Knowledge, Literacy, and Elementary Education in the Old Babylonian Period (SpringerBriefs in History of Science and Technology) [1st ed. 2023] 9783031452253, 9783031452260, 3031452259

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SpringerBriefs in History of Science and Technology Robert Middeke-Conlin

Knowledge, Literacy, and Elementary Education in the Old Babylonian Period

SpringerBriefs in History of Science and Technology Series Editors Gerard Alberts, University of Amsterdam, Amsterdam, The Netherlands Theodore Arabatzis, University of Athens, Athens, Greece Bretislav Friedrich, Fritz Haber Institut der Max Planck Gesellschaft, Berlin, Germany Ulf Hashagen, Deutsches Museum, Munich, Germany Dieter Hoffmann, Max-Planck-Institute for the History of Science, Berlin, Germany Simon Mitton, University of Cambridge, Cambridge, UK David Pantalony, Ingenium - Canada’s Museums of Science and Innovation / University of Ottawa, Ottawa, ON, Canada Matteo Valleriani, Max-Planck-Institute for the History of Science, Berlin, Germany

The SpringerBriefs in the History of Science and Technology series addresses, in the broadest sense, the history of man’s empirical and theoretical understanding of Nature and Technology, and the processes and people involved in acquiring this understanding. The series provides a forum for shorter works that escape the traditional book model. SpringerBriefs are typically between 50 and 125 pages in length (max. ca. 50.000 words); between the limit of a journal review article and a conventional book. Authored by science and technology historians and scientists across physics, chemistry, biology, medicine, mathematics, astronomy, technology and related disciplines, the volumes will comprise: 1. Accounts of the development of scientific ideas at any pertinent stage in history: from the earliest observations of Babylonian Astronomers, through the abstract and practical advances of Classical Antiquity, the scientific revolution of the Age of Reason, to the fast-moving progress seen in modern R&D; 2. Biographies, full or partial, of key thinkers and science and technology pioneers; 3. Historical documents such as letters, manuscripts, or reports, together with annotation and analysis; 4. Works addressing social aspects of science and technology history (the role of institutes and societies, the interaction of science and politics, historical and political epistemology); 5. Works in the emerging field of computational history. The series is aimed at a wide audience of academic scientists and historians, but many of the volumes will also appeal to general readers interested in the evolution of scientific ideas, in the relation between science and technology, and in the role technology shaped our world. All proposals will be considered.

Robert Middeke-Conlin

Knowledge, Literacy, and Elementary Education in the Old Babylonian Period

Robert Middeke-Conlin Department of Cross-Cultural and Regional Studies University of Copenhagen Copenhagen, Denmark

ISSN 2211-4564 ISSN 2211-4572 (electronic) SpringerBriefs in History of Science and Technology ISBN 978-3-031-45225-3 ISBN 978-3-031-45226-0 (eBook) https://doi.org/10.1007/978-3-031-45226-0 © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Paper in this product is recyclable.

For my dearest friends

Acknowledgements

This brief owes much to many people. First, it results from my research as a Marie Curie Fellow in Copenhagen. I owe much to my advisor, Nicole Brisch, who provided insight and direction for my work, as well as support while I worked in Copenhagen. I owe much as well to the myriad conversations I had with my friend and colleague Anuj Misra. The same can be said of Carlos Gonçalves and our discussions. To Jürgen Renn, I owe a vocabulary that helped me frame my discussion. To my former Ph.D. advisor and now colleague Christine Proust, I owe insights into the mathematical education of Babylonia. Appreciation must be given to Willemijn J. I. Waal, as well as The Netherlands Institute for the Near East (NINO), for providing images and comments concerning the texts presented in Chap. 5 when my own images proved corrupt, as well as granting permission to produce the illustrations presented in Chap. 5. Finally, this project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie SkłodowskaCurie grant agreement No 841928. To each, I owe much and give my warmest thanks.

