thereafter, the alchemical tradition in Byzantium continues with Michael

946   Late Antique and Early Byzantine Science Psellus (11th century), Nikephoros Blemmydes (13th century), and Cosmas (15th century). The issue of identification of the commentators Olympiodorus and Stephanus with their namesakes the Neoplatonic commentators was raised very early by historians of alchemy and until now has made much ink flow. Indeed, in the alchemical literature, pseudepigraphy is a frequent phenomenon. In the corpus, we can find Plato, Aristotle, Democritus, and Theophrastus mentioned among the alchemical authors. From a chronological point of view, however, Olympiodorus and Stephanus constitute the borderline between these obviously false attributions and authentic attributions to known characters, such as Psellus. In the corpus of Greek alchemists these two authors are defined as “the masters famous everywhere and worldwide, the new exegetes of Plato and Aristotle” (Berthelot and Ruelle, Collection des anciens alchimistes grecs vol. 2, 425.4; hereafter CAAG). And there is good reason to attribute the writings of Olympiodorus and Stephanus, at least in their original versions, to their Neoplatonist namesakes. Indeed, the latest studies are turning more and more toward the hypothesis of identity, but for Olympiodorus, because of the especially composite and discontinuous form of his work, the question of attribution is more complex and delicate than in the case of Stephanus, who offers on the contrary a more homogeneous collection of treatises. As we shall see, the commentary of Olympiodorus the alchemist is an exemplary product of the alchemical literature.

2.1 Synesius Synesius is the author of a commentary on the Physika kai mystika of pseudo-​ Democritus in the form of a dialogue entitled Synesius to Dioscorus, Commentary on the Book of Democritus (CAAG vol. 2, 56.20–​69.11). Synesius is unknown to Zosimos but cited by Olympiodorus, who inserts long sections of Synesius in his commentary On the Kat’energeian of Zosimus. Dioscorus had been, as indicated by Synesius himself, a priest of Serapis in Alexandria. Synesius has been identified with the homonymous Christian bishop of Cyrene, Neoplatonic and student of Hypatia, but the dedication to Dioscorus, pagan priest, makes this argument difficult to sustain. In addition, this dedication shows that the work of Synesius is prior to the destruction of the Alexandrian Serapeion (391 ce). The conclusion of the dialog Synesius to Dioscoros reads (CAAG 2.69.5 and 11): “it suffices to say this briefly,” and a few lines later: “With the help of God, I will begin my review (hupomnēma).” This makes one think that it is at once a summary (or extract) and a preamble to a more extensive work. However, the text that has reached us presents an orderly and systematic development. The exegetical intent is explicit from the beginning:  it is necessary to investigate the writings of Democritus, to learn his thought and the order of succession of his teachings (CAAG vol. 2, p. 57.17).

Byzantine Alchemy   947 Democritus’ oath to reveal nothing clearly to anyone is explained in the sense that we should not reveal teachings to outsiders but reserve them solely for initiates and practiced minds (CAAG vol. 2, p. 58.12). The multiplicity of names that Democritus has given to substances thus has the goal of exercising and testing the intelligence of adepts (CAAG vol. 2, p. 59.5). The exegesis of Synesius bears at once on practical explanations (e.g., “the dissolution of metallic bodies” means bringing metals to the liquid state, CAAG vol. 2, p. 58.22), and on general principles (for example, the enunciation of the principle that liquids derive from solids, relative to coloring principles provided by dissolution, called “flowers,” CAAG vol. 2, p. 59.17). As in most of the texts of that period, the object of the research is identified with agents of transformations of matter (CAAG vol. 2, p. 59.25). The cause of the transformation is an active principle, called “divine water”, mercury, “chrysocolla,” or raw sulfur, and acts by dissolution. Mercury is at once the dyeing agent and the prime metallic matter, understood as the common substrate of the transformations and the principle of liquidity (CAAG vol. 2, p. 61.1). One can detect in the explanations of the general principles of the transformation of metals the strong influence of Aristotelian terminology. First, the object of the research is identified as an efficient cause. Then, the fabrication of metals is conceived as a mixture (mixis), especially among liquids (which according to Aristotle is the optimal condition, cf. Generation and Corruption 1.10, 328b 1); the preliminary condition is that of dissolution, which in Aristotle represents the culmination of the separation of compounds, thus of mixtures (see Meteorology 4.1, 379a4–​11). The transformation is conceived as a change of specific quality, generally through color. Mercury is compared to the material worked by the artisan (CAAG vol. 2, p. 62.23) who can change only the form. The distinction between potential and activity is applied to the coloring activity of mercury: “in activity it remains white, in potential it becomes yellow” (CAAG vol. 2, p. 63.6). As we will see in other authors, Synesius presents a natural conception of alchemy: it is always nature that, ultimately, is the true principle agent of the operations. The task of the artisan is to create the conditions so that the active properties, buried in the substances, become operative and act on the substances themselves in virtue of their affinity.

2.2 Olympiodorus Olympiodorus is one of the most interesting authors of the alchemical corpus. The question of attributing the Commentary On the “Kat’energeian” of Zosimos to his namesake the Neoplatonic commentator touches on two issues vital to the understanding of Greco-​Alexandrian alchemy: the constitution of treatises in the corpus, and the interest of Neoplatonist exegesis on Aristotle in alchemy. For this reason, it is worthwhile to devote to him a more detailed analysis.

948   Late Antique and Early Byzantine Science Let’s start with the Neoplatonic philosopher. Olympiodorus, pupil of Ammonius, taught the philosophy of Plato and Aristotle in Alexandria in the second half of the 6th century. Pagan and defender of Hellenism, he will have Christian successors, such as David (aka Elias) and Stephanus. We still have his three Platonic commentaries: on the Alcibiades I, on the Gorgias, and on the Phaedo, and two Aristotelian commentaries, one on the Categories (which contains the usual Prolegomena to the philosophy of Aristotle), and the other on the Meteorology, as well as fragments on the On Interpretation. Among his works, the only one that can be dated with certainty is the commentary to the Meteorologica, where Olympiodorus mentions (CAAG vol. 2, p. 52.31) a comet that made its appearance in 565 ce. The work of Olympiodorus is a rich source of information on cultural conditions and educational methods of Alexandria in the 6th century. A very typical form characterizes his comments: they are composed of a certain number of lessons (praxeis), each with the general explanation (theōria) and a particular explanation, of a section of text from Aristotle (generally designated as lexis). Following the tradition of the school of Alexandria, Olympiodorus was interested in Aristotle’s logic and natural philosophy. In particular, his commentary on the Meteorologica is an extremely interesting work for the history of science. Olympiodorus completes and fixes the Aristotelian classification of meteorological and chemical phenomena, thus performing a tremendous job of systematizing notions sometimes barely sketched by Aristotle, like that of “chemical analysis” (diagnosis) of homogeneous bodies in book 4 (On Aristotle’s ‘Meteorology’, p. 274.25–​29). He takes part in the debates of the commentators on difficult and problematic issues of the Aristotelian text, such as the theory of vision, on how the rays of the sun warm the air, or on the origin of the saltiness of the sea. Finally, it transmits much information about the state of science and technology of its period, such as mathematics, optics, astronomy, medicine, agriculture, and metallurgy. As for the commentary on book 4 of the Meteorologica, the first “chemical” treatise of antiquity, the systematic influence of Olympiodorus is fundamental: he contributes significantly toward defining a new field of investigation on the properties, states, and transformations of sublunary matter. His commentary is the most widely used not only by Arabic and Renaissance authors but also by Greek and medieval alchemists. It is therefore not surprising that there has survived under the name of Olympiodorus one of the most “philosophical” writings of the corpus of Greek alchemists, which presents itself as the commentary on a (lost) treatise of Zosimus and on the sayings of other ancient alchemists (CAAG vol. 2, p. 69.12—​104.7). In the principal manuscript of the corpus, the Marcianus Graecus 299 (M), the treatise has the title: “Olympiodorus, philosopher of Alexandria, On the book About the Action of Zosimos everything that was said by Hermes and the philosophers” (eis to Olympiodorou philosophou alexandreōs Kat’energeian Zosimou osa apo Hermou tōn philosophōn ēsan eirēmena). In the other manuscripts one finds:  “The Philosopher Olympiodorus to Petasius, king of Armenia, About the divine and sacred art of the stone of the philosophers,” where Petasius is probably a fictitious name and “philosophers’ stone” is a late term, added later by scribes to define the content of the commentary.

Byzantine Alchemy   949 The author explicitly presents his commentary as a work at once exegetical and doxographical. He explicitly claims that Greek philosophy, including pre-​Socratic philosophy, is the epistemological basis of transmutation. Indeed, near the middle of commentary (CAAG vol. 2, pp. 79.11–​85.5; par. 18–​27), Olympiodorus sets out the opinions of nine pre-​Socratic philosophers (Melissus, Parmenides, Thales, Diogenes, Heraclitus, Hippasus, Xenophanes, Anaximenes, and Anaximander) on the sole principle of things, and then sketches a comparison between these theses and those of the principal masters of the alchemical art (Zosimos, Chymes, Agathodaimōn, and Hermes) on the efficient principle of transmutation, designated as “divine water” (theion hudōr). Like most texts of the corpus of Greek alchemists, the commentary of Olympiodorus presents a composite and seemingly unstructured nature. It has neither preface nor conclusion: it begins and ends abruptly. One can divide the text into two sections. Only the first (CAAG vol. 2, pp. 69.12–​77.14; par. 1–​14) presents a coherent structure: the author begins by commenting on a saying of Zosimos about the operation to extract gold flakes from ore, through “maceration” (taricheia) and “washing” (plusis). Par. 1–​7 follow the typical schema of Olympiodorus the commentator: first the lemma, the phrase of Zosimos to explicate, and then a general explanation (theōria), and after that the detailed exegesis of terms (lexis). The general explanation also introduces the theme of the obscurity of the “ancients,” extended to Plato and Aristotle, which has a dual purpose, to hide the doctrine from the uninitiated and to stimulate adepts to research. Then he introduces gold “soldering” (chrysocolla: par. 8–​11), which consists of collecting the gold particles obtained into a homogeneous body. These two specific operations, separation and reunion, are here interpreted as allegories of the transmutation of metals. The three types of dyeing of the ancient alchemists come next (par. 11–​14): one that dissipates, one that dissipates slowly, and one that does not dissipate. The third attributes to metals an indelible nature. This means, in operative terms, to fix the color of a metal in a persistent manner. The second section—​the most extended part of the text (CAAG vol. 2, pp. 77.15–​104.7; par. 15–​55)—​consists of a suite of unstructured excerpta and digressions, accompanied by notes on the main alchemical operations. Par. 16 is focused on fire, because according to Zosimos, moderate fire has a fundamental function in the practice of the art of transmutation since it is the principle agent. The reflection on fire leads to the function of the four elements and theories of the pre-​Socratics on principles. In par. 18 a doxographic presentation starts on pre-​ Socratic doctrines about the single principle, which extends from par. 19 to par. 25. The author then compares (par. 25–​27) those principles with the principles of the ancient alchemists. The second half of the treatise (par. 28–​55) reproduces the arguments of the first part, plus the description of the stages of transmutation and theorizing of the prime metallic material. Par. 28 considers the status that the elements had for ancient alchemists: they constitute the dry, warm, cold, and wet bodies. Par. 32 returns to the distinction between a stable body and an unstable body sketched in par. 15. Olympiodorus now distinguishes substances and incorporeal substances, that is to say, between the fusible metallic substances and ores that have not been subjected to fire. The fragment of

950   Late Antique and Early Byzantine Science Zosimos’ Final Account about the role of alchemy among the kings of Egypt (par. 35) is connected to the discourse on minerals. From par. 36, Olympiodorus fixes attention on the prime metallic material, and he reports the dialogue between Synesius and Dioscorus on mercury. After reflections on the separative function of white, and the “comprehensive” function of black, in coloration (par. 38), Olympiodorus identifies, as Zosimos did, the prime metallic material with black lead. In par. 43, the divine water is cited as responsible for transmutation. In par. 44, Zosimos defines lead by the symbol of the philosophical egg formed of the four elements. The following paragraphs discuss the “powers” of lead and stages of transmutation, assimilated to colors (black, white, yellow, and red). In par. 54 we find a reflection on the art of transmutation, which is called eidikē (special) and not koinē (common). The conclusion (par. 55) recapitulates some key concepts of the work: substances like molybdochalc (lead-​copper) and etesian stone, the fusion and production of gold, the causal action of fire. Beyond this appearance of disorder, one can grasp a rational and coherent design as the treatise unfolds, revealed by two threads. The first is the red thread of the logic that links the alchemical operations, the principles, and the fundamental substances, which shows a progression in the presentation of the components of alchemy, ranging from basic operations (levigating, fusing, dyeing) to its active and material principles, to finish with epistemological considerations on this discipline as technē. The second red thread consists of expressions that one can define as “joining and accompanying,” where the author speaks in the first person and signals the transition between the different parts, as well as the purpose, method, and internal organization of his effort. His work proves to be an epitome and a summary with a protreptic goal, offering a selection of testimonies, with commentaries, extracted from the writings of the ancient alchemists, but also from philosophers properly so-​called, on the foundations of the art (the operations, the ingredients, and also the history). It seems addressed to someone young and high ranking, with the aim of offering him a “comprehensive view of the complete art” (par. 38). This suggests that at the origin of the text we have, there must have been a now-​ lost work of Olympiodorus, composed in a more structured form. The text that we have would consist of at least two layers:  the commentary of Olympiodorus on the Kat’energeian of Zosimos, and the arrangement by a compiler. This person could have copied Olympiodorus up to a point and then added a series of notes on the main alchemical operations, accompanied by excerpta of Zosimos and other alchemical authors, organizing everything according to the double criterion mentioned. Presumably, the original piece and a good part of the doxography on pre-​Socratics come directly from the commentary on the Kat’energeian by Olympiodorus the Neoplatonist. It is also entirely plausible that the Kat’energeian of Zosimus was already a doxographic work that concerned the opinions of alchemists, and that Olympiodorus in his commentary added a doxography on the pre-​Socratics, which is structured according to the typical pattern of Neoplatonic doxographies. The parts that derive directly from the commentary of Olympiodorus are characterized precisely by striking similarities that are formal (like the typical schema of Neoplatonic commentary in the beginning of the treatise and the

Byzantine Alchemy   951 arrangement of the doxography), terminological, and conceptual, with the commentary on the Meteorologica, and other works of Olympiodorus the Neoplatonic. Now if this is true, we can explain how later, this text was attributed in its entirety to Olympiodorus of Alexandria, by a sort of “attraction” of the initial part. The compiler could not have intended to allocate the patchwork to the name of Olympiodorus. The title only reflects precisely what this book is: the commentary of Olympiodorus on Zosimos and a collection of excerpta. As for the compiler, one could probably think of Theodore, who had assembled the entire collection of alchemical texts. Thus, the whole debate on the authenticity must be set in a new perspective, because the situation of this text is not that of a pseudepigraphy in the usual sense, but that of a typical product of this sui generis scientific literature that is Greco-​Alexandrian alchemy. The issue of pseudepigraphy among Greek alchemists thus rejoins that of the place of alchemy with respect to the official philosophical knowledge of its period. We will return to why Olympiodorus the commentator might have been interested in alchemy.

2.3 Stephanus Stephanus is the author of nine praxeis (lessons) on the divine and sacred art and a letter to Theodore (Ideler [1841] 1963, 2.199–​253). Lesson 9 is addressed to the Emperor Heraclius and therefore can be dated in the years of his rule (610–​641 ce). Some astronomical data in his work would moreover enable us to date it to exactly 617 ce. We saw that in the corpus of Greek alchemists, Stephanus is mentioned with Olympiodorus among “the masters famous everywhere and worldwide, new exegetes of Plato and Aristotle.” Indeed, the Emperor Heraclius appointed him “worldwide professor,” that is, professor of the imperial school of Constantinople. The current scholarly trend is to consider this Stephanus of Alexandria identical to the Neoplatonic commentator on Plato and Aristotle, author of a commentary on the On Interpretation and one on the third book of the On the Soul, and to Stephanus of Athens, commentator on Hippocrates. He would also commented on the Handy Tables of Theon of Alexandria and written an Apotelesmatical Treatise addressed to his pupil Timotheos. In his alchemical work, Stephanus comments in a very rhetorical style on the ancient alchemists, and he connects alchemy to medicine, astrology, mathematics, and music. He declares alchemy compatible with Christianity and defines it as “mystical” knowl­ edge, woven into a cosmology based on the principles of unity and universal sympathy. Alchemical transformations are considered natural and enter a close relation of analogies and correspondences between the microcosm and the macrocosm, the human body and the four elements, the heavenly bodies and earthly bodies. Berthelot characterized the commentaries of Synesius and Olympiodorus as “mystical commentaries” and attributed to them an undeniable philosophical value. He considered, however, successive commentators, such as Stephanus, the Christian Philosopher, and Anonymous, as “Byzantine glossators” who have expressed, in

952   Late Antique and Early Byzantine Science an exalted tone, scholastic subtleties devoid of any scientific interest (CAAG vol. 3, p. 377). But on the contrary, the Praxeis of Stephanus are very interesting philosophically, from the point of view of both method and contents. Indeed, on the one hand, Stephanus plans to build a new system through the critical comparison of theories and admission of their difference. This form of “status quaestionis” of existing theories is one of the most “scientific” aspects, in the modern sense, of the work of Stephanus. On the other hand, he creates a synthesis of Aristotelian, Platonic, and Neoplatonic doctrines to build his alchemical doctrine. In particular, he presents a model of matter and the transformations of metals that is one of the most original in the corpus of Greek alchemists, since it appears to be based both on the theory of surfaces in Plato’s Timaeus, and on the theory of exhalations in Aristotle’s Meteorology. Indeed, to explain the constitutions of metals, Stephanus introduces “bodies indivisible and without parts,” the “very special figures” that are fundamentally “solids of every kind extended in three dimensions, and composed of length, width, and depth” (praxis 6, p. 223.22 Ideler). These are “planar surfaces” (epipeda) that correspond to the ethereal particles resulting from the decomposition of the metal body (praxis 3, p. 209.4 Ideler), a decomposition necessary so that the dyeing spirit can slip into a body and achieve the transmutation. The vaporous exhalation (“dyeing spirit,” pneuma, “cloud”), responsible for composing and coloring metals, is thus likened to the planar surface. An abstract geometric principle is thus identified with something physical and elemental (pneuma, humid exhalation, made of water and air), but subtle and rarefied, at the limit of body. The work of Stephanus was well-​known by the Arabs. According to the Arab-​Latin tradition transmitted by the Morienus (Stavenhagen 1974), it will be precisely one of his students, the monk Morienus (or Marianos), who will broadcast alchemy in the Arab world between 675 and 700 ce, by initiating the Ummayad prince Khalid ibn Yazid (Bacchi and Martelli 2009).

2.4 The Christian Philosopher, the Anonymous Philosopher, and the Four Alchemical Poems We thus arrive—​with Stephanus and two anonymous commentators commonly called the “Christian Philosopher” (CAAG vol. 2, pp. 395.1–​421.5) and the “Anepigraphos” (or Anonymous) (CAAG vol. 2, pp. 421.8–​441.25)—​at the period when the first collection of Greek alchemists was constituted. As in other “commentators,” these two anonymous works present themselves as compilations, with commentaries, based on ancient writers (Hermes, Zosimos, Democritus), about specific topics or questions. For example, the Christian wrote a work Objection That Divine Water Is One According to Species (CAAG vol. 2, p. 405.6), and the Anonymous wrote a work On the Divine Water Eater of Whitening (CAAG vol.

Byzantine Alchemy   953 2, p. 421.6). As Berthelot remarked, these compilations, especially that of the Christian, follow the general system adopted by Byzantines of the 8th and 10th centuries, which was to draw from ancient authors excerpts and summaries, such as those by Photius and Constantine Porphyrogenitus, a method that has preserved fragments but also contributed to the dismemberment of the texts. Berthelot records a dozen fragments of the Christian Philosopher, which concern essentially the notion of divine water and the method and operations of the science. As with Synesius and other commentators, the obscurity of the language of the ancient alchemists is explained as having the dual purpose of deceiving the jealous and of exercising the minds of adepts. As for the divine water, the active principle of transmutation, the Christian insists upon the apparent disagreement among the ancient alchemists as to its designations, and especially the meaning of its unity (CAAG vol. 2, pp. 400.9‒401.16). As Zosimos would already have done, the Christian wants to show the basic agreement among the authors about the specific unity of this principle (CAAG vol. 2, p. 40.5). In particular, he shows that Democritus speaks of the unique species in general, and that Zosimos speaks of its multiple material species (CAAG vol. 2, p. 407.6), and he concludes that ultimately all multiplicity is reduced to unity. Some considerations bear on the method. The distinctions of materials and treatments show the influence of the descriptions of states of physical bodies (liquids, solids, composite nature) and transformative processes (cooking, melting, decomposition by fire or liquid) in book 4 of Aristotle’s Meteorology. The treatments are compared to planar geometric figures (CAAG vol. 2, p. 414.13‒415.9), a comparison that recalls the concept of metals by Stephanus and Plato’s Timaeus. Finally, the Christian applies the dialectical method of Plato, which divides and unites by species and genera, to the explanation of the operations, with the aim of clarity (CAAG vol. 2, p. 418.4). Far from being without scientific interest, the compilations of the Christian show a direct application of the conceptual tools of philosophy, especially of Aristotle and of Plato, to alchemical exegesis. One notes also some features of classical exegesis by the commentators, such as the search for agreement among opinions and the effort to derive the multiplicity of principles from a single one. The “Anonymous” presents a doxography on the “prime ministers” of aurifaction. He mentions Hermes, John the Archpriest, Democritus, Zosimos, and then “the famous worldwide philosophers, commentators of Plato and of Aristotle, who used dialectical principles, Olympiodorus and Stephanus”: they deepened aurifaction, they composed vast commentaries, and they bound by oath the composition of the mystery (CAAG vol. 2, p. 425.4). In particular, the Anonymous examines the mixture of substances by liquid means, without the assistance of the fire of which Olympiodorus also speaks (CAAG vol. 2, p. 426.7). There is still, as we saw with Synesius, influence from the Aristotelian theory of mixture, the basic composition of all natural bodies (CAAG vol. 2, p.  439.21). As for methodology, the Anonymous makes a curious analogy between the general and

954   Late Antique and Early Byzantine Science specific instruments of music and the general and specific parts of the alchemical science (CAAG vol. 2, p. 433.11–​441.25). Finally, close to Stephanus are four iambic poems on the divine art, placed under the names of Heliodorus, Theophrastus, Archelaus, and Hierotheus (7th–​8th centuries ce). These poems, highly mystical in inspiration, contain litanies about gold and show parallels with Stephanus in style and in content. Some scholars think the names probably refer to a single character, namely Heliodorus, who said he sent his poems to the emperor Theodosius, probably Theodosius III (716–​7 17 ce).

3.  The Alchemists and Their Knowledge 3.1 Transmutation and Its Principles Although these authors have their individual characteristics, from their writings we can reconstruct the lines of a fairly homogeneous theory of transmutation. The idea of the transmutation is based on the concept that all metals are constituted of the same material. We must first remove the qualities that particularize a metal, reverting it to the indeterminate prime metallic material, and then assign to it the properties of gold. Thus, the production of gold results from a synthesis out of a common and receptive prime metallic material, onto which are incorporated the “qualities,” that is, substances which are responsible for the coloration or transmutation into gold, according to the principles of sympathy. Among these substances, “divine water” (theion hudōr) or “sulfur water” (hudōr tou theiou) plays a fundamental role. It is frequently indicated as the goal of research and the principal agent of transmutation. It is an active principle derived from the metallic material itself, endowed with a double power, generative and destructive, which one then causes to act on the material itself. The common metallic material is not a substrate inseparable from the form, unknowable and indeterminate in itself, but is a concrete body having an independent existence and on which one can operate. It can be black lead or mercury. Similarly, the active principle is identified with dyeing agents, which in practice are volatile substances, such as mercury vapor. The distinction that the alchemists made, starting with Zosimos, between two components in metals, the one nonvolatile (sōma) and the other volatile (pneuma), was surely inspired by observing the coloring action of some vapors on solid metals, such as mercury and arsenic vapors that give a silvery color to copper. Often, transformation into gold is described as a deep dyeing. From this perspective, the coloring agent and the colored body become a single thing through transmutation.

Byzantine Alchemy   955

3.2 The Discipline and Its Method We now turn to some reflections of the alchemists on the nature and method of their knowledge. Let us start with Olympiodorus. We saw that he presented his writing both as a commentary and protreptic book, addressed to someone who wants to learn the principles of alchemy. It defines both the object of research and the method. Consequently, it is, in the intention of the author (or his compiler), a philosophical work, not just a technical treatise. Indeed, in his treatise, he designates the discipline sometimes as technē, sometimes as philosophy. The inextricable link between the two is expressed early in his doxographic statement where he says that the ancient (alchemists) were properly philosophers and addressed themselves to philosophers, that they introduced philosophy to technē, and that their writings were doctrines and not works (CAAG vol. 2, p. 79.16–​20). Stephanus, too, speaks of “philosophy,” which he identified with the imitation of god: “So there is a great relationship among the principles, especially between God and the philosophical soul. For what is that philosophy, if not assimilation to God, as far as it is possible for a human?” The philosopher, bringing the multiplicity of compositions to unity, will succeed in “theoretical and diagnostic accuracy” (praxis 6, p. 224.25 Ideler). The most important features of the method described above are, firstly, the profound study and critical comparison of all philosophical theories on the subject, and secondly, the construction, from these, of a philosophical system of nature. Stephanus also designates this discipline as chēmeia and distinguishes it as “mythical” (muthikē, fabulous) and “mystical” (mustikē, symbolic, allegorical, but also for insiders). The mythical is reduced to a mass of empty statements, whereas: “The mystical chemistry methodically deals with the creation of the world by the Word, so that the man inspired by God and born of him is instructed by a proper effort (eutheias ergasias) and by divine and mystical statements” (Letter to Theodore, p. 208.29 Ideler). These passages show that, for the alchemist, to know and to make, or better, to remake, are the two inseparable moments of a single act: it is through analysis, the reconstruction of the unity and accuracy of the process, that the work of the craftsman reproduces the organization of the world. Note that the analysis is not just about the distinction of the components but also about the “theories” that concern the compositions. The Christian, in a writing entitled What Is the Purpose of This Treatise, characterizes the knowledge in question as both “divine science” (theia epistēmē) and as “valuable and excellent philosophy” (entimos kai aristē philosophia) (CAAG vol. 2, p. 415.10). We saw that he applies to the operations the dialectical method that divides and unites by species and genera. The Anonymous, for his part, compares alchemy to music to show the affinity of the structure of these two disciplines, characterized by the development of multiple practical applications rigorously regulated by a single principle (CAAG vol. 2, p. 437.13).

956   Late Antique and Early Byzantine Science Note that these authors agree on two fundamental points: the need to proceed by a rigorous method, and also their own philosophical identity. Indeed, with the exception of Stephanus, who first employs (only once) the proper term chēmeia, all alchemists, including Stephanus, refer to themselves and their predecessors as “philosophers” and conceive their knowledge as a philosophy, an art (technē) or science (epistēmē), often accompanied with attributes such as “divine,” “excellent,” and “universal.” The epistemological status of this discipline is that of a reflection at once on the theory and practice, on the natural world, and on the rational method of the technē. Theory and practice are always dialectically and indissolubly linked. Stephanus speaks of “theoretical practice” (theōrētikē praxis) and “practical theory” (praktikē theōria) (praxis 1, p. 201.27–​33 Ideler). Medicine often appears as the most appropriate term of comparison for this form of knowledge. This is in fact a dual theoretical education, concerning on the one hand the principles of nature, and on the other of the principles of medicine. Aristotle also said that the “expert” (empeiroi) physicians are those who complete their education through manuals (Nicomachean Ethics 10.10, 1181b2–​5). These manuals classify particular cases according to general principles. As for the relationship between technē and nature, we have seen in the Greek alchemical texts the emergence of a view by which the technitē, just like the doctor, does not replace nature but creates conditions for nature to act, so that natural processes can happen. In Olympiodorus’ commentary, one finds this idea repeated in several places, shared with Zosimos. The correct method is to proceed according to nature, without violence or opposition to it. Ultimately, it is nature that acts because man cannot replace it. This method demands, therefore, a profound knowledge of the specific properties of bodies to make them react naturally. We can now summarize some characteristics of the alchemical literature of the commentators. First, we found that most of these treatises are excerpts and summaries of other lost works, but they nevertheless have an order and purpose. The exegetical intention is often declared and focuses especially on the deliberate obscurity of the authors. This obscurity has a double explanation: first, it is a strategy for defending the doctrine against those who do not deserve it; second, it has the pedagogical and protreptic function to exercise the intelligence of adepts and push their minds toward the ultimate principles. These are the same reasons that the Neoplatonic commentators give for the obscurity (asapheia) of Aristotle’s writings. For example, Simplicius attributes obscurity to the precise and concise language of Aristotle, who often expresses in a few syllables what another would have said in numerous clauses. Next, the exegesis of the Alexandrian alchemical commentators touches on both the practice of operations and the theoretical and methodological principles, frequently expressed through well-​ known concepts of Aristotelian natural philosophy (e.g., notions of mixing, of change of species, of potential/​actuality, of matter/​form), or of Platonic natural philosophy (such as elementary surfaces which form bodies).

Byzantine Alchemy   957 Finally, all the Greek alchemical commentators, having identified the basic purpose of research with the principle responsible for transmutation, generally identified with the divine water (the “philosopher’s stone” of the Middle Ages), that which represents, in Aristotelian terms, a form of efficient and effective causality. Alchemists consider this goal, like the art and method concerned with it, unique. On this point, one can observe, especially in doxographies, research on the agreement among opinions, both of alchemical authors as well as of philosophers, such as the pre-​Socratics, Plato, and Aristotle. However, the agreement among the doctrines of Aristotle and Plato on a single object of research is also a common topos of Neoplatonic exegesis.

3.3 Philosophy and Alchemy: The Case of Olympiodorus Although one can spot among Greek alchemists the influence of the philosophy of their period, testimonies about alchemy are rare in the writings of contemporary philosophers. Thus, even if one can perceive many similarities in the alchemical commentary of Olympiodorus with the commentary on the Meteorology, as well as with other texts of Olympiodorus the Neoplatonist, in contrast, in the commentary on the Meteorology, there is no explicit connection with the art of transmutation. One may thus wonder what interest a Platonist philosopher like Olympiodorus could have in alchemy. One can overcome this impasse by noting that what we now mean by “alchemy” would not be perceived in the same way in the period of Olympiodorus and Stephanus. When we talk about alchemy, we immediately think of transmutation, of knowledge defined and characterized by a precisely determined goal, the transformation of lead into gold, and so forth. Indeed, while this may be true for alchemy during the Middle Ages, Western and Arabic, the boundaries of this knowledge would have seemed much more fluid in the Greco-​Alexandrian world. First, the proper name of this knowledge, “al-​chemia,” is an Arabic term consisting of the article “al” and a Greek word of uncertain etymology, “chēmeia, chumeia.” This is also a late term, used by the Byzantines. We saw that on one occasion Stephanus employed it. The Byzantine lexicon Suda (10th century) defines “chēmeia” as the art of making money and gold (Χ–​280). As we have seen, the authors speak instead of the “divine art,” of the “great science,” of “philosophy.” Its scope is not only the production of gold and of precious metals, or the path of self-​transformation, but the primary recipes also concern the coloring of stones and fabrics, that is, the production of pigments. Hence the use of a repertory of organic and inorganic substances and processes that affect matter and matter’s transformations. The revolutionary concept—​revolutionary in the Greek world—​of transmutation is absent from the first “technical” treatises, but it appears in the more philosophical authors such as Zosimos (4th century), and then in the commentators. And even among those authors who speak of transmutation, there are also concrete substances and clearly identifiable procedures, which are in no way mysterious or

958   Late Antique and Early Byzantine Science metaphysical. This is the case with the descriptions of the distillation devices of Zosimus, whose ambix (a term that will, via Arabic “al-​anbīq,” give us the well-​known “alembic”), or as we shall see later, the recipe for making “black bronze” found in fragments of Zosimos in Syriac, or Olympiodorus’ description of “maceration” and the phases of extraction and washing of gold ore. It is therefore understandable that Olympiodorus, the commentator on the Meteorologica, could be interested in these texts we group in the category of Greek alchemy, to fill out his commentary and update the Aristotelian data, especially those of book 4 about craft skills. For example, Olympiodorus mentions glass artisans (On Aristotle’s ‘Meteorology’, p. 331.1 Stüve), while Aristotle never mentions artisanal glass. Olympiodorus describes techniques of purifying and refining metal, effecting a separation of metal from its impurities, primarily of an earthy nature, or of one metal from another, as in the case of silver and gold. In particular, he explains the metaphorical “boiling” of gold in Meteorology 4.3 (380b29), in terms of a technique that has been identified with “cupellation” (which involved separating the metals by an oxidation, during which the impurities were absorbed in part by the cup into which the mixture had been poured; p. 292 Stüve). It is interesting to note that for Olympiodorus, each metal is a different species. Separation of silver and gold by heat is cited as an example of the fact that heat unites things of the same species (homoioeidē) but separates things of different species (anomoioeidē) (pp. 274.38‒275.1 Stüve). So, it is not absurd to suppose that Olympiodorus the commentator on Aristotle might have wanted to go further and choose to comment on a work by one of the most prominent authors of this science under construction, namely the Kat’energeian of Zosimos of Panopolis, which probably was already itself a doxographic and protreptic work on the foundations of alchemy. That’s why Olympiodorus represents an emblematic case of Alexandrian alchemy and constitutes a fundamental step in the epistemological identification of this fluid knowl­ edge and the transition from the chemistry of the Meteorology to alchemy. This transition will in turn be theorized and formalized in the Middle Ages by authors such as Albert the Great, Avicenna, and Averroes.

4. Conclusions: Methodological Questions; Toward a Multidisciplinary Approach Now we come to the second question posed: How should we study Byzantine alchemy? What is the approach most consistent with its specific nature? This question is crucial for all periods of the history of alchemy. But the period of the commentators is privileged because it contains an explicit epistemological reflection on an already established tradition. From this, one can envisage an interdisciplinary

Byzantine Alchemy   959 approach, which can account, in a fruitful way, for the composite nature of the writings and for the wealth of content that this tradition conveys.

4.1 A Fluid Manuscript Tradition The relationships among the three main manuscripts containing the alchemical corpus—​M, B, and A—​have long been discussed. They indeed display important textual differences in the number and in the organization of the texts they contain. The structure of M would seem dictated by a theoretical choice, B would be more practical, and A would have both features at once. The tradition of Greek alchemical texts is “fluid,” meaning open to additions, alterations, clarifications, rewrites, and updates. Like other practical scientific texts, these writings were considered texts for use, as instruments to adapt to the latest discoveries and to the experiments performed by their authors. Furthermore, various anthologies of alchemical texts circulating in the Byzantine period were the sources of the chief manuscripts and were the explanation for their composite nature, as well as differences in presentation and elaboration of the same material. However, this situation calls for a revision and adaptation of the usual criteria of philology, because one is dealing with a literature sui generis whose contents evolve over time. Indeed it has to do not with reconstituting a unitary text in its original form out of the manuscript transmission, as could be done for a treatise of Aristotle or a dialogue of Plato, but with understanding the reasons for the choices, presentations, and taxonomies adopted in different witnesses, which precisely reflects the ongoing constitution of alchemical knowledge. Therefore, the choice to provide a “broad” critical apparatus, as recent editors of Greek alchemical texts have chosen to do, based on the principal manuscripts, on the indirect tradition of testimonia, and on parallel passages in the alchemical corpus, as well as on the Syriac versions, is fundamental. Now, these two characteristics of the manuscript tradition of alchemical texts, fluidity and anthological character, paradoxically seem to reduce the importance of the question of relationships and mutual dependence of manuscripts, since each witness has its own scientific value and history just as much as do each treatise or group of treatises.

