Thales the Measurer 9780367687090, 9781003138723

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Thales the Measurer

Thales the Measurer offers a comprehensive and iconoclastic account of Thales of Miletus, considering the full extent of our evidence to build a new picture of his intellectual interests and activity. Thales is most commonly associated with the claim that ‘everything is water’, but closer examination of the evidence that we have suggests that he could not have said anything of the sort. His real interests, and his real innovations, lay in challenges of quantitative measurement, especially measurements related to the movement of the sun. In this he had no ­predecessors – and, for centuries to follow, no real successors either. Scholars and advanced students of Presocratics will probably enjoy to explore the new paths through sources and see things from a different perspective. And since the Greek is systematically confined in the footnotes, this book is accessible to a more general readership too. Livio Rossetti, now retired, served for many years as Professor of the History of Ancient Philosophy at the University of Perugia, Italy. His most recent books are Convincere Socrate (Pistoia 2021) and Verso la filosofia: nuove prospettive su Parmenide, Zenone e Melisso (this is a book to which several editors and interlocutors contributed; Baden Baden 2020). The provisional title of his next book is Rethinking the Presocratics.

Issues in Ancient Philosophy Series editor: George Boys-Stones, University of Toronto, Canada

Routledge’s Issues in Ancient Philosophy exists to bring fresh light to the central themes of ancient philosophy through original studies which focus especially on texts and authors which lie outside the central ‘canon’. Contributions to the series are characterised by rigorous scholarship presented in an accessible manner; they are designed to be essential and invigorating reading for all advanced students in the feld of ancient philosophy. The Hieroglyphics of Horapollo Nilous Hieroglyphic Semantics in Late Antiquity Mark Wildish Taurus of Beirut The Other Side of Middle Platonism Federico M. Petrucci Ancient Logic, Language, and Metaphysics Selected Essays by Mario Mignucci Edited by Andrea Falcon and Pierdaniele Giaretta The Stoic Doctrine of Providence A Study of Its Development and of Some of Its Major Issues Bernard Collette Investigating the Relationship between Aristotle’s Eudemian and Nicomachean Ethics Giulio Di Basilio Thales the Measurer Livio Rossetti For more information about this series, please visit: https://www.routledge. com/Issues-in-Ancient-Philosophy/book-series/ANCIENTPHIL

Thales the Measurer Livio Rossetti

First published 2022 by Routledge 4 Park Square, Milton Park, Abingdon, Oxon OX14 4RN and by Routledge 605 Third Avenue, New York, NY 10158 Routledge is an imprint of the Taylor & Francis Group, an informa business © 2022 Livio Rossetti The right of Livio Rossetti to be identifed as author of this work has been asserted in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identifcation and explanation without intent to infringe. British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data A catalog record has been requested for this book ISBN: 978-0-367-68709-0 (hbk) ISBN: 978-0-367-68710-6 (pbk) ISBN: 978-1-003-13872-3 (ebk) DOI: 10.4324/9781003138723 Typeset in Times New Roman by codeMantra

Contents

List of figures vii Sources and Translations ix Foreword xi PART I

Approaching Thales

1

1 Who were these ancient masters? 3 2 A context for Thales 16 3 Elements of a biography 36 PART II

Five quantitative inquiries

47

4 How to measure the height of a pyramid 49 5 Thales dates the tropai

66

6 From the dating of the tropai to the dating of the ise¯ meriai

76

7 What explains a solar eclipse? 85 8 A measurement of ½˚ 100

vi Contents PART III

Three further investigations on earth, waters and rocks

109

9 Surface water, arche¯ , earth, and, it seems, some fragments of Thales 111 10 The periodic flooding of the Nile and the ‘Atlantic corollary’ 129 11 Thales and the stones of Magnesia 138 PART IV

Other investigations: real and presumed

143

12 The sky according to Thales 145 13 To measure the distance of a ship from land 151 14 Thales and the theorems of plane geometry 154 15 Thales ‘el injenioso hidalgo’ 158 16 Thales the sophos

164

PART V

Final remarks

167

17 The ‘new’ fragments of Thales 169 18 Thales the measurer 184 19 The research bug 189 Appendix to Chapter 7 193 Bibliography 196 Concordances 202 Locorum Index 205 Index 209

Figures

2.1 Marsiliana tablet abecedarium 22 4.1 An Egyptian pyramid where it is possible to establish that the shadow forms an isosceles triangle. Courtesy of Dirk Couprie 55 4.2 An Egyptian pyramid where the shadow forms an isosceles triangle 59 4.3 An Egyptian pyramid to be analysed according to the suggestions made by Redlin, Viet, and Watson 62 13.1 Device allowing to establish how far is a ship according to Tannery 152 13.2 Device allowing to establish how far is a ship according to Bretschneider 153

Sources and Translations

DK Hermann Diels–Walther Kranz, Die Fragmente del ­Vosokratiker, Berlin 61953. LM André Laks–Glenn W. Most, Early Greek Philosophy, ­Cambridge MS 2016 [Loeb Classical Library 524–532]; Les débuts de la philosophie, des premiers penseurs grecs à Socrate, Paris 2016. KRS G.S. Kirk–J.E. Raven–M. Schofield, The Presocratic ­Philosophers, Cambridge 21983. W Georg Wöhrle, Die Milesier: Thales, Berlin 2009. W–MK  Georg Wöhrle–Richard McKirahan, The Milesians: Thales, ­Berlin 2014. Few quotations, marked as ‘(n.)Ar W’ or ‘(n.)As W’ refer to Wöhrle, Die Milesier: Anaximander und Anaximenes, Berlin 2012. Most translations from Greek and Latin authors come from either LM or W–MK, but a few from J. Barnes, The Complete Works of A ­ ristotle (Princeton 1895) or those available in the Perseus Digital Library (www.perseus. tufts.edu).

Foreword

No surprise if this book had a long gestation. Leaving aside its most remote antecedents, I can report that I began working on this project immediately after finishing ‘La filosofia non nasce con Talete, e nemmeno con Socrate’ in 2015, although in 2016–2018, I was committed to demanding schedule of research on Parmenides. Some of the suggestions made in this book, notably those in Chapters 2 and 17, are likely to become the starting point of more thorough investigations. This is, at least, my hope. Many people contributed to the refinement of what follows. After 2018, it occurred to me to knock at the door of Fulvia De Luise (Univ. Trento), Flavia Marcacci (Pontificia Univ. Lateranense Roma), Giuseppe Mazzara (Univ. Palermo), Dmitri Panchenko (Univ. St. Petersburg), Massimo Pulpito (Taranto and Univ. Brasilia), Marian Wesoly (Univ. Poznan), and Georg Wöhrle (Univ. Trier), and then of Marco Beconi (Castiglione del Lago), Alberto Bernabé (Univ. Complutense Madrid), Cipriano Conti (Univ. Perugia), Dirk Couprie (Amsterdam), Nicola Galgano (Univ. São Paulo), Ursula Gärtner (Univ. Graz), Laura Gianvittorio-Unger (Univ. Vienna), Robert Hahn (Univ. of Illinois at Carbondale), Gianfranco Maddoli (Univ. Perugia), Massimo Nafissi (Univ. Perugia), Jaume Portulas (Univ. Barcelona), Francesco Prontera (Univ. Perugia), Emilio Rosamilia (Univ. Perugia), Amneris Roselli (Univ. Napoli “L’Orientale”), Danijela Stefanovich (Univ. Belgrade and Vienna), and our son Giotto Rossetti (Firenze). An anonymous reviewer summoned by Routledge was also greatly helpful. As to the English version of my Italian manuscript, I am very thankful towards Ugo Zilioli (Durham; University of Oxford), to Anthony Antunes (University of Toronto) and, in the highest degree, to the series editor, George Boys-Stones (University of Toronto) since, without the latter’s intervention, this book would have been intolerably worse than it is, and in many regards. So, I acknowledge with gratitude George’s multifarious help.

xii Foreword The usual caveat about my sole responsibility for the residual shortcomings affecting the fnal version applies. This Thales is a gift for my beloved wife, Fiorella, 61 years after our engagement. Livio Rossetti Perugia APRIL 2022

Part I

Approaching Thales

1

Who were these ancient masters?

1.1 A disconcerting oblivion “Thales is all about water, Anaximander the apeiron and Anaximenes air; who doesn’t know that?” These associations are almost automatic, and this frst impression is asserted in most current reference works as well as other, more specialised discussions. But it signals that any curiosity about the Milesians has been all but extinguished. A great fog, as it were, has descended upon their study. But the fog sometimes clears, and one sees that, for example, one of these ancient masters, Anaximander, saw how a graphic representation of lands and seas might be produced by delineating the coastline. This amounts to imagining a view from above, rather than working with the perspective we would normally achieve with our eyes. This had not yet occurred to anyone, and Anaximander was the frst to take concrete steps toward cartography and maps. Another Milesian sophos, Hecataeus, wrote a book entitled Periēgēsis (Περιηγήσις) οr Periodos gēs (Περίοδος γῆς, that is, Tour of the Earth), in which he gathered, for the frst time ever, all the information then available concerning more than three hundred places (mostly towns) along the Mediterranean coast and in some inland areas (in particular, in the inland areas of Egypt and the Anatolian peninsula). It is easy to imagine how valuable this could have been, even if this information was only partially reliable. Thanks to the work of both of these thinkers, who were active some 2,500 years ago (before the Persian Wars, so before 490–480 BC), people began to have access to basic information about distant places and other peoples. A third Milesian, the subject of this book, surveyed cosmic events, especially related to the sun; he saw how to date solstices and equinoxes, and understood why solar eclipses occur; he saw how it would be possible to use the shadows cast by the sun to measure the height of the pyramids; and he was able to measure the apparent amplitude of the solar disk. Anaximenes, the fourth, had the daring notion that everything could be explained by air, a substance which could transform itself into other substances – water, in the frst place – and which explains the origin of life.

DOI: 10.4324/9781003138723-2

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Approaching Thales

This is already enough to show that associating Thales, Anaximander, and Anaximenes only with their refection on water, apeiron, and air, respectively, is almost bizarre. Yet this is true even of the professional literature on these authors. A striking case is the book In the Light of Science. Our Ancient Quest for Knowledge and the Measure of Modern Physics (Amherst NY, 2014). The author of this book, the physicist Demetris Nicolaides, asserts that modern physics “is both an expansion and a refection of various scientifc ideas elaborated by prominent Presocratic philosophers”, and that “scientists of the twentieth century are still grappling with the fundamental problems they raised twenty-fve centuries ago” (pp. 11–12). In Nicolaides’ eyes, Thales is precisely the water-theorist: this is inferred from the supposed fact that Thales merely taught that everything comes from water, a point Nicolaides exploits to claim that Thales established “the core concept of modern physics”, sameness, that is “the universal, underlying, simple principle that is a characteristic of all things in nature” (105).1 But even passing over what we in fact know about Thales’ conception of water (see Chapter 9), and passing over the odd claim that these ancient intellectuals were the ones who identifed the fundamental principles of modern science (which seems like an exaggeration), there is no doubt that this impoverished image of Thales (as well as Anaximander and other Presocratics), which became widespread in the twentieth century, dissolves upon closer inspection.

1.2 It is urgent to go beyond Aristotle Most of the responsibility for the prevalence of this impoverished image of Thales and the others lies, unwittingly, with Aristotle. In a well-known text, the frst book of his Metaphysics, he is thinking about the origins of the idea of an archē (a principle or primordial substance), and answers the question with this remark: But Thales… says (phēsin) that that principle is water, and for this reason he also highlighted (apephaineto) that the earth foats on water. Perhaps he has derived this assumption from seeing that what nourishes all things is moist and that what is warm itself comes from this [i.e. water] and lives because of it (the principle of all things is that from which they come to be)—it is for this reason that he had this idea, and also from the fact that the seed of all things has a moist nature, and for things that are moist, water is the principle of their nature.2 The immediate problem here is that if Thales believed that the earth foats on water and that water nourishes all things (all seeds are moist, he adds), then it is very unlikely that he was talking about an originating principle, something to which for example even the stars can be traced. His conception of water rather seems to have been a resource internal to the world system in

Who were these ancient masters?

5

which we live – the water, namely, that manifests itself in rivers, springs, and wells. “That from which everything is generated” is not a cosmic element, but the humidity of the soil, as well as, perhaps, the liquid in the fertilized mammalian uterus or bird egg. However, what Aristoteles has in mind is the question of what everything derives from, and into which, at the end (teleutaion), it dissolves.3 So the question naturally arises: are Thales and Aristotle talking about the same thing? It seems doubtful. In Chapter 9, I shall show that Aristotle himself provides us with reasons to distrust what he says here. Nevertheless, in the meantime, almost everybody has followed Aristotle’s lead, and taught that the main doctrine and the core of Thales’ teaching consisted in identifying the archē as water – just as Anaximander later would have identifed the archē with apeiron.4 It might help, in fact, to spend a little time with Anaximander. As I noted, he saw how one could represent the lands and seas on a map, and in fact attempted to draw a map of the entire Mediterranean area. This was the frst such attempt in history, and was largely successful, despite the obvious challenges.5 But he did more than this too. He also defned a sort of primitive Astronomical Unit, equal to the diameter of the earth,6 and used it to estimate some cosmological distances – for example, the distance of the sun from the earth.7 And there was more. So why does this not feature more in current pictures of Anaximander – why does it not take up more space in discussion of him than his ruminations about the apeiron?8 Anaximander must have devoted more time to set up his map of the world and his work with (what I am calling) the Astronomical Unit than to refne his theory of the apeiron. And he must have been much prouder of making a map allowing everyone to ‘see’ not only Rhodes and Crete, but even Sicily, the Nile Delta, the Pillars of Hercules and the eastern edge of the Black Sea, and of his measurement of cosmic distances, than of having something to say about the apeiron. I believe that the same is true of Thales. I cannot understand why less attention continues to be paid to his astonishing measurements than to his ruminations about water, not least because he was quite unique in his achievements in measurements. The fact that Aristotle’s own interest blinded him to Thales’ true creativity does not excuse us, who live in an age when quantitative data is so much more important. These few considerations are enough to reach the conclusion that we will do well to extend our feld of observation far beyond water and apeiron to which Aristotle (and, following him, Cicero) has directed attention.9 This is why I wanted to make a clean break with deeply rooted historiographical habits, and look for more solid foundations to reconstruct the signifcance of Thales. We have an abundance of information about him and, as we shall see, some is of real value. Little by little, I found myself in a condition similar to that of someone who owned a feld traditionally sown with wheat and suddenly realized that there were splendid Roman mosaics just beneath the surface, and then began to uncover those mosaics. As a consequence, in the

6

Approaching Thales

interpretation of Thales that I offer in this book, a number of texts which are usually overlooked receive much greater attention.

1.3 But we should go beyond Cherniss too Cicero’s role in mediating evidence about the Presocratics to us (nn. 4 and 9, above) helps us to see that we need to achieve a critical distance from our sources; it is certainly useful to remember that each pursues its own ends and moves within its own context. However, it would be a mistake to assume that all we need to do is record where there is bias or oversimplifcation, in the manner of Harold Cherniss.10 Sometimes our sources themselves lacked relevant information or understanding (for example, concerning the difference between equinox and equilux: see Chapter 6). In the case of Aristotle, a lot can be explained by his own use (unknown to Cherniss) of work by Hippias of Elis. Hippias wrote a work, the Sunagōgē, which contained, as it has been possible to ascertain,11 a sort of proto-history of Presocratic culture from Homer to Gorgias. This scheme was immediately adopted by Plato in the Cratylus, Isocrates in his Antidosis – and by Aristotle in the Metaphysics.12 Hippias’ text has not come down to us, but these three texts do more than allow us to see that it existed. In Cratylus 402a–c, the Platonic Socrates lingers on the theme of water and affrms that, for Heraclitus, everything fows, and it is not possible to step twice into the same river; that Homer had already spoken of Okeanos as father of the gods (Il. 14.201); that Hesiod had said something similar (Theogony 337 ff.); and that Orpheus himself (1B2 DK) sang that the frst marriage was that of Okeanos to his half-sister Thetis. Similarly, Aristotle, when he is talking about Thales and water, writes that in remote antiquity, some “placed Ocean and Thetis at the origin of the generation of things”. We know, in fact, that Hippias wrote (I am summarizing here) that: some of these things were said by Orpheus, others by Musaeus … others by Hesiod, others by Homer and others by other poets, then there are the sungraphai [works in prose] by both Greeks and Barbarians; I put together ta megista [the most important points] etc. (86B6 DK = 36D22 LM) Isocrates, for his part, spoke of the speeches of the sophistai, for one of whom the number of beings is unlimited, while for Empedocles there are four, for Ion three, for Alcmaeon two, for Parmenides and Melissus one, and for Gorgias none (Antidosis 269). For the link between Aristotle and Hippias, compare also what Diogenes Laertius says: “Aristotle and Hippias reported, on behalf of Thales, that…” (Lives 1.24).13 It is easy to see that Plato, Aristotle, and Isocrates were all using Hippias. Apparently, Hippias identifed a common thread, a common interest in the origin of all things and found in water a connection between Thales and the

Who were these ancient masters?

7

poetic tradition. So, did Aristotle take Hippias on trust? Most likely yes, as we will see (in Chapter 9). It is his trust in Hippias that led him to think that water-as-origin was central to Thales’ teachings, and this, in turn, is what led Cicero, a large number of other ancient authors, and then innumerable historians of philosophy to suppose the same. Hippias wrote the frst literary chrono-topography,14 an attempt to bring order to the relatively recent past by tracing common threads uniting different characters. This sort of exercise always simplifes the data, often drastically. It seeks to tell us who stood before whom, after whom, higher than whom, and where; it helps its reader to remember the information by arranging it into a structure in which each character or event deemed signifcant is assigned a place. It is no wonder that Hippias’ scheme proved attractive to those who, like Plato and Aristotle, wanted to delineate their own more detailed chrono-topographical profles.15 And Plato and Aristotle were never interested in the sort of quantitative research which, as I shall show, was the real focus of Thales’ work. So they would be more attracted to the idea that Thales was interested in water as a frst principle than anything else they might have heard about him. The same might be said of more recent historians of philosophy (the people who, for example, also overlook Anaximander’s achievements in the feld of cartography). In fact, at least three of the four Milesians I referred to above were frst and foremost ‘makers’, not theorists. Thales sought quantitative data, Anaximander a map of the Mediterranean, and Hecataeus a collection of information on more than three hundred cities in the Mediterranean area. And there is no evidence that anyone in their day was famous for theories alone: the performative aspect of their work was much more signifcant. But this practical and performative aspect became less important to philosophy later on, so it is understandable if it came to be marginalised in retrospective surveys of Greek intellectual life. After that, it went largely unnoticed by historians of philosophy from Brucker and Zeller to Laks and Most.16 These considerations should be enough to help us see that, at least in the case of the Milesians, Aristotle (and the communis opinio that he gave birth to) is by no means a reliable guide. For those who are really interested in understanding who Thales was (as well as other Presocratics, starting with Anaximander), it is essential to put this hermeneutic scheme aside.

1.4 Positive and negative evidence Another important methodological issue is this. We need to report what has been duly documented, and indeed to strictly adhere to the available documentation, but sometimes due attention must also be paid to the absence of specifc evidence. I shall give just two examples. A passion for quantifcation characterized Thales; but no one else before him, nor anyone else after him, at least among the Presocratic sophoi and the Greek philosophers, showed a similar interest in measurement or for the devices needed to be able to make

8

Approaching Thales

them. This is very striking, but it emerges from what is not reported to us by generations of students of natural phenomena. Indeed, the list of later Greek intellectuals who did not dedicate themselves to measuring is very long, while the list of those who did anything of the sort is very short. So the information we have on Thales the measurer has special signifcance – and (just because it is not reinforced by later traditions of interest) is likely to be among our most reliable information about him. But if we are told about Thales’ interest in quantitative data, we are not told that he was interested in arithmetical calculation and the use of the four operations. In the Egypt of his day, the marked ability of some people in making calculations (for example, calculating the area of a non-square territory) must have been well established, but this was a skill that was not transmitted to the Greeks despite the relationships that are presumed to have existed between these two countries.17 Thales seems to have confned himself to, at most, elementary addition. (Pythagoras and his disciples, for their part, had their own ‘science’ of numbers, but it does not appear that they distinguished themselves for an ability to calculate, that is, for performing operations on numbers.) These two absences in our evidence help to make clear what Thales could and could not do: he knew how to measure and quantify, but not compute. (If Aristotle knew this, he did not have the occasion to remark on it.)

1.5 There is something to understand, not just to ascertain It seems equally advisable to draw attention to the difference between striving to provide novel insights into Thales and striving to understand him. The frst operation is absolutely necessary: I can at least say that I have done my best to dust off, clean up, lubricate, and carefully review the primary evidence, positive and negative, comparing my own conclusions with the most respected existing opinions. But it is also necessary to understand, on the basis of our re-examination, with whom we are dealing and what kind of character Thales was. Are we just tidying up the rooms of a small museum, or making more ambitious contributions to it? So in what follows, I attempt to get an idea not only about what the frst great Milesian did, taught, and wrote (as well as about what he did not do) and not only of the areas in which he should be viewed as a true innovator, but also, as far as possible, to think about what he believed he was and had done, about what frst of all enthused him. We need to do this if we suppose that he was himself in pursuit of meaningful knowledge and not mere diversion. I want to show that he was, in fact, the frst to appreciate the fascination of numerical data. This is something important to understand over and above what there is to know. So I need to undertake a sort of ‘second sailing’ and ask what Thales’ measurements may have meant for him, as well as for his contemporaries – and for the rise of the exact sciences in subsequent history.

Who were these ancient masters?

9

It may seem surprising, but this aspiration to give a face to Thales owes something to the rediscovery of Socrates in the Italian ffteenth century. For an entire millennium (approximately 400–1400 AD), no one, as far as we know, wrote about Socrates in his own right, in Greek and even less in Latin and Arabic. The reason is well known: it was because, during so many centuries, among the Romans and the Arabs no one had access to Plato’s Apology, or to any other dialogue with Socrates as protagonist, and among the Byzantines no one paid much attention to this work. The result is that Socrates was known to them only thanks to anecdotes, sayings and brief reports, precisely as were most Presocratics. But when the frst (rather good) Latin translations of the relevant texts were published in Florence, Socrates suddenly became an identifable character again, whom readers could imagine on the basis of lively representations.18 My attempt to get closer to the mental world of the ancient Milesians and give them back an identity is comparable: I would like to overcome the phase in which it seemed we had to be content with identifying and retelling the relevant information (e.g. “Of Thales we know that…, we also know that… and that…”). Instead, I would like to move (however incrementally) towards the identifcation of a personality.19

1.6 Some innovative studies on Thales 1.6.1 O’Grady Before diving into the world of Thales, we should review some significant studies. The only specifc monograph published so far on Thales is the volume by Patricia O’Grady entitled Thales of Miletus. The Beginning of Western Science and Philosophy (Aldershot, 2002). This was by far her most conspicuous contribution to the history of Greek science and ancient philosophy. The book is broad in scope. It contains notable learned excursuses on, for example, the travels of Thales (pp. 253–267), and on Thales as adviser to King Croesus (pp. 179–190); there is a high level of direct knowledge of the surroundings of Miletus (e.g. pp. 62 ff.) as well as the Anatolian hinterland (e.g. 184 ff.), on Thales as the frst of the Seven Sages (pp. 268–280), and on the Magnesian stone (pp. 112–125). There are pages on Lavoisier’s experiment to ascertain if water is able to ‘become’ earth (pp. 232 ff.), and discussions that range from human fertilization to spontaneous generation, from the metallurgy of the time to the silting up of the “Gulf of Latmus”, inside which Priene, Myus, and Miletus were located (pp. 46–63). O’Grady also puts emphasis on an often-forgotten fact, that Thales and Anaximander died within a short time of each other, and thus were making their claims at the same time. Thanks to these and many other insights, the panorama of the possible ways of framing the information in our possession has been decisively

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Approaching Thales

modifed by O’Grady’s book. In fact, after the release of her Thales, research found itself starting afresh and, almost always, on much more solid foundations. Particularly relevant is a sentence which, strangely enough, is to be found only in the second appendix of her book (p. 276): The astronomer who was credited with successfully predicting a solar eclipse, who fxed the solstices and who advised the Greeks to navigate by Ursa Minor, who perhaps attempted to devise a calendar that would serve all the Hellenes, and who was the founder of natural philosophy – this was Thales. Here the author comes around to telling us the essential thing: a relevant trait of Thales (his activity and work, not just his ideas) and what sort of image O’Grady had of him. As it happens, this statement is close to the profle that will be sketched in the present book, and it already raises questions about the centrality that O’Grady herself gave to the theme of water (which would have been mere theory, not an activity). Since this will help to put many things in focus, I want to talk about it immediately, albeit briefy. The third and fourth chapters of O’Grady’s Thales (the frst two are merely introductory) focus on the question of water-as-archē, and the author immediately sets up a discussion in which very little is taken for granted. Among other things, O’Grady argues (pp. 38 ff.) that Thales and Anaximander may have used the notion of archē (though there is no proof for this, and it is actually more likely that the term was frst used by Anaximenes). According to O’Grady, Thales would have had ample opportunity to do the work that would substantiate Aristotle’s claims, taking advantage of his knowledge of a wide range of phenomena that, at the time, must have been quite familiar to him and his public. So, the scholar concludes, it is very likely that, in associating Thales with the idea that water is a fundamental principle, Aristotle was right. O’Grady says: It is probable that Thales would have sought every possible opportunity to amass proofs to sustain his doctrine (62) and it may have been Thales who frst recognized and brought to notice the importance of evaporation as a natural event within the cosmic process. (63) She also identifes “the following common beliefs about water and generation …” (65). But note that O’Grady saw in this belief not an abstract philosophy but the point of arrival for a whole collection of supposed empirical observations. In other words, even when she dealt with water, O’Grady saw

Who were these ancient masters?

11

in Thales a practical person who was actively engaged in the study of the physical and biological environment (see also pp. 230 ff.). This already (appropriately) undermines her faith in Aristotle’s view. But there is no doubt that the ground-breaking work carried out by her was formidable. In fact, O’Grady is responsible for many undoubtedly important achievements, and not just those listed above. 1.6.2 Marcacci, White, Wöhrle Three other recent frst-rate contributions to the feld are by Flavia Marcacci, Stephen White, and Georg Wöhrle. The frst of these scholars dedicated her 2001 master thesis to Thales. Her great merit was to prepare the very frst inventory of what is reported of the teachings and other activities of Thales. This constitutes a crucial new starting point for any student of Thales. To Professor Marcacci, we also owe a good contribution (2009) on measuring the height of the pyramid. I credit Stephen White for publishing in 2008 the following list of measurements attempted by Thales:20 1 2 3 4 5 6 7 8 9 10 11 12

Solar eclipse (forecast). Solstices (exact dating). Equinoxes (exact dating). Seasons (exact duration in days). Days per year. Days per month. A lunisolar ratio. Pleiades (date of their dawn setting). Hyades. Ursa Minor. Nile foods (causes). Olive harvest.

The list, though questionable in some details (points 11 and 12, plus the lack of any reference to the measurement of the pyramids), is telling. It tells us that Thales was especially dedicated to measurements, and this is something that had never been said before.21 A year later, in 2009, Georg Wöhrle published an impressive collection of sources on Thales: 590 textual units from 120 different authors, while in Ritter–Preller (1869)4 only some 20, and in Diels–Kranz (1951)6 only some 54 sources are collected. His collection has fnally made it possible to reach a clear understanding of how vast the panorama of information available on Thales is, thus strengthening the impression that the study of Thales ought to restart from the new foundations thus acquired. So, Patricia O’Grady has found herself in very good company. Thanks to her achievements, and those of these three other authors, further directions

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Approaching Thales

in research became possible. This present book has the ambition of following in their wake – and, at the same time, of honouring the memory of Patricia O’Grady as an indefatigable researcher who died far too prematurely. Finally, I feel compelled to mention two further works by Robert Hahn and two by Pierre Vesperini that have (or could have) caused quite a stir. Hahn’s Anaximander and the Architects (2001) and The Metaphysics of the Pythagorean Theorem: Thales, Pythagoras, Engineering, Diagrams, and the Construction of the Cosmos out of Right Triangles (2017) share the author’s propensity to assume events without evidence or even plausibility. I will just quote this sentence (2017, 97): What Thales did was to show that the height could be calculated in a very different way from the formula used in the Rhind Mathematical Papyrus and the Moscow Mathematical Papyrus and this might well have led him to refect on the difference in their approaches, and to consider what these different approaches may have meant. My perplexity starts with the following questions: do we know that Thales was aware of the two papyri mentioned? that they interested him? that he found a way not only to study and understand any of it, but to understand it well? that he understood his own approach to measuring the pyramid as an alternative to something in the Rhind Papyrus? As far as I am aware, no evidence is available to support such a conjecture.22 Exegetical prudence requires, as everyone knows, ascertaining the facts, or at least reasoning on the basis of the evidence available. It is therefore disappointing to say I have not seen any evidence. It is true that our sources mention Thales’ interaction with Egyptian priests.23 If this happened – and it is quite possible that it did – surely a prolonged interaction with them would have been a rare formative experience for him; however, we are not able to say that, at that time, he learned of the Rhind Papyrus (or of any other mathematical text), nor that he had the opportunity to establish meaningful relationships with people who knew it well or who had studied it in depth, nor that he managed to have it explained to him in detail, to the extent that he understood signifcant aspects of those very ancient and very technical documents – or of some more modern document – and then decided to distance himself from that way of dealing with the pyramids. For reasons I will focus on in Section 4.1.3, it is much more likely that he remained unaware of so advanced a mathematical culture. This is not so strange. Goethe, for example, in his famous trip to Italy reports that he spent many months in Rome (where he had excellent acquaintances and had a portrait made) without knowing, or wishing to know, the most famous sculptor of the time, Antonio Canova, who found himself in Rome in the same period. Yet, it is to be admitted, he would have been able to appreciate Canova’s sculptures.

Who were these ancient masters?

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As to Pierre Vesperini, I have in mind his paper “De Thalès à Anaxagore: les Ioniens à l’école des dieux” (2017) and his book La philosophie antique. Essai d’histoire (2019). Both have great premises, but a totally untenable conclusion: ‘Thalès voit les dieux partout’. Vesperini simply fails to take into account the available evidence for Thales and his context, and relies uncritically on legends, hélas. These, then, are just some of the interlocutors with whom I will have the opportunity to engage in undertaking a detailed exploration of the sources on Thales.

1.7 An unexpected bonus: ‘as Thales said’ In these introductory pages, I cannot help hinting at a totally unexpected event that happened to me while revising a frst version of the present book. While rereading (and rewriting) Chapter 9, I started to pay attention to the ways in which Seneca and Aristotle give us some of their information on Thales. The former does so by writing ut Thales ait and inquit; the latter by saying φασιν εἰπεῖν Θαλῆν. For the frst time, I realised that I was reading phrases that typically report fragments (quotations); I subsequently ascertained that there is no discussion of this anywhere in the scholarship. Why not? Is there any reason not to read those statements (and others that are similar) as possible quotations? If we read Ἀναξαγόρας … φησιν, or καθάπερ ὁ Ἡράκλειτός φησι, we generally think that we are reading a fragment, but, starting with Zeller (1844) and Diels (1903), a consensus was apparently established that no fragment by Thales has survived. However, I do not know of any discussion of why this authority has been denied to any of our sources: it is as if a kind of aprioristic censorship has been applied and accepted with no further examination. It is evident that we are witnessing an anomaly, about which I will discuss in Chapter 17. This is a further reason to re-examine ab imis the few hints of statements openly attributed to Thales.

Notes 1 At pp. 141–144, he devotes some attention to other achievements of Thales; however, he does so under the title ‘The Sage’, suggesting that those achievements too have some value, but not the same than his speculation on water as the founding element. 2 Metaph. I.3, 983b20–24 (=11A12 DK = Th29 W = 5D3 and 5R32 LM): ἀλλὰ Θαλῆς μὲν ὁ τῆς τοιαύτης ἀρχηγὸς φιλοσοφίας ὕδωρ φησὶν εἶναι (διὸ καὶ τὴν γῆν ἐφ’ ὕδατος ἀπεφήνατο εἶναι), λαβὼν ἴσως τὴν ὑπόληψιν ταύτην ἐκ τοῦ πάντων ᾶν τὴν τροφὴν ὑγρὰν οὖσαν καὶ αὐτὸ τὸ θερμὸν ἐκ τούτου γιγνόμενον καὶ τούτῳ ζῶν (τὸ δ’ ἐξ οὗ γίγνεται, τοῦτ’ ἐστὶν ἀρχὴ πάντων)—διά τε δὴ τοῦτο τὴν ὑπόληψιν λαβὼν ταύτην καὶ διὰ τὸ πάντων τὰ σπέρματα τὴν φύσιν ὑγρὰν ἔχειν, τὸ δ’ ὕδωρ ἀρχὴν τῆς φύσεως εἶναι τοῖς ὑγροῖς. 3 The stoicheion kai archē tōn ontōn (983B8–11).

14  Approaching Thales 4 Yet about Anaximander and the apeiron Aristotle does not make assertions, limiting himself to rather generic indications, as if he does not know exactly. To be clear, it was once again Cicero who stated: is enim infinitatem naturae dixit esse e qua omnia gigneretur (Lucullus 118). 5 As is easy to imagine, he will have needed to devote time and energy to seeking information from those who had undertaken long journeys, not without extending the search outside Miletus. See Rossetti (2020). 6 At present, the Astronomical Unit is given by the distance from the earth to the sun, the light year and the Parsec; we appreciate the progression if compared to Anaximander’s very reasonably AU, which had no possible alternative for a very long period of time. It has to be noted that Anaximander did not dare to say, or to guess, how long the terrestrial diameter is or how far away the sun is. 7 See also Galgano (2021, 43). 8 Most scholars still treat the apeiron as the greatest achievement of Anaximander. I firmly disagree. 9 Cicero notably claimed that Thales aquam dixit esse initium rerum (de nat. deor. I 25). Compare Lucullus 118, ex aqua dixit constare omnia. Thus, Cicero made Aristotle’s views much more explicit. 10 In Aristotle’s Criticism of Presocratic Philosophy (1935), Cherniss devoted himself to highlighting some possible elements that could have influenced Aristotle in his approach to the Presocratics, leading to this or that misunderstanding. 11 A famous article by Snell (1944), one by Mansfeld (1983), and a short monograph by Patzer (1986) are usually seen as the basic bibliography on the topic. 12 The direct sources with which to compare the statements by Plato, Isocrates, and Aristotle are Athenaeus (86B4 DK = 36D3 LM) and Clemens of Alexandria (86B6 DK = 36D22 LM). 13 We shall meet Diogenes Laertius many times. He was an erudite scholar working perhaps around 200 AD. He is known from his Lives of the Philosophers, a vast and important compilation in which one can find much information and, sometimes, direct quotation. The greatest limitation of the work is that the author, although curious, well-informed and generally precise, is substantially reporting at second hand, without having any real competence in the material he is actually reporting. However, he had a lot to say. Having screened his information carefully, he favored what is most immediately intelligible and most intriguing. Given the abundance of information about Thales he resolved to select, one can imagine how rich the documentation available to him must have been. His contemporary, Sextus Empiricus, managed to fare much better and with greater competence in the telling excursus of Adv. Math. 7.46–261, but without the tireless curiosity that animated Diogenes. 14 ‘Literary topography’ is an expression most often used, but ‘chrono-topography’ seems to me more appropriate. 15 Even the choice to put Thales among the philosophers and to make him the first among them was meant to construct a chrono-topographical structure and to give him a definite place in it. 16 Clearly enough, it would not make sense to object that Hecataeus was an historian and a geographer, not a philosopher. When we talk of the great four Milesians, we are talking of pioneers, nothing else. 17 More on this point in Section 4.1.3 below. 18 The first product, yet still imperfect, of this new season was the Vita Socratis of the humanist Giannozzo Manetti (1440). 19 I did something comparable with the two volumes on Parmenides I authored in 2017.

Who were these ancient masters?

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20 White (2008, 91 ff.). In White (2002, 3), it is suggested that “Thales, it seems, pioneered the quantitative treatment of empirical data”. 21 Malcolm Schofeld briefy mentions measurements when he writes (1997, 43): “These two thinkers (Thales and Anaximander) were evidently fascinated by measuring”. But there is a major difference: while one of them strived to fnd out actual quantitative data, the other just envisaged largely approximate ones. 22 Another daring conjecture by Hahn is that Thales and the Pythagoreans managed to discover the famous theorem of the hypothenuse since they understood how to build up a rectangle with the same area of a square (2017, 9 ff.). Again, though, are we in a position to say that Thales knew this theorem? 23 See the section devoted to Thales’ biography below.

2

A context for Thales

2.1 Cultural resources in the time of Thales 2.1.1 Society and culture I need to contextualize the fgure of Thales, and the pitfalls of such an operation do not escape me. Since any society is the result of multiple, sometimes contradictory, pressures and counter-pressures, in a certain sense it is structurally unrealistic to try to imagine the pressures felt most strongly by a given individual. Nevertheless, trends always emerge, and it makes sense to pay attention to these, at least. In the case of the Miletus in which Thales was formed, we have the privilege of being able to detect a large number of specifc factors. Perhaps the most striking fact is the prolonged absence of a larger political entity of which Miletus would have felt itself to be part. On the contrary, the political and institutional context was formed by autonomous urban entities which, in the period under consideration, must have experienced considerable vitality and substantial prosperity. In particular, Miletus stood out for its constant activity in founding new colonies,1 all located, with the exception of Naukratis, to the north, beyond, and sometimes well beyond, the Hellespont. The creation of such important contacts ensured the city some useful relationships and additional resources. Another signifcant factor, entirely congruent with this, is the space for individual and/or small-group initiatives, starting with those undertaking expeditions by sea to new shores. Political and economic frameworks (and, to a lesser extent, whatever gives shape and meaning to communal life) tend to set boundaries within which things move. These things include, frst of all, the brilliant poetry that for us is summed up in the name of Homer, which permeated the whole Greek community. In fact, if, over time, Greece became Greece (see, for example, Cicero, De fnibus 5.1 ff., a text that tells us what Greece had come to mean in the eyes of cultured Romans), it was frst of all because bards, elegiac poets and lyric poets – and later other fgures, including the so-called Presocratics – nourished the minds of the Greek-speaking people in a way that was exceptional. It helped to make them a people made up of citizens

DOI: 10.4324/9781003138723-3

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rather than of subjects. Culture, institutionalized beliefs, and the collective imaginative world defned the tracks along which creativity unfolded. As Andrea Ercolani (2006, 71) has well said: originally the epos was the collector and the primary vehicle of transmission for the knowledge acquired by a historically given oral society. In this sense, epic poetry represented a real ‘tribal encyclopedia’, according to the formulation of Havelock. It contains technical knowledge stricto sensu, experiential data, behavioural models, systems of ethical values, relevant historical events, cosmogonic explanations, theodicy, ritual acts and behaviours. 2.1.2 The age of the epic and beyond The success of the epic was of incomparable importance for Greece, since it forged a common store of mental resources for the Hellenes.2 Much depended on two or three characteristics of the Homeric poems: evident care in visualizing scenes and situations, very often represented in such a way that one could imagine that one were present at the scene; their systematic verbalization; and the construction of a network of decidedly homogeneous tales both about gods and humans, despite the fact that it is a network of almost unlimited proportions. It also depended on two characteristics of the public who enjoyed listening to their narration: on the one hand the fact that they had no alternative body of narratives comparable in breadth, organicity, and appeal, and on the other hand the phenomenon of colonization. The latter circumstance is likely to have contributed decisively to enhancing the social function of bardic performance: when they went to perform in the colonies,3 the bards gave people a way of expressing themselves, and created a sense of belonging to a larger community, that of the Hellē nes: they offered stories, customs (a series of unwritten rules), ways to talk, reason, think, face situations and much, much more, and made people feel part of the same imaginative world. Moreover, since the action of both Homeric poems is resolved, for the most part, in verbal interaction, the primary object of the representation was constituted not so much by the facts as by the way in which each character was represented while evaluating them, ‘doing things with words’ and, not infrequently, giving voice to his or her emotions. Consequently, the audience listening to recitations could pay attention to the way, almost always shrewd, in which each character represented him- or herself as a person who understands (or believes that they understand) the situation in which they fnd themselves immersed, and who, while speaking, interacts in a congruent (and understandable) way with other characters involved in the same event or, at the most, in situations that (seem to) escape the control of one or the other.4 Precisely because actions and reactions have, in these poems, a high level of intelligibility, we can assume that their audience grasped the

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situations and saw the plausibility and the reasons behind each individual step. And since every element of the whole was presented with a highly structured complexity, in which situations, characters, actions, speeches, and the effects of what is said and done were all intertwined, engagement with this complexity, with situations, characters, and speeches that multiply almost indefnitely, must have had important educational implications. Such an articulated whole could enrich (indeed, ‘fll’) and confgure the mind of the public, who in this way were systematically encouraged to think about not only the situation but also its protagonists, as well as their conduct and the logic of their speeches. Skilful verbalization, which was certainly the mature fruit of a long exercise by a wide community of singer-storytellers,5 must have constituted another real novelty for the time,6 a Greek achievement and something which would also win attentive reception. In fact, the diffusion of the songs through the most diverse poleis offered shared modes of expression, a distinctive speech culture, a common panhellenic lexicon, and helped to consolidate the linguistic and cultural identity of the Hellenes. A desire to hear the same stories about gods and heroes that had been sung successfully in other poleis was therefore likely to emerge more or less simultaneously in hundreds of different poleis. At the same time, a continuous metamorphosis of the narrative took place, with the occasional reformulation of individual groups of words as well as alternative versions of the same story.7 Thus it was that an entire culture was subtly taking form wherever Greek was spoken.8 A primary side-effect of all this was the stabilization of the collective, socialized imagination, which was confgured as an entire apparatus of beliefs and customs concerning the gods – their names and epithets, the properties of each, cultic practice, funeral honours, how one ought to conduct oneself in a large number of situations, and so on. The diffusion of epic therefore also led to shared ideas about how to regulate different situations, ending up with the delineation of a whole set of unwritten rules, including assembly practices, limits to the rigidity of social hierarchies,9 rites to which to appeal in a host of diffcult or delicate situations, as well as ideas about what is beautiful and ugly. The narratives proposed by the bards, who were able to sing their stories in the most diverse places and on the most diverse occasions, constituted a massive and large-scale indoctrination of Greek-speaking populations. In this way, a subtle, imperceptible, but very effective process of cultural convergence was triggered and an implicit but decisive collective education emerged, with wide-ranging effects. The result was that being Greek frst of all came to mean sharing language, expressive forms,10 customs, and the collective imagination that was elaborated by epic.11 A point probably worthy of some attention in this jumble of different observations12 is the function performed by those narratives in making the public used to the gods’ being characterized in such a way as to make them representative of feelings and emotions, resources and experiences of fragility in everyone’s life (Aphrodite evoking beauty and female attraction,

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Ares aggression, Dionysus release and madness, Ate blindness and insanity, Athena intelligence, etc.).13 With these associations epic gave a great gift to the Greeks, since it enabled them to perceive themselves or others in the grip of this or that feeling, this or that drive and, in addition to giving the emotions commonly recognized names, to talk about them and refect on emotional states.14 In this way people were provided with many resources with which to make sense of behaviour and thus circumscribe the sphere of their fears (as well as hopes) by being able to interpret a certain emotional state as “occurring under the infuence of such-and-such a divinity”, and then being able to talk about it and, in the meantime, get ideas on what to do, if necessary, to act on a given form of malaise. It became normal for the Greeks to embed emotions within the horizon of Olympian mythology, in ways that were harnessed, formatted, and made understandable because they were widely shared. Indeed, they were assimilated so profoundly that, in the ffth and fourth centuries BC, playwrights and orators still felt authorized to systematically exploit this same frame of reference in the (legitimate) presumption that it was a way to get in tune with their public.15 Now consider that this imposing and imperceptible process of cultural convergence is likely to have unfolded in many additional ways. Indeed, the impression that plausible stories were being told, combined with the uniqueness of the ideas and models on offer, can only have favoured their taking root and establishing shared feelings and a cultural horizon capable of being understood. A comparison with the Nibelungs may help to understand the matter even better. There is too much blood among the Nibelungs and a ‘hero’ like Hagen is too uniformly fearful and merciless. The hero par excellence, Siegfried, is betrayed and killed without reasonable compensation, and in the end they all die: all the survivors end up killing each other, so horror at the carnage prevails over any evaluation. On the other hand, the heroes among the Nibelungs only know how to be strong, jealous, possibly clever and able to tackle deception; almost every other quality is lacking (the superior beauty of few of them apart). Among other things, a story conceived in this way could hardly speak to women as much as to men (it is less universal), and the displays of pride that lead to annihilation do not open any door to refection on how people might live together. The events narrated by Homer, at least in the form in which they have come down to us, are infnitely less grim. Homer, so good at visualizing characters, places, and events so that they are easy to imagine, offers intelligible, not confusing, stories; stories of characters and events, simplifed and embellished, in which the art of making speeches appropriate for each situation stands out. Furthermore, many events are given a civic twist, especially in the Odyssey, with appreciation for people who are welcoming (the Phaeacians) and, in Ithaca, for people who are faithful, who remain in their place while cultivating hope (of the return of Odysseus). Overall, a credible and enjoyable world is outlined, albeit a complicated one: it is not horrible even if it is not uniformly beautiful; it is often softened by images such as

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that of rosy-fngered dawn, or by comparisons with scenes of everyday life. It is also interesting to note that in this representation there is no one who is a priori cut off from the civic body, and there is almost no torture.16 I also note that the narratives gathered under the name of Homer have been conceived in such a way as to promote different forms of appreciation for many aspects of the lifestyle that the bards sing, and of self-satisfaction for the deeds of those Achaeans in whom, for people speaking Greek, it was easy to recognize themselves. In this sense, their songs have been bearers, from the very beginning, of a precise ideological colouring. In fact, they were able to confgure themselves as one of those Great Narratives that had the power to delineate the self-image of an entire people.17 The Greek epic poems had, in fact, considerable aptitude for inculcating the perception of belonging to a rather special people. If the battle of Marathon and the exploits of Themistocles have become memorable, it is also because both could ft into this pre-existing narrative scheme that could be used to amplify them. In turn, the emergence of such a self-celebratory climate strongly supported the success of this sort of cultural proto-industry. Thanks to its diffusion, and also to this climate of self-glorifcation, epic probably made a great contribution to forming and strengthening the linguistic and cultural identity of the Hellenes as well as the sense of belonging to an ethnic group that believed itself to be successful. Greek-speaking people were in fact scattered in territories which sometimes lay very far from each other, and they might easily have lost a common matrix; Homer was as indispensable for their common identity as the Olympic games or the oracle of Delphi. 2.1.3 Beyond epic Yet, in the same way that people in the twentieth century began to suspect that the American Dream was not a reality, but the product of a prosperous cultural industry, so in archaic Greece appetite for the song of the Trojan War and the return of the Greek heroes – or the custom of singing hymns to Hermes, Apollo, Aphrodite, Artemis, Poseidon, Hera… – on almost every occasion, soon knew satiety, so much so that it opened the door to something very different. Already in the middle of the seventh century BC, Hesiod, who in the Theogony was content to distil a genealogical tree of the gods from Homeric-type narratives, with his other main poetic composition, Works and Days, did not hesitate to speak in the frst person, like Callinus of Ephesus and, probably, a few others (Tyrtaeus, Solon), as well as appealing to the Muses in their choral, elegiac poems. Callinus expressed himself in the frst person, not in the manner of Hesiod, but to criticize young people tempted to avoid participation in military enterprises decided by the polis; others (e.g. Solon) spoke in the frst person with other aims in view. This matters much less than the fact that, in the wake of Hesiod, more than one private individual began to attribute to himself, as a poet,

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the faculty of entertaining the public by giving voice to his own opinion, his own exhortation. With Hesiod, Callinus, Tyrtaeus, Solon, and others, we remain, of course, in the sphere of public ethics, but now the poet was a citizen attributing to himself the right to speak in public, manifest his opinion and speak of himself as an authority. While this innovation (not exactly a minor innovation, I presume) was taking shape, or shortly after, perhaps with Archilochus, a third poetic age began, an entirely new way of being a poet, with poets who composed their own texts and performed them themselves, accompanying themselves on the lyre and always trying new harmonic modes; poets who indulged in evoking, with substantial realism, aspects of everyday life, both their own and that of others. The poet-songwriter was being born.18 Archilochus and his followers were the new singers of Thales’ youth.19 Their distance from the traditional ways of being a poet was considerable. While the singers of the Trojan War outlined a fantastic world that included gods, heroes, and many adventurous tales, the songs of this new generation of poet-songwriters20 – who felt and were different even from those who intoned elegiac verses and spoke in the frst person – drastically innovated by often (although, of course, not always) breaking with tradition in ways which were unexpected, or even fashy. They insistently challenged deference to heroic themes or descriptions of rules of conduct, good manners, and other things, and they worked to shift their focus to the experience and emotions of the moment, which means to the ephemeral dimension of life: loves, fears, joys, parties, acts of cowardice, and sexual attraction.21 We could say that, from time to time, they disregarded civic duties to focus attention on the personal and the ephemeral, and this was undoubtedly a frst-rate innovation – made possible by the embryonic culture of emotional expression begun in the Homeric poems. Understandably, the new songwriters, who fourished in places often far removed from one another, did not regularly perform at the most solemn, public, and therefore also popular holidays, but at symposia, understood as gatherings of (small groups of) the elite, gatherings that could demand something different and special in musical entertainment. They consciously broke rank to conduct themselves in ways deplored by poets such as Hesiod, Callinus, Tyrtaeus, and Solon, and tuned into the less publicly declared aspirations of the elite. They tried to give voice to the desire to relax, have fun, and to let even ephemeral aspects of one’s own experience emerge, and succeeded, probably because people were rather tired of having to always and only look to the heroes (with an attitude of uniform and predictable admiration), or at least to public ethics. The success of this third generation of poets speaks, indeed, of an audience in which there was a certain impatience to see a different, more elaborate, more intimate and, often, unexpected image of themselves.22 What counts most is, however, the birth of a shared and popular culture where people had access to a peculiarly Greek mix of complex messages

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and, in this way, could become more confdent with all these forms of entertainment. By means of these forms, they learned how to deal with stories, situations, emotions, reasoning, and maxims, all while humming a song, appreciating, interiorising; they also began to feel different because they were becoming more or less aware of the fact that other peoples did not have the slightest idea of all that. Such an unsystematic and randomly accumulated tradition, available to everybody who could appreciate what was on offer on the musical scene, was decisive and, in all likelihood, had a deep impact. 2.1.4 Other strands of innovation: learning to write Of course, there was not just innovation in entertainment – singing, dance, music, poetry. The Olympic games, the Pythian games, the Panathenaic games, and other similar gatherings were also ways of presenting a distinct self-image. Funeral statuary too began to develop among the Greeks, with the portrayals of the dead assimilated to the heroes of the myth, so that they were as beautiful as those heroes and, often, of superhuman dimensions. The aspiration to surround themselves with images that, in their own way, spoke23 became for the frst time an aspiration and a possibility for the most infuential families, including those who had no access to power: their tombs, exposed as they were to public admiration, could be a way to gain credit as families ready to play the game of power in the city. This too deserves to be considered a signifcant turning point, given that in Persia and Egypt the fgurative arts were no less developed,24 but remained exclusive to the sovereign and his court. Around the same time, there were important developments in public works, and in sculpture and ceramics, which probably made no less important a contribution to the development and shaping of an ‘Ionian dream’. Meanwhile, there was unprecedented social organization based on the multiplicity of autonomous poleis, on their decision-making capacity, on the laws that each polis knew how to give itself and, as Kurt Raablauf recently wrote, on the absence of “hierarchies sanctioned by a strong connection with the divine”.25 It is easy to understand that the same logic widely inspired this kind of social organization among the Hellenes. The range of innovative phenomena of the period includes the shared adoption of alphabetic writing, and this is likely to have been another major event for the whole Hellenic world. Consider the Greek alphabet as it appears on the border of an Etruscan tablet found in Marsiliana which, if I am well informed, is slightly prior to the time of Thales. It is written, as is apparent, from left to right (see Figure 2.1):

Figure 2.1 Marsiliana tablet abecedarium.

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26

Facts related to the spread of the alphabet are many and important. I shall just mention the following: • • • • •

the very small number of new signs (just over 20!) the simple geometrical shape of many of them (which tends to consistency and intelligibility) letter-naming (“this is an alpha and this is a bēta”, etc.) use of letters also to identify and represent numbers widespread interest in learning to recognize and use these letters precisely because they “are so few”.27

Furthermore, the custom arose of marking coins with the name of the polis that issued it. (This is a custom which apparently arose in Ionia during the frst half of the sixth century, so precisely at the time of Thales.)28 This must have been a considerable boost to large-scale literacy, since one only had to use the currency to see the name of one’s own polis written (or that of others), and so strengthen familiarity with at least some of those signs.29 While all these innovations were being introduced, it is likely that a new generation of experts in reading, writing, and engraving texts on stone also appeared, and that they no longer constituted a powerful caste because, compared to the texts in cuneiform or in hieroglyphics, those in Greek were, since the beginning, incomparably easier to decipher. As a consequence, the key move that changed in depth the Greek-speaking people is likely to have been, rather, the idea of a written document. A number of meaningful changes probably occurred, and the very frst ‘letters’ between affuent members of the society, the very frst written contracts and the transcription of what was normally memorized (e.g. hymns, choral compositions, small poems) began to be prepared (and circulate). The very frst public inscriptions were decided and produced. Nothing of the sort seems to have survived, but the mere possibility (for singers to send elsewhere one or two of their poems, or for a Thales to get a written copy of the poem Alcaeus dedicated to him [Section 3.5, below], or for somebody else to prepare a small sylloge of potential interest for both its author and some other people) gave rise to several options available for learned people irrespective of their access to public and/or military power. Besides, that a decree or another major event could give rise to an engraved stone beginning with the words ἇδ’ ἔϝαδε πόλι (“This was decided by the polis”:30 law of Dreros, before 600 BC), or something comparable, and not with the name of a king was another highly representative event.31 Just consider how simple, whatever the origin, aim, and content, this procedure was in comparison with cuneiform or hieroglyphics, how accessible it became at least for learned people, and how easily texts could be controlled by their originator as well as other people. This too is likely to have made the Greeks visibly different from other peoples and more or less aware of that.

24 Approaching Thales However, it was the result of a further process to be able to set out learned records, as did those who gave rise to the very frst ‘books’: for a book presupposes a particular means of communication, of expectations about what would be appropriately included or excluded, of how to begin and how to end, of how to use and preserve it, of how it should be copied, and so on. All that could only result from a long series of trial and error, and decades may have been needed to distill just one or two models. In the meantime, there would have been a number of further changes in orthohraphy, choice of words, formal sentence-schemes, etc. Clearly, epic singers, songwriters, architects (from Theodorus and Rhoecus onwards), Anaximander, and other fgures must have been attracted by this unprecedented medium which made it possible to codify, preserve, copy, make known, and disseminate information about their work with an ease, and with that reduced dependence on a grapheus, which was still unimaginable elsewhere. Even if we know nothing or very little about these professionals, it will be admitted that something like this must have happened,32 while Egyptians, Mesopotamians, and other peoples, with whom the Hellenes were in frequent contact, remained, as I said, foreign to the privilege of living in a world characterized by such a wealth of previously unknown innovations and opportunities. Likewise, education (learning to read, write and count)33 took off in some cities of Greece and soon became a widespread and valued practice because all it required was to become familiar with just over 20 signs and a certain number of names (e.g. bēta, duo, deuteros, and so on). 2.1.5 In conclusion What should we think about the populations that found themselves faced with this formidable fow of innovations (which went even wider, as we shall shortly see)? That it had an impact is as certain as the fact that epic had shaped the mental horizons and the self-image of signifcant sections of the population. But that the message of the songwriters also had an impact is equally probable. It is a matter of course that that the emergence of writing, coins, and high-quality funerary sculpture fnanced by individuals would have been noticed – and we are talking about innovations that could not fail to please people. It can be inferred, I think, that all these innovations will have aroused, in vast swathes of Greek-speaking populations, an inclination to look at the new with favour and, above all, with a pride that will have encouraged many to feel at ease with it. Indeed, there are good reasons to assume that the emergence of important differences between the Greeks and other peoples (or at least the sentiment that “we are ‘ahead’ of them”) was also perceived by quite a few foreigners. But further strands of innovation are also to be considered.