vii

About This Book

A scribal education is well documented in the Old Babylonian period. Lasting from roughly 2003 to 1595 BCE, the Old Babylonian period was a time of dramatic change and instability. Politically, it began with the fragmentation and collapse of the last Sumerian Kingdom, the Kingdom of Ur, and ended with the sacking of Babylon and the fall of its eponymous dynasty. At the same time, there was significant social change. Part of this change was a dramatic increase in literacy and a massive shift in knowledge. However, both literacy and knowledge change are poorly understood. What defined this shift? What did it look like? What made up such literacy? How was it attained? This volume explores these questions and more. It examines education in the Old Babylonian period as a means to investigate knowledge and literacy. It presents a new method to pursue this topic. While numerous studies exist on the subject, there is no global study of the early elementary education, that is, this education in its entirety. Typically, education is examined in a piecemeal fashion. It’s as if education centred on lexicography alone or mathematics alone. One gets the impression that there was no purpose to education beyond training a kind of elite. This despite several studies showing a widespread literacy in this period and place. Such methodologies lead to numerous blind spots in how we perceive education. The study of knowledge has been affected by our misunderstanding of education as well. There are few examinations of local knowledge beyond the admission that some must have existed. This work starts by introducing the topic, the place, and the problems. We see multiple kinds of literacy, from a broad functional literacy to an erudite scholarly literacy at play in Babylonia. Knowledge is defined, as well as the knowledge economy. Lexicality and mathematics are presented as the two pillars of scholarly scribal education. The Old Babylonian epistemic shift is presented and traced from the preceding period into the Old Babylonian period. This is followed by a study of the document as a means to present education, as well as the various iterations of scholarly education in Babylonia. The work shows this scholarly, elite education was by no means uniform throughout Babylonia, but each scribal centre had its own variations on how to present the Old Babylonian knowledge system. Technical literacy comes to the fore starting with chapter five, which proposes the role ix

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About This Book

of documents in fostering a kind of learning by doing. The final, concluding chapter presents the places where technical literacy was acquired and then ties this into a general discussion of education and literacy in Mesopotamia. In this final chapter, orality and the home learning environments come to the fore as a broad functional literacy is redefined. Throughout this work, prior evidence is recontextualized to account for the entire knowledge system. New evidence is presented that challenges how we view ancient Babylonian education. The very nature of the textuality is called into question and redefined as technical literacy and then functional literacy is explored. The result is an image of the places of knowledge and education in Babylonia—a tapestry of local knowledge from which global knowledge arises—as well as a new means to explore this subject.

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Historic Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Knowledge and Literacy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Knowledge Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 2 6 8 12

2 At the Eduba . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Signs and Lexicality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Numbers and Metrology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15 16 25 30

3 The Old Babylonian Shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Sexagesimal Place Value Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 The Tabular Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Signs and Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33 34 42 47 49 57

4 Variety and Uniformity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 The Document . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Educations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Nippur . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 Ur . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 Larsa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.4 Uruk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.5 Isin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.6 Babylon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.7 Kiš . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.8 Sippar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Metatextual Variety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

61 62 65 65 68 69 71 73 75 75 78 81 89

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Contents

5 Stabilizing Knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 5.1 Lagaba . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 5.2 The Texts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 5.3 Learning by Doing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 5.4 Additional Tablet Illustrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 6 Outside the Eduba . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Technical Literacy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Localizing Functional Literacy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

129 130 133 137

Tablet Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 General Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

Abbreviations

A ABAW 143 AO Ashm BM BRM 4 CAD CBS CT 9 CUNES Erm HS IB Ist L Ist Ni Ist O LB M MCT MDP 22 MHET 1/1 MHET 3/1 MLC MKT 1 MS MSL 11 MSL 14

Tablets in the collections of the Oriental Institute, University of Chicago Wilcke et al. 2018 Tablets in the Louvre (Antiquités orientales) Tablets in the Ashmolean Museum, Oxford Tablets in the British Museum, London Clay 1923 The Assyrian Dictionary of the University of Chicago Tablets in the University Museum in Philadelphia (Catalogue of the Babylonian Section) Cuneiform texts from Babylonian tablets, &c. in the British Museum. Part IX Tablets in the Cornell University Near Eastern Studies collection Tablets in the Hermitage Museum, St. Petersburg Tablet in the Hilprecht Collection in Jena Tablets from the Isin excavation (Ishan Bahriyat) Tablets in the Archaeological Museum in Istanbul (Lagash/Girsu) See Ni Tablets in the Archaeological Museum in Istanbul (Kiš) Tablets in the de Liagre Bohl Collection (Leiden) Tablets in the Kelsey Museum of Archaeology (Ann Arbor) Neugebauer and Sachs 1945 Scheil 1930 Van Lerberghe and Voet 1991 Tanret 2002 Tablets in the Morgan Library Collection of the Yale Babylonian Collection (New Haven) Neugebauer 1935 Tablets in the Schøyen Collection (London and Oslo) Civil and Reiner 1974 Civil et al. 1979 xiii

xiv

N Ni PRAK RA 12 SM SPVN TAD TLB 1 VAT YBC

Abbreviations

Tablets in the University Museum, Philadelphia (Nippur) Tablets in the Archaeological Museum, Istanbul (Nippur) Genouillac 1924; 1926 Scheil 1915 Tablets in the British Museum in London (Smith) Sexagesimal Place Value Notation Langdon 1911 Leemans 1964 Tablets in the Vorderasiatisches Museum, Berlin (Vorderasiatische Abteilung. Tontafeln) Tablets in the Yale Babylonian Collection (New Haven)