4.2. Composite Knowledge, Varied Competences We have already noted that the nature of the Greco-​Alexandrian alchemical knowledge appears undeniably twofold: theoretical and practical. It comprises texts and recipes that concern at once mystical, physical, and cosmological ideas, and the production of concrete and historically identifiable objects, such as working and coloring of metals, fabrics, and precious stones. So, it concerns not just the ideal goal, dreamed of and never attained, of aurifaction, that is to say the production of gold out of other metals. The earliest texts are probably artisan’s notebooks, published in the milieu of the goldsmiths

960   Late Antique and Early Byzantine Science of the Egyptian pharaohs. That is why we can consider Greek alchemy as a domain shared between the history of philosophy and of religion, between philology and the history of science and technology, a composite subject that therefore demands sharing of many competences, not only theoretical and historical but also practical and technical, in direct contact with matter, such as archeology, metallurgy, and chemistry that studies the materials and their transformations by artistic processes. On this point, I would like to cite two recent and emblematic examples of the fertility of an interdisciplinary collaboration among philologists, historians, archaeologists, and chemists around a common object of study. The first consists of the recipe for making “black bronze” found in fragments of Zosimos in Syriac (Cambridge Manuscript Mm.6.29). This is the only ancient recipe that we have for this famous and mysterious “black bronze” of Corinth, prized by the Romans and mentioned by Pliny (34.8), which is a real head-​scratcher for archaeologists and chemists who have long wondered about the link between the allusions of the classical authors and some objects in museums that have an amazing black patina. Modern laboratory analyses reconstructed the history of this technique, which involved enriching a copper alloy with a small amount of gold and/​or silver, which then enabled, via a chemical surface treatment, the formation of an artificial black patina that was particularly shiny and served to emphasize the beauty of the metallic decorations. The Syriac recipes of Zosimos are the only ancient recipes for this technique that have survived, and their reproduction could provide the key to this process, on the condition of a very close cooperation with philologists to decipher the texts. The second example concerns the first lines of commentary of Olympiodorus on the Kat’energeian of Zosimos, speaking about “maceration” (taricheia), the paradigmatic operation of processing gold ore, involving several stages. Here Olympiodorus commented on the passage of Zosimos regarding the operation of extracting flakes of gold ore, through “maceration” (taricheia) and “washing” (plusis) (1–​7), followed by the description of “soldering” (chrysocolla) the gold (8–​11), which is collecting the gold particles obtained into a homogeneous body. These two specific operations, separation and reunion, are here interpreted as allegories of the transmutation of metals but, in fact, the exegesis of Olympiodorus, beyond a number of obscurities, seems essentially technical and refers to real processes concerning the steps, the times, the tools, and the phases of the operation of levigating gold ore. Now among nonalchemical testimonies, these technical stages of ore extraction and its processing up to its transformation into gold are described in detail by the geographer Agatharchides, tutor to Ptolemy III (2nd century bce), who left a vivid account of the activities of the gold mines in the Eastern Desert (Diodorus 3.12.1–​14.5; Strabo 16.4.5–​20, and Photius, Library, 250). This testimony is not entirely outside the corpus since we find an abstract in the alchemical manuscript Marcianus 229 (folii 138–​141). The precise descriptions of Agatharchides on the four fundamental technical operations of ore processing—​crushing, grinding, washing, (or levigating), and refining—​ allow confirmation that the passage from Olympiodorus referred to real procedures, long-​established and which would form the fundamental technical basis against which

Byzantine Alchemy   961 alchemists developed their theoretical reflection, both in theorizing methodological principles and in the allegories of transmutation. But there is also another very recent and concrete testimony on the procedure for extracting and washing the gold ore, which represents another element of crucial importance for reconstructing the operations of the Greek alchemists. These are the results of excavations in Egypt in 2013 at the gold-​mining sites of the Ptolemaic period (late 4th to mid-​3rd century bce) at Samut, by the French mission in the Eastern Desert (Brun et al. 2013). The great clarity of the surface remains revealed facilities illustrating different stages of the work: first the mechanical phase of the sorting; crushing blocks of gold-​bearing quartz; transformation into “flour” (powdered ore) by mills; then the washing phase, in washing basins, for separating the metal particles to melt; and finally the metallurgical phase of refining on site, shown by the presence of an oven. The testimony of Agatharchides was essential in interpreting the remains of these facilities. Indeed, the four basic technical operations of transforming ore after its exit from the mine that he described, crushing, grinding, washing, and refining, have been located on the site. By putting together the pieces of this puzzle, we can advance a hypothetical reconstruction of what Olympiodorus tells us in his commentary, and we can show that Olympiodorus, or Zosimos, refer to concrete and real operations. These two examples illustrate well the fecundity and the necessity of applying a multidisciplinary approach to the Greek alchemical texts. Indeed, on one hand, the appeal to other disciplines and evidence, whether literary, archaeological, or chemical, allows us to interpret the alchemical texts. On the other, alchemical texts shed light on the historical and archaeological investigations. In the current state of research in this area, it appears essential to continue research on a multidisciplinary front and enhance the systematic and positive side of alchemy, which is legitimate because the ancient authors often opposed natural and rational research as a deceptive practice subject to the laws of chance and the will of demons.

Bibliography Texts Albini, Francesca, ed., Michele Psello, La Crisopea:  ovvero come fabbricare l’oro. Genova: Edizioni culturali internazionali, 1988. Bidez, Joseph, Franz Cumont, J. L. Heiberg, and Otto Lagercrantz, ed. Catalogue des manuscrits alchimiques grecs. 8 vols. Bruxelles: Lamertin, 1924–​1932. Berthelot, Marcellin, and C.-​É. Ruelle. [CAAG]. Collection des anciens alchimistes grecs. 3 vol. Paris: Steinheil, 1888–​1889. Reprint Osnabrück: Otto Zeller Verlag, 1967. Vol. 1, Introduction, by Berthelot; vol. 2, Greek texts; and vol. 3, French translations. Colinet, Andrée, ed. Alchimistes grecs. Vol. 10: Anonyme de Zuretti. Paris: Les Belles Lettres, 2000. —​—​—​, Alchimistes grecs. Vol. 11: Recettes alchimiques (Par. Gr. 2419; Holkhamicus 109)—​ Cosmas le Hiéromoine—​Chrysopée. Paris: Les Belles Lettres, 2010.

962   Late Antique and Early Byzantine Science Goldschmidt, Günther. Heliodori carmina quattuor ad fidem codicis Cassellani. Giessen: Töpelmann, 1923. Halleux, Robert. Alchimistes grecs. Vol. 1: Papyrus de Leyde, Papyrus de Stockholm, Recettes. Paris: Les Belles Lettres, 1981. Holmyard, Eric John, and Desmond C. Mandeville, ed. Avicennae De congelatione et conglutinatione lapidum. Paris: Guethner, 1927. [See esp. 53–​54.] Irby-​Massie, Georgia L., and Paul T. Keyser, eds. Greek Science of the Hellenistic Era:  A Sourcebook. New York: Routledge, 2002. [See pages 226–​254.] Ideler, J. L. Physici et medici graeci minores. 2 vols. Berlin: Reimer, 1841.Reprint Amsterdam: Hakkert, 1963. Jackson, Howard M. Zosimos of Panopolis:  On the Letter Omega. Missoula, MT:  Scholars’ Press, 1978. Martelli, Matteo. Pseudo-​Democrito, Scritti alchemici con il commentario di Sinesio. Milano: Archè, and Paris: Société d’étude de l’histoire de l’alchimie, 2011. —​—​—​. The Four Books of pseudo-​Democritus. Society for the History of Alchemy and Chemistry. Wakefield: Maney, 2013. Mertens, Michèle. Alchimistes grecs. Vol. 4:  Zosime de Panopolis, Mémoires authentiques. Paris: Les Belles Lettres, 1995. Papathanassiou, Maria K. Stephanos von Alexandreia und sein Alchemistisches Werk: Die kritische Edition des griechischen Textes eingeschlossen. Athens: Cosmosware, 2017. Taylor, F. Sherwood. “The Alchemical Works of Stephanus of Alexandria.” Ambix 1 (1937): 116–​ 139, and 2 (1938): 39–​49.

Scholarly Literature Entries in EANS: Agatharkhidēs, 40–​41 (Burstein); Agathodaimōn, 43 (Hallum); Aineias of Gaza, 48 (Karamanolis); Anonymous Alchemist Christianus, 87–​88 (Viano); Anonymous Alchemist Philosopher, 88 (Viano); Eugenios (Alch.); 316 (Viano); Hēliodōros (pseudo?) et  alii, 364 (Viano); Hērakleios Imp., 371 (Viano); Isis, 446 (Hallum); Kleopatra, 482 (de Nardis); Maria, 531 (Hallum); Olumpiodōros of Alexandria (alch.), 589–​590 (Viano); Ostanēs, 599–​600 (Panaino); Pammenēs, 605–​606 (Hallum); Pēbikhios or Pibēkhios, 632 (Hallum); Pelagios, 633 (Viano); Stephanus of Alexandria (Alch.); 760–​761 (Viano); Sunesios, 769 (Viano); Zosimos of Panopolis, 852–​853 (Hallum). Bacchi, E., and Matteo Martelli, “Il principe Halid bin Yazid e le origini dell’alchimia araba.” In Conflitti e dissensi nell’Islâm, ed. Daniele Cevenini and Svevo D’Onofrio, 85–​120. Bologna: Il Ponte, 2009. Bain, David. “Melanitis gê. An Unnoticed Greek Name for Egypt: New Evidence for the Origins and Etymology of Alchemy.” In The World of Ancient Magic, ed. David R. Jordan, Hugo Montgomery, and Einar Thomassen, 221–​222. Bergen: Norwegian Institute at Athens, 1999. Berthelot, Marcellin. Les origines de l’alchimie. Paris: Steinheil, 1885. —​—​—​. Introduction à l’étude de la chimie des anciens et du moyen âge. Paris: Steinheil, 1889. Brun, Jean-​Pierre, Jean-​Paul Deroin, Thomas Faucher, Bérangère Redon, and Florian Téreygeol. “Les mines d’or ptolémaïques:  résultats des prospections dans le district minier de Samut (désert Oriental).” Bulletin de l’Institut Français d’Archéologie Orientale 113 (2013): 111–​142. Descamps-​Lequime, Sophie, with Marc Aucouturier and François Mathis. “L’encrier de Vaison-​la-​Romaine et la patine volontaire des bronzes antiques.” Monuments et Mémoires de la Fondation Eugène Piot 84 (2005): 5–​30.

Byzantine Alchemy   963 Festugière, A.-​J. La Révélation d’Hermès Trismégiste. Vol. 1: L’astrologie et les sciences occultes. Paris: Les Belles Lettres, 1944; 3rd ed. Paris: Lecoffre, 1950; nouvelle édition Paris: Les Belles Lettres, 2014. Giumlia-​Mair, Alessandra, ed. I bronzi antichi: produzione e tecnologia (Atti del XV Congresso internazionale sui bronzi antichi, Grado-​Aquileia 2001) = Monographies Instrumentum 21. Montagnac: Editions Monique Mergoil, 2002. —​—​—​. “Zosimos the Alchemist—​Manuscript 6.29, Cambridge, Metallurgical interpretation.” In Giumlia-​Mair 2002, 317–​323. Halleux, Robert. “L’affinage de l’or, de Crésus aux premiers alchimistes.” Janus 62 (1975): 79–​102. —​—​—​. Les textes alchimiques. Turnhout: Brepols, 1979. —​—​—​. “Méthode d’essai et d’affinage des alliages aurifères dans l’Antiquité et au Moyen-​ âge.” In L’or monnayé I: Purification et altérations de Rome à Byzance, ed. Cécile Morrisson et alii = Cahiers Ernest Babelon 2, 39–​77. Paris: CNRS, 1985. Hershbell, J. P. “Democritus and the Beginnings of Greek Alchemy.” Ambix 34 (1987): 5–​20. Holmyard, Eric John. Alchemy:  The Story of the Fascination of Gold and the Attempts of Chemists. Harmondsworth: Penguin Books, 1957. Reprint New York: Dover, 1990. Hopkins, Arthur J. “Transmutation by Color. A  Study of Earliest Alchemy.” In Studien zur Geschichte der Chemie:  Festgabe E.  O.  von Lippmann, ed. Julius Ruska, 9–​ 14. Berlin: Springer, 1927. —​—​—​. Alchemy, Child of Greek Philosophy. New York: Columbia University Press, 1934. Hunter, E. C. D. “Beautiful Black Bronzes: Zosimos’ Treatises in Cam. Mm.6.29.” In Giumlia-​ Mair 2002, 655–​660. Jung, Carl Gustav. “Einige Bemerkungen zu den Visionen des Zosimos.” Eranos Jahrbuch 5 (1937): 15–​54. Kahn, Didier, and Sylvain Matton, eds. Alchimie: Art, histoire et mythes. Paris: Société d’étude de l’histoire de l’alchimie, and Milano: Archè, 1995 = Textes et travaux de Chrysopœia 1. Lindsay, Jack. The Origins of Alchemy in Graeco-​Roman Egypt. London: Muller, 1970. Magdalino, Paul, and Maria Mavroudi, eds. The Occult Sciences in Byzantium. Genève:  La Pomme d’or, 2006. Martelli, Matteo. “‘Divine Water’ in the Alchemical Writings of Pseudo-​Democritus.” Ambix 56 (2009): 5–​22. Mertens, Michèle. “Graeco-​Egyptian Alchemy in Byzantium.” In Magdalino and Mavroudi 2006, 205–​230. —​—​—​. “Zosimos of Panopolis.” In New Dictionary of Scientific Biography, ed. Noretta Koertge, vol. 7, 405–​408. Detroit: Scribner’s and Thomson-​Gale, 2008. Needham, Joseph. Science and Civilisation in China. Vol. 5.2. Cambridge:  Cambridge University Press, 1974. Newman, William R., and Lawrence M. Principe. “Some Problems with the Historiography of Alchemy.” In Secrets of Nature: Astrology and Alchemy in Early Modern Europe, ed. William R. Newman and Anthony Grafton, 385–​432. Cambridge, MA, London: MIT Press, 2006. Papathanassiou, Maria K. “L’œuvre alchimique de Stéphanos d’Alexandrie:  structures et transformations de la matière, unité et pluralité.” In Viano 2005, 113–​133. —​—​—​. “Stephanos of Alexandria: A Famous Byzantine Scholar, Alchemist and Astrologer.” In Magdalino and Mavroudi 2006, 163–​204. Principe, Lawrence M. The Secret of Alchemy. Chicago: University of Chicago Press, 2013. Saffrey, H.-​ D. “Historique et description du Marcianus 299.” In Kahn and Matton 1995, 1–​10.

964   Late Antique and Early Byzantine Science Viano, Cristina. “Olympiodore, l’alchimistes et les Présocratiques: une doxographie de l’unité (De arte sacra, sec. 18‒27).” In Kahn and Matton 1995, 95–​150. —​—​—​, ed. L’alchimie et ses racines philosophiques. La tradition grecque et la tradition arabe. Paris: Vrin, 2005. —​—​—​. La matière des choses. Le livre IV des Météorologiques d’Aristote, et son interprétation par Olympiodore, avec le texte grec révisé et une traduction inédite de son Commentaire au Livre IV. Paris: Vrin, 2006. —​—​—​. “Les alchimistes gréco-​alexandrins et leur savoir: la transmutation entre théorie, pratique et ‘expérience.’” In Expertus sum: L’expérience par les sens dans la philosophie naturelle médiévale = Micrologus’ Library 40, ed. Thomas Bénatouïl and Isabelle Draelants, 223–​238. Firenze: SISMEL Edizioni del Galluzzo, 2011. —​—​—​. “Une substance, deux natures: les alchimistes grecs et le principe de la transmutation.” Dualismes:  Doctrines religieuses et traditions philosophiques, ed. F. Jourdan et A.  Vasiliu. Chôra, Hors-​série (2015): 309–​325. Vickers, B. “The Discrepancy Between res and verba in Greek Alchemy.” In Alchemy Revisited. Proceedings of the International Conference on the History of Alchemy at the University of Groningen, 17‒19 April 1989, ed. Z. R. W. M. von Martels, 21–​33. Leiden: Brill, 1990. Wellmann, Max. Die Physika des Bolos Demokritos und der Magier Anaxilaos aus Larissa. In Abhandlungen der Preußischen Akademie der Wissenschaften (Phil. Hist. Klasse), 1928, #7. Wilson, C. Anne. “Philosophers, Iôsis and Water of Life.” Proceedings of the Leeds Philosophical and Literary Society (Lit. and Hist. Sect.) 19 (1984): 101–​219.

chapter E6

B y z antine Me di c a l E ncycl opedias a nd Educati on Svetla Slaveva-​G riffin

In the field of Byzantine studies, the subject of medical encyclopedias is unknown. The names of Oribasius of Pergamum, Aëtius of Amida, Alexander of Tralles, and Paul of Aegina do not make it to the pages of The Oxford Handbook of Byzantine Studies (Jeffreys et al. 2008). The contribution of these authors to late ancient and particularly Byzantine scientific thought, that is, the composition of comprehensive repositories of medical knowledge, still awaits full examination. The import of these authors has not gone completely unnoticed, however. Byzantinists have neglected these authors, but surgeons and physicians (Adams 1834–​1847; Prioreschi 2001), medical historians (Bloch [1902] 1971; Garrison 1921; Sarton 1927; Temkin 1977; Scarborough 1984a, Nutton 1984 and 2004) and scholars of ancient philosophy (Dickson 1998; van der Eijk 2010) have been hard at work bringing to light the voluminous body of medical literature in the 300 years between the founding of Constantinople in 324 ce and its successful defense from the Arabs in 678 ce. Looking ahead, the ensuing discussion highlights the achievements and the aspirations in our understanding of this specialized scientific prose.

1.  Geopolitical and Cultural Context Byzantine medical encyclopedias and education stand at many crossroads. Historically the collection of knowledge from antiquity to the present reflects the foundational need of Byzantium to adjoin itself to the traditions of classical knowl­ edge. That means to revive not only the cultural icons of Homer and Plato but also the scientific prestige of “Hippocrates” (the historical evidence for whom remains

966   Late Antique and Early Byzantine Science inconclusive, Craik 2015, xxi) and Galen. The latter are the founding fathers of the art (technē) and science (epistēmē) of medicine in antiquity influencing the course of medicine into the early modern times. Geographically the proponents of this genre—​Oribasius of Pergamum, Aëtius of Amida, Alexander of Tralles, Paul of Aegina, aided by the exegetical acumen of commentators as John of Alexandria and Stephanus of Athens/​Alexandria—​reveal something unique about the subject. As a discipline, medicine originates with the legendary Hippocratic school on the Aegean island of Kos, establishes educational centers in Pergamum, Smyrna, Antioch, Tarsus, Corinth, and above all in Alexandria, and ultimately arrives in Rome to associate itself with the imperial court. With the early Byzantine medical compilers, medicine does not return, figuratively speaking, to its roots in Asia Minor because culturally and conceptually it never left the region. Instead, it re-​appropriates its Greekness through the intellectually cosmopolitan prism of its premier teaching institution at Alexandria and the patronage of the imperial court in Constantinople. This development in itself traces the sociopolitical unification of the eastern Mediterranean, despite the incessant barbarian invasions or the unremitting religious tensions fracturing the “inhabited earth” (oikoumenē) of Late Antiquity. The endurance of medicine as a body of knowledge also stems from more than its lasting legacy in the Greco-​Roman world. Medicine is encoded in human existence, universally conceived. Therefore any medical advances, however geographically localized, are globally integrated in our, only human, understanding of the preservation of life. The large collections nurture the kernels of this universalization, already detectable in the Hippocratic Epidemics or Airs, Waters, and Places as well as in the works of the Roman encyclopedic forerunners, particularly in Celsus’ On Medicine. The early centuries of the Byzantine Empire (to adopt Temkin’s periodization, 1977, 202) unfolded in the shadow of the most dynamic period in the history of ancient medicine. The first Byzantine medical encyclopedist, Oribasius, is separated by less than 150 years from Galen and by about 250 years from the constellation of other luminary physicians, surgeons, and pharmacologists in the caliber of Dioscorides, Rufus, Soranus, Archigenes, and Antyllus. These leading scientific minds, in turn, built their knowledge upon the theories and practices contained in the earliest medical writings that have come down to us in the collection of treatises known as the Hippocratic Corpus. More than half a millennium then lies between these texts and Oribasius. The passage of time places on the Byzantine medical writers the responsibility not only to preserve but also to explicate and apply the diverse knowledge they inherited. This process is not an act of sterile refrigeration—​to recall Nutton’s much-​cited quip on the Byzantine encyclopedists as “the medical refrigerators of antiquity” (Nutton 1984, 2)—​but a vigorous and laborious process that conjoins tradition and current practice in a sophisticated scientific discourse. This remodeled ideological program comes with new literary criteria of form, style, authorial voice, and methodological flexibility.

Byzantine Medical Encyclopedias and Education    967

2.  A Phantom Literary Genre At the outset, we identified the conspicuous absence of medical encyclopedias from the current state-​of-​the-​art survey of Byzantine studies, despite the consistent scholarly interest in them. We face the same problem if we would like to ground our understanding of the subject in the context of ancient encyclopedism as a whole. It is omitted in the most recent survey of Encyclopaedism from Antiquity to the Renaissance (König and Woolf 2013), yet not altogether. The collection features a chapter, by Magdalino (2013), on the later phase of Byzantine encyclopedism in the 9th and 10th centuries highlighting the accomplishments of Photius’ Bibliotheca and the Suda. The chapter defines Byzantine culture as encyclopedic by nature, founded on continuous “collecting, summarizing, excerpting and synthesizing” of earlier texts (Magdalino 2013, 219). This definition fully applies to the work of early Byzantine authors such as Stobaeus’ Anthology and the medical writers, currently under consideration, as well. These authors strive to achieve the same goals as their successors:  comprehensiveness, organization, and proliferation of knowl­ edge. Magdalino’s treatment of the later stage of the Byzantine movement indirectly provides the conclusion that the compilers of the first medical compendia are in the forefront of founding the Byzantine intellectual culture. The encyclopedia as a genre is not an ancient, but modern, literary phenomenon, created as late as the 16th century (Marrou 1982, 176–​177). Recent scholarship, as showcased in the aforementioned edited volume, contextualizes it in the broader intellectual enterprise of embodying universal or specialized knowledge, in parallel to the expansion of political power in the central Mediterranean from Hellenistic times onward (Doody 2010, 42–​46). While this clarification compels us to apply the term “encyclopedia” more cautiously to the works here, the same caution need not be exercised in referring to their authors as encyclopedists. Their struggle to compile, to organize, and to utilize global knowledge meets our modern understanding of the job of an “encyclopedist.” To get the right perspective, the knowledge the medical encyclopedists compile is covered in at least six different chapters in this Handbook (the most obvious being medical sects, alchemy, pharmacy, dietetics, and surgery). Moreover, the achievement of each author is singular in comparison with the anonymous team work behind the compilation of modern encyclopedias such as, for example, the 100-​plus team of international collaborators of The Encyclopedia of Ancient Natural Scientists (Keyser and Irby-​Massie 2008), the work which is overall closest to the Byzantine collections in reconstructing the highly populated and variegated world of ancient medicine. Hellenistic times and the Roman Empire gave rise to the accumulation and proliferation of knowledge (König and Whitmarsh 2007). It is not coincidental that the Hippocratic Corpus comes in circulation in the 3rd century bce, as a collection of 60 treatises of various length, thematic diversity, and anonymous authorship (with the

968   Late Antique and Early Byzantine Science exception of On the Nature of Man attributed, yet questionably, to Polybius). From its inception, medical literature is built upon the principles of dividing and organizing a diverse body of knowledge sourced by equally diverse number of physicians. The rapid growth of Roman political power further amplified this process of epistemological aggregation, which fostered the encyclopedic efforts of Cato, Varro, Pliny, and Celsus (see Beagon chap. D4, this volume). The paradigm for the comprehensive treatment of medicine, in all its diversity, from foodstuff to surgery, and everything in between, is elaborated by Galen. His written oeuvre is a world in itself, relentlessly gathering, correcting, and promulgating medical knowledge in order to complete the art of medicine itself. As author, Galen is sensitive to questions of the individual and overall organization of his works. According to him, the composition of the individual treatise depends on the nature of its subject. Thus in his three-​volume work on the properties of food, he arranges the material according to the kind of substances and in the order of their usefulness, starting from the most beneficial cereals and pulses, moving to herbs, fruits, vegetables, meat, and fish (Wilkins 2007, 72). In his 11-​volume compendium On the Compounding of Drugs According to Places, he employs a similar method, this time “according to places.” Nutrition and, to some extent, pharmacology lend themselves to this type of catalogue organization. Nosology and pathology, however, by nature depend on the anatomy of the body and are often organized in a downward presentation “from head to toes” (a capite ad calces). Since the time of the pharaohs, for practical reasons, this method has been the standard for both patient examination and medical presentation. While Galen does not always adhere to it (Flemming 2007, 248), he appreciates the benefit of its systematizing structure in matters of pathology and therapeutics, where the anatomical organization of the body supplies the best method for presenting the conditions pertinent to it. In works dedicated to long, itemized lists, such as On the Mixtures and Properties of Simple Drugs or Hippocratic Glossary, he employs an alphabetical order of organization. He also uses the commentary-​type structure in treatises, such as On the Natural Faculties and On the Doctrines of Hippocrates and Plato, which heavily rely on well-​established texts.

3.  From Knowledge to Information The accumulation of medical knowledge is both fostered and obscured by the passage of time. The continuously growing body of knowledge and the immediate instructional needs of the medical profession make organizing and preserving the existing medical literature a most pressing demand. Written texts require physical and conceptual space for preservation and comprehension. Such curricular undertaking is intellectually meritorious in its own right, requiring thematic vision, didactic acumen, astute sense of excellence, and up-​to-​date information.

Byzantine Medical Encyclopedias and Education    969

3.1  Oribasius (ca 350–​ca 400 ce) As mentioned, the genre of Byzantine medical compendia has not faired well in the scholarship. Oribasius’ work, however, is a notable exception. He is called “one of the last savants of the Alexandrian schools” and “a torch-​bearer of knowledge” whose “compilations are highly valued by scholars” respectively by Albutt ([1921] 1970, 407) and Garrison (1921, 122). Most recently Scarborough (in Keyser and Irby-​Massie 2008, 595) introduces him as “a well-​educated member of the non-​Christian aristocracy in Asia Minor” who deserves credit for designing “a careful system of editing, summarizing, and fusing much of the self-​contradictory, scattered, and obtuse work of Galen.” At the same time, these accolades come with grave observations about Oribasius’ lack of literary originality and overall pedantic citation style (Garrison 1921, 122; von Staden 1993). A testament to the timeliness of Oribasius’ achievement is the appearance of Latin translations of the Compilations as early as the 5th century. For better or worse, the Byzantine encyclopedists in the 9th and 10th centuries and the Arabic translator-​ physicians (Iskandar 1976; Pormann 2010)  knew Galen’s works through Oribasius’ compilation. The name of Oribasius is synonymous with the world of Byzantine medicine and the genre of medical encyclopedias East and West. His Medical Compilations (Collectiones medicae; hereafter Med. Comp.), in 70 (or 72)  volumes, stands as tall as the Galenic corpus. While Galen ambitiously produces tract after tract to complete the art of medicine, Oribasius compiles book after book to unify all knowledge, imparted by Galen and other medical dignitaries (Archigenes, Rufus, Dioscorides, Herodotus the physician, Soranus, Philagrius, Philoumenus, and Posidonius). Oribasius is no Galen, for sure, but he is no Celsus either. He is altogether a different kind of medical writer. Unlike Celsus, he does not set out to construct a repository of every piece of knowledge under the sun. As a practitioner, he directs his focus—​in part pragmatic, in part programmatic—​at providing a comprehensive and reliable one-​stop venue for authoritative medical information (Med. Comp. 1.1.4, Corpus medicorum graecorum [hereafter CMG] 6.1, 1, p. 4). The result of his industrious effort displays a felicitous match between a manual (on nutrition, Materia medica, prophylactics and therapy), and a compendium (on diagnostics, prognostics, and theoretical matters such as the nature and constitution of the body). The span of his historical coverage is almost a millennium. He provides information predominantly on the authority of Galen but also of other authoritative minds, from Alcmaeon of Kroton (ca 500–​480 bce) to Oribasius’ own contemporaries Philagrius of Epirus (300–​340 CE) and Adamantius of Alexandria (ca 412/​415 CE). The derivative nature of the information he compiles does not detract from his judicious goal “to collect the principal writings of all the best physicians” (Med. Comp. 1.1.2, CMG 6.1, 1, p. 4). To visualize it, the diachronic spectrum of Oribasius’ magnum opus is compatible with that of the modern reference tool in the history of ancient science and medicine today, the Encyclopedia of Ancient Natural Scientists. As pointed out earlier, the difference between

970   Late Antique and Early Byzantine Science the collections is that the latter celebrates the global scholarly achievement of more than 100 international experts, when the former is product of a single man’s untiring commitment in a remote pre-​electronic age. The known facts of Oribasius’ life afford a rare glimpse into the perks and perils in the life of the royal physician (archiatros) at the Byzantine court. Born in Pergamum, most likely to an affluent family, he studied medicine in Alexandria under the medical professor, Zenon of Cyprus, highly esteemed at the time. He then returns to his native Pergamum to practice medicine where, soon after, he encounters the young, soon-​to-​ be-​emperor, Julian. Oribasius is inseparably by Julian’s side during his short-​lived reign. Upon the emperor’s untimely death, his ideological alliance with Julian led to confiscation of his estate and exile “among barbarians” (Eunapius, Vitae Sophistarum 498). His reputation, however, shined even brighter at the barbarian court, and he eventually secured his safe return to the imperial capital and a complete rehabilitation (Baldwin 1975). Oribasius’ works have weathered relatively well over time. We have more than a third of his Medical Compilations (about 25 books), some in more fragmentary state than others; the nine-​book synopsis of the above compendium that he made for his son, Eustathius (Synopsis ad Eustathium); and a four-​part treatise on medications for laymen—​after Rufus’ model—​dedicated to his life-​ long friend Eunapius (Ad Eunapium). Lost is his first major undertaking, the abridged summaries (epitomai) of Galen’s works, commissioned by Julian during his Gallic campaigns in 355 CE. It is possible to discern Julian’s admiration for the past from Oribasius’ enthusiasm for organizing the body of medical knowledge. Julian’s interest in Galen’s works foreshadows his future revival program of Hellenic culture and philosophy. Although a nephew of the emperor, who posed Christianity as the avatar of the new Roman Empire, Julian sees himself as a philosopher and a pontifex maximus, wearing the imperial purple. His education, steeped in the classical literature and philosophy, inspires his full embrace of Greco-​Roman culture. His appreciation for Galen and the medical tradition, however, casts a new light on his restorative agenda. The production of an abridged edition of Galen’s works is only the first half of Julian’s commitment to medical knowledge. The second half is “to search and collect the principal writings of all the best physicians and everything that is useful for the completeness of the art of medicine” (Med. Comp. 1.1.2, CMG 6.1, 1, p. 4; trans. Grant 1997). In essence, Julian orders Oribasius to complete the vision Galen pursues in his writing career. Julian’s interest does not only reflect Galen’s permanent mark on history, but also institutionalizes the first program, after the Hellenistic times, for centralization and preservation of medical knowledge. Julian’s commitment recognizes medical literature as one of the heights of the classical tradition. The conceptual program of Oribasius’ Compilations, presented in Med. Comp. 1.1–​4 (CMG 6.1, 1, p. 4), is built upon the principles of (1) completeness; (2) clear organization; (3) objectivity; (4) evaluation of sources; (5) accuracy; (6) identifying the best medical authority and the best medical practice; and (7) keen awareness of the historical value of medical contributions. Collectively, these principles lay the foundation of the

Byzantine Medical Encyclopedias and Education    971 “encyclopedia” as a genre of scientific literature. Oribasius is aware of the weight of his undertaking and earnestly assures the reader that he will do his best (Med. Comp. 1.1.2, CMG 6.1, 1, p. 4). This upstanding compilatory program has earned him the grudging respect of modern scholars, inclined to have more appreciation for the thrill of making, rather than the drill of compiling, medical discoveries. Without Oribasius’ undertaking to convert medical knowledge into a wealth of information, medical discoveries would have been left unattributed or lost. His engagement with the professional texts is thorough. As a medical student at Alexandria, he was inevitably exposed to the rich collection of the Alexandrian library. In fact, he is the only Byzantine medical encyclopedist who must have had the fortune to use the Alexandrian library before the fatal burning of the Serapion in 391 CE. His imperial connection further placed him in the favorable position of acquiring copies of medical works. He is not as forthcoming as Galen about his book antiquarianism, but his report, in the opening sentence of the Compilations (Med. Comp. 1.1, CMG 6.1, 1, p. 4) that Julian ordered the abridged summaries of Galen’s treatises (epitomai), suggests that Oribasius had if not a complete, at least an almost full, set of Galen (Nutton 1984, 2–​3). Oribasius explains the organization of the collection at the end of its prologue. He starts with substance (“the material side of things”) including foodstuffs, diet, and pharmacology. Next he moves to the nature and constitution of man, followed by therapeutics, diagnostics, prognostics, and pathology (Med. Comp. 1.1.4, CMG 6.1, 1, p. 4). This arrangement differs from the thematic order of the Alexandrian medical curriculum (Iskandar 1976) and Galen’s recommendations for the order in which his works should be read. Galen considers nutrition and dietetics as part of therapeutics (de Libris Propriis, Kühn 19.30–​31) and pharmacology as part of the section on the four primary elements (de Ordine Librorum suorum, Kühn 19.55), which Oribasius frontloads in the collection, but Galen places later in his syllabus. In comparison with Galen’s organization, Oribasius’ arrangement has a utilitarian rather than an instructional goal. The central section of the work is more theoretical and presents the principal Hippocratic understanding of the nature and constitution of the body, espoused in the eponymous treatise in the Hippocratic Corpus and further elucidated in Galen’s commentary on it. This is a unique feature of his compendium that remains faithful to the theoretical branch of medicine but which is on its way out from the later collections. The remaining books cover the standard branches of diagnostics, prognostics, and pathology. A point of interest is the absence of a separate section on surgery, but surgical vignettes are peppered throughout, such as the excerpts from Antyllus’ major surgical treatises on aneurysm and tumors (Med. Comp. 45.2, 45.10, 45.24, 45.25; CMG 6.2, 1, pp. 161, 166, 179–​181) and those on the surgical procedures by the renowned Heliodorus of Alexandria (Med. Comp. 44.5, 44.20; CMG 6.2, 1, pp. 118 and 121, among others). Twenty-​five books of the Compilations have reached us. The largest portion of them contains Galenic excerpts on grains, diet, food preparation, water, on bodily evacuating, air, baths, the distinction of terms, the powers of drugs, brain, and circumcision. There are also excerpts from On Bed-​rest by Antyllus (100–​260 ce), On the Preparation of

972   Late Antique and Early Byzantine Science Hellebore by Archigenes (95–​115 ce), On the Power of Simple Drugs and On the Power of Metals and Their Preparation by Dioscurides (ca 40–​80 ce), Anatomical Nomenclature by Rufus (ca 70–​100 ce), On Bandages by Heraklas (110–​140 ce), On Limb-​Setting by Heliodorus of Alexandria (70–​110 ce). More than 20 other names of distinguished physicians are featured (Grant 1997, 96–​97). This wide range of works and authors demonstrates Oribasius’ inclusive approach to medical sects (Pneumatists, Methodists, and Rationalists), while maintaining and emphasis on Galen’s reception of Hippocratic doctrines. In the rapidly globalizing world of Late Antiquity, Oribasius’ compendium fills the need for a comprehensive work that gathers in one place, as implied by the title Compilations (sunagōgai), the expansive and diverse medical tradition. The imposing size of the collection has most probably made it difficult to use, especially for ad hoc consultation. Still this shortcoming pales in comparison to its achievement. While the other epistemological branches, like philosophy, have to look for ways to adapt to the swift ideological reorientation of the times, medicine’s challenge is not one of identity or content but one of volume and availability. The growing body of medical literature poses two main challenges: (1) how to centralize the authority of this knowledge in a way that would keep the art of medicine from false epistemological and therapeutic claims, and (2) how to transform this knowledge into a user-​friendly wealth of information.