2.2 The age of the sophoi, Aesop, and riddles Around the time of Thales’ youth, a new movement arose of people who entertained the public not by singing but by teaching, unmediated by poetry

A context for Thales

25

or song; and the new ideas they put into circulation often came with an emphasis on their truth. This was an important innovation: these people went beyond merely narrative accounts, and looked to an audience who would be attracted not by the internal dynamics of a good story, but by the objective plausibility they felt in what they were told. Bias, for instance, is supposed to have said, among other things: akoue polla, lalei kaira: “Hear many things, but speak to the point” (Stobaeus, Anth. 3, 172.93 Wachsmuth-Hense). It is notable too that we are told the names of these people: it seems, indeed, that they were the frst people to enjoy popular fame without being either poets or political leaders. (It is a pity that there is, as yet, no collection of sources, or a comprehensive study, for this important strand of pre-Presocratic wisdom!) 2.2.1 The birth of cultured mythology The frst group of these new thinkers arose alongside the last of the epic poets and authors of the so-called Homeric cycle (e.g. Eumelus of Corinth and Arctinus of Miletus). They include names such as Orpheus, Acusilaos, Pherecydes, and Epimenides. Instead of retelling the myths that formed their shared heritage, this new generation discussed them, offering their own guidance through the vast and sometimes unwieldy agglomeration of tales. In fact, Olympian mythology and iconography had by then become fxed and institutionalized: it demanded interpretation more than it needed retelling. Acusilaos, for example, hypothesized that everything began with Chaos. Chaos, he says, generated Erebus (male) and Night (female), who would later generate Aither, Erōs, and Mētis. Pherecydes, on the other hand, asserted that Zeus and Cronos have always existed, and likewise Chthoniē, and that Zeus hounded certain gods who had committed atrocities into Tartarus; he also said that, on the occasion of a marriage between divinities, Zeus made (poiei) a large cloak on which were painted the earth, the ocean, and “the houses of the ocean”. Epimenides, for his part, claimed that the Harpies were daughters of Okeanos and G ē and were killed in the surroundings of the city of Rhegium.34 Solon was an unequalled legislator, and spoke, among other things, of dusnomia, eunomia, and isonomia, abstract entities that he made objects of discussion; but he also talked with conviction about Zeus. Signifcantly, none of these people posed as the founder of new religious orthodoxies. They rather offered themselves as interpreters of the mountain of tales concerning the Olympian divinities and heroes, identifying some stories as more credible than others. They reinterpreted and renewed the mythology of the poets on the basis of their claims to personal authority. Especially elaborate traces of this process of appropriation and reinterpretation can be seen in the writings of Solon and Theognis, as well as in the Hipponion tablet. The process of making sense of the existing theogonies, and perhaps of ftting them into a smaller number of cosmo-theogonies, must have helped people to use them to feed their understanding of the world. In contrast to the unrestrained freedom of thought that new poets

26

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were showing in the meantime, these intellectuals worked with the existing Olympian architecture, but brought their own authority to bear on its interpretation – a delicate operation which claimed to go beyond mere entertainment, and also beyond the authority of Homer and many beliefs now commonly taken for granted. A signifcant transition took place with them: the transition from a shared cultural horizon, to the choice of a worldview associated with some authoritative individual. This is why, of course, we start to know their names. 2.2.2 An investment in popular wisdom Also part of the cultural scene in the time of Thales were characters like the Scythian Anacharsis, who specialized in maxims: a way of displaying wisdom that disregarded mental structures altogether (above all, references to mythological structures) in favour of extemporaneous and fragmented topics. Two representative collections of these teachings have come down to us. One, attributed to Demetrius of Phalerum, contains a long list of exhortations; the other is a series of questions and answers.35 Maxims like these could not have been produced either before or after the time of Thales: not before, because during the seventh century there was no alternative to mythology; and not after, because the cultural context produced by a new generation of sophoi contemporaneous with Thales quickly made those maxims obsolete. It is in the appearance of this second group of intellectuals, much more than in the timid attempts of the former group to interpret mythology, that we can recognize traces of innovation characteristic of Thales’ times. The elegiac poets had begun to offer exhortations in the frst person; the mythological exegetes could argue over the legacy of epic poetry; but the frst to operate with a programmatic detachment from the mythographic heritage altogether were, as far as we can tell, the authors of these sapiential maxims. The wholesale decision to set aside the mythology clearly encouraged the leading thinkers of the time to go even further: and Thales is among those who built on this opportunity – to the extent that he promoted a sense of ‘truth’ quite different from the ‘pre-rational’ idea of truth, that is, as Detienne said, the “system of thought of the soothsayer, the poet and the king of justice, the three sectors where a certain type of word is defned as Aletheia”.36 Rational thought (so called) naturally tends to distance itself at least partly from tradition (and, in particular, from appeals to purely narrative explanations), so there are good reasons to recognize in the work of this second group of intellectuals the really signifcant turning point, the opening to innovative work of Thales. 2.2.3 Aesop We cannot precisely identify the personal contribution of Aesop to the collection of fables that was subsequently associated with his name, but we

A context for Thales

27

have to admit that he at least contributed to the design (if not the fnal form) of the model, and devised more than one fable. Moreover, the chronology makes him a contemporary of Thales (he would have been born around 620 BC); he must have lived frst in Samos, then at the court of Croesus, then elsewhere. The salient fact is his creation of witty stories which invite us to refection; with few exceptions, gods and heroes are absent from them. These details are enough to bring Aesop very close to the sophoi just mentioned, because he too was contributing to the process of overcoming the horizon constituted by mythology. His wit and levity constitute a sort of ‘new wine’, having been substantially absent from all the other forms of entertainment widespread in Hellenic culture, and the morals of his fables are even more pregnant than those of the maxim-writers. In fact, the fables were designed to impress the moral much more clearly in the mind: each fable starts by encouraging more or less tentative attempts to decode the story, and ends with a universal truth: a point of reference immediately available when someone’s conduct took on dynamics similar to those of a given tale, e.g. the story of the wolf and the lamb. It is therefore very likely that the emergence of higher standards of reason – and communication – owes a lot also to characters like Aesop, although all they are often overlooked.37 2.2.4 Riddles This brief excursus cannot end without saying something about riddles as well. The origin of the famous riddles we know of cannot be located within well-defned spatial and temporal boundaries, but they are clearly also the fruit of the stage in which people were freeing themselves from mythology and learning to appreciate the alternatives to shared belief. We are therefore encouraged to think that their fowering may have taken place around the time of Thales or, perhaps, in a slightly earlier period, for the reasons given in Section 2.2.2 above. These riddles speak of an era in which pleasure was taken in creating ever new alternatives to shared knowledge. It is in fact rather diffcult to devise a riddle that is suffciently refractory to attempts at decoding. It is a delicate process to disguise the underlying story the right way, for a riddle either succeeds perfectly or not at all. But if it succeeds, it can unlock intellectual energy, and provoke thought more than anything else. The riddles of the Sphinx, as well as that of lice mentioned by Heraclitus (22B56 DK = 9D22 LM), are well known, but there is a third riddle that deserves to be held in even higher regard, although it has not previously been recognised as part of this genre: Odysseus’ naming of himself as Outis, “Nobody”, in the Odyssey (9.366 ff.), in order to play a trick on the Cyclops Polyphemus. Polyphemus is thus made to complain that he has been attacked by Nobody, Outis – intending by this something quite different from what the other Cyclopes understood. The story, beautifully set in a narrative which, in turn, is steeped in Olympian mythology, has its own

28  Approaching Thales narrative autonomy – and even greater power than the riddle of the lice in which Homer himself was supposed to have been caught, or the riddle of the Theban Sphinx. They lack the threat of contradiction and ridicule which comes with Polyphemus’ confusion. It is a pity that we do not know when this story entered the Odyssey, because with it contradiction entered European culture, and it opened up a totally new avenue, one that certain Presocratics (e.g. Xenophanes) began to exploit. 2.2.5  Toward ‘stronger’ truth The coexistence of mythological exegesis, maxims, question-and-answer, fables, and riddles suggests a time when the traditional, ‘weak’, idea of truth found itself more and more often coexisting with forms of thought governed by a much ‘stronger’ version. Aesopian fables and riddles especially furnish an opportunity to pass from a diēgēsis that pretends to be true to a diēgēsis that is known to be true; from a narrative that seeks its external references to a narrative that seeks its own references; from a hetero-regulated discourse to a self-regulated discourse.38 This opportunity became available to anyone who could see through sustained fiction (in the case of the Aesopian fables) and enjoy the risk of being fooled by riddles. The opening of such windows (and we should assume that there were others such windows of which we have no trace) constitutes, in my opinion, an event that deserves the most careful attention,39 first and foremost as a further development of that intellectual movement that had been advanced by poets born in the wake of Archilochus; secondly, because these new forms of intellectual exercise were embedded in stories and stories capable of circulating widely; thirdly, because with them a powerful and distinct alternative arose to the ‘weak’ explanations typical of mythology. So we have reached a turning point, a moment of explosive potential. I shall argue that it was Thales who took the next step.

2.3  A ‘minimalist’ approach to Thales40 This review of the intellectual culture that stood behind Thales helps us to see how out of place is the claim of those scholars who still insists on anchoring Thales to a time in which only ‘pre-rational’, or mythological, forms of truth were available, and read him in the framework of those schemes.41 The evidence just adduced clearly shows that a new, reflective, rationality had already gained currency at his time, independently of him, and even among a public that was not particularly well educated.

A context for Thales  29 Thales’ teaching went beyond even this. Note, to begin with, that we know infinitely more about Thales, and in more detail; we also have indirect evidence about him from those, starting with Anaximander, who dissented from some of his claims (Section 6.3.1) and conjectures (Chapter 10). But we shall see that our sources tell us of a character concerned for precision and certainty in knowledge, the desire to say exactly how much or exactly when – and these are things that nobody who lived before him, none of his contemporaries, and none, even, of the other Presocratics who came after him appear to have pursued. This point is important if we are not to believe what many people have said (e.g. Dicks 1959, 295), that diverse achievements have been attributed to Thales with no basis in fact, just as in the case of Pythagoras. In reality, the two cases are profoundly different. Consider, for example, Thales’ interest in measuring the height of the pyramids, reported in our sources. What is interesting is that these sources are in some ways extremely inaccurate: none of them has any idea of how Thales must have reasoned. Yet all of them, unanimously, cite the use of stick producing a shadow as long as its height. This means that they knew that Thales’ method had to do with identifying the shadow produced by a pyramid when the sun is at about 45°, something that the stick can help to ascertain. This is not a line of reasoning invented with no basis in truth: yet it is ascribed exclusively to Thales. Or consider the sources which tell us that Thales dates the solstices (Section 5.1). There are multiple and convergent sources on this and, again, the claims they make are ascribed only to Thales – who, as other sources tell us, was also interested in the equinoxes and in the number of days between the equinox and the dawn setting of the Pleiades. We are even told the number he put on this: 25 days. Now, one cannot say that 25 days have passed without knowing which day to begin counting, and it is unimaginable that someone would be interested in dating of equinoxes without someone’s having already tried to date the solstices. Furthermore, we are told that Anaximander and then two professional astronomers, Euctemon and Eudoxus, set out to improve upon Thales’ results – something that is unthinkable if Thales had not followed a credible method to arrive at an answer that was at least approximately correct. A third example: the solar eclipse. Hero of Alexandria reports (in As22 W) that, according to Eudemus, it was Anaximenes who explained tina ekleipei tropon, how the sun is eclipsed. But from Cicero onwards, a whole group of diverse sources says that Thales identified the dynamics by which the sun darkens. Are these sources (which come from very different times and contexts) all wrong? (Do they intend to mislead us?) Or do they rather give us reason to admire Thales? The case of Pythagoras is very different, because the sort of general claims that he was the first person to conceive the earth as a sphere and to speak of its five climatic bands, or to identify the solar origin of the light of the moon, are in evident conflict with what much

30  Approaching Thales more thoughtful sources, and in one case two fragments, associate with the work and writing of Parmenides. In conclusion, despite the incongruous comparison with Pythagoras that has been suggested by Dicks, it can be said that Thales was distinguished for having set up genuine investigations aimed at acquiring data, and there is no doubt that doing this meant taking a mighty leap forward.

2.4  With Thales a new start It is important that we should not ignore ephemeral cultural activity, because ‘minor’ figures serve to give a sense of the context from which the significance of the more important work derives. But there is a conspicuous discontinuity between Thales and his contemporaries, and the leap from the maxims of popular wisdom, from the first Aesopian fables and from riddles (if not from poetry and mythology) to the innovations of Thales is really impressive. We will see that he planned lines of research with ambitious intellectual aims, imposed on himself surprisingly rigorous methodological criteria – so rigorous that they were not even adopted by his first students – and set out a detailed body of knowledge based on transparent forms of reasoning and assessment. The fact that Thales shares the title of ‘Sage’ with six (or more) sophoi engaged in the production of wisdom maxims does not mean that they had anything in common with him. The intellectual horizons of Thales compared to those of his contemporaries, and in particular compared to the other sophoi honoured by Athens along with him, were profoundly different. We know that a new generation of sophoi, radically different from those discussed in Section 2.2, arose in the wake of Thales, first with Anaximander, then with Cleostratus of Tenedos (the latter together with Matricetas of Methymna and Phaenus of Athens),42 then with Anaximenes, Pythagoras of Samos,43 Hecataeus (the fourth great Milesian), Theagenes of Rhegium (sources put him in the reign of Cambyses, i.e. 529–522),44 and Xenophanes of Colophon. And it is clear that what unites this group of diverse personalities is the fact that each was, in his own way, a man of science, a champion of his own knowledge, who invested in an attempt to expand the panorama of available understanding. Some of them wrote new works, Peri physeōs, which were more comprehensive than previous ones. It is therefore only to them that one should allude when talking about the “inquisitive men of the sixth century”.45 So where does this shared passion for new knowledge come from? Who infected them with this bug? There is little doubt: Thales, the model for Anaximander, who trained with him, and for the other two great Milesians. But … there is a sentence by Theophrastus, reported by Simplicius, that suggests a quite different picture.46 Thales is reported to have been the first to reveal the study of nature to the Greeks; many others had preceded him, as in the view of

A context for Thales  31 Theophrastus too, but he was far superior to them so that he eclipsed all his predecessors.47 This sentence is an outlier, and, in the absence of names, we cannot guess who the predecessors of Thales alluded to here might be. So we are still left without the least evidence about the existence of predecessors to Thales. We can only conclude that a turning point took place with Thales, that he was the first and, initially, the only person among the Hellenes to set himself up as a researcher interested in learning and, in particular, in ascertaining; moreover, he was also the first person to undertake, as a private citizen, research for purely intellectual purposes, among other things while he was prepared to incur expenses for this purpose. In fact, until the contrary is proven, there is no latitude to presume that Thales encountered any other proto-researcher (or that Hellenic society could support the aspirations of anyone who wanted to advance knowledge this way). Thales’ methodology and objectives (privileging, within the limits of possible, the search for quantitative data) were not even taken up among the later Presocratics. But for him, they became a reason for living.

Notes 1 Or rather, apoikiai. The following clarification is noteworthy: “The sub-colonies are independent poleis, endowed with their own civic individuality, evidenced by the way in which the settlers of these communities are defined in the sources and define themselves as citizens, that is, as Hipponiats, Medmeans, Posidonians and so on” (Braccesi-Raviola 2008, 65). On the difference between apoikiai and emporia see now Grecchi 2022, 121–125. 2 Awareness of affinity or even ‘sameness’ occurs not when people, such as the Homeric heroes, are close to each other (in fact, that is when they pay particular attention to their differences) but when they are far apart (and that is when they condense their vision to some salient and common characteristics of identity). So Malkin (2011, 54). 3 The point is conjectural because – as was pointed out to me – all the reports that we have (scarce and unreliable as they are) tend in the opposite direction: it is the poets of the colonies who go to perform in the motherland. The Homeric tradition travels from Ionia to Greece; Stesichorus, from Sicily to Greece; Alcman, from Lydia. Only Hesiod, one of the oldest, is a continental poet (and he himself tells us that his father travelled from Cyme of Eolia to Boeotia …). But if there was widespread acculturation and if, in particular, the Olympic mythology, a common heritage of the Hellenes, was quickly institutionalized (to the extent that it gave rise to a large number of places of worship dedicated to this or that divinity, while its iconography helped to ensure the recognizability of individual mythological characters) – if all this happened, then there must have been some form of wandering by the singers, and it must have started very early. Besides, there would not have been the conditions for the formation of a tradition of ‘intellectuals’ (from Hesiod to Thales’ contemporaries) who based their reputation on the ability to rethink in an original way the patrimony of beliefs that in the meantime had been conveyed through song.

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4 Battezzato (2019) offers a beautiful analysis of the mental world of the heroes and of what they had the opportunity to say by interpreting the situation in which, from time to time, they found themselves immersed. 5 The ‘epic’ label summarizes an indefnable plurality of epic traditions: local and panhellenic, heroic and didactic, agonistic and domestic, textual and oral, etc. It is not important who the protagonists of the epic were, who did what, what was done or what exactly is known about X, but what traces came to people, how the Greeks were affected by them, how their mental world was imperceptibly shaped under the infuence of the entertainment offered by the bards (and then by other generations of entertainers). 6 The comparison with what we can read in the story of Gilgamesh is telling, despite what Michael Clarke (2019) has recently claimed. See also Seaford (2004), 71. 7 “For example, there were three versions of Stesichorus relating to the kidnapping of Helen, one corresponding to that of the Iliad, another following the version narrated by Hesiod, and fnally a third, called Palinodia, according to which the Spartan heroine would never have followed Paris to Ilium … Unlike us, due to the typical orientation of archaic culture and the mental and psychological attitude of the listeners, singing was not evaluated in terms of textual fdelity or belonging to the author” (Tedeschi 2020, 23–24). 8 Havelock (1963) is seminal on these issues. 9 Only a few details will be mentioned here: the poems offer us a visibly inadequate Agamemnon as supreme leader (Porter 2019) and an unfamiliar Achilles, exponent of youth protest, as well as other ‘unwelcome’ characters such as Thersites, and the suitors and the disloyal female slaves (at Ithaca). The fact that there is room for them too is signifcant precisely because it suggests pluralism in embryo, something which, not surprisingly, fnds confrmation in the freedom of debate (Seaford 2004, 181). 10 Huxley (1966, 46) wrote: “One of the most striking features of early epic fragments, indeed, is their uniformity of language and resistance to local dialects.” 138). 11 See the interesting remarks of Lebedev (2020, 138). 12 As it easy to imagine, behind these remarks there are many authors I could have mentioned. Let me just remind that, thanks to the contributions of Snell (1946) and others, we now realize that the Greeks of the time of Thales understood and expressed themselves in forms we still use today and established many new forms of understanding people and things, minds and events. 13 Obviously, by this I refer to the consolidated image of these divinities. But the decanting was a long process, and it is interesting to note what is reported about Theagenes, who lived a few decades after Thales and Anaximander: he associated the name of individual deities with slightly different diathēseis (dispositions of mind), for example Athena’s name with self-control (phronēsis), Ares’ name with uncontrolled conduct (aphrosunē), Aphrodite’s name with desire (epithumia), Hermes’s name with logos (reasoning, reasoned decisions). There is a trace of this in a scholion to Homer, Il. 20.67 (=8.1 DK = T4 Biondi). 14 Seaford (2004, 77) reminds us that, unlike the Mesopotamian and Egyptian ones, “the Greek image of the divinity can be prayed to, but it is not thought of as living” and consequently it does not eat or drink. The opposite would have compromised their ability to represent emotions and a series of well-characterized human behaviors. 15 A brief profle of this problem is given in my 1991 paper. 16 Torture make its painful appearance on the occasion of the celebrations in honour of Patroclus (Il. 24.15–23, 50–54, 416-417.), and then in 15 verses of Od. 22 (462–477); for the rest, the poems know of killings (including those evoked in Il. 23 175 f.) but not torture.

A context for Thales  33 17 As is widely known, in a 1979 book, La condition postmoderne, Jean-François Lyotard launched this notion with particular reference to the American Dream, an imposing stream of novels, films and other forms of entertainment aimed at defining the American model and giving a ‘beautiful’, optimistic (and therefore false) image of that society. These models outlined a precise idea of what it was supposed to mean to be American and which nourished a large cultural industry, one aimed at promoting itself in the shadow of the supposedly enviable “American model”. Not that in continental Europe it was necessary to wait until 1979 to become aware of it but, of course, Lyotard’s book codified and objectified the artificial (as well as unreliable) side of such an image of America. 18 Students of Greek Epic avoid mentioning this term, but the actual songwriter is the one who not only writes music and words, but also performs them. People such as Archilochus, Alcaeus and Sappho and many others did this. It seems significant that in 2007 a ‘Network for the Study of Archaic and Classical Greek Song’ was established, which is still very active today. 19 There are strong reasons to believe that Thales was active roughly between 590 and 550 BC and that, therefore, he was born 2–3 decades before 600 BC, and that Archilocus was two generations younger. Alcaeus and Sappho should have been slightly younger than Thales. 20 I am thinking in particular of two creative poets younger than Archilochus (Alcman and Stesichorus); then of Alcaeus and Sappho. 21 There is a widespread tendency not to emphasize these aspects, as if, in the light of epic and elegiac poetry, it were not shocking in its own way to allow oneself to sing, let us say, that “I gently took hold of her breasts in my hands,… and caressing (all) her lovely body I released my (white) force, just touching her blonde (hair)” (these are the final lines of the sophisticated poem by Archilochus known as ‘the Cologne Epode’, transl. Swift 2019, 85). As a matter of fact, the detachment from what may have been perceived as suitable to be said in public (based on current patterns of conduct and discourse) must have been, I imagine, striking. These circumstances do not prevent us from recognizing that “Archilochus, like most other early poets, includes typical gnōmai, which offer reassuring statements of accepted morality” (Swift 2019, 23); however, these are concessions to common feeling, while phrases such as those of the Cologne papyrus implied a clear break with the unwritten rules of epic and elegiac poetry, and of the same life in society. 22 It is easy to find similarities between the innovations accredited to these ‘storytellers’ and the innovations introduced by 1968, when radio, television, cinema and newspapers contributed to a certain liberation of customs and clothing (especially female). Even that need, which immediately became impatience, to give oneself new models and new costumes and, in the meantime, to speak a new language, took the form of a formidable break in tradition. 23 On this point see the perspicuous Section II 2 of Costantini (1992). 24 A couple of significant differences were pointed out by Robin Osborne (1997, 11 f.). 25 Raablauf (2018, 42). 26 On this point, see Havelock, esp. 1977. 27 Other evidence concerns the use of letters of the alphabet to identify different ceramic pieces to be joined together in order to set up pipes (we have an Athenian evidence). In this case, and with reference to the appearance of coins accompanied by names (or at least some letters), we are certainly talking about the sixth century but, of course, it is difficult to establish to which part of the century a given coin or the Athenian artefact dates. 28 On this topic, Seaford (2004), esp. 125–129, has a lot to say.

34  Approaching Thales 29 The anecdote, linked to Tyrtaeus, about the Spartans who, having decided that they had to win or die, engraved their names on the shields in order to be recognized in case of death, is not without significance. Even if it were unfounded, the anecdote would still speak to us of the importance attached, even in very ancient times, to noting one’s name in writing. It seems significant to me that in ancient times the story seemed likely because nothing comparable happened, or could have happened, where writing continued in cuneiform or hieroglyphics (nor where troops were not drawn from the citizenry, of course). 30 Here ἆδε should mean τάδε. 31 Many years later a herald could be presented on the stage asking “Who is the tyrant here?”, to be answered by the king: “You have got off on the wrong foot!” (Euripides, Suppliants, 399 and 403). The production and circulation of public documents seems to have predated texts due to private citizens. 32 The book of Anaximander and the proto-book of Thales (on which see Sections 17.3–17.4) already did this, and therefore presuppose a phase of increasing familiarization with writing as well as with the very idea of book. During this phase, I cannot imagine that the ‘songwriters’ were not interested in the transcription of their poetic-musical texts. The lack of specific evidence does not prove otherwise. 33 To acquire basic familiarity with numbers may have meant, for a while, to learn to recognize and name at least some correctly, and understand what they mean, not necessarily to learn how to operate with them. See Section 4.1.3 below. 34 However, Epimenides treats of the legend according to which he slept for 150 years ‘in the company of the gods’, as meaning that the truth is not about what is discovered at the end of a search, but about what is received. Indeed, at the time of Epimenides, very few (if any) had any idea of truths discovered at the end (and as the result) of investigations marked by something one tries to establish. 35 Snell (1938) was the first attempt to edit all relevant texts. A new edition is still awaited. Also noteworthy is Kindstrand 1981. The relevant bibliography, updated in the early 2000s, is due to Ilaria Ramelli and appears in Snell–Ramelli (2005, 221–259). 36 Detienne (1967), Preface. 37 In the letter with which she announced a conference on Aesop, to be held in Graz in 2021, Ursula Gärtner rightly wrote: “The ancient fable had long been overshadowed by other genres and was mostly treated with regard to motifs and tradition”. 38 Thus, in a penetrating way, the late Paolo Impara (1996, 11). 39 A strong exegetical tradition, well represented in the first chapter of KRS and chapters 2–4 of LM, insists on appreciating the contribution of Hesiod, Pherecydes and a few other intellectuals who would have the merit of having prepared the way for the advent of the Presocratics. But isn’t the turning point perhaps due to the emergence of reasons that were not of a narrative nature? Decisive is this step, in my opinion, hardly anything else. 40 The expression comes from Graham (2013, 57), who thus characterizes the exegetical proposal put forward by D. R. Dicks (1959) and referred to below in the text. 41 Pierre Vesperini, in a book entitled La philosophie antique. Essai d’histoire, from 2019, spoke of Thales as still totally immersed in the purely ‘narrative’ causes – a stance which in my opinion is little less than outrageous. 42 In a sense, my whole book on Thales is devoted to support this claim. 43 Cleostratus lived after Thales (not before, as Diels–Kranz suggests by assigning to Cleostratus Chapter 6 while Thales is Chapter 11), like Matricetas and Phaenus. Thibodeau (2019, 269–273) limits himself to indicating a single conjectural date, 510 BC (clearly after Thales).

A context for Thales  35 44 His personal story is too poorly known and too shrouded in legend, however, to be representative. I will limit myself to recalling the well-known fragment of Heraclitus (22 B129 DK) in which he speaks of the writing Pythagoras produced while he was still in Samos, which, again, characterizes him as the bearer of a knowledge. In all likelihood, it was knowledge nourished by Milesian culture. On the subject see Rossetti (2013). 45 I note that Theagenes developed wide-ranging skills on Homer and the Greek language, developing new forms of interpreting the poetic tradition. On Theagenes v. spec. Biondi (2015). 46 West (1971, 3). 47 Simpl. Phys. 923.29 (=11B1 DK = Th409 W = 5R10 LM): Θαλῆς δὲ πρῶτος παραδέδοται τὴν περὶ φύσεως ἱστορίαν τοῖς Ἕλλησιν ἐκφῆναι, πολλῶν μὲν καὶ ἄλλων προγεγονότων, ὡς καὶ τῷ Θεοφράστῳ δοκεῖ, αὐτὸς δὲ πολὺ διενεγκὼν ἐκείνων, ὡς ἀποκρύψαι πάντας τοὺς πρὸ αὐτοῦ.

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3.1 Some dates Thales lived in a time when, even in the case of works that became famous, it was not customary to pay attention to the life of their authors and, in theory, we should expect to know nothing or almost nothing about Thales’ life. Fortunately for us – and to our surprise – some signifcant evidence survives. As for dates,1 we know that, according to Theophrastus (certainly one of the leading experts on the Milesians), Anaximander was Thales’ diadochos kai mathētēs, “successor (as head of the school) and pupil”. One sees immediately that Theophrastus has retrojected the customs of his own age: Theophrastus himself was a pupil and then the successor of Aristotle at the head of the Peripatos, and it is attractive to suppose that he thought of Anaximander and Thales in similar terms.2 We also know, from the chronology specialist Apollodorus, that in the second year of the 58th Olympiad Anaximander was 64 years old and died shortly after.3 Since the second year of the 58th Olympiad corresponds to 547/546 BC, Anaximander would have been born in 612/613 or shortly after (610/609, as Hippolytus claims).4 Taking into account the data thus acquired, the third datum, offered by Diogenes Laertius, is also useful. He reports that, according to Apollodorus himself (en tois Chronikois, in his work Chronology), Thales was born in the frst year of the 31st Olympiad and died at the age of 78 during the 58th Olympiad, when Anaximander also died.5 (The text transmitted does not in fact say the 31st, but the 35th: this must be the result of an oversight, as the other two fgures provided clearly point towards the 35th. Moreover, what is reported about Thales with reference to the 58th Olympiad – a journey to Tenedus,6 his presence on the banks of the Halys river, advice offered to the Milesians – would have been the deeds of a man ca. 90 years old if he were born in the 31st Olympiad; 75 years old seems more plausible.) However, there is a problem, raised by Philip Thibodeau. This scholar argues that Anaximander was born half a century later than what is reported by commonly accredited sources, i.e. in or around 560 (when Thales would have been 55 or more), and was the same age as Pythagoras (Thibodeau

DOI: 10.4324/9781003138723-4

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2019, 227–261). Against this conjecture, which I will not discuss in detail because it would take me too far, I think I can put forward one weighty argument, namely that, on this hypothesis, Anaximander, a researcher no less creative than Thales, would have learned to become a researcher not from Thales (now too old, if not already deceased) but through whatever writings about him he was able to get his hands on. But it is improbable that this would have been enough to form him into an investigator into the secrets of the cosmos: on the hypothesis put forward by Thibodeau, Anaximander would have to have formed, developed, and elaborated his cultural identity as a researcher solely on the basis of oral and written memories. This, frankly, is hard to believe. The transmission of excellence can hardly follow such a path, and Thibodeau would need to explain how this could have happened at this age. So, setting aside Thibodeau’s hypothesis, I maintain that Thales was 14 years older than Anaximander or thereabouts (or perhaps, dating from 35th Olympiad, about 30; but certainly not 54 or 70): a difference in age not very great but still suffcient to mark an important distance between teacher and pupil. The two were, as it seems, active in the same city for many decades until their deaths. It can be deduced that each knew everything about the other, and since Anaximander conducted research and developed teachings many of which were obviously different from those of Thales, we must assume that he was able to enjoy great intellectual autonomy, as if the two had been colleagues – not, as Theophrastus’ conjecture suggests, bound by a hierarchical relationship.

3.2 Ancestry Another area on which we are surprisingly well informed concerns the family of Thales. Diogenes Laertius provides numerous details: Thales, as Herodotus, Duris, and Democritus report, had as father Examuas and as mother Cleobuline, of the family of the Thelides who were Phoenicians, the most noble of the descendants of Cadmus and Agenor… He became a citizen of Miletus when he went there with Neileus, who had been exiled from Phoenicia. but according to what most authors report, he was of genuine Milesian lineage and belonged to an illustrious family.7 Diogenes Laertius is, in this case, our only source. As for the reliability of the individual details, it is prudent to maintain reservations, but there is the unequivocal suggestion that Thales belonged to a prominent Phoenician family8 that had already established itself in Miletus. This is a good premise for understanding how the young Thales could have made a trip (not just a short visit) to Egypt.

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3.3 Egypt Our sources of information in this regard converge in telling us that Thales, in addition to going to Egypt, had the opportunity to meet priests there (and therefore educated people) and to spend time with them. Diogenes Laertius clearly writes that, “having arrived in Egypt, he spent time with the priests”,9 and Iamblichus that since was in poor health, he [Thales] encouraged him to sail towards Egypt to meet the priests of Memphis and of the City of God [Diospolis = Thebes] as he had been able to obtain with them what made him a renowned sophos.10 A third source, Aetius,11 reports that, after practising philosophy in Egypt, Thales returned to Miletus in old age. That his trip to Egypt was driven by the pursuit of knowledge and that Thales was able to establish signifcant relationships with some Egyptian cultural centres is certainly possible. We would like to know at what age he went, and how long he had stayed in Egypt. That he went there and stayed there for a long time when he was at an advanced age (as ps.-Plutarch suggests) is however unlikely if, as seems to be the case, at around the age of 45 his fame had already reached Athens. Furthermore, we have reason to presume that he not only had the chance to see the pyramids of al-Gīza, but that he was able to ascertain that, when a stake driven into the ground produces a shadow which is as long as the stake is high (which means, when the sun is at 45°), the great pyramid too generates a substantial shadow. This is something he could only personally ascertain if he stayed for a while in the neighbourhood of some pyramids (see Section 4.1.2). Moreover, this presupposes the early development of a very specifc curiosity, and the pursuit of questions which were far from obvious. That this happened when he was still quite young is therefore plausible, even if it cannot be properly proved.

3.4 Fame in Athens 3.4.1 The awareness of a title It is attractive to think that, on returning from Egypt, Thales continued to refect on the topic of the height of the pyramids, arriving at some important conclusions; but obviously we are not able to affrm that things went this way. On the other hand, there is a report that his adulthood was marked by a signifcant event that took place in Athens: under the archonship of Damasias (582–580 BC) he was given the title of Sophos in a public ceremony, and this event was probably followed by the extension of the title to six or more other personalities.

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In his account of Thales, Diogenes Laertius begins with a reference to Plato in which the text is incomplete but clear: “… as Plato also says” (καθὰ καὶ Πλάτων φησί, 1.22). It is likely that Diogenes Laertius is referring to Protagoras 343a, so that the lacuna can be flled to read: “, as Plato also says”. However, immediately after this, Diogenes Laertius mentions a work by Demetrius Phalereus, the Archontōn anagraphē (which is a catalogue of the eponymous archons of Athens, whose names were used to identify the year) from which he reports that in Athens, under the archonship of Damasias, Thales prōtos sophos ōnomasthē, “was frst named Sophos”. On the same occasion, or a bit later, the other intellectuals who formed the group known as hoi hepta sophoi, the Seven Sages, were also chosen.12 The Damasias in question here is obviously not the much earlier eponymous archon of 639/638 BC, but must be eponymous archon of 582–580 BC. The archonship of this Damasias is associated with an anomaly: he remained in offce for a second year and for the frst two months of a third year, when he was deposed following a revolt by which the Athenians managed to prevent the transformation of Damasias into an autocrat (tyrannos).13 Those were also the years in which Solon returned to Athens after a long period of voluntary exile (the dates of which can be assigned roughly to the decade 593–584). Taking these circumstances into account, we can assume that in Athens the initiative to honour Thales was taken by Damasias – perhaps at the suggestion of Solon, as was the subsequent decision (kath’ hon kai, writes Diogenes) to honour other prominent fgures, including some heads of state, as Periander, tyrannos of Corinth, Thrasiboulos, tyrannos of Miletus, and Pittacus, autocrat of Mytilene,14 and Solon himself. The choice seems well explained by political expediency, and looks to the powerful positions they occupied. The exceptional nature of the ceremony is also noteworthy: nothing of the kind ever happened again in recognition of intellectuals either in Athens or elsewhere. Their exceptional nature constitutes a good reason to believe that these reports attest to real events. If not, the convergence of the individual fctions here is an extraordinary coincidence: the reference to Athens, Solon, and Damasias, the choice of the year, the nature of the recognition, the reference to Thales, the report concerning the Seven Sages as a group, the trip of Thales to Athens for the occasion. And this is without considering the stories about the tripod, which I will come to shortly (Section 3.4.3). The hypothesis that all these reports are false is baseless and diffcult to sustain: the alternative, that they are grounded in real facts, is much more likely and more credible.15 After all, all the events centre on just one crucial detail: that there was a public event for Thales, conceived of as an initiative by the Athenians designed to celebrate and honour him. If this is right, then Thales had already emerged as an exceptional character. (It also follows that towards 583 BC, the 30-year-old Anaximander had

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not yet established himself to such an extent that he too could be a candidate for being offered such a recognition in a distant city.) But it is not surprising that he was recognised for his pre-eminence: he could be seen as a character unique for the time, because of his amazing innovations and because of the unimaginable knowledge he could boast. It is by no means implausible that Damasias and Solon might have entertained the idea of honouring him – with the intention of honouring, at the same time, the city of Athens and themselves. Such a circumstance seems congruent with the identity of Athens. The polis, which had recently distinguished itself for having endowed itself with laws written by Solon, distinguished itself further in the decades immediately following for the institution (or the reform, or revival) of the Panathenaic festivals and for the delicate process that led to the fxing of the text of Iliad and Odyssey. All of this cultural investment is too great to be anything other than the result of specifc policy. The story about the Seven Sages harmonizes with this. In conclusion, Athens already counted itself among the most important cities of the Aegean, alongside Thebes, Megara, Corinth, and Argos and, on the other side, Miletus, Samos, and Ephesus, and for decades sought credit for its unique cultural policy. But how did Solon and the Athenian authorities justify the decision to honour Thales? His name must already have been linked to something exceptional, but what precisely? It is attractive to think that the relevant fact is his explanation of the dynamics of solar eclipses – some perhaps popularised in the story of his having predicted an eclipse in recent times. 3.4.2 “Sophos” As for the qualifcation for being a Sophos: the offcial conferral of this qualifcation too might have amounted to transforming an epithet already in circulation into a real honour. It is interesting to note that, despite its use as an offcial titled conferred by Athens, there were no restrictions in its wider use. Heraclitus, for example, speaks, albeit with a hint of sarcasm, of Homer as “the wisest of all” (soph ōteros pantōn: 22B56 DK) and, elsewhere, of the “wisest of men” (soph ōtatos) who, when compared to divinity, one might rather call monkey (22B53 DK). Not even Xenophanes’ passage on “we, the sophoi” (in the elegy on sport: 21B2 DK) can be said to be particularly emphatic. This means that in the case of the Seven Sages an attempt was made to load this specifc epithet with added value – but that it clearly had no long-lasting infuence on its meaning. What tells us more about the qualifcations of a sophos are the stories connected to the award of a prestigious tripod “to the most sophos”.

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3.4.3 Thales and the tripod Diogenes Laertius offers a detailed and, to some extent, well-documented account of this theme in the chapter dedicated to Thales. At the end of DL 1.27 we read, to begin with, that a tripod found by some fshermen was sent tois sophois (to the wise men) “by the people of Miletus”. A more detailed account follows in 1.28: some boys bought a whole haul of fsh. Having found the precious tripod inside it, they discussed what to do with it, and concluded that they should consult the oracle of Delphi about it. The oracle’s response was that the tripod should be given to whoever was preeminent among all people for wisdom (sophiēi pantōn protos). It was thus offered to Thales, who passed it on to others until fnally it came to Solon, who ultimately refused the gift, believing that excellence in sophia could belong only to the divinity. Immediately after this, Diogenes Laertius reports that, according to Callimachus, a prized phialē (a highly worked dish) was destined “for the best among the sophoi”. The phialē was also offered, in the frst instance, to Thales. He refused it; so the phialē passed from hand to hand and in the end returned to him – and he this time decided to send it to the temple of Apollo Didymaeus, not without mentioning that he had received it twice as a sign of his excellence (aristeion dis labōn: 1.29). And Eudoxus, continues Diogenes Laertius, told of a chalice (potērion) which was to be given to the most sophos of the Greeks. It was given to Thales and then passed from hand to hand, again within the circle of the Seven Sages; as a consequence, the god of Delphi was consulted again. Diogenes Laertius then reports (1.30–31) that it was the Argives who made the tripod a gift for the wisest person, and that the tripod ended up in the hands of Chilon (one of the Seven Sages), then came to Periander, tyrant of Corinth, who sent the tripod to Thrasybulus, tyrant of Miletus, by a ship which sank near the island of Kos. The tripod was subsequently found in the sea near Athens, and was sent to Bias (another of the Seven Sages). Diogenes continues by reporting (1.32–33) that the tripod was made by Hephaestus and had belonged to Paris and then Menelaus, and was thrown into the Coan sea, that it gave rise to arguments among those who found it, after which the Milesians were informed about it. A war between Miletus and Kos ensued with many casualties. The oracle intervened, prescribing that the tripod should be given “to the wisest” of all; it was agreed to give it to Thales who, in turn, donated it to the temple of Apollo Didymaeus. This intricate narrative tells us something signifcant.16 The details change from version to version, but a substantial core is constant and speaks to us not only of the high reputation and wide recognition of Thales, but also of a society that had developed the inclination to identify and honour those who stood out for their wisdom. All of this must have happened around 585–580 BC, when Thales had already established himself (we do not know how), while none of those who might otherwise have competed with him (e.g. Anaximander or, even more so, Eupalinus) had yet achieved fame in Ionia.

42 Approaching Thales Moreover, from what Diogenes Laertius reports, it is easy to infer that the story must have been told by many different people, suggesting that an awareness of its signifcance was widespread. Everything, including the different ways in which the story is told, points towards a factual basis despite its fctional overlay. (The latter point, in turn, encourages us to imagine that, in those ancient times, there were already ‘reporters’ who sought a certain sensationalism.)

3.5 The notoriety acquired at Mytilene and elsewhere The story of the honours granted by the city of Athens to Thales is not an isolated episode, because we also have reports of another very singular event, which must have taken place on the island of Lesbos (so, at approximately the same distance from Miletus as Athens). A fourth-century-AD author, Himerius of Prusa, wrote the following: Pindar sang on the lyre the glory of Hieron at the Olympic festival, Anacreon sang the fortune of Polycrates, who sent (precious) offerings to the goddess of Samos, and Alcaeus sang Thales in his odes (καὶ Ἀλκαῖος ἐν ὠιδαῖς εἶχε Θαλῆν) when also Lesbos celebrated its festival.17 What should we think of this unexpected reference to Thales, the subject of an ode by a famous poet, Alcaeus, on the occasion of a panēguris held on the island of Lesbos?18 The account has no confrmation from other sources, but it is so singular and so unexpected that, allied with the fact that the reference to Pindar and Anacreon is entirely plausible, it seems quite possible that Thales was invited to Lesbos where he was the recipient of a poem by Alcaeus (sadly not now extant) – that is, he was treated as a celebrity. It would seem that in Mytilene there was an event where many people gathered and where, on this particular occasion, an established poet wrote and sang a song in honour of the main guest, presumably while the sophos was actually there: a sign of his great authority, as well as his fame. It is a pity that we do not know more about this singular event. (There is also the story of Mandrolytus of Priene, which I shall deal with in the course of Chapter 8.) Another circumstance to consider concerns Cleostratus of Tenedos. He seems to have been younger than Anaximander,19 and we know that he observed the solstices, like Thales, and that he worked to establish how many days there are between the summer solstice (or the autumn equinox) and the dawn setting of a particular constellation – not the one in which Thales appears to have been interested, the Pleiades, but Scorpio (and, perhaps, other constellations of the Zodiac too). Cleostratus gives the impression of having been a true disciple of Thales, and having independently taken up investigations comparable to those conducted by the Milesian. Something is also known about two other characters, Matricetas of Methymna (in

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north Lesbos) and Phaenus of Athens, who also conducted observations on the solstice.20 In conclusion, it is evident that we possess many traces of Thales’ rare fame. Already during his lifetime, Thales distinguished himself from his contemporaries and was perceived as a character without equal, and that the news of more than one of his discoveries was rather widespread.

3.6 Economic and political activity? The story concerning Thales’ purchase and exploitation of oil presses in Miletus and on the island of Chios is well known, as are the stories concerning his advice to the authorities of Miletus and to Croesus. All this will be discussed in detail in Chapter 15. Here it suffces to say that there are strong indications that all these narratives are unreliable. The story of the conversation between Thales and Mandrolytus of Priene, however, has quite a different favour: the conversation concerned what was perhaps the last memorable measurement Thales made during his life, namely the angular width of the sun (Chapter 8).

3.7 Death in Tenedos? The account of Thales’ trip to the island of Tenedos (north of Lesbos) has a very different favour too. Two traditions inform us that Thales died in Tenedos. The reports have some weight because Tenedos was home to a character unknown to most people: the aforementioned Cleostratus, an astronomer who was active ‘after Anaximander’ (see above). Since Cleostratus’ research seems to take inspiration and develop investigations conducted by Thales (and by nobody else before him), it has been suggested that he was a student. Webb wrote a hundred years ago: Cleostratus fourished at Tenedos after Thales. As to the place, there is a tradition that Tenedos was where Thales died. He may have founded a school there of which Cleostratus, twenty years later, was the chief representative.21 That this is what really happened is not all that far-fetched. Besides, who would have invented it as a story if it had no basis in fact? And if Thales could go to Athens and Mytilene as a prominent individual, why should he not have made the trip to Tenedos as well? Apollodorus tells us only when Thales died, not where, and the possibility that in old age the Milesian went to visit one of his ‘pupils’ and admirers in distant Tenedos does not have the typical features of a baseless invention. So it is not inconceivable that the old Thales spent a signifcant time in Tenedos, during which he fell ill and died. We do not know Cleostratus’ dates. Fotheringham placed his akmē towards 520 but, if there was a personal connection with Thales, the chronological

44

Approaching Thales

distance (more than 30 years) between the death of Thales and the time in which Cleostratus affrmed himself as an astronomer must have been shorter (in Diels–Kranz, Cleostratus is even placed before Thales).

Notes 1 On the chronology of the Presocratics, there is now a substantial, yet not quite fawless, book by Philip Thibodeau (2019). 2 Cicero, in turn, in the Academica Priora (118 = Th71 W) makes a reference to Anaximandro populari et sodali suo (thus neither the diadochos nor a mathētēs), while shortly after he talks of suus auditor Anaximenes. 3 Diogenes Laertius reports this in 2.2 (=12A1 DK = Ar25 W = 6P2 LM): ὃς καί φησιν αὐτὸν ἐν τοῖς Χρονικοῖς τῷ δευτέρῳ ἔτει τῆς πεντηκοστῆς ὀγδόης Ὀλυμπιάδος ἐτῶν εἶναι ἑξήκοντα τεττάρων καὶ μετ’ ὀλίγον τελευτῆσα (“He [i.e. Apollodorus of Athens] also says in his Chronology that he was sixty-four years old in the second year of the 58th Olympiad and then he died a little later”). 4 Hippolytus in the Refutatio (1.6.7 = 12A11 DK = Ar75 W = 6P1 LM) tells us that he was born in the third year of the 42nd Olympiad: οὗτος ἐγένετο κατὰ ἔτος τρίτον τῆς τεσσαρακοστῆς δευτέρας ὀλυμπιάδος. 5 1.37–38 (=11A1 DK = Th237 W = 5P1 LM): Φησὶ δ’ Ἀπολλόδωρος ἐν τοῖς Χρονικοῖς γεγενῆσθαι αὐτὸν κατὰ τὸ πρῶτον ἔτος τῆς τριακοστῆς ἐνάτης Ὀλυμπιάδος. ἐτελεύτησε δ’ ἐτῶν ἑβδομήκοντα ὀκτώ (“Apollodorus in his Chronicles says that he was born in the frst year of the 31st Olympiad. He died at the age of seventy-eight”). 6 This is a not insignifcant detail, but it is ignored by Thibodeau (2019, 13 ff.) in his monograph. See below. 7 Diog. Laert. 1.22 (=11A1 DK = Th237 W = 5P2 LM): Ἦν τοίνυν ὁ Θαλῆς, ὡς μὲν Ἡρόδοτος καὶ Δοῦρις καὶ Δημόκριτός φασι, πατρὸς μὲν Ἐξαμύου, μητρὸς δὲ Κλεοβουλίνης, ἐκ τῶν Θηλιδῶν, οἵ εἰσι Φοίνικες, εὐγενέστατοι τῶν ἀπὸ Κάδμου καὶ Ἀγήνορος. … ἐπολιτογραφήθη δὲ ἐν Μιλήτωι, ὅτε ἦλθε σὺν Νείλεωι ἐκπεσόντι Φοινίκης· ὡς δ’ οἱ πλείους φασίν, ἰθαγενὴς Μιλήσιος ἦν καὶ γένους λαμπροῦ. 8 On this, see Wöhrle 2015. I remark that the information about the Phoenician legacy is not likely to be an ad hoc invention, but must come from some ancient source about Thales. 9 1.27 (=1A1 DK = Th237 W = 5P3 LM) εἰς Αἴγυπτον ἐλθὼν τοῖς ἱερεῦσι συνδιέτριψεν. 10 De vita Pythagorica 2.12.9–10 (=11A11 DK = Th249 W = 5P5 LM): καὶ τὴν ἑαυτοῦ ἀσθένειαν προετρέψατο εἰς Αἴγυπτον διαπλεῦσαι καὶ τοῖς ἐν Μέμφει καὶ Διοσ μάλιστα συμβαλεῖν ἱερεῦσι· παρὰ γὰρ ἐκείνων καὶ ἑαυτὸν ἐφωδιάσθαι ταῦτα, δι’ ἃ σοφὸς παρὰ τοῖς πολλοῖς νομίζεται. 11 Or, more, precisely, pseudo-Plutarch, Placita philosophorum 1.3.1 (=11A11 DK = Th147 W = 5P4 LM). 12 In 1.22, we read: καὶ πρῶτος σοφὸς ὠνομάσθη ἄρχοντος Ἀθήνησι Δαμασίου, καθ’ ὃν καὶ οἱ ἑπτὰ σοφοὶ ἐκλήθησαν, ὥς φησι Δημήτριος ὁ Φαληρεὺς ἐν τῆι τῶν Ἀρχόντων ἀναγραφῆι (“He was the frst to receive the name of Sage, in the archonship of Damasias at Athens, when the term was applied to all the Seven Sages, as Demetrius Phalereus mentions in his List of Archons”). 13 On these events, see esp. Leão (2010). 14 The case of Chilon from Sparta is a bit different since he became ephor some decades later. 15 We cannot say the same thing, for example, for the meeting between Solon and Thales or about the exchange of views on Thales as a bachelor and without offspring put forward by Plutarch (Vita Solonis 6–7 = Th112 W).

Elements of a biography 4

45

16 Taking these as mere tales, as Bruno Snell did in 1938 (1971 ; see now Snell 2005), has no possible justifcation whatsoever. 17 Himerius, Declam. 28.4–8 (=11A11a DK = Th303 W ≠ LM): Ἦιδε μὲν Ὀλυμπιάσι τὴν Ἱέρωνος δόξαν πρὸς λύραν ὁ Πίνδαρος, ᾖδε δὲ Ἀνακρέων τὴν Πολυκράτους τύχην Σαμίων τῇ θεῷ πέμπουσαν ἱερά· καὶ Ἀλκαῖος ἐν ᾠδαῖς εἶχε Θαλῆν, ὅτε καὶ Λέσβος πανήγυριν . 18 A panēguris was a big festival, not necessarily religious, which involved a large crowd and many entertainments. 19 See Pliny (Nat. Hist. 2.6.31): Anaximander … deinde … Cleostratus. 20 These three characters will be discussed again in Section 6.3.2. 21 Webb (1921, 70). See also Fotheringham (1919, 1925). It was at that time that Cleostratus was at the centre of a great debate. – The historical tradition about Thales’ death at Tenedos is to be found in Eklogē Historiōn Parisina 2.263, Chronicon Paschale 214, 15–22 and Simeon Logothetes, Chronikon 42.12.52–53 s. (=11A8 DK = Th477 and Th492 W ≠ LM). These sources agree in reporting that Thalēs ho Milēsios en Tened ōi apethanen.

Part II

Five quantitative inquiries

It is fairly clear that the most spectacular results obtained by Thales have the sun as the common factor. This is not because he carried out inquiries concerning the sun itself (e.g. by asking questions such as: What is the sun? What is it like?), but his main inquiries dealt with phenomena which were connected with the sun: the height of the pyramid based on the shadow it casts; solstices and equinoxes (tropai and isēmeriai); the eclipse; and, fnally, the attempt to give a number to the angular width of the solar disc. Other investigations by Thales have nothing to do with the sun. They will be examined later.

DOI: 10.4324/9781003138723-5

4

How to measure the height of a pyramid

When people talk about Thales measuring the height of the Egyptian pyramids, several tacit assumptions are normally at work. These will be discussed to begin with, mainly in order to identify the limits within which Thales was able to operate; in particular the conditions which he was bound to take into account. In fact, his research, assuming it took place (this is obviously the frst question that needs to be addressed) did not take place in a vacuum, but in a particular context, and many features of the story will make little sense without understanding this context.

4.1 Some preliminary issues 4.1.1 Doubts about historicity No question is more fundamental than this: did Thales in fact attempt such an investigation? To my knowledge, there is no proof that the information we have lacks a basis. In recent years, however, Jedrkiewicz went so far as to argue that the episode must have been invented because a pyramid ‘contains’ always a part of its shadow, which must therefore be estimated; but to do this it is necessary to know the measure of the angle at the base and the half-length of the side of this solid; now to calculate the height it is enough to know these two quantities, so the measurement of the shadow on the ground is neither necessary nor suffcient. (Jedrkiewicz 2000, 80)1 Dührsen also downgraded the story to a “well-known anecdote” (2013, 248), but without arguing the point; White chose not to include the measurement of the pyramid on his list of Thales’ accomplishments (2008, 91–92), but again without justifying his choice. By contrast, the indications that it did take place are, at least in my opinion, much more convincing. I am thinking frst of all of the consistency of the reference in our sources to a shadow cast by a stick. As we shall see, we are dealing with informants who know little and can say little on the subject, so it is signifcant that they DOI: 10.4324/9781003138723-6

50 Five quantitative inquiries consistently make specifc reference to the stick (or pole)2 which at a certain time produces a shadow equal to its height. This unequivocally tells us that Thales was interested in the shadow produced in a similar way by the pyramid when the sun reaches 45°.3 That someone might have investigated the shadow produced by the Egyptian pyramids when the sun is at 45° is signifcant, frst of all, because it is not at all obvious that the Pyramid of Cheops would have sides steep enough to allow even a small shadow to be cast when the sun is 45°.4 Presumably, nobody would have thought about this until there was a very specifc reason for wanting to be sure that a shadow would be cast in the relevant conditions. All of this means that Thales must have been on the spot5 to ascertain that the pyramid would cast a shadow that could be used to measure its height. He worked out that the only hope of being able to establish how high the pyramid is, is through the knowledge that, with the sun at 45° (and coaxial: see below), the pyramid generates a shadow that could be measured. It is no coincidence, moreover, that there is no report of anyone else, Greek, Egyptian, or Roman, who was interested in this question. This was one of the questions which only Thales pursued. The consistent reference to the stick makes sense only if we suppose that he frst suspected, and then actually found, that the pyramid has sides steep enough that it casts a shadow when the sun is at 45°. But this does not mean that Thales wandered for weeks or months among the pyramids of Giza in an attempt to fnd an answer to his curiosity: the Egyptian authorities probably would not have allowed him, and he would not have dared. But he might still have found a way to observe from a distance, taking care, while observing the shadow of the pyramid, to have a stick with him to hold upright and, I imagine, a string with which to trace an arc on the sand marking the length of a shadow that would equal the height of the stick. So Thales did go to Egypt and actually observed the shadow of some pyramid with the sun at 45°, using a stick and its shadow to ascertain when the sun was at 45°. At least on this matter it is hard to entertain reasonable doubt. 4.1.2 Did the Egyptians know how tall their pyramids are? If Thales was in Egypt and developed a special curiosity about the size of the pyramids (probably those of Giza), it makes sense to ask whether the Egyptians had a similar interest in determining their height. If they had asked this question, and knew the answer, then Thales could have had his curiosity satisfed immediately. Many scholars have assumed that this is exactly what happened, often drawing on the evidence found in the celebrated Rhind papyrus. The Rhind papyrus was acquired in Luxor by Henry Rhind in 1858. It is a copy made, as we read at the very beginning of the scroll, by the scribe

How to measure the height of a pyramid 51 Ahmose on a date, judging from the evidence, close to 1550 BC. The papyrus begins with an account of fractional numbers – something which is remarkable in itself – which leads straight into an account of how to perform multiplication and division; after that, it moves on to volumes, units of measurement, and the reformulation of the numerical data necessary to switch from one unit of measurement to another. Towards the end of the discussion of volume, there is a group of problems – fve, from no. 56 to no. 59B – which are dedicated to calculating the exact inclination of the sides of a pyramid (and to the notion of seqt). Two other spectacular mathematical papyri have been identifed,6 one now in Moscow and one in Berlin, which date from the nineteenth century BC. One of these, the Berlin Mathematical Papyrus, begins with the following question: “The area of a square of 100 units of measurement is equal to that of two smaller areas. The side of one of these two squares is ½ + ¼ of the side of the other” – a striking anticipation of Pythagoras’ theorem. In these papyri there is a surprisingly advanced wealth of basic knowledge of computation (that is, of the execution of operations on numbers). They show that advanced specialism in mathematics was fourishing at a very early period as part of the lively cultural activity at the heart of what we might think of as the ‘Egyptian miracle’. Given this material, frst Caveing (1997) and O’Grady (2002, 208), then with greater insistence Hahn (2017, 97 and elsewhere), came to suppose that these elaborate techniques of calculation were known to (that is, studied and correctly understood by) Thales. But a hypothesis like this is only credible if the mathematical culture of this earlier period, around 1900–1500 BC, had been transmitted without too many changes through successive generations to Egyptian contemporaries of Thales a thousand years later. Is there any suggestion that this might have happened? If there is any evidence that it did, I am not aware of it. Indeed, the Egyptian scholar Marianne Michel could talk in 2014 of “the many problems and accounts that are an integral part of the mathematical corpus of the Middle Kingdom, but equally of the administrative documents as well as the most recent documents”. Unfortunately, no qualitative distinction between the mathematics of the Rhind papyrus and the Egyptian mathematics of other periods surfaces from her book. Corinna Rossi was slightly more cautious when she wrote (2004, 218): the evidence available to us does not “suggest that the Egyptians were acquainted with more or less complicated versions of the Theorem of Pythagoras as early as the Old Kingdom”. I thus ask again: where are the documents that show that the mathematical culture, impressive as it is, dating back to fve to seven centuries before the Trojan war, was preserved or developed over the centuries? The case that Thales had access to this knowledge cannot be made on the basis of documents going back to one thousand or more years before Thales. In fact, it seems much more probably that the absence of subsequent documents testifes to the loss of an earlier, and so distinguished, interest in

52

Five quantitative inquiries

mathematics7 and the loss of the knowledge that went with it. Thales was in Egypt more than a thousand years later, and there is no reason to think that the Egyptian intellectuals he could have met were aware of the earlier mathematical culture. 4.1.3 What do we know about the arithmetical culture of the Greeks between Homer and Herodotus? Whatever the mathematical competence of the Egyptians in general, and in particular that of the priests with whom Thales might have come into contact, the real question for us is what Thales himself learned while staying in Egypt: what did he bring back to Miletus and teach there? If it is the case that he had learned, not even the most advanced mathematics documented in the Rhind papyrus, but just the basic ‘four operations’ (that is, addition, subtraction, multiplication, division), then, given his fame in Miletus and beyond, he must surely have shared it with people who came to learn from him. Surely, if he returned to his homeland possessing computational skills in advance of those with whom he had left for Egypt, he could scarcely have kept this new knowledge to himself. It is likely enough that he would have rethought them and rephrased them in Greek, assuming he had understood them correctly. But there is no evidence that he did this. Note in particular (a) that knowledge of the four operations involves quite a few specialized terms (such as ‘equal’, ‘minus’, and ‘subtraction’) which we might have expected to hear about if Thales had coined them in Greek; and (b) that, anyway, given Thales’ fame (during his life and immediately after his death: Section 17.1), we would expect to have some evidence, direct or indirect, of this innovative work. There are, in fact, many indications that the mathematical skills of the Greeks at Thales’ time were less developed than those of contemporary Egyptians. I start by highlighting the fact that the quantities indicated by Thales (e.g. ‘25 days’ for the distance between the solstice and the dawn setting of the Pleiades) are quantities which can be simply stated and recorded: they are not the basis for further, more elaborate operations. Note also that, at a time when writing was becoming more established, Homer and the archaic poets (including Thales’ contemporaries) were involved in the process of settling on the words to be used in naming the numbers, and so in establishing criteria for generating these new names. As can be seen from the very useful overview given by Jason Hawke (2008, 58–63), the poets began to name relatively large numbers when they started writing, but never going beyond 10,000, and never grappling with the complex numbers that appear later on in Herodotus. What is more, in these authors there are no numerical calculations (no operations performed on numbers): numbers are only mentioned. This is not surprising, because knowing the number-series and having a criterion for naming every number in a fairly large series is not the same as having any idea of the operations that can be performed on

How to measure the height of a pyramid 53 numbers and with numbers. A fortiori, knowing how to name numbers does not even remotely imply the acquisition of familiarity with some operation. Besides, to learn how to identify and name different numerical fgures (and then become able to count and to state that, for example, something occurred x days ago) may well have been a task of its own for a considerably long time. What happened subsequently? Herodotus is probably a good witness: he “performs few subtractions or divisions, but a large number of additions and multiplications” (Keyser 1986, 232) and has no diffculty in grappling with big fgures. If these are Herodotus’ strengths, the fact that he does not act with a sure hand when it comes to division (there are errors), the fact that he uses only one expression to indicate any type of calculation (logizesthai, in the sense of extracting a new fgure through calculation, i.e. giving the result of the operation), and the fact that he does not show any other skills in this direction, not only tells us that the great Herodotus could not do any better; it also tells us that he thought that he would be appreciated by his readers for this very reason. In other words, the cultural avant-guarde of Athens at his time was, at best, at his level. Even more signifcant, for our purposes, is the fact that Herodotus affrms that “the Greeks, and in particular the Ionians, do not know how to calculate (ouk epistamenous logizesthai)” (2.16.1). In fact, words with which numerical relations are identifed (e.g. ‘plus’ and ‘minus’, ‘equal’) were not standardized in Greek for many centuries to come, which tends to support this declaration by a native of Ionia, concerning the Ionians of his time, that basic arithmetic competence was not widespread. Even supposing that Herodotus exaggerates a little, it is reasonable to suspect that he himself learned to calculate in the course of his travels, or perhaps in Athens, not in Halicarnassus. (It is only later, with the Attic inscriptions dedicated to the accounting of expenses for public works, such as those relating to the construction of the Parthenon, e.g. IG I2, 352, from the year 434–433, found in Athens, that we fnd evidence of a certain professionalism in the management of the accounts,8 though none of these date back to before 445, and none of them go beyond listing the results of computation. Nevertheless, one can presume that by then the four operations were known and used to get these results.) Another piece of evidence about this, eloquent though negative, concerns the frst generation of Pythagoreans. The type of mathematics that the frst generation of Pythagoreans boasted did not go beyond a very basic numeracy. Indeed, even the simplest forms of computation do not appear to have been part of that numerological culture. As to Miletus, where Thales returned after visiting Egypt (about a century-and-a-half before Herodotus was writing his magnum opus), nothing suggests any advancement in arithmetic culture. All of this implies that Thales did not learn anything relevant while he was in Egypt. Therefore, he could not count on an ars computandi that was not quite elementary.