List of Figures

Fig. 1.1 Fig. 2.1 Fig. 2.2 Fig. 3.1 Fig. 3.2 Fig. 3.3 Fig. 3.4 Fig. 3.5 Fig. 3.6 Fig. 3.7 Fig. 3.8 Fig. 3.9 Fig. 3.10 Fig. 4.1 Fig. 4.2 Fig. 4.3 Fig. 4.4 Fig. 4.5 Fig. 4.6 Fig. 4.7 Fig. 5.1 Fig. 5.2 Fig. 5.3 Fig. 5.4 Fig. 5.5 Fig. 5.6 Fig. 5.7 Fig. 5.8 Fig. 5.9 Fig. 5.10

Map of Babylonia (following Charpin 2004a, b) . . . . . . . . . . . . . Incipit of Ura (tablet CBS 11392) . . . . . . . . . . . . . . . . . . . . . . . . . Incipit of list Izi (tablet N 3796 + N 3885) . . . . . . . . . . . . . . . . . . Ni 18 edition and interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . The Old Babylonian table of reciprocals . . . . . . . . . . . . . . . . . . . . Incipit of abbreviated reciprocal table . . . . . . . . . . . . . . . . . . . . . . Edition of the table of multiplication on YBC 11,924 . . . . . . . . . Incipit of abbreviated multiplication table . . . . . . . . . . . . . . . . . . . Metrological table of weight on HS 242 and Ashm 1923–410 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Arrangement of data in metrological tables . . . . . . . . . . . . . . . . . Arrangement of data in multiplication tables . . . . . . . . . . . . . . . . Arrangement of data in reciprocal tables . . . . . . . . . . . . . . . . . . . . Incipit of SM 2685 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary of Nippur scribal curriculum . . . . . . . . . . . . . . . . . . . . . Comparison of lexical curricula at Uruk and Nippur . . . . . . . . . . Summary of elementary scribal curriculum at Isin . . . . . . . . . . . . Summary of scribal curriculum at Kiš . . . . . . . . . . . . . . . . . . . . . . Comparison of elementary curricula at Sippar and Nippur . . . . . Edition of MHET 3/1 2, 62 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Colophon of type III tablet YBC 11924 . . . . . . . . . . . . . . . . . . . . LB 1974 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LB 1977 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Edition of NBC 6288 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Edition of LB 1971 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Edition of LB 1972 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Edition of LB 1824 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Edition of LB 1975 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Edition of LB 1967 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . NBC 8874 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Edition of LB 1969 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 21 23 35 37 37 39 39 41 44 45 46 52 66 72 74 78 79 80 81 99 100 100 104 105 107 109 112 114 115 xv

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Fig. 5.11 Fig. 5.12 Fig. 5.13 Fig. 5.14 Fig. 5.15 Fig. 5.16 Fig. 5.17

List of Figures

Edition of LB 1963 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Edition of LB 1960 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LB 1961 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LB 1968 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LB 1970 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LB 1976 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LB 1979 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

117 119 122 123 124 124 125

List of Tables

Table 2.1 Table 2.2 Table 3.1 Table 3.2 Table 3.3 Table 3.4 Table 3.5 Table 3.6 Table 4.1 Table 5.1 Table 5.2 Table 6.1

Additional lexical texts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Common fraction signs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Normalized and non-normalized numbers . . . . . . . . . . . . . . . . . . Ur III and Old Babylonian sign forms . . . . . . . . . . . . . . . . . . . . . . Reciprocal tables from the Ur III period . . . . . . . . . . . . . . . . . . . . Reciprocal tables from the Ur III period transition into the Old Babylonian period . . . . . . . . . . . . . . . . . . . . . . . . . . . Reciprocal tables from the Early Old Babylonian period . . . . . . Normalized and non-normalized numbers by line in SM 2574 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dated mathematical student practice texts . . . . . . . . . . . . . . . . . . Breakdown of tablets from Lagaba . . . . . . . . . . . . . . . . . . . . . . . . Index of tablets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Breakdown of texts from Lagaba by archive and date . . . . . . . . .