3.2  Aëtius of Amida (500–​550 ce) Oribasius’ Compilations leave the challenge of synthesis and streamlining to those who come after him. First in line is Aëtius of Amida, with his Tetrabiblos. Aëtius’ life, although largely obscure, hits all the high points in a physician’s career in Late Antiquity. He was from Amida, a city in the easternmost corner of the Byzantine realm, near the border with the Sassanid Empire. He most likely studied medicine in Alexandria and, at some later point, was summoned, like Galen and Oribasius before, to move to the capital to join the court of Justinian. These slim facts, however, map the globalizing trend in medical education and practice at the time when an aspiring physician from anywhere in the empire, even from its outskirts, could study medicine at its flagship institution and could secure, with his reputation, an imperial post as a physician (archiatros) and a lord high chamberlain (comes obsequii, Garrison 1921, 123; Scarborough 2010, 236). The historical record is silent whether Aëtius, like Oribasius, undertook the composition of a major compendium on imperial orders. Although Julian and Justinian pursue opposite ideological ends, the two emperors share a common vision about the need of organizing and centralizing knowledge and the texts that carry it. As explained earlier, Oribasius credits Julian with spearheading the popularization of the Galenic corpus and the preservation of the best of the medical tradition. About 200 years later, Justinian likewise orders the codification of all laws in a legal compendium, known today as Codex Justinianus. It is ironic from the perspective of the preservation of knowledge

Byzantine Medical Encyclopedias and Education    973 that Justinian began his codification project in the year he closed the Athenian Academy (529 CE). At any rate, both emperors show commitment to consolidation and utilization of specialized knowledge at a large, imperial scale. Aëtius’ high standing in Justinian’s court puts him in a favorable position to continue what Oribasius has begun. Aëtius composes a collection of 16 Medical Books (Libri medicinales), organized in four groups of four, hence its more popular title, Tetrabiblos (four books). Thematically the collection follows the organization of Oribasius’ Compilations by ordering the material, from pharmacology to diagnostics to pathology. After a sizeable prologue introducing Galen’s classification of drugs according to the “degree” of their properties, the first five books cover simple drugs, minerals, foodstuff, exercise, baths, pediatric and geriatric nutrition, and symptoms of diseases. The central books (6–​13) focus on pathology in the standard “from-​head-​to-​toes” order. Book 14 deals with surgery and demonstrates Aëtius’ interest in synthesizing the information, as opposed to Oribasius’ more diffuse treatment of the subject. Book 15 discusses edema and other inflammatory conditions; the last book is dedicated to gynecology and obstetrics. His notable presentations include ophthalmology (book 7), toxicology (book 13), and inguinal hernias (book 16). The subject of gynecology expands Oribasius’ thematic range, at least in its present form. The usefulness of the topic does not need to be justified, but its inclusion demonstrates Aëtius’ interest and familiarity with advanced medical procedures as abortion, embryotomy, and mastectomy. Aside from its clinical importance, his addition of the topic pays homage to the strong gynecological tradition in the Hippocratic Corpus and to Soranus’ impressive Gynecology. Photius, too, recognizes the importance of the section (Bibliotheca sec. 221, p. 177a; CMG 8.1. p. 1, line 11). Aëtius’ Tetrabiblos displays the next stage in the development of the Byzantine medical encyclopedia as a genre. The thematic arrangement of the collection reveals its practical and instructional purpose. In the medical books, the presentation guides the reader through the proper order of examining the body and provides easy access to the information, when needed. The pharmaceutical and nutritional books function as practical manuals. The collection shifts away from the theoretical side of medicine, presented in the Hippocratic treatise On the Nature of Man and its Galenic commentary. Oribasius makes explicit his allegiance to the Hippocratic principles (Med. Comp. 1.1.3–​4; CMG 6.1, 1, p.4) and its signature theory of the four humors (blood, phlegm, yellow bile and black bile). But the above treatises are not part of the Hippocratic or Galenic curriculum and perhaps Aëtius is influenced by this syllabus in the decision to exclude the topic from the collection. Indeed, his calling on Hippocrates’ authority is not as ubiquitous as we might expect. When used, it is by name and most often with formulaic expressions such as “Hippocrates says or said,” “Hippocrates thinks,” or “Hippocrates orders” (among others, Tetrabiblos, CMG 8.1, pp. 119, 129, 277, 383). On these occasions, he cites specific texts in the Hippocratic Corpus but does not discuss specific Hippocratic principles. Aëtius’ utilitarian purpose is reflected in the size of the collection. In comparison to the 72 books of the Compilations, the 16 books of the Tetrabiblos show a distinct attempt at streamlining the information. The difference in volume does not result from sorting out significant from less-​significant topics but from Aëtius’ analytical method

974   Late Antique and Early Byzantine Science of presenting the material. He selects the most important texts dealing with a particular issue from the same author and arranges them in a clear and straightforward presentation, avoiding repetition and digression, as aptly shown by Scarborough (1984b, 224–​ 226) and more recently by van der Eijk (2010, 532–​534). Unlike Oribasius, Aëtius does not explain the rationale of his work in the prologue of the collection. But his careful selection of sources and the experiential tone of his voice do not leave doubt about its didactic purpose. This educational intent dictates the consistency with which he uses the “from-​head-​to-​toes” principle of organization, which also serves as a built-​in index for easily locating topics on demand. The kernels of the instrumental role of this scientific genre are already detectable in Oribasius’ Compilations. But while Oribasius conceives of his work as “a collection” or “compilations” (sunagōgai), Aëtius’ books circulate as “expositions” (logoi), lecture-​like notes for practical instruction. Although the individual books are labeled as “accounts” or “expositions” (logoi) in the manuscript tradition, Photius perceives them in their unity as a single “practical guide” (pragmateia: Bibliotheca sec. 221, p. 177a = CMG 8.1, p. 1). The orderliness of Aëtius’ exposition may give the impression of “dryness” of style, but in the challenging environment of globalized knowledge what we may conceive as “weakness” of style is in fact “strength” of vision.

3.3  Alexander of Tralles (ca 525–​605 ce) While the spotlight of medical writing in the first half of the 6th century falls on Aëtius at the court in Constantinople, in the second half of the century it shifts its focus from the Byzantine capital to Alexander of Tralles’ itinerant medical career. Alexander comes from a small town in Lydia, boasting its archaic origin from the ancient Pelasgians. His father, Stephanus, is a physician, with five sons, each of whom finds his true calling. According to Agathias (Historiae 5.6.3–​6 [Keydell 171.3–​6]), two of the brothers, Anthemius and Metrodorus, distinguish themselves respectively in architecture and education. Their hometown success secures them an invitation from Justinian to move to Constantinople where Anthemius designs Hagia Sophia and Metrodorus thrives as a teacher. Two of the other brothers remain home, where Olympius practices law and Dioscorus medicine. The fifth brother, Alexander, also becomes a physician in his father’s footsteps. Agathias’ account does not preserve more details about Alexander’s life, education, or whereabouts, aside from the remark that in his advanced age he settled in Rome, where he was summoned “to occupy a position of great distinction” (Historiae 5.6.5 [Keydell 171.18]; Scarborough 1997). If we try, with many scholars, to fill in the gap in Alexander’s life between Tralles and Rome through a close reading of the geographical references in his works, we can envision him as an itinerant physician, much like the Hippocratic physicians from classical and Hellenistic times. Alexander’s practice may have led him through Asia Minor down to the coast of northern Africa and across the Mediterranean to Spain, Gaul, and Italy (Allbutt [1921] 1970, 411). His educational path certainly brings him to Alexandria, as expected, while his professional career

Byzantine Medical Encyclopedias and Education    975 stays off the beaten track and does not take him to the Byzantine court. The erudition of his works shows a well-​rounded education that felicitously complements his natural talents: acuity of observation, critical discernment, and deep humanism. Alexander is the author of a large medical collection entitled Therapeutics (Therapeutica) in 12 books that, in turn, give the collection the name The Twelve Books of Medicine (Libri duodecimi de re medica); a treatise On Fevers, which often is appended to the previous collection; and the one-​of-​a-​kind work entitled On Intestinal Worms. This output is not trivial for someone whose goal is—​since age has slowed him down—​to convert his practical experience (peira) into a written expertise at the service of anyone, genuinely interested in medicine. Practical experience is in the foundation of Alexander’s career as a medical writer. His emphasis on it places him together with Galen in the exclusive group of physicians outspoken about the invaluable benefits of the empirical side of medical knowledge. The same high regard for experience also puts him at odds with Galen whom he otherwise reveres as “the most divine.” For instance, when his experience contradicts Galen’s prescribed treatment for chest congestion, Alexander firmly parts way from the master by recommending a therapy he knows is efficient (On Fevers 2.153–​155 [Puschmann]). He firmly believes the duty of a physician is to provide the treatment that works best. This conviction prompts him to make the proverbial statement: “Plato is my friend, but so is truth, and when the two are at issue, the truth must be preferred” (On Fevers 2.155 [Puschmann], trans. Temkin 1991, 232). The prologue of his treatise On Fevers (Dedicatio ad Cosman 1.289.1–​12 [Puschmann]), dedicated to his friend Cosmas, formulates Alexander’s writing program. While the other medical writers conceive of their works as “compilations” or “expositions,” Alexander perceives of them as “cures”, that is, written embodiments of his medical practice. Driven by the sober realization that his advanced age does not allow him to practice medicine, he is eager to convert his knowledge into a book (biblion) “after he has organized (suntaxas) the experiences (peiras) he has gathered from his long contact with men’s diseases” (Dedicatio ad Cosman 1.289.9–​10 [Puschmann]). Alexander’s realism and humanism are disarming. He speaks with the wisdom and simplicity he has gained over the years and with the sharp discerning eye of a diagnostician. The enthusiastic tone of his remarks equals the eagerness and commitment with which he would take on a challenging medical case. He also has a clear idea about the merits of his work such as the good reasoning of his medical theories (to eumethodon tōn theōrematōn) and the concision (to suntomon) and clarity (to saphes) of his style (based on Bouras-​Vallianatos’ translation in 2014, 341). Alexander is a seasoned reader, with a knowing taste for informative medical prose. The clarity he envisions for his writing is part of the instructional and practical goals of his work. In this autobiographical prologue, Alexander comes to life as a very different kind of medical writer—​and perhaps physician—​than Oribasius and Aëtius. For all the above reasons, the prologue of On Fevers is commonly considered as a representation of his writing program in the Therapeutics. The title of his compendium

976   Late Antique and Early Byzantine Science echoes the title of one of the main texts in the beginner’s course in the Alexandrian medical curriculum—​Galen’ Therapeutics for Glaucon. It employs the standard “from-​head-​ to-​toes” organizing principle. Book 1 begins with diseases of the head (loss of hair, scalp disorders, mental conditions). Books 2–​3 deal respectively with the eyes and the ears. Books 4–​6 cover subsequently angina, pulmonary diseases, and pleurisy. Books 7–​10 treat conditions of the heart and the gastrointestinal tract. Book 11 presents urinary diseases, and book 12 gout. The number of subtopics in the individual books varies. Some books (1, 7, 11) contain numerous entries, while others (2, 4, 6, for example) are more homogenous. Regardless of their internal variegated structure, the books are comparable in length. The collection strives for comprehensiveness that runs from the overarching organization of the collection to the composition of the individual entries. At first the thematic range of Alexander’s Therapeutics may appear thin in contrast to the expansive sections on pharmacology and nutrition in Oribasius and Aëtius, even without counting Oribasius’ theoretical coverage. For this reason, Temkin (1991, 232) has been reluctant to include the collection among the medical encyclopedias of the period. A closer examination of the internal organization of the individual entries, however, does not substantiate the notion of limited thematic range but underlines Alexander’s innovative method of presentation. He organizes the information for each entry in six sections: definition, typology, diagnostics, treatment, remedies, and “natural remedies.” Among them the pharmacological section runs the longest. It lists all relevant drugs, divided in groups of simples and compounds (with recipes). The last section, dealing with what Bouras-​Vallianatos translates—​for the lack of a better word—​as “natural remedies” (phusika), is based on folk medicine, which relies on amulets and other alternative therapies. This layout of the structure of the individual entries overlaps with the full thematic range of Oribasius’ and Aëtius’ collections. In line with his practical purpose, however, Alexander breaks down the monolithic presentation of the major medical branches into heterogeneous but thematically cohesive individual entries. This ad locum approach is user-​friendly and flexible should one wish to expand upon the information in the future. The presence of “irrational” elements such as the abovementioned “natural remedies” is striking (Temkin 1991; Bouras-​Vallianatos 2014). It is difficult to reconcile Alexander’s inclusion of this type of “remedies” with the critical approach he adopts toward the effectiveness, or what he calls “the truth” of treatment, cited earlier. This anomaly may seem more palatable if we take into account the author’s commitment to do everything in his power to help the patient, even if “some people rejoice in natural remedies and amulets and they seek to use them” (Therapeutica 1.557.14–​15 [Puschmann]). If there is any absoluteness to Alexander’s therapeutic “truth,” it is his principle of “what works best for the patient.” He is not ignorant of the implications of this all-​inclusive approach, and he takes on the responsibility to instruct his reader-​physicians about all means of therapy so they are well informed when patients ask about them. He shows compassion for the patient’s holistic well-​being and sensitivity to the fragility of the patient-​ physician relation.

Byzantine Medical Encyclopedias and Education    977 Alexander stands out as the most real among the Byzantine medical writers. His humanism enhances the professional appeal of his works, and his critical empirical approach to therapeutics has earned him the praise of being “the greatest physician of the centuries after Galen” (Allbutt [1921] 1970, 411), “the first original physician after Galen” (Sarton 1927, 453), and “the most modern” of the Byzantine physicians (The Oxford Dictionary of Byzantium). In his Introduction to the History of Science, Sarton honors him by labeling the second half of the 6th century as “the time of Alexander of Tralles” (Sarton 1927, 443). Alexander’s Therapeutics were almost immediately translated into Latin (7th century ce) and soon after in Arabic and Hebrew (Bouras-​Vallianatos 2014, 339).

3.4  Paul of Aegina (ca 630–​670? ce) Paul comes just before a new wave of compilatory activity, at the end of the 7th century, which moves farther east to yield new translations and compendia in Armenian, Syriac, and Arabic. His lifetime stands at a watershed: introducing cultural and ideological changes in the Eastern Roman Empire with impact equal to the legalization of Christianity ca 325 ce, and its imposition as official ca 390 ce. We do not have any details of his life. The written record associates him with the island of Aegina, a few miles south from the Athenian harbor of Piraeus. The island could have been either his birthplace or workplace. In some sources, he is described as “a traveler” and “a teacher of medicine,” in others he is praised as “the obstetrician” (Pormann 2004, 6). These scraps of information are too small to materialize anything more concrete about his career. And yet they eloquently paint an idealized portrait of a physician who has expert skills in gynecology and obstetrics. The rich Arabic reception of his works associates him with the two pillars of medicine in Late Antiquity: Galen and Alexandria. Paul composes a seven-​book compendium Epitome of Medicine (Epitome Medica). The number of the books motivates the Arabic rendition of the title as the Compendium of the Pleiades (Pormann 2004, 5). In line with his reputation as “the obstetrician,” he is also credited with authorship of a book on gynecology and a monograph On the Therapy and Treatment of the Child. Only the compendium is extant today. Paul’s Epitome, as implied by its title, is the most compact of the early medical collections. Its thematic design does not diverge significantly from the one in Oribasius and Aëtius. It covers hygiene and nutrition (specifically for infants and elderly, book 1), fevers (book 2), “from-​head-​to-​toes” nosology (book 3), pathology (book 4), toxicology (book 5), “from-​head-​to-​toes” surgery (book 6), and pharmacology (book 7). The collection reverts to the centralized presentation of the separate medical branches as opposed to Alexander’s ad locum method of organization. Concision is the main characteristic of Paul’s style of presentation. In a comparative study of the compilatory methods of Oribasius, Aëtius, and Paul, van der Eijk (2010, 536–​552) visualizes the programmatic difference between the compilatory styles of the three encyclopedists. While Oribasius and Aëtius cut the original medical works

978   Late Antique and Early Byzantine Science approximately in half, Paul condensed the original passages to less than 10 lines. This bare minimum method was determined by considerations of portability and utility. With Oribasius and Aëtius, we noted the growing awareness, shared by emperors and physicians, of the need for ordering and stabilizing the branches of specialized knowl­ edge. Julian commissions the abridged editions of Galen’s treatises, whereas Justinian orders the codification of laws. In the beginning stage of the medical encyclopedia as a genre, Oribasius sketches the professional agenda for this globalized undertaking. Three centuries later, Paul is in a better position to articulate more clearly the importance of it. In the prologue to the Epitome, he draws a parallel between the physician’s need of reference tools at hand and the portable legal synopses available to lawyers. He is puzzled by the absence of such tools in medicine, and the discrepancy between the portability of medical handbooks and legal digests. While lawyers daily peruse concise reference manuals, physicians cannot, although—​Paul’s puzzlement grows—​the physician’s job oftentimes places him away from consultation resources, either in the countryside or in emergencies, when time is life-​saving (Epitome, CMG 9.1, pp. 1–​2). Paul identifies the need for such medical tools as professional necessity and takes it upon himself to fill it in. In the Epitome, he shows deft familiarity with the full parameter of the medical tradition, from important advances to the major names in the field, to the latest compendia of Oribasius, Aëtius, and Alexander. His evaluation of his contribution to medicine is humble, as he perceives it to be no greater than an exercise (gumnasion, Epitome, CMG 9.1, p. 1, line 8). He respects the longevity of the medical tradition and makes sure to clarify that his work is not meant to correct the opinions of those who stand before him (their contribution, he insists, is faultless). His goal is to make the medical tradition accessible to the younger generations of physicians who, Paul observes, have stopped reading the ancient authorities. Not so much the passage of time, but the changes in the intellectual environment have affected how students learn medicine. Paul’s concern about the shallowness of medical knowledge and the limited interests of younger physicians is faintly detected in Oribasius’ emphasis on the importance of preserving the knowledge of the best physicians. Like Oribasius, Paul is concerned with the ordering together of medical knowledge (suntagma) in the form of a reminder (hupomnēma) for posterity.

4.  From Information Back to Knowledge Paul’s concern about the ability of the new generations of students to master their subject directs our attention to the state of medical education in early Byzantium. One of the driving forces behind the development of this scientific genre is the adaptation of the rich medical tradition to the changing didactic environment of Late Antiquity. The

Byzantine Medical Encyclopedias and Education    979 first stage of this process, examined in the previous section of this chapter, is the conversion of medical knowledge into a wealth of medical information. This challenge naturally predetermines the second stage of the process in which the wealth of information is repackaged in a way to meet the new instructional needs. The encyclopedists are aware of the didactic importance of their work. The conceptual variety with which they conceive of their work suggests they grappled with it. The terminological fluidity (“collection,” “compilation,” “compendium,” and more cautiously “encyclopedia”) with which we have been referring to their work reveals the authors’ original difficulty. Oribasius conceives of his Compilations as “collections” (sunagōgai), the individual books of Aëtius’ Tetrabiblos are divided into “accounts” or “expositions” (logoi), Alexander refers to his Therapeutics as “a book” (biblion), and Paul describes his work as “a handbook” (pragmateia), a collection (suntagma), and “a memorandum,” “explanatory notes,” “commentary” (hupomnēma). The term “encyclopedia” does not appear in this flexible semiotic array since, as mentioned, the term per se is a modern invention based on the ancient idea of enkuklios paideia as circular, in the sense of consecutive, and all-​around education (Anna Comnena, Alexiad 1.2, 15.7.9; Markopoulos 2008, 787). The original meaning of the phrase comprises the ideas of completeness and education. Our modern derivative has retained the former, but it has expanded the latter to convey the notion of a reference tool either in a general or in a specialized subject. The titles if examined together, also show a growing articulation of the didactic goal of their works. The title of Oribasius’ “collections” captures the preliminary stage of education in which knowledge is collated into a body of information. The definition of Aëtius’ “expositions” (preserved in the manuscript tradition) denotes the lecture stage of education in which information is selected and systematized as knowledge (in this light, the characterization of Aëtius’ style as “scholastic” is complimentary). Alexander’s conception of the Therapeutics as “a book” underlies the unity of education in which the individual parts present the subject as a whole in a user-​friendly format for self-​paced instruction. Paul’s understanding of the purpose of his Epitome brings out the complexity underlined by his predecessors’ attempts at working out the nature of this kind of writing. He perceives his text as a sophisticated work that has more than one nature and more than one goal, namely three: ordered composition (suntagma), memorandum (hupomnēma), and concise presentation (suntomos). The primary significance of the latter inspires the heading of the work as Epitome, “an abridged edition.” With time, conciseness becomes the driving principle behind the evolution of the medical collection as a genre. Even Oribasius is concerned with the abundance of medical information and the lack of quality control over it. Aëtius, as Scarborough (1984b, 224–​226) has shown, is more sparing in his method of selection and organization. He logically arranges the excerpts from different textual sources, even by the same author, in order to present the material in a clear, precise, and instructive form. Paul spells out the reason for such conciseness as “for the sake of instruction” (Epitome, CMG 9.1, p. 1, lines 2–​3). The result of this development is materialized by the steady downsizing of the volume of the collections successively from 70 (or 72) installments in Oribasius, to 16

980   Late Antique and Early Byzantine Science in Aëtius, to 13 in Alexander, and to 7 in Paul. The numbers speak for the success of the outcome. The large collections of the early Byzantine medical writers—​let us finally allow ourselves to call them “encyclopedias”—​constitute a unique kind of hybrid, multifunctional prose that draws upon the other major genera of medical literature in Late Antiquity, such as summaries, commentaries, and branch diagrams (Pormann 2010, 421–​423). These genera are directly related to the educational needs of medicine. The differences between them also seem to fulfill specific didactic goals:  the summaries such as the Alexandrian Summaries (Summaria Alexandrinorum) provide comprehensive and synthesized one-​stop-​for-​all information, an aspiration of the early Byzantine encyclopedists and in particular Oribasius and Aëtius; reminiscent of the epistemological and empirical remarks in Alexander’s Therapeutics, the commentaries explicate the concepts, theories, and practices presented in the Hippocratic and Galenic texts at the foundation of the medical curriculum; the branch diagrams such as the Viennese Tables (Tabulae Vindobonenses) schematize the information at a glance (in particular, on nosology and pathology) echoing the concerns for portability and availability of medical texts, expressed by Alexander and Paul. In general, from its inception, medicine as an art (technē) is built on a strong educational model. Regardless of one’s natural abilities and intuition, one cannot become a self-​taught medical practitioner (unless one does not mind joining the many vagrant impostors of the art in antiquity). The notion of passing down knowledge from a master to a pupil is embedded in Asclepius’ education by the centaur Chiron, in the father-​ and-​son apprenticeship in the first medical school at Kos, in the famous lineage of the medical guild of the Asclepiadae, and in the prestige of the pupils of famous medical professors (iatrosophists) such as Zeno of Cyprus and Gessius of Petra. In its most basic form, medical education combines oral instruction with physical observation and supervised practice. In the second half of the 5th century bce, the earliest treatises in the Hippocratic Corpus start to record and thereby indirectly organize the current medical knowledge in written form. In the 3rd century bce, these written texts start to gravitate into a collection (albeit very porous), which leads to the circulation of the Hippocratic Corpus (Craik 2015, xxiii). The organized circulation of the texts raises their visibility as an instructional, not only epistemological, resource and prepares the ground for the development of a medical curriculum. All of this takes place in Alexandria, at its libraries, “academies,” and museums (Duffy 1984; Wilson 1996, 42–​49; Watts 2006, 145–​151; Pormann 2010). No other discipline can boast such geographical continuity. Since the times of Herophilus of Chalcedon (ca 330–​260 bce), all distinguished physicians passed through Alexandria. Also since that time, physicians such as Bakcheios of Tanagra (ca 270–​200 bce) and later Erotian at Nero’s court (60–​80 ce), work at drawing together the Hippocratic Corpus into a collection. Between then and the times of the Byzantine encyclopedists, the Hippocratic Corpus has given rise to a fully developed medical curriculum the details of which are best documented in ‘Ali Ibn Riḍwān al-​Misrī’s Useful Book on the Quality of Medical Education (Iskandar 1976). There we learn that the medical curriculum in Alexandria

Byzantine Medical Encyclopedias and Education    981 in the 6th and 7th centuries consisted of Aristotle’s works on logic (Categories, On Interpretation, and the two treatises on Analytics), four Hippocratic treatises (Aphorisms, Prognostic, Regimen in Acute Diseases, and Airs, Waters, and Places), and 16 of Galen’s works, some listed below. The full course of the medical curriculum is divided in seven grades, as outlined by Iskandar (1976, 245–​253). The beginner’s grade covers the introductory texts: Galen’s On the Three Medical Sects for Beginners, general accounts of theory and practice, On the Pulse, and the Therapeutics to Glaucon. The second grade studies the topics of “physics” (elements, temperaments, faculties, organs). Grades three to six focus on nosology, etiology, symptoms, pathology, diagnosis, prognosis, and therapy. Grade seven teaches the subject of hygiene. The medical curriculum the Byzantine encyclopedists study is most likely similar to this syllabus. Many of the texts from this curriculum find place on the pages of their medical collections and oftentimes their presentations have strong pedagogical overtones, practical lessons, and tips for symptom recognition (Duffy 1984; Scarborough 2010). From archaeological remains, we discover 20 lecture halls in Alexandria from the 6th century ce (Sorabji 2014). The rooms vary in size and in architectural design. Most are in an amphitheater shape, one has an apse, and four rooms have a trench, one of which shows signs of a waterproof lining at the bottom. Sorabji (2014, 35)  suggests that these rooms may have been used for medical, and more specifically anatomical, demonstrations, for example, animal dissections of the kind that Galen proudly recounts in his works. These lecture halls also bring to life Galen’s poignant remark that one learns anatomy only after examining the individual bones with one’s own eyes, an opportunity formally possible only in the medical school at Alexandria (Galen, Anatomicarum administrationum libri, Kühn 2.220–​221). This material information reconstructs the general layout and architecture of the famous school at Alexandria, the flagship academic institution in Late Antiquity, especially after Justinian’s closing of the Academy in Athens in the beginning of the 6th century. The archaeological record also uncovers the concomitant path of philosophical and medical education in Late Antiquity. The convoluted relation between the two disciplines goes back to Empedocles, Plato, and Galen. In his life and in his works, Galen fully embraces the credo that “the best physician is also a philosopher,” as he passionately argues in a tract with the same title. The world of knowledge Galen depicts, and sometimes deplores, in his writing teems with intellectuals, laymen and specialists, who pursue both philosophy and medicine. Half of the students in Plotinus’ inner circle (254–​270 ce) are physicians (Paulinus of Scythopolis, Zetus of Arab descent, and Eustochius of Alexandria: Slaveva-​Griffin 2010, 93–​94). Later, at Theodosius’ university in Constantinople, the philosophical syllabus contains medical lectures and the famous scholar Agapius (470–​510 ce) is invited to move from Alexandria to Constantinople to take the chair of medicine (Vogel 1967, 288–​289). As we learned earlier, the Alexandrian medical curriculum begins with the study of logic, comprising Aristotle’s treatises On Categories, On Interpretation, and the

982   Late Antique and Early Byzantine Science Analytics. But there is a reciprocal movement on the philosophical side when the subject of medicine both as an art and a science slowly but steadily makes its way in the works of all major Neoplatonists from Plotinus to Proclus (ca 430–​485 ce). While Plotinus applies Galen’s cardiovascular advances to explain the seat of the soul (Enneads IV [27].3.23), Proclus applies Hippocrates’ authority on critical time (kairos) to matters of psychology (On Plato’s Alcibiades 1.120.15 [Westerink]) and the Hippocratic understanding of the nature of man according to On the Nature of Man (On Plato’s Timaeus 2.28.24–​26 [Diehl]). He is also the first among the leading Neoplatonic philosophers to mention by name Herophilus (On Plato’s Republic 2.33.9–​11 [Kroll]) and Galen, in particular his treatise that “the powers of the soul depend on the mixtures of the body” (On Plato’s Timaeus 3.349.21–​25 [Diehl]). The expansion of knowledge and the accumulation of written works purport the development of the commentary in Late Antiquity. As adumbrated by the references to Proclus above, the genre of the commentary quickly becomes one of the leading modes of philosophical exegesis. Its productivity exceeds the domain of philosophy to reach the disciplines of astronomy, mathematics, and medicine. The establishing of a medical curriculum raises the opportunity for updated explications of the Hippocratic and Galenic texts. The bustling academic life in Alexandria in the 6th century fosters a new prolific line of medical commentaries featuring the names of John of Alexandria, Palladius, Stephanus of Athens/​Alexandria, also probably Gessius. All of them are physicians and medical professors, recognized with the title of iatrosophist or archiatros. Regrettably, no concrete details are preserved about their lives and works, aside from a few titles, some fragments, and even fewer intact treatises. John of Alexandria (ca 500–​700 ce) is the author of commentaries on at least two Hippocratic texts (Epidemics VI and Nature of the Child) and on Galen’s On the Sects for Beginners, Theriac, and On Pulses. Palladius (ca 500–​600 ce) produces a commentary on the Hippocratic On Fractures, attributed in the manuscript tradition to his colleague Stephanus (ca 540–​680? ce). He also has lecture notes on Hippocrates’ Epidemics VI and Galen’s On the Sects for Beginners (Wilson 1996, 48–​49). History has been more charitable to Stephanus’ works, although there is much speculation about his connection with Athens and Alexandria or even whether this is one and the same person (Dickson 1998, 1–​5). It appears that he (in his “bi-​urban” identity) extensively commented on texts from the philosophical and medical parts of the curriculum. In the philosophical part, he wrote on Aristotle’s On Interpretation (extant) and on the now-​lost Categories and Prior Analytics. In the Hippocratic part, he covered the Aphorisms, Fractures, and Prognostics. In Galen’s part, he commented on the Therapeutics to Glaucon and Pulses. He also branched out to Theon’s Commentary on Ptolemy’s Handy Tables, the art of mathematics, astrology, and the making of gold. The format of the commentaries is closely related, if not derived, from the teaching methods of the time, featuring lectures (praxeis) and discussions (theōriai). Their exegetical model consists of (1) lexical observations and different manuscript readings, (2) lemmatic expositions, and (3) examinations of established and new interpretations (Duffy 1984, 22). In comparison to the bird’s-​eye-​view nature of the medical compendia,

Byzantine Medical Encyclopedias and Education    983 the commentaries zoom in at the microscopic level of the individual text to tease out concepts and ideas. The final result is a sophisticated blending of philosophical and medical themes that gives birth to the curious, impossible to define, genre of medical philosophy, with works such as Porphyry of Tyre’s To Gaurus On How Embryos are Ensouled, Nemesius of Emesa’s On the Nature of Man, or the pseudo-​Galenic tract On the Seed. The wealth of philosophical and medical information opens new directions of scientific thought and writing.

5.  Future Directions The development of the medical encyclopedia as a genre in early Byzantium embodies the globalizing processes shaping the world of Late Antiquity. These processes are based upon the principles of expansion and centralization of sociopolitical organization, education, and accumulation of knowledge. The redrawing of the political borders in the East, from a certain perspective, is an aftermath of the long cultural and religious processes carving the ideological landscape of Asia Minor. The place and role of medicine in this bubbling whirlpool is unique because medicine has enough stamina and hypermobility to adapt seamlessly to this unstable environment. The Byzantine medical encyclopedia, like Byzantine medicine in general, has been cast aside as a less desirable offspring of the muddied world of Late Antiquity. The winds have changed in the last 20 years, and we have discovered the hidden philosophical and medical treasures of this period thanks to the intellectual curiosity and commitment of papyrologists, text editors, translators, and historians of science, medicine, and philosophy. Their pioneering work has drawn a new research map, with unlimited possibilities, the main directions of which can be charted as follows: 1. To produce updated text critical editions, translations, and commentaries of the available texts. For example, there is no complete edition of Aëtius’ Tetrabiblos. The first eight books are edited in two volumes by Alexander Olivieri (CMG 8.1 and 8.2). There are no editions of books 10 and 14, while the remaining books are edited randomly. The best source for the latter half of the collection remains the 1542 Latin translation by Cornarius (Scarborough 2010, 238, n. 19). 2. To examine  thoroughly the doxographical and historiographical methods and techniquess of the Byzantine encyclopedists in light of van der Eijk’s 2010 study. 3. To construct and contextualize the network of medical information in Late Antiquity. According to The Encyclopedia of Ancient Natural Scientists, there are approximately 200 physicians, practitioners, and/​or medical writers, who lived from around the turn of the first millennium up to the first seven centuries of the Common Era. About a half are mentioned just in the first eight books of Aëtius’ Tetrabiblos. It is too early to draw any conclusions about the significance of this data, but we do not need further proof of its promise.

984   Late Antique and Early Byzantine Science 4. To contextualize the style of each author in his intellectual and literary environment. 5. To study the authorial persona of the encyclopedists and their reliance on professional knowledge and personal experience. 6. To construct the mechanism in which medical advances are incorporated in the medical literature. 7. To examine the sociopolitical presence in the works. 8. To examine the religious climate in the works, with subthemes such as elements of paganism and Christianity or standard medicine versus alternative means of therapy. All of the above and more proves that early Byzantine medical literature, from encyclopedias to commentaries and medical philosophy, does not stand paralyzed, as “a burial of talents” or “embalmment” (Allbutt [1921] 1970, 396), at the crossroads of Late Antiquity. Instead it is one of the active intellectual developments weaving the web of knowledge in the Middle Ages. And so, we shall move away from the “refrigerators” of compartmentalized scholarship to explore the new horizons before us.