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Five quantitative inquiries

So when Thales was asking about the height of the great pyramids, it is quite possible that his plan was simply to add two lengths: the length from the tip of the shadow to the middle of the side at the base of the pyramid, and half the length of one of the base sides, to give a total length from the middle, beneath the apex, to the tip of the shadow. 4.1.4 Greek geometry before Hippias and Antiphon Our fourth question concerns the ‘theorems’ allegedly discovered and defned by Thales and Pythagorean mathematics. These ‘theorems’ will be examined in Chapter 14: suffce it to say for now that we will see compelling reasons to deny the credibility of what our sources report about this.9 One of them is that it is only in the middle of the ffth century that a fully developed interest in geometry took shape in Greece. Perhaps we can assume that Thales had given some thought to the right-angled isosceles triangle, and realized that, if you knew the length of one of its sides, you could work out the length of the other (see the next section). This would be no small matter, and very much to Thales’ credit if he worked this out. But there is no evidence that he went any further than this (pace Hahn 2017, ch. 2).10 Archaeological evidence, for its part, shows that Greek temple builders had defnite ideas about locating the centre or axis of columns, making them perfectly circular and, probably, ensuring the regularity of their grooves, but there is no evidence to suggest that they went beyond (and, anyway, how far beyond?) these performative abilities, or that Thales exploited their knowledge. 4.1.5 Was Thales free to spend time at Giza? At this point, I want to consider the practical conditions necessary for research into the height of one of the pyramids – a rather different sort of question. It does not go without saying, as I noted, that a pyramid will cast a shadow when the sun is at 45°. Will the Egyptians have known whether any did? Will they have had an interest in knowing it? Did Thales notice the fact thanks to them? None of this is likely: there is the complete silence of our sources (above, Section 4.1.2), but there is also the fact that pyramids were royal tombs, places of great symbolic value, and therefore carefully protected.11 But the question needs to be addressed, because not every shadow is equally useful for research into the height of a pyramid. Not only do we need a shadow produced by the sun when it is at 45°, but also one that is coaxial with the pyramid, because in all other cases the shadow would not form a triangular area with two equally long sides, but rather a scalene triangle. Consider Figure 4.1. A precise calculation can only be made if a shadow is formed by the isosceles triangle HCO. It would not work if, with the sun at 45°, the vertex of the

How to measure the height of a pyramid  55

Figure 4.1  A n Egyptian pyramid where it is possible to establish that the shadow forms an isosceles triangle. Courtesy of Dirk Couprie

pyramid generates the triangle HC1O instead (see below, on page 59, Figure 4.2). The reason for this is that BN1 is not as long as BN (it is a bit longer) so that the distance N1C1 would be shorter than NC. Under these conditions, only an approximation of the height of the pyramid would be possible. Let us therefore suppose that Thales aimed to restrict his field of observation to the cases in which the shadow does form an isosceles triangle. On this hypothesis, what he was aiming to identify was point C, that is, a point where the shadow produced by the sun at 45° will reach to form an isosceles (not a scalene) triangle. Only in this case would he be able to work out the length BC, adding to the length of the shadow the length of half of the side of the pyramid at the base (for example, DH), to produce a length equal to the height, BA. In order to identify point C, Thales would have to trace the line NC2 (­Figure 4.2 below), then he could wait and see whether, when the sun reaches 45°, the pyramid’s shadow is coaxial, namely, if its vertex touches the straight line NC2. But how to identify NC2? This would probably have required tracing lines OO2 and HH2, and then plotting NC2 with the help of a long rope, and marking it clearly on the ground. (The alternative to this is that, when the sun approaches 45°, Thales would have had to undertake rather demanding measurements to ascertain whether the triangle formed by the shadow is or is not isosceles.) It is also worth bearing in mind that the sun could reach 45° not only when it is in the west, but also in other positions, so that the relevant shadow might fall on a different side of the pyramid (see Section 4.4).

56

Five quantitative inquiries

The question now is whether it is conceivable that a foreigner would have had the opportunity to stay near the pyramids, equipped with rope and other tools, and possibly accompanied by one or two collaborators, so that he could mark out NC2 on the ground, and then spend several more weeks there (alone?) waiting for the right moment. Clearly this could not have been done covertly; but it is reasonable to assume that it could not have been done at all because of the status of the royal tombs, places freighted with symbolic value. It would have been hard for Thales to explain to an Egyptian guard why he was doing all this. 4.1.6 Summary The conclusions reached so far are the following: – It is virtually certain that Thales travelled to Egypt and, during his stay, seriously thought about how the height of the pyramids could be measured. We can be equally confdent that he ascertained that the pyramids cast a shadow when the sun reaches 45°. – It is virtually certain that the Egyptians themselves were not interested in the height of the pyramids either before, during, or after the visit of Thales. – The Egyptians of the time appear to have had widespread familiarity with the four operations and with fractions: but if Thales had learned all this, or at least the four operations, he would certainly have used these formidable tools for managing numerical quantities when he returned to Miletus, would have coined a terminology to refer to them, and would have done everything to promote knowledge of them. Since there is no evidence that he did any of this, we must assume that, during his stay in Egypt, Thales did not have the opportunity to learn anything new in mathematics. – Thales’ inferior knowledge of mathematics, in comparison with the Egyptians, is replicated in the case of geometry. He is likely to have been familiar with few properties of right-angled triangles, but no evidence suggests that he went further. – It is unlikely that he could have stayed long in the vicinity of any pyramid, let alone with collaborators, let alone to mark the ground in a way that would have been more than superfcial. My fve preliminary considerations supply important data points: they help us understand the context in which Thales was operating, how far he could go, and what he was in a position to understand, to learn, and to do. These results allow us to pass from the abstract to the concrete: we cannot imagine that Thales had special familiarity with geometric fgures or with numbers; we cannot imagine that he was able to discover who knows

How to measure the height of a pyramid 57 what from learned Egyptians; we cannot imagine that he had the freedom to spend weeks or months around the pyramid chosen for his research; we cannot even assume that he returned from Egypt with specifc numerical conclusions to boast (“Know that I know how tall the largest pyramid of all is: it has a height equal to x units of measurement, while another nearby has a height equal to y units … & c.”). This last is certainly the most disturbing inference: Thales certainly came to understand that, when a pyramid generates a shadow shaped as an isosceles triangle at a time when a stick generates a shadow that is equal to its height, then the shadow of the pyramid should allow us to work out how high the pyramid is, by virtue of complex reasonings that, no doubt, he was ready to explain. But hardly more than that. If these considerations have anything going for them, then our investigation is set on realistic tracks; but it has also discovered enormous and, to a certain extent, unexpected restrictions.

4.2 The information available Only Pliny the Elder, Plutarch, and Diogenes Laertius speak of how Thales might have gone about fnding out how high the pyramids are. Pliny reports that Thales of Miletus discovered how to measure the pyramids by measuring their shadow at the hour when it is equal to (scil. the height of) the body.12 Plutarch’s account is dramatized, but also gives more details: In your case, for instance, my king13 fnds much to admire in you [Thales], and in particular he was immensely pleased with your method of measuring the pyramids because, without making any ado or asking for any instrument, you placed a stick at the edge of the shadow which the pyramid made, and as two triangles were formed by contact with the sunbeam, you demonstrated that the pyramid is in the same ratio to the stick as the shadow of the one was to the shadow of the other.14 Diogenes Laertius, for his part, referring to an Aristotelian philosopher, Hieronymus of Rhodes, reports that Thales “measured [the height of the pyramids] exactly on the basis of their shadow, by waiting for the moment when [our own shadow] has the same size as we do”,15 that is, the moment when our body creates a shadow as long as our height. There is a signifcant difference between what the three authors declare and what they only let us glimpse. The detail that is not even touched on by the three statements concerns the diffculty of knowing the length of the shadow of the pyramid when the shadow of the stick is equal to its height. The full length of the pyramid’s shadow is unknown, since most of it is occupied by the base of the monument, and these sources do not even hint at the need to add the visible shadow – its height measured when the sun is at 45°

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and coaxial (conditions also ignored in these reports) – and half the length of the side of the pyramid. From this it follows that those who reported Thales’ measurement did not know the substance of his reasoning, and did not even try to reconstruct it. It would seem, indeed, that none of our three witnesses took serious steps to understand whether the measurement could really be made and, much less, what practical steps it would have required. They are content to let us know that Thales’ reasoning was based on a shadow that is exactly as long as the object that projects it; no one goes further. But this only makes it more likely that Thales did in fact discover the “way to calculate their height [of the pyramids] by measuring their shadow at the time in which [a shadow] is equal to that of the body”, and worked out the basic intuition. For this is the only motivation for the reference to the stick and its shadow at all. However, his achievement would not have been signifcant if he himself had stopped at saying that the stick could be of some use: he must have devised a defnite procedure of applying it.16 If our reports say that Thales “succeeded” in measuring the height of a pyramid, then he must at least have shown in detail how this could be done.

4.3 A merely theoretical, but rewarding, measurement So let us examine Thales’ method, or approach, more closely. The starting point, to repeat, consists in realizing that, when the sun is at about 45° (i.e. when the shadow of a stick is as long as the stick itself) and coaxial to a pyramid, the pyramid might generate a shadow (this would have to be confrmed be observation) and that, if it had cast a shadow, that could be used for the calculation. In fact, it is true that, under those conditions, a shadow is cast, and a fairly sizeable one at that.17 The next step, I suggest, was the following: Thales reasoned that, if, instead of the pyramid, there had been a large pole, as high as the pyramid, then, when the shadow of the stick was equal to its height, the shadow of the large pole would be as long as the pole is tall; therefore, ascertaining how long the shadow is would be tantamount to knowing the height of the pole. And it is clear that the shadow of the hypothetical pole would reach exactly the point reached by the tip of the pyramid’s shadow. In the pyramid in Figure 4.2, AB corresponds to the imaginary large pole and BC to the shadow of the pole when the sun is at 45°. But this makes it clear that part of the length, BN, is obscured by the body of the pyramid, and cannot be walked or measured. Nonetheless, with the sun at 45°, it is a matter of certainty that the shadow cast is identical in length to that which the imaginary pole would have cast. Given the shape of the pyramid, any shadow cast would only be useful if it happens to have the shape of an isosceles triangle, OCH, in Figure 4.2. This would make it possible to take the visible length NC as a simple continuation of the invisible segment BN – which will be exactly half as long as one of

How to measure the height of a pyramid 59

Figure 4.2 An Egyptian pyramid where the shadow forms an isosceles triangle.

the four sides of the pyramid at ground level (e.g. DH). We would then know, by analogy with the stick and its shadow, that BA has the same dimensions as DH + NC (or, if you prefer, DH + HE); moreover, it is quite easy to see that it is (or should be) easy to measure the length of DE (as in Figure 4.1, above). The diffcult but essential thing is to fx point C. The result is threefold: (1) Thales has come to know (or, rather, was in a position to know) the data relevant for establishing how high a certain pyramid is, (2) he knows all of this for certain, and (3) he knows the reasons why this knowledge is indisputable, but (4) he also knows that he would not have the opportunity to make the measurements needed even if he could get near  the pyramids.18 But we could imagine instead that Thales set up, perhaps in the immediate vicinity of his home in Miletus, a fair-sized model (perhaps in stone) of the pyramid, to measure it and demonstrate his ideas to people… and perhaps inspire them. It is not unlikely that he might have done something like this: he must have realized the unique nature of the knowledge and of the certainty that it allowed. This would have been his frst successful investigation – one that became both a model for further inquiry, and proof that it was possible to aim high.

4.4 The big hindrance The great obstacle concerns the possibility of fxing the position of C (in Figures 4.1 and 4.2). There are more factors that make this diffcult than those considered in Section 4.1.5 above. With a stick, the operation is very simple; but with a pyramid things are considerably more complicated.

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This  is because of how much more likely it is, when the sun is at 45°, that the resulting shadow will be slightly scalene. The sun may well not be at 45° when it is in coaxial position; but then, when it is at 45°, the shadow cast will not be ‘in the middle’. Consider again Figure 4.1 above: We can easily see that, when the vertex of the shadow falls at C1, the distance BC1 remains the same as BC, but BN1 is slightly longer than BN, while N1C1 (and, to a greater degree, N2C1) is proportionally shorter. Therefore if, when the sun moves to 45° (as the correspondence between the stick and its shadow will show), the shadow is scalene, we can only conclude that the sum of DH (the substitute for BN) plus N2C1 is some approximation of the height BA, but that in fact the pyramid is certainly a little higher. So exactly how diffcult would it be to observe the moment when the two requisites – the sun at 45° and a perfectly balanced shadowy triangle, that is, with the vertex on C – occur simultaneously? At this point it is relevant to recall the claims of Hahn and of Redlin– Viet–Watson. The frst writes (2017, 103) that, after repeated experiments on location at Giza, he succeeded in identifying, for each year, 15 occurrences, three of which take place on the same days at around 8 a.m. and 3 p.m. (with the shadow, obviously, on opposite sides of the pyramid). He also points out that only on one of those 15 dates is the position of the sun very near to exactly 45°. Redlin–Viet–Watson come to similar conclusions exclusively through deduction. They note (2000, 351) that “This moment of ‘equal shadow’ can actually happen at the most four days in any given year”; they specify: “there are two days of the year in which the phenomenon of ‘equal shadow’ occurs on the east or west wall”; “Again, it is unlikely that the phenomena ‘equal shadow’ and ‘perpendicular shadow’ coincide in these days, so some inaccuracies are inevitable here too”. That these two assessments, one empirical, the other based on astronomical calculations, confrm each other is very signifcant. Behind both there is a rather sophisticated feature, known as the lemniscate curve (or analemma).19 Astronomers discovered that, at the same time and in the same location on different days of the year, the sun does not fnd itself exactly in the same place, but its positions form a curve that reminds us of the number 8. It is because of these variations that the ‘equal shadow’ coincides with the ‘perpendicular shadow’ only seldom. Therefore, if Thales had wanted to be present in person when both of his requirements for making a calculation were met, he would have had to stay around the pyramid for a long time, and to have been constantly vigilant. More than this, he would have had to have devised, in advance, a specifc strategy for identifying the axis along which the vertex of the shadow needed to fall, because only in this way could he discover when the phenomena ‘equal shadow’ and ‘perpendicular shadow’ occur simultaneously. In order to identify a perpendicular shadow, he probably would have needed to equip himself with a very long rope, and then (with reference to Figure 4.2 above):

How to measure the height of a pyramid 61 (1) measure the length OH by means of this rope; (2) fold the string in two in order to locate point N and mark it; (2) trace an extension of PO and JH in the direction of the shadow; (4) identify on the extension of PO and JH two arbitrary points, O2 and H2, located at the same distance from O and H and mark them; (5) use the rope to connect O2 to H2: (6) locate the intermediate point C2 and mark it; (7) connect C2 with N; (8) mark the ground in some way so as to make the line NC2 visible and recognizable for a substantial length of time; and fnally (9) repeat the operation on two other sides (he would not need to bother with the west-facing side). To mark NC2 would have been a considerable achievement,20 if only because it requires devising practical and theoretical procedures totally foreign to the world of sophoi from which Thales was now differentiating himself. But he could hardly have put all of this into practice, just because, as I said, the pyramids were royal tombs, and therefore he was hardly in a position to locate point C. The existence of all these signifcant complications leads us to presume that Thales devised a clear method to establish how high a given pyramid is, but that he would not have the opportunity to make a precise measurement himself.21 Consequently, when he talked about this measurement, Thales must have devoted himself to a careful description of the theoretical procedure, rather than tell what he actually did.

4.5 Are there alternative ways to achieve the same result? All known alternative methods, including the computational strategies documented by the Rhind papyrus, involve the use of surveys and computations that were not within Thales’ reach. For example, he could not have estimated the difference between NC and N2C1 precisely because of the diffculty of locating point C. However, another elementary solution to the problem – albeit one that is not compatible with Thales’ conceptual resources – has been proposed more recently. In a 2000 article that went largely unnoticed,22 Lothar Redlin, Ngo Viet, and Saleem Watson started by locating the vertex of the shadow of both the stick and the pyramid in a largely arbitrary place (and time), and then tracing a circle with its centre as the vertex of the stick’s shadow, wherever it happens to be, making the radius of the circle equal to the height of the stick. At the same time, the location of the vertex of the pyramid’s shadow is noted. Inevitably, sometime later, the tip of the shadow of the stick will touch the circle at some point, and at that moment the shadow of the pyramid should be noted as well. Since the two points where the vertex of the stick’s shadow have been marked must be at a distance equal to the height of the stick (since it will be a radius of the circle drawn around the frst point), then the two points where the vertex of the pyramid’s shadow have been marked will also equal the height of the edifce – and with this, all obstacles will have been circumvented!

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Figure 4.3 An Egyptian pyramid to be analysed according to the suggestions made by Redlin, Viet, and Watson.

The three write (2000, 351) that theirs is a not static measurement (where the shadows are observed under particular circumstances) but a dynamic one (based on observing how the shadows lengthen and shorten during some given interval of time). It is all the more so since, strictly speaking, point M (in Figure 4.3) could be at any distance from point L; likewise, the shadow of the stick does not even have to be as long as the stick. In fact, any other length (e.g. double, one-and-a-half times, 80%, etc.) would be equally fne. As Redlin and colleagues comment (2000, 353): “the idea of measuring the height of an object so tall using only its shadow is so beautiful and surprising that it overshadows any practical application”. This is, if I understand it properly, impeccable reasoning that starts from the reference in our texts to shadows and avoids the need to look for a time when the sun is at 45° and coaxial, as well as the need to calculate separately the distance from the point beneath the apex of the pyramid to the edge of its shadow (=BN in Figure 4.2 above). Instead, we are asked to consider the simultaneous movement of the shadows cast by the tip of the vertical stick and the tip of the pyramid for a short interval of time; the only adjustment might be the need to make the displacement of the pyramid’s shadow proportional to the relationship between the height of the stick and the distance travelled by its shadow. The result will be that the distance travelled by the vertex of the pyramid’s shadow is equal (or at least in the same proportion)23 to the height of the pyramid.

How to measure the height of a pyramid 63 It goes without saying that this new methodology, however attractive (since it gives a new perspective on the challenge facing Thales), is of no help in understanding what he himself tried to do, or in solving the diffculties with which he is likely to have had to deal: objective diffculties (it happens too rarely that the sun reaches 45° just when it is frontally illuminating one of the sides of the pyramid), lack of tools for calculation and graphic rendering (for Thales it will have been relatively easy to make a miniature pyramid; however, he certainly will not have even been able to sketch a graphic rendering: no precedent, no model), regulatory impediments (the likely impossibility of staying close to any of the pyramids and, even more so, of marking the ground in the way needed). The expedient devised by Redlin and his colleagues ignores the existence of these complications; but to the extent that it disregards them, it performs no function, other than to show that an alternative method of achieving the relevant result has been devised. So it makes only a marginal contribution to our understanding of Thales.

4.6 Practical failure and subtle reasoning The conclusions reached in Section 4.1.4 suggest that we can say, at best, that Thales might have been able to make a rough estimate of the height of some minor pyramid. He would not have been able to mark the ground with lines that would have allowed him to know whether the shadow was aligned with the pyramid or not, and he had no way of predicting the rare occasions on which the shadow touched the axial line and the sun was at 45° and making sure he was there. However he explained his failure to obtain accurate results during his visit (if indeed that had been his aim), Thales returned from Egypt with a theoretical result that was still of the frst magnitude: the idea that, in order to come to know for certain how high a certain pyramid is, all that was needed was for the sun to be at 45° when its shadow fell on its axis. A result like this might in itself have been thought of as powerful inspiration for others to seek out intuitively diffcult measurements. Indeed, there was a certain perfection in the operation Thales proposed, and an almost superhuman promise: to achieve knowledge of the height even of the great pyramid, itself such an extraordinary artefact that, if there were not the other, smaller, pyramids next it, one might have thought it a superhuman work. Certainty about something like this must have excited and ignited the imagination of the (still) young Thales like none of the other accomplishments ascribed to him. This intellectual adventure probably imbued him with a certain investigative tenacity, the search for expedients with which to circumvent obstacles to knowledge, the rejection of approximate solutions and, what may have affected his whole life thereafter, a pleasure in investigating that may well have been superior to any possible expectations, to the point that he resolved to make such research his principal occupation.

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Notes 1 Jedrkiewicz proposed to interpret the references to the measurements of the height of the pyramid as a popular riddle (“the exploit of a sophos”: 2000, 82). But this can be excluded as long as no one can suggest a solution that is imaginative and purely verbal and that does not presuppose a detailed scheme of calculation. Not unlike Vesperini (2017, 2019), Jedrkiewicz insists on making Thales a clown or, worse, a crook, proposing to read many of our reports, including the story about the olive harvest, as mere games. 2 We will see that one of our sources (Diogenes Laertius) suggests a reference to the shadow of a human body, yet with such a suggestion, identifying the moment in which the shadow reaches the same length would be very approximate. 3 Obviously enough, Thales could not talk of 45° but only of the equivalence between the height of an object and the length of its shadow; but this happens when the sun is at 45°. My reference to 45° is conventional and for the sake of brevity. 4 The inclination of the sides of the Great Pyramid (and of the majority of the others) seems to be slightly greater than 50°. Details are available in Verner (2001, 461–465). 5 Panchenko simply states (2016, 786) that “Thales is likely to have visited Egypt”. 6 Caveing (1995, 237–240) mentions the slabs of Akhmin (ca. 2000 BC), the fragments of Kahun and Berlin (ca. 1850), the “Golenischev” (same period), the “Leather Roll” and the “Rhind”, which “surely are the most recent ones: the original one dates between 1850 and 1800 BC, while the copy we have is between 1700 and 1600 AD. As for their actual content, all these texts date back to the XII dynasty; they are examples of hieratic writing.” 7 It is interesting to note that something along the same lines happened in Mesopotamia in the second millennium, as I read in Caveing (1995, 21–23). It is also to be noted that Neugebauer 1955 dealt exclusively with the ephemeris detected during the Seleucidan period, hence with something dating not earlier than the third century BC (and so wholly irrelevant for Thales). 8 IG I2 352, for example, begins with data about the initial balance, carries on with the money coming in and with detailing how much was spent to buy materials (for workers, for sculptors) and on monthly pay (we do not know for whom); after all this, it ends with the closing balance. See also Faraguna 2008. 9 The contrary of the extraordinary optimism manifested by Caveing (1997, 33–53). 10 See again Hahn (2017, 97), as reported above in Sections 1.5 and 4.1.2. 11 An Egyptologist of repute, Danijela Stefanovic (working in Belgrade and Vienna), has written to me: “The curiosity so characteristic for, let’s say, Western – democratic – people (I am aware that this is a politically incorrect statement!) was unknown to Ancient Egypt. A pyramid is a tomb, a house for preserving and maintaining the royal KA of the deceased ruler, and as such in a way an element of a divinely created order which humans need to maintain on earth (maat). A king is not a divine being by his birth. When chosen, during the ‘coronation’ ceremony, the gods reshape his nature and establish a special link with their world. In the same time, all divine KA-s of his predecessors (coming from their tombs) are joining the KA of the new king. With all this, a special link between king and god is established, and in Ancient Egypt, the king is the only living creature with such abilities (Pyramid texts are preserving elaborate accounts). Just for example, in Egyptian mythology gods do not interact with humans, that is, as you know better than me, in sharp contrast with Greek and Roman mythology, but also with Mesopotamian. So, the royal tomb is a part of the divine plan, a necessary element for preserving the cosmic order. An ordinary human cannot question such things, or to be curious to check anything (however, there are

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12 13 14

15 16 17 18 19 20 21

22 23

texts questioning ‘the existing situation’, but again they were created to justify the restoration of the divine order). In addition, royal funerary complexes were guarded. We know, for example, that the prince Khaemweset, one of the sons of Ramses II, restored the monuments of earlier kings (according to the statement preserved on the pyramid of Djoser) but again for preserving and maintaining their KA-s.” In Naturalis Historia 36.82 (=11A21 DK = Th107 W = 5R31b LM): Mensuram altitudinis earum omnemque similem deprehendere invenit Thales Milesius umbram metiendo, qua hora par esse corpori solet. He is talking of a fictional character, Nilossenus of Naucrates, who rather generically alludes to a Pharaoh. The clause hē skia pros tēn skian logon eiche is worth highlighting as much as the relationship being established: the short shadow is to the long one as the short object is to the long one, i.e. A:B:C:D. I translate from Plutarch, Convivium Septem Sapientium 2.147A (=11A21 DK = Th119 W = 5R31c LM): ἐπεὶ σοῦ γε καὶ τἄλλα θαυμάζει, καὶ τῆς πυραμίδος τὴν μέτρησιν ὑπερφυῶς ἠγάπησεν, ὅτι πάσης ἄνευ πραγματείας καὶ μηδενὸς ὀργάνου δεηθεὶς ἀλλὰ τὴν βακτηρίαν στήσας ἐπὶ τῷ πέρατι τῆς σκιᾶς ἣν ἡ πυραμὶς ἐποίει, γενομένων τῇ ἐπαφῇ τῆς ἀκτῖνος δυεῖν τριγώνων, ἔδειξας ὃν ἡ σκιὰ πρὸς τὴν σκιὰν λόγον εἶχε τὴν πυραμίδα πρὸς τὴν βακτηρίαν ἔχουσαν. Our source is Diogenes Laertius, Vitae 1.27 (=11A1 DK = Th237 W = 5R31a LM): ὁ δὲ Ἱερώνυμος καὶ ἐκμετρῆσαί φησιν αὐτὸν τὰς πυραμίδας ἐκ τῆς σκιᾶς, παρατηρήσαντα ὅτε ἡμῖν ἰσομεγέθεις εἰσίν. But the statement is not very accurate, it seems: see below, Section 4.1.4. I repeat that a useful prospectus is to be found in Verner (2001, 461–465). One possibility is that he came back to Miletus with regret at not having been able to produce a measurement that was not approximate. Flavia Marcacci kindly alerted me to this point. The line would have to mark all the points equidistant from O and H. After all, our sources just say that he “measured” (ekmetrēsai). Given the lack of further information, we may have thought either that Thales took a measurement and managed to give an answer, or that he “managed to understand how to do it”, or that “he taught how to do it”, or that “he made those pyramids measurable”. The fact is that our sources report this activity of measurement in a rather imprecise way. I discovered this through Couprie (2020). Thales would have known how to use only the most simple proportions (e.g. 1:1, 1:2), while Redlin and others have no difficulty in considering a much wider range.

5

Thales dates the tropai

Compared to measuring the pyramids, fxing the dates of solstices and equinoxes would have required even more demanding investigation, and an entirely new epistemological challenge.

5.1 From curiosity to a research plan It is, once again, signifcant that we have any information about Thales’ research on the tropai (the solstices) given how diffcult it must have been for his own contemporaries to grasp how important it was to fx their exact dates. Diogenes Laertius, in his Lives, tells us that Thales “was the frst to predict eclipses of the sun and to fx the solstices; so Eudemus states in his History of Astronomy”.1 In another place, he says that Thales “was the frst to determine the sun’s course from solstice to solstice”,2 adding a bit later that “he is said to have discovered the seasons of the year”.3 Hero of Alexandria and Theon of Smyrna,4 in turn, report exactly the same: “in his work Astronomy5 Eudemus reports that… Thales [was the frst to discover] the eclipse of the sun and that its path between the solstices is not always equal”;6 Apuleius talks of solis annua reverticula.7 Similarly, in a scholium to Plato’s Republic, we read that Thales “was the frst of the Greeks to recognize the Little Bear and the solstices”.8 Note that, among these sources, those which link Thales closely to the tropai show no interest whatsoever in enlarging on their information, nor do they offer it in a context which suggests that it matters very much to them (when we ask whether a given sources is trustworthy, this is an important feature). The sources for the dating of the equinoxes (see Chapter 6) are another indicator that these testimonies are trustworthy, since the dating of the equinoxes was, one can presume, an operation complementary to the dating of the solstices, and in fact would have been rather harder. It would be surely too hasty to assume, with Graham (2013, 50), that “there is one way one might ‘predict’ a solstice without advanced methods: one might do one’s best to identify a solstice and then use the 365-day year to anticipate the next”. This does not do Thales’ work justice. As I have hinted DOI: 10.4324/9781003138723-7

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in Section 2.3, if Eudoxus, Euctemon before him, and Anaximander before them strove to improve Thales’ estimates about the number of days intervening between the autumnal equinox and the dawn setting of the Pleiades, this means that they took Thales’ dates for the equinoxes seriously, and took his dates for the solstices even more seriously. And someone who worked out how to measure the height of the pyramids might well have been capable of putting exact dates to the solstices. Another objection by Graham (ibid.) is that “for several days around the solstice the sun hardly seems to move”. But this does not take into account the fact that Thales could have carefully dated the last perceptible movements before the solstice and the frst perceptible movements after it, so as to identify the day in the middle of the two extremes as the exact day of the solstice. He would not have needed elaborate skills, either technical, mathematical, or procedural, to do this. He would certainly have needed to be careful in taking the actual measurements, but there is no reason to suppose that Thales was unable to do that (more on this point in Section 5.2.2 below). It is also worth highlighting the fact that no one else – until at least Epicurus – seems to have had any interest in making this kind of measurement.9 The fact that our sources are generally late does not mean that they are likely to have misidentifed Thales’ interests here. The sources differ in detail; but they are reporting a rather complex idea. The three statements in Diogenes Laertius cohere rather well: Thales managed to predict the tropai, discovered the passage from one tropē to the other, and discovered the times (that is, the seasons) of the year – likely based on the dates of both tropai and equinoxes. Hero and Theon of Smyrna tell us that he was the frst to specify the sun’s cycle as given by the tropai. Let us then ask, to begin with, what “the passage from one tropē to the other” refers to. There can be little doubt about this. We know for sure that the term tropai refers to “changes” of the sun, namely those that take place when days stop shortening and begin to become longer and vice versa. These changes were thought of as “turns” (tropai), because they were characterized by fairly observable reversal. That a semi-annual tropē takes place in June and in December is not only evident, it is also an important marker for the year: so this was something that, at Thales’ time, was already known and could not be taken as a novelty. To get approximate dates, only some simple observations need to be made with the eye – they do not even need to be particularly accurate. So, for example, one could remark that in Greece (and, more generally, in the Northern hemisphere) in June the sun rises ever more to the observer’s left, and sets ever more to the right; but a moment comes when this trend seems to stop, and the opposite starts to happen. It is obvious, then, that Thales must have done more than to teach what many people already knew, that is, that the tropai take place twice a year. If he became known for having ‘identifed’ and ‘predicted’ them, this must be because he managed to establish how many days there are between one tropē

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and the other, between solstices and equinoxes – and also to tell people, on a fairly solid basis, how long a year is. A hint in this direction is given by the report concerning the number of days that lapse between the autumn equinox and the setting of the Pleiades at sunrise. Pliny the Elder says this: Hesiod … reports that the morning setting of the Pleiades takes place at the autumnal equinox, Thales twenty-fve days after the equinox, Anaximander thirty-one, Euctemon forty-three, and Eudoxus forty-eight.10 Euctemon was an Athenian, slightly younger than Socrates (460–390 BC), who was famous as the author of a calendar, called Parapēgma, reporting the dates in which the constellations rise and set.11 We know something about it because many sources give us information on the dates of astronomical events like this; they do so by relying on the dates of solstices and equinoxes (which are useful also giving rough indications of the actual phases of meteorological and agricultural cycles). Euctemon is often mentioned for information he gathered about some day of the calendar or other.12 As for Eudoxus of Cnidos (south of Miletus), he lived between 395–390 and 345– 340 BC; when he was in his thirties, and Plato went on his second trip to Syracuse, Eudoxus stood in as head of the Academy. As an important mathematician, his name was closely associated with, among other things, the idea of concentric heavenly spheres, whose movement could explain anomalies which seemed to affect the motion of the planets. One can easily guess that the interest of Euctemon and Eudoxus was fed by access to a work which reported the measurements carried out by Thales and Anaximander. As for Hesiod – he wrote, in Works and Days 383–384, that the exact period when one can attend to ploughing and hence to sow wheat is when the Pleiades set at dawn. A bit later in the text (448), Hesiod makes it clear that the right time is when the cranes fy overhead. This is of course an approximate indication (the dawn setting of the Pleiades will only occasionally coincide with the fight of the cranes in any given place). The relevant fact here is that both Thales and Anaximander put a fgure on the number of days between the equinox and the setting of the Pleiades at dawn: 25 and 31, respectively. This means that they disagreed on the length because they presumably disagreed on the date of the autumn equinox.13 So Thales cannot have limited himself to giving an approximation. We have to presume that he could say how to date both solstices and equinoxes with some accuracy. It is highly likely that he was the frst person to do this. The dates had always been known approximately; but after Thales, they were more precisely identifed. This means that Thales learned how to give exact dates to both tropai and isēmeriai. How did he do this? With what degree of accuracy? We cannot know the answer for sure, but we can offer some conjectures.

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5.2 Some possible expedients 5.2.1 Five conjectures There are a few methods compatible with the culture of Thales’ time that he might have used to achieve his goal. (a) The most intuitive method consists in concentrating the attention on that point of the horizon at which the sun rises in the morning and the one at which it sets in the evening: in June, the distance between these two points reaches its greatest, while in the second part of the year the two points get closer, so as to reach their maximal proximity in December. It is therefore possible to restrict observation to that point of the horizon where the sun rises, and sets, so as to locate the points of greatest distance in June and those nearest in December,14 and note the dates. On this hypothesis, it would be simpler if Thales could have fxed the point under observation and the position of himself as observer,15 and devised a way to set up a series of poles in the ground close to each other,16 which he could use to measure the progress of the sun – to be able to say, for example, that yesterday the sun rose closer to the fourth pole, while this morning it was closer to the ffth. The only limitation is on how precisely Thales could have judged the position of the sun relative to these poles. (aa) A brief remark is merited on the hēliotropion (“the tool with which the tropai of the sun are measured”), which, according to Diogenes Laertius 1.119, existed on the island of Syros, home of Pherecydes. Diogenes’ account brings to mind the place that Homer (Od. 15.403–404.) called “Syria… above Ortygie, where are the turnings of the sun”. A scholiast on this passage writes: “they say that there is a cave of the sun (entha phasin einai hēliou spēlaion), by means of which the people living there sēmainontai, take note about, the sun’s tropai.” A second scholiast adds: “They say there is a cave of the sun there, through which they mark the sun’s turnings. As it were towards the turning of the sun, which is the westward direction, above Delos”. A third scholiast adds that this information comes from Aristarchus and Herodianus. In fact, Syros is west (and slightly north, i.e. ‘above’) Delos (=Ortygie), so the scholiasts’ reference to the hēliotropion at Syros, albeit lacking precision, is to the point. But what can we learn from this? Perhaps that Pherecydes managed to set up a hēliotropion on his island, in a cave, by means of which he could account for the dates of the tropai? On this hypothesis, there should have been a place in the cave which the sunlight reached only at the summer solstice. But could this have happened? Kirk–Raven–Schofeld plausibly remarks (1983, 54 ff.) that, if such a tool ever existed on the island of Syros, it must have been set up at a later age – specifcally, during the Alexandrian period, when it would have been natural for someone to establish “a historical

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association between the only two apparently scientifc products of Syros – Pherecydes and the solstice-marker”. This is confrmed by the fact that the coinage hēliotropion does not appear to be very old. So this account can tell us nothing about how Thales might have studied the tropai. (b) A possible alternative consists in taking note of the shadow of a vertical stick. Thales must have known that the highest point the sun reaches at noon is always (though perhaps not exactly because of the lemniscate: Section 4.1.3 above) at the same point in the south; as a consequence, as the shortest shadow of every day will lie (with some irrelevant approximation) in the same direction, lengths become relatively easy to mark, and then compare. So Thales could have compared the noonday shadows of June to identify the days when it is shortest: then he would know when the summer tropē occurs. In the same way, the longest noonday shadow in December would signal the winter tropē. The taller the pole (ensuring that it is set perfectly vertical and well-rounded on the top), the more accurate would be the data to be compared. (c) Further uses of shadow-casting sticks are possible. The frst consists in following the procedure in (a), but instead of observing how far the sun goes toward North-East in June when it emerges on the horizon, one observes how far the very frst morning shadow formed by the pole of a gnomon goes in the opposite direction on an ad hoc wall,17 and this in the relevant periods, both of June and December. (d) As an alternative, one can use the same stick to note the positions of the sun’s shadow at noon. Consider the summer solstice. In the Northern hemisphere (hence, in Miletus), in the second half of the year, at noon, the sun stops lower and lower; if we have a gnomon, this tool will generate a shadow that gets shorter and shorter. The decremental differences would be millimetric, but, theoretically speaking, one could identify the shortest shadow of all, which would occur sometime in late December (according to our calendar). At least, one could identify those days in which the length of the shadow seems to remain the same: the day at the midpoint would be easy to work out. The same procedure could be put in place to fnd out the longest day of the year, when the meridian shadow stretches to its maximum. 5.2.2 A comparative assessment Let us now weigh the pros and cons of each hypothesis. To begin with: that Thales used a gnomon in the demanding ways envisaged by hypotheses (c) and (d) is hardly credible, not least because he could rely on more direct observation strategies. Some sources tell us that, while observing the sun, when the date of the solstice approaches, the sun rises more and more towards the North-East or sets more and more towards the North-West, but at a certain point it stops and, within a few days (two or three weeks?), it begins to reverse its path. All this was frstly remarked, it seems, by a possible pupil of Thales, Cleostratus of Tenedos, and two other contemporaries of his, Matricetas and Phaenus.18

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This report may allow us to conclude that this is the method Thales had devised. But how precisely could the position of the sun have been measured relative to a given marker? The measurement of the length of the shadow on the ground would have allowed for far more accurate measurement, as long as one could count on a rather tall (and pointed) vertical pole.19 One might only wonder whether Thales might have run the risk of ridicule by dedicating himself to the obsessive measurement of shadows. For all the hypotheses taken into consideration so far there is systemic diffculty. Around the solstice, the differences in the position of the sun become so small that it is impossible to discern the exact day of the tropē. When the sun ‘stops’ and then turns back, its maximum (or minimum) height remains substantially unchanged for several days.20 As previously suggested, there is a remedy. It is not trivial. One has to give up the attempt to see which is the topical day and be content with conjecture based on estimation from the many days in which the position of the sun seems constant, and identifying the midpoint as the likely day21 of the solstice. Note, though, that it would be easier to do this using the meridian shadow than direct observation of the rising (or setting) of the sun, because it would be easier to mark for reference the days in which the shadow remains the same. Is it conceivable that Thales used dichotomy in order to identify the middle date? I would say yes, since it was a structural feature of his investigations to look for a solution allowing him to establish something frmly. Why not in this case too? Besides, if it is reasonable to presume that the tropē occurs at a certain day, would the intermediate day not be the best candidate?

5.3 The possible complications of an investigation carried out over many years Methods of calculating the length of the day, identifying where the sun rises every morning (in order to accurately identify the six hours that go from dawn to noon), etc., are documented in cuneiform texts produced in the Persia of the Seleucids (third and second centuries BC), but seem to have no earlier precedent (see Neugebauer 1975, 366–373). Greek astronomy reached, thanks above all to Hipparchus of Nicaea (second century BC), incomparable new levels of precision. This can be seen, among other things, in the precision with which, at the time of Hipparchus, the eccentricity of the solar orbit was described. Relying on Hipparchus, Ptolemy reports, for example, that the sun takes 94½ days to go from the spring equinox to the summer solstice, while it takes 92½ days to go from the summer solstice to the autumn equinox.22 The distance of these astronomers from Thales (who certainly could not consider half-days) is obviously enormous. In times and societies foreign to Thales, astronomers were able to obtain not only accurate and useful data, but also make use of extended observations (over years) conducted, not at the whim and expense of a private citizen, but with

72  Five quantitative inquiries the support of a powerful (and rather enlightened) state authority. It is no coincidence that the definitive introduction of the leap year occurred only much later, in the context of institutionalized research projects like this. 5.3.1  Thales and the leap year Our sources tell us that, once the date of one or two consecutive tropai had been established more or less precisely, Thales tried to establish how many days elapse between the summer and winter solstices and, again, between the winter and summer solstices, and that this way he established precisely how many days there are in a year. This gives us a very important insight. Any attempt to date the solstices would require methods of taking, recording and interpreting the data – and dealing with the possibility that, because of bad weather or for other reasons, from time to time a whole solstice might pass without observations being possible. Likewise, the aspiration to establish how many days there are between two solstices would require surveys, to be entrusted to one or more collaborators, and repeated observation to correct for inevitable inaccuracies and errors. This is a process that could not fail to take several years. Moreover, since the figure of 365 days is an odd figure, the duration of the two semesters marked by the tropai have to be, of necessity, 182 and 183 days, respectively, something that certainly will not have been easily confirmed by observational data. Panchenko (2016, 788), on the basis of an Arabic text referable to Galen (Th487 W), went so far as to affirm that: “It is equally conceivable that Thales was able to establish that the duration of a year was 365 days and a quarter instead of 365 days”, but in order to identify the delay of six hours, much more sophisticated research, based on observations taken over decades, would have been needed, and it is unthinkable that a private individual, however keen and wealthy, could have conceived and implemented such an ambitious programme. Moreover, “no parapēgma contains a reference to the leap year”.23 It is therefore possible that Thales observed occasions when three semesters in succession contained 183 days (due to the accumulation of those six additional hours which, in our society, give rise to the leap year), but not that he saw the importance of this detail. For him, it would have been more logical to attribute the anomaly to a small error that occurred in counting the days. Besides, the method of identifying the exact day of the solstice by looking to the midpoint of the period in which the sun seems to stay still (n. 21, above) is by its nature liable to little inaccuracies. 5.3.2 Ho¯s ouk ise¯ aei sumbainei Hero and Theon, as noted in Section 5.1 above, reported that, according to Eudemus, “Thales [was the first to discover]… that the path [of the

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sun] between the solstices is not always equal”. The statement is likely to be signifcant in this context. In fact, it speaks of an ancient expert who, unlike countless others, was not satisfed with researching and identifying forms of regularity in cosmic events but also as someone who took seriously suggestions of irregularity. In fact, Thales’ name is associated with the detection of two other anomalies. One concerns the duration of the new moon and the other those apparently inanimate bodies which, to our surprise, reveal themselves to contain kinetic energy (see, respectively, the Appendix to Chapter 7, and Chapter 11). This interest in anomalies is unusual, and is not ascribed to anyone else for some generations. This seems to be another of Thales’ virtues. In this case, however, the reference to the peculiarities of the annual cycle, and frst of all to the tropai, is not helpful since the tropai are distinguished, if anything, for their regularity. Even the fve days that prevent the neat division of the year into months of 30 days each are a constant. The equinoxes too are phenomena with a high level of regularity. It is therefore very diffcult to identify a plausible reason for speaking of irregularities in relation to tropai. Nothing disproves what is reported by Hero and Theon, but the reference to the annual cycle conveys no plausible information. So we can only report the testimony, and admit that we do not know what it is alluding to.

5.4 Cognitive curiosities and intangible assessments The fgure of a sophos who aimed to acquire precise knowledge is beginning to emerge. Thales not only devised devices for discovering knowledge; he also set up a substantial – and expensive – programme of surveys to be carried out over several years. And it is likely that each new result strengthened his confdence (and that of an ever-growing circle of people around him) in the value of repeated observation. In fact, it stands to reason that he needed repetition, and confrmation, not only to be believed by other people, but also to believe himself in the soundness of his procedure. In the meantime, however, he would have needed to bear costs (e.g. in order to be able to count the 182 or 183 days with the utmost care). All this while he will have been well aware of the fact that the beneft of the investigations on the tropai consisted in something quite intangible: just dates and numbers! There was something unheard of in all this. Knowing how to determine the height of an Egyptian pyramid and how to determine exactly when the tropē takes place (and the further enquiries to which that led) indicates an interest in abstract values that no one who was used to riddles, or Aesop’s fables, or the maxims that the sources associate with some of Thales’ contemporaries, or the invention of the alphabet and numerals, etc., could have been able to appreciate. In fact, wider interest in the value of the abstract comes only with Plato, some two centuries later.

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Notes 1 In Diogenes Laertius 1.23 (=11A1 DK = Th46 e Th237 W ≠ LM), we read: δοκεῖ δὲ κατά τινας πρῶτος ἀστρολογῆσαι καὶ ἡλιακὰς ἐκλείψεις καὶ τροπὰς προειπεῖν, ὥς φησιν Εὔδημος ἐν τῇ Περὶ τῶν ἀστρολογουμένων ἱστορίᾳ. 2 In Diogenes Laertius 1.24 (=11A1 DK = Th237 W = 5R14 LM) we read: πρῶτος δὲ καὶ τὴν ἀπὸ τροπῆς ἐπὶ τροπὴν πάροδον εὗρε. 3 In Diogenes Laertius 1.27 (=11A1 DK = Th237 W ≠ LM), we read: τάς τε ὥρας τοῦ ἐνιαυτοῦ φασιν αὐτὸν εὑρεῖν. The fact that Diogenes goes back to the topic after having written on something else may be taken as evidence that he got his information from a source that was different from the one used in 1.23. 4 The mathematician and inventor Hero of Alexandria, who must have lived in the frst century AD, was a brilliant scientist; Theon of Smyrna, who was active between the end of the frst and the beginning of the second century AD, was not so signifcant as a scientist. 5 The title of this work by Eudemus (who was a direct pupil of Aristotle) is commonly given as History of Astronomy. However our sources call it also Peri tōn astrologoumenōn (“Investigations on the celestial bodies”) and Astrologiai (“books of Astrology”, i.e. science of the celestial bodies). 6 Both Hero in Defnitiones 138.11 (=Th93 W) and Theon of Smyrna in De utilitate mathematicae 198.14–18 (=11a17 DK = Th167 W ≠ LM) write that Εὔδημος ἱστορεῖ ἐν ταῖς Ἀστρολογίαις, ὅτι Οἰνοπίδης εὗρε πρῶτος τὴν τοῦ ζῳδιακοῦ διάζωσιν καὶ τὴν τοῦ μεγάλου ἐνιαυτοῦ περίστασιν·Θαλῆς δὲ ἡλίου ἔκλειψιν καὶ τὴν κατὰ τὰς τροπὰς αὐτοῦ περίοδον, ὡς οὐκ ἴση ἀεὶ συμβαίνει. More on this statement below, Section 5.3.2. 7 In Florida 18.31 (=11A19 DK = Th178 W = 5R13 LM). 8 Scholia vetera in Rempublicam 600a (=11A3 DK = Th578 W ≠ LM): καὶ μικρὰν ἄρκτον αὐτὸς ἔγνω καὶ τὰς τροπὰς πρῶτος Ἑλλήνων. Strictly speaking, egnō means that Thales was the frst to know, to get some information on, to teach something meaningful about, the tropai. 9 I do not mean, of course, that there were not sporadic attempts to reconstruct Thales’ measurements, but that no one, apparently, tried to undertake new measurements of their own. Aristotle, for instance, mentions solstices and equinoxes many times in the Meteorologica, but he does so only to collocate certain events in given periods of the year, without entering dates. 10 In Nat. Hist. 18.213 (=11A18 DK = Th106 W = 5R21 LM): occasum matutinum vergiliarum Hesiodus … tradidit feri, cum aequinoctium autumni confceretur, Thales XXV die ab aequinoctio, Anaximander XXXI, Euctemon XLIII, Eudoxus XLVIII. 11 On the Parapegmata, Lehoux (2007) is fundamental, but see also Neugebauer (1975, 587–589). 12 On Euctemon, see Hannah (2002). Democritus of Abdera, who must have been older than Euctemon, is usually regarded as the frst person to gather this kind of information. The textual evidence available (not less that 50 reports) are gathered in 68B14DK, and in only one case a title is given. For reasons I am unable to grasp, Laks–Most accepts only two pieces among a much fuller set of references. 13 One possibility is that Anaximander took the equinoxes as occurring some 91 days after each solstice, i.e., without considering the difference between equinox and observable isēmeria (Section 6.2.2 below). 14 This obviously applies to the Northern hemisphere. 15 Corre (2015, 353) has insightful remarks on the second aspect. 16 A modern story – Our Lady Goddess & The Femicide of the Heroes (see https:// www.academia.edu/34749607/Our_Lady_Goddess) can help us understand. Santilli relates of a lady who at the beginning of the summer opens a window,

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18 19 20

21

22 23

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early in the morning, to sing a song to the rising sun. Now and then, she asks a boy to put a stick in the very place in which the sun rose every day. The series of sticks becomes denser, with many more sticks east-oriented, but a day comes when the boy is ready with a new stick and the lady tells him: “we do not need another; now the sun goes back”. This option, although slightly modifed, is to be found in Charles Kahn (1970, 114): “They need only have set a vertical gnomon at a place with a clear view of eastern and western horizons, and noted the line of the gnomon’s shadow each day at sunrise and at sunset”. I remark that to do so, the gnomon needs to be installed on a vertical wall, oriented east-west, and of considerable dimensions even if the stick is very short. This is likely to have been impracticable. These three already appeared in Section 3.5 and will again be taken into account in Section 6.3.2. On the contrary, the short horizontal axis of a gnomon would make it much more diffcult to single out almost identical positions, all the more if each daily position should be associated to a date. Corre (2015, 352) rightly said that the tropai “take place very slowly, and it is diffcult to say on which day they occur. … We could even believe, and for a long time, in a stop extended for several days, of which the Latin etymology of the term still testifes today (from sol ‘sun’ and sistere ‘stop’) … Dicks (1972, 172) estimates such imprecision in nine days of uncertainty ‘with optimism’.” Corre (2015, 357) rightly spoke of a dichotomy. O’Grady (2002, 161): “For several days the Sun seems to rise at the same spot, the difference being negligible. If he halved that period of days when the Sun seemed to rise at the same point, and declared that day to be the solstice, he may not have been far wrong.” Neugebauer (1975, 58) (he refers to Ptolemy, Almagestum 3.4). Lehoux (2007, 87) with reference to the parapēgmata (which survives, at least in part). Lehoux also observes (ibid.) that those who made use of parapēgmata probably needed, for their correct use, to have recourse to an external source of knowledge: the date of the summer solstice. In this way the parapēgma was calibrated, so as to adjust for the imbalances associated with the accumulation of delays of about six hours per year. See also Lehoux (2007), 80 ff.

6

From the dating of the tropai to the dating of the ise¯meriai

6.1 In search of other ‘cosmic’ dates: the sources There is good evidence that Thales was able to identify the days of the tropai and use them as starting points for other dates and durations which mark the year. The possibility that his dating of the tropai was not his only achievement is based both on positive information (which, in my opinion, leaves little room for doubt), and on the length of time (fve years? six years?) he must have taken to work on establishing the tropai. Diogenes Laertius reports that Thales divided the year into 365 days and ‘found’ the seasons of the year.1 He also tells us that, according to some, Thales wrote only two works, On the Tropē and On the Equinox.2 The Suda (under “Thales”) reports that he wrote various works, including one entitled On the Equinox. And the Suda goes on to report that he kateilēphen (understood, explained) tas isēmerias, the equinoxes.3 Furthermore, Pliny relates4 that Thales was able to establish (further) that the dawn setting of the Pleiades5 occurs 25 days after the autumn equinox: evidently, no one could have said ‘how many days later’ without knowing (i.e. believing that they had correctly identifed) the exact day of the autumnal equinox. There is no counter-indication to these converging voices; and we should keep in mind that, except Anaximander no one else showed any interest in these fndings for a century or more after Thales. So the fact that our sources for Thales are late does not, in itself, constitute a reason to doubt them. If it is reported that Thales believed that he was able to establish how many days after a certain isēmeria a certain event took place, and if Anaximander, Euctemon and Eudoxus took the trouble to correct the number of days he proposed6 (and that despite the fact that there may have been no one else who was even interested), then we have a solid reason to believe that Thales really did posit a gap of 25 days. This in turn make it reasonable to assume, frst of all, that Thales ‘worked’ on the dating of the equinoxes no less intensely (and with no less concrete results) than on the dating of the solstices; consequently, and for the reasons indicated (Section 5.3.1), it is very likely that he was also interested in the duration and partitions of the year as a whole. Consequently, it is not

DOI: 10.4324/9781003138723-8

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surprising to learn, from various sources, that he not only taught that the year is 365 days long, but he also identifed quarters (between solstices and equinoxes) and months, as well as the exact date of the dawn setting of the Pleiades, and perhaps similar dates for other constellations, following what was asserted for example by Hesiod (see Section 6.3 below). So, the sequence of dated events he established probably extended to several other astronomical facts. If this were the case, his data collection might even, in theory, have given rise to a calendar (or parapēgma) based on the experimental dating of the four fundamental astronomical events of the year. Recall that, according to Diogenes Laertius (1.24), Thales was also the frst to call the last day of each lunar month triakas (“the thirtieth”).7 The word triēkadas already appears in Hesiod (Works and Days 766), with the specifcation that “the thirtieth day of the month is the best to inspect the works and distribute the agreed rations”.8 Furthermore, Aristarchus of Samos, who in POxy 53.3710, col. 2, r. 41–42 (=Th91 W = 5R17 LM) talks about Thales, has occasion to observe that what “some call triakas and others noumēnia” (‘the new moon’) is the eclipse (or, rather, the day on which the solar eclipse did or could take place).9 So Diogenes Laertius may not be right about the authorship of this neologism – and he is certainly wrong about others too (e.g. he was able to argue that the term antipodes was invented by Plato, although it appears to have been used already by Zeno of Elea).10 But while triakas is only a name, quarters and months are important notions that cannot ignore the extra fve days that disrupt the division of the year into periods of 30 days. And knowing that Thales also worked on these topics is very important because, if he arrived at the correct dating of the equinoxes in the absence of clocks, it is likely that the operation was much more demanding than the dating of the solstices.

6.2 The strategy most likely adopted. Astronomical equinox or equilux? To be able to say that Thales tried to date the equinoxes too, and achieved good results, does not yet mean that we know how he did it. In theory, he could have contented himself with saying that the equinox can only take place in the middle of the 182 or 183 days of a semester, that is, at 91 days after the last observed solstice, or thereabouts. This is often suggested, recently, for example, by Stephen White (2008, 14). However, Thales, who was distinguished for the meticulous accuracy of his other measurements, would surely have been interested in empirical verifcation of this duration. This seems more than likely if only because the Greek term, is ē meria, expressly speaks of effective equality between the two parts of the day, one with sunlight and one without sunlight. Now the is ē meria day is not something to be identifed deductively; it requires the right measurements.