24 29 47 49 51 53 54 55 83 94 121 132

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Chapter 1

Introduction

Abstract This chapter introduces the current work, first by providing an historical context to this study, then concepts of literacy and knowledge respectively. The Old Babylonian period is introduced in Sect. 1.1. In Sect. 1.2, literacy is discussed. Three levels of literacy are described: Scholarly, technical, and functional. Literacy is explored as exemplary of knowledge systems. These knowledge systems are described in Sect. 1.3. Three aspects of literacy are mentioned: the prose, the numeric, and the document. Definitions are provided that help frame this study. Problems are presented that will be overcome with this study. By the end of this chapter the reader will understand the goals and aims of this brief. Keywords Old Babylonian · Knowledge · Literacy · Education

A scribal education has been well established in southern Mesopotamia during the Old Babylonian period. Past studies focused on education in the larger cities,1 including Ur, Larsa, Uruk, Isin, Nippur, Kiš, and Sippar (see map, Fig. 1.1.), or on specific aspects of these educations. Studies also discuss texts that outline the scribal curriculum itself,2 paleography in education,3 the education of specific professions,4 and the education of women.5 We know much of the education of the aristocracy of Babylonia, of lexicality and mathematics, of the literature learned in the scribal school, and even of the scribal school itself. Yet each discussion takes education piecemeal. They treat lexicality and mathematics as separate educations with little interaction even if modern researchers understand full well that these subjects went hand in hand. By focusing on elite education little is said of the education of the rest of society. It’s clear that many craftspeople were educated, to greater or lesser

1

See Sect. 4.2 for education in these cities. See also most recently Gadotti and Kleinerman (2021). See, for instance, Tinney (1999, 159–72), Delnero (2010a, 53–70), Delnero (2010b, 32–55). 3 Wagensonner (2019). 4 For instance, see Middeke-Conlin (2020b). 5 Lion and Robson (2005). 2

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. Middeke-Conlin, Knowledge, Literacy, and Elementary Education in the Old Babylonian Period, SpringerBriefs in History of Science and Technology, https://doi.org/10.1007/978-3-031-45226-0_1

1

2

1 Introduction

degrees. Where, how, and what these educations looked like, on the other hand, is seldom discussed. This brief investigates knowledge and literacy as a means to explore education in the Old Babylonian period. After this chapter’s introduction, Chaps. 2, 3, and 4 focus on a kind of scholarly literacy and the education that produced this literacy. In Chap. 2, two branches of erudite knowledge are introduced: lexicality in Sect. 2.1. and numeracy in Sect. 2.2. Discussion in Chap. 2 leads to Chap. 3, which delimits the Old Babylonian knowledge systems from their prior iterations. New methods of calculation (Sect. 3.1), textual format (Sect. 3.2), and writing (Sect. 3.3) are all discussed before moving to a concrete example of epistemic change (Sect. 3.4). Chapter 4 focuses on the education systems that transmitted this scholarly literacy from teacher to pupil. The mediums of transferal are explored in Sect. 4.1, followed by the different curricula between larger scribal centers in Sect. 4.2, and then a concrete example of variety in Sect. 4.3. A kind of specialized, technical literacy is introduced in Chap. 5. This chapter explores education in a smaller urban center, the city of Lagaba, by examining educational texts from this city. This brings the reader to the concluding Chap. 6, which synthesizes the content of the texts from Lagaba into a coherent education (Sect. 6.1) and then hypothesizes on the place and role of a general functional literacy within Babylonian society (Sect. 6.2). We know much about education in the Old Babylonian period. This brief proposes a global view of education in Babylonia. It introduces a new method that contextualizes knowledge, literacy, and education in Mesopotamia within the broader realm of the history of knowledge. However, before this work can move forward, the Old Babylonian period must be demarcated. Thus, what follows is a discussion of this vibrant period in history.

1.1 Historic Context The Old Babylonian period was marked by political change and instability. Following the collapse of the third dynasty of Ur, a kingdom that ruled much of Mesopotamia between circa 2110 and 2003 BCE, numerous city states vied for supremacy.6 Five kings had ruled the powerful kingdom of Ur, starting with king Ur-Namma who reigned from 2110 to 2093 BCE and ending with the reign of his great-grandson Ibbi-Sîn (2026–2003 BCE).7 Decline began already during the reign of Ur-Namma’s grandson Šu-Sîn (2035–2027 BCE), when Amorite incursions into the kingdom’s heartland became a problem.8 6

For a recent discussion of the Ur III kingdom, including its decline, see Garfinkle (2022). See also Lafont (1995) and then Michalowski (2011) for more in-depth studies of the Sumerian kingdom of Ur and its collapse. 7 See Sallaberger and Schrakamp (2015, 131) for these dates. 8 Garfinkle (2022, 156–58). The Amorites were seen as semi-nomadic pastoralists, outsiders to the settled life of the Sumerian urban centers (Ibid., 166), despite the many Amorites who entered society, even acting as members of the royal court (Ibid., 153).