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chapter E7

L ate Encyc l ope di c Approach e s to Knowled ge i n L at i n Literatu re David Paniagua

1. Introduction Over the last few decades, a clearer awareness of the need to avoid risky anachronisms applied to the ancient world and its culture has been increasingly acquired. Much has been written about the (mis)use of the term “encyclopedia” to qualify some literary products of the Roman world and the implications of projecting backward a modern concept that simply did not exist as such (Codoñer 2011; Fowler 1997; Zimmermann 1994). The debate has intensified due to the growing interest in Pliny’s Natural History (Historia naturalis, traditionally considered the first encyclopedia), and there has been no shortage of engaging contributions on the case. Della Corte’s classical Enciclopedisti latini (1946) may be still a reference point on the definition of the canon of Latin encyclopedic authors, but—​I think—​there is general agreement in not recognizing the encyclopedia as an ancient genre. It is undeniable that whoever turns to Pliny, Celsus, or Capella as if their work were an encyclopedia, does so because he finds therein what he would have found in an ancient encyclopedia, should it have existed at all. But the point is that a work should not be automatically labeled an encyclopedia merely on the basis that it presents a coherent collection of facts or data, unless we do so in a metaphorical sense. Thus, we have to acknowledge that the “encyclopedia” is in the eye of the modern (probably from Otto Jahn onward) beholder. The aim of these pages is precisely to consider those works of late Latin literature that offer an organic array of facts or data; for this is what here is presented as “encyclopedic approaches to knowledge”: works resulting from the author’s attempts to provide

988   Late Antique and Early Byzantine Science a coherent, comprehensive and organized exposition of human knowledge. And it is in this kind of authorial attitude where we can make out an “encyclopedic spirit.” Latin works dealing with a single discipline, albeit systematic and thorough, will not be taken into account here, unless they comply with the prerequisite of tackling the transmission of knowledge from an encyclopedic (read coherent, comprehensive, organized) standpoint, as in the case of Boethius. Their relevance, however, should not be undervalued in any way since they are often the very bricks used for constructing the works considered here (Formisano 2013). Encyclopedic approaches to knowledge represent a specific intellectual activity of Roman culture. There was not an encyclopedic literature in Greece as there was in Rome, but more fluid traditions of knowledge on discrete subjects; the Greeks of all periods preferred to use separate handbooks on individual subjects, as Fowler (1997, 17) points out. What characterizes all the encyclopedic projects gathered in this chapter is the common purpose of constructing a systematic and coherent view of the omne scibile (everything knowable). However, omne scibile is not to be understood as total, universal or absolute knowledge (which is the purpose of holistic encyclopedias such as today’s omniscient Wikipedia): the Romans never attempted a complete repertory of the world. The comprehensiveness of omne is referred to two different approaches to knowledge. Firstly, we find a type of complete approach to the knowledge of the physical world (natura), as a natural evolution of the philosophical concern about ta phusika. Lucretius’ De rerum natura (On the nature of things) is a poem on natural science because it is a poem on philosophy. Pliny the Elder’s Natural History attempts to provide a complete description of the physical world and this applies also, on a minor scale, to Solinus. Ampelius adopts this scheme too for the first part of his Liber memorialis (although in the second part he focuses on human geography and history). The same could be said about the anonymous Epitoma disciplinarum, if it actually did not lose a section on arithmetic. For the aforementioned reason, it is not surprising that in works like these (as also in works whose scope is more restricted, like Seneca’s Naturales quaestiones [Natural questions]) a philosophical—​usually Stoic—​standpoint underlies. The other “phenotype” of encyclopedic approach to knowledge in this period is characterized by trying to provide an articulated educational project by means of the exposition of the liberal arts: first the triuium (grammar, rhetoric, and dialectic) and, secondly, the quadriuium (arithmetic, geometry, astronomy, and music). To this type of approach belong the works of Capella and Cassiodorus and also Augustine’s abandoned project. Boethius is aligned as well with this same type through his translations of Greek treatises on arithmetic, music, geometry and, probably, astronomy. Therefore, in this second type of approach the omne scibile corresponds to the summa of knowledge within an educational program. A final prefatory remark regards the question of periodization. The chronological margins of this approach to Latin encyclopedic works roughly overlap with the period we tend to call Late Antiquity. As in any historical periodization, when it is used for framing cultural phenomena, inaugural and closure dates are artificial constructions; in

Late Encyclopedic in Latin Literature    989 a given moment, in a given place there were simultaneously manifestations of classical and of late antique culture, of late antique and of medieval culture. Therefore, if for convenience’s sake, I adopt the mid-​3rd century as starting point, it does not mean that I consider all the Latin literature of mid-​3rd century (and beyond) as late antique literature. On the other extreme, problems grow to define a chronological framework; with the Roman Empire disintegrated, different kingdoms in different places had disparate rhythms in the evolution of their sociopolitical and cultural spheres. Particularly, with respect to the Latin encyclopedic approaches to knowledge, my perception is that Isidore of Seville’s Etymologiae (Etymologies) and De rerum natura (On the nature of things) are a milestone in the historical process of transmission of knowledge to be placed at the threshold of a new era. With his synthesis of ancient culture, Isidore closes a chapter but, at the same time, opens a new book—​the book of medieval encyclopedism.

2.  Lucius Ampelius’ “All the Things You Should Know by Heart” Very little is certainly known about Lucius Ampelius, and very little can be inferred directly from his work. On the condition of accepting a late chronology for them (mid-​ 3rd–​4th century?), Ampelius and his brief book, Liber memorialis (Book of Memory), deserve serious consideration within any approach to late encyclopedic approaches to knowledge in Latin literature. It cannot be otherwise, for it is a work aiming for nothing less than satisfying a reader who wants to know everything. Such a purpose is declared in the epistolary preface: Since you desire to know everything (omnia nosse), I  have written this book of memory (hunc librum memorialem) so that you can know what the world is, what the elements, what the geography of the earth bears and what humankind has achieved.

In the addressee Macrinus some scholars tend to see a young Marcus Opellius Macrinus, the future emperor, for which reason the work and its author are assumed to be located in Mauritanian Caesarea at the last quarter of the 2nd century. Undoubtedly, some elements in the work might support a northern African origin and, from the point of view of chronology, the hypothesis might also be plausible, given the terminus post quem (the mention of Trajan, chap. 47). Nevertheless, the identification of the addressee with the Emperor, which relies basically on the onomastic match, does not seem sufficiently persuasive (for other Macrini in the 3rd–​4th centuries, see Jones-​Martindale-​Morris 1971, 529). Despite its conciseness—​the Latin text barely fills a 50-​page critical edition—​the work is introduced by Ampelius as the answer to Macrinus’ omnivorous curiosity. On the basis of the author’s pedagogical attitude and of such a voracious appetite for

990   Late Antique and Early Byzantine Science learning as the addressee possesses, the context of the triangle author-​reader-​work has been probably oversimplified. Ampelius has been identified with a teacher, probably a rhetor, Macrinus with his young pupil, and the liber with a school handbook. In this construction, however, underlies the assumption that any educational enterprise in Roman literature is automatically to be confined to the realm of school, taking it for granted that there was not any form of written transmission of knowledge beyond the boundaries of school or any educational communication but that existing between teachers and students. And this is not consistent with our experience of Roman culture and literature. What we find in this brief work is a small repository of knowledge to be learned by heart (mandare memoriae is the operation expected for the contents of a liber memorialis like this). It must be noted, however, that this repository does not host any kind of knowl­edge whatsoever, but, quite the contrary, a very particular selection of subjects. The answer to Macrinus’ will to know everything is an encyclopedic program. This program starts with some basic notions ranging from cosmology to astronomy and astrology, to meteorology (chap. 1–​5). Then, it focuses its attention on the earth, describing the four zones in which it is divided: where Romans dwell, that dwelt by the antichthones, and two symmetrical zones underneath (the antipodes); and, finally, the three parts of their own zone (Asia, Libya, Europa) (chap. 6.1–​2). Once the pattern of the earth is outlined, Ampelius opens a geographical catalogue, providing lists of the most renowned peoples, mounts, rivers, and islands. Afterward, he turns to the outer limit of the earth, the Oceanum, which traces the whole perimeter and, in some places, enters inland shaping the inner seas (chap. 6.3–​7). The following chapter (chap. 8) gives an overview of marvelous places in the world (mostly paradoxographica) and marks the transition to the third main element of Ampelius’ formative program, namely humankind. Some of the marvels gathered there are man-​made, but even when this is not the case, the tacit assumption that a beholder is the prerequisite for a marvel to be labeled such prepares the ground for the next section. The third and largest part of the work is dedicated to the human being and to his history: it starts from the legendary beginnings, with the ante-​historical men, who became gods in the collective memory according to an Euhemeristic view of the Pantheon (chap. 9); then the different dynasties ruling the world from the beginning of history (Assyrians, Medes, Persians, Spartans, Athenians, Macedonians, Romans) are recalled, illustrated through the biographical profiles of their kings and most glorious generals (chap. 10–​18). At this point, when the historical review arrives at the current empire ruling the world, the focus narrows and zooms in on specifically Roman history. First a detailed catalogue of Roman generals is offered and then—​unlike for other peoples—​ attention is paid to the most illustrious Roman statesmen as the counterpart to the glorious generals, making clear the point that for the Romans military action and politics are two sides of the same coin. But after this meaningful concession to politics, military history returns to the forefront: the following lists present those citizens who sacrificed themselves for the common good; those who obtained the spolia opima; those who, challenged to single combat, defeated the enemy, and so forth. Civilian conflict is not silenced and place is given to the different plebeian seditions and to the four civil wars of

Late Encyclopedic in Latin Literature    991 Rome. Interestingly, the book ends with a short section dealing with Roman assemblies (de comitiis) and political system (de rebus publicis), proudly introduced as the perfect combination of the three classical political systems: monarchy, aristocracy, and democracy. Equally noteworthy is that the second part of this third section, on Roman history, is almost exclusively concerned with Republican history, while events of the imperial age are systemically omitted. The extreme brevity of Ampelius’ preface just lets the reader see that the Liber memorialis represents a formative enterprise aiming to satiate Macrinus’ hunger for knowledge. In absence of any programmatic indication about his plan, Ampelius’ definition of his encyclopedic endeavor needs to be based upon an attentive reading of the work itself. By considering the global structure and the single themes addressed, it is possible to notice some parallelisms between Ampelius’ educational project and the sort of approach to universal (natural) knowledge pursued by Pliny the Elder. The macro-​ structural pattern for conveying information adopted by Ampelius corresponds with that of books 2 to 7 of the Natural History: the point of departure is a description of the world from a physical geography perspective. First, the world is described as a whole (cosmos) and, second, in its parts (geography of the world). Then, proceeding down (or up?) the scale, both Pliny and Ampelius give entrance to the human being. The subsequent development diverges: Pliny offers a panoramic anthropocentric view of nature, with the human being located in the center and, in a way, with all the rest of nature depending on him; he continues with animals, plants, medicines from plants and from animals and, finally, mineralogy. Ampelius takes another path: he focuses on the human being not from a physiological point of view but from that of human geography, via a thorough review of political geography and history. Rather than expanding his physical exposition of the world by giving place to zoology, botany, and mineralogy, he prefers to point exclusively in the direction of human history. This structure reveals a careful conception of how acquisition of knowledge must proceed, from general to specific, and within the specific from past to present, so that Macrinus may realize that his present time is the last step in a long historical process. Furthermore, it is remarkable that Ampelius’ strategy for presenting and transmitting the bulk of knowledge that an educated Roman of his time should know is based on an enumerative rhetoric, privileging the use of lists and catalogues, more extensive than intensive by their own nature, and obviously much more memory friendly than any other method of transmission of knowledge.

3. Solinus’ Treasure of  Memorabilia As for Ampelius, lack of relevant information makes dating Iulius Solinus’ work a difficult—​and hitherto unsolved—​issue. As a terminus post quem, Vespasian is the last emperor explicitly mentioned, whereas for the terminus ante quem, Servius’ mention and Augustine’s quotations of Solinus indicate circa the end of the 4th or the beginning of the

992   Late Antique and Early Byzantine Science 5th century (Ammianus Marcellinus is likely to have used Solinus as a source, but a systematic study should be still conducted). Attempts to provide a more definite date have not been lacking, nevertheless theories advanced so far are not fully convincing (e.g., Schmidt’s hypothesis that the second version of the work was dedicated to Constantius II on the occasion of his visit to Rome in 357 CE is far from being demonstrative). What we know for sure is that Solinus was definitely not a Christian writer (Paniagua 2014, 139), which somewhat alleviates the effects of the chronological uncertainty. His work poses a further problem: the overwhelming manuscript tradition (over 250 manuscripts from 9th to 16th century) attests two distinguishable versions, presenting different titles, the second being a sort of polished enlarged revision of the first. The most likely reconstruction of events is that Solinus composed this work, entitling it Collectanea rerum memorabilium, but the work began to circulate without his permission. Consequently, Solinus turned back to his unfinished work, polished it by introducing the necessary corrections and enhanced it with different additions, not only of stylistic tone but also with further contents. Then, he changed the title to Polyhistor, with the explicit scope of distinguishing it from the “pirate version,” wrote a new preface where the situation was explained, and addressed the new work to a new dedicatee, which is difficult not to interpret as a sign of his blaming the first dedicatee. Mommsen, last editor of the work, considered that the second version had been enlarged by a 6th-​or 7th-​century forger, who had added the second prefatory letter as an attempt to pass off the forgery as genuine. As a consequence, Mommsen systematically dismissed the second version and only the most prominent additions were reported in an appendix. Therefore, paradoxically, the edition of reference for Solinus only allows for reading the first imperfect version of his work, Collectanea rerum memorabilium, while his second and ultimate version, Polyhistor, remains unedited. In the first preface Solinus introduces his work as a compendium (praef. 2): The book has been designed as a compendium, restrained with moderation to the extent which seemed reasonable so that it would not be overburdened (prodiga copia) or harmfully synthetic (damnosa concinnitas).

In his search for the golden mean, Solinus claims that his work “contains rather the yeast of knowledge than the layers of eloquence,” in such manner that only the essential aspects for the transmission of knowledge have been included, whereas embellishing elements have been discarded. One of the most interesting features of Solinus as an author committed to the transmission of knowledge is his declared consciousness of his lack of originality. He is not a researcher himself, but a bookish man; albeit not close to research in first person, his idea that the ancients were as diligent and careful as to have dealt with every single aspect of scientific knowledge, makes his own investigation unnecessary:  “For what could be ours, when the industriousness of the ancients has left nothing to remain untouched for our generation?” Hence, Solinus envisions his role as guardian of a legacy to be safeguarded and transmitted, at a time of progressive decadence and degeneration

Late Encyclopedic in Latin Literature    993 (1.87). In that situation, it is not surprising if he preferred to choose among the theories so far advanced rather than trying to develop new theories: “we have opted for making a selection from all the existing opinions rather than innovating (innouare).” A perfect instance of his attitude toward plurality of theories can be seen in the opening of his work, where different explanations for the name of Rome are provided, sometimes identifying the promoter of the idea, sometimes just reproducing an opinion without an explicit attribution (1.1–​3): There are those who propose that the name of Rome was first given by Evander, when he besieged the town that was there . . . Heraclides is of the opinion that after the siege of Troy some Achaians came to the place where now is Rome navigating the Tiber, and then by the suggestion of Rome, the most noble among the female prisoners, . . . once they burned their ships, they established their settlement . . . and named the city Rome after her . . . Agathocles writes that Rome was not a prisoner, as said above, but Ascanius’ daughter, Aeneas’ granddaughter.

But the fact that Solinus has chosen the path of personal silence (infantia, which, unlike silentium, means the inability to utter an articulated language, as that of an infant), privileging the voice of tradition (especially from Pliny’s Natural History, his main source), does not mean that his book is just an impersonal compilation wrought from other works. When there is no place for new information, the efforts to innovate and improve must focus on the structure, on the strategic arrangement of that information drawn from the authoritative sources. This implies that in the case of Solinus, his encyclopedic approach to knowledge cannot be characterized only by the sort of observations and notions included in his work but, above all, by the way all this bulk of information is processed and organized within an organic exposition. Where Solinus really takes the helm and gives his personal stamp to the work is at the structural level. The guiding thread that determines the flow and development of the different topics included in the work is of a thematic nature. Solinus finds in the geographical description of the world the leitmotiv for his collection of memorable things: The record of places in the world (locorum commemoratio) comprises most of the work; all the contents are particularly amenable to this aspect. The record of those places has been accomplished in such a way that the renowned lands of the world and the famous tracts of sea have been introduced by us in due order (suo quaeque ordine), following the geographical arrangement.

Precisely for this reason, the Collectanea rerum memorabilium has been traditionally considered a sui generis geographical treatise. Acknowledging the main role of geography as providing the structural frame for the work, Solinus, however, did not write a geographical treatise. His approach to transmission of knowledge formally follows a geographical pattern (remarkably using a map of the oikoumenē rather than applying the traditional periplous scheme, as shown by Brodersen 2011), but he by no means limits his work to geography nor are the rest of topics merely subsidiary to a geographical interest

994   Late Antique and Early Byzantine Science or scope. History and ethnography, alongside mythology and antiquarianism, were part of ancient geography lato sensu, but among the fields of knowledge that Solinus pays attention to, we also find a conspicuous interest in natural science in all its branches: zoology, botany, and mineralogy (as a rule, in this same order). For the structure of his work, nevertheless, he adopts a Romancentric position, starting from Rome as befits the very head of the whole world (caput mundi). The world description, he says, will proceed as any painting of a human figure does; descending from the head to the next parts of the body, respecting the principle of proportionality. It can hardly be a coincidence that the extension of the first chapter, on Rome and on the human being and civilization, holds a bit more than a seventh of the whole work. Solinus’ starting point is, therefore, the origins of Rome and the chronology of the foundation of the city; intertwined with it, he offers a synthetic account of Roman history, from monarchical times to Augustus. With Augustus, Solinus opens an exposition regarding the computus of the year and the reforms of the Roman calendar by Caesar and by Augustus himself. From there, he moves on to considering human physiology: conception, pregnancy, childbirth, and different features (first physical, second moral) of the human being like laugh, strength, genetic traits passed on, Doppelgängers, speed and running endurance, and so forth. After the summary of Roman history and the physiological description of man, Solinus begins his itinerary from Italia, developed along a counterclockwise outward spiral:  Corsica, Sardinia, Sicilia, Graecia, Thessalia, Macedonia, Thracia—​ and the Aegean islands—​Hellespontus, Pontus, the river Hypanis, the lands of the Hyperborei and the Arimphaei, the Oceanus septentrionalis, Germania, Gallia, Britannia, Hispania, Libya, Mauretania, Numidia, Africa, Nassamones, Garamantes, Aethiopes, Aegyptus, Arabia, Ostracine, Iudaea, the Tigris and the Euphrates, Cilicia, Asia, Phrygia, Lydia, Galatia, Bythinia, Paphlagonia, Cappadocia, Assyria, the portae Caspiae, and then the Seres, India, Taprobane (henceforth the spiral trajectory is broken to come back to the West), the Sinus Persicus and the Arabicus, Parthia and Babylonia; and, finally, the islands belonging to the Indian Ocean and, back to the west, to the Atlantic Sea. Solinus’ formula proved successful: the compilation became the vademecum of scientific culture par excellence in the Middle Ages, being the Latin-​prose work transmitted by a larger number of manuscripts between the 9th and the 12th centuries.

4.  The Anonymous Epitoma disciplinarvm (aka Fragmentvm Censorini) The anonymous Epitoma disciplinarum, traditionally known as Fragmentum Censorini, is a piece as engaging as seldom read. This compendium of disciplines has

Late Encyclopedic in Latin Literature    995 been transmitted with Censorinus’ De die natali (On Birthdays, 238 ce). The two best manuscripts transmitting Censorinus’ treatise and the Epitoma disciplinarum derive from an exemplar where the De die natali ended without an explicit. Immediately after the last words of the De die natali and without an incipit or any other sign that there was a transition from one work to another, the second work began with a chapter entitled De naturali institutione. Yet, this chapter is not the beginning of the second work, for the author refers to contents already mentioned in a former section of the work (alias opiniones supra rettuli), now lost. Despite the loss of its beginning and possibly its end, the Fragmentum is a coherent piece that thoroughly reviews phenomena linked to the physical description of the world. Because of this coherence and completeness, the hypothesis that the text, as it is transmitted, might be the result of a material loss in the transmission process (i.e., a folio or a number of folios dropping after the De die natali) is scarcely plausible. The strong likelihood is that the so-​called Fragmentum was an excerptum drawn from a work totally unknown to us, and that it circulated in this manner as a perfectly intentional selection. The excerptum was attached to the De die natali, undoubtedly due to the thematic affinities. With the loss of the explicit closing the treatise of Censorinus, the excerptum was assumed to be part of it. And so it was until Louis Carrion edited the text in 1583. Carrion was the first to separate the second work from the De die natali and presented it as a Fragmentum quoddam nescio cuius scriptoris, antea Censorino tributum (“A certain fragment of an unknown writer, formerly ascribed to Censorinus”), following Vinet’s opinion, expressed in his edition (1568, f. cc iiii), that what came from the chapter De naturali institutione onward was not apparently part of Censorinus’ work. Having thus acquired an existence of its own, the excerptum began to be referred to as Fragmentum Censorini—​misleadingly, since it is unrelated to Censorinus—​or more properly as Fragmentum Censorino tributum (or adscriptum)—​even if, as said before, it is not a fragment but an excerpt. Lately, Sallmann has chosen for his Teubner edition a different, more descriptive title, Anonymi cuiusdam Epitoma disciplinarum, remarking on its autonomous nature, its compilatory character, and its unknown authorship. As is often the case in Latin literature, all we know about the treatise is what it says about itself or what we can distill from it. As to dating, a quotation of the opening verse of Lucan’s Pharsalia furnishes a terminus post quem, while for the terminus ante quem we depend directly on the date of the oldest manuscripts transmitting the work, although the fusion with Censorinus could have already happened by the 6th century (Rouse and Thompson 1983, 48). Furthermore, the Latin formulation of Euclidean Definitions, Postulates and Common Notions (all from Elements 1) provided in ­chapters 6–​8, shows no sign of influence from Boethius’ translation, which would imply that the Epitoma was written before the Boethian Euclid entered into circulation. On the basis of the character of the compilation, the examples provided to illustrate the theoretical exposition and the sources deployed, it is usually thought to have been written in the 3rd century, more or less in the same period as the De die natali itself. However, a wider chronological hypothesis (at least, 3rd–​4th centuries) might be advisable, in view of the close parallels with other 4th-​century writers dealing with similar

996   Late Antique and Early Byzantine Science topics (e.g., the Antiscioi are only mentioned here and in Ammianus Marcellinus [c. 330–​395 ce] 22.15.31: cf. Thesaurus linguae Latinae, s.u. antiscius). The treatise, as transmitted, contains 15 chapters. Regarding the missing part at the beginning of the work, we can only conjecture that a certain amount of chapters have fallen, on account of the author’s statement in chap. 4: The book, filled with the necessary contents, might seem already finished, but since geometry complements not only the dimensions of the world but also many other elements, we shall say a few things on numbers and measures.

Owing to the importance of the ratio geometrica, a few considerations on numbers and measures (pauca de numeris mensurisque dicemus) will be added. Thus, if c­ hapters 5 to 15 are quantitatively considered few (pauca) by the author, this should mean that the first four chapters are nothing but a small part of the treatise. Likewise, the possibility of deeming the first four chapters a complete book on its own is quite odd and seems to imply that before the first transmitted chapter there was a substantial part of the work, now lost. Therefore, chances are that the loss of material has been significant. Regardless of the lost part of the work, the extant chapters of the Epitoma display an encyclopedic approach to the physical world, in which Stoic physics have a major role. • Chapters 1–​4 deal with cosmology, astronomy, and astrology; therein, the treatise offers an exposition of Stoic physics starting from their elements and principles, conflagration being the mechanism of renewal of the whole cosmic cycle. After cosmology, the treatise provides a description of the vault of the sky with its five circles, the zones of the earth, and the zodiac along with its astrological divisions. Then, it moves to the fixed and wandering stars, considered from an astronomical-​ astrological point of view, and finally an outline of the earth’s configuration is sketched. • Chapters 5–​8 explain the principles of geometry; first of all, the treatise advances a definition of geometry (5)  and, then, reproduces a Latin version of Euclid’s Definitions (6–​7), Postulates, and Common Notions (8). • Chapters  9–​12 deal with music; the author first traces the history of poetry to show how music became increasingly independent as lyrical and melic poetry were developed (9); subsequently, the mythological origins of the word “rhythm” (rhythmos) are explained as deriving from Rhythmonius, son of Orpheus and the nymph Idomena (10); the etiological account paves the way for the following section, which offers an explanation of the relationship between poetry and music (11). Finally, the last section furnishes the basics of harmonics. • Chapters 13–​15 tackle metrics, being, in a way, a natural continuation of the music section (cf., e.g., Capella’s book 9). In the first place, metric feet are set out (13) and then comes the turn for a typological distinction of verses into legitimi and simplices (14‒15).

Late Encyclopedic in Latin Literature    997 The distribution of the scientific topics within the treatise matches well with the quadriuium guideline, with the sole absence of arithmetic. In this situation it is not easy to decide whether arithmetic was dealt with in the lost part of the work, which therefore contained a complete description of the quadriuium (albeit with an unusual arrangement of disciplines), or if arithmetic was never part of it. In this latter case, what the Epitoma offered was essentially a Stoic-​based physical description of the world. One of the most remarkable traits of this compendium is the use of ancient and very authoritative Greek and Latin sources; this is particularly noticeable in the field of terminology and, especially, in some translations of Greek technical terms, translations that not always came out victorious within the tradition they belong to (e.g., tenor for hexis, instead of the usual habitus, or nota for the Euclidian sēmeion [punctus in Boethius]). The author of this mysterious text was surely well trained; his acquaintance with the most important Greek texts of every discipline (Cleanthes, Euclid, Aristoxenus, etc.) and his ability to translate and reformulate synthetically notions from Greek, demonstrate he was not an amateur writer. Moreover, the tenor of the contents consigned to the work shows that even if most of the notions aim to educate a beginner, there is a solid, perfectly arranged doctrinal basis upon which a further approach to the disciplines can be developed.

5.  The Encyclopedic Project That Never Was: Augustine of Hippo Any reader of Augustine of Hippo (354–​430 ce) knows that there were, actually, several Augustines within one. His personal, intellectual, and spiritual evolution was so intense during his lifetime that a general description of a particular aspect of his thought on or his attitude toward a given problem can be hardly provided, unless it bears a panoply of exceptions and deviations from the proposed statement. Augustine, like very few ancient writers, is resistant to a static approach; his attitude toward transmission of knowl­ edge and encyclopedism serves to confirm it. His retreat from the chair of rhetoric in the imperial court at Milan in 386—​the peak of his professional career, after teaching at Thagaste, Carthage, and Rome—​barely two years after obtaining it, marked a decisive turning point in his intellectual trajectory. At first, he was probably forced to retire from his teaching duties as a consequence of a pulmonary affection that hindered the normal exercise of his activity (Confessiones 9.2.4), but what began as a temporary retirement ended up as an irreversible retreat. On Easter 387, he received baptism from Ambrose, archbishop of Milan, who had a strong influence over him throughout his stay in northern Italy. One year later, Augustine abandoned Milan to return to Africa. But between his withdrawal from his academic

998   Late Antique and Early Byzantine Science position and the return to his homeland, he intended to carry out an ambitious project. It is summarized in his Retractationes (Retractations), his ultimate review of his own literary career (1.6): In the period that I spent at Milan on the brink of receiving baptism, I also attempted to write some books about the disciplinae, since I asked those who surrounded me and they were not averse to this kind of studies . . . But of those disciplines I only could achieve the book on grammar, which later I lost from my shelves, and six volumes on music, concerning what is called “rhythm.” But I wrote those six books, already baptized and back to Africa from Italy; at Milan I made only the first approach to the discipline. As regards the other five disciplines, which likewise I first approached there, namely dialectic, rhetoric, geometry, arithmetic, philosophy, the enterprise was limited to the mere beginnings. However, I also lost these, but I believe that some people are in possession of them.

Much has been discussed about the nature, contents, and models underlying Augustine’s encyclopedic project, but beyond doubt is that he was persuaded of the need to articulate a comprehensive approach to secular knowledge anew, harmonized with the Christian vision of the world. The traditional (pagan) scientific heritage had always run parallel to the Christian discourse, with which it had never found a point of convergence so far. It is no coincidence that in the same period Ambrose of Milan opened the door to the groundbreaking possibility of adapting ancient natural history in the framing of his Christian expositions, in order to improve, particularly, the zoological observations of his Exameron. Augustine had a profound knowledge of the pagan literary tradition and knew how to exploit it as no other Christian writer had done before. His intense and pervasive employment of classical sources in service to his Christian discourse is impressive and marks a real difference in Christian rhetoric. In this context, Augustine conceived his ambitious proj­ect of giving a new raison d’être to the bulk of traditional knowledge, reorienting it for a Christian mind, setting it into a Christian context. Some issues are raised by the text of the Retractationes quoted above. For present purposes, the main issue concerns the canon of disciplines presented by Augustine: he begins by mentioning grammar, the sole discipline he managed to discuss in a complete work. Then he refers to music, which was never finished, though the section about rhythm was fully completed in six books. Subsequently, he mentions the other disciplines (dialectic, rhetoric, geometry, arithmetic, and philosophy), but all of them remained a mere outline if, as seems, sola principia is to be intended not in the sense of structural arrangement (principia = opening, introduction) but in that of development (principia = sketches, drafts). The list raises an eyebrow from the reader with the last item, philosophia, since it actually breaks the expectations of finding a different discipline, astrologia. This detail is significant because the resulting canon does not match the quadriuium. Moreover, the introduction of philosophy along with the others is really puzzling because philosophy is not at the same level as the seven disciplines. Nevertheless, this troublesome evidence

Late Encyclopedic in Latin Literature    999 should not be overstated; in two other treatises written when Augustine had in mind his encyclopedic project, we find unequivocal statements of how the canon of disciplines had to be constructed. In De ordine (On Order), composed in 386, Augustine provides a neat description of his educational program. For the first stage, grammar, dialectic, and rhetoric remain undisputed: 2.14.39: First it (i.e., ratio) began from hearing (ab auribus), because it claimed ownership over the very words from which it had fashioned grammar, dialectic and rhetoric.

Next, Augustine sets forth the elements shaping the second stage: 2.14.41–​43: This discipline partaking sense and intellect received the name of music. From here reason advanced to the eyesight and, scanning the earth and the sky, realized that nothing pleased it but beauty, and in beauty shapes, and in shapes dimensions, and in dimensions numbers. . . These distinct and separate elements she also reduced to a discipline and called it geometry. The motion of the sky also concerned reason and invited her to consider it dutifully. And there, too, from the constant alternations of the seasons, from the fixed and definite courses of the stars, from the regulated extension of distances, she understood that dimension and numbers held sway. Linking them in order by means of definition and division, it gave birth to astronomy (astrologia), a great subject for religious men and a torment for the curious. In all these disciplines reason interpreted everything as consisting of numbers.

After music, geometry and astronomy, comes arithmetic, whose name, however, is not explicitly uttered. It was not strictly necessary since he had already presented the second part of the itinerary, distinguishing the four disciplines included therein (2.5.14): “Thus, order holds sway in music, in geometry, in the movement of the stars, in the fixed relationship of numbers.” The coincidence is complete not just for the disciplines themselves but also for their arrangement within the sequence. In his De quantitate animae (On the Quantity of the Soul), composed in 387–​388, Augustine lists the disciplines once again (33.72): [Grammar] . . . the invention of so many signs in the alphabet, in the words, in the gestures, in sound of every kind, in paintings and images; so many languages of peoples, . . . [Dialectic] the power of reasoning and contriving, [Rhetoric] the rivers of eloquence, [Music] the diversity of songs, the thousand forms of imitation for the sake of joy or playing, the expertise in measuring rhythmically, [Geometry] the exactness of measuring surfaces, [Arithmetic] the knowledge of numbering, [Astronomy/​ Astrology] the forecast of the past and the future based on present things.

This passage, in spite of the inversion of arithmetic and astronomy, confirms the solidity of the quadriuium as part of his educational plan. Therefore, regardless of the reason for omitting astrologia in the list of the Retractationes, the inclusion of this discipline in his

1000   Late Antique and Early Byzantine Science encyclopedic project is beyond doubt. The De ordine, which in a sense holds Augustine’s theoretical reflections on his project at the time, provides the key to understanding the relationship between the seven disciplines and philosophy, and the purpose of his program: 2.5.14: [after mentioning the seven disciplines] Such a learning, if it is used moderately, . . . nurtures such a soldier, or rather general, of philosophy that, following the path he chooses, he can fly, can reach and can lead many men to that utmost point beyond which he cannot, he must not, he does not desire to search anything.

According to Augustine, his encyclopedic project, the result of combining triuium and quadriuium, nurtures the conditions for becoming a “militant” philosopher. In this sense, we have to recall another passage where Augustine insists on the importance for education of proceeding in order, so that only when the basics are learned can further steps be taken (De ordine 2.7.24): Yet if we were to hear that some schoolmaster is trying to teach syllables to a boy, whom no one has taught the alphabet before, I do not say that he ought to be laughed at as a stupid, but we would think that he ought to be chained up as a madman, for no other reason, in my opinion, that he did not respect order in his teaching.

The example of letters and syllables persists for any kind of content, and ultimately for any kind of learning. The aim of his encyclopedic program was to sow the seeds of secular learning as a necessary first stage for the subsequent search for the truth that brings happiness. It is, therefore, a propaedeutic itinerary from material to immaterial things, as training their minds to contemplate God (De ordine 1.8.24): The learning of the liberal disciplines, however moderate and limited, makes those who love the truth more eager, more steadfast, more competent to embrace it, in such a way that they show a more ardent appetite for what we call happy life, my dear Licentius, they seek it more relentlessly and, at the end, they adhere to it more delightfully.

But in the following years, Augustine progressively abandoned his enterprise as he was losing faith in the usefulness of education for Christians by means of studying the disciplines. It has been argued that Augustine asked of the traditional disciplines what they could not deliver, condemning his project to unavoidable failure; but the example of Cassiodorus easily refutes this view. Augustine was the first to gain insight into the possibilities of pagan learning as a preparation for achieving divine knowledge, but he did not explore it in depth. For Basil and Ambrose the pagan sources could be a useful tool for illustrating a particular point; Augustine, on the other hand, was the first among the fathers of the Church to realize that pagan learning could be systematically exploited not just as a sporadic tool but also as part of Christian education. For Basil and Ambrose pagan learning was an “external resource,” while Augustine did not want

Late Encyclopedic in Latin Literature    1001 it to be “external” anymore. But Augustine’s study of Paul’s Epistles to the Romans and the Galatians made him definitively change his mind, convinced that salvation was only possible through the grace of God and that, in the field of transcendence, the disciplines were completely sterile. In his De doctrina Christiana (On Christian Doctrine), Augustine reconsiders the possibilities of the disciplines for the Christian intellectual, but there they are presented as merely instrumental notions, as many other, subordinated to the correct understanding of the Holy Scriptures. The disciplines do not configure a coherent path leading to philosophy anymore, they simply offer particular knowledge on particular points, and as such they are inserted within Augustine’s hermeneutics at the service of a full understanding and complete explanation of the biblical message. Therefore, the seven disciplines are not a formalized itinerary leading to a level of knowledge needed for achieving happiness. Augustine affirms at the opening of his work that any approach to the Holy Scriptures is based either on giving the means for understanding its message or, once understood, for exposition of that meaning. The first aim stands, on one hand, on grammar as the tool that allows mastering the language of the Holy Scriptures and clarifying any textual obscurity, and on arithmetic and music as competences to comprehend a number of subtleties and nuances in the Bible (2.25–​26: “Ignorance of numbers prevents us from understanding elements that are set down in the Holy Scriptures in a figurative and mystical way . . . ignorance of music closes and obscures, too, not a few things.”). The second aim, on the other hand, stands on rhetoric and dialectic, as they provide the means to transmit and explain the message. Fortunately, some textual traces of his abandoned project of adapting the triuium and quadriuium to a new Christian setting remain alive: the six books on rhythm (all he wrote on music) are preserved in the De musica (On music); and manuscripts also transmit short and unfinished treatises on grammar, dialectic, and rhetoric (probably rightly) ascribed to Augustine, that are, with few exceptions, mostly neglected by scholars.