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6.2.1 The Charles Kahn Conjecture The hypothesis put forward by Charles Kahn (1970, 114) tries to ignore this need. Kahn started from the observation (or rather, from what, as he writes, Howard Stein told him) that, on the day of the equinox, and on no other day of the year, the morning shadow and the evening shadow together form a right angle (I suppose Kahn meant to refer to the direction of the frst shadow formed at sunrise and the last shadow formed at sunset). He says: But to use it [the gnomon] for equinoctial observations, one does not even have to compare the line of the shadow from one day to the next: the equinoctial phenomenon can be recognized on the day when it occurs, and consists simply in the fact that the morning shadow and the evening shadow form a straight angle, i.e. are diametrically opposed.11 The conjecture was defended by Graham (2002, 359 n.), and in favour of it there is Thales’ apparent familiarity with right angles (e.g. as used in measuring the height of the pyramids: see Chapters 5 and 13). However, there are other considerations which diminish its attraction: (1) although the stick was used to measure the height of pyramids, and this reminds one of the gnomon, no source associates Thales with the use of a gnomon; (2) to acquire the data of which Kahn speaks, he would have needed to have a gnomon installed on a vertical wall, carefully oriented East-West; (3) he would have needed a large and functional square, with very precise angles, to be hung in a strategic position, its vertex coinciding with the shaft of the gnomon; (4) moreover, he would have needed to carry out observations with a precision more than millimetric; (5) and the measurements would have had to be repeated for several days (certainly not just for the day of the equinox, as suggested), to spot when the coincidence was perfect. These are already contraindications of some weight, but weightier still is (6) the possibility that the idea did not even occur to Thales in time, (7) that he was not able to set up a large square to hang in the way required, and also (8) that he did not have a highly developed awareness of the potential of the gnomon. Brilliant ideas may not come immediately or at all, and it needs to be shown that Thales had the necessary familiarity with the instrument. What is more, an approach like this to the equinox does not make reference to the duration of day and night, which would have been what Thales was interested in. 6.2.2 From the equinox to the equilux There are additional complications. To identify equal duration, astronomers have learned to use the notion of equilux, distinguishing it from the moment (or rather: from the day) in which the sun happens to fnd itself perpendicular to the equator. The commonly used astronomical equinox (dated to 21st

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March, etc.) takes place, predictably, on dates almost equidistant from the two solstices; but this is not the date on which duration of day and night is equal. In Europe, the night is the same length as the day two to three, or even four days before the spring (astronomical) equinox, two to three, or even four days after the autumn equinox. So if we count by the days of equal duration, the September–December quarter and the December–March quarter are signifcantly shorter than the other two quarters (by approximately one week each). A glance at our calendars allows us to see only that, if 90 days elapse from 21st December to 21st March, the following quarter is 92 days long, and something similar happens in the second semester. But reference to the equilux gives us a much larger difference between the two colder quarters and the two warmer ones: they are around 88 and 94, and 87 and 95 days, respectively. Besides, as our world is illuminated from the very frst appearance of the sun until it has completely set, an evident 12-hour isēmeria (or equilux) can only occur several days before the vernal (and after the autumnal) astronomical equinox. On these grounds (not to consider further intricacies) to date the actual occurrence of an equilux is rather complicated. Now the Greek term isēmeria suggests precisely the same length of day and night; therefore, the same effective and verifable duration is the identifying mark of an isēmeria. It can be deduced that Thales probably tried to date the actual occurrence of the isēmeriai. I therefore propose that Thales set himself the Sisyphean task of pouring (or rather, making other people pour) small quantities of water into an hourglass12 (a simple container with small hole), continuously, night and day, for at least two weeks, keeping exact count of the buckets of water poured in each day and each night.13 It is an easy conjecture that the number of buckets poured (or collected) during the night and those poured (or collected) during the day would initially be unequal, then become approximately the same and then return to being unequal (but in the opposite proportion) whatever the criterion used to decide exactly when the day begins and when it ends. This is a conceptually simple and direct solution – albeit an expensive one, because the task would have required the coordinated intervention of many people: a frst group with the task of pouring water into the hourglass (or both pouring in and collecting the water coming out of the hourglass), alternating without interruption; a second ‘team’ responsible for signalling the moment of transition from night to day and from day to night with nonrandom criteria14; and a third ‘team’ responsible for keeping count with the utmost care. On the other hand, the formula would certainly have worked to identify the stretch of days within which the isēmeria occurred, and perhaps even to identify the exact day in middle of these. 6.2.3 Analogies with the strategy adopted by Cleomedes A page of Cleomedes of Astypalaea – an astronomer who lived six or even ten centuries after Thales, and whose Caelestia is expressly dedicated to

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spreading the astronomical knowledge of the Stoics – has the singular merit of describing a method of detection very similar to the one hypothesized above. In 2.75, he discusses how an hourglass can be used to establish another typically Thalean proportion, that between the angular amplitude of the sun and the course of its 24-hour cycle, which traces a round angle (360°).15 Cleomedes proposes to start by establishing how much water fows out of the hourglass as the sun rises (from when the sun makes its frst appearance until the full disk becomes completely visible), and then take that amount of water as his unit of measurement. The next operation would have consisted in keeping track of the number of cups flled with this quantity of water went through the hourglass in a 24-hour period (from dawn to dawn). Cleomedes declares the answer to be 750. This proves nothing about what Thales did, of course; but what it does do is to show that, even several centuries later, manual counting by this sort of method over long durations (24 hours) was considered practical and not at all bizarre.

6.3 Equinoxes and constellations, Cleostratus 6.3.1 Generalia As I noted above (Section 5.1), Pliny the Elder reports that: occasum matutinum vergiliarum Hesiodus… tradidit feri, cum aequinoctium autumni confceretur, Thales XXV die ab aequinoctio, Anaximander XXXI, Euctemon XLIII, Eudoxus XLVIII.16 This comparison of thinkers from Hesiod to Eudoxus was not the work of Pliny himself, but perhaps of Theophrastus, and must have been based on documents dating back to different eras. That makes it quite likely that what is reported corresponds to the truth. In addition to the Pleiades, Thales seems to have dealt with the Hyades. In fact, in one of the scholia to Aratus’ Phaenomena, we read that, according to Thales, there are two Hyades, a northern constellation and a southern one.17 So it might be that he was interested in the dawn setting not only of the Pleiades, but also of the Hyades and other constellations. More than one clue points in this direction: – already in the Odyssey (15.403) the tropai are at least mentioned; – Hesiod spoke not only of the Pleiades but also of Arktouros, asserting (in Works and Days 564–565) that the star reappears at sunset 60 days after the winter tropē18; – Cleostratus of Tenedos “used to say: ‘Whenever it is the third day after eighty of permanence, Scorpio sets in the sea at the same time as dawn breaks’”;19

Dating of the tropai and the isēmeriai  81 – the sources gathered in 68B14 DK associate Democritus with information concerning the Pleiades as well as another seven constellations; – the Eudoxus papyrus (second century BC) outlines a sequence of astronomical events as follows: 22 days elapse between the setting of the Pleiades and the setting of Orion, two between the setting of Orion and the setting of Sirius, two between the setting of Sirius and the solstice.20 This dataset (small though it is) not only shows that there was widespread interest in such correlations before and after Thales. It speaks, more specifically, of an interest, established very early on, in identifying events that could be put in sequence by indicating the interval between them in days, so as to fill out a picture of the year on the basis of the few established data available. Perhaps some heterogeneous information could be added, even forecasts of typical weather. In other words, it speaks of the beginnings of the calendar (which, at the same time, could serve as a multifunctional almanac).21 Thales is linked to the provision of precise dates, rather than the approximate ones found in Hesiod, and only he is known to have invested a lot in the effective identification of exact dates concerning a multiplicity of relevant cosmic phenomena. 6.3.2  Cleostratus of Tenedos The little we know about Cleostratus of Tenedos, who lived close in time to Thales (cf. Section 3.5), allows us to affirm that was known for similar determinations: that is, of how many days after a given astronomical event a certain constellation sets at dawn. Perhaps Thales taught him, and possibly others, how to date the setting or the rising of constellations other than the Pleiades. Pliny too, in another point of his Naturalis Historia, after having attributed to Anaximander the merit of having first understood the obliquity of the zodiacal circle (signiferi… obliquitatem eius intellexisse... primum), reports that signa deinde in eo Cleostratus (sc. intellexisse), et prima arietis et sagittarii (Nat. Hist. 2.30). According to Pliny, Cleostratus followed Anaximander in identifying and studying signs of the Zodiac: in his case, Aries and Sagittarius. The sentence, not entirely perspicuous, must be compared with the only two surviving verses of Cleostratus’s Astrology. The source is a scholium: The ancient Cleostratus of Tenedos, for example, expressed himself thus:

But whenever it is the third day after eighty of permanence, Scorpio sets in the sea as dawn breaks.22

I will not dwell on some controversial details of these two verses. What is relevant here is that Cleostratus appears to be associated with the study of

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the times of three (or more?) constellations, each time in connection with their appearing or disappearing at dawn. It would therefore seem that he dedicated his research to identifying the dates when these (and perhaps other) constellations set or rise at dawn. The likely goal was to provide not absolute dates, but dates relative to the solstices or equinoxes. If this is right, it would have been a signifcant sequel to Thales’ research on the setting of the Pleiades, whose essential starting point was the dating of the autumn isēmeria. Something else, linked to a third source, is worth noting. In De signis, Theophrastus reports that Matricetas of Methymna, in Lesbos, observed the solstices (ta peri tas tropas) when the sun rose behind Mount Lepetymnos, Cleostratus observed them in Tenedos when the sun rose behind Mount Ida, and Phaenos watched them from Athens as the sun rose from the Lycabettus.23 Huxley (1963, 99) observes that, from Methymna, Matricetas should have observed the winter solstice, because Mount Lepetymnos is south-east of there, and Cleostratus, from Tenedos, could also have observed the winter solstice given his location.24 So we learn that Cleostratus was not alone in cultivating the astronomical tradition of which Thales laid the foundations, nor in moving from mere observation to the collection of signifcant data. These details can, among other things, dispel most of the doubts one might have about the quality of research carried out by Thales on the solstices and equinoxes. Anaximander, Cleostratus, Matricetas and Phaenos would have had no other model to inspire them, and each could have undertaken investigations at his own expense in just the manner of Thales. This all confrms the reports suggesting that Thales was famous far beyond Miletus.25 (I am not going to deal here again with Thales’ fnal journey to Tenedus, the island where Cleostratus lived, and the possibility that he died there; but see Section 3.5 above.)

6.3.3 In conclusion In conclusion, what we have seen is a coherent group of assessments concerning the partitions of the year based on careful compilation of data. The research behind it can be easily explained: it was motivated by a desire to fx the calendar, anchor the representation of the solar year (not the lunar year anymore!) and to overcome the inevitable randomness associated with traditional calendars.26 The ultimate goal was not achieved. At least, we have no evidence of a calendar reform associated with Thales or Miletus. Even the dating of the equilux, with the accompanying fnding that the length of the quarters is conspicuously uneven, did not have much of an impact, and comes to us only as an echo in our reports, which no one, until now, has ever tried to account for.

Dating of the tropai and the isēmeriai

83

Notes 1 In DL 1.27 (=11A1 DK = Th237 W ≠ LM), we read: τάς τε ὥρας τοῦ ἐνιαυτοῦ φασιν αὐτὸν εὑρεῖν καὶ εἰς τριακοσίας ἑξήκοντα πέντε ἡμέρας διελεῖν. 2 In DL 1.23 (=11A1 DK = Th237 W = 5R6 LM), we read: κατά τινας δὲ μόνα δύο συνέγραψε Περὶ τροπῆς καὶ Ἰσημερίας. 3 In Lexicon theta 17–18 (11A2 DK = Th495 W ≠ LM), we read ἔγραψε Περὶ μετεώρων ἐν ἔπεσι, Περὶ ἰσημερίας καὶ ἄλλα πολλά (“He wrote on astronomical subjects in verse, “On the Equinox” and many other works”) and a bit later: καὶ ἰσημερίας κατείληφεν (“and left a work entitled Equinoxes”). 4 We will deal with this passage from Pliny shortly (Section 6.2). 5 Since Hesiod, ‘dawn setting’ referred to a given constellation setting as the sun rises. One can imagine how diffcult it would be to decide whether the relevant date is when the frst or the last stars of a given constellation sets. 6 Text supplied in Chapter 5, note 10 above. 7 In DL 1.24 (=11A1 DK = Th237 W = 5R14 LM), we read: πρῶτος δὲ καὶ τὴν ὑστέραν τοῦ μηνὸς τριακάδα εἶπεν. 8 Hesiod clearly alludes to some sort of payment ‘in kind’, that is, with an agreed quantity of olive oil, wine and, perhaps, some other sort of edible stuff. 9 On the point, Aristarchus was probably much better informed than Diogenes Laertius. 10 And devised by Parmenides. I deal with it in detail in Rossetti (2017, Chapter 6). 11 NB ‘diametrical’ means an angular width of 180° (not of 90° as with a square). 12 Small, in order to ensure that the water pressure (as it fows out) does not experience any meaningful fuctuation. It is interesting to note that a document found in the library of Ashurbanipal in Nineveh, takes into consideration the procedure to be followed in order to establish how much water comes out of an hourglass in a given period of time. 13 As an alternative, one can think of counting the cups catching water coming out from the hole. 14 For instance, the arrival of the very frst ray of the sun and, at the sunset, of the very frst contact between the solar disc and the water (if the observation were being made from the seashore). 15 We shall get back to this when we deal with the ways used by Thales to establish the angular width of the sun (Section 8.5). 16 Pliny the Elder Naturalis Historia 18.213 (=11A18 DK = Th106 W = 5R21 LM). 17 This is a scholium to Aratus, Phenomena 172 (p. 369.24 = 11A2 DK = Th495 W  = 5R22 LM), where we read: Θαλῆς μὲν οὖν δύο αὐτὰς εἶπεν εἶναι, τὴν μὲν βόρειον τὴν δὲ νότιον. See Panchenko (2016, 790) for some insightful remarks. To talk about two Hyades meant – as is evident – to have noted that two groups of stars (two constellations) have the same disposition, that is, they are rather similar, despite being very far one from the other. Not a minor accomplishment. 18 The fact that a two months interval is mentioned, is a good indication that a rough quantifcation was actually made. 19 6B1 DK; see further below Section 6.3.2. 20 This is reported by Lehoux (2007), 207. 21 In Lehoux (2007, 145–491), there is a full catalogue of ancient Greek and Latin parapēgmata: 87 documents, surprisingly different one from the other, where information such as this is very rare, at least rarer than I would expect. 22 These verses are preserved in a scholium (anonymous) to verse 518 of Euripides’ Rhēsos: (=6B1 DK): ἀλλ’ ὁπόταν τρίτον ἦμαρ ἐπ’ ὀγδώκοντα μένηισι | σκορπίου εἰς ἅλα πίπτει ἅμ’ ἠοῖ φαινομένηφι. 23 Theophrastus, De signis 4 (6A1 DK): ἀστρονόμοι ἔνιοι οἶον Ματρικέτας ἐν Μηθύμνηι ἀπὸ τοῦ Λεπετύμνου καὶ Κλεόστρατος ἐν Τενέδωι ἀπὸ τῆς Ἴδης καὶ Φαεινὸς Ἀθήνησιν ἀπὸ τοῦ Λυκαβηττοῦ τὰ περὶ τὰς τροπὰς συνεῖδε.

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24 The Lycabettus, on the contrary, is approximately north-west of the Acropolis’, therefore this reference may well be out of place’. 25 A recap of this information is to be found in Section 17.1 – I understand that these references to people observing the solstices could have been examined at the end of the preceding chapter, given that here we are dealing not with solstices but with equinoxes/isēmeriai/equilux, but the starting point for these remarks was the 25-day interval between the autumn isēmeria and the setting of the Pleiades. 26 White (2002, 14) argues that Thales and Anaximander “constructed the frst systematic calendar of the Greek world … They thus paved the way for the parapēgmata of the following century”. Besides, we are working on conjectures that are not supported by information as specifc as would have been desirable.

7

What explains a solar eclipse?

Even the famous story of Thales’ prediction of a solar eclipse requires radical rethinking.

7.1 Primary documentation I note as a preliminary point that, although the fame of the alleged prediction – which would have happened a few years before the celebration of Thales in Athens around 580 BC – could have contributed to the Athenians’ decision to proclaim Thales a sophos (Section 3.3.1 above), this does not imply that his reputation rested on this prediction (any more than on the doctrine of water as archē). No one disputes that he would have been unable to establish the year – let alone the exact date – of any subsequent eclipse that would be visible from his geographical region, and it is hardly conceivable that Thales predicted a solar eclipse on the basis of knowledge or calculations that he was master of.1 Moreover, as we will see, a group of witnesses agree in reporting that Thales understood how solar eclipses occurred, but say nothing about his having made a prediction. Indeed, we only fnd brief and sporadic claims about this.2 The currency of the claim – which has led, for example, to the speculation that Thales was like a “lucky charlatan who manipulates Babylonian records” (Lebedev 1990, 85; cf. e.g. Kirk–Raven–Schofeld 1983, 82, and Vesperini 2019, 74)3 – owes much to the fact that it occurs in Herodotus. It probably ought to be set aside. On the other hand, it is worth trying to understand if Thales advanced understanding, not about when and where the next eclipse will occur, but rather about a more fundamental question: Why do eclipses take place? There is more than one piece of evidence that Thales was interested in this. The attention Thales paid to the solar eclipse is emphasized by the abundance of references that we fnd in ancient authors. In fact, Wöhrle (2009, 30) has identifed as many as 29 passages by ancient authors in which something is said on the subject4 – although, of these, only a few give us details of any signifcance.

DOI: 10.4324/9781003138723-9

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Five quantitative inquiries [1] Our oldest source of information is a well-known passage in Herodotus: After this, since Alyattes would not give up the Scythians to Cyaxares at his demand, there was war between the Lydians and the Medes for fve years; each won many victories over the other, and once they fought a battle by night. They were still warring with equal success, when it happened, at an encounter which occurred in the sixth year, that during the battle the day was suddenly turned to night. Thales of Miletus had foretold this loss of daylight to the Ionians, fxing it within the year in which the change did indeed happen. So when the Lydians and Medes saw the day turned to night, they stopped fghting, and both were eager to make peace. Those who reconciled them were Syennesis the Cilician and Labynetus the Babylonian.5

It is worth quoting this text at length to give an idea of context for the claim. Herodotus assumes that the prediction, as well as being public, was unexpected and substantially inexplicable: it must have had a considerable impact, if it really led to the end of a war. So if Herodotus were right, the eclipse of May 585 BC – which in Miletus must have appeared as a partial eclipse – must have been immediately connected with Thales, who would have had to foretell the year in which the eclipse occurred. Putting this report into a network of detailed circumstances contributes greatly to its plausibility. [2] After Herodotus, the frst person to make any reference to this prediction again was, as far as we know, one of Aristotle’s best pupils, Eudemus of Rhodes. As Hero of Alexandria and Theon of Smyrna report (using the same words, which shows that they are both drawing on the same source), Eudemus en tais Astrologiais asserted that “Thales discovered the eclipses of the sun” (that is, we must assume, he came to understand what they depend on), and the tropai too (which we have already discussed)6; they go on to specify, a few lines later, that credit for a conjecture on how a moon eclipse occurs belongs to Anaximenes. Diogenes Laertius and Clement of Alexandria also mention a work by Eudemus when they speak about eclipses: the former, at 1.23, refers to Eudemus en tōi Peri tōn astrologoumenōn, and hints at the prediction7; the latter writes that en tais Astrologikais historiais Eudemus mentioned the prediction made by Thales – 8 then enters into details concerning the battle of the Lydians and the Medes. Four witnesses therefore converge in reporting that, according to Eudemus, Thales dealt with the eclipse, but without being clear to what exact end. [3] Next is an anonymous papyrus commentary on the Odyssey that some experts date to the second century AD. Here we read: That eclipses take place at the new moon is explained by Aristarchus of Samos, who writes: “Thales said that the sun is eclipsed when the moon comes to be located in front of it, so that the day when the eclipse occurs is marked by . Some call that day triakas (= the thirtieth day) and others neomēnia (= new moon).”9

What explains a solar eclipse? 87 Clearly the expression “Aristarchus wrote that Thales said” suggests a statement by Thales (see further Chapter 17). But we should ask what Thales said according to Aristarchus. Three claims are identifed: (a) that there is an eclipse of the sun when the moon is in front of the solar disk; (b) that this obscuring of the sun is the eclipse; and (c) that the phenomenon occurs, when it does, on the thirtieth day of the lunar month. The second of these claims is merely defnitional; but the frst and third are important. Nothing is said about forecasting. As to the lacuna, the suggestion made by the frst editor of POxy 3710, M. W. Haslam, has been widely accepted. That said, we come to the expression “Thales said that the sun eclipses when the moon goes in front of it” (selēnēs epiprosthen autōi genomenēs). This is a very precise claim that, in addition to being consistent with other reports, also clarifes something: it sometimes happens that the lunar disk, which is not so easily visible in broad daylight, moves in front of the sun, and obscures it. Aristarchus of Samos (310–230 BC) was a professional astronomer who dealt in depth with the moon and its light in his only surviving work, the ambitious De magnitudinibus et distantiis solis et lunae, so he speaks with rare expertise when he remarks that Thales made an important discovery when he identifed the circumstances of the eclipse (the moon moving in front of the sun in broad daylight and, for a while, obscuring it). So Aristarchus’ silence on the story of the eclipse of 585 BC, and on the question of prediction in general, is also relevant. What he does testify to, though, are two no less signifcant ideas: (1) that, around the time of the new moon, the moon is in the sky throughout the day, even though it is rather diffcult to see,10 and (2) that an eclipse takes place during the day and in conjunction with the new moon.11 [4] Next, there is a lengthy statement by Cicero, who writes: For when the sun was suddenly obscured and darkness reigned, and the Athenians were overwhelmed with the greatest terror, Pericles, who was then supreme among his countrymen in infuence, eloquence, and wisdom, is said to have communicated to his fellow-citizens the information he had received from Anaxagoras, whose pupil he had been – that this phenomenon occurs at fxed periods and by inevitable law, whenever the moon passes entirely beneath the orb of the sun, and that therefore, though it does not happen at every new moon, it cannot happen except at certain periods of the new moon. When he had discussed the subject and given the explanation of the phenomenon, the people were freed of their fears. For at that time it was a strange and unfamiliar idea that the sun was regularly eclipsed by the interposition of the moon – a fact which Thales of Miletus is said to have been the frst to observe.12 Cicero too shows that he knows (indeed, he assumes that it has been known for a long time) what leads to the temporary darkening of the sun. He reports that Pericles also knew this well, having learned it from Anaxagoras, but then he specifes that the frst to ‘see’ (that is, I presume, to understand)

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the phenomenon was, as far as anyone knows, Thales. While the reference to Thales is relatively feeting, Cicero’s explanation goes into signifcant details. In fact, here it is specifed, among other things, that the eclipse can only take place during the intermenstruum, the apparent interval between one lunar month and another, when the ‘new’ moon still has to reappear. But when it happens that its trajectory intercepts that of the sun, it suddenly becomes visible. Cicero goes into all these details with reference to Pericles (and indirectly to Anaxagoras), only to add that “Thales, they say, saw this frst”, without specifying what precisely Thales ‘saw’, that is, what he came to understand and to teach. It is not possible to know what Cicero’s sources were here, but Aristarchus’ writing (which we know thanks to POxy 3710) is a candidate. I will also note that Cicero does establish a connection between this sort of knowledge and the ability to predict an eclipse – but in De divinatione,13 not here. [5] We now come to a diffcult passage from Aetius: Thales was the frst to say that an eclipse of the sun occurs when the moon, which by nature is made of earth, passes perpendicularly beneath it; this is seen in the manner of a mirror, when the disk comes to be placed under it.14 “When the moon passes vertically between the sun and the earth”: this may have been an unsuccessful attempt to express the idea of a straight line between the sun and the earth. The mention of the vertical suggests an attempt to be clear, but in fact only complicates and confuses things. The underlying idea seems to be that, when the solar eclipse takes place, the moon is right on a line going from the sun to the earth. So the moon intercepts the sun’s rays. But what do the words βλέπεσθαι δὲ τοῦτο κατοπτρικῶς (‘[the sun] is seen in the manner of a mirror’) mean? It makes no sense to imagine that, when the eclipse occurs, the sun becomes visible (blepesthai) by mirroring: the sun becomes, if anything, invisible. Besides, at the time no one, absolutely no one, had any idea of cosmic mirrors. One hypothesis is that the lunar disk places itself ‘under’ the sun and, although it is not a mirror, it intercepts and defects the sun’s rays as if it were a mirror (katoptrikōs, “in the typical way of mirrors”15), to the point that it leaves the earth (or, rather, a portion of earth) in the dark. On this hypothesis, Thales might well have asserted that the side of the moon that is exposed to the sun has the power of intercepting and defecting (or refecting back) the sun’s rays more or less as if it were a mirror: if the sun is darkened, this is to be explained because of this effect (but there is no discussion here of how the moon affects the sun’s rays). Another signifcant detail surfaces from the ousēs phusei geōdous clause. Why should the moon be of the nature of earth? An easy conjecture comes to mind: if, as it seems, it is able to block the rays of the sun, it would have

What explains a solar eclipse? 89 to be a solid body. Moreover this round object, the moon, that seems like a mirror, if it has the enormous power of preventing the majority or totality of sun’s ray from illuminating and warming the earth for a while, must necessarily be totally different from the sun, and be something of considerable size, including depth. So, according to this source, Thales frst explained the mechanism of the eclipse and, in connection with that, came to make a substantial conjecture about the nature of the moon. Though it has passed unnoticed, this detail has a value of its own. If it goes back to Thales, as is quite likely, it would amply reassure us on the question of whether he was making a prophecy (possibly post eventum), or rather trying to understand what happens in the sky when the sun is darkened by a round object. [6] Now we come to another doxographic passage, evidently connected to the previous one, which comes from ps.-Galen: Thales was the frst to say that an eclipse of the sun occurs when the moon, which by nature is made of earth, passes vertically beneath it.16 Again “vertically”, that is, right below. Here too the idea is unequivocal: the sun’s rays descend vertically and the moon stands there intercepting them (as if it were a mirror). This mean that there has been some elaboration – but elaboration of what? There is little doubt: the starting point must have been the claim that a solar eclipse takes place if and when the moon goes right in front of the sun (that is, ‘below’, because the sun fnds itself ‘above’). In short, reports [5] and [6] together tell us that, according to their source (probably Theophrastus), Thales understood the dynamics of solar eclipses very well. But again, there is no reference to prediction. We also note the specifcation that the moon is similar in composition to the earth (ousēs phusēi geōdous). The idea that Thales anticipated one of the battles fought by Anaxagoras by a whole century (and that Anaxagoras could have appealed to Thales) can be doubted, but it is certainly not impossible.17 [7] Finally, it is time to mention a scholium to Plato’s Republic, datable to after the sixth century AD, which has all the appearance of being a careful summary of the information offered in Diogenes Laertius, but with an exception that concerns precisely the topic of the eclipse. Diogenes does, at 1.23, talk about the prediction of eclipses, but the scholiast says something very different: Thales of Miletus, the son of Examyas… was the frst to be called a sage. For he discovered that the sun is eclipsed because the moon is beneath it in its course.18 A few words about the notion of going ‘beneath’ are needed. The term hupodromē which this translates, correctly evokes the progress of the lunar disk

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as it goes to place itself right where the solar disk appears by passing beneath the sun, that is, in the space between the sun and the earth. Since this is the right word (even in the eyes of us moderns), the scholiast (or his source) must have had a very precise idea about what Thales taught about the eclipse. This begins with his setting aside Diogenes’ claim about the prediction, and telling a story he thought more credible. Together, then, texts [5], [6], and [7] elaborate on the idea that the moon comes to be under the sun, between the sun and the earth.19

7.2 A prediction or a post eventum prophecy? In conclusion, starting with Aristarchus, a group of sources agree in dissociating Thales from the notion of prediction, and in identifying precise knowledge concerning the dynamics of an eclipse. Sources [3], [4], [5], [6], and [7] – Aristarchus, Cicero, Aetius, ps.-Galen, and the scholiast – all converge in reporting (probably on the authority of Theophrastus, and Aristarchus of Samos) that Thales explained that an eclipse happened when the moon was relatively near the sun and ‘below’ it, and during the new moon (indeed, only during the new moon, and around noon). These authors are clearly not relying on mere second-hand claims (as Herodotus is), but on the report of some competent informant, and a text that Theophrastus, Aristarchus, and others were able to read. This account of the dynamics of the eclipse seems quite independent of the claims about forecasting. A whole group of relatively late sources attribute specifc technical claims to Thales that certainly could not have been made up, not least because of the very different sort of story, concerning prediction, that came into circulation after his death. Note too, that we are dealing with original conjecture (these claims have no precedent in anyone else’s teachings), that offer real knowledge, and are very specifc. Nobody could have made this up. In other words: (1) this is an original conjecture (2) ascribed only to Thales; (3) it is a valuable conjecture which (4) is not the sort of thing to have been improvised; therefore (5) it is quite possible that its ascription to Thales has good foundations. As for the prediction, Guthrie’s point of view still has some interest: he admits that Thales may have foretold an eclipse using information elaborated in Mesopotamia, but he takes care to specify the following (1962, 48–49): That the eclipse of 585 occurred at the time and place of the battle, was nearly total, and had the dramatic consequence of causing the combatants to cease fghting and negotiate a truce, was a happy chance by which his statement, in retrospect, acquired very naturally an air of precision that grew with the centuries and ensured its notoriety among his country-men. In fact, that the event (an eclipse in the middle of hard-fought battle) could have occurred and that the news caused a certain sensation, all seems to me

What explains a solar eclipse? 91 quite plausible; but that Thales may have attempted a prediction seems to me excluded not only for the reasons already given (above) and for chronological reasons (Sections 3.4 and 15.3–4), and also for reasons that will be offered shortly (Section 7.3.1) concerning the diffculty Thales would have had in acquiring relevant data. It should also be considered that the hypothesis of a non-professional researcher who, on the basis of imprecise knowledge about the results of research conducted at Nineveh, attempts a prediction and gets lucky, is really very arbitrary. Nor can I believe that, given the ‘serious’ and pioneering research otherwise ascribed to him, Thales could have behaved, even once, as a charlatan. In my opinion, it is far more likely that Herodotus was told about a prediction and believed it, but that it started from a mere rumour. In fact, while it is unlikely that this whole story was invented by Herodotus from scratch (he lacks the motive), it is not so unlikely that a popular story might arise. The report of a war that ended as a result of the eclipse could cause a sensation; the fact that Thales, at the time about 40 or 45 years old, was dealing with eclipses, or had even begun to make his conjecture known, might have helped. The sensational news about the solar eclipse coupled with rumours about Thales’ research could easily have turned “Do you know that Thales talked about eclipses recently?” into “Thales foresaw this eclipse!”20 O’Grady (2002, 142) writes that Aristarchus “attributed to Thales a certain understanding of the phenomena of the eclipse that is mostly denied him”, but I would rather say, in conclusion, that Thales was credited with having understood why it sometimes happens that an eclipse of the sun occurs, and nothing else. Two objections remain to be considered. Burnet (1908, 40) noted that the explanation attributed to Thales was certainly unknown to Anaximander and his successors, “and it is incredible that the correct explanation for this phenomenon was once formulated to be forgotten so quickly”. To this, I note that, in fact, Anaxagoras, at least, appears to have fully understood the dynamics of solar eclipses. This is unequivocally attested by Hippolytus in 59A42.9 DK. Beyond that, it would seem appropriate to observe that all these intellectuals – starting with Anaximander – were capable of forging their own very individual paths of discovery, independently of their teachers and colleagues: there should be no presumption that they were interested in preserving the legacy of their masters. (Anaxagoras himself seems to have invested much more in trying to explain the lunar eclipses than the solar eclipses.) Lebedev (1990, 79) wondered whether someone representing the moon as an object that shields the sun would not have needed elaborate representations of the spatial relations between earth, moon and sun which were unavailable to Thales. But the answer is: not necessarily. In the case of a solar eclipse, the possibility that the opaque body temporarily shielding it is the moon itself, is very concrete, so concrete that it does not require the support of additional conjectures about the place that the earth, moon and sun occupy in space. The suggestion certainly invites further questions, but it can

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transform itself into an observation even before any such theorizing takes shape. In other words, Thales could have contented himself with achieving certainty as to the identifcation of the opaque body that makes the sun temporarily invisible from (a portion of) earth, without wanting to raise further questions. Lebedev himself concluded his article (1990, 85) by hypothesizing that the explanation of the dynamics of solar eclipses must go back not to the “Posidonian doxography of the frst century” but to a much more ancient tradition.21 It makes sense, however, to ask why we can go back to Anaxagoras but not directly to Thales: I see no reason, especially in the light of Diogenes Laertius 9.34.

7.3 Many bold conjectures to support the prediction I will now move on to discuss some especially bold conjectures, which have in common the desire to agree with Herodotus’ claim that Thales predicted an eclipse. 7.3.1 Thales learned from the Assyrians First are the Assyrian texts selected and reported by O’Grady (2002, 133– 141). About 70 years before the eclipse that supposedly caused so much sensation in Miletus and elsewhere, the Assyrian monarchy had appointed staff in charge of observing the sky. Their work allowed them to note that solar eclipses occur only in conjunction with the 29th or 30th day of the moon, that is, when the moon becomes invisible at night, and hardly visible at morning. This is intriguing: if Thales had access to a report of this kind, it would actually support my reconstruction of what he claimed. But how many intermediaries and how much good fortune would it have taken for this to happen? If it was a question of accessing the Assyrians’ reports, then Thales must have: a b c d e f g h j

already become interested in the phenomenon of the eclipse himself (so far so good); known of the existence of the Assyrian reports; known of their probable relevance to his interests; wanted, tried, and been able, to access them; been able to rely on an interpreter who could give him a good account of their contents; been able to identify and note signifcant observations; been able to make use of them. We must also consider: that the territory of the Assyrians was located a vast distance away (almost 2000 km!); that the city of Nineveh, where the sovereign resided, had been razed to the ground in 612BC, that is, 37 years before the event; and

What explains a solar eclipse?  93 k that the protection and conservation of the royal archives probably ended on that occasion. I also note that it is never enough simply to have information. The relevant information is normally embedded in a torrent of other information; so: l

the relevant information needs to be present in a form making it capable of being isolated from information irrelevant to the particular question; m Thales would have needed to be capable of so isolating it. (Blanche [1968, 165] suggests that “Babylonian astronomers did predict solar eclipses before 600 BC”, but they did it at the king’s court, while the monarchy survived: it does not appear that they did it in public.) Given the extent of these complications,22 each of which alone would constitute a serious impediment, the hypothesis of a dependence on Mesopotamian culture is simply unlikely.23 It is true that further ‘astronomical diaries’ were produced in Babylon (see now Haubold–Steele–Stevens 2019), but these started, it seems, from the year 568 BC, more than 15 years after the event of 585 BC. So it is virtually impossible that Thales could have heard of them. (Conversely, it is extremely unlikely that the Babylonian ruler had heard of Thales’ achievements and set out hastened to emulate him.) O'Grady also reports (2002, 140) that the Assyrians discovered the interval of 23½ lunar months between a lunar exlipse and a subsequent solar one, but it remains to consider, i.a., that a partial solar eclipse easily goes unnoticed if it is unable to affect the luminosity of the sky. 7.3.2  Thales learned of the cycle of 223 lunations Similar considerations can be brought against the hypothesis that Thales used the Babylonian saros, so called – a period of 223 lunations, equal to about 18 years, which is supposed to separate one solar eclipse from the next. There is the insuperable difficulty of knowing precisely when the 18 years would have begun – that is, to know exactly when the Assyrian data placed the last eclipse (would anyone in Greece have been able to do this?); but anyway, two complete solar eclipses happen too rarely and too irregularly in the same place for it to be possible even to pretend to derive constants from them. What is more, talk of a cycle of 223 lunations is documented, in the Babylonian environment, only for the Seleucid era (and the Parthian after that), so from the third century BC, as it is apparent from Neugebauer’s Astronomical Cuneiform Texts.24 In conclusion, Babylonian ‘science’ could not have been known to Thales (certainly not in any form he could use).25 On the other hand, the notion of a black disk that moves in front of the sun, covering it at least partially for a

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while, is not particularly mysterious. Thales could certainly have made his discovery without the support of Assyro-Babylonian knowledge. 7.3.3 Other ‘explanations’: Panchenko According to Panchenko, Thales might well have predicted at least one eclipse because the Ionians were present in many locations ranging from the Nile delta to the northern shores of the Black Sea. Now, to predict that “an eclipse of sun could be visible somewhere within a vast region that stretched between 31° and 48° north is not the same as predicting its visibility ‘for a particular place’”. So Panchenko observes that Thales might have been able to predict the repetition of eclipses at 76-year intervals and, since an annular eclipse took place on January 12, 662 BC, and “it is possible that the event was, at the time, delivered into written documents or (transmitted) by oral tradition”, then if “Thales was informed of the eclipse of January 12, 662 BC, he could equally be informed of the eclipse of June 27, 661 BC” and “expect a new eclipse to occur in 586/5” (2016, 784). In support of these hypotheses, Panchenko goes so far as to conjecture that “Many people who worked for the kings of Assyria certainly chose to emigrate [when he was overthrown in 612 BC] – for example, at the court of the Necho Pharaoh” and “Interpreters expert on celestial signs sent by the gods found themselves in all regions. That was, moreover, an era of contacts between the Greeks (in particular the Ionians) and Egypt, and Thales probably visited Egypt” (2016, 786). On this basis, he concludes that “Thales’ prediction was not a legend” (2016, 785). Unfortunately, this conclusion would require a great number of additional intermediate steps;26 but there is not even the minimum licence to introduce them. Quite apart from the scarcity of concrete data about the circulation of culture between the Mesopotamian area and Greece,27 and quite apart from the fact that we are under no obligation to go out on a limb to fnd a way of making every claim in Herodotus plausible, absolutely nothing allows us to imagine that the Milesians of the seventh century BC were able to record long-term data on solar eclipses. Panchenko’s thesis is more than a little weak. 7.3.4 Other ‘explanations’: O’Grady According to O’Grady (2002, 129, cf. 145), eclipses fell within the ‘competence’ of the gods. “If the gods were going about their business, performing their assigned duties, as it was generally believed they did, why question the validity of common belief” and run the risk of incurring their wrath? It is certainly likely that, in solar eclipses, “one sees in general, in pre-scientifc cultures, the effect of a divine will”, as Panchenko writes (2016, 786); but one should also consider that, as far as is known, the religious beliefs of Greeks of the archaic era was anything but dogmatic. The Olympian religion of archaic, classical, and Hellenistic Greece did not involve an exaggerated

What explains a solar eclipse? 95 concern for divine punishment, or increased rigidity around what one had to say one believed, much less any obsession with orthodoxy. Religion could give a whole series of easy answers to questions that otherwise had no answer, but there was ready acceptance that ‘mythological truth’ should yield to precise and credible explanations that did not involve divine intervention in literal terms of mythology. For example, Anaximander propounded elaborate meteorological theories that made it unnecessary to invoke Zeus when a lightning bolt appeared – or at least downgraded the invocation to a harmless convention.28 Religious hostility to ‘scientifc’ research (e.g. in Athens at the end of the years when Pericles was dominant) was unusual. For these and other reasons (cf. Section 2.2.5), I presume that Thales could have felt quite free to investigate eclipses without any need for fear.29

7.4 Towards a conclusion Let us now try to draw some conclusions about Thales and the solar eclipse. 7.4.1 The prediction of an eclipse is a legend Niels-Christian Dührsen wrote (2013, 239) that From nothing else Thales achieved such fame in antiquity as from the accurate prediction of an eclipse. Thanks to this performance, which already caused amazement among contemporaries (Xenophanes DK 21 B 19), Thales immediately became the founder of Greek astronomy. Panchenko too wrote (2016, 783) that “The ancient tradition… attributes to Thales a certain number of discoveries. The prediction of a solar eclipse is the most famous one”. And these two are not alone. But Burkert (2013, 226) recalls what Otto Neugebauer, in his time the best connoisseur of Babylonian mathematics and astronomy, acutely formulated as early as 1957: “There is no cycle for the visibility of the solar eclipse in a certain place” and “In 600 BC there was no Babylonian theory to predict a solar eclipse”.30 In other words: a scientifc forecast of the solar eclipse in a certain sense was simply impossible for Thales, and so also for many subsequent centuries. Similar conclusions were reached by Guthrie (1962, 48) and Lehoux (2007, 116 ff.). For my part, I observe, in the frst place, that it is not decisive whether Babylonian experts were or were not able to predict solar eclipses, but rather (a) whether the information was able to reach Thales and (b) whether Thales was even interested in making a prediction, rather than in understanding the phenomenon. In the second place, Thales had many merits but, as far as

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the literary sources tell us, the supposed prediction believed and given currency by Herodotus, was not found worthy of note by Eudemus of Rhodes,31 is only feetingly hinted at in Cicero (Th75 W), Pliny the Elder (Th105 W), Clement of Alexandria (Th203 W), Eusebius of Caesarea (Th265 W, with Jerome), Augustine (Th311 W), and Sidonius Apollinares (Th387 W). If I am not mistaken, there is nothing else to speak for it between the age of Thales himself and the dissolution of the Western Roman Empire. The fact is that the reference to prediction (which Apuleius, signifcantly, neglects when outlining the innovative knowledge for which Thales was responsible: Florida 18.31, a passage to be examined in Chapter 8) somehow became important to us moderns, but was not among the Greeks and Romans. On the other hand, references to Thales’ identifying the cause of the eclipse are not only more numerous, but are detailed and preserve primary and important knowledge – knowledge which, however, was of no particular interest either to Anaximander or to other Presocratics (with the exception of Anaxagoras). Furthermore, comparison with the measurements previously reviewed allows us to note that, in this case, in order to make his discoveries, there was no need to set up special apparatus, to hire trustworthy collaborators, to carry out repeated checks or take other such measures. All Thales needed to do was to conjecture that the eclipse, whether partial or total, is constituted by the approach, superimposition, and separation of the two celestial bodies – a conjecture that is not particularly daring. In short, the enterprise was well within Thales’ conceptual reach: the point is, again, that he “observed what others saw”. I also note that, while measuring the height of the pyramids requires attention to a detail which is not at all intuitive (that the pitch of the sides of the pyramid need to be greater than 45°), in the case of the eclipse it was only a question of whether the black shadow that seems to be advancing across the sun happens or fails to be identifed with the moon. After that, Thales did not even need a theory: the fact is that the moon passes right in front of the sun. Incidentally, we know that, in other contexts, Thales said ouk isē aei sumbainei (above, Section 5.1). So it is quite easy to think that he was happy to accept that eclipses of the sun, which appear after what seem to be irregular intervals, are another phenomenon that ouk isē aei sumbainei. Thales’ explanation of the eclipse transforms a class of events once perceived as strange, or even threatening, into understandable events completely devoid of disturbing implications, and ultimately not even depend on Zeus or other divinities.32 Not surprisingly, this discovery ended up becoming (despite the apparent lack of interest among Anaximander and other Presocratics) a gift to humanity, and it is quite possible that it inspired his contemporaries by showing that we could understand something about how the cosmos works. 7.4.2 Uncovering the secrets of nature Also worth mentioning is what connects Thales’ explanation of the eclipse and his refections on the Magnesian stone (Chapter 10). These three

What explains a solar eclipse?  97 teachings are united by uncovering secrets of nature, albeit in diverse fields. In fact, alongside his extraordinary ability, unique for the time, in quantification, he was no less distinguished for the way he used observation: he saw that the Magnesian stone (the magnet) shows that some form of life might emerge even from inanimate bodies. Besides, as Thales came to say something about the nature of the Magnesian stone, so he seems to have been able to say something significant about the nature of the moon, namely that it must be a terrestrial body (testimony [5] in Section 7.1 above, from pseudo-Plutrarch, i.e. Aetius) and therefore have a consistency of its own, so as to block, albeit temporarily, the force of sun’s rays. In fact, this kind of conclusion has the power to establish a proto-science of the stars, which was initially called astrology. In the wake of Thales, Parmenides, for example, was able to understand that the sun must always be illuminating half of the (spherical) moon, regardless of what one can see from the earth, and once again this result was obtained without doing special research, but only by reflecting on what we can all see. If Parmenides was able to reach such conclusions, it is probably because he had learned from Thales how to study the celestial bodies and what it is possible to discover.

Notes 1 It is very unlikely, indeed, that a master in calculation would appreciate an arbitrary prediction, no matter whether confirmed or denied by the facts. 2 More information is to be given in Section 7.4. Here some pertinent remarks by Heath (1913, 13) are worth noting: “it is in fact necessary, if the occurrence of a solar eclipse at any specified place on the earth’s surface is to be predicted with any prospect of success, to know more of the elements of astronomy than Thales could have known, and in particular to allow for parallax; besides “only one other supposed prediction of the same kind is referred to. Plutarch relates that, when Plato was on a visit to Sicily and staying with Dionysius, Helicon of Cyzicus, a friend of Plato’s, foretold a solar eclipse ... This story is, however, not confirmed by any other evidence, and the necessary calculations would have been scarcely less impossible for Helicon than for Thales.” (In making these remarks Heath refers to an article by T.-H. Martin, published in Revue Archéologique in 1864, which, however, I have not been able to access.) 3 On the topic, see also Section 7.3.1. 4 Blanche (1968, 154 ff.) lists 12 items only. 5 1.74.1–3 (=11A5 DK = Th10 W = 5P9 LM): μετὰ δὲ ταῦτα, οὐ γὰρ δὴ ὁ Ἀλυάττης ἐξεδίδου τοὺς Σκύθας 1ξαιτέοντι Κυαξάρῃ, πόλεμος τοῖσι Λυδοῖσι καὶ τοῖσι Μήδοισι ἐγεγόνεε ἐπ’ ἔτεα πέντε, ἐν τοῖσι πολλάκις μὲν οἱ Μῆδοι τοὺς Λυδοὺς ἐνίκησαν, πολλάκις δὲ οἱ Λυδοὶ τοὺς Μήδους· ἐν δὲ καὶ νυκτομαχίην τινὰ ἐποιήσαντο· διαφέρουσι δέ σφι ἐπὶ ἴσης τὸν πόλεμον τῷ ἕκτῳ ἔτεϊ συμβολῆς γενομένης συνήνεικε ὥστε τῆς μάχης συνεστεώσης τὴν ἡμέρην ἐξαπίνης νύκτα γενέσθαι. τὴν δὲ μεταλλαγὴν ταύτην τῆς ἡμέρης Θαλῆς ὁ Μιλήσιος τοῖσι Ἴωσι προηγόρευσε ἔσεσθαι, οὖρον προθέμενος ἐνιαυτὸν τοῦτον ἐν τῷ δὴ καὶ ἐγένετο ἡ μεταβολή. οἱ δὲ Λυδοί τε καὶ οἱ Μῆδοι ἐπείτε εἶδον νύκτα ἀντὶ ἡμέρης γενομένην, τῆς μάχης τε ἐπαύσαντο καὶ μᾶλλόν τι ἔσπευσαν καὶ ἀμφότεροι εἰρήνην ἑωυτοῖσι γενέσθαι. οἱ δὲ συμβιβάσαντες αὐτοὺς ἦσαν οἵδε, Συέννεσίς τε ὁ Κίλιξ καὶ Λαβύνητος ὁ Βαβυλώνιος. 6 Hero says this in the last section of his Definitiones 138.11 (=Th93 W), while Theon does so in De utilitate mathematicae 198.14–18 (=11 A17 DK = Th167 W =

98  Five quantitative inquiries 5R16 LM): Εὔδημος ἱστορεῖ ἐν ταῖς Ἀστρολογίαις, ὅτι Οἰνοπίδης εὗρε πρῶτος τὴν τοῦ ζῳδιακοῦ διάζωσιν καὶ τὴν τοῦ μεγάλου ἐνιαυτοῦ περίστασιν· Θαλῆς δὲ ἡλίου ἔκλειψιν καὶ τὴν κατὰ τὰς τροπὰς αὐτοῦ περίοδον, ὡς οὐκ ἴση ἀεὶ συμβαίνει. The question of the tropai is widely dealt with in Chapters 4 and 5. 7 DL 1.23 (=11A1 DK = Th237 W = 5R15 LM): δοκεῖ δὲ κατά τινας πρῶτος ἀστρολογῆσαι καὶ ἡλιακὰς ἐκλείψεις καὶ τροπὰς προειπεῖν, ὥς φησιν Εὔδημος ἐν τῇ Περὶ τῶν ἀστρολογουμένων ἱστορίᾳ. 8 Clem. Alex. Strom. 1.14.65.1 (=11A5 DK = Th203 W = 5P10 LM): Θαλῆν δὲ Εὔδημος ἐν ταῖς Ἀστρολογικαῖς ἱστορίαις τὴν γενομένην ἔκλειψιν τοῦ ἡλίου προειπεῖν φησι (“Eudemus says in his History of Astronomy that Thales had predicted the solar eclipse just occurred”). 9 This information has been known only since 1986, the year of publication of POxy 3710. In col. II, r. 36–43 (=Th91 W = 5R17 LM) we read: ὅτι ἐν νουμηνίαι αἰ ἐκλείψεις δηλο[ι] Ἀρίσταρχος ὁ Σάμ[ι]ος γράφων ἔφη τε ὁ μὲν Θάλης ὅτι ἐκλείπειν τὸν ἥλ [ι] ον σελήνης ἐπίπροσθεν αὐτῷ γενομένης, σημειουμέ [νης [gap of 6 or more letters among which, it is assumed, τῆι κρύψει] τῆς ἡμέρας, ἐν ῇ ποιεῖται τὴν ἔκλειψιν, ἣ[ν] οἰ μὲν κτλ.]. See further the Appendix to Chapter 7. 10 There is a hint of it in Burkert (2013, 232). Burkert extends this conjecture even to the stars (“the stars are always in the sky, even near the sun”, p. 230), but unfortunately such a conjecture is never associated with the ancient masters of Ionia. 11 I refer to the diurnal hours that precede and follow the moonless nights – three nights, according to Heraclitus (this is what this same papyrus attests to below), but sometimes one more or one less. If so, solar eclipses can occur only during 13 groups of 2–4 days a year. 12 De re publica 1.25 (=Th75 W): Pericles ille … cum obscurato sole tenebrae factae essent repente, Atheniensiumque animos summus timor occupavisset, docuisse civis suos dicitur, id quod ipse ab Anaxagora cuius auditor fuerat acceperat, certo illud tempore fieri et necessario, cum tota se luna sub orbem solis subiecisset; itaque etsi non omni intermenstruo, tamen id fieri non posse nisi intermenstruo tempore. quod cum disputando rationibusque docuisset, populum liberavit metu; erat enim tum haec nova et ignota ratio, solem lunae oppositu solere deficere, quod Thaletem Milesium primum vidisse dicunt. 13 Cic. Div. 1.112 (=Th78 W) Primus defectionem solis, quae Astyage regnante facta est, praedixisse fertur (“he is said to have been the first man to predict the solar eclipse which took place in the reign of Astyages”). 14 The passage is to be found in ps.-Plutarch, Placita 890F1–5 (=11A17a DK = Th158 W = 5R18 LM): Θάλης πρῶτος ἔφη ἐκλείπειν τὸν ἥλιον τῆς σελήνης αὐτὸν ὑπερχομένης κατὰ κάθετον, οὔσης φύσει γεώδους. βλέπεσθαι δὲ τοῦτο κατοπτρικῶς ὑποτιθεμένη τῶι δίσκωι. 15 Abundant archaeological items tell us that a typical mirror was circular, with a handle. 16 In De historia philosophica 66.1.3 (Th399 W): Θαλῆς πρῶτος εἶπεν ἐκλείπειν τὸν ἥλιον τῆς σελήνης αὐτὸν ὑπερχομένης κατὰ κάθετον οὔσης φύσει γεώδους. 17 Diog. Laert. 9.34 (=59 A5 DK = 25R1 LM) tells us of a criticism of Anaxagoras by Democritus, that “the doxai on the sun and the moon are not his, but are ancient (archaiai)”. “I.e. from the Milesians”, as Lebedev (1990, 81) convincingly puts it. 18 Scholia in Platonis Rempublicam 600A1–10 (=11A3 DK = Th578 W ≠ LM): Θάλης Ἐξαμύου Μιλήσιος, Φοῖνιξ δὲ καθ ‘Ἡρόδοτον. οὗτος πρῶτος ὠνομάσθη σοφός · εὗρεν γὰρ τὸν ἥλιον ἐκλείπειν ἐξ ὑποδρομῆς σελήνης. 19 Besides, Graham (2013b, 149) rightly pointed out that “We can see by observing both bodies (sun and moon) when they are in the sky together that they are roughly the same size. So the moon could, in principle, obscure the sun”.

What explains a solar eclipse?  99 20 Blanche (1968, 154) objects that no one contested the prediction of which Herodotus speaks, but evidently it was far easier to believe Herodotus than to be wary on this specific point. 21 Unnecessary to offer a much more precise conjecture, as when he speaks of the “pre-peripatetic tradition of the fifth century BC” (ibid.). 22 Other relevant considerations will be proposed in Section 19.4. 23 An extreme hypothesis would consist in imagining that the memory of those ancient ‘astronomical’ observations had been handed down from father to son, perhaps even to a slave or other acquaintance of Thales who thought it appropriate to mention them to the great Milesian – but I ask: does it make sense to imagine this? The idea Thales had access to such a precedent is so unlikely that it should not be taken as a valid option at all. 24 Neugebauer (1955, 6) (see also Section 7.4.1 below). 25 On the material impossibility of predicting a new eclipse at the time of Thales, see also Lehoux (2007, 99–101 and 103–109). Another option worth being mentioned deals with the interval between lunar and solar eclipses. O’Grady (2002, 140) reports that a lunar eclipse was known to occur 23 months and a half before the occurrence of a solar one, but when and where these eclipses were substantial enough to generate at least some darkness, if not an awesome blackout? 26 See also Stephenson–Fatoohi (1997). 27 The scarcity and insignificance of the evidence found by Burkert in his 2013 article despite his prolonged and expert investigation, proves, against his own will, that the hypothesis of a vast circulation of knowledge between these two areas is still lacking substantial basis. 28 I would add that the appearance of the rainbow continued to arouse amazement not only until scientists discovered its secret but, at the popular level, until it was possible to generate small rainbows by hand with a small spray – that is until around 1940–1950, when electric pumps and hoses became widely available in the countryside. 29 I understand that I am opening the door, with this, to a heap of arguments and objections; but this is not the place to enlarge on the subject. 30 With just one exception, namely the interconnection between lunar and solar eclipses (p. 93, above). 31 We know something about it thanks to a fleeting hint in Clement of Alexandria (Th203 W) and a fleeting hint that appears in Diogenes Laertius (1.23). On the other hand, Hero of Alexandria (Th93 W) and Theon of Smyrna (Th167 W) speak of the book of Eudemus in relation to Thales and the eclipses, and are very fleeting about the supposed ‘prophecy’. 32 It seems to me pertinent to approach these considerations with a famous passage from Aristophanes’ Clouds. The clouds show that rain does not depend on Zeus and explain (v. 371): “in fact, if there are no clouds, the rain does not fall”.

8

A measurement of ½˚

We have already examined some attempts to make precise measurements despite the predictable diffculty of the enterprise, and so seen something of Thales’ determination. At the same time, we have begun to suspect (or understand) that these non-intuitive measurements – “observing what others saw” (O’Grady), obtaining precise information from events that were observable – probably constituted Thales’ principal occupation for years, given the time required for repeated observation (and, between times, for refning his procedures), and given the effort needed to explain his conclusions, his procedures, and the signifcance of his investigations. His study of the amplitude of the solar disk is particularly signifcant, because it is a challenge that was taken up by several people after Thales – although only, it seems, many centuries later.

8.1 Thales astonishes Mandrolytus of Priene About seven centuries after Thales, we fnd this surprising information in the Florida of Apuleius: Thales of Miletus was easily the most outstanding of those seven men remembered for their wisdom; for he was the frst among the Greeks to discover geometry, a most accurate investigator of nature, and a most skillful observer of the stars; by means of small lines he discovered the greatest things: [31] the circuits of the seasons, the blasts of the winds, the wanderings of the stars, the marvelous resounding of thunder, the oblique courses of the constellations, the annual revolution of the sun; likewise, the waxing of the new moon, the waning of the old, and the obstacles that make it lose its light.1 Did Apuleius hit the mark? Plato’s Socrates says, in a passage from the Republic, that “many ingenious inventions for the arts or any other practical activity” are not reported for Homer “as they are for Thales the Milesian and Anacharsis the Scythian”.2 With reference to Anacharsis3 other sources credit him with inventing the bellows, the double anchor and the potter’s DOI: 10.4324/9781003138723-10

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wheel, but these are isolated reports, lacking context, and obviously open to doubt. This suggests that the wide-ranging intellectual interests of Thales surpassed the achievements of Anacharsis and others, and that it was he who set out on investigations which might have involved relatively complex mechanisms and operations. We will see in a moment that, in order to (try to) measure the angular amplitude of the sun and moon, he certainly needed to put in place special – and complex – mechanisms. That said, I propose to return to the considerations made by Apuleius to see where they end up. He continues: He also, when far advanced in old age, devised a divine theory about the sun, which I have not only learned but confrmed by experience, namely, by what multiple of its size the sun measures its own orbit.4 Thales is reported to have explained this when he had just discovered it to Mandrolytus of Priene, who was delighted by the new and unexpected knowledge, and asked him to name whatever remuneration he wanted to receive as a reward for so wonderful a proof. “It will be enough of a reward,” said Thales the Sage, “if, when you begin to make known to others what you have learned from me, you do not attribute it to yourself, but declare that I, and no one else, is responsible for the discovery.” A handsome reward indeed, worthy of such a man, and everlasting! For still today, and forever in the future, that reward will be given to Thales by all of us who are truly aware of his interest in the heavens.5 The passage shows us an Apuleius who speaks with knowledge of the facts, who knows much more about Thales (in particular, specifc things about the ‘dimensions’ of the sun, based on measurements that he personally repeated), and who clearly understood the meaning of the answer to Mandrolytus. Yet, he was neither an astronomer nor an unconditional admirer of Thales; in fact this is the only occasion on which he mentions Thales. We must therefore assume that, somehow, Apuleius had the good fortune to read something written about Thales which went into detail and accounted for the information given to Mandrolytus with a certain precision, so much so that Apuleius became interested in this measurement and set out to verify it for himself. It is a pity that we lack more precise information about the text that Apuleius might have read, but his own clarity – quite different from the generic indications which come down to us on how Thales managed to measure the height of the pyramids (Section 4.2) – can only be explained by assuming that his source of information was equally clear. In fact, this report suggests the care taken not only by the authors of the text that reached Apuleius, but by Thales himself in promulgating his research. The information sought here – in this case a quantitative datum – presupposes a large number of related considerations, and a series of rather complex and coordinated actions.6

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But there is more: Mandrolytus “was delighted by the new and unexpected knowledge, and asked him to name whatever remuneration he wanted to receive as a reward for so wonderful a proof. ‘It will be enough of a reward,’ said Thales the Sage, ‘if, when you begin to make known to others what you have learned from me, you do not attribute it to yourself, but declare that I, and no one else, is responsible for the discovery.’” Apuleius, in turn, comments: “today, and forever in the future, that reward will be given to Thales by all of us who are truly aware of his interest in the heavens”. The reward to which he alludes is evidently due in return for the freedom Thales granted to Mandrolytus to make use of this particular teaching. For an incredibly long time, no attention was paid to this corollary of the story.7 Yet what is prefgured here is that free access to information without restrictions that we have known for several decades under the name of open source or open access, an option widely used since this concept was introduced between 1985 and 1990, on the initiative of Richard Stallman and Linus Torvalds8 – although of course neither had any idea that they had such an illustrious precedent. This point of comparison allows us to see an aspect of this narrative that previous generations could only overlook. That said, let us get to the substance of the question, starting with the fact that a hint of this same narrative also emerges, surprisingly, in Flavius Julian (the emperor traditionally referred to as the Apostate): When someone asked him [Thales] how much pay he should give for what he had learned, [Thales] said “if you agree that you have learned from me, you will pay me my worth.”9 For his part, Diogenes Laertius reports of Thales: He was also the frst to discover the sun’s path from solstice to solstice, and, according to some, the frst to declare that the size of the sun is one seven hundred and twentieth of the solar orbit and the size of the moon is one seven hundred and twentieth of the lunar orbit.10 As we can see, the frst of these statements confrms information provided by Apuleius, while the second allows us to understand precisely what it meant to measure the circle of which Apuleius spoke, and in particular what the proportion (the divina ratio) was: it was 720 times (i.e. 1/720). However, Archimedes11 (the Syracusan scientist who lived between 287 and 212 BC) reports that the value 1/720 was ‘discovered’ by Aristarchus of Samos12 and subsequently measured by himself, arriving at the same result. In the case of Aristarchus, there is a strange circumstance. As Heath (1913, 23) writes: It is diffcult to believe that Thales could have made the estimate of 1/720 of the sun’s circle known to the Greeks; if he had, it would be very

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strange that no source earlier than Archimedes mentioned it, and that Aristarchus should in the frst instance have used the grossly excessive value of 2° which he gives as the angular diameter of the sun and moon in his treatise On the size and distances of the sun and moon, and should have been left to discover the value of ½˚ for himself as Archimedes says he did. Nonetheless, Apuleius’ narrative is not only “worthy of mention for the touch of humanity it contains” (Heath 1913, 20), since it makes use of information that is too precise to be without foundation. It was quite possible that a document at that period could be known to one person but not another – and at the time of Aristarchus (about 310–230 BC) the library of Alexandria was still young. So I fnd it reasonable to suppose that Apuleius might have had access to information other than that which Aristarchus and later Archimedes could rely on. Apuleius and Diogenes Laertius are more likely to be right than wrong. Another remark by Heath (1913, 20) is also worth noting: Thales… could hardly have stated the result in the precise form in which Diogenes gives it. If, however, he stated its equivalent in some other way, it is again pretty certain that he learned it from the Egyptians or the Babylonians. In this case, I disagree with Heath, mainly because the measurement of the angular amplitude of the solar disk is a matter of individual intellectual curiosity which would not have been capable of mobilizing the learned men of a royal court. What is more, it does not appear that the notion of the angular amplitude of the solar and lunar disk was available in Mesopotamia, Egypt, or Greece at the time of Thales (or for a while later). Consequently, the premises are lacking to support Heath’s conjecture. For the reasons indicated, it therefore makes sense to think that the notion of angular amplitude was invented (if not named) by Thales, then taken up by Archimedes and Aristarchus, and later by Apuleius (and possibly others). All of them reached the same or almost the same result. We are talking about the attempt to give the dimensions of a heavenly body as a fraction of its orbit (i.e. a fraction of the so-called round angle).13 Imagining such an operation without having the prior concept of angular amplitude is very complicated. Aristarchus and others, not unlike Thales, apparently lacked a common term for angular amplitude, but they still reached the brilliant idea of relating the angular amplitude of the sun (and the moon) to the circle. The implicit premise is that, even if we are not able to establish the actual width or diameter of these celestial bodies, nevertheless, with the naked eye we can notice that the two bodies seem to have the same dimensions and can have an idea of their angular amplitude. As to calculation, it seems to require the assumption that the sun completes

104 Five quantitative inquiries a circle in its course through the night. We know that a contemporary of Thales, Anaximander, supposed this, and Thales may have been well aware of the fact. The idea can also be expressed by saying that, if the two mammoth stars could make a circular path around the earth in 24 hours, they would travel the path corresponding to their angular amplitude a considerable number of times. But how many times exactly? Let us assume, at least for the moment, that Thales did suppose that the sun and moon are perfectly capable of ‘passing under’14 the earth, and deal with the fraction 1/720, equivalent to ½°. Astronomers assure us that the solar and lunar discs have an angular amplitude very close to ½°, so Thales was able to estimate their angular amplitude with a surprisingly high level of precision. However, posing the question, conceiving the search for the relationship between the small angle of both cosmic bodies and the round angle, then carrying out the evaluation and translating it into numbers – all of this presents enormous conceptual and practical challenges. The practical challenge in particular is noteworthy: even in our days, it would be very diffcult to design (let alone make) a model in wood or metal having an angular amplitude equal to precisely half a degree. Anyone else would have given up – but not the elderly Thales!