Fig. 1.1 Map of Babylonia (following Charpin 2004a, b)

1.1 Historic Context 3

4

1 Introduction

Šu-Sîn died in the ninth year of his reign and his son, Ibbi-Sîn, inherited a rapidly deteriorating kingdom. Deterioration is seen in the absence of texts bearing year names attributed to Ibbi-Sîn. At Ešnunna, his texts disappear after year 2, at Susa his last dated text is to year 3, at Girsu it is year 5, and at Nippur, the religious center of the kingdom of Ur, it is year 7.9 Išbi-Erra (2017–1985 BCE), an official of IbbiSîn, set himself up as an independent ruler of the city of Isin by the eighth year of Ibbi-Sîn’s reign, gaining control of Nippur shortly after.10 The final blow came in the twenty-fourth year of Ibbi-Sîn’s reign, but not from the Amorites. Instead, the king of Elam—a predecessor state of Persia formerly under the king of Ur’s control—sacked and occupied the city of Ur, snuffing out the dynasty.11 The city of Isin dominated the political landscape through the beginning of the Old Babylonian period.12 However, six years before the rise of Išbi-Erra and Isin, around the accession of Ibbi-Sîn of Ur to the throne, an Amorite dynasty began consolidating power around the city of Larsa.13 Four Amorite chieftains probably dominated Larsa until it gained firm independence from Isin by the reign of king Gungunum (1932– 1906 BCE).14 A further dynasty consolidated power in the city of Uruk around 1890 BCE, coming to prominence with king Sîn-kašid of the Amorite Amnanu tribe, and ultimately falling to the kingdom of Larsa in the 21st year of the reign of R¯ım-Sîn (1822–1762 BCE).15 The Kingdom of Larsa eventually supplanted Isin as suzerain over the south of Mesopotamia. R¯ım-Sîn conquered Isin in the thirtieth year of his reign (1794 BCE), before falling to Babylon in 1763 BCE.16 Founded by Sumu-la-El (1840–1845 BCE), the kingdom of Babylon started as a small city state that was part of a pan-tribal confederation of Amorite rulers led by Sumu-abum.17 The Babylonian state expanded considerably under Sumu-la-El, conquering Kiš and Kazallu while gradually absorbing Sippar.18 Babylon was one 9

Ibid., 159, especially Footnote 71. See Wagensonner (2022, 204–210) for a discussion of Išbi-Erra’s rise to power. 11 Garfinkle (2022, 160–61). 12 See Charpin (2004a) for the Old Babylonian period in general. For the kingdoms of Isin, Larsa, and Uruk during this period, see most recently Wagensonner (2022). For the kingdom of Babylon and the Sealand Dynasty, see Boivin (2022). For the reign of Hammurabi in particular, see Charpin (2003) and Van de Mieroop (2005). Years and year-names will be mentioned throughout this section. For Isin year-names, see Sigrist (1988). For Larsa year names, see Sigrist (1990) as well as Fitzgerald (2002). For year names of the first dynasty of Babylon, see Horsnell (1999). For a searchable, up-to-date database of year-names from the Old Babylonian period, see Charpin (2009). 13 Wagensonner (2022, 227). 14 For the beginnings of this dynasty, see ibid., 226–230. For Gungunum in particular, see ibid., 230–234. 15 Ibid., 257–266. 16 See Ibid., 280–296 for the reign of R¯ım-Sîn. 17 Boivin (2022, 578–81). 18 Ibid., 582–3. 10