6.  Martianus Capella’s Invitation to a Wedding Capella’s De nuptiis Philologiae et Mercurii (On the Marriage of Philology and Mercury) is one of the most astonishing displays of technical virtuosity, culture, and erudition in all late antique literature. Scholars are irreconcilably divided between those who consider the work was composed between circa 410–​439 and those who believe it was written by the end of the 5th or the early 6th century. The date of Capella’s work is certainly relevant because his relationship to Augustine’s encyclopedic project and later works, for example, the De doctrina Christiana, is a crucial factor for evaluating his own enterprise.

1002   Late Antique and Early Byzantine Science Should Martianus be dated to the second half of the 5th century, his entire work ought to be read as a dialectical response to Augustine’s “Christian way.” The chronological limits on which everybody agrees are those depending on his use of the Neoplatonist Iamblichus (ca 280), and the latest—​but not the sole—​possible dating (534) for a subscription on one of his manuscripts. Many, however, accept as a terminus ante the date of Boethius’ De consolatione philosophiae (The Consolation of Philosophy, ca 524), where the formal and philosophical influence of Capella is very clear. In either case, Capella, drenched in Paganism and Neoplatonism, can be fairly considered the first and, perhaps, the most illustrious representative of African Renaissance literature, to which poets like Dracontius, Luxorius, Reposianus, the anonymous author of the epyllion Aegritudo Perdicae (The Sickness of Perdica), Corippus, or the enticing prose writer Fulgentius also belonged. The De nuptiis is hard to classify as a work because it is many different things at the same time:  an educative program leading through triuium and quadriuium, a Menippean satire, a sophisticated prosimetrum, a refined allegory, a spoudogeloion (as in Diogenes Laërtius 9.17), a story of Gods and Muses (fabula), a philosophical manifesto, and a theological novel. The result is a holistic product: a literary, philosophical, and scientific work, absolutely tricky to read and understand even for expert classicists: the language is often artificial and extravagant, ambiguous, and full of connotations; the style is mannerist, pompous, and flamboyant—​formerly defined as “barbarous,” missing completely how late antique aesthetics worked. Together with those factors, the opacity of allusions and echoes both in his prose and verse, and the complex nature of the subjects treated, should be counted as ingredients in the recipe of this unique encyclopedic work. Add to the foregoing, the many textual troubles, owing to the manuscript transmission, explain why so few people (editors and translators excluded) have read the De nuptiis from cover to cover. In such a situation, it is even more surprising how Capella’s work could bloom and flourish to the point of becoming an essential reading for some of the seven arts in the Carolingian period and a central text in the medieval school curriculum. The huge number of manuscripts transmitting the work in this period, and the copious Carolingian glosses and commentaries from mid-​9th century onward, attest the enormous interest it raised. The De nuptiis comprises nine books, though it is neatly divided into two different parts. Books 1 and 2 set out the mythos (cf. 2.220: “now, therefore, the myth is concluded; now the following books, which will exalt the arts, begin”), while books 3 to 9 expose the seven liberal arts, arranged in sequential order: (Triuium) 3. grammar, 4. dialectic, 5. rhetoric; (Quadriuium) 6. geometry, 7. arithmetic, 8. astronomy, 9. music. Books 1 and 2, as mentioned, provide the narrative of the mythos. The use of the mythos as a framework for the exposition of the disciplines is to be understood as a Neoplatonic feature, for Neoplatonism claimed the usefulness of myths as functional narrative tools in the philosophical-​religious search for truth (Bovey 2003, 35–​48, cf. Macrobius, Somnium 1.2.9 “narratio fabulosa”). Thus, in the frame of the story (fabula) a particular mythos occurs in the two opening books: the introduction of Philology, her initiation-​like ascent to the heavens and her supreme union to Mercury, god of hermeneutics.

Late Encyclopedic in Latin Literature    1003 Mercury has decided to get married, and the candidates for marriage are many, but Apollo advises him to wed a mighty and much-​learned maiden, of ancient lineage, named Philology. However, she lacks divine rank, so Jupiter must approve the wedding. Mercury’s father will do so because he likes the bride, despite her being much too learned! (1.93: “docta quidem nimis”). A risk indeed, since she can subdue the gods and force them to bow to her commands as Apollo reminds in the introduction (1.22): In many ways she has power over us, she can oblige the gods to obey her commands; and she is able to achieve what no other divine power can; she knows she has power over Jupiter, even against his will.

So Jupiter decrees that henceforth Philology shall be considered divine. The ritual begins; the Muses come to sing at the threshold of her house and, then, she is carried on a star-​ filled litter on the ascent to the abode of the gods, a traveling from home to heaven in which she drinks from the cup of immortality (as Psyche had to do to marry Cupid), offered by her mother Apotheosis. When finally she arrives to Jupiter’s palace in the presence of all the gods, heroes, and immortal souls, Mercury presents his gift to his bride: the seven arts. The seven maidens will sequentially parade showing off their competences, learning, and talents during the remaining seven books (3–​9). From book 3 onward, the fabula proceeds, the mythos is over, philosophical and religious themes almost completely disappear from the front line and the work becomes a truly technical and scientific handbook, interspersed here and there with references to the story and the characters. With Martianus Capella the curriculum of disciplines becomes completely formalized. If Augustine formulated the scheme of his formative program, Capella develops it, giving shape and contents to his encyclopedic project of the liberal arts, thereby ensuring the stability of the pattern. Capella presents the sevenfold program as the result of his decision of leaving aside two other disciplines, medicine and architecture, for they deal with earthly matters and lack any transcendental scope. The real influence of Varro over both Augustine and Capella remains a particularly controversial subject (recent approaches to the problem, like those by Schievenin 2009 and Shanzer 1986, yield contrasting results). However, the fact is that his triuium + quadriuium cycle became the dominant structure for general education. The ordering of the seven disciplines within the triuium and, especially, the quadriuium raises a different issue. For Capella (as for the pseudo-​Agennius Urbicus, in the 6th century), geometry opened the quadriuium, while Augustine set music as the first discipline of this second stage. But some years later, Boethius would add a twist to the formalization of the triuium and the quadriuium with his fresh approach to them.

7.  Boethius, “Ervditorvm vltimvs” Historically, Boethius has been considered one of those figures of antiquity marking a turning point, a point of no return. Lorenzo Valla depicted him as “the last of the

1004   Late Antique and Early Byzantine Science learned” (Dialecticae disputationes 1.praef.7), and Sandys (1921, 253) offered an enhanced description:  “the last of the learned Romans who understood the language and studied the literature of Greece; . . . the first to interpret to the Middle Ages the logical treatises of Aristotle,” remarking that in every historical process when one door closes another opens. Born in Rome (ca 480)  into an illustrious aristocratic family, the Anicii, Anicius Manlius Severinus Boethius can be regarded as the apex of his kin line. And this, paradoxically, was the result of a family disgrace:  the death of his father not long after holding the consulship (487), when Boethius was still a boy. The young orphan was adopted by Aurelius Memmius Symmachus, the most outstanding intellectual of his time, and author of a (lost) Historia Romana (Roman History) in seven books, who took him into a household still more powerful than the Anicii. The family bond was further strengthened by his marriage to Symmachus’ daughter, Rusticiana. Symmachus’ prominence in Roman politics in the era of Odoacer became even greater when Theoderic, king of the Ostrogoths, defeated Odoacer’s troops and seized the political control of Italy (493). Theoderic, raised and finely educated in Constantinople as a hostage, found in Symmachus’ philhellenism and keenness for the Greek belles lettres a valuable quality and a point of affinity. This common background and intellectual esteem allowed an easy understanding between the newcomer king and the spokesman of the traditional senatorial aristocracy, respected by all in Rome as a “new Cato.” For nearly 25 years, until Justin I ascended the throne of Constantinople in 518, the reign of Theoderic was a sort of “Indian summer” in the autumn of the decline of Rome (the metaphor is borrowed from Lafferty 2013). Due to the new king’s mildness, the transition after the defeat of Odoacer was not traumatic; the fear of Catholics at a new Arian king proved unfounded since Theoderic was tolerant of them and even built new churches and temples, preserving those already existing for the Catholics as their legitimate owners. The king of the Ostrogoths was on good terms with bishops and senators and respected the traditional civic Roman culture; he even conceded to apply Roman law to native Italians (but Ostrogothic law to his own people and others). For these 25 years, Theoderic fitted the profile of the enlightened governor, giving to Italy a period of felicitas. Procopius describes him (Bellum Gothicum 5.1.27–​28) as a ruler “exceedingly careful to observe justice,” who “preserved the laws on a sure basis, . . . attained the highest possible degree of wisdom and manliness (andria), . . . committed scarcely a single act of injustice against his subjects nor would he brook such conduct on the part of any one else.” The Anonymus Valesianus (Valesian Anonymous), also called Origo Constantini (The origin of Constantine), asserts (post. 12) that he governed Romans and Goths as one single race, never attempting anything against Catholics, and the Romans addressed him as a “new Trajan” or “new Valentinian.” Throughout this auspicious period, Boethius found the perfect climate to devote himself to his readings and studies of the Greek authors and to composing his own works. Everything changed when Justin I was crowned emperor of Constantinople. Once internal problems were solved, by 523–​524 he focused on re-​establishing the unity of the Church by putting an end to all the schisms and heresies (Arianism included) not

Late Encyclopedic in Latin Literature    1005 only in the Eastern Empire, but also in the West. When Theoderic’s respectful policy toward the Italic Catholics was confronted with Justin’s persecutions of Arians in the East, Theoderic threatened to unleash retaliatory persecutions against Catholics in Italy. The Anonymus Valesianus recounts that a patrician, named Albinus, was accused of conspiring against Theoderic; Boethius came to his defense and claimed the accusation was unfounded but, if Albinus had somehow failed, responsibility should fall on himself and on the whole Senate. The accusation was extended also to Boethius and supported with false witnesses; Boethius was declared guilty without trial and was imprisoned in Pavia where he was executed. Shortly after, Symmachus and Pope John were put to death too. Boethius died in his 40s. His entire literary production, namely the allegorical prosimetrum entitled The Consolation of Philosophy—​written in prison in the last days of his life—​his theological writings, his translations, and commentaries of Greek philosophical and scientific treatises, and his own works, reflect different manifestations of a common intellectual concern; the Christian, the Neoplatonic philosopher, and the scientist are three intertwined facets of the same learned man. In his work we see what is quite rare, how the boundaries separating philosophy from theology and from science in Late Antiquity are hardly distinguishable. His approach to the transmission of knowledge never had the comprehensiveness and systematic articulation of that seen in other writers mentioned above. Thanks to a letter sent to him by Theoderic (Variae 1.45.4, ca 506), we know he cultivated all four disciplines of the quadriuium: Through your translations Pythagoras the musician and Ptolemy the astronomer are now read as Italics; Nicomachus the arithmetician and the geometer Euclid are now heard as Ausonians; Plato the theologian and Aristotle the logician dispute in the language of Quirinus; you have even brought back to the Sicilians Archimedes the engineer, in Latin.

Despite the encomiastic tone of the letter, the existence of translations by Boethius on music, astronomy, arithmetic, and geometry (and a Latin version of Archimedes) seems difficult to deny. According to this statement, Boethius translated the four Greek authorities of each quadriuium discipline. Of these four translations only the Institutio arithmetica (The Principles of Arithmetic) and the Institutio musica (The Principles of Music) have been preserved. The Institutio arithmetica is indeed a translation of Nicomachus’ Introductio arithmetica, not a literal one but a translation where the model is sometimes summarized or even excerpted, sometimes developed or expanded for ease of understanding. But Boethius never strays far from Nicomachus perhaps because, this translation being a youthful work, he lacked the competence to innovate in such a complicated field. His work, in any case, is aimed at beginners (ingredientium animos), as the choice of the title Institutio implies; and the same goes for his Institutio musica. The Institutio arithmetica comprises two books: the first, in 32 chapters, exposes the general structure of the mathesis (arithmetic, music, geometry, and astronomy) and

1006   Late Antique and Early Byzantine Science the preeminence of arithmetic over the rest; the concept and definition of number, and the notions of evens and odds, perfect numbers and multiples. The second book consists of 54 chapters dealing with equality and inequality, linear and solid numbers; the concept of arithmetic proportion; arithmetic, geometric and harmonic mean, and their respective properties. The case of the Institutio musica is somewhat different; of course, it could not be a treatise of Pythagoras in translation: in the letter Pythagoras stands for the Pythagorean tradition. In absence of a definite model, scholars believe that the treatise on music is the result of a combination of sources, which implies a personal selection of materials. Scholars suppose that Nicomachus of Gerasa again (probably through a lost Introductio musica), Ptolemy’s Harmonics, Euclid and, perhaps, Gaudentius (in the Latin version of Mutianus) are the main sources employed by Boethius. Of the five books on music, the last one is incomplete: book 1 presents a general introduction to the subject, with special attention to inequality (inaequalitas) as the basis for intervals and consonances; book 2 sets forth the arithmetical aspects underlying to the intervals, and book 3 follows naturally the exposition of book 2 by discussing the semitone; book 4 introduces basic issues related to acoustics, outlines the Greek musical notation system, and offers an accomplished description of the monochord; book 5 abridges the first book of Ptolemy’s Harmonics and discusses the main disputes among earlier writers. Two works on geometry have been also transmitted in association with Boethius’ name and auctoritas but, although, quite probably in both the cases, the texts are constructed from Boethian materials, neither is genuinely Boethian. The so-​called Geometria I was probably composed at Corbie (in Picardy, 8th–​9th centuries), while the Geometria II was likely written by Franco of Liège shortly before 1050. The ascription to Boethius of the Euclides Latinus conserved in a Verona palimpsest datable to the end of the 5th century remains controversial. As for the last discipline of the quadriuium, Boethius’ translation of Ptolemy’s astronomical work has left absolutely no trace. On the other hand, he did not greatly concern himself with the triuium, but asserting he did not cultivate it at all would be misleading, for in his works on logic, albeit written from a markedly philosophical standpoint, dialectic plays a strong role. Boethius’ main contribution to the sciences of the quadriuium (a term seemingly coined by him) was not their development, but rather providing new tools for learning with his translations of Greek propaedeutic works to those sciences, and in fact he was already remembered as an outstanding translator by his contemporary Cassiodorus.

8.  Cassiodorus: Architect of the Medieval Trivivm and Qvadrivivm A man of great learning and distinguished for having hold many high offices, despite his young age; when he was counselor of his father

Late Encyclopedic in Latin Literature    1007 Cassiodorus, patrician and Praetorian Prefect, he delivered an eloquent speech in praise of Theoderic, King of the Goths, by whom he was first appointed Quaestor, later Patrician and Consul, and afterwards Master of the Offices (magister officiorum), and became responsible for the release of chancery documents, which he arranged in twelve books and entitled Variae; by request of King Theoderic, he wrote a history of the Goths setting forth their lineage, origins, and traditions in various books.

This is how Cassiodorus introduces himself in the Anecdoton Holderi (aka Ordo generis Cassiodororum), probably composed sometime between 522 and 536. Cassiodorus and Boethius belonged to the same generation: the latter held his consulship in 510, the former four years later. Their lives ran parallel also when Cassiodorus became magister officiorum (523–​528) to succeed Boethius, who occupied the position barely for a year as a consequence of falling from grace with Theoderic. A few years after the king’s death, Cassiodorus was appointed praetorian prefect (533 to ca 539), which granted him legislative and administrative authority throughout Italy. It was during this time when he and Pope Agapetus (535–​536) conceived the idea of employing learned teachers in Christian public schools of Rome, as had been traditionally done in Alexandria and was being done at that time in Nisibis (Syria). According to Cassiodorus, the pursuit of secular learning was in excellent health at the time thanks to its celeberrima traditio, but that was not the case for the learning of the Holy Scriptures. Yet fiery wars and struggles in Italy kept the idea from being effectively developed. When Constantinople signed the “Eternal Peace” treaty with the Persian Sassanids, the new Emperor Justinian was committed to recover the western territories of the empire and his General Belisarius first subdued the Vandals in North Africa and later the Ostrogoths in Italy; in 540 he seized Ravenna. Thenceforth, Cassiodorus disappears from sight; he probably was in Constantinople from 540 to 554, voluntarily or not. The details remain obscure but, with the Fifth Ecumenical Council putting an end to the Three-​ Chapter controversy and the Pragmatic Sanction of 554 restoring peace in Italy under Byzantine rule and allowing refugees to return home, the strong likelihood is that Cassiodorus returned to his native Scyllacium (mod. Squillace), on the coast of the Ionian Sea. At his return, he converted to Christianity and abandoned mundane concerns; he was in his mid-​60s. From his former life, before his exile, only the decision of founding a Christian learning institution remained; a project he undertook on his properties at Vivarium. Cassiodorus describes it as a monastery, completely isolated from the outer world by a wall but furnished with irrigated gardens and fish hatcheries, next to the river Pellena: a city on a small scale. Although the Institutiones diuinarum et saecularium litterarum (Principles of Divine and Secular Learning) in two books was produced at the end of his life, the manuscript tradition demonstrates that a draft on secular learning (the δ recension) was ready sometime between 536 and 554, and another (φ), more distinctively Christian, before 562. At a later stage, probably in Vivarium, a treatment of divine learning was composed

1008   Late Antique and Early Byzantine Science as the mirror-​image counterpart to the former; and then both parts were assembled in a sole comprehensive treatise. With this work Cassiodorus sought to carry out Augustine’s youthful project for reconciling the traditional triuium and quadriuium program with a Christian education. For him, the knowledge transmitted by the traditional disciplines was undoubtedly necessary for the correct understanding of the Holy Scriptures. At the end of his exegetical magnum opus, the Exposition of the Psalms (cap. 150), he summarizes all the categories of knowledge present in the Psalms as follows: [W]‌e have hereby shown that the series of the Psalms is full of grammar and etymologies, of figures of speech, of rhetoric, of topics, of dialectic, of definitions, of music, of geometry, of astronomy and of proper phrases of divine law.

A passage very close to the one in the Institutiones (chap. 27) where he emphasizes the importance of secular letters: both in the Holy Scriptures and in the writings of the most learned interpreters we are able to understand many things through figures of speech, definitions, grammar, rhetoric, dialectic, the discipline of arithmetic, music, the discipline of geometry, astronomy.

Cassiodorus believed that knowledge of those disciplines was necessary for the study of the sacred texts and, therefore, it should not be rejected; otherwise whenever one of those subjects was treated in the Holy Scriptures, a correct understanding of the text would not be feasible. Thus, albeit formerly circulating on its own, the draft on secular learning was in the end joined with the part on Christian learning in a single treatise embracing all knowl­ edge to be acquired, according to Cassiodorus’ idea of what a complete education ought to be. When, in his years as praetorian prefect, Cassiodorus and Pope Agapetus tried to collect money to hire the best professors for the Christian schools of the city, the enterprise proved impossible for various reasons. The interesting thing about the Institutiones is that in this mature work Cassiodorus does not present just an ideological project of how he conceived the education of the monks of Vivarium and how he considered that it should be carried out, nor does he furnish merely a detailed program of studies; the Institutiones are altogether the very tool for developing and putting into practice his formative project. The experience gained from the first failure led him to try another path; teachers would not be sought anymore. What Cassiodorus proposes instead is that his own books might take the place of teachers as introductions to the different disciplines (1.praef.1: . . . introductorios libros . . . ad uicem magistri). For this reason, the Institutiones are written in a plain style since their aim is not to display a polished eloquence but the description of essentials. They are intended as a guide to the different sources both of profane and Christian knowledge. Accordingly, the Institutiones do not contain Cassiodorus’ own teaching, but the teaching of the authorities in their different fields, filtered and in small doses. Therefore, Cassiodorus’ main role in his project is to serve as a compass for

Late Encyclopedic in Latin Literature    1009 the students, which gives rise to a crucial question: Cuius in usum? Cassiodorus models his work as a tool to be used by those monks who, after studying the sacred texts, have become familiar with them. The Institutiones comprise a step-​by-​step program, inasmuch as the formative itinerary is envisaged as an ascent to the full contemplation of God. The first stage involves the study of the Holy Scriptures, as well as their interpreters and commentators, without disregarding Christian historians. Once this stage has been completed, Cassiodorus recommends the study of the relevant geographical treatises (Julius Orator  =  Honorius’ Cosmographia; Count Marcellinus, Dionysius Periegetes and, as an advanced reading, Ptolemy’s Geographia). At this point, students move to the study of the second formative stage, that regarding secular learning. Nevertheless, for those whose simplicitas does not allow them to proceed to the second stage, Cassiodorus prescribes a sketchy approach, to let them get acquainted with the structure, uses, and virtues of the subjects of the liberal arts. For monks unable to receive a complete education in either secular or sacred knowledge, Cassiodorus suggests a different framework, oriented toward a different type of knowledge, such as agriculture and gardening or medicine. Interestingly, also in this case, Cassiodorus offers a number of readings (Gargilius Martialis, Columella, and Palladius for agriculture; Caelius Aurelianus, and Latin versions of Dioscorides, Hippocrates and Galen, for medicine), referring the main issues treated by each of them and, occasionally, even their stylistic features. The second stage of learning leads the student through the triuium and the quadriuium (which Cassiodorus calls mathematica). It is worthwhile noting that the discipline that takes up most of his attention is dialectic, covering over a third of the second book. In this manner, Cassiodorus follows Augustine’s steps, who gave the utmost relevance to dialectic, explicitly regarded as disciplina disciplinarum. At the other extreme, his treatment of geometry is short and superficial, a surprisingly disappointing overview. As in the former sections, here Cassiodorus furnishes a brief history and the basic notions of each discipline and, subsequently, he points out which authors to be read to achieve a solid competence or to gain a deeper insight into the matter: Helenus, Priscian, Palaemon, Phocas, Probus, Censorinus, Donatus, and Augustine for grammar; Cicero, Quintilianus, Marius Victorinus, and Fortunatianus for rhetoric; Porphyry, Aristotle (in the Latin translations of Victorinus and Cicero), Boethius, and Apuleius for dialectic; Nicomachus of Gerasa (in the Latin translations of Apuleius and Boethius), Alypius, Euclid, Gaudentius, and Ptolemy—​among the Greeks—​and Albinus, Apuleius, Censorinus, and Augustine—​among the Romans—​for music; Euclid (in the Latin translation of Boethius), Apollonius of Perga and Archimedes for geometry; Ptolemy for astronomy. The aim of an elaborated bibliographical apparatus is not merely ornamental or erudite: with this sort of “annotated bibliography,” Cassiodorus gives specific instructions to the monks for exploiting the resources of the library, and he is unknowingly setting out the “canon” of auctores for the medieval triuium and quadriuium. Therefore, the Institutiones provide an encyclopedic approach to knowledge, sacred and secular, theoretical and applied, within the framework of the educational proj­ect for the monastery of Vivarium. Through his work Cassiodorus manages to bring forth Augustine’s failed project of integrating traditional learning within the program of a

1010   Late Antique and Early Byzantine Science complete Christian education, a project that, ultimately, laid the basis for the Western medieval school.

Bibliography General Entries in EANS: Palladius Aemilianus, 35–​36 (Rodgers); Albinus 52 (Irby-​Massie); Alupios, 62 (Mathiesen); Ambrose, 63–​ 64 (Bjornlie); Ampelius, 67 (Keyser); Apuleius, 119–​ 120 (Opsomer); Aurelius Augustinus, “St. Augustine,” 182 (Mathiesen); Boëthius, 195 (Guillaumin); Caelius Aurelianus, 201–​202 (Scarborough); Censorinus, 212 (Karamanolis); Martianus Capella, 205–​206 (Guillaumin); Dionusios of Alexandria, Periēgētēs, 261–​262 (Dueck); Gargilius Martialis, 343 (Rodgers); Gaudentius, 343–​344 (Mathiesen); Iamblikhos of Khalkis, 430–​431 (Lautner); Isidore of Seville, 445 (Somfai); Iulius Honorius, 454 (Lozovsky); Iulius Solinus, 455–​456 (Lozovsky); Iunius Columella, 456–​457 (Rodgers); Mucianus /​Mutianus, 564 (Keyser and Irby-​ Massie); Nikomakhos of Gerasa, 579 (Jones); Cassiodorus Senator, 731–​732 (Bjornlie); Macrobius Ambrosius Theodosius, 790 (Bjornlie). Codoñer, C. “La enciclopedia. Un género sin definición. Siglos I  a.C‒VII d.C.” In L’enciclopedismo dall’Antichità al Rinascimento:  Giornate filologiche Genovesi (1‒3 ottobre 2009), ed. C. Fossati, 116–​153. Genova: D.AR.FI.CL.ET, 2011. Della Corte, F. Enciclopedisti latini. Genova: Libreria Internazionale di Stefano S.A., 1946. Díaz y Díaz, M. C., Enciclopedismo e sapere cristiano. Tra tardo-​antico e alto Medioevo. Milano: Jaca Books, 1999. Formisano, M. Tecnica e scrittura. Le letterature tecnico-​scientifiche nello spazio letterario tardolatino. Roma: Carocci, 2001. —​—​—​. “Late Latin Encyclopaedism:  Towards A  New Paradigm of Practical Knowledge.” In Encyclopaedism from Antiquity to the Renaissance, ed. J. König and G. Woolf, 197–​215. Cambridge: Cambridge University Press, 2013. Fowler, R. L. “Encyclopaedias:  Definitions and Theoretical Problems.” In Pre-​Modern Encyclopaedic Texts: Proceedings of the Second COMERS Congress, Groningen, 1‒4 July 1996, ed. P. Binkley, 3–​29. Leiden: Brill, 1997. Jones, A. H. M., Martindale, J. R., and J. Morris. The Prosopography of the Later Roman Empire. Vol. 1: A.D. 260–​395. Cambridge: Cambridge University Press, 1971. Pizzani, U. “Quadrivio.” In Letteratura scientifica e tecnica di Grecia e Roma, ed. C. Santini, 445–​ 554. Roma: Carocci, 2002. Ribémont, B. Les origines des encyclopédies médiévales. D’Isidore de Séville aux Carolingiens. Paris: Champion, 2001. Sandys, J. E. A History of Classical Scholarship. Vol. 1: From the Sixth Century B.C. to the End of the Middle Ages. 3d ed. Cambridge: Cambridge University Press, 1921. Zimmermann, B. “Osservazioni sulla ‘enciclopedia’ nella letteratura latina.” In L’enciclopedismo medievale, ed. M. Picone, 41–​51. Ravenna: Longo, 1994.

Ampelius Arnaud-​Lindet, M.-​P., ed. L. Ampelius, Aide-​ mémoire (Liber memorialis). Paris:  Belles Lettres, 1993.

Late Encyclopedic in Latin Literature    1011 —​—​—​. “Le Liber Memorialis de L. Ampélius.” Aufstieg und Niedergang der Römischen Welt 2.34.3 (1997): 2301–​2312. Lashbrook, A. M. “Lucius Ampelius: Liber memorialis. Translation and Commentary.” PhD diss., University of Pennsylvania, 1960. [The sole English translation of this work.]

Solinus Brodersen, K. “Mapping Pliny’s World: The Achievement of Solinus.” Bulletin of the Institute of Classical Studies 54 (2011): 63–​88. Mommsen, T. C. Iulii Solini Collectanea rerum memorabilium. 2nd ed. Berlin: Weidmann, 1895. Paniagua, D. “El guardián de la memoria. Solino y sus Collectanea rerum memorabilium.” Voces 19 (2008): 103–​113. —​—​—​. “Iisdem fere uerbis Solini saepe sunt sententias mutuati:  Solinus and Late Antique Christian Literature, from Ambrose to Augustine. An Old Assumption Re-​examined.” In Solinus: New Studies, ed. Kai Brodersen, 119–​140. Heidelberg: Verlag Antike, 2014.

EPITOMA DISCIPLINARVM Cristante, L. “Appunti su Pseudo Censorino frg. 9‒11 (con una proposta di edizione).” In Ways of Approaching Knowledge in Late Antiquity and the Early Middle Ages. Schools and Scholarship, ed. P. F. Alberto and D. Paniagua, 104–​119. Nordhausen: Traugott Bautz, 2012. Freybourger, J. “Le savoir philologique du grammairien Censorinus.” Ktema 13 (1988): 149–​154. Rouse, R. H. and R. M. Thomson. “Censorinus.” In Texts and Transmission: A Survey of the Latin Classics, ed. L. D. Reynolds, 48–​50. Oxford: Clarendon Press, 1983. Sallmann, N. Censorini De die natali ad Q. Caerellium. Accedit Anonymi cuiusdam epitoma disciplinarum (Fragmentum Censorini). Leipzig: Teubner, 1983.

Augustine of Hippo Hadot, I. Arts libéraux et philosophie dans la pensée antique. Paris: Vrin, 1984. Law, V. “St. Augustine’s De grammatica:  Lost or Found?” Recherches Augustiniennes 19 (1984): 155–​183. Marrou, H.-​I. Saint Augustin et la fin de la culture antique. 4th ed. Paris: Boccard, 1958. Shanzer, D. “Augustine’s Disciplines:  Silent diutius Musae Varronis?” In Augustine and the Disciplines, ed. K. Pollmann and M. Vessey, 69–​112. Oxford, New York: Oxford University Press, 2005. van Flateren, F. “St. Augustine, Neoplatonism, and the Liberal Arts: The Background to De doctrina christiana.” In De doctrina christiana: A Classic of Western Culture, ed. D. W. H. Arnold and P. Bright, 14–​24. Notre Dame: University of Notre Dame Press, 1995.

Martianus Capella Bovey, M. Disciplinae cyclicae. L’organisation du savoir dans l’œuvre de Martianus Capella. Trieste: Edizioni Università di Trieste, 2003. Cristante, L., ed. Martiani Capellae De nuptiis Philologiae et Mercurii libri I‒II. Hildesheim: Olms, 2011. LeMoine, F. Martianus Capella: A Literary Re-​evaluation. Munich: Arbeo-​Gesellschaft, 1972.

1012   Late Antique and Early Byzantine Science Schievenin, R. Nugis ignosce lectitans. Studi su Marziano Capella, Trieste: Edizioni Università di Trieste, 2009. Shanzer, D. A Philosophical and Literary Commentary on Martianus Capella’s De nuptiis Philologiae et Mercurii, Book 1. Berkeley, Los Angeles, and London: University of California Press, 1986. Stahl, W., et  al. Martianus Capella and the Seven Liberal Arts. 2  vols. New  York, London: Columbia University Press, 1971–​1977. Willis, J., ed. Martianus Capella. Leipzig: Teubner, 1983.

Boethius Caldwell, J. “The De Institutione Arithmetica and the De Institutione Musica.” In Gibson 1981, 135–​154. Chadwick, H. Boethius. The Consolations of Music, Logic, Theology, and Philosophy. Oxford: Clarendon, and New York: Oxford University Press, 1981. Folkerts, M. Boethius Geometrie II. Ein mathematisches Lehrbuch des Mittelalters. Wiesbaden: Franz Steiner, 1970. Gibson, M., ed. Boethius: His Life, Thought and Influence. Oxford: Blackwell, 1981. Guillaumin, J.-​Y., ed. Boèce. Institution arithmétique. Paris: Les Belles Lettres, 1995. Lafferty, S. D. W. Law and Society in the Age of Theoderic the Great: A Study of the Edictum Theoderici. Cambridge: Cambridge University Press, 2013. Matthews, J. “Anicius Manlius Severinus Boethius.” In Gibson 1981, 15–​43. Oosthout, H., and J. Schilling, eds. Anicii Manlii Seuerini Boethii, De arithmetica (Corpus Christianorum. Series Latina 94A). Turnhout: Brepols, 1999. Pingree, D. “Boethius’ Geometry and Astronomy.” In Gibson 1981, 155–​161.

Cassiodorus Adriaen, M., ed. Cassiodorus. Expositio Psalmorum. Corpus Christianorum. Series Latina 97–​ 98. Turnhout: Brepols, 1958. Della Corte, F. “La posizione di Cassiodoro nella storia dell’enciclopedia.” In Flavio Magno Aurelio Cassiodoro. Atti della settimana di Studi Cosenza-​Squillace 19‒24 sett. 1983, ed. S. Leanza, 29–​48. Soveria-​Mannelli: Rubbettino, 1986. Galonnier, A. “Anecdoton Holderi ou Ordo generis Cassiodororum. Introduction, édition, traduction et commentaire.” Antiquité Tardive 4 (1996): 299–​312. Halporn, J. W. and M. Vessey. Cassiodorus: Institutions of Divine and Secular Learning. On the Soul. Liverpool: Liverpool University Press, 2004. Mynors, R. A. B., ed. Cassiodori senatoris Institutiones. Oxford: Clarendon Press, 1937; 2nd ed., 1963. O’Donnell, J. J. Cassiodorus. Berkeley, Los Angeles: University of California Press, 1979. Ribémont, B. “Cassiodore et ses Institutiones.” In Ribémont 2001, 19–​38.

chapter E8

M edical Wri t i ng i n the L ate Roma n We st Louise Cilliers

1. Introduction The 4th to the 7th centuries were a turbulent period in the history of the western Roman Empire. Civil wars, incursions by pagan and Christian Germanic tribes, and the sack of Rome on two occasions, concomitant with economic problems and epidemics, culminated in the deposition of the last Roman emperor in the West in 476 ce. The passing of Italy and the provinces under Germanic kings followed, but lasted less than half a century, after which Justinian, the Christian emperor of the Eastern Roman Empire, reconquered Italy and Africa. The city of Rome was ravaged and, with aqueducts cut and walls breached, it was reduced to a miserable village and entered the medieval period of its existence. In the next century, Islamic Arabic onslaughts swept away the last traces of Byzantine rule in Italy and Africa. And yet, despite these unsettled circumstances, various writers made valuable contributions to ancient medicine, either by way of translations of Greek texts or writing books in Latin based on Greek texts. These works emanated mainly from two centers, namely Ravenna in northern Italy, and Carthage (and other cities) in North Africa.

2. Time Frame The time frame of this discussion, namely 300‒650 ce, is primarily determined by the historical circumstances. Temkin (1977, 167)  describes the period after the death of Galen—​the 3rd century and the first half of the 4th century—​as “one of the most obscure epochs as far as the history of medicine is concerned,” which brings us to the second half of the 4th century as our starting date. Our ending date is the 7th century. After the

1014   Late Antique and Early Byzantine Science Byzantine reconquest of parts of Italy and North Africa in the 6th century, it was overrun by the Arabs in the 7th century. In North Africa all traces of Roman/​Byzantine influence were obliterated completely, as if the Romans had never set foot there, and North Africa turned its back on Europe and became part of Africa and the Islamic East. In Italy the 7th century also marked the beginning of the Dark Ages, in contrast to the flourishing world of Christian Byzantium and the Islamic caliphate. The intellectual centers became increasingly isolated, “dismembered fragments of a deteriorating Empire” (Green 1985, 130). For the next five centuries, knowledge would be stored away in the isolated courts of Germanic kings and monastic libraries.