8.2 How to ‘take measurements’ of the sun We do not know how Thales managed, but we can speculate. At the time of Thales, as well as at the time of Aristarchus, Archimedes, and Apuleius, in order to estimate the angular amplitude (that is, the visible amplitude of the solar disk), it would have been necessary to place an observer at a given point, A, and then at B, a point set at a known distance (say, ten metres?) away from A, to erect a suitable structure (made out of wood?), where someone else could be ready to cover the sun some way or the other. The challenge was to make a physical object which appeared exactly the same size as the solar disk when viewed from a known distance (in this case, the distance between A and B). Thales might have prepared a series of tablets of different sizes to fnd one that was the best ft. This method has the advantage of being repeatable (like the measurements concerning the solstices and equinoxes). Indeed, it would make sense to repeat the search for the right tablet several times, assigning different people both to act as observers located in point A, and to act as assistants in charge of the tablets at B. The aim would have been to eliminate or reduce as much as possible variation from observer to observer in the selection of the tablet. (Modern scientifc experimental method, of course, has precisely the same requirement of eliminating subjectivity from its measurements – so this may be something else it owes to Thales.)

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8.3 How to determine how many parts make up the whole? There is little doubt about the next steps in the operation. If it could be ascertained that the sun is as large as a given tablet when the observer is at the established distance, then it would simply be a matter of comparing the size of the tablet to that of a circle having as its radius the distance AB. I assume that Thales would have built a physical circular structure (of considerable size) allowing him to measure out with the tablet.15 The count will surely have been repeated several times and perhaps it will have been carried out by several different people. Obviously, it cannot have always given the same result, but at least a reasonably narrow range of results will have been obtained, after which someone – Thales, then Aristarchus, then others – will have found himself having to choose the fgure he deemed most accurate. Note that in this method it is not necessary to create a triangular object (tablet) with an angular amplitude equal to ½°, which would have been impossible. The key lies in being able to measure out a large circle with the chosen tablet, which one could think of as the bottom of a very narrow and long triangle with its apex at the centre of the circle (in this case, then, a triangle 10 metres high). Of course we cannot be sure, but something like this must have been done, because otherwise the number 720 would never have been arrived at. One can imagine that the experiment would have been very impressive, and drawn observers.16 There will also have been a need for several collaborators, who would need training. The planning and invention required of Thales was considerable. The recording of measurements should not be underestimated either: this novel procedure was vital to the success of the operation. So perhaps only someone respected as Thales could have secured the means necessary. The experiment must have been quite an event. It is attractive to think that the ring structure could also have been used to model the sun’s path around the earth – anyway, in the meantime, Anaximander had developed the theory according to which the sun did take a circular path around the earth.

8.4 All this just to acquire a ‘number’? Apuleius, in saying quoties sol magnitudine sua circulum quem permeat metiatur, is really unequivocal, within his linguistic resources, in speaking of angular amplitude, of a radius and a unit of measure. And these are not things one can just make up. It is simply unthinkable that Apuleius’ story, including the evocation of Mandrolytus’ emotional response, was invented from scratch. But, if that is right, then it is likely that an impressive wooden structure (of no negligible size) would have been made, put in place, and

106 Five quantitative inquiries used just in order to get a number. Only a Thales with his prestige and a whole collection of previous quantifcations could have dared to devise something of the sort! For these reasons, our curiosity about how Thales was able to achieve a result so sophisticated as to impress and even move Mandrolytus (and others as well) has full right to be indulged, even at the expense of some speculation.

8.5 Revival of the ‘method’ of Thales in the imperial age It is now time to recall the counting method developed by Cleomedes (see Section 6.2.3). In Caelestia 2.75, Cleomedes explained how an hourglass can be used to establish a proportion between the angular amplitude of the sun and the 24-hour cycle (that is, a round angle).17 The fact that he arrived at a fgure of 750, apparently without having any idea that others had calculated 720, perhaps shows that he was aware of the problem but not the solution that they had adopted, and that the method he used was his own, and not as good as the one devised by Thales. Conversely, of course, there is also the theoretical possibility that Thales had used the strategy described by Cleomedes, both to date the equinoxes and to calculate the angular amplitude of the sun and moon. But the precision he achieved suggests otherwise. Would it have been possible to reach the fgure of 720 by counting out cups? There is more room for imprecision in Cleomedes’ method (the size of the cup, the precision needed in flling them): the fgure of 750 is probably the result of imprecision inherent in his method.

8.6 Preliminary Conclusions 1 In all the cases examined so far, the available evidence may well seem, at frst sight, too poor to be able to authorize the daring conjectures offered. In each case, however, there are some things that are certain. It is a certainty, for example, that Thales personally ascertained that the inclination of the pyramids allowed the sun to generate a shadow even when it was only at 45°. It is equally a fact that we have too many reports on his commitment to dating the tropai to doubt that he tried to establish them. And it is a fact that the numbers 25 and 720 have not been simply made up by our sources. In short, we have all we need to be sure that, in each investigation examined so far, Thales identifed a problem and worked out a way of solving it with the greatest determination. I have already said several times that all this took place, as far as we know, in a context totally devoid of precedents and models. I have also pointed out that many of these investigations must have involved other people as observers (or operators), a circumstance that will have turned his work into a shared enterprise, to the extent that it prefgured the requirement for objectivity and repeatability that marked modern experimental method.

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The height of the pyramid was not in fact measured, although a defnite idea of how it could be measured was established; a method for dating (and so predicting) the tropai and isēmeriai was established; the secret of the solar eclipse was defnitively revealed; we know that the measurement of the angular amplitude of the sun was successful. Thales did not establish a tradition to take on his work, but luckily for us something of his own work was told and remembered.

Notes 1 In Florida 18.30–31 (=11A19 DK = Th178 W = 5R13 LM) Apuleius writes that Thales Milesius ex septem illis sapientiae memoratis viris facile precipuus – enim geometriae penes Graios primus repertor et naturae rerum certissimus explorator et ast(r)orum peritissimus contemplator – maximas res parvis lineis repperit: temporum ambitus, ventorum fatus, stellarum meatus, tonitruum sonora miracula, siderum obliqua curricula, solis annua reverticula; idem lunae vel nascentis incrementa vel senescentis dispendia vel delinquentis obstiticula. The passage continues with further information that will be considered in shortly (n. 5 below). 2 R. 10, 600a4-6 (=Th22 W = 5P14 LM): Ἀλλ ‘οἷα δὴ εἰς τὰ ἔργα σοφοῦ ἀνδρὸς πολλαὶ ἐπίνοιαι καὶ εὐμήχανοι εἰς τέχνας ἤ τινας ἄλλας πράξεις λέγονται, ὥσπερ αὖ Θάλεώ τε πέρι τοῦ Μιλησίου καὶ Ἀναχάρσιος τοῦ Σκύθου. 3 The extreme scarcity of information emerging from fctional narratives encourages us to assume that Anacharsis did not live later than Thales. 4 At this crucial point, the turn of the sentence may not be intuitive, but it is still unequivocal: measuring how many times a segment (equal to the angular width of the sun) ‘enters’ the circle. The implication is that this measurement is not abstract but empirical, since it is a question of ascertaining how many times the segment actually ‘enters’ the circle. 5 Following the text reported above (n. 1) we read the following (Apuleius, Flor. 18.32–35 = 11A19 DK = Th178 W = (partially) 5R13 + 5P18 LM): Idem sane iam proclivi senectute divinam rationem de sole commentus est, quam equidem non didici modo, verum etiam experiundo comprobavi, quoties sol magnitude its circulum quem permeat metiatur. Id a se recens inventus Thales memoratur edocuisse Mandraytum Prienensem, qui nova et inopinata cognitione impendio delectare optare iussit quantam vellet mercedem sibi pro tanto document rependi. ‘Satis’ inquit ‘mihi fuerit mercedes’ Thales sapiens ‘si id quod a me didicisti cum proferre ad quosdam ceperis, tibi non adscriveris, sed eius inventi me potius quam alium repertorem praedicaris’. Pulchra merces prorsum ac tali viro digna et perpetua; nam et in hodiernum ac dein semper Thali ea merces persolvetur ab omnibus nobis, qui eius caelestia studies vere cognovimus. 6 If Thales really had made this measurement at an advanced age, as Apuleius relates, an implicit criticism of Anaximander’s extremely inaccurate measurements (the latter said that the sun is 27 or 28 terrestrial diameters from the earth) is likely to have emerged. 7 In fact, until just over 30 years ago, it would have been impossible to pay due attention to this circumstance. 8 So far as I know, the two men chose not to protect their invention with a patent. They just asked that future developers of the operating system (Linux) agreed to recognize the authorship of the same (that is, not to appropriate it themselves) and abide by the same rules, and tried to make the open access policy widely accepted and shared.

108 Five quantitative inquiries 9 Julian, Panegyricus in honor of the empress Eusebia 16 (Or. 3.162.2–5 = 11A19 DK = Th296 W ≠ LM): ἐρομένου γάρ τινος, ὑπὲρ ὧν ἔμαθεν ὁπόσον τινὰ χρὴ καταβαλεῖν μισθόν «ὁμολογῶν», ἔφη, «τὸ παρ’ ἡμῶν μαθεῖν τὴν ἀξίαν ἡμῖν ἐκτίσεις». 10 Diogenes Laertius I 24 (=11A1 DK = Th237 W = 5R14 LM): καὶ πρῶτος τὸ τοῦ ἡλίου μέγεθος τοῦ σεληναίου ἑπτακοσιοστὸν καὶ εἰκοστὸν μέρος ἀπεφήνατο κατά τινας. 11 In Arenarius 137.12–18, a passage that does not appear in any of the collections of texts concerning Thales. On the subject, see now Panchenko (2016, 787). 12 An Alexandrian astronomer active in the frst half of the third century BC, Aristarchus was sometimes called “the Copernicus of antiquity” due to the fact that he was one of the ancient supporters (a small group of experts, all active, approximately, in the 100 years following the death of Aristotle) of the heliocentric theory. 13 Here I note that, to indicate an angular amplitude of 87°, Aristarchus found nothing better than to use the expression ἔλασσον τεταρτημορίου τῷ τοῦ τεταρτημορίου τριακοστῷ, “a quarter (of a circle) less than one-thirtieth of the quarter”, i.e. (90 − 3)°. 14 This was, as we know, Anaximander’s idea. Something more on the subject will be presented in Section 12.4. 15 It may be worth noticing that the tablet to be used for calculation could not be rectangular since two sides had to converge, though imperceptibly. 16 The very construction of a large circular structure, and the establishment of a refned functional correlation between what Thales set out to ascertain and what he was doing in the various phases, will have constituted, I presume, a ‘lesson’ in itself. Perhaps, the progressive dismantling of the ‘beautiful’ circular structure, even as a result of fortuitous events, did arouse regret! 17 It is assumed that Cleomedes lived after not only Aristarchus and Archimedes, but also Apuleius and Diogenes Laertius; however, defnite evidence is lacking.

Part III

Three further investigations on earth, waters and rocks

9

Surface water, arche¯, earth, and, it seems, some fragments of Thales

Only two doctrines concerning terrestrial matters appear to be ascribed to Thales. Aristotle mentions both. In a very famous passage from Metaphysics book 1, he says that Thales identifed the frst principle and source of all things in water. When he returns to the subject in the De caelo and introduces some extra details, namely that, according to Thales, “the earth is above the water”, and that “it foats like a log”, it is not clear how Aristotle views these claims. To understand them, we need to look to our other evidence, especially Seneca.

9.1 The testimony of Aristotle 9.1.1 An artifcial combination In the frst book of the Metaphysics, Aristotle wants to give a basic account of philosophy and to underline the orientation of sophia, and so of philosophy, towards knowledge. So when in Metaph. 1.3 he sets out his account of four causes, he begins by evoking “those who before us have undertaken the investigation of entities and have philosophized around the truth”,1 then speaks of “the majority of those who frst philosophized”, and who “held that the archai of all things are only those of a material kind”.2 His reasoning continues as follows: [1] Yet they do not all agree as to the number and the nature of these principles. Thales, the founder of this school of philosophy, says the principle is water (for which reason he declared that the earth rests on water). Perhaps he had derived this assumption from seeing that what nourishes all things is moist and even what is warm comes from this [i.e. water] and lives because of it (and what things come about from is the principle of all things)—it is for this reason, then, that he had this idea, and also from the fact that the seed of all things has a moist nature; and for things that are moist,3 water is the principle of their nature.4

DOI: 10.4324/9781003138723-12

112 Further investigations on earth, waters and rocks Here, Aristotle is attributing to Thales the idea that the archē is to be identifed as water, in the sense that that water is the origin of everything (including the earth? including the stars?). Without being any more specifc about this,5 he immediately goes on to offer a whole series of claims: (A) Thales “also explained that the earth is above water”; (B) he probably came to this conclusion “when realizing that the nourishment of everything is moist6 and that even heat is generated by the humidity and lives on this, i.e. draws from this the resources that are necessary to live”, that is, by investigating the dependence of (many? all?) forms of life and even heat (bodily heat?) on moisture; (C) it was he who came to the conclusion that “that from which generation takes place, this is the archē of everything” (perhaps “of every living being”); (D) this conviction was formed on the basis of the considerations just referred to, but also “on the basis of the fact that the seeds of everything have a humid nature and that, for humid things, water constitutes the origin of nature”. (So, does water constitute the origin of the nature of each humid thing and, in particular, of all seeds?) (E) Even heat (note: not fre!) is generated from humidity.7 That there is a discrepancy between the doctrine of the archē and the fve claims introduced in support of this theoretical core has been noted many times, of course. The basic one is between water and moisture: moisture is an instable and changing ‘thing’ we humans see and touch on different occasions. It therefore cannot be identifed as the cosmic water. Nevertheless, all fve of these claims do in fact rely on things that Aristotle thinks Thales himself had thought. The very fact that they are ill-adapted to the context, as well as their very specifc nature, makes this clear. We can be sure, thanks to Aristotle, that Thales dealt with the environmental conditions that support the generation of new living beings (vegetable and animal) and with the role that humidity, associated with a reasonable warmth, continuously plays in the generation (and preservation) of very different living creatures. In fact, between the idea that the archē of everything is to be identifed in the water and the idea that water penetrates the soil and generates moisture enabling seeds to germinate and give rise to plants (as well as enabling other beings to come to life), there is an enormous conceptual distance. So did Aristotle perhaps suspect that the second block of remarks and conjectures has very little to do with the frst? Apparently not: it seemed to him that they were part of the same discussion. Two things as different as an all-encompassing idea of the universe and a set of observable empirical details (the humidity of the ground and its analogues) end up being combined by him in quite an unnatural way. Aristotle’s authority has led to this being overlooked ever since.

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To complicate matters a little, the frst specifcation he introduces, that the earth is above water, creates a further diffculty. Being introduced by a dio clause, it would seem that a sort of corollary is presented: “if water constitutes the archē, it is understandable that the earth is above water”. But why on earth should this be the case? There is no inferential relationship between the two statements. On the contrary, they seem mutually exclusive.8 At least, Aristotle does nothing to clarify what connection he glimpsed between these two statements. However, as is well known, in a chapter of De caelo there is a series of remarks that help to clarify the meaning of ‘above’. At 2.13, Aristotle is wondering about what we call gravity: any bit of earth, if we lift it and let it go, falls downwards and, if there were no obstacles, it would sink to the centre of the earth; but this does not apply to the whole earth, which in fact does itself not fall. Why? This is how he puts it: [2a] Why does a little bit of earth, let loose in mid-air, move and will not stay still, and the more there is of it the faster it moves, while the whole earth, if one could leave it free in mid-air, should show no movement at all?9 Right after he adds: [2b] Others say that it [the earth] rests upon water. This, indeed, is the earliest account that we have received, and they say that Thales of Miletus stated it: that is at rest because it foats like wood or something else of that sort (for it is the nature of such things that they rest not upon air but upon water), as if the same account that holds for the earth did not hold for the water that carries the earth! For it is not the nature of water to be at rest in mid-air; it must have something to rest upon. [294b] Again, as air is lighter than water, so water than earth; so how can what is lighter lie beneath what is by nature heavier?10 Aristotle begins by dwelling on the disanalogy between a piece of earth that can only fall and the earth as a whole that has no diffculty in standing still at the centre of the universe – in other words, between the small bit of the world made up of what I usually see if I look out the window, and the earth understood as an immense spherical body. The next step is to speak in many ways about the land–water relationship: the earth rests (keisthai) on water; the earth is static (einai menousan); the earth foats (dia to plōtēn) and looks like a wood or something like that. These specifcations, even without context, are obviously convergent. Instead of explaining himself a little better, Aristotle hastens to add that even water needs to rest on something, something that is certainly not air; and water is lighter than earth. So, he argues, how can a heavier thing rest on a less heavy thing? Shouldn’t ‘the earth’ sink into water?

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A crucial question is, what could he have meant here by ‘earth’? The terrestrial sphere or the lands on the surface of which we live? Aristotle has Thales say that the earth rests on water without specifying what the water in turn rests on, nor what water and which earth we are talking about. Still abstractly he objects that, since water is lighter than the earth, it should be the earth underneath and supporting the water, not vice versa – without considering that this would have been obvious to Thales too. To substantiate such considerations, Aristotle exploits statements whose meaning he fails to understand. For he reports that the earth rests on water or foats like a log of wood. It does not occur to Aristotle to note that water supports tree-trunks, but not clods of earth, nor to keep in mind that, in the corresponding passage of the Metaphysics, he thought that the relevant issue was the environmental condition needed for the generation of new living beings. Under these conditions, the connection Aristotle suggests here is mysterious or, worse, bordering on nonsense. It is no coincidence that Schofeld spoke, in this regard, of an “unappealing version of fat-earthism”; yet he also imagines (1997, 43–48) that Thales probably held a position similar to that of Anaximenes. Schofeld’s evaluation evidently depends on the presumption that Aristotle must have spoken competently and must be taken literally, among other things without taking into account either the reference to the environmental conditions evoked in the Metaphysics or the observational data relating to solid bodies (stones, sand, more rarely muddy earth) which invariably sink in seas and lakes. In doing so, he ends up by attributing to Thales the paternity of a rather extravagant fantasy. So we need to ask what kind of earth it is, according to Thales, which rests on water. Aristotle was quick to generalize, but what seems to support his generalization boils down to very little. It turns out, then, that the attribution of the thesis that water is the archē to Thales is surprisingly insecure. The evidence adduced offers only very fragile supports in favour of what Aristotle was claiming in the Metaphysics passage. Everything he says about Thales and water – that water promotes life, or that it is to be found under the earth (so that the earth foats on it) – appears quite inappropriate as support for the thesis that water is the archē. 9.1.2 A teaching that sinks… There are many reasons to suspect that Aristotle may not have understood Thales’ thought about earth and water. In fact, if he had understood correctly, he would not have written, in the Metaphysics passage, that “Perhaps (isōs) he had derived this assumption (hupolēpsis) from seeing that what nourishes all things is moist”. Likewise, in the De caelo passage he would not have admitted that he does not understand why Thales, instead of declaring that it is water that foats on the earth, may have affrmed the exact opposite. True, these teachings were of interest to Aristotle only as an attempt to explain why Thales thought that water was the archē. Indeed, in a sense, he is

Surface water, arche¯, earth  115 the first to acknowledge that he cannot really explain it. He would have liked to find statements closer to the thesis of water-as-archē but, in the absence of better material, resorted to what he found. 9.1.3  …and a teaching that surfaces The other sources available on the subject still remain for us to consider, of course (they will be examined below). In the meantime, it is desirable to take good note of what Aristotle reported on Thales. These are things that are not trivial or obvious: that “even heat (auto to thermon) is generated from the humid and lives from this”, that “the seeds of everything have a humid nature”, that “for humid things water constitutes the origin of nature”, that “ rests (keisthai) on the water”, that “the earth is in a static position (stands still: einai menousan) while floating (dia to plōtēn) as a wood or something similar”. These teachings are of interest to him, I repeat, only as a way of explaining the attribution to Thales of the thesis that water is the archē, but they also provide us with valuable information. Indeed, a whole group of remarks on the presence of humidity and water on earth and under the earth, are surfacing, and seem to constitute a definite view to be ascribed to Thales. As will be shown in a moment, this finds confirmation in later authors, above all in Seneca’s Naturales Quaestiones. It is also interesting that, in the Metaphysics, we read: “Thales said…” In what sense did he ‘say’? Is Aristotle reporting something unexpected that Thales actually said – so that this is truly a quotation (therefore a fragment) from him? It will be objected that this is excluded from the outset. Yet the formula “Thales said” appears more than once. Chapter 17 will be devoted to the question.

9.2  The testimony of Seneca The evidence of Aristotle’s remarks in De caelo is not unique – even in its use of the expression “Thales said”. Comparable remarks are found, in particular, in Seneca’s Naturales Quaestiones, where Thales, surprisingly, has a place of some importance. He first appears in the third book, which is dedicated to the origin of terrestrial waters. Seneca writes: [3] [3.13.1] I would add that water is, as Thales said, “the most powerful of the elements”. He thinks it was the first of them, and that all the others sprang from it. We Stoics, too, are also of the same opinion. Indeed we claim that it is fire (etc.). [4] [3.14.1–2]. The following view of Thales is silly. He says that the world is held up by water and rides on it like a ship, and because of its mobility, when it is said to tremble it is actually moving with the waves. “Therefore it is not surprising if there is plenty of moisture to make

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Further investigations on earth, waters and rocks rivers fow since the whole world is located in a fuid.” Reject this crude and outdated view.11

(There is also a third statement from Seneca which we will come back to shortly.) Not unlike Aristotle, Seneca reports in rather general terms the claims (1) that water is the most powerful of the elements, (2) that water was before , (3) that everything is derived from water, (4) that the earth as a whole is supported by water, and (5) that the whole world is as if it were placed in water. But what does he adduce in support of all this? To begin with the phenomenon of its quaking – compared to a ship whose ‘trembling’ is a feature of its movement in the water. We see a similar tension as in Aristotle between these claims and what they are supposed to explain. Indeed, there is an even more striking tension with the reference to the source of rivers: after all, the water that feeds the rivers does not come from the other side of the earth, but from just below the surface. But even the fact that ships occasionally tremble can only suggest a model for how limited portions of the surface layers of the earth can shake. Therefore it is of no use to explain and lend credibility to the fve generalizations identifed above. Seneca himself does not understand how the specifc claims relate to or help explain the more general ones. These sentences claim to report what Thales said: Ait enim terrarum orbem aqua sustineri et vehi more navigii, mobilitateque fuctuare tunc cum dicitur tremere; Non est ergo mirum si abundat umore ad fumina profundenda, cum mundus in umore sit totus. But quae sequitur Thaletis inepta sententia est and hanc veterem et rudem sententiam explode tell us (a) that, Seneca is recalling statements made by Thales, (b) that, nevertheless, he was himself unable to understand what Thales was talking about. Let us focus now on Seneca’s third statement. The shaking of the earth (earthquakes) to which he gives a feeting mention in Book 3, is illustrated in more detail in a passage in Book 6 (which is entirely dedicated to earthquakes). Here he writes: [5] That the cause [of earthquakes] is found in water is stated by more than one person, and more than one account is given. Thales of Miletus judges that the whole earth is carried and foats upon moisture that lies underneath it, whether you call it the ocean, the great sea, or water of a different nature that is still uncompressed and simply the moist element. “On this water the earth is supported,” he says, “as a big heavy ship is supported by the water which it presses down upon.” It is superfuous to give the reasons why he thinks that the heaviest part of the world cannot be carried by breath, which is so thin and mobile; for the present subject is not the location of the lands but their motion. He offers this argument that water is the cause of the earth’s agitation: in every major earthquake new springs usually burst forth, as it also happens that ships take on water if they tilt and lean to one side, and if they are pressed down

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too much when they are carrying excessive weight, either the water overwhelms them or it rises on the right and left sides more than usual.12 This is a rich text, with a lot to tell us, and it is surprising that it did not fnd a place in either Diels–Kranz or Laks–Most, especially since it includes a direct quotation, which is introduced and, as it were, certifed by the word inquit.13 Here we are offered a Thales with a well-structured system of teachings not attested elsewhere. The earth, Thales inquit, resembles a large and heavy ship resting on water. From time to time earthquakes shake the earth as waves shake ships.14 When this happens, new springs open up on the surface of earth, a circumstance that makes one think of water spraying onto the deck of the ship in a rough sea.15 The new springs, in turn, confrm the suspicion that there is a considerable quantity of water underground: those same bodies of water which, as Seneca told us in 3.14, feed the rivers – and which, we can add, explain the discovery of water when wells are dug. The implication seems to be that, if you go down to a considerable depth (as happens when you dig wells), you often reach regions rich in water, that is, the layer which, in contemporary English, is called the aquifer. We are not being asked to imagine that rivers and springs fow from a very great depth (certainly not from a depth of kilometres). What is thus emerging is a vast and complex range of detailed observations, with particular attention to the relatively superfcial layers of the earth, and water for which we have evidence at an indeterminate, but certainly not extreme, depth (given that it gives rise to surface streams and rivers, and also feeds the springs). From another point of view, the reference to the foating trunk in Aristotle and to the navigium, also as something which foats, in Seneca (3.14 and 6.6) is very reassuring. In fact, we see that the two have had access to the same information. Their close similarity is an excellent reason for thinking that we have a doctrine unequivocally ascribed to Thales alone. And both Aristotle and Seneca seem to report without understanding: this is an excellent guarantee that they have not manipulated the information they are reporting. Seneca writes, moreover, that Thales “brings as an argument to demonstrate that water plays a role in earth movements”, such as the eruption of new water sources which sometimes follows an earthquake. This shows that Seneca is not only reporting a series of convergent observations, but also an argumentum, a line of inferential reasoning that starts from a hint: Thales iudicat that under the earth there should be a layer of water everywhere and demonstrates this by citing the formation of spontaneous springs as well as the water that feeds rivers. This is momentous. In the other cases, we had reasons to think that Thales began with the shadow of the pyramid with the sun at 45°, or the appearance of a sort of black disk that obscures the sun, or that he collected quantitative

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data of demanding precision. In this case, what we have are traces of a line of reasoning made by Thales. The evidence from which he started, what he took as legitimate evidence, and what he inferred from it, all that is invaluable because it uniquely tells us about his way of thinking. And now a word on the primacy of water, another area of apparent convergence between Aristotle and Seneca. Seneca too seems ready to attribute a general claim to Thales (text [3] above): I would add [that water] is, as Thales said, “the most powerful of the elements”. He thinks it was the frst of them, and that all the others sprang from it…. (adiciam, ut Thales ait, “valentissimum elementum est”. Hoc fuisse primum putat, ex hoc surrexisse omnia; then cum mundus in umore sit totus …) One might suppose that these statements simply follow Aristotle, but that would be to ignore something else he says: “the present subject is not the location of the lands but their motion” (non enim nunc de situ terrarum sed de motu agitur, Nat. Quaest. 6.6.1–2). Seneca himself, in fact, takes care to clarify that Thales’ emphasis on the importance of water does not have reference to the earth as a whole or to the entire universe. The movements Seneca is referring to are those concerning ‘lands’ (and therefore not the whole earth), and are circumscribed and occasional ones, known as earthquakes. So the topic concerns what is observable, what happens on the earth’s surface (or at a shallow depth): on the one hand, earthquakes (which put one in mind of the slight instability of large ships, and are related to springs and waterways); on the other hand, the humidity of the soil that allows the seeds to give rise to the formation of (a great amount of) new living beings. Thales is very clearly appealing to local observations that anyone can make. The sentence non enim nunc de situ terrarum sed de motu agitur is especially key to our conjectures as it tells us that here we are talking not about “where the lands are” in general and in the abstract, but about circumscribed phenomena: earthquakes. By contrast, the Aristotle of the Metaphysics saw in these claims an attempt to develop a theory of the formation of the cosmos as a whole. Seneca, in turn, does not also deal with humidity, germination, and related phenomena (all taking place in more superfcial layers of earth), but the shared reference to foating objects (a trunk in Aristotle, a ship in Seneca) proves that both were borrowing from the same Thaletan ‘doctrine’. It looks very much as if Aristotle and Seneca read the same pages, but that the more celebrated of the two has substantially misunderstood them. That is no small conclusion! And not only this. In light of these considerations, the expression “everything is derived from water”, found in [3], lends itself to a different meaning from the one that Aristotle gave it. It is possible instead to take from it that all forms of life, and a series of other phenomena observed on the earth’s surface and in the immediate subsoil, are only possible because

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there is water (or, conversely, could not occur unless there were a reasonable abundance of water). That this is the correct interpretation is not certain, but at least it cannot be ruled out.

9.3 The testimonies of a doxographical nature These themes are taken up in different ways in the doxographical sources. In ps.-Plutarch, there is a rather long stretch in which the anonymous author frst tries to argue that the original stoicheia cannot consist of earth and water but must consist of (a) shapeless matter and (b) form or entelecheia.16 After this, ps.-Plutarch identifes Thales as the person who initiated philosophy and from whom the Ionian school was formed as a philosophical school. Moreover, he makes a cursory reference to Egypt and declares that “in his [Thales’] opinion everything derives from water and dissolves into water”. It is at this point that pseudo-Plutarch produces a valuable excursus on the reasons that Thales allegedly adduced in support of this more general thesis: [6] Thus it is likely that indeed all things have their principle from moisture. Second, that all plants are nourished and bear fruit because of moisture and dry up when they lack it. Third, that even the very fre of the sun and stars is nourished by the exhalations of waters, and so is the cosmos itself. This is why Homer too lays down this thought about water: “Okeanos, which is the origin of all things”.17 Not unlike text [5], this doxographic passage deserves to have been included in both DK and LM. In fact, the frst two points – that all plants are nourished and bear fruit because of moisture and dry up when they lack it – outline a structured set of considerations (on the importance of wetness for all living beings) which harmonize very well with the statements of Aristotle (and Seneca). If we had any doubts about the meaning of those arguments, the frst two reasons given here (and in text [7]) effectively concur to dispel them. As for the third point, it is easy to see that the idea, as well as the verb anathumiaō, refers to a specifc teaching of Xenophanes on the daily formation of celestial bodies (see 21A40 DK and many other testimonies),18 a teaching that was promptly repeated by Heraclitus (22B12, cf. 22A12 DK), so it is impossible not to suspect that this third point, as well as the reference to Thales, is spurious (its real source is Xenophanes, not Thales). The relevance of the frst two “reasons”, however, remains frm. In other doxographic sources we read: “Thales and Democritus attribute the cause of the earthquakes to water”.19 (This combination will be discussed again in Section 9.5.) The passage from ps.-Plutarch (text [6]) has much in common with what we read in Stobaeus:

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Further investigations on earth, waters and rocks [7] Thales of Miletus declared that water is the principle of things-thatare, for he says that all things are from water and all things are dissolved into water. He bases this conjecture frst on the fact that seed, which is moist, is the principle of all living things. Thus it is likely that all things have their principle from the moist. Second, from the fact that it is because of moisture that all plants are nourished and bear fruit, but dry up when they are deprived of it. Third, that even the very fre of the sun and the stars is nourished by exhalations from water, as is the cosmos itself.20

Taken together, texts [6] and [7] show that these two excerptors, as well as Aristotle (and Seneca), drew from the same Greek source. But they offer further arguments to suggest that their common source openly credited Thales with a theory concerning the crucial role water has in the formation and survival of all living beings (pantōn tōn zōiōn, not just panta phuta). This point is quite explicit. At the most, the common source could have stated that water is the archē of every living being. From that it follows that Aristotle probably overlooked the reference to living beings and wrongly credited Thales with a statement concerning the whole world. This is why texts [6] and [7] are so important, despite their exclusion from both DK and LM.

9.4 The testimony of Servius and Simplicius One of the statements found in texts [6] and [7], that all things are dissolved into water, fnds unexpected confrmation in Servius, the learned commentator of Virgil who was active around 400 AD. In his Commentaries, Servius mentions Thales six times. In fve of these passages, he limits himself to affrming that “others, like Thales of Miletus, from moisture, and this is the source of the expression ‘and Okeanos, the father’”.21 This is signifcant, since these passages suggest that even Hippias probably made a reference to moisture in his survey (Section 1.3 above). However, the sixth reference is much more specifc: [8] But Thales, who maintains that all things are created from moisture, claims that bodies must be buried in order to be able to be dissolved into moisture.22 It is interesting that Servius frst generalizes (omnia… ex umore), to the extent that he evokes the ocean, but then talks about corpses, and their dissolution into the moist (or their progressive transformation into water). It goes without saying that what is reported here could not concern the earth as a whole. Simplicius confrms this. Almost 11 centuries after the time of Thales (Simplicius was active in the frst half of the sixth century AD), this well-informed commentator of Aristotle writes:

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[9] Of those who said that there is one principle and that it is in motion, whom he specifcally calls natural philosophers, some declare that it is limited – like Thales of Miletus, the son of Examyas, and Hippo, who seems to have become an atheist. They said that the principle is water, having been brought to this view by things that appear to perception. For the hot lives on the moist, dead things dry up,23 the seeds of all things are moist, and all nourishment is moistened (i.e. contains a measure of humidity) – and it is the nature of all things to be nourished by the very thing of which they are composed. Moreover, water is the principle of the nature of moisture and is what connects all things. This is why they supposed that water is the principle of all things and declared that the earth rests on water. Thales is traditionally said to have been the frst to reveal the study of nature to the Greeks, although many others had preceded him, as Theophrastus thinks too, but he was far superior to them and so he eclipsed all his predecessors. He is said to have left no written works except the one called Nautical Astronomy.24 Speaking of water, Simplicius attributes conjectural generalizations to Thales (“brought to this view by things that appear to perception”) based on observations of living organisms: heat lives on humidity, corpses dry up (if left in the open air: precisely the reason, as Servius tells us, that Thales thought it desirable to bury them), seeds are moist, all nourishment is moist, everything is ultimately nourished by water and (Plutarch, Stobaeus, Servius) dissolves in water; moreover, the earth rests on water. Only at the beginning and at the end does Simplicius, remembering Aristotle, go back to the question of the origin of all things, but starting from observable facts, with curious attention given to the fate of corpses. The water he is talking about here is something… very earthly, very concrete, very tied to everyday life. Indeed, when one says that everything ultimately feeds on water (Simplicius) and that everything dissolves in water (Stobaeus), and when one talks about earthquakes too (Seneca), the water referred to is, necessarily, water that is present in the ground and under the ground. It is the water of our everyday experience, water into which, over time, buried corpses end up dissolving. Similarly, when they talk about the earth that “rests on water”, it is reasonable to assume that these authors are referring to the same ‘terrestrial’ water, the water that lies just below the earth beneath our feet. If this is wrong, then discussion of burial and earthquakes and the generation of plants and animals would have been completely incongruous. Also noteworthy is the convergence between Servius and Simplicius. In fact, it is likely that Simplicius was ignorant of the existence of Servius and his celebrated commentary. Nevertheless, the same body of information has left signifcant – and independent – traces in both of them. What better proof that the two had access to accurate and detailed information about Thales?

122 Further investigations on earth, waters and rocks Still, it makes sense to ask whether, the references to corpses apart, Simplicius’ source is just Aristotle? I would say no. He also adds non-Aristotelian information when he writes: “Of what everything is made up of, of this also is nourished by nature” (i.e. water). This is a point absent in Aristotle and, indeed, in Seneca. This tells us that Simplicius probably had independent access to the text that was read by Aristotle and Seneca, but he used details from it that both overlooked, including a detail that also caught the eye of Servius. The teachings jointly or separately credited to Thales by these authors give a rather comprehensive and coherent outline of the connections between water and living beings which, in turn, is hardly compatible with the generalizations found in Aristotle. Simplicius preserves both of them, without properly establishing a connection: in his commentary they just coexist.

9.5 The earthquake from Anaximander to Democritus At this point, let us look at the conjectures on earthquakes that are documented for Anaximander, Anaximenes, and Democritus. We can start from what Aristotle reports in Meteorologica 2.7, where he gives an initial overview of the accounts of Anaxagoras, Anaximenes, and Democritus. Of Anaxagoras he reports that earthquakes were explained by pockets of ether underground, with some theories that do not interest us. But for Democritus, Aristotle reports that “the earth moves under the effect of rain-water.”25 The idea is that, when the earth is saturated with water, its cavities fll up with vast amounts of water and, in a certain sense, explode; conversely, in periods of drought, the water present in the ground suddenly falls into empty cavities located further down, causing – we would say – strong vibrations. This cannot but make us think of Thales. Next is Anaximenes, according to whom (again according to Aristotle): the earth, if soaked with water and then dried up, generates fractures and is shaken by these mounds of earth that detach and fall.26 Other sources (Seneca and Ammianus Marcellinus) attribute the same ideas to Anaximenes. From Ammianus Marcellinus we also learn that these conjectures had a rather specifc precedent in Anaximander, who argued that,27 when large cracks form in the ground, the air penetrates it from above, giving rise to currents of air, sometimes very strong ones (vehementi spiritu), which would be at the origin of earthquakes. All of this tells us that Thales initiated a tradition of theorizing on the possible causes of earthquakes, which led to a succession of different conjectures, among which Democritus stands out for the fact that he goes back to the idea that water (rain) can generate instability in the earth’s surface. These circumstances constitute indirect confrmation of the credibility of the doxai on earthquakes concerning the frst master of Miletus.

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9.6 Final considerations 9.6.1 A profle Overall, our sources are surprisingly homogeneous and convergent, to the point that this somewhat neglected doctrine could well have the best textual support of all. In fact, both Aristotle and Seneca as well as the doxographers, as well as Servius and Simplicius, agree in attributing to Thales complex teaching about terrestrial waters. The central idea seems to be the widespread presence of water on the earth’s surface and under the (upper) layers of the earth, a fact that Thales apparently merely observes without trying to explain, but with which he seems to have associated a number of different phenomena: – the widespread underground waters which feed the rivers; – earthquakes, understood as a brief, but recurrent structural instability of the upper terrestrial strata; – the occasional formation of new springs following an earthquake (which could be used as another proof of the presence of large underground water reserves); – the birth of new organisms, plants, animals, and/or humans, which is always associated with a considerable level of humidity (and of warmth); – the nourishment of plants (whose roots seek out moisture); – the diffculty of surviving without access to moisture (or water); – food which, apparently, ‘must’ have an appreciable level of humidity; – decomposition of once-living organisms (a human corpse, a dead animal, fallen leaves): in the frst instance everything that dies invariably gives rise to something wet, and possibly becomes water over time. To this already long list, it seems logical to add a reference to wells, which reach the underground water. Rain is not mentioned, but it is unlikely that it could have been far from Thales’ thoughts. Thales would therefore be said to be committed to lining up a lot of observational data, and then focusing his attention on the preconditions for all these phenomena: the widespread presence of water, including the (presumably) large quantities of water underground which, in addition to feeding springs and rivers (and wells), offer a plausible, if not quite certain, way of explaining earthquakes. The whole story is clearly coherent. The conclusion is not surprising: in a certain way, the primacy of water is proclaimed: as we read in [4], valentissimum elementum est. Clearly, the Thales who tells us about earthquakes, springs, seeds, nourishment, and corpses is not trying to answer questions of a cosmological nature. His interest is limited to what happens on the surface of the earth, or just below it, as well as to the generality of living beings upon it. Conversely, whenever Aristotle and others ascribe to him a theory about cosmic water, they support this claim with patently inappropriate evidence (e.g. about moisture).

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9.6.2 The interest of the frst Milesians in the forms of life When we wonder who, among the Presocratics, started to refect on the forms of life, it is normal to think of Alcmaeon. But thanks to the evidence that emerged in this chapter, it becomes clear that Thales had already taken signifcant steps in this direction, and that Anaximander followed in his wake. Anaximander dealt, among other things, with the appearance of animals, conjecturing that the frst animals (fshes) were formed in the sea, and that the appearance of amphibians led to the very frst terrestrial animals (exposed to the sun, they lost their scales); after that, the animal species multiplied and diversifed on an earth that, we must assume, was already full of grasses and trees.28 Thales prepared the ground for Anaximander’s conjectures. Anaximander also appears to have laid the foundations of meteorology: he hypothesized that the clouds are comparable to large skins full of water which, when they move one another, make a noise (the friction between them causes thunder), adding that, due to this friction, it sometimes happens that these bags break, so it rains.29 The two thinkers look complementary. If Thales tried to understand what we commonly see happening on earth (and underground), Anaximander tried to understand what we commonly see happening in ‘heaven’. They are united by their aim to understand something about the living world – paving the way for the much wider intellectual interests of Alcmaeon. 9.6.3 Aristotle or Cicero? I now propose to return to the idea that the archē is water. In fact, the word archē is not directly and explicitly connected to water by Aristotle. As we have seen, Aristotle introduces the notion of archē in Metaph. 1, 983b7 and 11, but only a few lines later (at 983b21) he states that Thales “says that it is water” (ὕδωρ φησὶν εἶναι). He never returns to the subject. Cicero for his part took from Aristotle the dry affrmation that Thales aquam dixit esse initium rerum (“he said that water is the beginning of things”: De natura deorum 1.25 = Th72 W). Later, Vitruvius asserted that Thales primum aquam putavit omnium rerum esse principium (“declared that water is the frst principle of all things”: De architectura 2.2.1 = Th85 W) and that Thales Milesius omnium rerum principium aquam est professus (“Thales the Milesius declared that water is the principle of all things”: De arch. 8, Praef. 1 = Th87 W). After them, Heraclitus Homericus (1st century AD) declared that “there is agreement in thinking that Thales was the frst to identify in water the cosmogonic element of all things”.30 Similarly, Plutarch was able to assert that: [the Egyptians] believe that Homer, and likewise Thales, have learned from them to recognize in water the principle and origin of all things. In fact the Ocean would be identifed with Osiris, and Thetis with Isis, because nourishes and gives vital force to all beings.31

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These declarations on the subject of water-as-archē are then repeated lazily many other times (in all, a hundred times, as the indications available in the Wöhrle collection of sources: 2009, p. 50, show) and, if I read them correctly, without any hint of independence. In these passages, the starting point is the same for everyone: each gives a sort of elementary summary of the passage we know from the frst book of the Metaphysics, with a simpler statement of what in Aristotle is slightly more nuanced. More importantly, these summaries repeat the basic statement without ever evoking the links by which Aristotle connects the two concepts. This is not a minor point. If to us moderns it seems right to treat the notion of water-as-archē as the central and defning doctrine of Thales, and to overlook the reference to the foating trunk and a whole series of other dissonant details, this is because all these sources, often in Latin, have created a kind of consensus. These 100 voices speak as if Aristotle had certain, explicit and therefore unequivocal report (professus est, writes one of these voices). But the important words – phēsin, ut ait, inquit, putat, iudicat [Thales] – are not used by Aristotle and Seneca about water-as-archē. They are used by them about Thales’ research concerning groundwater and the role of humidity in the generation of living beings and related phenomena. This gives us further reason to think that the notion of water-as-archē was not a doxa of Thales. Instead, it is an unwarranted simplifcation of Aristotle’s report, a simplifcation that acquired the force of legend. By contrast, the reports about Thales’ ideas on the role of terrestrial water gives a much more plausible account of his achievements – and complements his search for quantitative data. Thales did not ask about the nature of water, the nature of fertile land or the essence of life, or try to defne them; his intellectual objective was a series of functional relationships, a dynamic: the circumstances favourable for the formation (and preservation) of living beings. 9.6.4 Finally… To conclude, I observe – but it is almost a banality – that the information reviewed in this chapter has been ignored for so long for a combination of reasons: Aristotle seemed reliable a priori, and some of our evidence for Thales has been overlooked (and Diels–Kranz ignored some important primary testimonies, such as [5], [6], and [7]). To this can be added a widespread tendency to a superfcial reading of Thales. But we do not have to do the same; and the new evidence discussed here lifts the veil on an area of innovative work in which the frst two Milesians were both interested.

Notes 1 Metaph. 1.3, 983b1–3 (=11A12 DK = Th29 W = 5R32a LM): τοὺς πρότερον ἡμῶν εἰς ἐπίσκεψιν τῶν ὄντων ἐλθόντας καὶ φιλοσοφήσαντας περὶ τῆς ἀληθείας. 2 Metaph. 1.3, 983b6–8: τῶν δὴ πρώτων φιλοσοφησάντων οἱ πλεῖστοι τὰς ἐν ὕλης εἴδει μόνας ᾠήθησαν ἀρχὰς εἶναι πάντων.

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3 I.e., for every kind of seeds as well as for any other moist entity. 4 Metaph. 1.3, 983b18–27: τὸ μέντοι πλῆθος καὶ τὸ εἶδος τῆς τοιαύτης ἀρχῆς οὐ τὸ αὐτὸ πάντες λέγουσιν, ἀλλὰ Θαλῆς μὲν ὁ τῆς τοιαύτης ἀρχηγὸς φιλοσοφίας ὕδωρ φησὶν εἶναι (διὸ καὶ τὴν γῆν ἐφ’ ὕδατος ἀπεφήνατο εἶναι), λαβὼν ἴσως τὴν ὑπόληψιν ταύτην ἐκ τοῦ πάντων ὁρᾶν τὴν τροφὴν ὑγρὰν οὖσαν καὶ αὐτὸ τὸ θερμὸν ἐκ τούτου γιγνόμενον καὶ τούτῳ ζῶν (τὸ δ’ ἐξ οὗ γίγνεται, τοῦτ’ ἐστὶν ἀρχὴ πάντων)—διά τε δὴ τοῦτο τὴν ὑπόληψιν λαβὼν ταύτην καὶ διὰ τὸ πάντων τὰ σπέρματα τὴν φύσιν ὑγρὰν ἔχειν, τὸ δ’ ὕδωρ ἀρχὴν τῆς φύσεως εἶναι τοῖς ὑγροῖς. 5 “Aristotle ... did not set himself the goal of historically reconstructing the details of antecedent thought, but drew on it to criticize errors or fnd incomplete and primitive anticipations of concepts which he himself would eventually fulfll” (so Calenda 2015, 12). 6 It is easy to suppose that there is a connection between the warmth of spring (which, combined with the humidity of the soil, favors the sprouting and fowering of many plants), the warm water which is a favorable condition for the formation of tadpoles, and the substantial heat needed by the fetus during pregnancy in mammals. 7 The term to thermon is used to indicate the heat (including hot water and hot baths), not fre. So it makes sense to associate it with body heat, including the hot liquid that protects the fetus. In the case of body heat, it also makes sense to ask what gives rise to it, and it is conceivable that water would be among the possible candidates. 8 While it is conceivable that someone might claim that, if water is the principle, archē, then everything – earth, air etc. – comes from water, the claim that the earth is above and the water below conficts with common experience. Moreover, it cannot be deduced from the previous statement (nor does it lend support to it). 9 De caelo 2.13, 294a13–16: πῶς ποτε μικρὸν μὲν μόριον τῆς γῆς, ἂν μετεωρισθὲν ἀφεθῇ, φέρεται καὶ μένειν οὐκ ἐθέλει, καὶ τὸ πλεῖον ἀεὶ θᾶττον, πᾶσαν δὲ τὴν γῆν εἴ τις ἀφείη μετεωρίσας, οὐκ ἂν φέροιτο. This passage does not appear in any of the collections of texts concerning Thales, but is crucial in order to identify Aristotle’s line of reasoning. 10 De caelo 2.13, 294a28-b4 (=11A14 DK = Th30 W = 5D7 plus 5R33a LM): οἱ δ’ ἐφ’ ὕδατος κεῖσθαι [sc. τὴν γῆν]. τοῦτον γὰρ ἀρχαιότατον παρειλήφαμεν τὸν λόγον, ὅν φασιν εἰπεῖν Θαλῆν τὸν Μιλήσιον, ὡς διὰ τὸ πλωτὴν εἶναι μένουσαν ὥσπερ ξύλον ἤ τι τοιοῦτον ἕτερον (καὶ γὰρ τούτων ἐπ’ ἀέρος μὲν οὐθὲν πέφυκε μένειν, ἀλλ’ ἐφ’ ὕδατος), ὥσπερ οὐ τὸν αὐτὸν λόγον ὄντα περὶ τῆς γῆς καὶ τοῦ ὕδατος τοῦ ὀχοῦντος τὴν γῆν· οὐδὲ γὰρ τὸ ὕδωρ πέφυκε μένειν μετέωρον, ἀλλ’ ἐπί τινός ἐστιν. Ἔτι δ’ ὥσπερ ἀὴρ ὕδατος κουφότερον, καὶ γῆς ὕδωρ· ὥστε πῶς οἷόν τε τὸ κουφότερον κατωτέρω κεῖσθαι τοῦ βαρυτέρου τὴν φύσιν; 11 Nat. Quaest. 3.13.1–14.2 (=11A15 DK = Th99 W, part = 5D8 LM): [13] Adiciam, ut Thales ait, “valentissimum elementum est”. Hoc fuisse primum putat, ex hoc surrexisse omnia. Sed nos quoque aut in eadem sententia, aut in vicina eius sumus. Dicimus enim ignem esse... [14] Quae sequitur Thaletis inepta sententia est. Ait enim terrarum orbem aqua sustineri et vehi more navigii, mobilitateque fuctuare tunc cum dicitur tremere; “non est ergo mirum si abundat umore ad fumina profundenda, cum mundus in umore sit totus”. Hanc veterem et rudem sententiam explode. 12 Nat. Quaest. 6.6.1–2 (Th101 W): In aqua causam esse nec ab una dictum est nec una modo. Thales Milesius totam terram subiecto iudicat humor portari et innare, sive illud oceanum vocas, seu magnum mare, sive alterius naturae simplicem adhuc aquam et umidum elementum. ‘Hac’, inquit, ‘unda sustinetur orbis velut aliquod grande navigium et grave his aquis quas premit’; supervacuum est reddere causas propter quas existimat gravissimam partem mundi [non] posse spiritu tam

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13 14 15 16 17

18 19

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tenui fugacique gestari; non enim nunc de situ terrarum sed de motu agitur. Illud argumentum loco ponit, aquas esse in causa quibus hic orbis agitetur, quod in omni maiore motu erumpunt fere novi fontes (sicut in navigiis evenit ut si inclinata sunt et abierunt in latum, aquam sorbeant, quae nimio eorum pondere quae vehunt si immodice depressa sunt, aut superfunditur aut certain dextera sinistraque solito magis surgit). The expression quae nimio eorum pondere is the result of an emendation (to replace ordine) that I have discussed with my colleague Cipriano Conti: it is required by the sense. Wöhrle (2009, 97) has “durch das Gewicht”, although he does not amend the text. Similarly, Oltramare (1961, 257) translates “les charges qu’il porte” without amending, while Traglia (1965, 34–35) translates “per l’eccessivo carico”, taking care to amend in quae vi omni eorum onere. This is not an isolated case: in [3] we met ait and putat; in [5] there is also iudicat. See further Chapter 17 below. “Earthquakes ... must ... have been a recurring event in the history of Miletus” (Greaves 2003, 7). Greaves (2003, 10) dwells on the presumed importance of the many springs while describing the hydrology of the area. Placita 1.3, 875D8-F5 (=Th146 W). Ps.-Plutarchus, Placita philosophorum 1.3, 875E6-F4 (=Th147 W): πρῶτον, ὅτι πάντων τῶν ζῴων ἡ γονὴ ἀρχή ἐστιν, ὑγρὰ οὖσα· οὕτως εἰκὸς καὶ τὰ πάντα ἐξ ὑγροῦ τὴν ἀρχὴν ἔχειν. δεύτερον, ὅτι πάντα τὰ φυτὰ ὑγρῷ τρέφεται καὶ καρποφορεῖ, ἀμοιροῦντα δὲ ξηραίνεται· τρίτον, ὅτι καὶ αὐτὸ τὸ πῦρ τὸ τοῦ ἡλίου καὶ τὸ τῶν ἄστρων ταῖς τῶν ὑδάτων ἀναθυμιάσεσι τρέφεται καὶ αὐτὸς ὁ κόσμος· διὰ τοῦτο καὶ Ὅμηρος ταύτην τὴν γνώμην ὑποτίθεται περὶ τοῦ ὕδατος, ‘Ὠκεανός, ὅσπερ γένεσις πάντεσσι τέτυκται.’ A detail worth noticing is that, if fire is a secondary effect of the exhalation of waters (a point reminiscent of 21B30 DK), then it has nothing to do with the origins of warm living creatures (text [1] above). The same sentence – Θαλῆς καὶ Δημόκριτος ὕδατι τὴν αἰτίαν τῶν σεισμῶν προσάπτουσιν – appears elsewhere in ps.-Plutarch (3.15, 896B9-C2 = Th163 W) and in ps.-Galen (Historia philosophica 86.1 = Th403 W). A mention also appears in Hippolytus (Refutatio 1.1 = Th 210 W). Stobaeus, Anthol. 1.10.12 (=Th343 W): ἐξ ὕδατος γάρ φησι πάντα εἶναι καὶ εἰς ὕδωρ πάντα ἀναλύεσθαι. Στοχάζεται δὲ πρῶτον ἐκ τούτου, ὅτι πάντων τῶν ζῴων ἡ γονὴ ἀρχή ἐστιν, ὑγρὰ οὖσα. οὕτως εἰκὸς καὶ τὰ πάντα ἐξ ὑγροῦ τὴν ἀρχὴν ἔχειν. Δεύτερον, πάντα φυτὰ ὑγρῷ τρέφεται καὶ καρποφορεῖ, ἀμοιροῦντα δὲ ξηραίνεται. Τρίτον, ὅτι καὶ αὐτὸ τὸ πῦρ τὸ τοῦ ἡλίου καὶ τῶν ἄστρων ταῖς τῶν ὑδάτων ἀναθυμιάσεσι τρέφεται καὶ αὐτὸς ὁ κόσμος. Commentarii in Vergilii Bucolica 6.31 (=Th319 W): alii dicunt omnia ex igne procreari, ut Anaxagoras; alii ex humore, ut Thales Milesius, unde est Oceanumque patrem. DK and LM omit this, as well as four other occurrences (Th317, Th320, Th321 and Th322 W) where essentially the same thing is said. Commentaria in Vergilii Aeneida 11.186 (=11A13 DK = Th318 W ≠ LM): Thales vero, qui confirmat omnia ex umore creari, dicit obruenda corpora, ut possint in umore resolvi. Presumably Simplicius means that, in the case of corpses left in the air, the moisture content of these bodies decreases dramatically, that is, the dehydration process begins immediately. Simplicius, In Aristotelis libros Physicorum 9.23.21–33 (=11A13 DK = Th409 W = 1T14 LM): Τῶν δὲ μίαν καὶ κινουμένην λεγόντων τὴν ἀρχήν, οὓς καὶ φυσικοὺς ἰδίως καλεῖ, οἱ μὲν πεπερασμένην αὐτήν φασιν, ὥσπερ Θαλῆς μὲν Ἐξαμύου Μιλήσιος καὶ Ἵππων, ὃς δοκεῖ καὶ ἄθεος γεγονέναι, ὕδωρ ἔλεγον τὴν ἀρχὴνἐκ τῶν φαινομένων κατὰ τὴν αἴσθησιν εἰς τοῦτο προαχθέντες. καὶ γὰρ τὸ θερμὸν τῷ ὑγρῷ ζῇ καὶ τὰ νεκρούμενα ξηραίνεται καὶ τὰ σπέρματα πάντων ὑγρὰ καὶ ἡ τροφὴ πᾶσα χυλώδης·

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25 26 27 28

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ἐξ οὗ δέ ἐστιν ἕκαστα, τούτῳ καὶ τρέφεσθαι πέφυκεν· τὸ δὲ ὕδωρ ἀρχὴ τῆς ὑγρᾶς φύσεώς ἐστι καὶ συνεκτικὸν πάντων. διὸ πάντων ἀρχὴν ὑπέλαβον εἶναι τὸ ὕδωρ καὶ τὴν γῆν ἐφ ‘ὕδατος ἀπεφήναντο κεῖσθαι. Θαλῆς δὲ πρῶτος παραδέδοται τὴν περὶ φύσεως ἱστορίαν τοῖς Ἕλλησιν ἐκφῆναι, πολλῶν μὲν καὶ ἄλλων προγεγονότων, ὡς καὶ τῷ Θεοφράστῳ δοκεῖ, αὐτὸς δὲ πολὺ διενεγκὼν ἐκείνων, ὡς ἀποκρύψαι πάντας τοὺς πρὸ αὐτοῦ · λέγεται δὲ ἐν γραφαῖς μηδὲν καταλιπεῖν πλὴν τῆς καλουμένης Ναυτικῆς ἀστρολογίας. Meteor. 2.7, 365b2 (=68B97 DK = 27D119 LM): ὑπὸ τούτου κινεῖσθαι. Meteor. 2.7, 365b6–8 (=13A21 DK = 11D27 LM): Ἀναξιμένης δέ φησιν βρεχομένην τὴν γῆν καὶ ξηραινομένην ῥήγνυσθαι, καὶ ὑπὸ τούτων τῶν ἀπορρηγνυμένων κολωνῶν ἐμπιπτόντων σείεσθαι. Ammianus Marc. Res gestae 17.7, 12 (=12A28 DK). Sources include Plut. Quaest. conv. 8.8.4, 730D-F (=12A30 DK = Ar45 W = 6D40 LM), ps.-Plut. Placita 5.19, 908D11–14 (=12A30 DK = Ar67 W = 6D38 LM), Hippol. Refutatio 1.6.67 (12A11 DK = Ar75 W = 6D7 LM) and Censorinus De die natali 4.7 (12A30 DK = Ar90 W = 6D39 LM). The sources, which agree, are Seneca, Nat. Quaest. 2.17–18 (=12A23 DK = Ar37 W = 6D33b LM), ps.-Plut. Placita 3.3 893D7–11 (=12A23 DK = Ar63 W = 6D33a LM) and ps.-Plut. Placita 3.7 895A6–8 (= Ar64 W = 6D34 LM). Heraclitus, Allegoriae 22.3 (=Th94 W): Θάλητα μέν γε τὸν Μιλήσιον ὁμολογοῦσι πρῶτον ὑποστήσασθαι τῶν ὅλων κοσμογόνον στοιχεῖον τὸ ὕδωρ. Plut. De Iside et Osiride 34.364C-D (=11A11 DK = Th116 W ≠ LM): οἴονται δὲ καὶ Ὅμηρον ὥσπερ Θαλῆν μαθόντα παρ’ Αἰγυπτίων ὕδωρ ἀρχὴν ἁπάντων καὶ γένεσιν τίθεσθαι· τὸν γὰρ Ὠκεανὸν Ὄσιριν εἶναι, τὴν δὲ Τηθὺν Ἶσιν ὡς τιθηνουμένην πάντα καὶ συνεκτρέφουσαν.