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of several aggressively expansionist states at this time, forcing the Babylonian kings succeeding Sumu-la-El to fend off neighbors and to consolidate the lands controlled by Babylon.19 Hammurabi ascended the Babylonian throne in 1792 BCE at a very unstable time. King R¯ım-Sîn of Larsa had just conquered the rival kingdom of Isin, leaving him master of southern Mesopotamia. Samsi-Addu, based in Šubat-Enlil, had just annexed the kingdom of Mari leaving him master of Upper Mesopotamia. A protracted war raged between Samsi-Addu and the kingdom of Ešnunna to the east of Babylon. Mari would eventually break free with the return of Zimri-Lim to the throne at the dissolution of the kingdom of Upper Mesopotamia upon the death of Samsi-Addu. In this turbulent environment, Hammurabi focused on building and infrastructure for the first three decades of his kingship, undertaking only three military forays in these years.20 This all changed when the powerful kingdom of Elam occupied the city of Ešnunna and shortly after marched along the Tigress. This move threatened both Babylon and Mari and prompted an alliance between the two kingdoms in 1775 BCE. This alliance resulted in Elam’s defeat and withdrawal from Ešnunna. Hammurabi swiftly capitalized on this victory with a series of campaigns against his rivals. Within a few short years he conquered the kingdom of Larsa to his south (1763 BCE), subdued the kingdom of Ešnunna to his east (1762 BCE), and then conquered and destroyed the kingdom of Mari to the north (1761 BCE). Hammurabi now controlled the realms of Sumer and Akkad, the Diyala valley, the middle and parts of the upper Tigris River, the middle Euphrates, and perhaps the Habur triangle.21 Hammurabi’s reign ended with his death in 1750 BCE, when his son Samsuiluna officially took on the trappings of power.22 The beginnings of Samsu-iluna’s reign were relatively calm, but by his eighth year in power, around 1742 BCE, the empire forged by his father began to break apart. A combination of factors led to the establishment of two rebel kings, R¯ım-Sîn the second in Larsa and R¯ım-Anum in Uruk. Around the same time, the Kassites began causing trouble, forcing SamsuIluna’s intervention in his ninth year in power. In this year, Samsu-iluna began a counteroffensive that brought victory against Ešnunna, Larsa, Uruk, and Isin. The rebel kings would eventually fall so that by 1740/39 BCE most urban centers were again under Babylonian control. Campaigns continued for the next few years, leaving the southern cities depopulated and nearly abandoned. Recovery would not begin 19 For instance, in the second year of Sumu-la-El’s successor, Sabium (1844–1831 BCE) a coalition formed between Larsa, Uruk, and Ešnunna against Babylon. (Guichard 2014) In a similar vein, several of the year names of Sabium’s successor, Apil-Sîn (1830–1813 BCE) record fortress, city wall, and canal construction works throughout his reign, especially along the river Tigris and in Babylon. 20 Boivin (2022, 589–93). This is especially evident in Hammurabi’s year names. See especially years 7 and 10 for military expedition against Larsa (year 7) and the conquest of Malgium (year 10). 21 These events are summed up well in ibid., 594–598. 22 Towards the end of Hammurabi’s reign, Samsu-iluna probably acted as regent (Ibid., 615).

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until one hundred fifty years later under the First Dynasty of the Sealand. Having reclaimed control over a diminished Babylonian kingdom, Samsu-iluna turned his attention to fortifying the realm.23 Samsu-iluna passed on a weakened kingdom to his son, Abi-esuh (1711–1684). In the south the Sealand dynasty ruled while the heartland faced˘ both an influx of refugees from the south and Kassite migrations that began during his father’s reign.24 Three more kings reigned after Abi-esuh: Ammi-ditana (1683–1647 BCE), ˘ Ammi-s.aduqa (1645–1626 BCE), and then Samsu-ditana (1625–1595 BCE). With the final two kings the situation in Babylon deteriorated rapidly until a Hittite raid from Anatolia brought an end to the dynasty. The fall of Babylon appears thus to have been the result of attacks by several opposing forces, whether coordinated or not: the Hittite raid by Mursili I; possibly an attack by other powers which may have included the Sealand and Elam; and a revolt of mercenaries once in the employ of Babylon, the latter probably fostered by difficult economic conditions.25

1.2 Knowledge and Literacy The Old Babylonian period was a time of change. Beyond the numerous political changes, this period is marked by a significant change in knowledge from that witnessed during the Ur III kingdom. This changed knowledge, the latest iteration of cuneiform culture and the scribal art, is exemplified by the literacy instilled in the scribal education. While the complexity of cuneiform writing can lead to the supposition that literacy was an exercise limited to the elite, several studies dispel this belief.26 In particular, Veldhuis sums up three levels of literacy: a basic functional literacy, a technical literacy, and a scholarly literacy.27 To Veldhuis, the concept of functional literacy, describes the knowledge of cuneiform that is extensive enough to write or read a letter or an ordinary business document. The search for functional literacy is a search for literacy that is not professionalized, that takes place outside of the great institutions, and that is not aimed at aggrandizing the king, or thinking about the universe, but rather at the mundane issues of accounting and communication.28

Veldhuis points to evidence for a broad functional literacy available to most Old Babylonian households.29 Widespread functional literacy is something new to the Old Babylonian period but illusive to document. Underlying this is perhaps greater 23

The tribulations of Samsu-iluna’s reign are very aptly discussed in ibid., 615–625. See especially ibid., 615–618 for the events just cited. 24 Ibid., 626. See also Pientka (1998, 179–195) and Charpin (1999, 323–324) for this king. 25 Boivin (2022, 638). The final three kings are discussed in ibid., 631–639. 26 Including Wilcke (2000) as well as Charpin (2004b, 2008). 27 Veldhuis (2011, 70). 28 Veldhuis loc cit. 29 Ibid., 70–71 citing Wilcke (2000) and Charpin (2004b).