3.  The Decline of Bilingualism and the Need for Translations After Galen (129–​199/​216 ce), the literary output of the medical sciences in the Latin West consisted of • translations of earlier Greek works into Latin; • the writing of new books based on Greek texts, but written in Latin; and • a large group of anonymous or pseudonymous texts in Latin (Sigerist 1958, 131). In the western part of the empire, elite Roman society was essentially bilingual through ca 200 ce (Horace, Odes 3.8.5; see also Pliny, Letters 3.1.7; Augustine, City of God 8.12; Sabbah 1998, 137–​138). Latin was the language of law and the forum, while Greek was the language of science, philosophy, and medicine (Marrou 1982, 255). However, by the late 2nd century, the knowledge of Greek had begun to decline in the west. After the “Constitutio Antoniniana” in 212, giving Roman citizenship to all inhabitants of the empire, Roman law applied to all citizens, and Latin became the universal language of the courts and the administration throughout the empire. Sigerist (1958, 131) also points out that Latin was the vernacular language of Italy, Sicily, Sardinia, Gaul, and Spain, and the literary language of North Africa, Germany, and Britain. Greek therefore gradually lost ground in literature and science. By the 3rd century in the West, few doctors were familiar with Greek, and by the late 4th century, knowledge of Greek was becoming rare, even among educated classes (Green 1985, 133; Kotula 1969, 386–​392). This resulted in a growing need to make the rich Greek medical tradition accessible to all by translating it into Latin. Sabbah (1998, 147) points out that two conditions were necessary to meet this need, namely a knowledge of the Greek language and Greek medical texts, and the realization of the urgency to pass on the treasures of the Greek masters of old into Latin, a language understood by the masses. This happened to be the serendipitous situation in North Africa, where the Roman physician Vindicianus (ca 330 to ca 410 ce) was the first of a number of medical authors to translate Greek works into Latin. In the introduction

Medical Writing in the Late Roman West    1015 of his Gynaecia, he explicitly states that the work is a rendering of “Greek books” into Latin for the sake of those who no longer understand Greek. In the 5th and 6th centuries, various other authors followed his example. In this period translations were also made at Ravenna in northern Italy. Temkin (1977, 166) is of the opinion that the efforts of these translators “to salvage the tremendous treasures of a great past can be seen as the historical achievement of the first half of the millennium.” These translations were indeed a feat in themselves, since there was no recognized scientific Latin vocabulary and the translators had to adapt Greek works to the Roman mentality while remaining faithful to the spirit and content of the original. Another important characteristic of this era was making compilations in which the emphasis was on preserving and systematizing existing knowledge rather than on original research. Nutton (1984, 2) refers to the authors of the 4th and 5th centuries as “the summarizers, the encyclopedists.” He refers to the Greek authors Oribasius, Aëtius, Alexander, and Paul (of the 4th to 7th centuries) as “the medical refrigerators of antiquity.” One should, however, not fail to see the originality of the work of translation. Nutton rightly concedes (1984, 3) that the translators were not “dumb copyists,” but that their compendia were the outcome of a process of selection, categorization, adaptation, and rearrangement, and should be seen on their own terms.

4.  A Choice Between Greek and Roman Models and Its Implications The process of translating, adapting, and abbreviating classical learning from Greek into Latin had, of course, started much earlier, as can be seen in Celsus’ encyclopedic De medicina (On Medicine: 1st century ce) and the 37 books of Pliny the Elder’s Natural History. In these two works, the Roman inclination “to extract and collect, to minimize theory (and even consistency) in favor of the practical uses of specific, sometimes incompatible units of knowledge” (Cadden 1993, 42) was evident and would dominate the trend during the following centuries. This Roman tendency coexisted with the Greek alternative: “the theoretical, systematic, and even grandiose vision of medicine and natural philosophy, represented by Galen” (Cadden 1993, 42). Authors of the later Roman Empire in the West were therefore faced with two divergent models: one intending to present information, the other philosophical principles. The model provided by Pliny initially prevailed, but even his encyclopedic approach proved too comprehensive, and in the early Middle Ages his works were scaled down. Practicality, brevity, eclecticism, and indifference to theory were the characteristics of the Middle Ages (Cadden 1993, 42–​43). Extensive theoretical discussions were omitted (e.g., Soranus’ effort to prove women suffered from the same kind of diseases as men). This affected medical thought: the opportunity for debate, speculation, and especially system building was lost and the content was at times

1016   Late Antique and Early Byzantine Science narrowed to something resembling the question-​and-​answer genre, amounting to a mere catechism containing just the bare essential knowledge for specific situations.

5. North Africa In a sense, geography determined not only the choice of the model but also the works to be translated. North Africa, facing Rome on the west coast of Italy, followed the predilections in medicine characteristic of Roman society since the Republic. Ravenna, the other center of translation, was, thanks to its location as a harbor city on the east coast of Italy, open to trends from the East, and “showed the influence of new currents in medicine being developed contemporaneously in the Byzantine world” (Green 1985, 133). A large number of medical texts were produced during the Late Roman Empire in North Africa, particularly in the Roman province of Africa Proconsularis with Carthage as its capital. This density of Latin medical works led Sabbah (1998, 131–​150) to propose the existence of an “African school” of doctors and/​or medical writers between ca 370 and ca 450 ce. The question arises how this rather neglected province could be the source of such productivity—​it was ruined after the Third Punic War (149–​146 bce), then left to itself until the time of Caesar when Carthage was officially refounded as a Roman city (46 bce). Even during the empire, emperors seldom visited it, since it was regarded as a military backwater. See the map in figure E8.1. Various reasons can be adduced, the most important its peace and stability in the 3rd and 4th centuries while the rest of the Roman world was ravaged by civil wars, plundering, and epidemics. In the meantime, storm clouds were gathering on the horizon with Germanic hordes from the northeast descending on the empire’s frontiers and culminating in the sack of Rome in 410 by Alaric and his Goths. North Africa was the last province to be overrun by the Germanic peoples. A stable society is also a prerequisite for agriculture, and North Africa’s prosperity depended mainly on the export of agricultural products, particularly olives. The enormous quantities of olive oil shipped to Italy and the provinces brought great wealth to the area: various authors referred to the country’s wealth, for instance, the 5th-​century Gallic monk, Salvian, stated, “Africa was so rich that thanks to the opulence of her commerce she seemed to possess the treasure house of the whole world” (Governance of God 7.13–​17, in Corpus Scriptorum Ecclesiasticorum Latinorum 8.173–​181). This peace and stability made intellectual pursuits and cultural activities possible. A further clue to understanding the great number of medical works emanating from North Africa is found in the schooling system. Augustine (354–​430 ce) commented that though he was taught Greek in his native town, Thagaste, he was not very good at it (Confessions 1.13.20 and 1.14.23). This shows that while knowledge of Greek was becoming rare in the West, it was still taught at a primary school in a small provincial town in Africa. This is an important observation, revealing why North African

Medical Writing in the Late Roman West    1017 authors were able to translate Greek medical works into Latin and adapt it for their use. Augustine of Hippo finished his schooling at Carthage, which at that stage was regarded as second only to Rome as a center of Latin studies. Salvian mentions with admiration that the liberal arts, Greek and Latin literature and philosophy were taught in Carthage (Governance of God 7.16, in Corpus Scriptorum Ecclesiasticorum Latinorum 8.173–​181). Medical sciences would also have been part of the syllabus (Sabbah 1998, 131–​150). There is also evidence of contact between scholars and physicians from Carthage and the famous Alexandrian medical school, which experienced a revival in the 4th century. This school, which Sabbah calls “the lighthouse of medicine in the 4th century” (1998, 148), attracted brilliant scholars from all over, including Galen, some of whose works were included in the Alexandrian medical curriculum (Nutton 1972, 172). This stimulation would undoubtedly have influenced the unusual medical and scientific activity in Carthage in the 4th and 5th centuries. The renowned physician Vindicianus (ca 330‒ca 410 ce), for instance, was clearly familiar with the views of medical authors in Alexandria. Against the above background of the intellectual climate in Carthage in the 3rd and 4th centuries, Sabbah’s suggestion of an “African school” of doctors and/​or medical writers, translators and adapters of earlier Greek medical works, seems plausible. Although there is no specific mention of such a medical “school,” Sabbah believes there is enough evidence to postulate such a school, in the broad sense of the word, could have existed in the flourishing metropolis of Africa, “actives, renommées, fréquentées par des étudiants nombreux ” (active, famed, attended by many students; 1998, 144). He bases his view on the nature of the various medical works of the late 4th and 5th centuries, for instance Vindicianus’ Gynaecia and his Epistula ad nepotem Pentadium, Theodorus Priscianus’ Euporiston, and the De medicina of Cassius Felix. These works are dry, dogmatic manuals, summarizing aspects of anatomy, gynecology, and pharmacology, and could well have been basic handbooks for medical students. The fact that they were written in Latin supports this view, since subsequent generations of youngsters no longer understood Greek.

5.1.  Vindicianus (ca 330‒ca 410 ce) The growing need in the West for the translation of Greek medical works into Latin was first realized—​and met—​by the Carthaginian physician, Helvius Vindicianus (erroneously identified with one Avianus Vindicianus, vicarius in a diocese in the West and consularis Campaniae (CIL Corpus Inscriptionum Latinarum 10.1683; 6312–​3; rectified by Beschaouch 1968, 133–​135 and 209–​210; see also Marasco 1998a, 259 n. 46 and Fiorucci 2012, 483). In the introductory chapter of two of the manuscripts of his Gynaecia, he clearly states that the work is a rendering of “Greek books into Latin for the sake of those who no longer understand Greek.” Vindicianus was born in North Africa (“Vindicianus Afer,” Cassius Felix 32.4) and probably also educated there, but in the 60s and 70s of the 4th century he served as

1018   Late Antique and Early Byzantine Science one of the archiatri sacri palatii under Emperor Valentinian I (r. 364–​375 ce) and his son Gratian (r. 367–​383 ce) in their court in the Gallic city of Treviri (Trier) (Matthews 1975, 72–​73; Fiorucci 2012, 485). Thanks to meritorious service he was appointed head of the College of Master Physicians (Comes archiatrorum: see Codex Theodosianus 13.3.12), established by Valentinian in 368 ce; in that role, he had to guard the privileges and obligations of the other physicians of the college. While in Trier, Vindicianus probably met the Greek physician, Julius Ausonius, whose son, the well-​known poet, Decimus Ausonius, had great influence at the court, being the tutor of the young Emperor Gratian; Decimus could have played a role in the appointment of Vindicianus, then already at a mature age, as proconsul of Africa Proconsularis for 380/​1 ce (Fiorucci 2012, 486). Now a Vir Clarissimus, Vindicianus entered the ruling senatorial order and as such represented the new cultural elite. The career of Vindicianus illustrates the tendency in the late empire that archiatri, when transferred by favor of the emperor to an administrative career, could assume a more important role in public life and society (Marasco 1998, 282). On the evidence of Vindicianus’ exceptional career, Sabbah (1998, 143–​144) suggests he could have been the founder of the proposed medical “school.” The confident and dogmatic tone of his letter to Emperor Valentinian and his negative remarks regarding the competence of fellow doctors that highlighted his own expertise could well support Sabbah’s suggestion. However, Vindicianus was not only held in high regard in his official capacity but also as physician and person. When he was back in North Africa he had on one occasion to present the prize of a poetry competition to a young student, Augustine, whom he got to know well in the following years. In his Confessions 4.3, Augustine of Hippo, while a student in Carthage, left the following testimonial to the mentor of his youth: “There was at that time a man of deep understanding, who had an excellent reputation for his great skill as a doctor.” His fame even spread to Gaul, where Marcellus of Bordeaux (see sec. 7) knew of him and quoted one of his recipes for coughing (On Medicine 16.100). Vindicianus’ works, written in the late 4th century, are among the earliest Latin medical writings to have come from Africa and are also the first of a number of Latin medical compilations produced in North Africa in the late 4th and early 5th centuries. Langslow remarks that these works heralded “the beginning of what may be seen as a ‘Golden Age’ of ancient Latin medical compendia, in that a number of stylish, sophisticated and authoritative compilations were produced in Latin by practicing doctors during the period ca 370–​450 ce” (2000, 63). The contribution of these Latin medical works lies in their transmitting the legacy of the past rather than in inventing a new system of thought in contrast to the Arabic East where the inheritance was “actively manipulated to create an entirely novel entity” (Green 1985, 171–​172). In the West the manipulation consisted mainly in the condensation and adaptation of the existing material. Time has not been kind to Vindicianus, and the only works that have been transmitted are the Gynaecia and two letters, one to his nephew Pentadius and the other to Emperor Valentinian. A  number of other works on human anatomy, said to be related to the Gynaecia, have erroneously been ascribed to Vindicianus:  (1) the so-​called Epitome

Medical Writing in the Late Roman West    1019 Altera, (2) the fragment in the Codex Parisinus 7027 referred to as the De natura generis humani (On the Nature of Mankind), and (3) the treatise referred to as the De semine (On Semen) in the Codex Bruxellensis 1348 (see Cilliers 2005, 154–​155 for a succinct overview regarding the relation of these manuscripts and their erroneous attribution to Vindicianus). The Gynaecia is a concise treatise on the anatomy of the human body in the usual format a capite ad calcem (“from head to heel”: Cilliers 2005, 166–​195), with the professed aim of providing knowledge normally gained during dissection, which the Romans were not allowed to perform (see von Staden 1989, 138–​153). Some chapters on conception and the development of the embryo/​fetus follow the anatomical section. The work was probably written as a textbook for medical students or as a vademecum for doctors when traveling. Owing to its practical value, the Gynaecia was a very popular treatise in early medieval times—​it was, according to Langslow (2000, 65), “one of the standard texts on anatomy and physiology in the pre-​Salernitan period.” The Epistula Vindiciani comitis archiatrorum ad Valentinianum imperatorem (Letter of Vindicianus, Head of the Master Physicians, to Emperor Valentinian) contains the introduction to Vindicianus’ lost collection of pharmaceutical recipes (Niedermann and Liechtenhan 1968, 46–​52), dedicated to Emperor Valentinian I  (r. 364–​375 ce). The letter was written during 371–​375 ce, while Vindicianus was still in Trier (Fiorucci 2012, 496): his confident tone reflects his superiority as head of the College of Master Physicians. It is written in the first person and addressed to the emperor personally—​ the only instance of a physician being so close to the emperor, besides Oribasius, who was the personal physician to Emperor Julian (r. 361–​363 ce) (Fiorucci 2012, 495). Five recipes that have survived are referred to in the works of other authors. In the letter itself, which is a self-​recommendation parading the author’s superior knowledge rather than a mere dedication, Vindicianus describes two case studies: in the first patient he diagnosed extreme constipation; the second patient had a continuous flow of tears. The Epistula ad Pentadium nepotem suum, de quattuor humoribus in corpore humano (Letter to His Nephew Pentadius, on the Four Humors in the Human Body) was an authoritative work throughout the Middle Ages (Rose 1894, 484–​492). This brief treatise gives an elementary account of physiology based on the Hippocratic theory of the four humors and was written for Vindicianus’ nephew, Pentadius, who was starting his medical studies. The work differs from the Hippocratic versions in that it is adapted to Roman circumstances and in addition discusses the characteristics of the different humoral types (Deichgräber 1961, 31–​32). There is at present a lively debate on the date and authorship of the letter, after some articles by the French scholar Jacques Jouanna (2005a, 138–​167; 2005b, 1–​27; and 2006, 117–​141) who dated it to the so-​called second renaissance in Alexandria, 6th century ce, which immediately makes the authenticity of the letter problematic. Reaction has come from various scholars, which cannot, due to space, be discussed here; convincing arguments against Jouanna’s view have however, been forwarded by Stok (2012a,137–​143 ; and 2012b, 517–​532), and by Fiorucci (2009, 67–​ 90), who emphasizes the complexity of the problem and proposes a far more detailed investigation of certain aspects, such as the language and manuscript tradition.

1020   Late Antique and Early Byzantine Science These three short works of Vindicianus were among the most widely excerpted medical works throughout postclassical times and the Middle Ages (Langslow 2000, 65).

5.2. Theodorus Priscianus (ca 400 ce) We know very little about Theodorus Priscianus apart from the fact that he had been a student of Vindicianus (Physica par. 3), which implies that he was also a native of North Africa. He himself states that he was already an old man (Faenomenon par. 5) when he wrote the Euporiston (Accessible, sc., remedies; Rose 1894), which situates him in about 400 ce. It is possible that he was also an archiater (master physician) like his mentor, Vindicianus. Theodorus is the author of an extant three-​part medical handbook, the Euporiston, consisting of the Faenomenon on external ailments, described a capite ad calcem, the Logicus on acute and chronic diseases of the internal parts, and the Gynaecia on female disorders. A  fragmentary fourth book, the Physica (sc. remedia), written for his son Eusebius, contains an introduction, a chapter on headaches, a section on epilepsy, and various folk remedies, the effect of which depends on a network of sympathetic and antithetic forces designated as magic. As one of the bilingual translators active in the early 5th century, Theodorus initially wrote the Euporiston in Greek (now lost) because he believed he would win fame that way (Faenomenon par. 1). He then translated it into an abbreviated Latin version himself, showing the same mastery of both Latin and Greek as his mentor, Vindicianus. The Euporiston is a compendium of popular and practical remedies for diseases. It was not written for learned doctors but for laymen and women, especially midwives, giving the medical information in an understandable form. As Theodorus was a fervent advocate of natural remedies, the compilation of recipes in the Euporiston consists of easily obtainable components—​plants and minerals, as well as ingredients of the popular “Dreckapotheke” (various animal dungs and urines) from which simple and easily concocted medicines could be made. The book also contains much folklore, magic, and incantations. In short, the Euporiston is a typical mixture of theoretical medicine combined with empirical and superstitious folk medicine (Meyer 1909, 38). Theodorus was an eclectic, and the Euporiston contains heterogeneous medical components. Galen partially underpins the Logicus (on materia medica, “drug ingredients”), yet there are also traces of the Greek author Dioscorides, the Latin authors Pliny and Scribonius Largus, as well as Gargilius Martialis (see sec. 5.6). The Faenomenon is based on natural remedies of local origin (Scarborough in EANS, 787–​ 788). The Gynaecia is mainly based on Soranus, although the etiology, symptomology and therapy are sometimes drastically simplified and abbreviated and not in the same order. It is devoted to pharmacological recipes for problems such as breast engorgement, various uterine conditions, infertility, and also discusses contraceptives. On one issue, however, Theodorus differs markedly from Soranus, namely in his discussion of uterine suffocation (Gynaecia par.6–​8). He ascribes this to the uterus “being drawn up

Medical Writing in the Late Roman West    1021 to the chest,” a condition for which he prescribes an odiferous therapy to lure the uterus down to lower parts, a theory Soranus had decidedly rejected: “For the uterus does not issue forth like a wild animal from the lair, delighted by fragrant odors and fleeing from bad odors” (Soranus, Gynaikeia 3.29). This theory of the “wandering womb,” which had its earliest extant explicit mention in Plato’s Timaeus 91a–​b, shows how a deeply ingrained belief about female physiology has in this case triumphed over a completely logical medical explanation. Regarding therapy, Theodorus was equally eclectic, using any procedure that seemed applicable, whatever its origin. There was no place in his work for theoretical discussion or for physiology and anatomy per se (although his remedies show that he must have had considerable knowledge in this regard). For the pathology of external diseases he used the Hippocratic humoral theory, while the Methodists’ status theory of constriction and relaxation was more suitable in the case of internal diseases. In the treatment of the diseases, Methodist views are prevalent: a distinction was made between acute and chronic diseases, each with its own treatment, and harsh and pungent remedies were avoided and only used in recalcitrant cases. The medical writings of Theodorus had been transmitted to Italy by the mid-​6th century. The Euporiston was not only known in North Italy, but was, according to Green (1985, 209), also used as a source for the Latin version of Oribasius’ encyclopedias. Judging from the number of extant manuscripts, the Gynaecia, which often circulated independently of the Euporiston, was popular until the late Middle Ages. Looking back, one realizes that the preservation and transmission of medical manuscripts from North Africa was a miracle. The 5th and 6th centuries were turbulent times in North Africa. The conquest by the Germanic Vandals, followed by the reconquest of North Africa by the Byzantine armies of Justinian, and then the invasion of the Islamic armies, caused enormous disruption of society, and sent waves of refugees across the Mediterranean to Europe. Many of these refugees would have taken with them to Italy and Spain manuscripts, among which there would have been the Latin translations of ancient medical texts. Green (1985, 209) sees this as “the principal reason why much late antique African literature has survived at all”. Travel was still possible, Carthage was still an open harbor and a stopping point for ships, and there still seemed to have been an effective postal system (one need only think of Augustine of Hippo, who maintained regular correspondence with friends in Italy, and sent manuscripts as far as Jerusalem).

5.3 Cassius Felix (ca 447 ce) Contrary to various other authors of this period who made use of popular Latin sources (for instance Gargilius Martialis, Marcellus of Bordeaux, and the author of the Medicina Plinii), Cassius Felix, like the other Roman authors of North Africa in the early 5th century, based his short Latin treatise, the De medicina, on Greek sources. However, it differs from the Euporiston of Theodorus Priscianus (which offers simple and accessible

1022   Late Antique and Early Byzantine Science medicine to heal oneself), by targeting a group of readers who were not only literate, but who also knew enough Greek not to be derailed by the many Greek terms used in the treatise. Fraisse (2002, xvi–​xvii) argues that the target group may have been young doctors, since the recurring criticism of the medical corps occurring in, for instance, Pliny the Elder, Vindicianus, and Theodorus Priscianus, is absent from Cassius Felix, and the few negative remarks are not as virulent and sarcastic as in the case of his predecessors. The De medicina consists of 82 chapters, each dealing with a specific disease or problem, and following the usual pattern of head-​to-​heel. The translation and citations are interspersed with numerous snippets from Cassius’ own experience as medical practitioner. It is dedicated to the consuls of 447 ce, Artaburus and Catalepius. Sabbah discusses Cassius’ African origin (1998, 138–​149). A  funerary inscription from Cirta (modern Constantine in Algeria) affirms that Cassius and/​or his ancestors were resident in this town (CIL 87566). It therefore seems probable that he was a respected physician in Cirta before moving to Carthage where he became an honored archiater (see the De Miraculis Sancti Stephani Protomartyris, in Patrologia Latina 41.833–​854). Cassius was a Christian, the only medical author from North Africa in the period discussed who openly professed a Christian faith (in the preface, Omnipotentis dei nutu: “at the will of almighty God”). Vindicianus and Theodorus Priscianus still remained attached to the philosophical and medical concept of natura /​physis (“nature” as a divinity). The impression that the De medicina was not written for the general public is confirmed by the fact that there is little discussion of magic, so frequent in popular works. Only four remedies would qualify as magic whereas they abound in Theodorus Priscianus. There are furthermore only three references to animal excrement or animal gall, the typical components of folklore recipes. The relatively technical level of certain recommended procedures, the treatment indicated and the surgery described, seem to indicate that Cassius was a specialist, writing for fellow physicians or those aspiring to become physicians. The recommended treatments and the use of surgery in the De medicina distinguish it from most other Latin medical works, which eschew surgery (Vindicianus disapproved of using the knife since it was too painful, and Theodorus only used phlebotomy). The De medicina clearly has a didactic approach, as Cassius’ penchant for etymological explanations shows—​24 names of diseases (usually derived from Greek terms) are discussed, making complex scientific concepts accessible. Cassius’ pedagogical approach gives rise to the question whether the De medicina could perhaps have been a course of lectures given by an archiater to some of his more advanced students. In his introduction, Cassius writes that his Latin breviloquium (brief discourse) provides us with a summary of the knowledge taken from the Greek authors of the Rationalist or Dogmatic sect. He pays specific attention to Hippocrates and Galen in adopting the humoral theory and in using his nosological notions of “mixture” (crasis, acrasia, and dyscrasia). The notion of critical days also clearly shows Rationalist pathology. In therapeutics Cassius adopts the Hippocratic principle of allopathy (contraria contrariis: opposites through opposites), medicaments of which the quality

Medical Writing in the Late Roman West    1023 is the opposite of that which dominates in the malady, for instance in c­ hapter 29.5, he recommends a mixture of the white of an egg and a woman’s milk to be instilled in a sore eye, to sweeten the pungency of the bad humor that causes the discomfort. Various Methodist elements can, however, also be discerned. Cassius combines the Hippocratic principle of allopathy with the Methodist theory of the commonalities, that is, of constriction and relaxation. He also adopted the Methodist view that each disease must be judged on its own merit and that, for instance, age, sex, strength, and time of the malady must be taken into account. The De medicina became very popular in early medieval times.; for example, ­chapter 24 (on ignis sacer, a skin disease whose symptoms included red patches on the face and legs) is quoted by Isidore of Seville, Etymologies (4.8.4), a book that became the basic encyclopedia of the medieval West.

5.4 Caelius Aurelianus (ca 400–​450 ce) Very little is known of Caelius Aurelianus’ life apart from the fact that he comes from Sicca Veneria in the Roman province of Africa Proconsularis (today Le Kef in Tunisia) and was the most important representative in the Latin language of the Methodist school. It is uncertain whether he was a practicing doctor himself. For want of further evidence he is dated to the first half of the 5th century. Linguistic parallels with Cassius Felix support this. Three works can with certainty be ascribed to him, namely the two books of Acute and Chronic Diseases (Drabkin 1950), and his partly extant version of Soranus’ Gynaecia (Hanson and Green 1996). Among his lost works is a (Greek) letter to a certain Praetextatus, who some scholars have identified as Rufus Praetextatus Postumianus, consul in 448 ce (Scarborough in EANS, 201–​202). In contrast, Sabbah (1998, 141–​142) identifies the addressee as Vettius Agorius Praetextatus, who died in 384 ce, which would make Caelius a contemporary of Vindicianus. (The question then arises why there is no mention whatsoever or reference to Caelius in the works of Vindicianus or Theodorus Priscianus, both fellow Africans.) Apart from some lost books on fevers to which Caelius himself refers, only one of at least nine books of his Medicinales responsiones (Medical Answers) has survived. The Celeres passiones (Acute Diseases) in three books and the Tardae passiones (Chronic Diseases) in five books are two vast treatises on diseases. In the preface of the Acute Diseases, Caelius states that its purpose is to make the works of the Greeks more comprehensible to a certain Bellicus, who is called his “best pupil.” The pathology, symptomology, diagnosis, and therapy of diseases as practiced by the Methodists are discussed in the two volumes (14 in the Acute Diseases, and 44 in the Chronic Diseases). This is then followed by an account of the therapeutics of earlier doctors. These therapeutics are resoundingly refuted without exception. These doxographic accounts are of great importance to us, since they preserved considerable material from the now-​lost works of famous physicians. However, the question arises: What relevance would they have had for contemporaries if all their predecessors’ therapies

1024   Late Antique and Early Byzantine Science had been refuted? This recounting of mistakes made by earlier physicians could have been useful to current practitioners who could learn from them (Scarborough in EANS, 201–​202); less likely is van der Eijk’s view (1999, 451–​452) that, in keeping with a widespread tendency to antiquarianism in the 2nd century ce (per van der Eijk’s argument), Caelius might have recorded the views of earlier physicians, however false and useless. The vexing question of the fidelity of Caelius’ versions to Soranus’ works is still being debated, especially regarding the Acute and Chronic Diseases. It was long believed that these two volumes were, if not literal translations, at least faithful renderings of Soranus’ work under the same title. However, in his discussion of this problem, van der Eijk mentioned some objections to this view and came to the conclusion that Caelius’ Acute and Chronic Diseases, “though no doubt heavily dependent on Soranus, cannot be treated as a work by Soranus preserved in Latin” (1999, 417). There is, however, a closer relationship between Caelius’ Gynaecia and that of Soranus, but even in this case the former’s work should be seen as “a version of Soranus’ Gynaecia” rather than a translation, “Soranian” rather than “Soranus” (Hanson and Green 1996, 977). Book 1 contains a discussion of pregnancy and some children’s diseases, while book 2 deals with gynecological problems. We seem to have a greatly abbreviated reworking of Soranus, and much of the doxographical material has for instance been omitted, but Fischer (forthcoming 2018) moots the idea that the abbreviation could have been done by a later scholar. It seems likely that Caelius’ longer Latin version of the Gynaecia, written as a practical manual of gynecology for midwives who could no longer read Greek, was used by his fellow African, Cassius Felix, who incorporated the gynecological chapters into what he calls his breviloquium, the De medicina (thus also Sabbah 1998, 142, n. 61). The small number of references to Caelius Aurelianus in later ages leads one to believe that many of his works were already lost in Late Antiquity. In the 6th century Cassiodorus mentions a work of Caelius (the De medicina) as one of those which should be read by his monks (see sec. 6), but it is uncertain whether this is indeed a reference to a work by Caelius himself or perhaps to a later Pseudepigraphon ascribed to him.

5.5 Muscio/​Mustio (ca 550 ce) Muscio/​Mustio is an otherwise unknown author of the 5th/​6th century, resident in North Africa. Only one work is extant, namely the Gynaecia or De muliebribus passionibus (Rose 1882), an extended Latin catechism (i.e., in question-​and-​answer format) on midwifery and women’s diseases. It is generally based on the gynecological works of Soranus, though much abbreviated and without much of the doxographic material. The work is written in Latin for midwives of the lower social classes who no longer understood Greek, and Muscio states his aim was to elevate the standard and status of these women by providing them with a systematic presentation of the necessary gynecological material, without any superstitious prescriptions or magic procedures. The Gynaecia is a translation/​adaptation of two Greek gynecological works; the author

Medical Writing in the Late Roman West    1025 begins with the longer Triacontas (Thirties; Hanson and Green 1996, 1030 and n. 30, and others, believe that this title probably refers to the full-​length version of Soranus’ Gynaikeia), but states that, fearing its length would overtax women’s minds, he changed to the catechistic Cateperotiana (from the Greek κατ᾽ + ἐπερωτάω, i.e., “by inquiry”), and when chapters were too short, he added passages from the Triacontas. It is likely that Muscio thought Soranus had written both works. Muscio largely maintains the essence of Soranus’ theories, except in the section on uterine suffocation where he reverts to the popular belief that “the uterus ascends upward toward the chest” (Gynaecia 2.4.26; see also Theodorus Priscianus, Gynaecia par. 6–​8), which Soranus had so clearly refuted. But then Muscio faithfully repeats Soranus’ censure of the odor therapy, contradicting his own adherence to the “wandering womb” theory. Muscio’s merit was that he adapted Soranus’ material and made it accessible to the public of his age; the influence of his work in the Middle Ages was profound, attested by the 13 transmitted manuscripts containing the text and the three adaptations made of it.

5.6 Gargilius Martialis (ca 220–​260 ce) Chronologically Gargilius Martialis, a native of the Roman province of Mauretania in North Africa, could have been mentioned much earlier, but the remedies in his Medicinae ex holeribus et pomis (Medicines from Greens and Fruits) only became popular in the early Middle Ages (Maire 2002). This work discusses the medicinal uses of about 60 field and garden plants. Riddle believes that Gargilius was probably not a doctor but a farm manager who had to treat illnesses and injuries (1984, 414). In his recommendation of simple household remedies or euporista in the running of a farm, Gargilius followed in the tradition of Cato, Varro, and Columella. His remedies met the needs of the farm, manor, and monastery in the Middle Ages.

5.7 Q. Serenus Sammonicus (ca 200? ce) Serenus Sammonicus, the author of the Liber medicinalis, is essentially undatable, although Scarborough (in EANS, 734) suggests identifying him with the antiquarian of ca 200 ce. This therapeutical poem offers remedies for about 80 diseases and is presented in hexameters. It was copied on the order of Charlemagne and was of great importance among the Humanists (Langslow 2000, 64).

6. Ravenna That Ravenna was a meeting place of cultures is clearly shown by, inter alia, the splendid early Christian and Byzantine mosaics that adorned its basilicas and reflected the methods, designs, and imagery of East and West alike. The city suddenly acquired

1026   Late Antique and Early Byzantine Science historic importance when, in 402, the ineffectual Emperor Honorius (r. 393–​423 ce), under pressure from the invading Germanic armies moved his court from Milan to Ravenna because of its safe location. Ravenna thus remained the royal residence and capital of Italy until the dissolution of the Roman Empire in the West in 476 ce. Within a few years, the Germanic mercenaries, who had deposed the last emperor, were defeated by the Ostrogoths under Theodoric who was proclaimed emperor and made Ravenna the capital of the Ostrogothic Empire. He was an enlightened ruler, maintained the Roman administrative system and was on friendly terms with his Roman subjects. For the more than 30 years of Theodoric’s rule (493–​526 ce) there was peace. Then Ravenna was conquered by the Byzantines and became the seat of direct representatives of the Eastern emperor for the next two centuries. Green (1985, 140) points out that during Theodoric’s reign ties with the East Roman government in Constantinople were strengthened. This had the advantage that scholars in Ravenna could again consult the incomparable resources of Greek and Hellenistic texts, which had become less and less accessible. But it was mainly the ties Ravenna had with Alexandria in Egypt that led to the production of translations of several of the “most important medical writings of classical and Byzantine times” (Green 1985, 40). The library in Alexandria, the seat of learning since its foundation ca 320 bce, contained the greatest collection of manuscripts ever assembled in antiquity (Parsons 1952, 71): 10 great halls, lined with shelves, housed thousands of manuscripts accumulated over centuries (cf. El-​Abbadi and Fathallah 2008). That Alexandria’s equally famous medical school still had a great reputation in the 4th century ce is attested by references in a number of authors. Ammianus Marcellinus (330–​395 ce), for instance, stated in passing, “it is enough for a doctor in advertising the merit of his art to mention that he was educated at Alexandria” (Histories 22.16.18). As for Ravenna, Sigerist (1958, 135) is of the opinion that this city was the center of a flourishing medical school, comparable to Alexandria’s, where works of Galen, Hippocrates, and others were translated into Latin. Among the scholars who spent some time in Ravenna during this period, was the politician, writer and monk, Cassiodorus (ca 490–​585 ce), who was the chancellor to the Ostrogothic king, Theodoric. Cassiodorus later withdrew to his monastery at Vivarium in southern Italy where he organized translations and manuscript copying. He wrote an introduction to the studies of the monks, called the Institutiones, which was a compendium of knowledge he thought necessary for his monks. Some medical works are recommended for reading in the compendium: the Herbarium of Dioscorides, “Hippocrates” (not otherwise specified), Galen’s Therapeutics to Glaucus (translated into Latin), and a work of Caelius Aurelianus (see sec. 5.4). Green (1985, 139)  points out that in the 6th century monks and clerics increasingly became the disseminators of knowledge. Owing to the increasing isolation from centers of learning in the East, the Latin West had to rely on what had been translated or borrowed from the Greek sources. This obviously reinforced the tendency to make compilations. Monasteries increasingly became the repositories of classical learning. The role of the Benedictine monastic order must be mentioned here. The original “rule,”

Medical Writing in the Late Roman West    1027 set down by its founder, Benedict of Nursia (ca 480–​547 ce), abbot of Monte Cassino in Italy, contained the imperative of caring for the sick. Somewhat later, the enterprise of copying manuscripts took root, spread to many other Benedictine monasteries, and eventually became one of their most important contributions. Also belonging to Theodoric’s court in Ravenna in the early 6th century was Anthimus (ca 475–​525 ce). His short treatise, Epistula Anthimi de observatione ciborum (Letter of Anthimus About Managing Food), was couched in the form of a letter to Theuderic, king of the Franks. This booklet on medical dietetics became very popular in the courts of the Germanic kings of the Roman West (Scarborough in EANS, 91).