10 The periodic fooding of the Nile and the ‘Atlantic corollary’

The periodicity of the fooding of the Nile – which must have seemed inexplicable and mysterious at the time – is another of the ‘curiosities’ on which Thales appears to have focused his attention. We can make use here of one piece of evidence, a passage from Seneca, Nat. Quaest., which, due to the fact that it refers explicitly only to Euthymenes, has only rarely been studied for what it can tell us about Thales. But it shows that, 50–100 years after his death, Thales’ account of the Nile foods was used as a model for explaining the ‘behaviour’ of a river that visibly fowed into the ocean. What is striking about this ‘Atlantic corollary’ is that someone, Euthymenes of Massalia, was able to make use of what Thales had taught about periodic foods to explain phenomena in a completely different part of the world, and it speaks to us only of the authority that was already recognized in Thales.

10.1 The basic documentation Our main source on this subject is, famously, Herodotus. It is signifcant that he fnds himself talking not only about Thales but also about other Greek intellectuals who were interested in explaining the periodic fooding. Herodotus, in fact, outlines all the contributions available in the specialist literature of his time: he gives us, in short, a competent and probably exhaustive status quaestionis.1 This is what he says: But some Greeks, wanting to distinguish themselves for their wisdom, formulated three different explanations regarding the variations in the fow of this river: I do not consider two of them worthy of being illustrated, but I limit myself to pointing them out. One states that the Etesian winds are the cause of the foods of the river as they would prevent the Nile from pouring into the sea. But often the Etesians do not expire at all, yet the Nile always behaves in the same way.2 Herodotus then dwells on the other conjectures, discussing them briefy and also putting forward his own explanation. (This, however, turns out to be even weaker than the others, being based on the idea that the winds DOI: 10.4324/9781003138723-13

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periodically push the sun towards south and, with the sun, they also move large banks of clouds, which then discharge rain at a great distance: 2.24.1, 26.1.) To confrm that Herodotus has Thales in mind here, we have at least three different statements from other authors. Diodorus Siculus writes: Therefore Thales, known as one of the seven wise men, says that the Etesians, blowing in the opposite direction, prevent the river from making the current fow into the sea, and for this reason, being swollen foods the territories adjacent to Egypt.3 A century later Seneca, in the treatment of the Nile that forms the fourth book of his Naturales Quaestiones, goes into more detail: If you believe Thales, the Etesians oppose the descent of the Nile, whose course they suspend by pushing the sea against its mouths. Thus rejected, the Nile comes back upon itself, does not grow, but stops in front of the closed exit, swells, and soon emerges where it can. Euthymenes of Massalia provides this testimony: “I sailed the Atlantic. From there the Nile 4 reaches the sea, swollen until the Etesians blow according to the season. Under the pressure of the winds, the sea is pushed. But when they calm down, the sea also calms down and the force of the Nile descending diminishes. For the rest, the taste of sea water there is sweet and the river animals are similar to those of the Nile”.5 Finally in ps.-Plutarch we read that: Thales believes that the Etesians winds, due to the fact of blowing in front of Egypt, cause the mass (that is the level) of the Nile to rise, so its course is prevented by the swelling of the sea, which hinders it.6 Before returning to what Seneca reports about Euthymenes, note that these sources converge in telling us that Thales is likely to have said (and probably, written) frst something about the Etesian winds, well known to the coasts of Ionia. They blow south and are particularly strong at the beginning of each summer – which is to say, a few weeks before the fooding of the Nile in middle and lower Egypt, which used to occur during the month of August.7 Thales allegedly asserted that those strong winds rise even in the vicinity of the Nile Delta, and that, when they are strong enough, they impede the outfow of the waters of the great river, so that the level of the watercourse rises and, consequently, foods. The implication is that these foods end only as the winds identifed as Etesians lessen their strength and cease.

The periodic fooding of the Nile 131 In what follows, having criticized the conjecture of Thales (see further below), Herodotus informs us about two other conjectures: one according to which the Nile has its source in the ocean surrounding the (fat) earth, and one that we know was suggested by Anaxagoras, according to which the origin of the phenomenon is the melting of snow in remote southern territories (Ethiopia is mentioned). The latter, says Herodotus (2.22.1), is by far the most plausible explanation but, at the same time, is the most (i.e. the most clearly) false. The reference to snow is so at odds with the increasingly high temperatures that are observed in Egypt as one goes upriver that Herodotus cannot believe it. The report is therefore unambiguous and clear: Herodotus alludes to Thales in the middle of his status quaestionis, his review of the only available conjectures about the fooding of the Nile (all formulated by Greeks, indeed by Ionians) which is preliminary to his own suggestion. All of this suggests the formation of an embryonic sense of a scientifc community of which Herodotus himself aspired to be part. But it also gives us some confdence that what is reported on this particular subject has not been affected by egregious distortion or embellishment.

10.2 Thales at the mouth of the… River Senegal? Before offering any other considerations on the subject, it seems desirable to pay special attention to what Seneca reports. In the passage I have quoted, a few people make an appearance: (1) Hecataeus of Miletus, for the reasons that will be given in a moment; (2) Euthymenes of Massalia;8 (3) a “Nile”, call it Nile2, that fows into the ocean; (4) this same Nile2, or the surrounding sea, which gives rise to phenomena similar to the periodic foods of the Nile we know, Nile1, these also being induced by the sea and, ultimately, the wind; (5) the presence near the mouth of Nile2 of river animals similar to those of the Nile1; and fnally (6) the presence, again near the mouth of Nile2, of a stretch of freshwater sea. Thales can also be glimpsed behind all these reports, as we will see in the following. Immediately after discussing the trade winds, Herodotus reports, in 2.21, that, according to another conjecture, “the Nile behaves in this strange way because it originates in the ocean, an ocean that would surround the whole earth”. Against this idea he argues (2.23) that “Whoever has spoken of the ocean escapes any refutation since brings the discourse into the feld of the unknown”. That he is alluding here to Hecataeus can be deduced from the scholium to Apollonius Rhodius (ad Argonautica 4.259), where we read that “according to Hecataeus of Miletus, they [the Argonauts] reached the Ocean through [i.e. going up] the river Phasis and from there they reached the Nile, through which they returned to our sea [i.e. the Aegean]”.9 This information is relevant for understanding Euthymenes. Hecataeus reasons as if the river Phasis, and the Nile as well, were in reality channels

132 Further investigations on earth, waters and rocks that go from sea to sea: the frst from the Black Sea to the Ocean (i.e. to what for us is the Caspian Sea), the second from an indeterminate point of the Ocean to its ‘mouths’ on the Mediterranean. That Hecataeus may have imagined a great circumnavigation including navigation along an indefnitely extended portion of the outer ‘river’ (the Ocean) does not help us to understand where he might have imagined placing the second exit of the Nile, the one I am calling Nile2. (Among other things, Hecataeus hypothesizes something vaguely comparable to the circumnavigation of Africa, made about a century earlier on the initiative of Pharaoh Necho II10; but is this true?)11 Regarding the amazing journey made by Euthymenes beyond the Pillars of Hercules,12 we now have an edition of the sources by F. J. González Ponce. Let us start with a statement by Johannes Lydus: Euthymenes of Massalia claims to have crossed the Atlantic (that is, to have ventured into the Ocean) and to have understood that the Nile rises from it and that its volume of water increases when the so-called Etesians blow. He explains that the sea overfows under the pressure of the winds and stops again when the winds subside. He adds that the waters of the Atlantic are more or less of the fresh kind and that the animals that live there resemble those of the Nile.13 Anonymus Florentinus, in turn, writes: After having sailed himself towards the outer sea, Euthymenes of Massalia affrms that this sea fows up to Libya and has turned towards Boreas and the Ursa.14 The sea is calm for most of the year, but as soon as the Etesians arrive, it swells due to the force of the winds and, on days, it rises towards the interior; instead, when the Etesians cease, it withdraws. And he adds that the sea in question is made up of fresh water and overfows with sea monsters similar to Nile crocodiles and hippos.15 And in Aelius Aristides we read: In any case, I enjoyed [hearing tales] of the freshwater sea on the other side of Libya, fowing inland under the infuence of the Etesians, as well as its crocodiles and the legends of Massalia.16 These sources converge in reporting that Euthymenes of Massalia was an exceptional navigator, who went beyond the Pillars of Hercules, into the Ocean, down the coast of West Africa, and into the mouth of a river which can only be what we know today as the Senegal (this is the frst great river that is encountered along the coast of Atlantic Africa). He produced a written memoir about his journey, that Periplus, from which, apparently, even Herodotus learned something.

The periodic fooding of the Nile 133 From these sources, which border on the legendary but which do not present signifcant contradictions, we learn: – that Euthymenes arrived at the mouth of a great river; – that he noticed, not only in that area but all along the outward journey, a northern wind (known to us as the trade wind), which he believed was the same wind that in the summer blows from the north in the eastern Aegean sea, and whose effects were supposedly felt also near the mouth of the Nile1. In other words, he identifed these Atlantic winds as quite similar to the Etesians; – that in his opinion, when a wind similar to the Etesians blows, this wind swells the sea near the mouth of the great river he came to,17 and so swells the river itself, not unlike what supposedly happens every summer with the Nile1; – that, again near the mouth of that river, during certain periods in particular, an area of fresh water is formed in the sea; – that the river is also like the Nile1 in having the same large animals that are known to live there. These features encouraged him to think that he had arrived at the other end of the very same great river. That all this could be a work of fantasy seems to me quite unlikely: in fact, the Senegal does experience annual foods, and the formation of a freshwater area around its mouth is still reported. Consequently, it is quite likely that the basic data are not made up. In his note to the passage from Anonymus Florentinus, González Ponce wrote, however: Modern research has serious doubts about the authenticity of this exploration. These are based on the shortcomings of ancient nautical science to cope with adversities such as the system of winds and water currents on the return journey – as well as the silence that writers of the caliber of Herodotus, very interested in other adventurous expeditions, maintain regarding this trip. In commenting on the passage from Seneca, he goes on to state that the Senegal “is subject to the same foods as the Nile – and with the same frequency – due to the rains which the monsoons are responsible for. Furthermore, its fresh water penetrates for about 10 km into the sea”. Therefore, “Euthymenes” conjecture gives the impression of being a logical reversal of the ideas of Thales. But it can be argued (1) that, if Euthymenes had not read Thales or Hecateus, and recognized similar phenomena in a completely different area, he could not even have considered the possibility of a comparison with the Nile1; (2) that Thales’ ideas about the Nile and its foods are simply repeated in Euthymenes; and (3) that the expedition ordered by the pharaoh Necho

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successfully skirted the African coast along which Euthymenes sailed, successfully going in the opposite direction to the trade winds. There is another remark which, in my opinion, is decisive. On the basis of the cartographic scheme outlined by Anaximander, Africa would coincide or almost coincide with the lower left quadrant of a circle of which Europe would constitute the upper left quadrant. This scheme, as to Western Europe and Africa, remained substantially the same in the conception of the oikoumēnē shared by Eratosthenes (late third century BC) and Strabo (in the age of the emperors Augustus and Tiberius). Moreover, Aelius Aristides speaks of “the other side of Libya”. These circumstances are very telling, because they imply that everyone thought of the Atlantic coast of North Africa not as it actually is (extending west from the Strait of Gibraltar for some thousands of kilometres),18 and without taking into account the curvature of the earth. Rather, they thought that the coastline conspicuously curved towards the east19 (and obviously had no idea about the Gulf of Guinea or the existence of a southern offshoot of Africa that extended south for thousands more kilometres). It follows that even Euthymenes, at the end of his long navigation, could not have assumed that he had reached a place situated some 5,000 km west of the southern reaches of the Nile, roughly, at the same latitude. On the contrary, he probably believed that he had travelled about a quarter of the route commonly attributed to the Ocean river, and reached the point where the Nile itself fowed into the ocean, without substantially altering his basically rectilinear course. If this is right, as the available evidence suggests, then one can well understand Euthymenes’ readiness to help himself to a conjecture made by Hecataeus (“the Nile connects the great inland sea to the ocean, like the Phasis”), as well as the more complex conjecture of Thales. He believed that he had reached the other end of the same great river – and encountered the same winds mentioned by Thales. In speaking of the Nile2, Euthymenes’ evaluations therefore seem to start from observational data (the trade winds are a reality, the Senegal River is actually subject to annual foods and, when these foods occur, a part of the surrounding sea actually does fll with fresh water), but then to come up with a hasty interpretation of the primary data: that he had found himself, quite unexpectedly, at the other end of the same river. The foods put him in mind of Thales’ explanation of the fooding of the Nile, which encouraged him to deduce that the same winds (the Etesians) blew in that area and the river presented the same phenomenon (foods connected to a sort of swelling of the facing sea).20 It follows that Euthymenes knew certain conjectures by Hecataeus and had access to a detailed account of Thales’ explanation of the foods of the Nile.

10.3 Post hoc, ergo propter hoc This is all signifcant testimony to the fame and authority of Thales – the more so since Euthymenes did not come from Ionia but from far-away

The periodic fooding of the Nile 135 Marseilles. This gives us a rare insight into the circulation, at a surprisingly early period,21 of written information on the master of Miletus and his teachings. The references to Euthymenes’ journey and conjectures are not simply curious variant of the theory of Thales that upstream winds dam back the Nile, but much more. In fact, they contribute to establishing what is reported for Thales and treat him as an acknowledged authority. Thales probably conjectured that the Etesian winds occur even 700 km or more south of the island of Rhodes, maintaining the same direction and, above all, the same strength and, perhaps, that the periodic foods affect only the terminal part of lower Egypt. Such assumptions suggest that his conjecture did not take shape while he was living in Egypt, by the way, but when he was in Miletus, and relying only on his memories. In fact, his conjecture proves that he had no idea that the foods frst affect Upper Egypt and only subsequently reach middle and lower Egypt and fnally the sea. Thales was in fact seriously underinformed about all this. Nevertheless it remains the case that he was the frst to put forward a rational hypothesis for this almost unique phenomenon. A signifcant feature of those who explained the fooding by snowfall, or the periodic movement of the sun towards the south, is that they started from the assumption that the large-scale phenomenon of the foods could only be explained by suitably large-scale causes: in other words, that cause must be proportionate to effect. Herodotus himself, in discussing the various hypotheses, shows that he adheres to a similar principle. Against the conjecture of Thales, for example, he complains that “often the Etesian winds do not blow at all, and yet the Nile behaves in the same way” (2.20.2); against Hecataeus, that he ends up explaining the known with the unknown (2.21); against Anaxagoras’ conjecture, that it is by far the most plausible in his view (pollon epieikestatē: 2.22.1), except that it clashes with the fact that the further south you go the hotter and drier it gets. Thales’ conjecture ignores all that, but the idea of a large-scale physical cause of the foods is his – another reason to be impressed and to claim this as one of his most signifcant theories.

Notes 1 This itself seems to me much to his credit. Such a conspicuous lesson in method was not taken up again before Aristotle and, for a very long time, it evaded the notice even of the modern translators and commentators of Herodotus. 2 Herodotus 2.20.1–2 (=11A16 DK = Th13 W ≠ LM) reports that Ἀλλὰ Ἑλλήνων μέν τινες ἐπίσημοι βουλόμενοι γενέσθαι σοφίην ἔλεξαν περὶ τοῦ ὕδατος τούτου τριφασίας ὁδούς, τῶν τὰς μὲν δύο τῶν ὁδῶν † οὐκ ἀξιῶ μνησθῆναι εἰ μὴ ὅσον σημῆναι βουλόμενος μοῦνον. τῶν ἡ ἑτέρη μὲν λέγει τοὺς ἐτησίας ἀνέμους εἶναι αἰτίους πληθύειν τὸν ποταμόν, κωλύοντας ἐς θάλασσαν ἐκρέειν τὸν Νεῖλον. πολλάκις δὲ ἐτησίαι μὲν οὐκ ὦν ἔπνευσαν, ὁ δὲ Νεῖλος τὠυτὸ ἐργάζεται. 3 Diodor. Bibl. 1.38.2 (=Th82 W) notes that Θαλῆς μὲν οὖν, εἷς τῶν ἑπτὰ σοφῶν ὀνομαζόμενος, φησὶ τοὺς ἐτησίας ἀντιπνέοντας ταῖς ἐκβολαῖς τοῦ ποταμοῦ κωλύειν εἰς θάλατταν προχεῖσθαι τὸ ῥεῦμα, καὶ διὰ τοῦτ’ αὐτὸν πληρούμενον ἐπικλύζειν ταπεινὴν οὖσαν καὶ πεδιάδα τὴν Αἴγυπτον.

136 Further investigations on earth, waters and rocks 4 That is towards North (the direction of water in Nile1). It follows that Euthymenes was not unaware that water of the Nile1 fow northwards. 5 Seneca, Naturales Quaestiones 4.2.22 (=Th100 W): Si Thaleti credis, etesiae descendenti Nilo resistunt et cursum eius acto contra ostia mari sustinent. Ita reverberatus, in se recurrit, nec crescit, sed exitu prohibitus resistit et quacumque mox potuit in se congestus erumpit. Euthymenes Massiliensis testimonium dicit: ‘Navigavi, inquit, Atlanticum mare. Inde Nilus fuit, maior, quamdiu etesiae tempus observant; tunc enim eicitur mare instantibus ventis. Cum resederunt, et pelagus conquiescit minorque descendenti inde vis Nilo est. Ceterum dulcis mari sapor est et similes Niloticae belvae.’ 6 Ps.-Plutarch, Placita Philosophorum 897F (=11A16 DK = Th164 W = 5D9 LM) reports that Θαλῆς τοὺς ἐτησίας ἀνέμους οἴεται πνέοντας τῇ Αἰγύπτῳ ἀντιπροσώπους ἐπαίρειν τοῦ Νείλου τὸν ὄγκον διὰ τὸ τὰς ἐκροὰς αὐτοῦ τῇ παροιδήσει τοῦ ἀντιπαρήκοντος πελάγους ἀνακόπτεσθαι. 7 “Given that the Etesian winds blow after the summer solstice and the rise of Sirius, it coincides with the beginning of the annual food of the Nile; the correlation between the two natural phenomena seemed logical, for which this theory had credit in antiquity” (so Pownall 2013 in his commentary on BNJ 1 F 302b). 8 It is by no means certain that Euthymenes was active in the second half of the sixth century, that is, that he established himself just after the death of Thales (as González Ponce 2013 suggests: see n. 258 below). Bianchetti (1998, 112), like other scholars, is inclined to conjecture that Euthymenes lived as late as the fourth century, at the time of Pytheas and Aristotle. However, this claim implies that Herodotus was unaware of his existence, and this seems hard to assume. The frst half of the ffth century seems a better candidate. 9 Schol. Apollon. Argonautica 4.259 (=BNJ 1 F 18a): Εκαταῖος δὲ ὁ Μιλήσιος ἐκ τοῦ Φάσιδος διελθεῖν εἰς τὸν ᾽Ωκεανόν, εἶτα ἐκεῖθεν εἰς τὸν Νεῖλον, ὅθεν εἰς τὴν ἡμετέραν θάλασσαν. 10 Necho or Nekau. Everything we know about the voyage is known to us only thanks to Hdt. 4.42.2–4. 11 If Hecataeus had been aware of it, he would probably not have imagined the existence of a ‘marine spring’ for the Nile, something not detected during that expedition; so the idea would not have been available to Euthymenes either. 12 According to González Ponce (2013) (‘Einleitung’), Euthymenes’ expedition took place before 509 BC, but this is a decidedly weak conjecture as it refers to an agreement between Phoenicians and Romans that does not appear to have also affected the seafaring out of Massalia or along the coasts of Gaul or Spain. It should also be considered that Euthymenes knew at least something of Hecataeus’s work, otherwise he could not have claimed to have seen the ‘other mouths’ of the Nile. Therefore, he must have been active after the Persian Wars (pace González Ponce). Doubts have also been raised regarding the completion of the journey narrated by Euthymenes: see further on this below. 13 De mensibus 4.107 (=FGrHist 2207 F (3) b): Εὐθυμένης δὲ ὁ Mασσαλιώτης φησὶ διαπλεῦσαι τὴν Ἀτλαντικὴν θάλατταν, ἐξ ἐκείνης τε ἰδεῖν τὸν Νεῖλον ἐκτρέχοντα καὶ τότε μᾶλλον ὀγκοῦσθαι, ὅταν οἱ λεγόμενοι ἐτήσιοι πνέωσι· τότε γάρ φησιν ἐξωθεῖσθαι ὑπὸ τῶν ἀνέμων τὴν θάλατταν, τούτων δὲ παυομένων ἡσυχάζειν. Γλυκὺ δὲ σχεδὸν τὸ τῆς Ἀτλαντικῆς θαλάττης ὕδωρ, καὶ ὅμοια ταύτης θηρία τοῖς τοῦ Νείλου. Especially the words on the portion of Atlantic see with unsalted water is sure proof of Euthymene’ arrival at the mouth of the Senegal river. 14 The orientation of the sea to the north remains an inexplicable detail, unless we assume that Euthymenes is referring to the direction that the fux of Nile1 ostensibly has while traversing Egypt. 15 Anonymus Florentinus 5 (=Cod. Laur. 56, 1 [ss. XIII-XIV] fol. 12 = FGrHist 2207 F 2): Εὐθυμένης δὲ ὁ Mασσαλιώτης αὐτὸς πεπλευκώς φησιν εἰς τὴν ἔξω θάλασσαν

The periodic fooding of the Nile 137

16 17 18

19 20

21

ἐπιρρεῖν ἕως εἰς τὴν Λιβύην ἐστραμμένην τε εἶναι πρὸς Βορέαν τε καὶ Ἄρκτους, καὶ τὸν μὲν ἄλλον χρόνον κενὴν εἶναι τὴν θάλασσαν, τοῖς δὲ ἐτησίαις ἀνωθουμένην ὑπὸ τῶν πνευμάτων πληροῦσθαι καὶ ῥεῖν ἔσω ταῖς ἡμέραις ταύταις, παυσαμένων δὲ τῶν ἐτησίων ἀναχωρεῖν. Εἶναι δὲ αὐτὴν καὶ γλυκεῖαν, καὶ κήτη παραπλήσια τοῖς ἐν τῷ Νείλῳ κροκοδείλοις καὶ ἱπποποτάμοις ἔχειν. Ael. Aristid. Or. 36.85 (=FGrHist 2207 F 1) Ἥσθην δὲ θαλάττv γλυκείᾳ Λιβύης ἐπέκεινα εἴσω ῥεούσῃ διὰ τοὺς ἐτησίας καὶ ταύτης καὶ κροκοδείλοις καὶ μύθοις Μασσαλιωτικοῖς. If, in his opinion, the river foods when the sea swells, Euthymenes could have taken the tides to suggest a correspondence with what Thales had asserted about the foods of the Nile1. Cf. Bianchetti (1998, 111 ff.). On the northern edge of Mauritania, near today’s Nouadhibou, well over 2,000 kilometres from the Gulf of Gibraltar. Francesco Prontera reminds me of this: “that Europe projected much more towards the West than Africa, was a widely shared opinion”. “Even the general run of the [African] coast, southward in the few indications given and really south-west, was hopelessly misread as south-east” (Thomson 1948, 76). The river-beasts found near the mouth of Senegal might have been interpreted as crocodiles and hippos which the navigator had himself never seen. Besides, Euthymenes could hardly have had any idea of the proportions that the fooding of the Nile assumed in his time. In saying this, I am no longer referring to Euthymenes (who was not well known during his lifetime) but to the much more detailed and widespread knowledge of Thales at the end of the sixth and during the ffth century BC: see Section 17.1.

11 Thales and the stones of Magnesia

Thales’ theory about the periodic fooding of the Nile perforce lacked empirical confrmation, while his ruminations about water, seeds, earthquakes, and related phenomena were supported by a vast amount of observation data. His thoughts on another puzzling phenomenon lay somewhere between these extremes. In Diogenes Laertius, we read that “Aristotle (Th31 W) and Hippias (Th16 W) say that he attributes souls even to inanimate things, citing the magnet and amber as evidence”.1 We have no independent knowledge about what Hippias wrote on the stones of Magnesia, but we do have Aristotle’s text. In De anima he writes: Thales too, to judge by what is reported, seems to have held that the soul causes motion, since in fact he said that the magnet has a soul because it moves iron.2 And, in a scholium to Plato, we read: Thales of Miletus, the son of Examyas, … was the frst of the Greeks… to claim that even inanimate things somehow possess soul, judging from magnets and amber.3 The ‘magnet’ in question must be the Magnesian stone. This phenomenon, known to us (after the name of the town) as magnetism, was probably observed near the Magnesia which lies ‘on the Meander’4 – though it could equally be another place bearing the same name. In one of these localities, stones were noticed which were endowed with the unexpected power of attracting iron, and so of ‘forcing’ it to move, approach and remain attached (and possibly the power to repel it as well). But Thales must also have known the Egyptian ēlektron: this is not the amber of Baltic origin, but a substance that, when rubbed, can attract hair and other very light bodies. The relevant point is, again, that the phenomenon of attraction or repulsion of ‘magnetic’ objects had for centuries struck the imagination and aroused curiosity,5 but Thales is said to have been the frst who tried to DOI: 10.4324/9781003138723-14

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139

understand it (he “observed what the others saw”). In the absence of anything to suggest that this report is entirely fabricated, we have to assume that it has a basis in fact. So, our sources report that Thales connected and compared these two distinct phenomena, that he refected on them, and that he made the unequivocal claim that there are at least two types of apsuchoi (inanimate) bodies that are not truly apsuchoi but, as people began to say a century later, empsuchoi. That is: they easily pass for inert bodies, devoid of the features typical of living organisms, yet they have some features which are absolutely incompatible with their being inert. They manifest surprising forms of causality and energy that allow them to move other things. We would not expect to encounter such properties in inert (apsuchoi) bodies. This implies a challenge to our ideas about inanimate and inert bodies. So where did Thales go from here? Aristotle, as we have just seen, ascribes three propositions to him: (a) “the stone moves the iron”, (b) “(then) the stone has a soul”, and (c) there is in the soul “something kinetic”, that is, something which generates movement, which is capable of moving other physical objects. That an observation like (a) gave rise to a conclusion like (b) is all but certain, because, otherwise, this time Aristotle would not have had any reason to mention Thales at all. If Thales also moved from (b) to the further conclusion (c), he would have actually taken two distinct steps: c1 some form of soul is present wherever a physical body is capable of generating movement, even if it is a stone; c2 a characterizing feature of the stone is that it has “something kinetic”, i.e., when associated with certain bodies (which would otherwise be inert), it is able to move them. So if a body has the power to move, or at least to make other bodies move, even if it frst appeared inert, then in fact there is something kinetic in it. On the basis of this, several scholars have hurried to the conclusion that, if some stone has a soul (on an understanding of soul as something essentially self-moving), then every stone and every other apparently ‘inert’ object has a soul. And if this is so, then we start to understand how Thales could have said that “everything is full of gods”, as another source asserts.6 But such inferences involve signifcant leaps of logic. To begin with, the Magnesian stone is capable of moving, not itself, but iron objects – and then only when these objects are brought quite close to it. Secondly, in the passage from De anima, Aristotle does not attribute to Thales a general thesis concerning all ‘inert’ bodies. Thirdly, our sources do not attribute to Thales any defnition of soul, not even the thought that the soul has the characteristic of moving the body in which it ‘resides’. Finally, it is not at all obvious that “everything is full of gods” is a statement connected to this topic.

140 Further investigations on earth, waters and rocks All this is reassuring. It would seem that Thales registered two anomalies: the Magnesian stone and the Egyptian ēlektron, and noted the similarity between them, although they were in other ways very different; from this he deduced that it would be wrong to treat stones and pebbles as inanimate and inert bodies without qualifcation. He may also have gone so far as to conclude that some inanimate objects have a share in ‘soul’ (but who knows what sort of soul, and who knows why). Such conclusions are striking, but not excessively so. Remember the conclusions that Thales drew concerning the irregularities of the trimesters, when he noted that what we expect to happen “does not always happen”. Similarly here, he would be saying that, sometimes, bodies we expect to be inert are not really inert. The universe of apparently apsuchoi bodies is just more varied than one might expect. Thales has here made a frst attempt at a general approach to surprising phenomena which avoids recourse to divine magic, but instead questions the reliability of our own intuitive distinctions, in this case between animate and inert objects. That this is what the story involves speaks in favour of the authenticity of our reports, since (i) no one before Thales appears to have ventured in that direction at all, (ii) few other intellectuals took notice of anomalies like this (Anaximander, for example, did not), and (iii) we do not know of any other Greek of Roman philosopher who offered such a specifc explanation of the magnet. (Lucretius devoted some 26 verses to magnetism, but in order to give an idea of it, rather than explain it.)

Preliminary conclusions 2 The gulf between the group of discussions dealt with in Part III and those in Part II is vast. In this case, there is no superhuman challenge, there is no requirement for specifc mechanisms, there is no attempt to quantify, and above all the outcome is not equally spectacular. Thales simply tried to understand something about three typically terrestrial phenomena, necessarily remaining cautious about the success of his own conjectures. In one case, in fact, the fooding of the Nile, his work encouraged other learned people to put forward alternative proposals. There is a lesson here: not everything can be learned by quantifcation; but where there is nothing to quantify, investigation can proceed by other means. Unfortunately, in the case of the Nile foods and the stones of Magnesia, it seems that Thales failed to see the way forward to further research.7 Again, his work was not taken up, even by Anaximander, who forged his own path.

Notes 1 In DL 1.24 (=11A1 DK = Th237 W ≠ LM), we read that Ἀριστοτέλης δὲ καὶ Ἱππίας φασὶν αὐτὸν καὶ τοῖς ἀψύχοις μεταδιδόναι ψυχάς, τεκμαιρόμενον ἐκ τῆς λίθου τῆς μαγνήτιδος καὶ τοῦ ἠλέκτρου.

Thales and the stones of Magnesia  141 2 In De an. 1.2, 405a19–20 (=11A22 DK = Th31 W = 5D11a LM), we read that ἔοικε δὲ καὶ Θαλῆς ἐξ ὧν ἀπομνημονεύουσι κινητικόν τι τὴν ψυχὴν ὑπλαβεῖν, εἴπερ τὴν λίθον ἔφη ψυχὴν ἔχειν. 3 Scholia vetera in Platonis Republica 10.600a1–10 (=11A3 DK = Th578 W ≠ LM): Θάλης Ἐξαμύου Μιλήσιος, … πρῶτος Ἑλλήνων … ἀλλὰ καὶ ἄψυχα ψυχὴν ἔχειν ὁπωσοῦν ἐκ τῆς μαγνήτιδος καὶ τοῦ ἠλέκτρου. 4 We know that an urban centre called Magnesia ‘on the Meander’ was located near the Meander river, a few tens of kilometres east of Miletus. Costantini (1992, 99) speaks of Magnesia of Sipylus, a polis located much further north of Miletus (in the hinterland of Smyrna), without however justifying this identification. 5 About half a millennium after Thales, the Roman philosopher-poet Lucretius, for example, reported that sometimes iron is rejected rather than attracted by ‘magnetized’ stone. In fact, he writes: “I also saw the iron rings of Samothrace, which jolted” (6.1044, which is part of a greater whole: verses 1042–1068). 6 Schofield (1997, 43) is among the scholars who have attributed to Thales the self-moving soul, and the reference to the gods. 7 In fact, once one has established that water has an important (or essential) role in the formation and development of the most diverse living organisms, the next step would have been to understand what the functions of water are, and this was not within the reach of the ancients.

Part IV

Other investigations Real and presumed

The following chapters cover a miscellany of different topics. Here the evidence is complex, and legends abound; we have to make judgement about when to trust our sources and, although it is often reassuring when independent sources agree, we still have to take into account the possibility of partiality or distortion.

DOI: 10.4324/9781003138723-15

12 The sky according to Thales

12.1 Quantifcation of astronomical events and embryonic astronomy We saw in Section 8.1 that Apuleius introduces the fgure of Thales in these terms (Florida 18.30–31): Thales of Miletus was easily the most outstanding of those seven men remembered for their wisdom; for he was the frst among the Greeks to discover geometry, a most accurate investigator of nature, and a most skillful observer of the stars; by means of small lines he discovered the greatest things: the circuits of the seasons, the blasts of the winds, the wanderings of the stars, the marvelous resounding of thunder, the oblique courses of the constellations, the annual revolution of the sun; likewise, the waxing of the new moon, the waning of the old, and the obstacles that make it lose its light. The same Apuleius concludes his excursus on Mandrolytus this way (Florida 18.35): For still today, and forever in the future, that reward will be given to Thales by all of us who are truly aware of his interest in the heavens. Eius calestia studia: it is quite evident that, for Apuleius, Thales investigated the sky and distinguished himself primarily as an admirable investigator of the sky. A few decades later, Hippolytus of Rome went so far as to affrm that “having dealt with the explanation and investigation of the stars, he (Thales) was the founder of this discipline for the Greeks”. For his part, Diogenes Laertius was able to write that “according to some (Heraclitus included) he was the frst to astrologēsai, to outline a knowledge on the stars” (1.23), and Augustine that he “was greatly admired for his ability to predict eclipses of

DOI: 10.4324/9781003138723-16

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Other investigations: real and presumed

the sun and moon through his understanding of astronomical calculation”.1 Aristotle tells the story of a Thales who grasped ἐκ τῆς ἀστρολογίας (“from his knowledge of astronomy”) that the coming olive harvest would be abundant, and capitalised on the fact (see Section 15.1 below), and Plato says that Thales fell into a well while studying the stars (see Section 15.2). “Thales was best known in antiquity as an astronomer”, wrote Stephen White (2002, 6). For Dimitri Panchenko too, a rational explanation of eclipses raises a whole series of questions about the constitution of the sun and moon, their light, their movement, their size and relative distances; that was the decisive step in the elaboration of a systematic conception of the universe. (2016, 786) There are many other such claims. The idea that Thales played a role in the emergence of astronomical knowledge has deep roots. Marcacci (2001, 25–27) gave concrete form to this claim when, in her effort to classify the teachings ascribed to Thales, she identifed an astronomical section encompassing 24 doctrines: fve about the sky as a whole, six about the sun, three about the moon, four about seasons, solstices and equinoxes, and six about eclipses. The impulse to think that we have in all this traces of a comprehensive theory is quite strong. But we must, at least, make a distinction. By an embryonic astronomy, we usually mean a frst representation of the celestial bodies, placing them in space and, perhaps, in time, along with a more or less sketchy account of how the sky is composed as a whole and how it works. Now, steps in this direction were made by Anaximander, who could also rely on the Astronomical Unit mentioned in Section 1.2.1. And Thales himself gestures in this direction in his dating of the solstices and equinoxes, his account of the eclipse, and his measurement of the angular amplitude of the solar disk. No doubt those were fruitful investigations, however, no general account of the heavens follows from them. It is worth noting, in this context, that what comes out of Marcacci’s review of Thales’ teachings on the heavens is obviously very heterogeneous, and far from giving rise to a systematic portrayal of the sky. It also contains claims whose right to be included is questionable: the division of the celestial sphere into fve parts (improbable); the description of the zodiac (equally improbable); the uniqueness of the cosmos (not distinctive); the ‘discovery’ of the blowing of the winds and of the prodigious sound of thunder (a point summarily indicated by Apuleius in the passage given at the beginning of this chapter, and not pertinent). Thales certainly did devote himself to the explanation of defnite celestial events, but to say that he tried to develop an account about the heavens as a whole would be to tell quite another story. Is it adequately supported by evidence?

The sky according to Thales 147

12.2 Astronomical culture: the stars Ps.-Plutarch and Stobaeus (both relying on Aetius) state that, for Thales, “even the very fre of sun and stars is nourished by the exhalations of waters”,2 and elsewhere that, according to Thales, “the stars are earthy, but fery”.3 The frst of these claims is obviously an illegitimate corollary of the confused account of Thales’ views about water. The second, is an equally illegitimate corollary of the terrestrial nature ascribed only to the moon (Section 7.1, texts [5] and [6], above).

12.3 Astronomical culture: Ursa Minor Things are better in the case of reports concerning Ursa Major and Ursa Minor. In a scholium to Plato’s Republic, we read that “frst among the Greeks, Thales identifed Ursa Minor, etc.”4 Meanwhile the learned Alexandrian poet Callimachus (ca. 310–235 BC) wrote: He sailed to Miletus, for the victory belonged to Thales. In general he was clever in his judgment, and in particular it was said that he mapped the little stars of the Wain, by which the Phoenicians sail.5 After another fve centuries (approximately), the same report resurfaces in the ps.-Hyginus when the latter writes about lesser Arctus (=Ursa Minor) that: Thales, who researched these matters carefully and was the frst to call it the Bear, was a Phoenician by descent, as Herodotus of Miletus says.6 Ps.-Hyginus continues by pointing out that the Phoenicians claim to have learned this from one of their compatriots, whom they called the Phoenix. Refecting on these data, Thomas Heath (1913, 23) mentioned that, according to Aratus, the Greeks ‘trusted’ Ursa Major while the Phoenicians ‘trusted’ Ursa Minor (Phaenomena 26–29). From that he inferred that Thales may have suggested (in vain?) to the Greeks the greater reliability of Ursa Minor in comparison with Ursa Major. One hundred years later, Walter Burkert observed (2013, 233) that the knowledge of Ursa Minor attributed to Thales is a marked progress compared to the vague reference to the ‘big bear’ in Homer (Od. 5.273, cf. Il. 18.487) because it implies the exact knowledge of the North Star. Burkert goes on to refer to the verses in which Callimachus reports that Thales identifed the ‘chariot’ (not exactly the Bear) hēi pleiousi oi Phoinikes, which was used by the Phoenicians to navigate, bearing witness to contacts between seafarers of different ethnic groups.

148 Other investigations: real and presumed It is natural to wonder if Thales was able to identify the exact point around which the ‘fxed’ stars rotate, that is, the pole star. The answer is available: the search for this was pursued only later. The North Star was identifed perhaps by Eudoxus of Cnidus (in the frst half of the fourth century). But still according to Hipparchus (second century BC): at the pole there is no star, but rather an empty space, near which there are three stars: joining the latter and the point that indicates the pole, we obtain a fgure very similar to a quadrangle, as Pytheas the Massaliot also says.7 At this early date, it was enough to identify what worked for orientation. If the Phoenicians had a predilection for Ursa Minor, Thales would have had no motive to champion a different sign, one which was also probably used by many seamen, on the basis that it could be used to correct the slight anomalies produced by the rotation of the two Ursae around a point that is diffcult to identify precisely. So there is no merit in the suggestion that Thales had any interest in challenging the work already done by experts to identify constellations.

12.4 Astronomical culture: the moon In Section 7.1 above, passages [5] and [6], we read that, according to ps.-Galen and ps.-Plutarch (=Aetius), the moon “is by nature terrestrial”. Stobaeus (or rather his source, Aetius) adds that the sun and the stars are “made of earth” (geōdē).8 However, the detail that the moon is fat explains nothing; to think that Thales anticipated Anaxagoras in conjecturing that the moon and the stars are “made of stone” (lithōdē) would be reckless. In Stobaeus too (1.24.1a, 1.25.3b and 1.26.1e = 11A17a DK = Th354–355–356 W = 5D6a-b LM), we read that according to Thales, the moon is terrestrial (while the second sentence adds that the sun too is terrestrial) and (in 2.28.5 = 11A17b DK = Th357 W= 5R19 LM) that Thales was the frst to teach that the moon is illuminated by the sun. While the frst point is well taken, the second is an isolated and ungrounded statement (and therefore to be ignored). The third follows from the identifcation of the moon as the physical obstacle able to cause an eclipse, but this does not mean that it offers an argument that the moon is constantly, uninterruptedly illuminated by the sun as we infer from Parmenides (28B14–15 DK) and Anaxagoras (59A76–77 and B18 DK).

12.5 Five celestial zones? Another report, from Aetius, suggests that Thales divided the sky into fve bands: Thales and Pythagoras and his followers [hold that] the sphere of the entire sky is partitioned into fve circles, which they call zones.9

The sky according to Thales 149 Parmenides did make a division into fve areas – but of the terrestrial sphere, not the sky (he divided the world into climatic zones: from top to bottom, cold, temperate, hot, temperate, cold).10 The very report of a division of the sky into zones is mysterious, given the intuitive diffculty of suggesting a criterion for identifying these areas. And it seems odd that Thales, with his interest in dating the dawn setting of constellations, would have divided the celestial hemisphere into zones, given that it is not something that remains stationary. Besides, the frst attempts to sketch a map of the sky were made only many centuries later (with Hipparchus). The mention of Pythagoras here also arouses suspicion, since enthusiastic Pythagoreans of a later age attributed the most disparate theories to him. So we have reason to assume that this report is wholly fctitious. In conclusion, the procedure for dating the setting of the Pleiades in relation to the equinox (Section 5.1 above) has more to do with the calendar than knowledge of the heavens; likewise, the refection on the constellations known as Ursa Major and Ursa Minor concerns more the practice of navigation than the identifcation and characterization of a particular point in the heavens. So, there is no evidence for any further theory about the heavens, or any desire on Thales’ part to pursue his investigations in that direction.

12.6 Thales anticipating Anaximander or informed about Anaximander? In addition to the earthy nature of moon, there is, however, another possible exception. This has to do with the angular width of the sun, examined in Chapter 8. Recall, to begin with, that the measurement of the angular amplitude has reference to the circular path the sun seems to take in 24 hours: quoties sol magnitudine sua circulum quem permeat metiatur, affrms Apuleius; Thales “frst showed that the size of the sun is one seven hundred and twentieth of the solar orbit and the size of the moon is one seven hundred and twentieth of the lunar orbit”, reports Diogenes Laertius. We are therefore not talking about the so-called round angle or simply about a circle, but about the circular path the sun is supposed to traverse in 24 hours (its orbit). In our sources, the idea that the sun’s path is circular and continues under the earth by night is regularly associated with Anaximander, not Thales. Yet it seems that the latter used this assumption. So what are we to think of this? Should we perhaps consider the possibility that Thales anticipated Anaximander? It probably is not necessary to do so. Apuleius points out that the measurement of the angular amplitude was performed by Thales in old age (sane iam proclivi senectute). If this is right (and it is quite possible that Apuleius had access to accurate information about it), then Thales could simply have deployed a view proposed by his pupil. The conjecture cannot be proved, but it has no contraindications, is plausible enough, and makes our evidence consistent.

150 Other investigations: real and presumed In conclusion, Thales certainly developed a great interest in several astronomical recurrent phenomena, with limited inferences on other conjectures, but no comprehensive idea of the sky, or of the celestial bodies, can be ascribed to him despite what some ancient sources and modern interpreters claimed.

Notes 1 De civ. dei 8.2 (=Th311 W): maximeque admirabilis extitit, quod astrologiae numeris comprehensis defectus solis et lunae etiam praedicere potuit. 2 Ps.-Plutarchus, Placita philosophorum 1.3, 875F (=Th147 W): τρίτον, ὅτι καὶ αὐτὸ τὸ πῦρ τὸ τοῦ ἡλίου καὶ τὸ τῶν ἄστρων ταῖς τῶν ὑδάτων ἀναθυμιάσεσι τρέφεται. The same sentence appears in Stobaeus, Anthol. 1.10.12 (=Th 343 W). 3 Ps.-Plutarchus, Placita philosophorum 2.12, 888D (=11A17a DK = Th156 W = 5D6ab LM): Θαλῆς γεώδη μὲν ἔμπυρα δὲ τὰ ἄστρα. We fnd the same sentence in Stobaeus, Anthol. 1.24.1a (=Th344 W). 4 The Scholia Vetera in Rempublicam 10.600a (=11A3 DK = Th578 W ≠ LM) reports that καὶ μικρὰν ἄρκτον αὐτὸς ἔγνω καὶ τὰς τροπὰς πρῶτος Ἑλλήνων. The verb form egnō by itself only tells us that Thales frst knew about the Ursa constellations and the tropai. 5 These are verses 52–55 of the frst iamb of Callimachus (the fr. 191 Pfeiffer taken from POxy 7.1011 = 11A3a DK = Th52 W ≠ LM): ἔπλευσεν ἐς Μίλητον· ἦν γὰρ ἡ νίκη | Θάλητος, ὅς τ’ ἦν τἆλλα δεξιὸς γνώμην | καὶ τῆς ἁμάξης ἐλέγετο σταθμήσασθαι | τοὺς ἀστερίσκους, ἧι πλέουσι Φοίνικες. Two of these verses surface in Diogenes Laertius at 2.23. Measuring or mapping (stathmēsasthai) the little stars (those of the Ursa Minor) can only be a modernizing account of what Thales may have done, which was probably just to claim that it is better for sailors to look to Ursa Minor than Ursa Major. 6 Ps.-Hyginus, De astronomia 2.2.3 (=Th 136 W) writes: Thales enim, qui diligenter de his rebus exquisivit et hanc primus Arctum appellavit, natione fuit Phoenix, ut Herodotus Milesius dicit. 7 Hipparchus, In Arati et Eudoxi phenomena I 4.1 = test. 1 Bianchetti. 8 Stobaeus, Anthologium 1.24.1a, 1.25.3b and 1.26.1e (=11A17a DK = Th354–355– 356 W = 5D6a–b LM). The relevant statements are affected by different editorial choices. 9 The source is ps.-Plutarch, Placita philosophorum 2.12, 888C1–5 (=11A13c DK = Th156W = W = 5R23 LM): Θαλῆς, Πυθαγόρας καὶ οἱ ἀπ ‘αὐτοῦ μεμερίσθαι τὴν τοῦ παντὸς οὐρανοῦ σφαῖραν εἰς κύκλους πέντε, οὕστινας προσαγορεύουσι ζώνας. 10 The complex information mentioned here has been examined in detail in Rossetti (2017, ii. 41–59).

13 To measure the distance of a ship from land

13.1 A measurement that cannot be carried out Coming back down to earth, so to speak, let us now turn to the idea of measuring the distance of ships from the shore. This is a case that involves an intellectual claim that is completely impracticable; but it is also a good example of what is theoretically possible once the characteristics of a right-angled triangle are understood. This looks like a sort of imaginative application of the reasoning that might allow us to establish how high a pyramid is. Our only source of information on this is Proclus, who reports that: Eudemus in his History of Geometry attributes this theorem to Thales. He declares that he must have used it, to judge by the method by which they say he proved the distance of ships at sea.1 Proclus introduces the note in his extensive commentary on Euclid’s Elements. It would be reasonable to expect more detail, but we do not get it. In fact, the theorem that Proclus is talking about is that according to which, in order to claim that two triangles are equal, it is enough to ascertain that one of the sides and the angles adjacent to that side are equal. But Thales could not have used this theorem to determine how far out to sea a ship was, since the distance is precisely what he sought! The reference to this theorem by Proclus is simply out of place. However, Proclus uses the verb deiknunai, ‘to show’ (i.e. ‘to prove’). This is an expression suitable for a theōrēma, something more theoretical. So what could this measurement show? The demonstrandum consists in establishing indirectly how far a ship is from the shore. Now, when two sides of a right-angled triangle have the same length (so the hypotenuse meets each at an angle of, as we would say, 45°), if we know the length of one of the two sides, we can know how long the other is (without actually measuring it). This is the same basic equation that Thales proposed for measuring the height of the pyramid. Many complications arise immediately. We can assume that our ship is identifed by its mast; but the ship is not still; and the coastline can be only

DOI: 10.4324/9781003138723-17

152 Other investigations: real and presumed roughly identifed, no matter whether we have to deal with a beach or a cliff. So any measurement would be extremely rough, as well as systematically fuctuating even assuming that the ship is at anchor. This distance strongly resists measurement. As a consequence, unless he was satisfed with very rough quantifcations, it is very unlikely that Thales judged an actual measurement in these conditions practicable. It is much more likely that he speculated that a measurement could in theory be carried out.

13.2 How to get around the obstacle? 150 years ago, the frst hypotheses for explaining what Thales might have had in mind was advanced. The conjectures outlined in the two images that follow refer, respectively, to Bretschneider 1870 and Tannery 1887.2 Bretschneider, in Figure 13.1, imagined the use of a tower (AC) equipped, as it seems, with a platform that would allow an observer located at point A to identify point E located on line AB (where B is the point where the ship is located). Fixing points A and E means knowing the length of both AD and DE. The relation AD:AC would allow us to calculate CB (the distance out of the ship). A problem here is that Thales hardly had any idea of proportional calculations (indeed, of calculations as such).

Figure 13.1 Device allowing to establish how far is a ship according to Tannery.

The hypothesis linked to the name of Tannery (Figure 13.2) is equally cumbersome. He imagined fxing two points, A and D on the shore, A being placed in front of the ship (at B), and D some way along from it, while assuming that the line AC forms a right angle with the line AB. Next, point C is identifed along the extension of AD, at the same distance from D as A. Then a line perpendicular to AC is projected inland from C. Finally, BD is extended to meet the line CE, and point E would thus be identifed. Its distance from C is assumed to be equal to the distance of the ship from point A at the time of the survey. Tannery’s scheme requires an entirely fat and bare ground to work on, but has the advantage of relying on measurements, not calculations (it is assumed that CE and AB are the same length).

The distance of a ship from land  153

Figure 13.2  Device allowing to establish how far is a ship according to Bretschneider.

Another way of achieving this measurement may be considered. Suppose, for a moment, that two wagons are placed on a clear and roughly straight beach: on wagon A, two horizontal grooves are set at right angles, and on wagon B, located at a considerable distance down the beach from the other, two grooves are set in such a way as to meet at an angle of 45°. Position wagon A in such a way that an observer on it could, at the same time, see the ship along the extension of one of the grooves, and wagon B along the extension of the other (in other words, at an angle of 90° to the sightline on the ship). Next, move wagon B so that an observer on it could, at the same time, see the ship down one of its grooves, and wagon A along the other (in this case, then, at an angle of 45° to the sightline for the ship). Between wagon A, wagon B and the ship, a right-angled, isosceles triangle is now formed; this means that the distance between A and B will be the same as the distance between A and the ship. This hypothesis has the advantage of explaining Proclus’ reference to the right-angled triangle. But it goes without saying that it is no less speculative than the other two. In conclusion, I can only reiterate that, in my view, we cannot know if Thales speculated about measuring the distance out of a ship, or whether that was attributed to him without foundation.

Notes 1 Procl. In Primum Euclidis Elementorum 352.14–18 (=11A20 DK = Th384 W = 5R29 LM): Εὔδημος δὲ ἐν ταῖς γεωμετρικαῖς ἱστορίαις εἰς Θαλῆν τοῦτο ἀνάγει τὸ θεώρημα. τὴν γὰρ τῶν ἐν θαλάττῃ πλοίων ἀπόστασιν δι’ οὗ τρόπου φασὶν αὐτὸν δεικνύναι τούτῳ προσχρῆσθαί φησιν ἀναγκαῖον. For a very careful study of this statement (and of its context), guided by firm confidence in the reliability of what Proclus asserted, see Caveing (1997, 33–53). 2 Bretschneider’s conjecture was re-proposed in Heath (1908, 46).

14 Thales and the theorems of plane geometry

14.1 The anachronistic theōrēmata ascribed to Thales In his mention of the measurement of the distance of a ship out to sea, Proclus used the notion of a theōrēma. He did so at other times as well. [1] On p. 156 of his commentary on the frst book of Euclid’s Elements, Proclus gives the Euclidean defnition of the diameter of the circle, and on the following page writes: They say that Thales was the frst to prove that the circle is bisected by its diameter. The cause of the bisection is the undeviating progression of the straight line through the center.1 [2] On p. 250, Proclus refers to Pappus to argue that two isosceles triangles, if their two sides are equal, also have the three internal angles equal. A few lines later he observes: We have the old Thales to thank for the discovery of this theorem and many others. For he is said to have been the frst to notice and state that the angles at the base of every isosceles [triangle] are equal, except that he rather archaically called the equal angles ‘similar’.2 [3] On p. 298, Proclus reports Euclid’s eighth theorem (relating to proposition XV) on what is observed when two straight lines are cut by a diagonal. Again, a few lines later, he notes: Now this theorem proves that, when two straight lines intersect one another, their vertical angles are equal. It was frst discovered by Thales, Eudemus says.3 [4] On p. 347, Proclus reports Euclid’s 17th theorem (relating to proposition XXVI) on the minimum conditions for asserting that two triangles are equal; he discusses them at length, and on p. 352 connects this theorem with the claim (derived from Eudemus) that Thales could measure the distance of ships at sea using this theorem. So much for Proclus. DOI: 10.4324/9781003138723-18

The theorems of plane geometry 155 [5] Diogenes Laertius, for his part, writes that Thales “was the frst to inscribe a right-angled triangle in a circle, and that he sacrifced an ox (scil. to celebrate this discovery)”.4

14.2 Potential theorems? Potential geometry? What are we to think of all this? Proclus and Diogenes Laertius add notes of colour (‘he did not fnd the right words’, ‘he sacrifced an ox’); only Proclus mentions the name of Eudemus as a source; both introduce notions that are very far from the conceptual and terminological world of Thales: theorem, right-angled triangle, straight lines, vertex, diameter, triangle inscribed in a circle… Moreover, it is made to sound as if Thales had formulated each proposition as an individual claim, and even undertaken the formal demonstrations of each of them. Such operations are possible where there is a network of experts, and an element of intellectual competition (e.g.: “my proof, i.e. the argument I devised, is direct and peremptory, while against yours one could counter-argue that…”). But in Thales’ Miletus there was no geometry, and no ‘professors’ of geometry, much less the need to prove that the diameter divides the circle into two equal parts (or that in every isosceles triangle the angles at the base are equal, or that, when two straight lines intersect each other, the angles at the vertex are equal). These demonstranda suppose levels of abstractions that certainly remained foreign to Thales. An additional obstacle is related to the very notion of a theorem, because Aristotle sometimes uses the term theōrēma, but never in the sense of a mathematical theorem. This means that the technical (‘Euclidean’) notion of ‘theorem’ probably remained unknown, or at least unfamiliar, to him. Therefore the concepts of a ‘theorem (of geometry)’ and of a ‘proof of the theorem’ were probably developed only after Aristotle. That means, in turn, that the mathematical meaning of theōrēma did not appear before the last decades of the fourth century, when, indeed, there was a vast mobilization of mathematicians engaged in identifying and proving such theorems – culminating of course in the work of Euclid. From this it is permitted to infer that to attribute an interest in mathematical theorems to Thales is sensationally anachronistic.5 To strip a theorem of all that is modern in its formulation may not be enough to identify the contribution of Thales. As Gino Loria wrote more than a century ago, We note in the frst place the strange reasoning made there to attribute to Thales the cited theorem of Euclid [I 26], a reasoning which, applied in all analogous cases, would lead to admitting any theory of which he indicated even a single application on the subject.6 Mueller tentatively remarked that “Thales’ ‘proofs’ were what we might call convincing pictures involving no explicit deductive structure” (1997, 267):

156  Other investigations: real and presumed but once the notion of the theorem has been dropped, what remains? Just that Thales had a certain propensity for drawing diagrams?7 Eudemus of Rhodes wrote a History of Geometry, a History of Arithmetic and a History of Astrology, as well as a book On Angles (works not extant today).8 It seems that Eudemus had more specific interests than, say, Theophrastus with his Physikōn doxai. Perhaps he was not exempt from the tendency to identify famous ‘first inventors’, a tendency which exaggerates the achievements ascribed to the most ancient sophoi. But what could have led him to attribute this whole (and rather heterogeneous) group of theorems to Thales? It is impossible to imagine. It is also worth noting that Proclus, when he spoke of the knowledge acquired by Thales (“he discovered many things himself and the principles of many others he set out for posterity, approaching some of them more generally and others in a way that is closer to perception”),9 did not quote Eudemus. He mentions Eudemus once in relation to Thales – but that is elsewhere, at a distance of almost 300 pages in Friedlein’s edition (Leipzig 1873), where he says that Eudemus reports in his Geōmetrikē Historia that Thales used a certain theorem to measure the distance of ships from the shore.10 So Eudemus must have had some responsibility for the attribution of an interest in theorems to Thales; but it is very hard to imagine why he thought this. Indirect confirmation of what I have just observed emerges, somewhat surprisingly, from a famous passage of Aristophanes’ Birds (see also Dührsen 2013, 247). At Birds 995–1009, Thales is associated with square and compass, which he is using in an attempt to square the circle. It is certainly significant that Thales as presented here engaged in ambitious intellectual research (trying to find a circle equivalent in area to a square): but note that there is no suggestion that he is trying to identify a formula for this. He is not behaving like a professor who enunciates and expounds theorems, but rather as a researcher trying to achieve something commonly believed to be impossible. Again, we are led to doubt Proclus’ testimony on the theorems of Thales, whatever the origin of the report that he claims to have found in Eudemus. Besides, Thales did not even know the so-called four operations; he was not familiar with the elaborate calculations proposed by the Rhind papyrus (Sections 4.2–4 above). He was very far removed from a mathematical culture which knew how to formulate theorems, or how to formulate a definition, e.g. the definition of number as monadōn sustēma (so Iamblichus).11 We should not feel bound to save anything from the reports about this: on closer inspection, there is nothing here to be saved.