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freedom experienced by scribes after the fall of the bureaucratic Ur III kingdom. Greater experimentation in writing, the use of writing, and mathematical practice came with the transition from the Ur III to the Old Babylonian period. Writing, no longer a tool of power and prestige controlled by the various state and temple institutions, became a tool for general, popular use instead.30 Functional literacy is only one level of literacy. There was also technical literacy. Citing the use of technical terms and jargon, and using the Old Babylonian Omen compendia as an example, Veldhuis refers to the extension of cuneiform to realize its utility in narrow specialties: The technical jargon of these disciplines uses specialized subsets of the available lexicon, or specialized meanings of common words. Similarly, technical orthography does not employ a new writing system, but rather utilizes little used readings, extending the system to accommodate the needs of the specialist. Technical literacy illustrates the flexibility of the cuneiform writing system.31

This was a technical, specialized literacy aimed at expanding specific branches of knowledge. Finally, during the Old Babylonian period a kind of scholarly literacy proliferated. As opposed to functional and technical literacy, which are acquired in order to interact within a specific community, “scholarly literacy refers primarily to the knowledge of the writing system for its own sake, collecting all possible and impossible readings of each sign and sign combination, and then studying the history of its use and palaeography.”32 Høyrup suggests a kind of ‘humanism’ local to the Old Babylonian culture, expanding what Veldhuis will term scholarly literacy to “art pour l’art”.33 To Høyrup, second degree “algebra”, for instance, was pursued because it was complex and therefore “non-trivial,34 leading to what Høyrup would eventually call, “supra-utilitarian mathematics” or, “mathematics that looks as if it has to do with the utilitarian tasks of scribes but at closer inspection turns out to go far beyond what could ever present itself in professional practice.”35 This kind of mathematical activity goes back to at least the early third Millennium BCE.36 Both Veldhuis and Høyrup see a kind of scholarly pride in the scribal craft, one that has ancient origins even by the Old Babylonian period. This pride was the heritage of a new class, the aw¯ılum class, that arose during the period of change and greater scribal freedom that occurred after the collapse of the kingdom of Ur.37 30

Veldhuis (2011, 72). Veldhuis further states, “This opposition between third-millennium writing and Old Babylonian writing is not an absolute one. There was, of course, writing for private or non-institutional purposes in the third millennium, but such uses were derivative. The raison d’être of writing was its role as an instrument of institutional power.” 31 Ibid., 74. 32 Veldhuis loc cit. 33 Høyrup (1991, 30). 34 Ibid., 56. 35 Høyrup (2011, 6). 36 Ibid., 5–6. 37 Veldhuis (2014, 223–225).

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1.3 Knowledge Systems Here we come to an interesting phenomenon in Assyriology, one that this work seeks to address: Knowledge in the Old Babylonian period is often treated in one of two ways: either through the lexical tradition or through the mathematical tradition. Thus, Veldhuis and Høyrup come to similar conclusions concerning the scholarly traditions of the Old Babylonian period, but their arguments interact little. It’s hard to blame either. For one thing, they are writing several decades apart. For another, each focuses on a different aspect of knowledge: Veldhuis focuses on lexicography while Høyrup focuses on mathematics. Veldhuis makes this especially clear in his 2014 work on the history of Mesopotamian lexical texts as a branch of knowledge. To Veldhuis, Lexical texts have a context and a use: a context and use that changed over time. Lexical lists deal with a writing system that no longer exists today. They deal with a type of knowledge that is to some extent practical and skill-related, but to a much larger extent abstract and symbolic. The history of knowledge in which this tradition is placed is by definition not linear and not accumulative and is not recognized by any modern discipline as its ancient ancestor. Rather, knowledge is studied as a social phenomenon, as something that people use to pursue their material, social, and cultural goals, embedded in a historical context.38

Veldhuis’s aim is, in part, to contextualize these lexical lists as a branch of knowledge. He certainly recognizes other branched of knowledge within the Mesopotamian tradition, specifically highlighting both mathematics and then astronomy.39 Mention is given to metrological lists and numerical tables, but only in a cursory manner as objects from the same environment as the lexical lists.40 Veldhuis’ work, while brilliant and vital to the study of the history of knowledge, is also endemic of a trend of divided branches of knowledge. A similar situation is seen in, for instance, Robson’s (2008) work on the social history of mathematics in ancient Iraq. Robson certainly contextualizes mathematics, incorporating studies of texts that are not typically viewed as mathematical, such as administrative and economic texts, but she focuses firmly on mathematics as a branch of knowledge. However, by examining administrative and economic texts, Robson discusses a further aspect of knowledge, the document, even if this is in pursuit of mathematical logic. This is especially observable in her earlier discussions on the development of tabular formatting in Mesopotamia.41 In any event, one could argue that all three authors, Høyrup, Veldhuis, and Robson, examine different aspects of of literacy. 38