6.1 Hippocrates and Galen in Ravenna Although the 4th-​and 5th-​century authors in the Latin West discussed above show no direct influence of Hippocrates (Temkin 1977, 176), there seems to have been renewed interest in his works in the later Roman Empire from the 5th to the 7th centuries. A compilation of some Hippocratic works was made in Ravenna in the 6th century and transmitted as a composite treatise, the Liber ad Mecenatem (Book to Maecenas). The treatise, introduced by an apocryphal letter supposedly written by Hippocrates to Maecenas and outlining the purpose and content of the work, contains a section on Diseases of Women, book 1.  Mazzini (1983), who compared this Hippocratic text with that in other manuscripts, indicated the alterations and adaptations made by the translator(s), showing that translation was not a mere mechanical process. Among the additions, he noted that Greek and Latin equivalents and botanical synonyms were given for some technical terms, and the symptomology of the diseases were more specific and detailed. Repetitions and digressions, as well as purely theoretical or “immoral” passages on the pleasures of the sexual act were omitted. There were also variations, for instance in the ingredients of recipes. Although the basic elements of the Hippocratic text were retained, the text was deliberately manipulated in this case. Another major Hippocratic work, Diseases of Women, book 2, as well as Aphorisms, was also translated into Latin, possibly also at Ravenna (Green 1985, 146). Owing to Ravenna’s connection with Alexandria, Galen gradually filtered through to the West via translations. Contrary to the popularity of his works in the Greek East where 129 of his treatises were translated into Arabic, only four were translated into Latin in the West, namely the De sectis ad introducendos (On Medical Sects, for Beginners), Ars medica (The Medical Art), De pulsibus ad tirones (On Pulses, for Novices), and De methodo medendi ad Glauconem (Method of Healing, to Glaukon; Green 1985, 149–​155). Galen was certainly known in the West, but as Temkin states (1977, 176–​177), “where only bare facts, shortened and summarized, were admitted, there Galen the systematist, the logician and sophist, could not possibly become a hero.” Though Galen left virtually no trace in Latin literature up to the 6th century, there could possibly have been a revival of interest when the works of Oribasius, who gave Galen pride of place, were translated into Latin in or near Ravenna in the 6th century (Mørland 1952, 43–​51). That Galen was

1028   Late Antique and Early Byzantine Science known in Ravenna by the 7th century is confirmed by the use of a Latin version of his On Medical Sects, for Beginners by the teacher Agnellus of Ravenna (ca 590–​615 ce). This work seems to have been one of the elementary texts taught as part of a curriculum probably also followed in Alexandria (Scarborough in EANS, 46).

7.  Elsewhere in Europe The 37 books of Pliny the Elder’s Natural History (77 ce) had a strong influence on Latin medical literature of Late Antiquity. It was still very much in vogue in the late 4th century but had become too extensive and cumbersome for the needs of the time. In answer to these needs, an anonymous author who called himself Plinius Secundus Iunior (he is also referred to as Plinius Medicus), made an abridgement of the medical sections in Pliny’s Natural History, especially books 20–​23 on pharmaceuticals derived from plants, animals, and minerals. This work, referred to as the Medicina Plinii secundi, proved to be very popular and was widely used in all levels of society in the West (Önnerfors 1964). In the introduction it says it was written primarily for travelers to protect them against quackery and ineffective drugs. It was in circulation by 400 ce, since Marcellus of Bordeaux states he had used “both Plinys” (Niedermann and Liechtenhan 1968, 2). About 420 ce, Marcellus of Bordeaux, motivated by the general distrust of doctors, or their absence, especially in the countryside, compiled a farrago of everything he thought useful for the populace at large to heal themselves. Marcellus held the high rank of vir illustris and was magister officiorum (chief of the chancellery) under Emperor Theodosius I in 394–​395 ce (he is also called “Empiricus” from the title given to the first printed edition of his book, by Janus Cornarius in 1530). The De medicamentis (On Drugs), which Marcellus wrote for his sons, is mainly devoted to “rural and popular remedies, checked by experience” (praef. 2). The work comprises 36 chapters, giving simple and compound remedies (about 2,500 in all) for numerous diseases, as well as superstitious practices, magical spells, and incantations for ailments from head-​to-​heel. This reflected the “real” world of Roman Gaul among farmers, country dwellers, drug sellers, and hawkers of potions (Scarborough in EANS, 75), in contrast to the “high” medicine of, for example, Scribonius Largus and Galen. The De medicamentis can thus be said to belong to the genre of euporista—​a genre that became very popular in Late Antiquity. Alexander of Tralleis (ca 550–​605 ce), the last great physician of antiquity, is found in Rome at the end of his career. He probably studied at Alexandria for a period of time but was eventually called to Rome to hold a position of the highest distinction (Scarborough in EANS, 58–​59). He traveled widely in the East and West, settling down in various places where he gathered local folk traditions on drugs and therapies. His works are consequently interspersed with local pharmaceutical recipes. Alexander was greatly admired; even modern doctors call him “the third Hippocrates” (Scarborough

Figure E8.1  Map showing late Roman sites mentioned. Ancient World Mapping Center.

1030   Late Antique and Early Byzantine Science in EANS, 59). His extant works are Twelve Books on Medicine (ailments and pathologies from head-​to-​heel), Books on Fevers, and a Letter on Intestinal Worms (the first parasitological work worthy of the name). Short anonymous or pseudonymous texts, that is, compilations of abstracts of well-​ known medical works and presented as epistles or catechisms or didactic treatises, were very popular in the early Middle Ages. These works were based on Greek originals of the 5th/4th bce century and translated into Latin in the 6th century ce. All branches of medical literature are found among the anonymous and pseudonymous works: dietetics, pharmacology, surgery, deontology, and magic. These texts are obviously not “great literature,” but Sigerist (1998, 146) points out that the greatest achievement of the anonymous compilers was “that they kept the torch alight for almost 800 years.” Until the new institutions of learning developed in the 12th‒13th centuries, compilations were in many cases the only texts from which ancient medical knowledge could be learned.

8. Conclusion The 4th to the 7th centuries were the twilight years of the western Roman Empire, passing over into the Dark Ages. And yet, amazingly, this was a period of great cultural activity, especially in North Africa and northern Italy, specifically Ravenna. The majority of Latin medical texts date from this period. Many works of Hippocrates, Aristotle, Rufus of Ephesus, and Galen, for instance, were translated almost unaltered into Arabic. Some of these works were later translated from Arabic into Latin by, for instance, Constantine the African and Gerard of Cremona. Though the texts were mostly “secondhand,” being translations or compilations of excerpts from earlier medical literature, the activity of translation was an achievement in itself: not only did the translators have to “create” a Latin scientific vocabulary, but also the spirit of the Greek original had to be adapted to the Roman mentality. The translations were made with a view to preserving the knowledge of old, and since the knowledge of Greek was declining in the West, it had to be translated into Latin to make it accessible. Vindicianus was the first of a number of practicing doctors in North Africa (which, fortunately, was still partly bilingual in the late 4th and early 5th centuries) to translate Greek works into Latin. Soranus was the preferred author in Africa, and several translations/​adaptations of his works were made. It was a turbulent period in the history of North Africa what with the invasions of the Vandals, the Byzantines, and finally the Arabs, which makes the vibrant cultural activity all the more remarkable. The fact, furthermore, that these manuscripts reached Italy and the rest of Europe is nothing short of a miracle. In the 6th century, the focus of the translating activity shifted from North Africa to Ravenna, which had more direct contact with Alexandria and to which we owe the translation of a number of Hippocratic and Galenic texts that were greatly in vogue in the East.

Medical Writing in the Late Roman West    1031 Its greatest contribution was that, at this time, the emphasis in the West was on the preservation of the rich medical legacy of the past and on passing on and disseminating existing knowledge in an accessible language, rather than on novel compositions based on ancient texts as in the East. From North Africa the knowledge passed to Spain and to Cassiodorus’ monastery in southern Italy, then to abbeys and monasteries in France, and in the 6th to the 8th centuries it even reached the Anglo-​Saxon countries (Sabbah 1998, 149–​150). The works of the authors in our period can consequently be seen as a bridge between the classical period and the Middle Ages when monasteries played a key role in the transmission of these texts.

Bibliography Entries in EANS:  Agnellus of Ravenna, 46–​ 47 (Scarborough); Alexander of Tralleis, 58–​ 59 (Scarborough); Anthimus, 91–​ 92 (Scarborough); Caelius Aurelianus, 201–​ 202 (Scarborough); Cassius Felix, 208–​ 209 (Scarborough); Muscio/​ Mustio, 566 (Scarborough); Q. Serenus Sammonicus, 734 (Scarborough); Theodorus Priscianus, 787–​ 788 (Scarborough). Beschaouch, Azedine. Mustitana. Recueil des nouvelles inscriptions de Mustis, cité romaine de Tunisie (Karthago 14). Paris: Klincksieck, 1968. Cadden, Joan. Meanings of Sex Difference in the Middle Ages: Medicine, Science and Culture. Cambridge: Cambridge University Press, 1993. Cilliers, Louise. “Vindicianus’s Gynaecia: Text and Translation of the Codex Monacensis (Clm 4622).” Journal of Medieval Latin 15 (2005): 153–​236. —​—​—​. “Roman North Africa in the 4th century AD:  Its Role in the Preservation and Transmission of Medical Knowledge.” Acta Classica, suppl. II (2008): 49–​63. Deichgräber, Karl. “Vindicianus.” RE 9.1 (1961): 29–​36. Drabkin, Israel E. ed. and trans. Caelius Aurelianus:  On Acute Diseases and On Chronic Diseases. Chicago: Chicago University Press, 1950. El-​Abbadi, Mostafa A., and Omnia M. Fathallah, eds. What Happened to the Ancient Library of Alexandria? Leiden, Boston: Brill, 2008. Fiorucci, Francesco “Osservazioni sulla Epistula ad Pentadium.” Appunti Romani di Filologia 11 (2009): 67–​90. —​—​—​. “Elvio Vindiciano: Aspetti storici.” Klio 94 (2012): 482–​497. Fischer, Klaus-​Dietrich. “On Caelius Aurelianus and Vindicianus and Theodorus Priscianus.” In Handbuch der lateinischen Literatur, ed. Peter L. Schmidt, vol. 6. Munich:  Beck, forthcoming 2018. Fraisse, Anne, ed. and trans. Cassius Felix. De la médecine. Paris: Les Belles Lettres, 2002. Green, Monica H. 1985. “The Transmission of Ancient Theories of Female Physiology and Disease Through the Early Middle Ages.” PhD diss., Princeton University. Ann Arbor: University Microfilms. Gourevitch, Danielle. “The Paths of Knowledge: Medicine in the Roman World.” In Western Medical Thought from Antiquity to the Middle Ages, ed. Mirko D. Grmek, 104–​138. Cambridge MA, and London: Harvard University Press, 1998. Hanson, Ann Ellis, and Monica H. Green. “Soranus of Ephesus:  Methodicorum Princeps.” Aufstieg und Niedergang der Römischen Welt II.37.2 (1996): 968–​1035.

1032   Late Antique and Early Byzantine Science Jouanna, Jacques. “La théorie des quatre humeurs et des quatre tempéraments dans la tradition latine (Vindicien, Pseudo-​Soranos) et une source retrouvée.” Revue des Études Grecques 118 (2005a): 138‒167. —​—​—​. “Un traité pseudo-​hippocratique inédit sur les quatre humeurs (Sur le pouls et sur le tempérament humain).” In Κορυφαιω ανδρι. Mélanges offerts à André Hurst., ed. Antje Kolde, Alessandra Lukinovich, and André-​Louis Rey, 449–​461. Genève: Droz, 2005b. —​—​—​. “La postérité du traité hippocratique de la Nature de l’homme:  La théorie des quatre humeurs.” In Ärzte und ihre Interpreten:  Medizinische Fachtexte der Antike als Forschungsgegenstand der klassischen Philologie, ed. Carl Werner Müller, Christian Brockmann, and Carl Wolfram Brunschön, 117–​142. München: Saur, 2006. Kotula, Tadeusz. “Utraque lingua eruditi. Une page relative à l’histoire de l’éducation dans l’Afrique romain.” In Hommages à Marcel Renard, ed. Jacqueline Bibauw, vol. 2, 386–​393. Brussels: Latomus, 1969. Langslow, David. Medical Latin in the Roman Empire. Oxford: Oxford University Press, 2000. Maire, Brigitte (ed. and trans.). Gargilius Martialis. Les remèdes tirés des légumes et des fruits. Paris: Les Belles Lettres, 2002. Marasco, Gabrielle. “I medici di corte nell’Impero Romano: Prosopografia e ruolo culturale.” Prometheus 24 (1998): 243–​263. —​—​—​. “I medici di corte nella società imperiale.” Chiron 28 (1998): 267–​285. Marrou, Henri-​Iréné. A History of Education in Antiquity. Translated by George Lamb. Madison: Wisconsin University Press, 1982. Matthews, John F. Western Aristocracies and Imperial Court ad 364‒425. Oxford:  Oxford University Press, 1975. Mazzini, Innocenzio, and Flammini, Giuseppe. De conceptu. Estratti di un’antica traduzione latina del Peri gynaikeion pseudoippocratico. Bologna: Pàtron, 1983. Meyer, Theodor. Theodorus Priscianus und die römische Medizin. Jena: Fischer, 1909. Mørland, Henning. “Theodorus Priscianus im lateinischen Oribasius.” Symbolae Osloenses 29 (1952): 79–​91. Niedermann, Maximilian, and Liechtenhan, Eduard. Marcellus. Über Heilmittel. Übersetz von Jutta Kollesch and Diethard Nickel = Corpus Medicorum Latinorum 5. Berlin: Akademie Verlag, 1968. Nutton, Vivian. “Ammianus and Alexandria.” Clio Medica 7.3 (1972): 165–​176. —​—​—​. “From Galen to Alexander:  Aspects of Medicine and Medical Practice in Late Antiquity.” Dumbarton Oaks Papers 38 (1984): 1–​14. Önnerfors, Alf. Plinii Secundi Iunioris qui feruntur De medicina libri tres  =  CML 3. Berlin: Akademie, 1964. Parsons, Edward Alexander. The Alexandrian Library: Glory of the Hellenistic World: Its Rise, Antiquities and Destructions. Amsterdam, New York: Elsevier, 1952. Raven, Susan. Rome in Africa. London:  Evans Brothers, 1969; 3rd ed., London and New York: Routledge, 1993. Riddle, John M. “Gargilius Martialis as a Medical Writer.” Journal of the History of Medicine and Allied Sciences 39.4 (1984): 408–​429. Rose, Valentinus. Sorani Gynaeciorum vetus translatio Latina nunc primum edita cum additis Graeci textus reliquiis a Dietzio repertis atque ad ipsum Codicem Parisiensem. Leipzig: Teubner, 1882. —​—​—​. Theodori Prisciani Euporiston Libri III accedunt Vindiciani Afri quae feruntur reliquae. Leipzig: Teubner, 1894.

Medical Writing in the Late Roman West    1033 Sabbah, Guy. “Notes sur les auteurs médicaux Africains de l’Antiquité tardive (IVe—​Ve siècles).” Recherches et Travaux: Université de Grenoble 54 (1998): 131–​150. Sigerist, Henry E. “The Latin Medical Literature of the Early Middle Ages.” Journal of the History of Medicine and Allied Sciences 13.2 (1958): 127–​146. Stok, Fabio “Fonte e datazione dell’ Epistola di Vindiciano a Pentadio.” Technai 3 (2012): 137–​143. —​—​—​. “Vindiciano e la teorie dei temperamenti.” Medicina nei Secoli 24 (2012): 517–​532. Temkin, Owsei, trans. Soranus’ Gynecology. Baltimore, London:  Johns Hopkins University Press, 1956. —​—​—​. The Double Face of Janus and Other Essays in the History of Medicine. Baltimore, London: Johns Hopkins University Press, 1977. van der Eijk, Philip J. 1999. “Antiquarianism and Criticism: Forms and Functions of Medical Doxography in Methodism (Soranus and Caelius Aurelianus).” In Ancient Histories of Medicine: Essays in Medical Doxography and Historiography in Classical Antiquity, ed. Philip J. van der Eijk, 397–​452. Leiden, Boston: Brill, 1999. von Staden, Heinrich. Herophilus:  The Art of Medicine in Early Alexandria. Cambridge: Cambridge University Press, 1989.

Index

accounting, 11–​13, 14, 15, 18, 51, 56, 876 Adamantius, 751, 759, 760, 762, 969 Adrastus, 458 Aëtius of Amida, 375, 556, 559, 569, 574, 590, 775, 965, 966, 972–​974, 975, 976, 977, 978, 979, 980, 983, 985, 1015 Agatharchides, 325, 334, 432, 960, 961 aithēr, 239, 244, 247, 304, 307, 687, 859, 860, 906 alchemy, 2, 409–​430, 438, 721–​742, 943–​964, 967 Alcmaeon, 149, 178, 185, 218, 219, 420, 481, 483–​484, 492, 969 Alexander of Aphrodisias, 3, 492, 494, 499, 508, 839, 842, 848, 853, 897 Alexander of Tralles, 574, 965, 966, 974–​977 algebra, 16–​20, 55, 92, 111, 117, 183, 184, 186, 833, 886, 891 Ambrosius of Puteoli, 706 Ammonius of Alexandria, 847, 850, 880, 881, 887, 898, 902, 948 Ampelius, 831, 835, 842, 988, 989–​991, 1010 Anatolios (mathematician and bishop: contrast Vindonius Anatolius, below), 833, 842, 848 anatomy, 63, 72, 100, 217–​218, 223–​226, 229, 361, 366, 368, 369, 372, 373, 375, 377, 485, 496, 500–​503, 527, 574, 575, 604, 693, 767, 771, 772, 773, 775, 776, 777, 778, 780, 968, 981, 1017, 1018, 1019, 1021 Andromachus (senior and junior), 520, 704, 705, 711 animals, 56, 160, 218, 229, 238, 239, 240, 243, 249–​254, 297, 337, 338, 345, 351, 360, 365, 368, 411, 413, 435–​436, 437, 439, 440, 463–​467, 470, 473, 477, 478, 486, 495, 526, 529, 641, 656, 657, 660, 669–​671, 672, 674, 681, 687, 688, 690, 699, 703, 706, 715, 730, 745, 747–​749, 750, 753, 754, 759, 830, 837–​838, 839, 841, 857, 901, 904, 905, 991, 1028 Anonymus Londinensis, 215, 216, 220, 374, 375

Antigonus of Carystus, 432, 433, 434, 435, 436, 438, 439, 440, 443, 478 Antigonus of Nicaea, 383, 389, 398–​405 Antikythera (device or mechanism), 342, 343, 598–​599, 611 Antyllus, 556, 566, 574, 966, 971 Apicius, 545 Apollonius of Pergē, 271, 272–​273, 275, 276, 278, 281, 284, 285, 286, 287, 289, 295, 794, 801, 802, 806, 832, 834, 872, 880, 881, 882, 883, 885, 889, 890, 1009 Apuleius Celsus (contrast (Cornelius) Celsus, below), 704–​706, 719 Apuleius of Madaurus, 478, 494, 499, 506, 508, 536, 538, 746, 755, 831–​832, 842, 1009, 1010 archaism, 42, 84, 112, 173, 467, 700, 829–​830, 835–836, 926 Archestratus, 531, 546 Archimedes, 120, 272, 275, 277, 278, 279, 280, 282, 287, 289, 319, 338, 339, 341, 346, 347, 352, 353, 355, 356, 360, 500, 506, 596, 598–​600, 660, 665, 799, 832, 872, 875, 880, 882, 885, 1005, 1009 Archytas, 149, 152–​154, 160, 164, 171, 177, 179, 180, 181, 182, 186–​187, 189, 191–​192, 275, 352, 451, 453, 454, 457, 461, 493, 494, 596, 607 Aristotle, 3, 4, 5, 147, 148, 149, 150, 151, 153, 160, 164, 165, 167, 171, 172, 173, 174, 176, 177, 178, 179, 180, 182, 185, 186, 187, 188, 211–​212, 215, 216, 222, 223, 228, 235–​256, 262, 264, 265, 275, 289, 300, 304, 305, 307, 310, 311, 316, 317–​318, 328, 337, 338, 339, 340, 346, 347, 354, 355, 356, 360, 361, 362, 363, 364, 389, 413, 417, 419, 420, 421, 423, 424, 431, 433, 434, 439, 440, 443, 451, 453, 456, 463, 466, 467, 475, 477, 482, 483, 485, 486, 487, 489–​491, 492, 494, 499, 504, 505, 511–​512, 593, 597, 599, 604, 609, 617, 656, 672, 674,

1036   Index Aristotle (cont.) 677, 679, 684, 685, 686, 687, 690, 691, 728–​731, 733, 744–​750, 752, 753–​754, 758, 770, 774, 777, 779, 791, 792, 806, 808, 811, 820, 821, 825, 826, 831, 832, 837, 838, 839, 840, 841, 842, 848, 849, 851, 852, 853, 854, 856, 857, 858, 859, 860, 862, 863, 864, 880, 895–​920, 923, 932, 946, 947, 948, 949, 951, 952, 953, 956, 957, 958, 959, 981, 982, 1004, 1005, 1009, 1030 Aristotle, pseudo, 350, 352, 353, 418, 432, 435, 436, 438, 493, 495, 506, 565, 745–​746, 751, 757 Aristoxenus of Taras, 179, 180, 446, 447, 448, 449, 451–​457, 609, 821, 997 Aristoxenus (Herophilean), 374, 375 arithmetic, 14, 20, 30, 31, 54, 66, 90, 111, 164, 165, 171, 172, 174, 179, 180, 181, 182, 183, 189, 192, 260, 274, 277, 284, 285, 288, 293, 297, 303, 308, 338, 388, 400, 450, 456, 461, 605, 659, 766, 803, 817, 818, 821, 822, 831, 833, 834, 859, 876, 878, 880, 882, 884, 885, 886, 887, 888, 891, 988, 997, 998, 999, 1001, 1002, 1005, 1006, 1008 Arius of Tarsos (Laecanius), 520, 529 Arius Didymus (doxographer), 688 Artemidorus of Ephesus (geographer), 323, 326, 327 Artemidorus of Sidē (doctor), 376 Artemidorus (astronomer), 834 arteries (compare “veins”), 38, 361, 362, 364, 370, 374, 377, 501, 641, 770, 771, 775, 778, 779, 780 Āryabhaṭa, 92 Asclepiades of Bithynia, 374, 376, 378, 530, 547, 602, 617, 625, 638–​641, 643, 645, 667, 701–​704, 771, 773, 777 Asclepiades (pharmacist), 372, 569, 705, 711 Asclepius (god of healing), 216, 217, 219, 222, 223, 366, 393, 558, 646, 650–​652, 766, 980 Asclepius of Tralles (late antique commentator), 880, 887 astrology, 2, 25, 26, 32, 35, 67, 130, 131, 138, 288, 293, 295, 298, 301, 302, 305, 308, 309, 310, 311, 381–​408, 649, 681, 694, 736, 738, 751, 789, 806, 810–​812, 820, 832, 871, 873–​874, 951, 982, 990, 996, 999

astrology, catarchic, 383, 391 astrology, horary, 382–​383 astrology, judicial, 381–​382, 393, 396 astronomy, 2, 17, 21, 25–​34, 35, 61–​70, 90–​91, 92, 129–​143, 147, 150, 154, 155–​157, 158, 159, 171–​194, 195, 202, 211, 247, 259, 260, 261, 263, 284, 287, 289, 293–​314, 322, 323, 338, 385, 387, 395, 424, 453, 461, 465, 474, 493, 494, 498, 507, 593, 594, 597–​600, 603, 605, 606, 622, 627, 656, 659, 660, 669, 673, 682, 692, 694, 790–​806, 808, 810, 817, 821, 822, 823, 831, 832, 833, 849, 850, 851, 859, 861, 864, 869–​894, 916, 922, 948, 982, 988, 990, 996, 999, 1002, 1005, 1008, 1009 ataraxia, 259, 262, 389 Athenaeus of Attalia (medical writer), 641–​642, 652, 667, 695, 696, 773, 830 Athenaeus Mechanicus, 338, 358 Athenaeus of Naucratis (author of Dinnertable Philosophers, aka Dons at Dinner, aka Partying Professors), 260, 349, 355, 373, 375, 376, 441, 453, 459, 467, 477, 531, 546 atoms, 161, 246, 261, 263, 264, 265, 267, 395, 420, 423, 488, 491, 492, 616, 617, 622, 624, 625, 627, 628, 629, 638, 657, 773, 832, 840 Augustine of Hippo, 395, 397, 605, 659, 674, 864, 988, 991, 997–​1001, 1002, 1003, 1008, 1009, 1010, 1014, 1016, 1017, 1018, 1021 Āyurveda, 95–​104 Bhāskara, 92 biology, 241, 243, 249, 251, 254, 308, 346, 694, 917 Boethius, 450, 458, 607, 864, 988, 995, 997, 1002, 1003–​1006, 1007, 1009, 1012 Bolus of Mendes, 423–​424, 466, 477, 478, 722, 725 Book of Nut, 63–​64 Brahmagupta, 92 breath (compare also “pneuma”), 39, 96, 97, 102, 151, 152, 218, 220, 254, 265, 337, 362, 364, 522, 601, 616, 628, 642, 684–​688, 689, 706, 779–​780. bronze, 77, 134, 179, 205, 342, 345, 349, 358, 373, 417, 418, 419, 484, 507, 556, 557, 568, 572, 574, 596, 598, 724, 726, 730, 731, 817, 909, 958, 960

Index   1037 Caelius Aurelianus, 368, 370, 374, 376, 556, 570, 572, 573, 587, 1009, 1010, 1023–​1024, 1026, 1031 Callimachus, 367, 432–​436, 439 canon(ical) and canonicity, 3–​4, 16, 31, 85–​86, 96, 108–​111, 129–​130, 225, 272–​274, 276, 283, 381–​382, 389, 433–​434, 455, 474, 616, 620, 658, 659, 666, 775–​776, 778, 780, 781, 783, 784, 785, 829–​830, 834, 870–​872, 888, 889, 896, 901, 917, 987, 998–​999, 1009 Caraka-​saṃhitā, 97–​101 Carneades, 390, 394, 604 Carthage, 203, 208, 323, 328, 465, 468, 475, 813, 997, 1013, 1016–​1017, 1018, 1021, 1022 Cassiodorus, 476, 606, 607, 669, 675, 988, 1000, 1006–​1010 Cassius Felix, 570, 572, 587, 1017, 1021–​1023, 1024, 1031 catapults, 288, 341, 346, 349, 353, 355, 663 (M. Porcius) Cato, 390, 441, 463, 467, 470–​471, 473, 475, 600–​601, 602, 611, 657, 662, 667, 668, 669, 670, 673, 968, 1004, 1025 cautery, 43, 220, 535, 536, 556, 559, 560, 561, 562–​563, 573, 581, 583, 651, 701 Celsus (writer against Christianity), 397, 746 (A. Cornelius) Celsus (medical writer: contrast Apuleius Celsus, above), 218, 359, 360, 363, 366, 370, 371, 372, 376, 470, 474, 478, 533, 547, 556, 558, 559, 562, 563, 565, 566, 567, 568, 571, 572, 573, 574, 575, 576, 588, 590, 638, 655, 660, 666–​668, 672, 700, 702, 707, 708, 772, 966, 968, 969, 987, 1015 Censorinus, 599, 605, 606, 674, 831, 832, 842, 1009 Censorinus, pseudo (Epitoma disciplinarum), 994–​997 ceramics, 240, 242, 346, 414–​415, 417, 418 chisels, 556, 557, 567–​568, 569, 583 Chrysippus of Knidos (doctor), 359, 363, 369 Chrysippus of Soli, 282, 423, 424, 498, 499, 500, 509, 678, 679, 680, 681, 682, 683, 686, 688, 690, 693, 694, 695, 696, 754, 774 (M. Tullius) Cicero, 237, 259, 261, 266, 309, 328, 329, 371, 386, 389, 390, 394, 395, 438, 474, 596, 598, 599, 602, 603, 604, 616, 618, 627, 628, 629, 630, 631, 659, 664, 665, 667, 669, 670, 675, 678, 679, 685, 699, 700, 752, 758, 810, 830, 1009

colors, 25, 39, 133, 134, 135, 238, 248, 252, 264, 397, 410, 411–​414, 416, 417, 418, 420, 421, 423, 454, 473, 481, 482, 484, 485, 488, 489, 490, 491, 492, 495, 496, 504, 505, 507, 528, 536, 545, 546, 548, 593, 644, 710, 713, 724, 728, 733, 751, 753, 754, 757, 771, 816, 817, 835, 852, 904, 945, 947, 949, 950, 952, 954, 957, 959 (L. Iunius) Columella, 463, 464, 469, 470, 471, 473, 474, 475, 477, 478, 594, 609, 611, 656, 657, 658, 660, 661, 662, 667, 669–​671, 672, 673, 725, 1009, 1010, 1025 combinatorics, 89, 282–283 constellations, 28, 29, 61–​62, 63, 64–​65, 66, 132–​135, 141, 178, 300, 307, 311, 386, 387, 395, 396, 403, 473, 475, 596, 598, 603, 831 constellations, the twenty-eight, 132–​135 contagion, 41–​43, 416, 473, 594, 663 cosmology, 32, 91, 112, 140–​142, 148, 149, 150, 151, 152–​153, 159–​161, 164–​165, 185, 196–​197, 202, 219, 244–​245, 381, 382, 388–​389, 453, 593, 602, 660, 671, 675, 682, 789, 806–​809, 831, 832, 922, 932–​933, 951, 959, 990, 996 Crateuas, 533–​534, 541 cupping vessels, 345, 349, 555, 558–​559, 566, 579, 640, 641 Damascius, 850, 855, 862, 867, 912, 914, 915 decans, 62–​63, 64, 65, 66, 383, 387, 388, 403 decimal system, 15, 50, 52, 85, 88, 115 Democritus, 161, 172, 183, 210, 211, 218, 222, 226, 257, 264, 300, 301, 367, 419, 420, 423, 452, 466, 472, 473, 475, 477, 482, 485, 487–​488, 489, 491, 492, 493, 494, 530, 593, 609, 612, 627, 629, 669, 777, 943 Democritus, pseudo (alchemist), 477, 478, 721, 724–​726, 731–​736, 943, 945–​946, 947, 952, 953 diagnosis, 36–​38, 42, 74, 100, 101, 367, 549, 640, 646, 648, 649, 650, 752, 757, 775, 780, 784, 810, 948, 981, 1023 Diagnostic and Predictive Series, 38–​41 Dicaearchus, 316, 318, 319, 320, 441 Didymus (writer on music: contrast Arius Didymus, above), 458 Diocles (mathematician), 275, 281, 282, 285, 288, 506

1038   Index Diocles of Carystus, 216, 364, 546, 562, 586, 770 Diodorus of Sicily, 26, 296–​298, 299, 302, 304, 305, 308, 309, 315, 333, 386, 960 Diodorus of Tarsus, 932 Diodorus the Empiricist, 371 Diogenes of Oenoanda, 615, 620–​622, 623, 625, 627, 628, 630, 631 Diogenes Laërtius, 149, 183, 185, 257, 258, 259, 260, 261, 262, 263, 315, 317, 363, 369, 371, 376, 378, 379, 491, 492, 493, 498, 609, 615, 619, 621, 622, 623, 677, 681, 682, 683, 685, 686, 688, 692, 744, 746, 754, 1002 Diophantus, 274, 284, 285, 288, 833, 871, 876, 878, 884, 886, 888, 890 Dioscorides of Anazarbus, 37, 365, 416, 519–​542, 551, 667, 711, 712, 713, 714, 732, 816, 836, 926, 966, 969, 972, 1009, 1020, 1026 Dioscorides “Phakas,” 372–​373 Dioscurides ⇒ Dioscorides Diphilus of Siphnos, 352, 531, 546 diseases, 38, 39, 40, 41, 42, 44, 72, 73, 74, 75, 76, 96, 97, 98, 99, 100, 101–​103, 152, 163, 215, 218, 220, 223, 224, 225, 228, 229, 236, 250, 261, 262, 362, 363, 365, 366, 368, 369, 370, 374, 376, 405, 409, 467, 478, 520, 521, 529, 548, 549, 551, 555, 556, 558, 562, 566, 570, 571, 572, 573, 574, 576, 594, 623, 625, 637, 638, 639, 640, 641, 642, 643, 645, 647, 649, 650, 652, 663, 665, 691, 693, 699, 702, 756, 757, 760, 767, 770, 771, 772, 773, 775, 780, 781, 782, 783, 784, 785, 812, 842, 973, 975, 976, 981, 1015, 1020, 1021, 1022 dissection, 100, 360, 361, 362, 363, 365, 367, 371, 483, 563, 646, 765, 778, 981, 1019 Dorotheus of Sidon, 383, 384 doṣa, 101, 102, 220 drills, 44, 450, 566–​567, 568, 569, 583, 584 dyes, 409, 411–​414, 417, 418, 421, 423, 424, 490, 648, 713, 723, 724, 725, 726, 738, 944, 947, 949, 950, 952, 954 Ebers Papyrus, 73, 75, 76, 219, 522 eccentric, 792–​795, 799, 802, 803, 806, 822 eclipses, 25, 27, 31, 66, 90, 91, 130, 131, 132, 136, 137, 139, 140, 157, 175, 176, 184, 211, 258, 298, 303, 309, 310, 382, 388, 447, 454, 495, 597–​ 600, 799, 804, 808, 809, 813, 834, 839, 861

Edwin Smith Papyrus, 73, 74, 76 elements (of matter), 102, 155, 160, 161–​162, 164, 190, 202, 228, 237, 238, 239–​245, 246, 247, 251, 265, 307, 418–​424, 547, 594, 597, 616, 617, 641, 642, 685, 686, 688, 693, 754, 756, 769, 771, 773, 775, 777, 778, 782, 783, 784, 789, 791, 792, 809, 811, 819, 820, 831, 832, 839, 840, 859–​862, 901, 904, 906–​908, 909, 917, 949, 950, 951, 952, 971, 981, 989, 996 Empedocles, 149, 163, 177, 215, 217, 218, 238, 246, 347, 356, 420, 481, 485–​486, 487, 488, 489, 498, 499, 608, 616, 686, 777, 839, 981 Empiricists, 261, 263, 359–​360, 361, 365–​367, 368, 369, 370–​372, 373, 377–​379, 395, 547, 638, 640, 642, 643, 648, 649, 650, 659, 766, 771–​773 encyclopedias, –​pedism, 91, 306, 438, 468–​ 469, 520, 655–​676, 725, 775, 830–​832, 875, 891, 965–​986, 987–​1012, 1015, 1021, 1023 Ennius, 597, 616 Ephorus, 210, 211, 315–​316, 320 Epicurus of Samos (philosopher), 4, 257–​268, 410, 423, 424, 491–​493, 498, 530, 615–​635, 677, 678, 691, 754, 838, 839 Epicurus of Pergamon (Empiricist doctor), 377–​378 epicycle, 793–​794, 799–​801, 801–​804, 806–​807, 809, 822–​823, 916 epilepsy, 40, 224, 365, 673, 1020 Equatorial System, 132–​134, 139 Erasistratus, 4, 72, 252, 359–​361, 363–​365, 366, 369–​370, 375–​377, 501, 535, 547, 601, 641, 693, 699, 770–​771, 780, 781 Eratosthenes, 120, 186, 200, 205, 212, 285, 288, 318–​322, 323, 324, 326, 327, 329, 330, 331, 332, 441, 457, 599, 600, 603, 607, 796, 813, 814, 824, 833, 835, 922 Erotian, 223–​224, 225, 366, 368, 369, 519, 980 Euclid, 19, 20, 171, 172, 173, 180, 181, 182, 183, 184, 185, 186, 189, 190, 261, 272, 281, 284, 285, 288, 312, 319, 322, 338, 353, 456, 496–​499, 500, 502, 504, 505, 506, 508, 607, 789, 816, 817, 832, 833, 851, 852, 871, 873, 875, 877, 879–​880, 881, 882, 883, 884, 885, 889, 890, 995, 996, 997, 1005, 1006, 1009 Eudemus of Alexandria (doctor), 361, 373