Notes 1 Procl. In primum Euclidis elementorum libri 157.10–13 (=11A20 DK = Th381 W = 5R30 LM): τὸ μὲν οὖν διχοτομεῖσθαι τὸν κύκλον ὑπὸ τῆς διαμέτρου πρῶτον Θαλῆν ἐκεῖνον ἀποδεῖξαί φασιν, αἰτία δὲ τῆς διχοτομίας ἡ τῆς εὐθείας ἀπαρέγκλιτος διὰ τοῦ κέντρου χώρησις.

The theorems of plane geometry  157 2 Procl. In Eucl. 250.20–251.2 (=11A20 DK = Th382 W = 5R28 LM): Τῷ μὲν οὖν Θαλῇ τῷ παλαιῷ πολλῶν τε ἄλλων εὑρέσεως ἕνεκα καὶ τοῦδε τοῦ θεωρήματος χάρις. λέγεται γὰρ δὴ πρῶτος ἐκεῖνος ἐπιστῆσαι καὶ εἰπεῖν, ὡς ἄρα παντὸς ἰσοσκελοῦς αἱ πρὸς τῇ βάσει γωνίαι ἴσαι εἰσίν, ἀρχαϊκώτερον δὲ τὰς ἴσας ὁμοίας προσειρηκέναι. 3 Procl. In Eucl. 299.1–5 (=11A20 DK = Th383 W = 5R26 LM): Τοῦτο τοίνυν τὸ θεώρημα δείκνυσιν, ὅτι δύο εὐθειῶν ἀλλήλας τεμνουσῶν αἱ κατὰ κορυφὴν γωνίαι ἴσαι εἰσίν, εὑρημένον μὲν, ὡς φησὶν Εὔδημος, ὑπὸ Θαλοῦ πρώτου. 4 Diog. Laert. I 24–25 (=11A1 DK = Th 236 W = 5R27 LM): πρῶτον καταγράψαι κύκλου τὸ τρίγωνον ὀρθογώνιον, καὶ θῦσαι βοῦν. 5 What Andolfi (2019, 3) writes about Acusilaus seems significant to me: “In the ancient testimonies Acusilaus is called historikοs, historiogrαphos and archaios sungrapheus. The first two labels are inappropriate as they refer to a literary genre that would emerge only later”. Speaking of theorems in the case of Thales is also a patent anachronism (cf. Röd 1998, 33: “ausserordentlich unwarscheinlich”). 6 Loria (1914, 19). One of the most strenuous defenders of the reliability of what Proclus said about Thales, Caveing, at the very beginning of the pages dedicated to Proclus’ testimony, writes: “the term ‘theorem’ is avoided : we have translated with ‘results’ in the plural” (1997, 33). This solution betrays the embarrassment of having to talk about theorems with reference to a ­sixth-century BC intellectual, but at the same time it undermines Caveing’s desire to believe Proclus without significant reservations. 7 This possibility, defended by Robert Hahn (see Hahn 2017), seems to be without the least foundation. 8 Eudemus was a disciple of Aristotle who created in Rhodes a Peripatetic cultural center which had a long life (cf. Rossetti–Liviabella 1993, §4–5). It is assumed that he was born around 350 BC, while Euclid’s Elements was composed around 300 BC, when he may have been around 50. 9 Proclus, In Eucl. 65, 3–11 (=11A11 DK = Th380 W ≠ LM): ὥσπερ οὖν παρὰ τοῖς Φοίνιξιν διὰ τὰς ἐμπορείας καὶ τὰ συναλλάγματα τὴν ἀρχὴν ἔλαβεν ἡ τῶν ἀριθμῶν ἀκριβὴς γνῶσις, οὕτω δὴ καὶ παρ’ Αἰγυπτίοις ἡ γεωμετρία διὰ τὴν εἰρημένην αἰτίαν εὕρηται. Θαλῆς δὲ πρῶτον εἰς Αἴγυπτον ἐλθὼν μετήγαγεν εἰς τὴν Ἑλλάδα τὴν θεωρίαν ταύτην καὶ πολλὰ μὲν αὐτὸς εὗρεν, πολλῶν δὲ τὰς ἀρχὰς τοῖς μετ’ αὐτὸν ὑφηγήσατο, τοῖς μὲν καθολικώτερον ἐπιβάλλων, τοῖς δὲ αἰσθητικώτερον. 10 Proclus, In Eucl. 352, 14–18 (=11A20 DK = Th384 W = 5R29 LM): Εὔδημος δὲ ἐν ταῖς γεωμετρικαῖς ἱστορίαις εἰς Θαλῆν τοῦτο ἀνάγει τὸ θεώρημα. τὴν γὰρ τῶν ἐν θαλάττῃ πλοίων ἀπόστασιν δι’ οὗ τρόπου φασὶν αὐτὸν δεικνύναι τούτῳ προσχρῆσθαί φησιν ἀναγκαῖον. 11 “Set of units”, as Iamblichus reports in his De communi mathematica scientia 21 (=Th252 W). Pizzani (2002, 447) is among the rare secondary sources mentioning the definition ascribed to Thales.

15 Thales ‘el injenioso hidalgo’

So far, we have seen a Thales who sets out to grapple with apparently intractable intellectual puzzles. On several occasions, he overcame the diffculties to obtain unexpected and even exciting results. But he knew the limits of his humanity (and a lot of what is attributed to him comes from the realms of fantasy). However, our sources also tell us of a Thales who brought unexpected solutions to practical problems.

15.1 How to get rich with olive oil Let us consider, to begin with, the story of the olive presses in Miletus and Chios. Aristotle tells a story in which the rich and well-known Thales becomes, for the sake of the story, “poor, as if philosophy were useless” (διὰ τὴν πενίαν ὡς ἀνωφελοῦς τῆς φιλοσοφίας οὔσης).1 But the impoverished Thales understood ἐκ τῆς ἀστρολογίας (“thanks to the study of the stars”) that the coming olive harvest was going to be especially abundant, and so he rented all (or many) of the olive presses, not only in the area around Miletus, but also in Chios (an island not all that close by). When the harvest came, his presses were able to work at full capacity, ensuring the supposedly impoverished Thales a considerable income, and demonstrating that it is easy for philosophers to get rich, if they wanted to. (But fortunately, Aristotle adds, this is not the goal they pursue.) After Aristotle, we fnd the story briefy evoked by Cicero (De divinatione 1.111–112 = Th77 W), Hieronymus of Rhodes (ap. Diogenes Laertius 1.26 = Th60 W), and Philostratus (Vita Apollonii 8.7.158 = Th225 W). Pliny (Naturalis Historia 18.68.273–4) tells a very similar story, but he credits Democritus with this prowess. So far as I know, commentators have never questioned this story,2 but Aristotle’s narrative is very implausible – starting with the fact that it asks us to imagine a person in poverty who nonetheless has considerable spending power. Neither poverty nor philosophy are essential to the story, while the ‘prediction’ could only have come down to speculation that there would be abundant rains. Then there is the mention of Chios, an island more than 200 DOI: 10.4324/9781003138723-19

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km from Miletus; and it would not have been enough to rent the presses, since Thales would have needed to enrol several agents to manage the plants and investments. It looks as if the whole story was a later concoction drawing on a recognized cliché of the impoverished philosopher – the sort of thing we fnd said (no less improperly) about Socrates, and a lot of others. But this kind of story could only have been told when the category of the ‘philosopher’ was extended backwards to Thales and other Presocratics.3 Therefore, it can hardly date from earlier than around 340 BC. In conclusion, this story is obviously a didactic fction: completely groundless as fact.

15.2 Thales the absent-minded We will now look briefy, and only for the sake of completeness, at the anecdote of the “Thracian servant”, who owes her fame to a passage in Plato’s Theaetetus: They say that Thales fell into a well while studying the stars and gazing aloft, and a witty and amusing Thracian servant-girl made fun of him because he was so keen to know about what was up in the sky but failed to see what was in front of him and next to his feet.4 Ben trovato, as they say. This is a nice piece of Platonic fction (the best there is on Thales): but everyone knows that Plato was an excellent storyteller.

15.3 How to cross the Halys River Another feat alleged of the elderly Thales is that he came up with a way to get a large number of soldiers over a river. The story is told by Herodotus in the context of his account of Croesus, the king of the prosperous Lydia who, among the Greeks, was famous for his wealth. (He ended up clashing with Cyrus, and being defeated by him.) Croesus attempted the conquest of Cappadocia in 547, when Thales was already very advanced in years (if not already dead). During this expedition, Croesus is supposed to have turned to him to solve an unexpected complication: a river which was hard to cross was blocking his troops. Herodotus names the river as the Halys, which fows into the Black Sea east of the city of Sinope and is about 1,500 km long.5 When Croesus reached the river Halys, he had his army cross it by the existing bridges. This is what I say, but according to the well known Greek account Thales of Miletus was responsible for the crossing: that those bridges had not yet been built and that while Croesus was at a loss as to how his army could get across, Thales, who was in the camp,

160  Other investigations: real and presumed caused the river, which flowed on the left side of the army, to flow on the right side as well. This is how he did it: beginning upstream from the camp he dug a deep crescent-shaped channel in order to divert the river from its old bed through the channel so that it would flow around the rear of the camp and after passing the camp it would return to its old course. And so as soon as the river was split in two both parts became fordable.6 Diogenes Laertius writes about “Croesus, whom he promised to bring across the river Halys without a bridge by diverting the stream”.7 What should we make of this story? At first, it is difficult to imagine how such a detailed narrative could have been made up (and Herodotus assures us that it was well established); and the fact that the river is named gives it an air of credibility. Perhaps Thales accompanied Croesus as a distinguished guest and found himself on hand to solve a problem for him? If things happened roughly in the way described, the diversion of the stream would be further testimony to Thales’ remarkable innovation and daring, his ability to think up solutions to particular problems using new devices. And who else back then could have thought of tackling the problem in such a creative way? Patricia O’Grady dedicates some very interesting pages to the subject (2002, 178–190). O’Grady points out, first of all, that the invasion of Cappadocia, undertaken by Croesus to oppose Cyrus’ expansionism, took place in the year in which we are told that Thales, then over 75 years old, died. Secondly, the river would have been encountered in May, that is, in a period when it was probably in flood. Thirdly, the Halys, which in its course follows a great U-shaped bend (with a radius of some 70–80 km), was crossed by the ‘via regia’ in two places. Fourthly, the total absence of bridges mentioned by Herodotus is apparently at odds with archaeological evidence. O’Grady finally reminds us that, according to the priests interviewed by Herodotus (2.90), in around 3000 BC an ancient Egyptian king (Min, Meni, or Menes) protected the city of Memphis (not far from present-day Cairo) from the floods of the Nile with massive works that diverted its course. If Thales knew about this, then he could have appealed to this illustrious precedent to justify his own proposal: his task would only have been to suggest a way of putting into practice here what he knew had worked elsewhere. So, for O’Grady, the diversion of the stream may well have really happened. She was persuaded by the following lines from Mott Greene (1992, 105), who said that this feat of Thales, “far from a spurious addition to a list of mythical accomplishments, was the final tour de force of his career – bringing together the experiences of a lifetime and the wealth of theoretical and practical skills.” However, one question remains: what happened to Thales in the course of the same war? Was he captured by Cyrus, as Croesus was? Or was he able to hurry back to Miletus just before this turn of events? Herodotus is

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silent on the matter. And there is something else that O’Grady did not consider. How can the report that Thales was welcomed and hosted by Croesus be squared with the fact that there was no alliance between Croesus and the city of Miletus then – indeed, that there was no alliance because Thales himself opposed making one?8 If the elderly Thales used his authority to prevent the Milesians from making terms with Croesus on his campaign to conquer Cappadocia, how could he have accepted the invitation to become a sort of courtier to the king of Lydia immediately afterwards? Old age, some respect for consistency, and fear of becoming an object of anger, or a hostage, or even part of the spoils of war (in the event that Croesus’ expedition failed) would have dissuaded him from accepting the invitation – assuming that there was an invitation. All in all, this story raises too many doubts about the role Thales could have played, so that it is, at best, hasty to give him the title of ‘engineer’ based on Herodotus’ story (as do, among others, Graham 2006, 4 and Laks– Most, 2016, ad loc.). It is quite likely that none of these events occurred – not least because Thales was probably already dead (and his death could have occurred in Tenedos, not in Miletus: Section 3.5 above).

15.4 Wise advice given to fellow citizens in Miletus Let us next consider something else that Herodotus claims: that, before Croesus lost his kingdom to Cyrus in 546 BC, Thales proposed that the cities of Ionia should confederate and establish a single boulē in Teos, which would have the power to deliberate in the interest of all the cities, but on condition of making of each of them mere dēmoi, that is, territorial and electoral districts of the envisaged federation: When the Ionians, despite their evil plight, nonetheless assembled at the Panionion, Bias of Priene, I have learned, gave them very useful advice, and had they followed it they might have been the most prosperous of all Greeks: for he advised them to put out to sea and sail all together to Sardis and then found one city for all Ionians: thus, possessing the greatest island in the world and ruling others, they would be rid of slavery and have prosperity; but if they stayed in Ionia he could see (he said) no hope of freedom for them. This was the advice which Bias of Priene gave after the destruction of the Ionians; and that given before the destruction by Thales of Miletus, a Phoenician by descent, was good too; he advised that the Ionians have one place of deliberation, and that it be in Teos (for that was the center of Ionia),9 and that the other cities be considered no more than demes. Thus Bias and Thales advised.10 This daring proposal would have been intended to address the imbalance between the power of individual poleis and that of state structures of very different proportions, such as the Lydia of Croesus and, subsequently, the

162 Other investigations: real and presumed Persian empire. We are presented here with a Thales capable of proposing unprecedented and pragmatic solutions to a problem that was becoming acute. If the proposal was dropped, perhaps that is because the threat of war was too close.11 Something of the sort, with the Ionians facing two extreme options, one advanced by Bias and the other advanced by Thales, in a rather dramatic moment, could have taken place, but did it? There is a strong impression of anachronism.12 The territory of Miletus was indeed divided into dēmoi in the Attic way, but well after the destruction of the town by the Persians.13 The mention of dēmoi and bouleutērion, in turn, suggests that Herodotus was expressing himself with an Athenian institutional model in mind. However, from that it does not follow that there is no factual basis for the Herodotean report. Who knows? Summing up: the whole story has turned out to be slippery, due to traditions millennia old that have cluttered the feld; so slippery as to require a lot of determination in order to discern the plausible from the unlikely. It is indeed likely that none of these events possibly took place.

Notes 1 Aristotle recounts this episode in the frst book of Politics 1.11, 1259a5–19 (=11A10 DK = Th28 W = 5P15 LM): οἷον καὶ τὸ Θάλεω τοῦ Μιλησίου· τοῦτο γάρ ἐστι κατανόημά τι χρηματιστικόν, ἀλλ ‘ἐκείνῳ μὲν διὰ τὴν σοφίαν προσάπτουσι, τυγχάνει δὲ καθόλου τι ὄν. ὀνειδιζόντων γὰρ αὐτῷ διὰ τὴν πενίαν ὡς ἀνωφελοῦς τῆς φιλοσοφίας οὔσης, κατανοήσαντά φασιν αὐτὸν ἐλαιῶν φορὰν ἐσομένην ἐκ τῆς ἀστρολογίας, ἔτι χειμῶνος ὄντος εὐπορήσαντα χρημάτων ὀλίγων ἀρραβῶνας διαδοῦναι τῶν ἐλαιουργίων τῶν τ ‘ἐν Μιλήτῳ καὶ Χίῳ πάντων, ὀλίγου μισθωσάμενον ἅτ’ οὐθενὸς ἐπιβάλλοντος· ἐπειδὴ δ' ὁ καιρὸς ἧκε, πολλῶν ζητουμένων ἅμα καὶ ἐξαίφνης, ἐκμισθοῦντα ὃν τρόπον ἠβούλετο, πολλὰ χρήματα συλλέξαντα ἐπιδεῖξαι ὅτι ῥᾴδιόν ἐστι πλουτεῖν τοῖς φιλοσόφοις, ἂν βούλωνται, ἀλλ’ οὐ τοῦτ ‘ἐστὶ περὶ ὃ σπουδάζουσιν. Θαλῆς μὲν οὖν λέγεται τοῦτον τὸν τρόπον ἐπίδειξιν ποιήσασθαι τῆς σοφίας (“For all these [stories about how people have succeeded in becoming wealthy] are useful to those who value the acquisition of wealth, as is the anecdote about Thales of Miletus. For this is an idea useful for acquiring wealth, but it is attributed to him on account of his reputation for wisdom, and it actually involves a general principle. They say that people used to reproach him for his poverty, which they believed showed that philosophy was a useless occupation. But he understood from his knowledge of astronomy that there would be a large olive crop in the coming year; so, since he had a little money, while it was still winter he put down deposits for the use of all the olive presses in Miletus and Chios, which he hired at a low price because no one was bidding against him. When the harvest time came, and many were suddenly wanted all at once, he rented them out for whatever price he liked and made a great deal of money. Thus he showed the world that philosophers can easily be rich if they like, but that this is not their aim. In this way Thales is said to have made a striking display of his wisdom.”) 2 Recently Panchenko (2016, 776) went so far as to affrm that “L’histoire est substantiellement authentique”, but his argument for this was the aid offered by Chios to Miletus on the occasion of a war with the king of Lydia (I 18.3), with the presumption that this could confrm the verisimilitude of the anecdote.

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3 The reason is very simple: Aristotle, but nobody else before him, is known for having discussed indifferently the theories of ancient sophoi as well as those of philosophers he knew personally. See Rossetti (2015) (esp. Section II 5). 4 Tht 174a4–8 (=11A9 DK = Th19 W = 5P12 LM): Ὥσπερ καὶ Θαλῆν ἀστρονομοῦντα, ὦ Θεόδωρε, καὶ ἄνω βλέποντα, πεσόντα εἰς φρέαρ, Θρᾷττά τις ἐμμελὴς καὶ χαρίεσσα θεραπαινὶς ἀποσκῶψαι λέγεται ὡς τὰ μὲν ἐν οὐρανῷ προθυμοῖτο εἰδέναι, τὰ δ’ ἔμπροσθεν αὐτοῦ καὶ παρὰ πόδας λανθάνοι αὐτόν. 5 Immediately afterwards (in 1.76.1) Herodotus himself specifes that Croesus’ troops would have faced this problem while they were much further north of Lydia, near the southern coasts of the Black Sea and the city of Sinope – so where the river must have had an impressive fow of water. 6 This is reported in Hdt 1.75.3–5 (=11A6 DK = Th11 W = 5P6 LM): ὡς δὲ ἀπίκετο ἐπὶ τὸν Ἅλυν ποταμὸν ὁ Κροῖσος, τὸ ἐνθεῦτεν, ὡς μὲν ἐγὼ λέγω, κατὰ τὰς ἐούσας γεφύρας διεβίβασε τὸν στρατόν, ὡς δὲ ὁ πολλὸς λόγος Ἑλλήνων, Θαλῆς οἱ ὁ Μιλήσιος διεβίβασε. (4) ἀπορέοντος γὰρ Κροίσου ὅκως οἱ διαβήσεται τὸν ποταμὸν ὁ στρατός (οὐ γὰρ δὴ εἶναί κω τοῦτον τὸν χρόνον τὰς γεφύρας ταύτας) λέγεται παρεόντα τὸν Θαλῆν ἐν τῷ στρατοπέδῳ ποιῆσαι αὐτῷ τὸν ποταμὸν ἐξ ἀριστερῆς χειρὸς ῥέοντα τοῦ στρατοῦ καὶ ἐκ δεξιῆς ῥέειν, ποιῆσαι δὲ ὧδε· ἄνωθεν τοῦ στρατοπέδου ἀρξάμενον διώρυχα βαθέαν ὀρύσσειν, ἄγοντα μηνοειδέα, ὅκως ἂν τὸ στρατόπεδον ἱδρυμένον κατὰ νώτου λάβοι ταύτῃ κατὰ τὴν διώρυχα ἐκτραπόμενος ἐκ τῶν ἀρχαίων ῥεέθρων καὶ αὖτις παραμειβόμενος τὸ στρατόπεδον ἐς τὰ ἀρχαῖα ἐσβάλλοι, ὥστε ἐπείτε καὶ ἐσχίσθη τάχιστα ὁ ποταμός, ἀμφοτέρῃ διαβατὸς ἐγένετο. 7 In Diogene Laertius 1.38 (=11A1 DK = Th237 W ≠ LM), we read: γεγονότα κατὰ Κροῖσον, ᾧ καὶ τὸν Ἅλυν ὑποσχέσθαι ἄνευ γεφύρας περᾶσαι, τὸ ῥεῖθρον παρατρέψαντα. 8 Cf. Diog. Laert. 1.25 (=11A1 DK = Th237 W ≠ LM): Κροίσου γοῦν πέμψαντος πρὸς Μιλησίους ἐπὶ συμμαχίᾳ ἐκώλυσεν· ὅπερ Κύρου κρατήσαντος ἔσωσε τὴν πόλιν (“when Croesus approached the Milesians for an alliance, he [Thales] prevented it, and this saved the city when Cyrus defeated him”). And once Croesus was defeated, “the Milesians … made a treaty with Cyrus himself and struck no blow” while the rest of Ionia was subjugated (Herodotus 1.169.2). 9 It is worth noticing that the citizens of Teos, or at least a great part of them, would have left the city to found Abdera (Herodotus 1.168) just in time, before the defeat of their city by the Persians. 10 Herodotus 1.170 (=11A4 DK = Th12 W = 5P7 LM): κεκακωμένων δὲ Ἰώνων καὶ συλλεγομένων οὐδὲν ἧσσον ἐς τὸ Πανιώνιον, πυνθάνομαι γνώμην Βίαντα ἄνδρα Πριηνέα ἀποδέξασθαι Ἴωσι χρησιμωτάτην, τῇ εἰ ἐπίθοντο, παρεῖχε ἄν σφι εὐδαιμονέειν Ἑλλήνων μάλιστα· ὃς ἐκέλευε κοινῷ στόλῳ Ἴωνας ἀερθέντας πλέειν ἐς Σαρδὼ καὶ ἔπειτα πόλιν μίαν κτίζειν πάντων Ἰώνων, καὶ οὕτω ἀπαλλαχθέντας σφέας δουλοσύνης εὐδαιμονήσειν, νήσων τε ἁπασέων μεγίστην νεμομένους καὶ ἄρχοντας ἄλλων· μένουσι δέ σφι ἐν τῇ Ἰωνίῃ οὐκ ἔφη ἐνορᾶν ἐλευθερίην ἔτι ἐσομένην. αὕτη μὲν Βίαντος τοῦ Πριηνέος γνώμη ἐπὶ διεφθαρμένοισι Ἴωσι γενομένη, χρηστὴ δὲ καὶ πρὶν ἢ διαφθαρῆναι Ἰωνίην Θαλέω ἀνδρὸς Μιλησίου ἐγένετο, τὸ ἀνέκαθεν γένος ἐόντος Φοίνικος, ὃς ἐκέλευε ἓν βουλευτήριον Ἴωνας ἐκτῆσθαι, τὸ δὲ εἶναι ἐν Τέῳ (Τέων γὰρ μέσον εἶναι Ἰωνίης), τὰς δὲ ἄλλας πόλιας οἰκεομένας μηδὲν ἧσσον νομίζεσθαι, κατά περ εἰ δῆμοι εἶεν. Οὗτοι μὲν δή σφι γνώμας τοιάσδε ἀπεδέξαντο. 11 Cf. Panchenko (2016, 776). 12 As remarked, for example, by Rodolfo Mondolfo (in Zeller–Mondolfo 19502, 102). 13 On this point, see Pippidi (1983).

16 Thales the sophos

With all has been covered so far, I believe we have exhausted the survey of the teachings that have been attributed to Thales, rightly or wrongly.1 We have also reviewed what is reported about his public life, and seen that, when we discard what could hardly have happened, there is hardly anything left at all. Much the same can be said on the topic of the individual maxims attributed to him. As we saw in Section 3.4, Diogenes Laertius has a lot to say about Thales’ designation as the frst of the Seven Sages, and the story concerning the tripod, or the phialē or the potērion, destined for the wisest human being of the time (and cultural area). Arguments were there put forward to suggest that there may well be some substance behind these stories. In this context, a series of questions and answers attributed to Thales by Plutarch (in the Convivium Septem Sapientium) is of some interest ‘What is the oldest thing?’ ‘God,’ said Thales, ‘for God is something that has no beginning.’ ‘What is greatest?’ ‘Space; for while the universe contains within it all else, this contains the universe.’ ‘What is most beautiful?’ ‘The Universe; for everything that is ordered as it should be is a part of it.’ ‘What is wisest?’ ‘Time; for it has discovered some things already, and shall discover all the rest.’ ‘What is most common?’ ‘Hope; for those who have nothing else have that ever with them.’ ‘What is most helpful?’ ‘Virtue; for it makes everything else helpful by putting it to a good use.’ ‘What is most harmful?’ ‘Vice; for it harms the greatest number of things by its presence.’ ‘What is strongest?’ ‘Necessity; for that alone is insuperable.’ ‘What is easiest?’ ‘To follow Nature’s course; because people often weary of pleasures.’2

DOI: 10.4324/9781003138723-20

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Although not every answer has the archaic favour we would expect, the question-and-answer form does. People did not consult the sophoi discussed in Section 2.2 above for complex theories, but for glimpses of some insight through thought-provoking answers. This is not to say that Thales is being accurately reported here; but the question-and-answer format is not incompatible with his period, a period in which no sustained doctrinal apparatuses were in circulation. We cannot even point to the absence of the Olympian deities in the answers in hopes of learning something about Thales, because we have no idea of what Plutarch’s sources were like, how creative Plutarch was being, or what his criteria were for attributing just these questions and answers to Thales. In these conditions, we can certainly presume that a certain circulation of maxims took place and knew some success, but no individual maxim can be ascribed to this or that sophos with some confdence. On all that we simply have to plead ignorance.

Notes 1 Some new documents, not even recorded in Wöhrle (2009), were found in the Herculaneum papyri and other papyri (a good survey is Vassallo 2015, 280–293). But these are very marginal and do not need special treatment here. 2 Plut. Convivium 9, 153CD (=Th121 W). There are also traces in Diogenes Laertius 1.35–37 (=11A1 DK = Th237 = 5P16 LM), and in the Anthologia Palatina (9.366 = Th89 W).

Part V

Final remarks

Our exploration of Thales has involved some obstacles, but has also uncovered some traces of his work underneath the accumulation of obscuring material, traces which allow us to make helpful, if not enlightening, conjectures about him, even where conjecture is all that is possible. This process has required decisions about how trustworthy our sources are: it is interesting to note that, while some sources distort through exaggeration, others have not appreciated what they were passing on. The authors who reported the measurement of the pyramids’ height, including a reference to the stick’s shadow, for example, clearly had no idea about how one might use the shadow to make the measurement, let alone the value of the attempts to measure what could not be measured directly. At times we see a Thales who advances fearlessly towards goals unimaginable to others – his approach is often unexpected and indirect, but leads him to impressive achievements (such as the method for measuring pyramids) even without the advantage of the four operations. At other times, we see a Thales who dealt with much less tractable questions, for example the attempt to explain the Magnesian stone, or the fooding of the Nile. Here too he gives the impression of having worked with a method and with discipline, focused on natural causes and avoiding recourse to the gods or other supernatural factors. His self-discipline is striking, as is his methodological rigour. But this is just one side of a much more complex story.

DOI: 10.4324/9781003138723-21

17 The ‘new’ fragments of Thales

17.1 Thales: a widely known character We know that Thales was, in his lifetime, a celebrity, and that his achievements were unique. We know he was publicly honoured in Mytilene and Athens; we have a defnite idea of the rumours about his public recognition as the most distinguished among the sophoi of his time; we know that some articulate account of his specialist knowledge gained currency outside Miletus (e.g. at Massalia) and contributed to his fame; we know that hardly another Presocratic who lived in the sixth or the frst decades of the ffth century (Anaximander, Anaximenes, Hecataeus, Pythagoras, Xenophanes, Heraclitus, and others), raised so widespread interests as he. Another thing we know is that Diogenes Laertius, who seems to have screened his information carefully, favouring what is most immediately intelligible and most intriguing (and leaving aside what was unnecessarily complicate), was able to select a rather impressive amount of news about Thales. Thanks to the abundance of information he resolved to select for this chapter of book one, we can at least fgure how vast the documentation exploited by him must have been. In particular, we know that Thales aroused the interest of: A

Hecataeus, Euthymenes of Massalia, and Anaxagoras, at least with regard to his conjectures about the fooding of the Nile (Section 10.2); B Anaximander, Euctemon and Eudoxus, at least as to the time interval between the autumn equinox and the dawn setting of the Pleiades (Section 6.1); C Anaximenes, who worked on the other kind of eclipse, the lunar one, and is known for a theory about earthquakes that resembles that of Thales (Section 9.5); D Heraclitus, possibly with regard to the transformation of bodies into water;1 E Mandrolytus of Priene because of the angular width of sun and moon (Section 8.1);

DOI: 10.4324/9781003138723-22

170  Final remarks F Cleostratus of Tenedos, Matricetas of Methymna, and Phaenus of Athens (Section 3.5), because of their research on the sunset dates of some (or several?) constellations; G Xenophanes, who in B18 DK spoke about research "in the manner of Thales” (compare his ἐφευρίσκουσιν with the word repertorem in the passage from Apuleius); H Alcmaeon, who is likely to have been the very first western (non-Ionian) investigator to read (thanks to Xenophanes?) at least part of what was authored by the Milesians, and was able to produce a creative sequel to their investigations. J Hippo, whose teachings are ostensibly near those of Thales. We also know: K that Democritus (i) took up Thales’ ideas about earthquakes (Section 9.5), (ii) attacked Anaxagoras, arguing (59A5 DK) that “the [sc. his] doxai on the sun and the moon are not his but ancient (archaiai)”: Lebedev (1990, 81) rightly commented: “i.e. from the Milesians;” L that, according to Diogenes Laertius, Pherecydes of Syros (2.46) and Xenophanes (1.23 and 9.18) were also interested in him, as well as Heraclitus (1.23) and Phocus of Samos (1.23), Democritus (1.22, 23), and Choerilus of Samos (1.24). This list of course continues – still with reference to the fifth century BC – with Herodotus (passim), Aristophanes (Section 14.2), and Hippias (Section 1.3.1). Each of these sophoi wrote something related to Thales’ teachings, and we have the privilege of being, often indirectly, acquainted on all these written references. For this reason it is easy to understand Aristotle when writing that τοῦτον γὰρ ἀρχαιότατον παρειλήφαμεν τὸν λόγον, ὅν φασιν εἰπεῖν Θαλῆν τὸν Μιλήσιον (De caelo 2.13, 294a28–30 = Th30 W), or that Θαλῆς ἐξ ὧν ἀπομνημονεύουσι (De anima I 2, 405a19–20 = Th31 W), or Apuleius when remarking: id a se recens inventus Thales memoratur edocuisse (Florida 18.33 = Th178 W). With so many direct and indirect references to Thales’ teachings, it cannot come as a surprise if Aristotle and others mention what has been reported about him. As a consequence, we’re entitled to presume that many learned people mentioned Thales in their writings and reported a lot about him well before Plato. Otherwise, how could they access such detailed information?

17.2  Eduard Zeller on possible fragments Other sources have emerged that offer statements explicitly ascribed to Thales. These statements are introduced with words like phēsin, inquit, and ut Thales ait. Usually, when a doxa is introduced with expressions like this,

The ‘new’ fragments of Thales  171 it is treated as a quotation, i.e. a fragment (albeit with the obvious reservation that the report may be unreliable). But in the case of Thales, there is a long-established custom that we should never talk about ‘fragments’, as if the possibility that quotations from him have survived is to be excluded from the outset. This is a point regularly left aside by the scholarly community since the nineteenth century, with just one exception known to me: Eduard Zeller. In the first editions of his great history of philosophy (1844) the issue is not treated, but in the fifth edition (1882, and now in Zeller– Mondolfo 1950, 110 ff.) we find a long note dedicated to the reasons why claims attributed to Thales are of very doubtful authenticity. This footnote ends with a mere list where, without further analysis, Zeller mentions “the citations in Seneca, Nat. Quaest., III, 13, 1 and 14, 1; IV, 2, 22; VI, 6, l; Plac., 1, 3; IV, 1; Diodor., I, 38; Schol. in Apoll. Rhod. IV, 269”. So at least he made some preliminary steps for us to consider whether we have fragments of Thales. Unfortunately, his all-too brief analysis had no sequel. After him, as far as I have been able to ascertain, no one else has felt the need to pay attention to the question. But perhaps further analysis can take these few lines of his to more positive conclusions. Let us look, to begin with, to the texts selected by Zeller in the 1882 edition of his magnum opus: 01 Seneca, Nat. Quaest. 3.13.1 (=Th99 W): ut Thales ait, ‘ valentissimum elementum est’; 02 Seneca, Nat. Quaest 3.14 (=Th99 W): Quae sequitur Thaletis inepta sententia est. Ait enim terrarum orbem aqua sustineri et vehi more navigii, mobilitateque fluctuare tunc cum dicitur tremere; ‘Non est ergo mirum si abundat humore ad flumina profundenda, cum in humore sit totus’; 03 Seneca, Nat. Quaest. 4.22.2 (=Th100 W): Si Thaleti credis (etc.); 04 Seneca, Nat. Quaest 6.6.1–2 (=Th101 W): Thales Milesius totam terram subiecto iudicat humor portari et innare, sive illud oceanum vocas, seu magnum mare, sive alterius naturae simplicem adhuc aquam et umidum elementum. ‘Hac’, inquit, ‘unda sustinetur orbis velut aliquod grande navigium et grave his aquis quas premit’; 05 Stobaeus Anthol. 1.10.12 (=Th343 W): ἐξ ὕδατος γάρ φησι πάντα εἶναι καὶ εἰς ὕδωρ πάντα ἀναλύεσθαι (“Thales of Miletus declared that water is the principle of things-that-are, for he says that all things are from water and all things are dissolved into water”); 06 Diodorus, Bibl. Hist. 1.38.1–2 (=Th82 W): Θαλῆς μὲν οὖν, εἷς τῶν ἑπτὰ σοφῶν ὀνομαζόμενος, φησὶ τοὺς ἐτησίας ἀντιπνέοντας (etc.) (“Thales, who is named as one of the Seven Sages, says that when the Etesian winds blow against the mouths of the river”, i.e. the Nile); 07 Anon. Schol. Argonautica Apollonii Rhodii 1.496–8 (=Th570 W): ὁ δὲ Θαλῆς ἀρχὴν ὑπεστήσατο πάντων ὕδωρ, λαβὼν παρὰ τοῦ ποιητοῦ λέγοντος (etc.). (“Thales postulated water as the principle of all things, taking the idea from the poet [Homer] who said ‘but may you all become water and earth’”: Iliad 7.99).

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Clearly, the value and interest of the statements reported by Zeller vary widely. Statements (03), (06) and (07) could refer to Thales’ ipsissima verba or to a doxa repeated many times, and the latter possibility is more probable than the former. Quite different are statements (02) and (04), which do not simply identify an opinion, but the words used to give voice to this opinion. Here, indeed, we are presented with opinions so striking and unexpected that they deserve the most careful consideration (all the more since they have no precedent and no subsequent history in other thinkers); moreover, Seneca acknowledges that these tenets encompass something he does not understand: no better evidence could be supplied that Thales in fact claimed what is reported. Sentence (04) goes even further. It shows us someone who is still struggling for the words – or images, and associations of ideas – capable of communicating his insights. Therefore, it becomes very diffcult not to assume we are in the presence of a fragment, even if we do not know from where it might have been taken. (Anyway, DK often does identify ‘fragments’ that come from unidentifed works.) There are in fact no good grounds for denying that (04) is a fragment. The case of (01) is slightly different because, at least at frst sight, it will put one in mind of the old theory of the primacy of water. But, even if the word elementum could not go back to Thales, it is possible that that valentissimum elementum est refects the way in which Thales himself emphasized the important role of terrestrial waters (and so, by extension, of water in general) in promoting the generation of plants and other living beings. If this is right, we would not be in the presence of another repetition of the view that was later to be repeated so often, but of the original thought which gave rise to Aristotle’s misunderstanding. Therefore, it may not, but could, be a fragment. Similarly, the frst sentence in (05), “everything comes from water”, could well be a lazily repeated doxa; however, in the second sentence the focus is on the dissolution of things into water. This statement has nothing cosmological about it: it is exclusively concerned with the cycle of life, and in particular with what happens when things die. Now Servius and Simplicius attest that, according to Thales, if you leave things that have died (e.g. leaves, corpses) on the ground, they liquify and rot, and before too long dissolve into water. This idea, that organic remains dissolve into water is not one with wide circulation, and this strongly suggests that an original insight has been preserved. Therefore, in Zeller’s suggestions there is some substance. Some of the passages he listed do deserve attention since behind them there could be something due directly to Thales. If so, his footnote lifts the veil on something that still has to be investigated. For, if this happens at least in texts (2) and (4), how could we exclude a priori the possibility that some further ‘fragments’ surface? Besides, if so many learned people had access to rather

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precise information on individual teachings of Thales, a detailed written presentation of many (or all) of his teachings must have been available to many among them and, from time to time, they could well have quoted individual statements from such a proto-document. If, on the contrary, Thales had done as little as some interpreters (e.g. Graham 2006; Bernabé 2019) suggest, how does it happen that, already in the sixth and then in the ffth century, so many interesting characters made explicit references to his teachings for the most different reasons, and we still know something about all that?

17.3 Documents without the idea of a document, and books without the idea of a book Before going in search of possible fragments, we should perhaps open a parenthesis on what it might mean to produce a book in Thales’ time. As I pointed out in Section 2.1.4, the very idea of a document had to be envisaged, taken seriously and carefully developed. Also the process that led to the production of the very frst books necessarily passed through many intermediate stages, with many tentative modalities that were quickly replaced by others. As a consequence, the book by Anaximander probably was a turning-point, more or less as Gutenberg’s Bible was. From these preliminary remarks a signifcant consequence follows. We may confdently presume that Thales wrote something about solstices and equinoxes, and perhaps on other topics, and that what he wrote might later have been thought of as ‘books’. But what did Thales do? He is likely to have dictated texts whose concern was a wider range of teachings; these texts were probably collected and, despite their understandable limits, had some circulation, while their fnal form was in the hands of copyists (not just Thales himself). To bear in mind such dynamics helps to understand how it was possible for people to get good information about his discoveries and conjectures: that is, through writings that were becoming prose books and sometimes had a considerable circulation, if any because they lacked precedents. Now, if something like this is right, then it is true that we cannot pretend to have access to faithful quotations from a book by Thales. Nevertheless, and despite the reports in Latin, at least a couple of passages by Seneca do suggest something like quotation of Thales. The absence of direct evidence for this proves very little, because a concern for archiving documents was not a characteristic of the age: relevant forms of archive had yet to be imagined, devised, and put in practice; their evolution would take a long time. There is an analogy here with the transcription of letters dictated by illiterate persons to their intermediaries: people found it normal to write words different from those dictated to them in order to produce a ‘normalized’ text. Besides, one can easily imagine

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that the rapid progress towards better aesthetic standards in writing at the time of Thales (leading, in later times, to those inscriptions with beautifully carved characters arranged stoichēdon, in a checkerboard pattern) meant that older texts which were harder to read, or simply judged ugly, were transcribed more than once, and modifed here and there, rather than properly preserved. So when Thales and his contemporaries dictated to grapheis, the result might have been texts subject to editing and re-editing, with obsolete words replaced by others deemed to be more appropriate. But does this mean that the original text was not recognizable? Not necessarily. It is just that we should expect ipsissima verba. A comparable situation exists with certain Heraclitean sentences that are known on four or fve versions. Faced with them, some editors (notably Pórtulas-Grau 2011) judged it advisable to preserve the range of variations without pretending to identify the supposedly original wording. This opens up a promising path: we can hope to fnd, not the ipsissima verba of Thales, but something close to what Thales actually said (i.e. dictated).

17.4 An Urtext of Thales? From the above it follows that it is not impossible to identify something that could be considered a fragment of Thales, at least if we are prepared to accept a number of specifc qualifcations. Besides, we already found in Zeller’s selection at least two texts which it is hard to deny are fragments. But fragments of what? An Urtext must at least have existed, a text from which dozens of learned writers quickly began to borrow different elements, depending on the interest and curiosity of each: one the time interval between the autumn equinox and the dawn setting of the Pleiades, another the dynamics of earthquakes, the foods of the Nile, or the exact (fractional) angular width of sun and moon. Now, who may have authored this Urtext? Someone other than Thales? This is quite unlikely since no disciple known to us was in command of the whole range of Thales’ teaching. A remark by Augustine in De civitate Dei (8.2 = Th311 W) deals precisely with Thales as author. Augustine writes: Iste autem Thales, ut successores etiam propagaret, rerum naturam scrutatus suasque disputationes litteris mandans eminuit maximeque admirabilis extitit, quod astrologiae numeris comprehensis defectus solis et lunae etiam praedicere potuit.2 Clearly Augustine knew little about Thales, but he knew some details, or at least he assumed he did. He mentions (1) Thales’ care in producing written accounts of his discoveries and theories, (2) some successors who disseminated his teachings, and (3) calculations concerning the celestial bodies. It

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would not have occurred to Augustine to write this if, in the course of his wide reading, he had not encountered some detailed information. So what did he know about Thales? Augustine mentions Thales only occasionally and was certainly not interested in him as a connoisseur of the Greek philosophical tradition (as Simplicius, for example, was). So we should assume that he knew something specifc that we do not. It follows that his testimony is quite signifcant, even if it is hard to see what lies behind it. On the other hand, it would seem useless to dwell on the titles handed down, since titles themselves may well have been the fruit of zealous people commanding a copy of selected portions of the Urtext. However there are two testimonies, whose existence was noticed, as always, by Georg Wöhrle in 2009, that are of some interest here. Th184 (by Galen) and Th191 (by Alexander of Aphrodisias) show, to begin with, a patent connection. Galen writes: We are not able to demonstrate on the basis of a treatise by Thales that he declared that water was the only element, even if this is what everyone believes.3 Alexander, in commenting on Metaph. 984a2–3 (Aristotle’s declaration identifed above with the number 10), writes: The phrase “people say that he expressed himself in this way” is appropriate; for no treatise by him is cited on the basis of which one could be certain that this was said by him in this way.4 These two extremely erudite ancient authors say exactly what led Eduard Zeller, 2,000 years later, to rule out of consideration the possibility that we have any real fragments of Thales. They argue that, so long as there is no known work by Thales to which any statement can be ascribed, there will be doubt over its authenticity. However, it is very likely that titles begun to be appended to these ancient texts only in the course of subsequent decades; this weakens their argument. In conclusion, it is not impossible to single out statements which are like fragments. If so, it is time to undertake the identifcation of passages where what Thales may have dictated seems to surface. All that with the proviso that it would be unrealistic to look for his ipsissima verba.

17.5 Some fragments incertae sedis suitable to be ascribed to Thales It should be clear that the dozen (or so) putative fragments which follow are the fruit of a tentative selection, preliminary to what I hope will be a more thorough examination of the whole matter on the part of the wider community of researchers.

176  Final remarks This is my list (according to Wöhrle’s numeration): Fr. 1 – Aristotle, De caelo 2.13, 294a28–33 (=Th30 W) Fr. 2 – Aristotle, Metaphysica 1.983b20–22 (=Th29 W) Fr. 3 – Diodorus Siculus, Bibliotheca historica 1.38.1 (=Th82 W) Fr. 4 – POxy 3710, col. II, r. 36–43 (=Th91 W) Fr. 5 – Hero, Definitiones 138.11 (=Th93 W) Fr. 6 – Theon, De utilitate mathematicae 198.14, 16–18 (=Th167 W) Fr. 7 – Seneca, Naturales quaestiones 3.13.1 (=Th98 W) Fr. 8 – Seneca, Naturales quaestiones 3.14.1 (=Th99 W) Fr. 9 – Seneca, Naturales quaestiones 3.22.2 (=Th100 W) Fr. 10 – Seneca, Naturales quaestiones 6.6.1–2 (=Th101 W) Fr. 11 – Pseudo-Plutarch, Placita 890F1–5 (=Th158 W) Fr. 12 – Apuleius, Florida 18.34 (=Th 178 W) Fr. 13 – Servius, Commentaria in Vergilii Aeneida 11.186 (=Th318 W) Fr. 14 – Stobaeus Anthol. I 10.12 (=Th343 W) Fr. 1 – Aristotle, De caelo 2.13, 294a28–33 οἱ δ’ ἐφ’ ὕδατος κεῖσθαι [sc. τὴν γῆν]. τοῦτον γὰρ ἀρχαιότατον παρειλήφαμεν τὸν λόγον, ὅν φασιν εἰπεῖν Θαλῆν τὸν Μιλήσιον, ὡς διὰ τὸ πλωτὴν εἶναι μένουσαν ὥσπερ ξύλον ἤ τι τοιοῦτον ἕτερον (καὶ γὰρ τούτων ἐπ’ ἀέρος μὲν οὐθὲν πέφυκε μένειν, ἀλλ’ ἐφ’ ὕδατος), ὥσπερ οὐ τὸν αὐτὸν λόγον ὄντα περὶ τῆς γῆς καὶ τοῦ ὕδατος τοῦ ὀχοῦντος τὴν γῆν. Others say that it [the earth] rests upon water. This, indeed, is the earliest account that we have received, and they say that Thales of Miletus stated it: that is at rest because it floats like wood or something else of that sort (for it is the nature of such things that they rest not upon air but upon water), as if the same account that holds for the earth did not hold for the water that carries the earth! It is very likely that the mention of water was added by Aristotle because of what he found hopelessly obscure. The fact that the text says φάσιν εἰπεῖν (instead of φησὶν or ἔφην) certainly invites prudence, but does not affect the mention of ὥσπερ ξύλον. The crucial point is that ὥσπερ ξύλον is unexpected, as if Aristotle was openly acknowledging that he read that Thales compared earth and wood. He clearly admits he cannot understand it, and therefore rejects the comparison. My tentative conclusion is that we have traces of the words chosen by Thales. See also pp. 113–115 above. Fr. 2 – Aristotle, Metaph. 1.983b20–22 τὸ μέντοι πλῆθος καὶ τὸ εἶδος τῆς τοιαύτης ἀρχῆς οὐ τὸ αὐτὸ πάντες λέγουσιν, ἀλλὰ Θαλῆς μὲν ὁ τῆς τοιαύτης ἀρχηγὸς φιλοσοφίας ὕδωρ φησὶν εἶναι (διὸ καὶ

The ‘new’ fragments of Thales  177 τὴν γῆν ἐφ’ ὕδατος ἀπεφήνατο εἶναι), λαβὼν ἴσως τὴν ὑπόληψιν ταύτην ἐκ τοῦ πάντων ὁρᾶν τὴν τροφὴν ὑγρὰν οὖσαν καὶ αὐτὸ τὸ θερμὸν ἐκ τούτου γιγνόμενον καὶ τούτῳ ζῶν (τὸ δ’ ἐξ οὗ γίγνεται, τοῦτ’ ἐστὶν ἀρχὴ πάντων)—διά τε δὴ τοῦτο τὴν ὑπόληψιν λαβὼν ταύτην καὶ διὰ τὸ πάντων τὰ σπέρματα τὴν φύσιν ὑγρὰν ἔχειν, τὸ δ’ ὕδωρ ἀρχὴν τῆς φύσεως εἶναι τοῖς ὑγροῖς.

Yet they do not all agree as to the number and the nature of these principles. Thales, the founder of this school of philosophy, says the principle is water (for which reason he declared that the earth rests on water). Perhaps he had derived this assumption from seeing that what nourishes all things is moist and even what is warm comes from this [i.e. water] and lives because of it (and what things come about from is the principle of all things) ̶ it is for this reason, then, that he had this idea, and also from the fact that the seed of all things has a moist nature; and for things that are moist, water is the principle of their nature.

The relevant statement is that in the parentheses: Θαλῆς… ὕδωρ φησὶν εἶναι [scil. the archē] (διὸ καὶ τὴν γῆν ἐφ’ ὕδατος ἀπεφήνατο εἶναι). Once more, Aristotle is faced with a statement which he says was authored by Thales, but which is obscure, if not meaningless, to him. This time too, the comparison can only have come from some complex and sustained claim, with arguments in support of it, made by Thales himself. See also pp. 113–115 above. Fr. 3 – Diodorus Siculus, Bibliotheca Historica 1.38.1 Θαλῆς μὲν οὖν, εἷς τῶν ἑπτὰ σοφῶν ὀνομαζόμενος, φησὶ τοὺς ἐτησίας ἀντιπνέοντας ταῖς ἐκβολαῖς τοῦ ποταμοῦ κωλύειν εἰς θάλατταν προχεῖσθαι τὸ ῥεῦμα, καὶ διὰ τοῦτ’ αὐτὸν πληρούμενον ἐπικλύζειν ταπεινὴν οὖσαν καὶ πεδιάδα τὴν Αἴγυπτον. Therefore Thales, known as one of the seven wise men, says that the ­Etesians, blowing against, prevent the river from making the c­ urrent flow into the sea, and for this reason, being swollen floods the territories adjacent to Egypt. ‘Thales… says’ or, rather, wrote. What he says/wrote is a unique conjecture about the supposed cause of the annual cycle of the Nile. The person who made this connection must have been familiar with Etesian winds, as well as having an idea of the Nile’s floods, so probably lived somewhere along the western coast of Asia Minor. Who could that be? This tenet was known, and held in high regard, by Euthymenes of Massalia, probably less than a century after the death of Thales (see Chapter 10 above), while other intellectuals of approximately the same period looked for a more plausible account of the causes of the Nile’s flooding, as Herodotus and others report.

178  Final remarks Fr. 4 – POxy 3710, col. II, r. 36–43 ὅτι ἐν νουμηνίαι αἰ ἐκλείψεις δηλο[ι] Ἀρίσταρχος ὁ Σάμ[ι]ος γράφων ἔφη τε ὁ μὲν Θάλης ὅτι ἐκλείπειν τὸν ἥλ[ι]ον σελήνης ἐπίπροσθεν αὐτῷ γενομένης, σημειουμέ[νης [gap of several letters among which, it is assumed, τῆι κρύψει] τῆς ἡμέρας ἐν ῇ ποιεῖται τὴν ἔκλειψιν, ἣ[ν] οἰ μὲν τριακάδα καλούσιν, ο[ἰ] δὲ νουμηνίαν. That eclipses during the noumēniai is illustrated by Aristarchus of Samos, who writes: “Thales said that the sun is eclipsed when the moon  comes to be located in front of it, so that the day when the eclipse occurs is marked by . Some call that day triakas (=the thirtieth day) and others neomēnia (=new moon).”‘Thales said’, i.e. wrote somewhere, and what he wrote was known  (and judged meaningful) by Aristarchus, the astronomer. The explicit statement of what Thales said is notable, and sets out a definite idea of when and why it happens that the sun eclipses. See pp. 87–88 above. Fr. 5–6 – Hero, Definitiones 138.11 Theon, De utilitate mathematicae 198.14, 16–18 Εὔδημος ἱστορεῖ ἐν ταῖς Ἀστρολογίαις, ὅτι… Θαλῆς δὲ… τὴν κατὰ τὰς τροπὰς αὐτοῦ περίοδον, ὡς οὐκ ἴση ἀεὶ συμβαίνει. In his work Astronomy Eudemus reports that… Thales [was the first to discover] the eclipse of the sun and that its cycle between the solstices is not always equal in time.

Two different compilations report the same unit of text: according to Thales, the cycle of the solstices suffers from some irregularity. But in fact the solstices occur with marked regularity: so, at least for the ancient Greeks, this claim is far from being true, enlightening or even interesting. Besides, neither Hero nor Theon offer the least additional detail, much as if they were aware that what they were reporting was a curious but obscure remark, interesting only because it was associated to two persons of renown, Eudemus and Thales. This suggests that Eudemus supposed that it really was a claim going back to Thales. Moreover, Thales and nobody else is known for having noted at least one other celestial irregularity, namely the number of nights when there is no moon (i.e. during the new moon). For these reasons the οὐκ ἴση ἀεὶ συμβαίνει sentence has some chance of echoing a statement by Thales. Fr. 7 – Seneca, Naturales quaestiones 3.13.1 Adiciam, ut Thales ait, ‘valentissimum elementum est’. Hoc fuisse primum putat, ex hoc surrexisse omnia.

The ‘new’ fragments of Thales  179 I will add, as Thales says, “it is the most powerful element.” He thinks it was the first and that all things have arisen from it. Ut Thales ait is an undisputable statement even if Seneca’s passage is probably influenced by Aristotelian simplifications. In fact, those who said that water is a very powerful thing (the notion of ‘element’ was evidently implemented by Seneca or its nearest source, but it will be agreed that it cannot in any way go back to Thales) do not ignore the existence of other not so powerful things. Likewise, the sentence ex hoc surrexisse omnia is not necessarily to be understood in the sense that the earth as well as the stars emerged from water. Other hypotheses are equally possible, e.g. that ‘omnia’ was originally intended in the sense of ‘all living beings’. If so, it is still possible to detect the ‘voice’ of Thales behind an Aristotelizing mantle. See also pp. 116 above. Fr. 8 – Seneca, Naurales quaestiones 3.14.1 Quae sequitur Thaletis inepta sententia est. Ait enim terrarum orbem aqua sustineri et vehi more navigii, mobilitateque fluctuare tunc cum dicitur tremere; “Non est ergo mirum si abundat humore ad flumina profundenda, cum in humore sit totus”. The following view of Thales is silly. He says that the world is held up by water and rides on it like a ship, and because of its mobility, when it is said to tremble it is actually moving with the waves. “Therefore it is not surprising if there is plenty of moisture to make rivers flow since the whole world is located in a fluid.” Reject this crude and outdated view. For Seneca, this statement is unreliable because it is incomprehensible. But he reports it anyway, either because he finds it curious or because it is due to the famous Thales. So it appeared to Seneca that Thales explicitly talked about waters that lie beneath the earth. According to Thales, it is not surprising that there is plenty of water to feed the rivers. Indeed, ‘everything’ is immersed in water. Seneca however, in the wake of Aristotle, understands this to mean that, according to Thales, the whole earth is immersed in water, and this understandably seems to him very unlikely. See p. 116 above. Fr. 9 – Seneca, Naturales quaestiones IV 22.2 Si Thaleti credis, etesiae descendenti Nilo resistant, et cursum eius acto contra ostia mari sustinent: ita reverberatus in se recurrit; nec crescit, sed exitu prohibitus resistit, et quaecumque mox potuit in se congestus erumpit. If you believe Thales, the Etesian winds hinder the Nile as it descends and hold back its current by driving the sea against its mouths. Beaten back in

180  Final remarks this way, it runs back on itself and does not actually increase, but since it is kept from flowing out, it stops and, piling up upon itself, it soon bursts forth wherever it can. Here we are faced with an articulated account of what supposedly happens to the Nile when the Etesian winds blow. Is it due to Seneca? It is much more likely that Seneca was here translating or summarizing some lines from Thales. See also pp. 130–133 above. Fr. 10 – Seneca, Naturales quaestiones 6.6.1–2 Thales Milesius totam terram subiecto iudicat humor portari et innare, sive illud oceanum vocas, seu magnum mare, sive alterius naturae simplicem adhuc aquam et umidum elementum. ‘Hac’, inquit, ‘unda sustinetur orbis velut aliquod grande navigium et grave his aquis quas premit’. … Illud argumenti loco ponit, aquas esse in causa quibus hic orbis agitetur, quod in omni maiore motu erumpunt fere novi fontes (sicut in navigiis quoque evenit ut si inclinata sunt et abierunt in latus, aquam sorbeant, quae nimio eorum pondere quae vehunt si inmodice depressa sunt, aut superfunditur aut cere dextra sinistraque solito magis surgit). Thales of Miletus judges that the whole earth is carried and floats upon moisture that lies underneath it, whether you call it the ocean, the great sea, or water of a different nature that is still uncompounded and simply the moist element. “On this water the earth is supported,” he says, “as a big heavy ship is supported by the water which it presses down upon.” … He offers this argument that water is the cause of the earth’s agitation: in every major earthquake new springs usually burst forth, as it also happens that ships take on water if they tilt and lean to one side, and if they are pressed down too much when they are carrying excessive weight, either the water overwhelms them or it rises on the right and left sides more than usual. In the omitted part, Seneca specifies among other things that Thales is not trying to explain where the earth is (‘above’ the water) but why the earth moves (non enim nunc de situ terrarum sed de moto agitur). ‘Sometimes’ because this reference to Thales is introduced in the context of a discussion on earthquakes (cf. the in omni maiore motu specification). Pondere is an emendatio (for onere), briefly discussed on p. 127 above. In this passage a complex thought emerges, which evidently does not belong to Seneca. However, the rather detailed account of water that, in the case of large cargo ships, sometimes reaches their deck, is such as to raise some doubts, since the notion of aliquod grande navigium seems plausible only as a formulation of Seneca’s. Perhaps an expansion of a genuine Thalesian comparison (see fr. 1 and fr. 8)? Orbis must be a modernisation for some other concept more likely to have been used by Thales. His aquis quas premit is an expression that cannot relate to the ocean or primordial water. In fact, it rather evokes the water that

The ‘new’ fragments of Thales  181 is likely to be found not far beneath some areas of land (e.g. under the fields of a flat territory – perhaps 20–50 m). Only under these conditions can the land above it be compared to a large cargo ship that is sometimes shaken, and only under these conditions does it make sense to associate this water with springs. See also pp. 117–118 above. Fr. 11 – Ps.-Plutarch, Placita 890F1–5 Θάλης πρῶτος ἔφη ἐκλείπειν τὸν ἥλιον τῆς σελήνης αὐτὸν ὑπερχομένης κατὰ κάθετον, οὔσης φύσει γεώδους. βλέπεσθαι δὲ τοῦτο κατοπτρικῶς ὑποτιθεμένη τῶι δίσκωι. Thales was the first to say that an eclipse of the sun occurs when the moon, which by nature is made of earth, passes perpendicularly beneath it; this is seen in the manner of a mirror, when the disk comes to be placed under it. This is a complex text. Wöhrle marked the final section (from βλέπεσθαι onwards) with cruces desperationis, but the reference to the mirror may suggest the round object (with a handle) that was in use at the time. The idea may have been that, when the moon happens to find itself ‘under’ the sun, it operates like a mirror which, when placed in front of the face, prevents others from seeing that face. The credibility of this report is considerable. There is no one else among the Presocratics to whom one could plausibly ascribe it instead. See also pp. 88–89 above. Fr. 12 – Apuleius, Florida 18.34 ‘Satis’ inquit ‘mihi fuerit mercedes’ Thales sapiens ‘si id quod a me didicisti cum proferre ad quosdam ceperis, tibi non adscriveris, sed eius inventi me potius quam alium repertorem praedicaris.’ “It will be enough of a reward,” said Thales the Sage, “if, when you begin to make known to others what you have learned from me, you do not attribute it to yourself, but declare that I, and no one else, is responsible for the discovery.” This statement also deserves our attention, because it is introduced in the context of a rather detailed narrative, refers only to Thales, suits his personality (Thales has probably devoted his entire life to research). It is also very difficult to imagine that anyone could have invented this story. It would be interesting to know if the word εὐρετῆς (which is what repertor probably translates) already appeared in the text used by Apuleius and what sort of text it could have been. See also pp. 100–102 above.