Index   1039 Eudemus of Pergamon (mathematician), 271 Eudemus of Rhodes (student of Aristotle), 171–​172, 175, 178, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 275, 593 Eudemus of Rome (patient of Galen), 377, 648, 767–​768 Eudoxus of Cyzikos, 327–​328 Eudoxus of Knidos, 157–​158, 176, 182, 186, 187, 189, 211–​212, 261, 263, 279, 296, 301, 305, 311, 312, 317, 327, 433, 434, 475, 599, 805, 806, 824 Eudoxus of Rhodes (paradoxographer), 438 Euphorbus, 524–​526, 571 Eutocius, 275, 285, 286, 288, 289, 870, 880, 882, 883, 885, 889 evolution, 51, 142, 238, 243, 265, 272–​274, 284, 409, 446, 465, 593, 608, 629, 829, 838, 839, 849, 860, 890, 899, 979, 988, 989, 997 experiment, 37, 38, 42, 152, 179, 349, 354, 360, 364, 366, 443, 451, 458, 459, 460, 471–​472, 473, 474, 502, 504, 507, 604, 661, 665–​666, 694, 726, 735, 736, 737, 765, 778, 780, 817–​818, 821, 836, 865, 959 fermentation, 253, 415–​416, 422, 992 final cause, 155, 241–​243, 251–​252, 770, 899–900, 902, 905, 910 Firmicus Maternus, 385–​386, 398, 400, 401, 403, 405, 874 forceps, 352, 556, 557, 564–​566, 568, 570, 580, 583 fractions, 21, 51–​52, 53, 54, 58, 65–​66, 85, 87, 111, 113, 114, 115, 118, 158, 172, 459 fractures, 74, 76, 100, 224, 225, 227, 344, 376, 563, 566, 567, 568, 569, 699, 706, 708, 767, 785, 982 Fuluius Nobilior, 596–​597, 600, 611 Galen, 3, 72, 75, 217, 218, 224, 227, 228, 346, 360, 361, 362, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 376, 377, 378, 379, 389, 392, 393, 406, 417, 423, 474, 482, 499, 500–​503, 504, 519, 520, 523, 525, 526, 531, 536, 537, 543, 544, 546, 547, 548, 549, 550, 551, 555, 556, 558, 564, 566, 567, 568, 569, 570, 571, 572, 574, 576, 593, 617, 625, 637, 638, 639, 640, 641, 642, 643, 644, 645, 647, 648, 649, 650, 651, 652, 664, 667, 680, 683, 689, 690,

691, 693, 694, 695, 696, 699, 700, 702, 703, 704, 705, 706, 707, 710, 711, 754, 755, 756, 757, 758, 765–​788, 829, 830, 841, 842, 914, 934, 966, 968, 969, 970, 971, 972, 973, 975, 976, 977, 978, 980, 981, 982, 983, 1009, 1013, 1014, 1015, 1017, 1020, 1022, 1026, 1027, 1028, 1030 Gargilius Martialis, 551, 1009, 1010, 1020, 1021, 1025 Geminus, 281, 302–​305, 307, 496, 497, 499, 500, 507, 509, 792, 803, 804, 808, 822 gems, 409, 418, 423, 723, 836 genethlialogy, 305, 382, 383, 387, 388, 392 geography, 56, 195–​213, 298, 308, 315–​335, 436, 441, 521, 603, 606, 607, 660, 671, 692, 694, 789, 812–​816, 823, 824, 831, 835, 870, 874, 921–​942, 988, 989–​991, 993, 994, 1016 glass, 342, 345, 349, 417–​418, 419, 424, 507, 559, 706, 707, 723, 817–​818, 958 gynecology, 38, 219, 220, 222, 224, 228, 229, 363, 368, 369, 375, 376, 527, 574–​577, 601, 639, 640, 641, 647, 701, 973, 977, 1017, 1024 harmonics, 131, 134, 138, 139, 147, 148, 154, 171, 179, 180, 191, 438, 446, 450, 452–​461, 604, 789, 820, 821, 832, 841, 859, 873, 996, 1006 Hecataeus of Miletus, 197, 203–​205, 206, 207, 326, 332, 441, 922 Heliodorus (alchemist), 945, 954 Heliodorus of Alexandria (astronomer), 874, 891 Heliodorus of Alexandria (surgeon), 556, 567, 574, 971, 972 herbals (compare also “pharmacy”), 38, 41, 74–​75, 467, 658, 668, 672, 712, 784. Hermes Trismegistus, 388, 723, 726, 727, 734, 737, 739, 943, 945, 948, 949, 952, 953 Herodotus of Halikarnassus, 38, 172, 196, 202, 203, 204, 205, 206–​210, 211, 218, 219, 221, 248, 250, 310, 315, 325, 386, 418, 431, 434, 476, 527, 558, 835, 922 Herodotus (addressee of Epicurus), 259, 261, 264, 265, 266, 491, 492, 498, 622 Herodotus (doctor), 379, 969 Heron of Alexandria, 20, 277, 284, 288, 290, 338, 340, 341, 342, 343, 345, 346, 347, 348, 349, 350, 351, 352, 354, 356, 357, 571, 587, 824, 833, 842, 871, 875, 887, 888

1040   Index Herophilus, 4, 72, 74, 252, 359, 360, 361–​363, 364, 365, 366, 367–​369, 372–​375, 501, 693, 699, 770, 771, 980, 982 Hesiod, 3, 196–​197, 202, 260, 388, 410, 463, 464, 465, 466, 469, 470, 474, 616, 805 Hierocles (geographer), 925, 926 Hierocles (Neo​platonist), 944 Hierocles (Stoic), 689 Hipparchus, 277, 282, 283, 296, 301, 308, 310, 311–312, 317, 322–324, 331, 354, 355, 387, 441, 792–793, 794–795, 799–800, 802, 803, 804, 805, 813, 823, 834, 835, 842, 871, 872, 873, 922 Hippocrates of Chios (mathematician and astronomer), 20, 153–​154, 171–​172, 178, 180, 183, 184, 185, 186–​189 Hippocrates of Kos (doctor), 3, 215–​232, 344, 360, 362, 364, 366, 367, 368, 372, 373, 377, 392, 415, 484, 499, 501, 502, 543, 544, 545, 547, 550, 555, 569, 570, 575, 639, 642, 689, 690, 691, 693, 694, 697, 700, 701, 704, 754, 755, 757, 765, 767, 769, 774, 775, 777, 779, 780, 784, 785, 786, 830, 841, 951, 965, 968, 973, 982, 1009, 1022, 1026, 1027–​1028, 1030 horoscope, 26, 32, 67, 293, 302, 381, 383, 384, 385, 387, 391, 392, 397–​405, 810 horoskopos (ὡρόσκοπος, the ascendant sign), 381, 388, 400, 812 Hypatia, 871, 874, 885, 946 Iamblichus, 288, 494, 610, 847, 848, 855, 859, 862, 863, 870, 871, 873, 874, 879, 880, 882, 884, 887, 889, 890, 898, 903, 907, 912, 914, 945, 1002 instruments (measuring), 131, 134, 135, 141, 304, 340, 342, 352, 394, 598–​600, 789, 795–​799, 806, 813, 819, 824, 861–​862, 872 internal medicine, 98–​103, 220, 228–​229, 362–​ 363, 364–​365, 638, 640, 641–​642, 1023–​1024 Isigonus of Nicaea, 434, 440 (Sextus) Iulius Africanus, 478, 835, 836–​837, 842, 933 Iulius Solinus, 835–​836, 842, 988, 991–​994, 1010 kerotakis, 732–​733 lathes, 342, 345, 358, 557 latitude, 158, 207, 211, 289, 316, 318, 319, 320–​322, 323, 327, 350, 354, 400, 600, 603, 666, 796, 797, 803, 804, 805, 807, 812–​816, 824, 923

Leonides of Alexandria, 556, 566, 587 Library of Alexandria, 319, 359, 360, 363, 375, 971, 1026 Lucretius, 3, 264, 265, 266, 390, 394, 410, 416, 423, 424, 491–​493, 597, 602, 615–​635, 988 luni-​solar calendar, 28, 130, 137, 176, 185, 805 magic, 42, 43, 71–​72, 73, 75, 76, 96, 149, 163, 200, 388, 396, 464, 469, 476, 477, 478, 601, 603, 650, 658, 672–​673, 707, 714, 723, 725, 726, 735, 759, 831, 1020, 1022, 1024, 1028, 1030 Mago, 465, 467, 468, 469, 471, 473, 475, 478, 602, 669 Manilius, 302, 384, 391, 401 maps, of earth (compare “periplous, periploi”), 176, 196, 197, 202, 203, 204, 205–​206, 207, 210, 211, 248, 320–​322, 812–​816, 824, 923, 925–​926, 935–​937, 993 maps, of sky, 27, 29, 130, 132–​137, 141, 400, 804 Marcian(us) of Heraclea (geographer), 326, 874, 891, 924, 925, 938 Marcianus (pharmacist), 704, 711, 717 Maria (alchemist), 731–​734, 962 Martianus Capella, 606, 607, 659, 674, 864, 878, 987, 988, 996, 1001–​1003, 1010 mathematics, 2, 11–​24, 49–​60, 83–​94, 107–​128, 147, 148, 152, 153–​154, 158, 160, 171–​194, 237, 246, 259, 263, 269–​292, 295, 312, 319, 322, 323, 338, 339, 388, 393, 447, 450, 456, 458, 692, 694, 766, 789, 791, 821, 832–​834, 841, 842, 849, 851, 859, 864, 869–​894, 922, 948, 951, 982 melothesia, 393 mercury (i.e., “quicksilver”), 412, 419, 724, 732, 733, 735, 947, 950, 954 Mercury (the planet), 91, 138, 150, 156, 157, 178, 300, 401, 403, 404, 405, 599, 606, 802, 807, 808, 809, 811, 916, 1001–​1003 meteorology, 211–​212, 238, 241–​242, 243, 247–​248, 259, 263, 305, 317, 320, 382, 386, 392, 419, 421, 422, 475, 494–​496, 506, 623, 660, 669, 694, 728–​731, 806, 831, 840, 901, 903, 906, 947, 948, 951, 952, 953, 957, 958, 990 Methodism, 373, 379, 393, 395, 473, 547, 637–​644, 647, 648–​650, 704, 767, 771, 773, 782, 972, 1021, 1023

Index   1041 Mithridates, 371, 533, 534, 602 Mnesitheus of Athens, 546, 601 models (of natural world), 1, 2, 28–​29, 30, 66, 90, 157, 158, 176, 246, 254, 261, 263, 267, 293, 343, 387, 397, 409, 418–​424, 447, 481, 483, 485, 487, 499, 692, 704, 731, 792–​795, 806, 822–​824, 873 Moderatus of Gades (contrast Columella, above), 609 moon, 11, 26, 27, 28, 29, 30, 31, 32, 61, 62, 64, 66, 88, 90, 129, 130, 131, 135, 137, 139, 140, 142, 150, 155–​158, 159, 165, 171, 176, 177, 178, 179, 184, 185, 211, 239, 244, 247, 248, 285, 298, 301, 303, 305, 309, 310, 312, 355, 373, 381, 386, 401, 402, 403, 404, 405, 465, 495, 597, 598, 599, 606, 607, 610, 673, 692, 739, 790, 791, 792, 798, 799–​801, 802, 803, 804, 805, 806, 807, 808, 809, 811, 813, 822, 823, 839, 862, 916 Moscow Mathematical Papyrus, 54 mummy, 72, 74, 76, 77, 727, 728 music, 4, 115, 137, 151–​152, 154, 159, 160, 164, 165, 179, 180, 191, 208, 260, 299, 445–​462, 544, 605, 606, 620, 659, 675, 694, 755, 820–​ 821, 831, 832, 833, 859, 951, 954, 955, 988, 998, 999, 1001, 1002, 1003, 1005, 1006, 1008, 1009 Mustio, 1024–​1025, 1031 needles, 556, 557, 560–​561, 563, 576, 581, 582 Nicolaus of Damascus, 439–​440, 443 Nigidius Figulus, 390, 603–​604, 605, 611, 831, 842 Numa Pompilius, 594, 595, 596, 597, 600, 602, 605, 607, 608–​610, 611 observations, 1, 21, 25, 26, 31, 32, 42, 44, 50, 62, 65, 71, 74, 76, 91, 96, 129, 130, 132–​137, 138, 154–​155, 157, 176, 178, 179, 186, 202, 206, 225, 237, 240, 245, 250–​251, 254, 297–​298, 305, 317, 349, 386, 393, 394, 395, 415, 431, 442, 470, 473, 475, 519, 520, 521, 524, 531, 544, 546, 547, 594, 626, 638, 639, 640, 649, 659, 694, 703, 705, 747, 750, 756, 760, 770, 773, 778, 790, 795–​799, 803, 804, 805, 813, 823, 839, 860, 861, 862, 874, 901, 902, 908, 916, 921, 923, 927, 929–​930, 975, 993, 998

Oenopides of Chios, 171, 172, 178, 180, 184, 185, 389 Olympiodorus of Alexandria (Neoplatonist), 727, 732, 737, 755, 850, 898, 902, 903, 911, 920, 943, 945, 946, 947–​951, 953, 955, 956, 957, 958, 960, 961 Olympiodorus of Thebes (historian), 928 optics, 263, 272, 284, 285, 288, 361, 362, 481–​ 518, 666, 789, 816–​818, 823, 881, 884, 917, 948 Oribasius of Pergamum, 361, 369, 375, 376, 546, 552, 556, 563, 564, 566, 567, 568, 569, 570, 572, 574, 775, 965, 966, 969–​972, 973, 974, 975, 976, 977, 978, 979, 980, 1015, 1019, 1021, 1027 Paccius Antiochus, 709–​7 10, 719 Panaetius of Rhodes, 602, 678, 679, 689, 694 Pappus, 272, 273, 274, 275, 276, 277, 278, 282, 284, 285, 287, 289, 870, 871, 872, 874, 875, 876, 877, 879, 881, 882, 883, 884, 885, 886, 888, 889, 890 paradoxa, 431, 433, 436, 437, 438, 440, 442, 477 parapegma, 186, 301, 302, 304, 305, 475, 480, 805 Paul of Aegina, 375, 376, 522, 569, 572, 775, 965, 966, 977 periplous, periploi (compare “maps, of earth”), 200, 201, 203, 204, 211, 213, 324–​326, 343, 437, 874, 924, 933–​935, 993 Peutinger Table (map), 936–​937 pharmacy (compare also “herbals”), 36, 37, 73–​77, 100, 308, 366, 367, 368, 369, 370, 371, 372, 375, 376, 377, 393, 519–​553, 555, 602, 699–​720, 767, 768, 776, 784, 835, 836, 966, 967, 968, 971, 973, 976, 977, 1017, 1019, 1020, 1028 Philinus, 365, 366, 367, 368, 370 Philodemus, 258, 260, 261, 494, 602, 615, 618–​620, 621, 623, 624, 625, 626, 627, 628, 629, 630 Philolaus, 148, 149–​152, 153, 159, 160, 164, 165, 177, 178, 180, 185, 186, 191, 216, 447, 448, 449, 450, 452, 454, 456, 599 Philon of Byzantium, 340, 341, 347, 348, 349, 351, 352, 354, 355 Philoponus, 862, 864, 866, 870, 880, 887, 896, 898, 902, 903, 905, 906, 907, 908, 909, 910, 911, 913, 915, 916, 918, 932, 933

1042   Index Philostorgius, 927 phlebotomy, 220, 363, 369, 377, 550, 560, 639, 770, 785, 1002 Phlegon of Tralles, 432, 434, 439 Phylotimus, 546 physics, 178, 183, 187, 188, 238–​244, 245–​246, 257, 258, 259, 275, 289, 338, 345–​347, 382, 389, 393, 401, 456, 460, 464, 493, 616–​618, 620, 622, 624, 679, 682, 683, 686, 687, 730, 731, 777, 792, 811, 821, 833, 841, 849, 851, 859–​863, 895, 896, 897, 898, 899, 900, 901, 902, 903–​917, 981, 996 physiology, 73, 74, 96, 97, 99, 100, 101–​103, 155, 216, 217, 219, 220, 223, 224, 229, 250, 253, 360, 362, 363, 365, 366, 369, 374, 375, 377, 435, 445, 481, 483, 484, 489, 496, 501, 519, 529, 535, 624, 625, 638, 641, 642, 686, 693, 703, 716, 748, 753, 756, 765, 770, 771, 776, 778, 779, 780, 782, 835, 991, 994, 1019, 1021 place-​value (numerals), 14–​15, 17, 21, 50, 88–​89 planets, 25–​32, 35, 64–​65, 67, 90–​91, 129–​132, 135, 136, 137, 138, 139, 140, 142, 150–​152, 155–​157, 157–​158, 165, 176, 177, 178, 179, 185, 243, 244, 261, 289, 295, 298, 300–​301, 304–​305, 307, 309, 337, 381, 382, 383, 384, 385, 386, 387, 388–​389, 390, 391, 394, 397, 398, 400, 401–​404, 454, 598–​600, 606, 688, 736, 739, 790, 791, 792, 801–​804, 806–​809, 810–​812, 813, 821, 822, 824, 832, 834, 860, 861, 862, 890, 904, 906, 916, 917, 923 plaster (material), 414–​415, 418 plaster (medical) 376, 522, 524, 532, 533, 534, 651, 699, 704, 706, 707, 708, 709, 710, 714 Plato, 3, 4, 5, 147–​148, 153, 154–​157, 158, 159–​165, 179, 182, 185, 189, 190, 191–​192, 215–​216, 220, 222, 227, 235–​237, 242–​243, 251, 262, 264, 265, 266, 300, 310, 326, 389, 390, 419, 420, 424, 446, 451, 457, 460, 482, 483, 484, 485, 488–​489, 492–​494, 499, 504, 597, 599, 604, 609–​610, 627, 629, 677, 679, 680, 682, 683, 684–​685, 686, 687, 690, 691, 692, 693, 723, 751–​755, 757, 758, 769–​770, 774, 777, 806, 808, 820, 829–​830, 831–​832, 838–​839, 840–​ 841, 848–​850, 851–​856, 858–​859, 859–​860, 862–​863, 873, 899–​900, 903, 905, 907–​908, 911, 912, 914, 915–​916, 948, 949, 951–​952, 953, 957, 959, 965, 975, 981, 1005, 1021

Pliny (the Elder), 218, 302, 305–​310, 317, 318, 324, 326, 329, 340, 348, 349, 365, 368, 371, 372, 375, 376, 386, 413, 415, 416, 419, 422, 423, 438, 439, 463, 467, 468, 469, 471, 475, 476, 477, 519, 520, 521, 525, 527, 531, 533, 534, 545, 551, 594, 595, 596, 597, 598, 599, 600, 601, 602, 605, 606, 639, 648, 649, 650, 656, 657–​658, 659, 660, 661, 665, 667, 668, 669, 670, 671, 671–​674, 675, 700, 707, 708, 709, 710, 714, 715, 724, 725, 732, 746, 813, 830, 831, 835, 836, 838, 960, 968, 984, 987, 988, 991, 993, 1014, 1015, 1020, 1022, 1028 Pliny (the Younger), 306, 662, 666, 671, 674 Plotinus, 3, 610, 755, 838, 840, 841, 844, 847–​868, 873, 874, 895, 897, 906, 907, 981, 982 pneuma (compare also “breath”), 220, 240, 248, 252, 288, 337, 340, 362, 364, 365, 370, 484, 489, 499–​500, 500–​503, 641–​642, 683, 684–​688, 689–​691, 695, 738, 770–​771, 773, 779–​780, 820, 840, 945, 952, 954. Pneumatism (medical sect), 373, 547, 637, 638, 641–​642, 644, 648, 667, 695, 766, 771 Polemon of Laodicea, 744, 746–​747, 750–​751, 755, 758–​760, 760–​761 Polybius (historian), 203, 309, 316, 323, 324, 327, 328, 331, 333, 340, 367, 370, 371, 602, 922, 968 Polybus (doctor), 223, 225, 228 Porphyry, 391, 460, 499, 549, 609, 623, 752, 838, 840–​841, 847–​849, 852, 853, 854, 859, 864, 865, 874, 895, 897–​898, 902, 907, 913, 983, 1009 Posidonius of Apamea (and later Rhodes), 212, 261, 303, 304, 317, 327–​328, 331, 333, 385, 390, 599, 629, 678, 679, 681, 683, 691, 692, 694–​695, 696, 753, 754, 792, 813, 824, 923, 969 Praxagoras, 216, 232, 359, 361–​363, 364, 365, 693, 696, 770–​771 predict(ions), prognosticate, 2, 25, 26, 28–​29, 30–​32, 38–​41, 90, 137, 175, 297–​298, 301, 304–​305, 310, 311, 382, 384, 385, 386–​387, 388, 390, 392, 398, 403, 405, 424, 598, 599, 603, 610, 744, 751, 756, 799, 800, 802, 805, 810 Priscus of Panion, 929

Index   1043 Proclus, 183, 184, 190, 261, 269, 272, 273, 274, 287, 755, 789, 795, 822, 847, 849, 850, 851, 852, 854, 855, 856, 857, 860, 861, 862, 863, 864, 865, 871, 873, 874, 875, 877, 879, 880, 883, 884, 889, 890, 895, 898, 899, 903, 907, 908, 911, 912, 915, 916, 917, 932, 944, 982 prognosis, 36, 74, 100, 217, 218, 223, 224, 225, 392, 548, 550, 639, 643, 645, 646, 648, 650, 651, 744, 751, 755–​758, 760, 768, 775, 780, 784, 785, 969, 971, 981, 982 proofs, 18–​20, 57–​58, 87, 89–​90, 117–​120, 147, 153, 172–​175, 180–​184, 186–​189, 270, 276–​ 283, 286, 451, 455, 472, 494, 503, 616, 789, 802, 860, 885–​887, 888, 904 Protagoras (early philosopher), 219, 222, 493 Protagoras (geographer), 923–​924, 938 Ptolemy (astronomer and mathematician), 26, 30, 66, 186, 272, 284, 289, 293, 294, 295, 323, 333, 382, 383, 385, 386, 387, 388, 393, 395, 397, 398, 400, 401, 402, 453, 454, 457, 458, 459–​461, 482, 497, 499, 503–​508, 593, 789–​828, 829, 832, 834, 841, 842, 861, 871, 873, 874, 877, 878, 879, 882, 884, 885, 886–​887, 889, 890, 916, 917, 923, 924, 925, 935, 982, 1005, 1006, 1009 Ptolemies (Greek rulers of Egypt), 66, 71, 319–​320, 324, 325, 327, 359–​360, 361, 363, 367, 368, 372–​373, 375, 723, 724, 960–​961 pulse (medical), 74, 252, 360, 362, 365, 367, 368, 370, 372–​374, 648, 650, 695, 770, 771, 775, 780, 784, 785, 981, 982, 1027 Pythagoras, 147–​149, 150, 151, 164–​165, 172, 174, 176, 177–​184, 184–​186, 211, 218, 300, 450, 451, 594, 595–​596, 596–​597, 597–​600, 600–​ 603, 604–​608, 608–​610, 669, 752, 754, 755, 829, 832, 833, 841, 848, 873, 877, 1005, 1006 Pythagorean theorem (or rule), 57, 87, 111, 112, 140, 182–​183 Pythagoreans, 149–​151, 153, 164–​165, 177–​184, 184–​186, 189, 191, 215, 218, 307, 447, 450, 451, 456, 457, 458, 459, 460, 461, 483, 489, 499, 594, 595–​596, 596–​597, 597–​600, 603–​604, 604–​608, 608–​610, 611, 662, 725, 755, 808, 821, 831, 833, 841, 848, 849, 853, 854, 902, 1006 Pytheas, 212, 316–​317, 319, 320, 322, 324, 325, 326, 327, 331, 333

quadriuium (compare also triuium), 988, 997, 998, 999, 1000, 1001, 1002, 1003, 1005, 1006–​1010 Ravenna, 1007, 1013, 1015, 1016, 1025–​1028, 1030 rectangles, 13, 18–​20, 58, 87, 118, 173, 183–​184, 186, 210 rhetoric, 54, 55, 216, 222, 227, 236, 260, 272, 299, 349, 461, 470, 602, 604, 605, 617, 620, 639, 643, 644, 646, 656, 659, 671, 744, 745, 747, 750, 758–​760, 833, 849, 871, 874, 876–​877, 878, 884, 888, 896, 898, 915, 927, 928, 930, 951, 988, 991, 997, 998, 999, 1001, 1002, 1008, 1009 Rhind Papyrus, 54 riddles, 12, 15, 16, 17, 18, 19, 20, 226 roots (square, cube, etc.), 52, 87, 111, 114, 117, 151, 164, 341, 879 scalpels, 530, 556, 557, 559–​560, 563, 565, 576, 580, 585 Scylax of Caryanda, 203, 208, 211 Scribonius Largus, 372, 522, 527, 571, 699–​720, 1020, 1028 (L. Annaeus) Seneca, the younger, 331, 423, 424, 555, 615, 616, 622, 630, 631, 664, 669, 678, 679, 680, 696, 911, 937, 988 Serenus of Antinoeia (mathematician), 274, 289, 834, 842, 881 Serenus Sammonicus (medical poet), 1025, 1031 sexagesimal, 11, 13, 14, 18, 21, 30, 459 Sextius Niger, 519, 524, 525, 527, 528, 666 Sextus Empiricus, 260, 266, 267, 379, 395, 492, 509, 682, 683, 810, 819, 824 shadow clocks, 64, 138, 139, 140, 300–​301, 475, 498, 795–​796, 812–​813 silphion, 219, 523–​524, 706, 707 Simplicius, 157, 265, 275, 289, 294, 303, 304, 355, 504, 509, 789, 849, 850, 860, 862, 863, 870, 895, 896, 898, 900, 901, 902, 904, 905, 906, 907, 908, 909, 910, 911, 912, 913, 914, 915, 916, 917, 956, 975 simultaneous linear equations, 113–​114 Sirius, 62, 63, 304, 474, 475 smelting, 417, 419, 731 Socrates, 169, 206, 451, 466, 532, 680–​681, 682, 743, 744, 751–​753, 755, 766

1044   Index Soranus, 44, 222, 368, 369, 370, 373, 376, 555–​556, 576, 639–​640, 647, 701, 773, 966, 969, 973, 1015, 1020–​1021, 1023, 1024–​1025, 1030 soul, 64, 148, 159, 160, 163, 165, 178, 239, 240, 253, 262, 265, 266, 307, 362, 363, 376, 389, 390, 391, 396, 419, 457, 481, 482, 487, 488, 489, 490, 491, 494, 499, 500, 508, 550, 597, 611, 617, 623, 624, 625, 628, 638, 681, 683, 684, 685, 686, 687–​688, 689–​691, 693, 694, 731, 736, 738, 744, 745, 746, 748, 749, 751, 753, 755, 756, 757, 758, 759, 760, 766, 769, 780, 812, 819–​820, 821, 839, 840, 841, 848, 849, 850, 851, 852, 853, 854, 858–​859, 860, 861, 863, 873, 890, 897, 900, 906, 912, 914, 915, 951, 955, 982, 983, 999, 1003 specula (medical instrument), 344, 557, 558, 575, 576 squaring the circle, 87, 171, 186–​188, 275, 276 star clocks, 62–​63 stars, 26, 27–​28, 29, 31, 61–​66, 129–​137, 139, 140, 141–​142, 150, 155–​157, 159, 176–​177, 178, 179, 185, 211, 239, 243, 244, 247, 251, 297, 298, 299, 301, 307, 309, 310, 337, 381, 383, 384, 385, 386, 388, 389, 390, 391, 392–​393, 394, 395, 396, 403, 465, 475, 598, 599, 606, 610, 649, 727, 736, 739, 792–​793, 797, 804, 805, 809, 810, 824, 831, 832, 839, 860, 861, 862, 874, 890, 904, 906, 916, 922, 996, 999 Stephanus (alchemist), 943, 944, 945, 946, 948, 951–​952, 953, 954, 955, 956, 957, 966, 982 Stephen (Stephanos) of Byzantium, 204, 326, 925–​926, 938 Strabo, 26, 200, 205, 295, 315, 316, 317, 318, 319, 320, 322, 323, 324, 325, 326, 327, 328–​329, 329–​331, 331–​333, 373, 375, 441, 674, 683, 813, 814, 835, 922, 923, 924, 925, 960 Sulpicius Gallus, 309, 597–​600, 606, 611 sun, 11, 26, 29, 31, 32, 42, 62, 64, 65, 90–​91, 129–​ 130, 132, 133, 135, 136, 137, 138–​140, 140–​142, 150, 154, 156–​157, 158, 159, 160, 165, 175, 176–​177, 178, 179, 184, 185, 208, 243–​244, 247–​248, 261, 285, 300–​301, 302–​305, 307, 309, 310, 312, 316, 324, 381, 386, 391, 400, 401, 402, 403, 404, 405, 474, 492, 493, 494, 495, 498, 500, 506, 532, 597–​600, 605, 606, 607, 626–​627, 674, 687, 727, 790, 791,

792–​795, 795–​796, 798, 799–​800, 802, 804, 805, 806–​809, 811, 813, 822, 835, 836, 839, 854, 856, 857, 861–​862, 916–​917, 922, 948 surgery, 72, 73, 76, 98, 99, 100, 224, 225, 229, 363, 367, 369, 370, 371, 372, 375, 533, 535, 536, 537, 555–​590, 601, 640, 646, 651, 666, 667, 699, 701, 706, 707, 714, 767, 785, 965, 966, 967, 968, 971, 973, 977, 1022, 1030 Suśruta-​saṃhitā, 97, 98, 99–​100, 101 swerve, 264, 625, 627–​628 Synesius, 732, 735, 736, 871, 943, 945, 946–​947, 950, 951, 953 tables (mathematical and astronomical), 14, 15, 30, 31–​32, 53, 54, 58, 63, 67, 131, 132, 136, 139–​140, 284, 385, 387–​388, 397, 398, 458, 459, 460, 461, 475, 803, 804, 821, 824, 834, 874, 879, 885, 886, 887, 900, 944, 951, 982 technē, 217, 224, 226, 695, 730, 731, 836, 882, 944, 950, 955, 956, 980 Terentius Valens, 705, 719 tetraktys, 148–​149 Themison, 639, 652, 704, 771, 773 Theodorus of Cyrene (mathematician), 177, 180, 182, 189 Theodorus Priscianus (doctor), 1017, 1020–​1021, 1022, 1023, 1025, 1031, 1032 Theon of Alexandria (Neoplatonist), 284, 289, 496, 795, 804, 824, 871, 874, 877, 879, 880, 881, 882, 884, 885, 886, 887, 889, 951, 982 Theon of Smyrna (mathematician), 185, 288, 458, 794, 806, 822, 824, 873 Theophrastus of Eresos (philosopher), 177, 219, 235, 236, 317, 328, 359, 363, 413, 417, 419, 420, 421, 422, 423, 424, 433, 435, 436, 437, 439, 455, 463, 467, 470, 472, 475, 476, 477, 482, 483, 484, 485, 486, 487, 488, 491, 495, 519, 523, 524, 530, 532, 534, 536, 753, 912, 944, 946 Theophrastus (alchemical poet), 945, 954 Thrasyllus (of Alexandria or Mendes), 391, 396, 458, 493, 609, 611 transmutation, 2, 162, 410, 722, 723, 725, 726, 728–​731, 733, 734, 735, 736, 944, 945, 949–​ 950, 952, 953, 954, 957, 960, 961 triuium (compare also quadriuium), 988, 1000, 1001, 1002, 1003, 1006–​1010

Index   1045 Tryphon of Gortyn, 706, 707, 708, 709 tubes (alchemical, optical, surgical, etc.), 44, 134, 140, 347, 348, 495, 557, 570–​574, 575, 584, 585, 732 unusual celestial phenomena (including comets, meteors, etc.), 25, 130–​131, 137, 185, 247, 298, 309, 391, 417, 831, 948 (M. Terentius) Varro of Reate, 329, 371, 438, 439, 463, 464, 467, 468, 470, 471, 472, 473, 475, 476, 477, 594, 600, 602, 604–​608, 655, 656, 657, 659, 661–​663, 669, 673, 674, 675, 830, 832, 842, 968, 1003, 1011, 1025 (P. Terentius) Varro of Narbo, aka “Atax,” 603 veins (compare “arteries”), 241, 361, 362, 363, 364, 365, 487, 501, 563, 601, 703, 770, 771, 775, 778, 779, 780 Vergil, 463, 464, 468, 478, 619, 671, 704 Vettius Valens (astrologer), 384, 386, 391, 398, 401, 649, 652 Vettius Valens (doctor), 705, 718 Vettius Valens (politician), 705 Vindicianus, 362, 1014, 1017–​1020, 1023, 1030 Vindonius Anatolius (agronomist: contrast Anatolios, mathematician and bishop, above), 469, 471–472, 478 vision (the sense), 351, 411, 481–​517, 624, 816, 948 Vitruvius, 289, 299–​302, 304, 305, 308, 309, 329, 339, 341, 344, 352, 386, 387, 413, 415,

423, 493, 594, 597, 656, 657, 658, 659, 660, 662, 663–​666, 669, 813 void, 142, 161, 205, 263–​264, 267, 360, 364, 395, 420, 488, 558–559, 616, 622, 625, 627, 628, 629, 777, 862 volume of a pyramid, 117, 119, 279 volume of a sphere, 117, 119–​120, 279–​280 water clocks, 64, 302, 355 wonders, 204, 210, 431, 433, 434, 437, 442, 443, 476, 477, 617, 673 Xenophon (historian), 209, 210, 463, 465, 466, 473, 680, 682, 752, 753 Zeno (Herophilean doctor), 366, 368, 370, 373 Zeno (Byzantine Emperor), 383 Zeno of Citium (founder of Stoic school), 183, 500, 509, 677, 678, 681, 682, 686, 689, 693, 696, 754, 838 Zeno of Cyprus (teacher of Oribasius), 970, 980 Zeno of Elea (early philosopher), 191, 264 Zeno of Sidon (Epicurean), 260, 261, 615, 618, 619, 620, 626, 631 Zeno of Verona (bishop), 396 zero, 50, 90 Zosimus of Panopolis, 722, 725, 726, 727, 731, 735, 736, 737, 738, 739, 943, 945, 946, 947, 948, 949, 950, 951, 952, 953, 954, 956, 957, 958, 960, 961