182  Final remarks Fr. 13 – Servius, Commentaria in Vergilii Aeneida XI 186 Thales vero, qui confirmat omnia ex umore creari, dicit obruenda corpora, ut possint in umore resolvi. But Thales, who maintains that all things are created from moisture, claims that bodies must be buried in order to be able to be dissolved into moisture. The information on the treatment of corpses, which is partially denied by Simplicius (according to which “dead things dry up”), introduces an argument in favour of burial (“it is good to burn the corpses because in this way they dissolve in the wet”). That this detail appears in a commentary on the Aeneid is only a little surprising, since Servius speaks briefly about Thales on five other occasions as well. This suggests that he developed an actual, if marginal, interest in Thales and acquired information about him. Servius also addresses the notion of dissolution into moisture, which is in no way support for the water-archē thesis. On the other hand, the theme of wetness is part of a very particular teaching by Thales. Before Servius, only Aristotle and Seneca wrote about it, both admitting that they were unable to find his statement on water defensible (cf. frr. 1, 2, 8, 9). These circumstances encourage us to recognize in the passage of Servius another genuine trace of the teachings of Thales. See also pp. 120–122 above. Fr. 14 – Stobaeus Anthol. 1.10.12 ἐξ ὕδατος γάρ φησι πάντα εἶναι καὶ εἰς ὕδωρ πάντα ἀναλύεσθαι.

Thales of Miletus declared that water is the principle of things-thatare, for he says that all things are from water and all things are dissolved into water. When speaking of the archē, Aristotle evokes the origin as well as the dissolution of everything; however here Stobaeus is explicit in ascribing dissolution into water to Thales. This fact, and the similarity with fr. 13, encourage the assumption that the information provided by Stobaeus is a rather accurate report of Thales. See also pp. 121–122 above. Few additional words may not be out of place here. So far I concentrated on passages or words suitable to be ascribed to Thales, but it may be advisable to pay further attention to those passages where a reasonment, an argument, or the search for appropriate words surfaces. This is another area worth of attention I resolved to leave aside just because these are the very first steps in the direction of ‘fragments’.

The ‘new’ fragments of Thales  183

Notes 1 This idea seems to have survived in 28B36 DK (“for souls it is death to become water, for water it is death to become earth, but from the earth water is generated, etc.”) and possibly B27 (“for men who die, things they do not hope for and do not imagine”). This echo of Thales’ ideas has passed, so far as I know, completely unnoticed. 2 “While Thales, in order that he might have a series of successors, investigated the nature of things and presented his findings in writings which made him prominent. He was greatly admired for his ability to predict eclipses of the sun and moon through his understanding of astronomical calculation.” 3 Galen, In Hippocratis de natura hominis 69.4–6 [or 27, or 37.9–11] (=Th184 W = 5D2 LM): ὅτι Θαλῆς ἀπεφήνατο στοιχεῖον μόνον εἶναι τὸ ὕδωρ, ἐκ συγγράμματος αὐτοῦ δεικνύναι οὐκ ἔχομεν, ἀλλ’ ὅμως ἅπασι καὶ τοῦτο πεπίστευται. 4 Alex. Aphrod. In Metaph. 1.26.16–18 (=Th190 W = 5R32b LM): Εἰκότως τὸ λέγεται οὕτως ἀποφήνασθαι· οὐδὲν γὰρ προφέρεται αὐτοῦ σύγγραμμα, ἐξ οὗ τις τὸ βέβαιον ἕξει τοῦ ταῦτα λέγεσθαι τοῦτον τὸν τρόπον ὑπ’ αὐτοῦ.

18 Thales the measurer

18.1 “Sun, my friend, look: I found you out!” It is now time to offer some conclusions. We have seen that Thales’ interest in measuring is only one face of a multi-faceted sophos; however, there is no comparison between the importance of this and his approach to explaining other phenomena. To be sure, his thoughts on groundwater were valuable as an attempt to account for a large range of diverse phenomena, and they contain an important lesson in method too. Nonetheless, this lesson could hardly have seemed as innovative and distinctive as that of the fve inquiries discussed in the frst part of this book because, by comparison, those fve inquiries carried a much more spectacular message. No one had ever thought about how to establish the height of an Egyptian pyramid, no one had ever thought of establishing the exact dates of solstices and equinoxes, no one had ever thought of associating the lunar disk with the solar eclipse; a fortiori, no one had ever wondered about the angular amplitude of the sun, or thought of how one might measure it. What is more, no contemporary of Thales had the least idea of how to establish any of this. Moreover, four of these cases (plus the question of the variable length of the new moon: Appendix to Chapter 7) seem to require something that could also be perceived as superhuman, to say, as it were, to the sun: ‘Sun, my friend, I have found you out! Now I know when the next isēmeria will come; I also know the periods when you are safe from eclipse (about 340 of the days of each year); and I know other things. I know a lot about you and this is just the beginning.” Meanwhile, to the Egyptians he may have been in a position to say: “Your ancestors built the great pyramids, but you cannot say how high ‘your’ pyramids are. But I saw how to do it: all I would need would be your permission to measure certain shadows.” These achievements are all Thales’ own: no other Presocratics made any attempt to acquire comparable data. (And for all we know Thales may have also attempted other measurements too.)

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18.2 Thales looking for telling clues But how did Thales manage to acquire such data? A statement by Lorenzo Brandi helps us to make a frst step in this direction. He wrote that: Unlike Western astronomy, usually very meticulous in calculating the rising and setting of the stars and the motion of the planets (including the Moon and the Sun) on the celestial sphere, Chinese astronomy was much more prone to identifying transient phenomena such as eclipses, meteor showers, comets, the appearance of new stars (called host stars).1 Whatever the accuracy of what is asserted here about Chinese astronomy (I am not in a position to judge), the statement about meticulous calculation offers useful clarifcation: this is something that Thales did, and to some extent taught others to do. In fact, he succeeded in establishing a good number of investigations that could well be called ‘meticulous’. He did so by (a) identifying diffcult intellectual objectives, (b) fnding effective ways of circumventing the diffculties, (c) working out how to acquire relevant information, and (d) correctly recognizing what the data thus acquired allowed him to understand (that is, making pertinent inferences). Western astronomy later evolved along the path of the so-called exact sciences, among other things authoritatively confrming some of Thales’ acquisitions, so it is diffcult not to acknowledge him as the remote ancestor of the ‘exact sciences’, astronomy in particular (within the limits pointed out in Chapter 12). Thales went in search of apparently unobtainable numbers. His focus on numerical quantifcation (rather than verbal description), without however going the way of numerology (as the Pythagoreans did), is so signifcant that it is perhaps not wrong to assume that it must have been to some extent self-conscious. In fact, he could hardly mount an original, complex, and demanding investigation with the hope of establishing a fgure (a quantity) without being aware of the apparent disproportion between the investment made and the results he hoped to obtain. For this reason, his success in doing so deserves to be considered an important part of his legacy. So too is his practical methodology – the ability to imagine the practical means to achieve certain ends (using A to ascertain B). This is still a long way from the experimental method of a Torricelli,2 but it involves clearly identifed and well-reasoned procedures and mechanisms that transcended the intellectual possibilities imagined by the bards, poets and other wise men of his time. What is more, these procedures offered a method of inquiry that was impersonal, that did not depend on who the observer was: the credibility of his data partly relied on the fact that each could be attained by anyone else. Again, there are at least impressive analogies with modern scientifc method, analogies that are quite suitable to support the doubts raised by Nicola Galgano (see Section 18.4 below).

186 Final Remarks

18.3 Funding research We should also consider the cost of Thales’ research. As I have already had the opportunity to point out, he must have incurred signifcant expenses, for example for the teams of observers he would have required. But there was no culture of inquiry, no patron (like Alexander the Great supporting Aristotle), no state willing to incur enormous expense to explore the mysteries of cosmology or medicine, as today. So the costs of Thales’ research, whether it involved carefully counting days and buckets, or setting up elaborate physical structures, could only have been borne by Thales himself. Anaximander too must have incurred considerable expenses in developing his famous pinax; on the other hand, he certainly did not incur any expense for the work that led him to conclude that the sun completed its diurnal journey with a complementary path under the earth during the night, or to elaborate the notion of an Astronomical Unit, or to think about clouds on the model of wineskins, much less to invent the apeiron. Even Anaximenes did not have to incur expenses to theorize about the centrality of the air; nor did Xenophanes incur expenses to argue that clouds form on the high seas and then give rise to rains on the mainland.

18.4 Was Thales a lone researcher? Again, though: can we really be sure that Thales did everything plausibly ascribed to him by himself? Nicola Galgano has offered the following objection in a personal communication to me (I summarize it a bit): that there are no documents about the possible masters of Thales is a fact, but from this it does not follow that he had no masters. Indeed, it is impossible that he did not have any. What they taught him we cannot know, but we must not even think that he extracted everything from his own magic cylinder. There was a leap forward but, if we deny the existence of masters, we end up making Thales take a step longer than the leg. This is an extremely pertinent observation, since what is ascribed to Thales seems to stretch credibility. However, to begin with, although we have many reports of Thales’ fame during his lifetime, and he was frequently referred to in the later sixth and ffth centuries BC, we have no trace or hint of any teacher. Secondly, what we have discovered is a consistent set of related innovations. Which part of this could have been anticipated or prefgured by Thales’ hypothetical teachers? As long as this last question remains unanswered, there should be no temptation at all to assume that Thales had forebears or masters in precisely the kind of investigations he undertook so successfully.3

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Then there is the recurring suggestion that he owed a debt to Mesopotamian ‘scholars’. Schofeld (1997, 42) wrote, for example, that the prediction of an eclipse of the sun “was not an impossible thing for someone familiar with the cycles of eclipses and a passion for the predictions of Babylonian astronomers, something that an inhabitant of Miletus on the coast of Asia Minor could have acquired”. In fact, this is a mere leap of faith, without foundation. I have already discussed this in Section 7.3.1, but here it is appropriate to refect on the great difference between acquiring technologies and acquiring information. A certain way of painting, of sculpting, of building may well inspire artists from another country, just as the practice of leavening bread or using (or making) metallic coins in commercial exchange quickly became widespread. But information, the association of ideas, a doctrine, a belief that arises in one socio-cultural context has many more obstacles to circulation, especially where there is not a well-established literary culture. A traveller who arrived in Mesopotamia or Egypt might perhaps wonder whether there is anyone there dedicated to forecasting eclipses, or whether they possess ancient papyri containing important knowledge about the operations with numbers. But this is an extremely remote possibility: who could have formulated such questions, and on what basis? And how would he discover who was in a position to answer them? In addition to that, Robert Hahn thought he had determined that the frst Milesians, including Thales, learned much from the creators of certain memorable public works,4 in particular the three great monumental temples built in Ionia almost at the same time: the Artemision at Ephesus, the Heraion of Samos and the temple of Apollo Didymaios in Didyma (a locality within the sphere of infuence of the city of Miletus). These three great buildings were characterized, as we know, by their extreme regard for geometry, having a parallelepiped structure, triangular pediment, a large number of perfectly cylindrical columns, all perfectly vertical, perfectly aligned, and perfectly equidistant from each other, that were probably equipped with the classic 20 grooves, very precisely spaced. But what could the architects in charge of these great works have taught the early Milesians, or how could they have inspired them? Hahn rightly emphasized the expression kioni lithōi paraplēsion (“similar to the stone drum [sc. of a column]”) that a very well-informed source (Hippolytus of Rome, 12A11 DK) attributed to Anaximander as a description of the earth. If Anaximander could say this having seen the work on the Didymaion, then Thales might have observed it too. So the connection is there to be made. But the idea that this work inspired Anaximander’s theories (rather than just their expression) does not seem to me at all certain; and in any case, we are talking now about Thales. Is the idea, perhaps, that, if he had not observed the tympanum (which is an isosceles triangle) of the great temples, he would not have been inspired to think about the shadow formed by the great pyramids?

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Final Remarks

Moreover, those large public works were permanent and designed to arouse the admiration of the many; while the apparatuses that Thales erected in the course of his research, for example the one used to ascertain when day and night have the same duration, were absolutely unspectacular and temporary objects. His measurements did not give rise to architectural masterpieces, but just to numerical values, which risked being considered devoid of any interest at all. There is not so much in common after all between the knowledge exhibited by the architects and the very different sort of knowledge achieved by this sophos. For these and other reasons, I tend to think that we have no basis to assume that Thales acquired signifcant elements of his knowledge from his contemporaries. The possibility that he found his way on his own does not therefore have any real alternative.

Notes 1 www.eanweb.com/2012/astronomia-in-cina-una-storia-plurimillenaria/. 2 I refer to the experiments conducted around 1644 by Evangelista Torricelli with the mercury tube, experiments aimed at establishing whether the altitude affects the height of the mercury, proving by this means that even air has weight. 3 Cf. Section 2.4 above. 4 Hahn (2001). In the case of Samos, Herodotus (3.60) records three most spectacular public works: the construction of the great temple (the Artemision), the tunnel created by Eupalinus and the sturdy barrier protecting the port. This too must have been of an impressive size.

19 The research bug

19.1  Let’s not be Aristotle’s prisoners Let me now summarize what Thales achieved when acting as a measurer: (a) he was not satisfied with narrative explanations,1 but (b) searched for evidence pointing to causes2; (c) he submitted his most demanding investigations to methodological rigour, working only with what would be shown to be objectively relevant; (d) he devoted huge energy to working out procedures for gathering information; (e) he must have reflected on the significance of his quantitative results and looked for answers that could be numerically expressed; and (f) he dedicated his whole life to research. These are conjectures about his approach, but not unwarranted given the results. However, this is not what we glean from Aristotle, starting with the impressive misunderstanding which leads him to extracting the idea of water-as-archē from Thales’ reflections on something quite different (Chapter 9). Aristotle, who after all only dealt with Thales in a very cursory way, cannot in fact help us at all in understanding Thales’ project as such. In particular, this means that we lose the connection people have wanted to see between Thales and ‘philosophy’. (Thales of course could have had no inkling himself of the category.)

19.2  The invention of research If Thales is not the father of philosophy, at least on the basis of his supposed reflections about water-as-archē, there is, however, something to be said for thinking of him as a proto-scientist, given the way in which he conducted his research. Besides, the drive to understand is something that scientists and philosophers have in common, and Thales was surely an important spur for the rise of a tradition of inquiry – the topic of inquiry being always crucial across the centuries, whether it is the date of the tropai, or the syllogism, universal gravitation, transcendental analytics, cancer … All of this began with the Presocratics, and ultimately with Thales, son of Examyas, the Milesian. The research bug was first incubated in him, and then transmitted to Anaximander … until at last it became a global phenomenon.

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190 Final Remarks Thales did what neither Aesop with his fables (Section 2.2.3), nor Homer in singing of Polyphemus and the riddle of Outis (Section 2.2.4), nor anyone else had previously been able to do: to establish a methodology of discovery which abandoned narrative for chains of causal reasoning, and to make of it a social practice, one which, thankfully, survived the relative neglect of subsequent periods. It is this of which we fnd a clear trace in Xenophanes who, some 50 years after Thales’ death, was able to proclaim (in B18 DK): Certainly the gods did not make everything known to mortals from the beginning, but it is they who, in research, fnd, over time, something better. This is the same Xenophanes who probably spread knowledge of the work of the Milesians in Southern Italy, so we can expect that he will have refected on it. In fact, the famous second elegy (21B2 DK), challenging the fame of the Olympic champions,3 confrms our impression that what distinguished Thales in the eyes of Xenophanes was his work as a researcher (as a repertor, in the words of Apuleius). The seed of opposition between true and apparent knowledge (or, if you prefer, between understanding and the ungrounded illusion of having understood)4 had been planted; and it turned out to nourish the advance of knowledge in general. The growth of philosophy in time, alongside other specifc areas of expertise, owes much to this seed, a seed that Thales (and nobody else) planted. So we can say that Thales did contribute to the birth of philosophy, and of other scientifc disciplines, at least as their remote cause, preparing the ground and providing the model in his life dedicated entirely to research. And something more, if a coherent imagine of him begun to surface. This means a step not only beyond disarticulated doxography, but also beyond ascertaining and towards understanding.

Notes 1 A little more than a hundred years after Thales, there were those who managed to move from narrative accounts to the identifcation of causes in the case of the so-called sacred disease. That too was an important event. 2 I note that it is not just a matter of having the leisure to pause, observe, to formulate questions, and to weigh the possible answers. 3 Marco Beconi points out to me that Xenophanes hints at the excellence of ‘researchers’ (zētountes), among whom he places himself, against rhapsodes who just repeat Homer: 21B2 DK. I will add that at the end of 21B2 it is even suggested that it is researchers, not athletes, who bring wealth to the city. 4 It is therefore regrettable that Vesperini (2019, 70–74) was able to make Thales (and later Anaxagoras!) an ‘excellent’ expert on narrative causes alone. In his chapter on Thales, he took into consideration only the legends about Thales, so that he saw in the story of the tripod only clues that “that for the ancients the

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wisdom of Thales depended on Apollo” as god of Delphi; he claims that, in the Magnesian stone, Thales “saw a sign sent by Apollo”, and that “in the temple of Apollo Didymus Thales devoted himself to geometry using a ‘sacred way’ according to a spatial arrangement typical of archaic cities”. Vesperini judges that “it is impossible to predict on the basis of the observation of the stars whether or not next year will be propitious to the olive harvest”, and goes so far as to assume that Thales must have been copying Egyptian priests who predicted crops on the basis of observation of the stars. When he then tried to predict an eclipse of the sun, “he saw, thanks to Apollo, that there would be (one)”, that is, he guessed and was lucky! Vesperini just let the best of Thales escape.

Appendix to Chapter 7

Let us now return to the Oxyrhynchus papyrus POxy 3710 (above Section 7.1, text [3]). After the small portion of the papyrus in which Aristarchus reports somes alleged words of Thales, someone else goes on to mention Heraclitus as having noticed that the lunar phases have oscillations and, in particular, that the period of the so-called new moon (neomēnia) has a variable duration, which is subsequently compensated for. In fact, if the full moon is shortened or prolonged (because the reappearance of the crescent lunar horn seems to be delayed to another night) or take place a night earlier, this does not mean that the lunar month is also lengthened or shortened. These variations do not affect the regular duration of the lunar month, which is 29½ days (easily counted as 30). Let us now read the whole passage: Aristonicus says that then it was the neomēnia’ (= the new moon), and therefore of Apollo, since he (= Apollo) identifes himself with the sun. That eclipses during the noumēniai is illustrated by Aristarchus of Samos, who writes: “Thales said that the sun is eclipsed when the moon comes to be located in front of it, so that the day when the eclipse occurs is marked by . Some call that day triakas (= the thirtieth day) and others neomēnia (= new moon).” Heraclitus : “At the meeting of the months (the lunar horn) does not appear for three consecutive days1: the eve, the neomēnia, the next day. Sometimes it changes in fewer days, sometimes in more days”. Diodorus gave the following explanation: since in fact the moon is hidden when2 it approaches the sun at the end of the month, when it runs into the rays of the sun … disappeared again … the lunar horn when … for the frst time … (Col. II 33–55) … there is no apparition … very pure (?) … say … “The lunar horn, when it appears on the third day, becomes a full moon on the sixteenth, in 14 days. It loses its defect (= it remedies the accumulated delay) in 13 days”. In fact, if it is a full moon in 14 days, having made its frst appearance in the third with respect to the neomēnia; it is clear that

194

Appendix it did not show itself …, so that – since, appearing as soon as possible, on the day of the neomenia, it becomes a full moon on the 14th,: if it makes its appearance at the latest, i.e. on the third day, it can become a full moon on the 16th, in 14 days.3 (Col. III 1–19)

The details in col. III column are, as is evident, of little use as they can hardly convey the idea of compensation. Mouraviev gave solid reasons for describing this as “scholarly accumulation” (1992, 242), meaning that Aristarchus’ own contribution probably concerned only the section on Thales; Aristonicus (who reports the lines of Aristarchus) and, after him, Diodorus add to this to provide a fuller picture. So, different authors report one teaching attributed to Thales and a complementary one attributed to Heraclitus. The frst attribution, entirely explicit (Aristarchus would have written: ephēn ho men Thalēs, etc.), comes from an expert in astronomy, Aristarchus; so far everything seems to be in order. Four different teachings emerge: (a) the solar eclipse takes place when the moon moves in front (makes an hupodromē, as another source specifes) of the sun; (b) the day on which the eclipse takes place is identifed ; (c) this day is the thirtieth of the lunar month; and (d) the moon is ‘terrestrial’ (i.e. shares some basic features with the earth). In researching solar eclipses, Thales would probably have noticed that the period in which the moon does not appear at all, not even as a thin sickle or horn, does not always have the same length. Remember that Thales, in his work on the solsticses, concentrated his attention on the considerably long period during which the sun seems to remain stationary before reversing its path; so he may well have thought about how many nights the moon is invisible, and noticed a certain irregularity. (It is quite possible that he extended his ouk isē aei sumbainei clause to the irregular duration of the new moon too.) The theory of compensation is ascribed to Heraclitus. This is the explicit declaration of Aristonicus, usually accepted without hesitations by the students of Heraclitus. Thales spoke of occasional delays or accelerations that characterize the reappearance of the moon after the new moon, and Heraclitus would have noticed that these irregularities do not affect the length of the lunar month. That Heraclitus may have contributed to Thales’ research with his own investigation is surprising, however, because it does not appear that he had any skill in studying astronomical phenomena. Appreciating Thales’ work in astronomy (“he was the frst to study the stars”, Heraclitus could have stated: 22B38 DK) is not the same as being able to pursue similar research himself. On the rare occasions when he makes some astronomical claim, he is happy to echo the teachings of others.4 The competence necessary was not part of the interests and skills possessed by Heraclitus. And what is stated by the papyrus does not have the support of any independent evidence. On

Appendix  195 the contrary, many clues suggest that the investigation attributed to Heraclitus presupposes a kind of education which does not fit anything else that we know about him. Heraclitus devoted himself to proclaiming and thinking about the interconnection of phenomena and in criticizing those who, in his opinion, did not understand such things. His interests were, one might say, metacognitive.5 Unlike Thales, he did not research particular phenomena serially. He had a different concern: he believed that he had insight into some one fundamental thing (the interconnection or interdependence of everything), and dedicated himself to teaching that. He expressed his ‘truth’ with images, for example of the one, god, war, fire, the unity of opposites, water, logos, hidden harmony. And these images themselves all need to be taken together since each is an approximation, an attempt to convey the idea, but none captures his ‘truth’. So it is not unreasonable to suspect that Aristonicus has just erroneously ascribed to Heraclitus what might have been another achievement of Thales. Certainly, given the lack of more definite evidence, we cannot free Heraclitus from this incongruous document, nor affirm that Thales completed his observations on the new moon with comments on the compensation that preserves the regular duration of the lunar month. We have to admit our ignorance: we cannot understand why Heraclitus is mentioned here, and although it would be attractive to attribute this research to Thales instead, we simply cannot.

Notes 1 Or, rather, nights. 2 Only sometimes, of course. 3 POxy 53.3710, col. II–III, commentary on Odyssey 20.156 (=Th91 W = 5R17 LM; trans. Mouraviev, 1992). Note that at the end of the second column and at the beginning of the third, a considerable number of gaps and small groups of letters appear, which defy recontsruction. To provide the Greek text in these conditions would be of no use. 4 At least the phrase “the sun is new every day” (22B6 DK) gives the impression of taking up Xenophanes’ idea that the sun is formed every morning and is extinguished every evening (21A38, B31 and B38 DK). 5 On this point, see Rossetti (2018) (also Rossetti 2008).

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Concordances

Wehrli (2009) Diels-Kranz (61952) Th10 W

11A5 DK

Laks-Most (2016) 5P9 LM

Th11 W

11A6 DK

5P6 LM

Th12 W

11A4 DK

5P7 LM

Th13 W

11A16 DK

Th16 W Th19 W

11A9 DK

5P12 LM

Th28 W

11A10 DK

5P15 LM

Th29 W

11A12 DK

5D3, 5R32 LM

Th30 W

11A14 DK

5D7, 5R33a LM

Th31 W

11A22 DK

5D11a LM

Th22 W

5P14 LM

Th32 W Th52 W

11A3a DK

Th60 W Th71 W Th72 W Th75 W Th77 W Th78 W Th82 W Th85 W Th87 W Th89 W Th91 W Th93 W

5R17 LM

Concordances  203  Th94 W Th98 W Th99 W

11A15 DK

5D8 LM

Th106 W

11A18 DK

5R21 LM

Th107 W

11A21 DK

5R31b LM

Th100 W Th101 W Th105 W

Th112 W Th116 W

11A11 DK

Th119 W

11A21 DK

5R31c LM

Th147 W

11A11DK

5P4 LM

Th156 W

11A13c DK

5R23 LM

Th158 W

11A17a DK

5R18 LM

Th164 W

11A16 DK

5D9 LM

Th167 W

11a17 DK

Th178 W

11A19 DK

Th121 W Th136 W

Th163 W

5R13 LM

Th184 W

5D2 LM

Th190 W

5R32b LM

Th203 W

11A5 DK

5P10 LM

Th210 W Th225 W Th237 W

11A1 DK

(several units)

Th249 W

11A11 DK

(several units)

Th252 W Th265 W Th296 W

11A19 DK

Th303 W

11A11a DK

Th307 W Th311 W Th317 W Th318 W Th319 W Th320 W

11A13 DK

204  Concordances  Th321 W Th322 W Th343 W Th354 W Th355 W Th356 W

5D6b LM

Th357 W

11A17b DK

5R19 LM

Th380 W

11A11 DK

Th381 W

11A20 DK

5R30 LM

Th382 W

11A20 DK

5R28 LM

Th383 W

11A20 DK

5R26 LM

Th384 W

11A20 DK

5R29 LM

11B1 DK

5R10 LM

Th387 W Th399 W Th403 W Th409 W Th477 W Th487 W Th492 W

11A8 DK

Th495 W

11A2 DK

Th570 W Th578 W

11A3 DK

5R22 LM

Index locorum

Aelius Aristides Orationes 36.85 Alexander Aphrod. In Aristotelis Metaphysicam 1.26.16–18 Ammianus Marcell. Res gestae 17.7, 12 Anaxagoras Peri physeos [Anon.] Chronicon Paschale 214.15-22 [Anon.] Codex Laurentianum 56.1, 12 [Anon.] Ekloge Historion Parisina 2.263 [Anon.] Lexicon theta 17-18 [Anon.] Scholia vetera in Rempublicam 600a

[Euthymenes] 137 [Th190 W] 182

[12A28 DK] 128 [moon] 148 [Th477 W] 45 [Euthymenes] 136 [11A8 DK ≠ W] 45 [Th495 W] 83 [Th578 W] 74, 99, 107, 141, 150 [Anon.] Scholia in Arati Phaenomena 1.4.1 [Pytheas] 150 [Anon.] Scholia in Apollonii Argonutica 4.259 [Hecataeus] 136 [Anon.] Scholia in Arati Phaenomena 172, [Th495 W] 83 p. 369.24 [Anon.] Scholia in Euripidis Rhesum 518 [Cleostratus] 83 Anonymus Florentinus 4.107 [Euthymenes] 136 Anthologia Palatina 9.366 [Th89 W] 165 Apuleius Florida 18.30-31 [Th178 W] 74, 96, 100, 107, 145, 149 18.32-35 [Th178 W] 101, 107 18.35 [Th178 W] 145 Archimedes Arenarius 137.12-18 [Aristarchus] 108 Aristarchus (POxy 3710) [Th91 W] 77, 98, 176 Aristophanes Birds 995–1009 [Th18 W] 156 Clouds 371 [not Thales] 99 Aristoteles De anima 1.2, 405a19-20 [Th31 W] 141, 170 1.5, 411a8 [Th32 W] 34 De caelo 2.13, 294a13-16 [on earth] 126 2.13, 294a28-b4 [Th30 W] 126 Metaphysica 1.3, 983b1-3 [Th29 W] 125 1.3, 983b6-8 [not Thales] 124, 125 1.3, 983b18-27 [not Thales] 126 1.3, 983b20-24 [Th9 W] 13, 176 Meteorologica 2.7, 365b2-8 [Anaximenes et al.] 128 Politics 1.11, 1259°5–19 [Th28 W] 162 Athenaeus Deipnosophistae 13.609A [Hippias] 14 Augustine De civitate Dei 8.2 [Th311 W] 150 Callimachus Iambus 1.32-77 [Th52 W] 150

206  Index locorum Censorinus De die natali 4.7 [Anaximander] 128 Cicero Academica Priora sive Lucullus 118 [Th71 W] 44 de divinatione 1.112 [Th77 W] 98, 153 de finibus 5.1 ff. [Cic.] 16 de natura deorum 1.25 [Th72 W] 124 de re publica 1.25 [Th75 W] 98 Clemens (Alex.) Stromateis 1.14.65 [Th203 W] 98, 99 Cleomedes Caelestia 2.75 [Cleomedes] 106 Cleostratus 6B1 DK [Cleostratus] 83 Diodorus (Siculus) Bibliotheca 1.38.2 [Th82 W] 135 Diogenes Laertius Lives 1.22 [Th237 W] 44 1.23 [Th237 W] 74, 83, 98, 150 1.24 [Th237 W] 74, 83, 108, 140, 157 1.25 [Th237 W] 98, 124, 157, 163 1.26 [Hieronymus] 158 1.27 [Th237 W] 41, 44, 65, 74, 83 1.27-33 [Th237 W] 41 1.37-38 [Th 237 W] 44 1.119 [heliotropion] 69 2.2 [Anaximander] 44 9.34 [Anaxagoras] 98 Euripides Suppliants 399 [Eur.] 34 403 [Eur.] 34 Eusebius Praeparatio Evangelica 10.14 [Th265 W] 96 Galen In Hippocratis de natura hominis [Th184 W] 182 69.4–6 (via Hunain ibn Ishaq) [Th487 W] 72 Galen, ps. De historia philosophica 66.1.3 [Th399 W] 98 86.1 [Th403 W] 127 Heraclitus 22A38 [Heracl.] 195 22B6 DK [Heracl.] 195 22B31 DK [Heracl.] 195 22B38 DK [Th8 W] 194 22B53 DK [Heracl.] 40 22B56 DK [riddle] 27, 40 Th91 W [lunar month] 193–195 Heraclitus Hom. Allegoriae 22.3 [Th94 W] 128 Hero of Alexandria Definitiones 138.11 [Th93 W] 29, 74, 98–99, 176, 178 Herodotus 1.74 [Th10 W] 97 1.75 [Th11 W] 163 1.76 [Croesus] 163 1.168 [Theos] 163 1.169 [Croesus] 163 1.170 [Th12 W] 163 2.16 [logizesthai] 53 2.20 [Th13 W] 135 2.21 [Homer] 135 2.22 [Anaxagoras] 135 2.23 [Homer] 131, 150 3.60 [Samos] 187 4.42 [Necho] 136 Hesiod Theogony 337 ff. [Okeanos] 6

Index locorum  207 Works and Days 383-384 [Pleiades] 68 448 [cranes] 68 564-565 [Arctouros] 80 Hieronymus Sporaden hupomnemata 2, [Th60 W] 158 fr. 39 Wehrli Himerius Declamationes 28.4-8 [Th303 W] 44 Hipparchus In Arati et Eudoxi phaenomena [Pytheas] 150 I 4.1 Hippias 86B6 DK [Hippias] 6, 14 Hippolytus Refutatio 1.1 [Th210 W] 127 1.6 [Anaximander] 44, 128, 186 1.8.9 [Anaxagoras] 91 Homer Iliad 7.99 [Th570 W] 171 14.201 [Okeanos] 6 23.175 f. [sacrifices] 33 24.15-23, 50-54, 416 s. [torture] 32 Odyssey 15.403-404 [Syria] 69 20.156 [POxy 3710] 195 22.462-477 [torture] 32 Hyginus ps. De astronomia 2.2.3 [Th 136 W] 150 Iamblichus De communi mathematica [Th252 W] 157 scientia 21 De vita Pythagorica 2.12.9-10 [Th249 W] 44 Inscriptiones Graecae I2, 352 [accounts] 53 Isocrates Antidosis 269 [Hippias] 6 Johannes Lydus De mensibus 4.107 [Euthymenes] 136 Julian Panegyricus Eusebiae 16 [Th296 W] 108 Orpheus 1B2 DK [Okeanos] 6 Papyrus Eudoxi 81 [parapegma] 81 Papyrus Oxyrhinchi 53.3710 col. 2, r. 36-43 [Th91 W] 98, 176, 178, 193 col. 2, r. 41-42 [Th91 W] 77 col. 3, r.1-19 [Th91 W] 193–194 7.1011 [Th52 W] 150 Parmenides Peri physeos 28B14-15 [Parm.] 148 Philostratus Vita Apollonii 8.7.158 [Th225 W] 158 Plato Cratylus 402a-c [water] 6 Republic 10.600a [Th22 W] 74, 99, 107 Theaetetus 174a [Th19 W] 163 Pliny (the Elder) Naturalis Historia 2.30 [Cleostratus] 81 2.6 [Anaximander et al.] 45 2.53 [Th105 W] 96 18.68 [Democritus] 158 18.213 [Th106 W] 74, 83, 158 36.82 [Th107 W] 65 Plutarch De Iside et Osiride 34, 364C-D [Th116 W] 128 Quaestiones conviviales 8.8.4, 730D-F [Anaximander] 128 Convivium Septem Sapientium 2, 147A [Th119 W] 65 9, 153CD [Th121 W] 165 Vita Solonis 6-7 [Th112 W] 44 Plutarch, ps. Placita philosophorum 1.3, [Th147 W] 44, 127, 150 875D-F 2.12, 888C-D [Th156 W] 150 2.24, 890F [Th158 W] 98, 176, 191 3.3, 893D [Anaximander] 128

208  Index locorum 3.7, 895A [Anaximander] 128 3.15, 896B-C [Th163 W] 127 4.1, 897F [Th164 W] 135 5.19, 908D [Anaximander] 128 Proclus In Primum Euclidis Elementorum [Th380 W] 157 65, 3–11 157.10-13 [Th381 W] 156 250.20-251.2 [Th382 W] 154, 157 298 [Euclid] 154 299.1-5 [Th383 W] 157 347 [Euclid] 154 352.14–18 [Th384 W] 153, 157 Ptolemy Almagestum 3.4 [days in a trimester] 75 Seneca Naturales Quaestiones 2.17-18 [Anaximander] 126 3.13.1-14.2 [Th99 W] 115, 126 4.2.22 [Th100 W] 136 6.6.1-2 [Th101 W] 116, 118 Servius Commentarii in Vergilii Aeneida [Th 317 W] 127 3.241 4.363 [Th320 W] 127 11.186 [Th318 W] 127, 176, 181 Commentarii in Vergilii Bucolica 6.31 [Th319 W] 127 Commentarii in Vergilii Georgica 4.379 [Th321 W] 127 4.381 [Th322 W] 127 Sextus Empiricus Adversus Mathematicos [Sextus] 14 7.46-261 Sidonius Apoll. Carmina 15.79-80 [Th387] 96 Simeon Logothetes Chronikon 42.12.52-53 [Th492 W] 45 Simplicius In Aristotelis Physicorum [Th409 W] 35, 127 9.23.21-33 Stobaeus Anthologium 1.10.12 [Th343 W] 127, 150, 176, 182 1.24.1a [Th354 W] 148, 150 1.25.3b [Th355 W] 148, 150 1.26.1e [Th356 W] 148, 150 2.28.5 [Th357 W] 148 3.172.93 [Bias] 25 Theagenes 8.1 DK [Theagenes] 32 Theon of Smyrna De utilitate mathematicae [Th167 W] 74, 98, 99 198.14-18 Theophrastus De signis 4 [Cleostratus et al.] 83 Vitruvius De architectura 2.2.1 [Th85 W] 124 8, Praef. 1 [Th87 W] 124 Xenophanes 21A38 DK [Xen.] 193 21A40 DK [Xen.] 119 21B2 DK [Xen.] 189 21B18 DK [Xen.] 170, 189 21B19 DK [Th7 W] 95 21B30 DK [Xen.] 127 21B31 DK [Xen.] 193 21B38 DK [Xen.] 193

Index

Acusilaos (of Argos) 25 Aelius Aristides 132, 134 Aesop 26–28, 30, 34, 73, 189 Aetius 38, 88, 90, 97, 147–148 Alcaeus 23, 33, 42 Alcmaeon 6, 124, 170 Alcman 31, 33 Alexander (of Aphrodisias) 175 Alexander (the Great) 185 Alexandria(n) 69, 103, 108 Alyattes 86 American Dream 20, 33 Ammianus Marcellinus 122 Anacharsis (the Scythian) 26, 100–101, 107 Anacreon 42 Analemma 60 Anaxagoras (of Clazomenae) 87–89, 91–92, 96, 98, 122, 127, 131, 135, 148, 169–170, 189 Anaximander (of Miletus) 3–5, 7, 9–10, 12, 14–15, 24, 29–30, 32, 34, 36–37, 39, 41–43, 45, 67–68, 74, 76, 80–82, 94–96, 104–105, 122, 124, 134, 140, 146, 149, 169, 173, 185–186, 188 Anaximenes (of Miletus) 3–4, 10, 29–30, 44, 86, 114, 122, 169, 185 angular amplitude 43, 47, 80, 83, 101, 103–108, 146, 149, 169, 174, 184 Anonymous Florentinus 132 Anthologia Palatina 165 Antiphon (of Athens) 54 antipodes 77 apeiron 3–5, 14, 185 Aphrodite 18, 20 Apollo 20, 41, 186, 190, 193–194 Apollodorus (of Athens) 36, 43–44 Apollonius (Rhodius) 136, 154, 171 apsuchos (-oi) 139–140

Apuleius 66, 96, 100–105, 107–108, 145–146, 149, 170 Aratus (of Soli) 83 archē 4–5, 10, 13, 85, 109, 111–115, 120, 124–126, 177, 182, 188 Archilochus 21, 28, 33 Archimedes 102–104, 108 Arctinus (of Miletus) 25 Ares 19, 32 Aristarchus (of Samos) 69, 77, 83, 85, 87, 90–91, 102–105, 108, 178, 193–195 Aristonicus 193–195 Aristophanes 99, 156, 170 Aristotle 4–8, 10, 13–14, 36, 74, 108–109, 111–126, 135–136, 138–139, 146, 155, 157–158, 162–163, 170, 176–177, 179, 182, 185, 188 Arithmetic(al) 8, 52–53, 156 ars computandi 53 Assyria (or Assyrian) 92–94 astronomical unit 5, 14, 146, 185 astronomy 66, 71, 74, 95, 97–98, 121, 145–146, 178, 185, 194 Ate 19 Athena 19 Athenaeus 14 Athens 30, 38–44, 53, 82, 85, 95, 169–170 Augustine (of Hippo) 96, 145, 174–175 Babylon(ian) 85–86, 93, 95, 103, 186 bards (Hellenic) 16–18, 20, 32, 184 Battezzato, L. 32 Beconi M. 189 Bianchetti, S. 136–137, 150 Bias (of Priene) 5, 25, 41, 161–162 Biondi F. 32, 35 Black Sea 5, 94, 132, 159, 163 Blanche L. 93, 97, 99 Braccesi L. 31

210 Index Bretschneider C.A. 152–153 Brucker J.J. 7 Burkert W. 95, 99–99, 147 Burnet J. 91 Calenda G. 126 calendar 10, 68, 70, 77, 81–82, 84, 149 Callimachus (of Cyrene) 41, 147, 160 Callinus (of Ephesus) 20–21 Cambyses 30 Canova A. 12 cartography (-aphic; see also literary) 3, 7, 134 Caspian Sea 132 Caveing M. 51, 64, 153, 157 celestial (bodies, events, zones etc.) 74, 96–97, 103, 119, 146, 147–150, 174, 178, 184 Censorinus 128 Cherniss H. 6, 14 Chilon (of Sparta) 41, 44 Chios 43, 158, 162–163 chronotopography 7, 14 Cicero 5, 7, 14, 16, 29, 44, 87–88, 90, 96, 124, 158 Clement (of Alexandria) 86, 96, 99 Cleomedes (of Astypalaea) 79–80, 106 Cleostratus (of Tenedos) 30, 34, 42–43, 45, 70, 80–82, 170 cognitive curiosity 73 computation(al) 51–53, 61 Conti C. 127 Copernicus 108 Corre J.-F. 74–75 Costantini M. 33, 35, 141 Couprie D. 55, 65 Croesus (king of Lydia) 9, 27, 43, 159–163 Cyaxares (king of Media) 86 Damasias (Athenian archon) 38–40, 44 days (how many) 11, 20, 29, 42, 52–53, 60, 67–68, 70–81, 92, 98, 183, 185, 193–194 Delos 69 Delphi 20, 41, 190 Demetrius Phaelereus 26, 39, 44 Democritus (of Abdera) 37, 74, 81, 98, 119, 122, 158, 170 Detienne M. 26, 34 Dicks D.R. 29–30, 34, 75 Diels H. 11, 13, 35, 43, 117, 125 dio (clause) 113 Diodorus (Siculus) 130, 171, 176–177, 193–194

Diogenes Laertius 6, 14, 36–41, 44, 57, 64–67, 69, 74, 76–77, 83, 86, 89–90, 92, 99, 102–103, 108, 138, 145, 149–150, 155, 158, 160, 164–165, 169–171, 176–177, 179–182, 185–186 Dionysius 97 doxa (doxai) 125, 170, 172 Dreros (law of) 23 Dũhrsen N.C. 49, 95, 156 Duris (of Samos) 37 Earth 3–5, 9, 14, 25, 29, 35, 64, 88–93, 97, 104–105, 107, 111–124, 126 earthquakes 116–119, 121–123, 127, 138, 169–170, 174, 180 eclipse (solar, lunar) 10–11, 29, 40, 47, 66, 77, 85–99, 107, 146, 148, 169, 178, 181, 183, 186, 191, 193–194 Egypt(ian) 3, 8, 12, 22, 37–38, 50–57, 59, 63–64, 73, 94, 103, 119, 130–131, 135–136, 138, 140, 160, 177, 183, 186, 190 Elegiac poets 16, 20–21, 26, 33 emotions (identified, named) 17–19, 21–22, 32 empsuchos (-oi) 139 Epic, Greek 17–20, 24, 26, 32–33 Epimenides (the Cretan) 25–34 equilux 6, 77–79, 82, 84 equinox 6, 29, 42, 67–68, 71, 74, 76–79, 83, 149, 169, 174 Ercolani A. 17 Etesian (winds) 129–130, 135–136, 171, 177, 179–180 Euctemon (of Athens) 29, 67–68, 74, 76, 80, 169 Eudemus (of Rhodes) 29, 66, 72, 74, 86, 90, 96, 98–99, 151, 154–157, 178 Eudoxus (of Cnidus) 29, 41, 67–68, 74, 76, 80–81, 148, 169 Eumelus (of Corinth) 25 Eupalinus (of Megara) 41, 187 Euripides 34, 83 Eusebius (of Caesarea) 96 Euthymenes (of Massalia) 129–137, 169, 177 Examyas (the Phoenician) 89, 121, 138, 188 Flavius Julian (emperor) 102, 108 Fotheringham J.K. 43, 45 four operations 8, 52–53, 56, 156, 167

Index  211 Galen 72, 89–90, 127, 148, 175, 182 Galgano N. 14, 184–185 Gärtner U. 34 Gilgamesh 32 Giza 38, 50, 54, 60 Gods 18, 20, 25, 27, 34, 64, 94, 149, 189 Goethe J.W. von 12 González Ponce F.J. 132–133, 136 Gorgias (of Leontinoi) 6 Graham D. 34–35, 66–67, 78, 99, 161, 173 Greaves, A.M. 127 Guthrie W.K.C. 90, 95 Hagen 19 Hahn R. 12, 15, 51, 54, 60, 64, 157, 186–187 Hannah R. 73 Harpies 25 Haslam M.W. 87 Haubold J. 93 Havelock E.A. 17, 32 Hawke J. 52 Heath T. 103, 147, 153 Helicon (of Cizycus) 97 heliotropion 69–70 Hera 20 Heraclitus (of Ephesus) 6, 27, 35, 40, 98, 119, 128, 145, 169–170, 193–195 Heraclitus (Homericus) 124 Hermes 20 Hero (of Alexandria) 29, 66–67, 72–74, 86, 98–99, 176, 178 Herodianus 69 Herodotus 37, 52–53, 85–86, 90–92, 94, 96, 99, 129–133, 135–136, 147, 150, 159–163, 170, 177, 187 Hesiod 6, 20–21, 31–32, 34, 68, 77, 80–81, 83 Hieron (of Syracuse) 42 Hieronymus (of Rhodes) 57, 158 Himerius (of Prusa) 42, 44 Hipparchus (of Nicaea) 71, 148–150 Hippias (of Elis) 6–7, 120, 138, 170 Hippolytus (of Rome) 36, 44, 91, 127, 145, 186 Hipponion (Tablets of) 25 Homer, Homeric 6, 16–17, 19–21, 25–26, 28, 31–32, 35, 40, 52, 69, 100, 119, 124, 127, 171, 189 hourglass 79–80, 83, 106 humidity 5, 112, 115, 118, 121, 123, 125–126 hupodrome 89, 194

Huxley G.L. 32, 82 Hyades 11, 80, 83 Hyginus 147, 150 Iamblichus 38, 156–157 Impara P. 34 intermenstruum 88, 98 investigation(s) see research(ers) Ionian dream 22 isemeria, isemeriai 47, 68, 74, 76–77, 79, 84, 98, 107, 183 Isocrates 6, 14 Jedrkiewicz S. 49, 64 Johannes Lydus 132 Julian (the emperor) 102, 108 Kahn C.H. 75, 78 katoptrikos 88 Keyser P. 53 Khaemweset 65 Kindstrand J.F. 34 Kirk G.F. 34, 69, 85 Labynetus (of Babylonia) 86 Latmus (gulf of) 9 Lavoisier A.-L. 9 Leão D. 44 Lebedev A.V. 32, 85, 91–92, 98, 170 Lehoux D. 74–75, 83, 95, 99 lemniscate curve 60, 70 Lepetymnos (mount) 82 Lesbos 42–43, 82 literary topography 7, 14 logizesthai 52 lunation(s) 93 Luxor 50 Lycabettus 82, 84 Lyotard J.-F. 33 Lyric Poets 16 Magnesia, magnet 87, 138, 140–141 Malkin I. 31 mammalian uterus 5 Mandrolytus (of Priene) 43, 100–102, 105–106, 145, 169 Manetti G. 14 Mansfeld J. 14 Marathon 20 Marcacci F. 11, 65, 148 Marsiliana (abecedarium of) 22 Martin T.-H. 97 Massalia (or Marseilles) 129–132, 135–136, 148, 169, 177

212 Index Matricetas (of Methymna) 30, 34, 42, 70, 82, 170 Meander (river) 138, 141 Melissus (of Samos) 6 Mesopotamia(n) 24, 32, 64, 90, 93–94, 103, 186 Methymna 30, 42, 82, 170 Michel M. 51, 189 Milesian(s), Miletus 3, 7–9, 14, 16, 25, 30, 35–43, 52–53, 56–57, 59, 65, 68, 70, 82, 86–87, 89, 92, 94, 98–100, 113, 115–116, 120–121, 125, 127, 131, 138, 141, 145, 147, 155, 158–159, 161–163, 170–171, 176, 160, 182, 186, 188 moist(ure) 4, 111–112, 114–116, 119– 121, 123, 126–127, 177, 179–180, 182 month(s) 11, 77, 87–88, 130, 193–195 moon 29, 73, 77, 86–92, 96–104, 106, 145–149, 169–170, 174, 178. 181, 183–185, 193–195 Mouraviev S.N. 194–195 Mourelatos A.P.D. 35 Musaeus 6 Mytilene 39, 42–43, 169 Myus 20 narrative explanation(s) 9, 18, 20, 25–28, 34, 41, 102–103, 158, 160, 181, 188–189 Necho (Pharaoh) 94, 132–133, 126 Neileus 37 neomenia 86, 178, 193 Neugebauer O. 64, 71, 75, 93, 95, 99 Nibelungs 19 Nicolaides D. 4 Nile 5, 11, 94, 125, 129–138, 140, 160, 167, 169, 171, 174, 177, 170–180 Nilossenus (of Naucrates) 65 numbers (names of, numerical operations) 8, 23, 34, 51–53, 73, 104, 106, 177, 184, 186 numerology (-ical) 43, 184 Ocean (or Okeanos) 6, 25, 116, 119–120, 124, 129, 131–132, 134, 180 Odysseus 19, 27 Odyssey 19, 27–28, 40, 80, 86, 193 O’Grady P. 9–12, 51, 75, 91–92, 94, 100, 160–161 olive (harvest) 11, 64, 146, 158, 162, 190 Oltramare P. 127 Olympian (mythology, religion) 19, 25–27, 94, 165

Olympic 20, 22, 31, 42 open access, open source 102, 107 Orion (constellation) 45, 81 Orpheus 6, 25 Ortygie (island) 69 Osborne R. 33 Osiris 124 Outis 27, 189 Panchenko D. 64, 82, 93–95, 108, 146, 162–163 paneguris 42, 45 papyri 12, 33, 50–52, 61, 86, 98, 156, 165, 186, 193–194 parapegma 68, 74–75, 83–84 Parmenides 6, 30, 83, 97, 148–149 parsec 14 Patzer A. 14 Periander (of Corinth) 39, 41 Peri Physeos 30 Persia(n) 3, 22, 71, 136, 162–163 Phaenus (of Athens) 4, 30, 35, 42, 70, 170 Pherecydes 25, 34, 170 Philostratus 158 philosophy 7, 10, 38, 111, 119, 158, 171, 188–189 pillars of Hercules 5, 132 Plato 6–7, 14, 39, 66, 68, 73, 77, 89, 97, 100, 138, 146–147, 159, 170, 197 Pleiades 11, 29, 42, 67–68, 77, 81–82, 84, 149, 169, 174 Pliny 45, 57, 68, 76, 80–81, 83, 96, 158 Plutarch (of Chaeronea) 38, 44, 57, 65, 97–98, 119, 121, 124, 127, 130, 136, 147–148, 150, 164–165 Plutarch, ps. 176, 181 Polycrates (of Samus) 42 Porter A. 32 Poseidon 20 Pownall F. 136 Preller R. 11 Presocratic(s) 4, 6–7, 9, 14, 16, 25, 28–29, 31, 34, 44, 96, 124, 159, 169, 181, 183, 188 Priene 9, 42–43, 100–101, 161, 169 Proclus 151, 153–157 Prontera F. 137 Ptolemy (of Pelusius) 71, 75 pyramid(s) 3, 11–12, 29, 71, 75 Pythagoras 8, 12, 29–30, 35–36, 38, 51, 148–149, 169 Pythagorean(s) 15, 53–54, 149, 184 Pytheas 136

Index  213 quantitative data 5, 7–8, 15, 31, 101, 109, 117, 125, 188 Raablauf K. 22, 33 Rainbow(s) 99 Ramelli I. 34 Raven G.E. 34, 69, 85 Raviola F. 31 Redlin L. 60–63, 65 research(ers), investigation(s) 7, 10, 12, 30–31, 34, 37, 42–43, 47, 49, 54, 57, 63, 71–74, 82, 91, 95, 97, 100–101, 109, 125, 133, 146–147, 149–150, 152, 156, 170, 175, 181, 184–185, 187–188, 194–195 Rhind H. 12, 50–52, 61, 64, 156 Rhodes 5, 57, 86 Rhoecus 24 riddle(s) 27–28, 30, 64, 73, 189 Ritter H. 11 Rossi C. 51 Santilli J. 74 Sappho 33 saros 93 Schofield M. 15, 34, 69, 85, 114, 141, 186 Seaford R. 32, 34 seasons 11, 66–67, 76, 100, 145–146 seed(s) 4, 111–112, 115, 118, 120–121, 123, 126, 138, 177, 189 Seleucid(s) 71, 93 Seneca (of Cordoba) 13, 111, 115–123, 125, 128, 131, 133, 136, 171–173, 176, 178–180, 182 Senegal (River) 132–134, 137 Servius 120–123, 172, 176, 181–182 Seven Sages (or sophoi) 9, 39–41, 44, 100, 130, 164, 171, 177 Sextus Empiricus 14 shadow 3, 28, 33, 38, 47, 49–50, 54–65, 70–71, 75, 78, 96, 106, 117, 167, 183, 186 Sicily 5, 31, 97 Sidonius Apollinares 96 Siegfried 19 Simeon Logothetes 45 Simplicius 30, 120–123, 127, 172, 175, 182 Snell B. 14, 32, 34, 44 Socrates 6, 9, 68, 100, 159 Solon 20, 21, 25, 39–41, 44 songwriter(s) 7, 21, 24, 34 Sparta(n) 32, 34, 44

Stallman R. 102 statuary 22 Steele J.M. 93 Stefanovic D. 64 Stesichorus 31–33 Stevens K. 93 Stobaeus 25, 119, 121, 127, 147–148, 150, 171, 176, 182 Strabo 134 Suda 76 sun 3, 5, 14, 29, 38, 43, 47, 50, 54–58, 60, 62–64, 66–72, 75, 77–80, 82–83, 86–94, 96–107, 117–120, 124, 127, 130, 145–149, 157, 169, 170, 172, 174, 178, 180–186, 188, 190–193 sun (coaxial position) 50, 54–55, 58, 60, 62 Sunagoge 6 sungraphai 6 Syennesis (of Cilicia) 96 Symeon Logothetes 45 Syracuse 68 Syros (island) 69, 70 Swift L. 33 Tannery P. 152–153 Tedeschi G. 32 Tenedus 36, 82 Theagenes (of Rhegium) 30, 32, 35 Themistocles 20 Theodorus 24 Theognis 25 Theon (of Smyrna) 66–67, 72–73, 86, 98–99, 176, 178 Theophrastus 30–31, 36–37, 80, 82–83, 89–90, 121, 156 theorem(s) 12, 15, 51, 151, 154–157 thermon 126 Thetis 6, 124 Thibodeau P. 35–37, 44 Thomson J.O. 137 Thrasiboulos (of Miletus) 39 torture 20, 32 Torvalds L. 102 Traglia A. 127 triakas triekadas 77, 86, 178, 193 trope, tropai 47, 66–76, 80, 86, 106–107, 150, 188 Troy, Trojan War 20, 21, 51 truth 25–29, 34, 80, 95, 111, 193 Tyrtaeus 20–21, 34 Ursa (Maior, Minor) 10–11, 132, 147–150

214 Index Verner M. 64–65 Vesperini P. 12–13, 34, 85, 189–190 Viet N. 60–61 Virgil 120 Vitruvius 124 water 3–7, 9–10, 13, 35, 79–80, 83, 109, 111–127, 130, 132–133, 136, 138, 141, 147, 163, 169, 171–172, 175–177, 179–182, 188, 193 Watson S. 60–61

Webb E.J. 43, 45 well(s) 5, 49, 117, 123, 159 White S. 11, 15, 49, 77, 84, 146 Xenophanes (of Colophon) 28, 30, 40, 119, 169–170, 185, 189, 193 Zeller E. 7, 13, 163, 171–172, 174–175 Zeno (of Elea) 77 Zeus 25, 95–96, 99 zodiac(al) 42, 81, 146