Ibid., 6. Ibid., 5–6, highlighting Høyrup (1996)’s historiography and Robson (2008) as a work on mathematical knowledge, then Brown (2000) and Rochberg (2004) as studies in astronomy. 40 Veldhuis is clear on the importance of metrology and mathematics but also clear they are not his targeted subject. See for instance, Veldhuis (2014, 207), “Metrological lists and mathematical tables do not belong to the lexical corpus strictly speaking. They need to be discussed here briefly because they do belong to the same curricular context.” 41 Robson (2003, 2004). 39

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Here, we hold that this literacy is representative of a knowledge system: cuneiform culture. And so, by pursuing literacy, we are setting out to define a knowledge system. We espouse a global exploration of this knowledge system. We seek to take a multifaceted approach to literacy and cuneiform culture. But what is implied by the phrase, “knowledge system”? In his pursuit of the evolution of knowledge in the Anthropocene, Renn describes a “knowledge system” as, Knowledge amalgamated by the connectivity of its element within their mental, material, and social dimensions. Knowledge systems are typically part of the shared knowledge of a community. Knowledge systems may vary according to their distributivity (the extent to which they are shared within the community); their systematicity (the degree of organizations, determining how closely the components are interwoven); and their reflexivity (their distance from primary material actions expressed by their order within a chain of iterative abstractions).42

Much of our evidence for knowledge in Babylonia comes from clay tablets that may be described as “external representations” of knowledge, or, Any aspect of the material culture or environment of a society that may serve as an encoding of knowledge…. External representations can be used to share, store, transmit, appropriate or control knowledge, but also to transform it. The handling of external representations is guided by the cognitive structures represented by them and may give rise to novel cognitive structures. The use of external representations may also be constrained by semiotic rules characteristic of their material properties and their employment in a given social or cultural context, such as orthographic rules or stylistic conventions in the case of writing.43

External representations of knowledge are essential to knowledge transmission and are therefore a vital aspect of a “knowledge economy”, or “all societal processes pertaining to the production, preservation, accumulation, circulation, and appropriation of knowledge mediated by its external representations.”44 During the Old Babylonian period, we have much information on this knowledge economy – a fully formed scribal curriculum has come down to us in several municipalities. Primary among them is the scribal curriculum visible in the city of Nippur, where the bulk of past research focused.45 These external representations bring us to a further aspect of literacy: the document. In this case it is the document within the context of the scribal curriculum. The external representations of knowledge at home in Babylonia must have been socially recognizable as a means to encode knowledge in order to maintain utility in perpetuating the knowledge system. The recognizability of external representations of knowledge is vital because they have what may be described as a “generative ambiguity”, to follow Renn’s assertion of knowledge evolution. They serve to stabilize knowledge transmission, assuring longevity of a knowledge system, while at 42

Renn (2019, 427). This work relies heavily on Renn’s study of knowledge as a framework to explain literacy and education. 43 Ibid., 424. 44 Renn introduces the “knowledge economy” in order “to describe and analyse the interconnection between society and knowledge.” (Ibid., 146). 45 See, for instance, Veldhuis (1997), Robson (2001), and Proust (2007).

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the same time they can act as agents of change, becoming the very tools used for thinking that brings about transformations of a knowledge system.46 For our purposes, these external representations afforded both knowledge transmission and allowed this epistemic change in a way that did not compromise activity outside of a scholastic environment, such as in a bureaucratic environment. For instance, the tablets studied in Chap. 5 here, which mimic real economic or administrative activity to greater and lesser extents, must have been recognizable as tools to transmit shared knowledge within the environment that produced them. They reflected professional activity within this community but must distinguish themselves from this activity or else they could compromise such activity. Chapter 4 shows that this variety of tablet was recognizable as an external representation of knowledge and therefore its use posed no danger to the administrative and economic activities mimicked by the texts written on it. There are, then, three distinct aspects of literacy that are emblematic of cuneiform culture: prose literacy, numeracy, and document literacy. Prose literacy is understood as the skills and knowledge needed to read and interpret continuous text. This is especially well exhibited in the lexical tradition of the Old Babylonian period as well as the literary texts prevalent in a more advanced education. Numeracy is the skills and knowledge needed to comprehend and carry out mathematical tasks. It is visible in the numerous metrological, numerical, and mathematical texts of this period. Document literacy is understood as the skill and knowledge to understand and manipulate document format and is visible in the variety of external representations of knowledge used to change, stabilize, and transmit cuneiform culture. The scholarly literacy mentioned above exhibits each of these aspects: prose in the lexical and literary traditions, numerical in the metrological and numerical traditions, and document in the variety of tablet types and text formats used to extend cuneiform culture. As noted above, the Old Babylonian scribes and literati acquired their scholarly literacy through the scribal curriculum. This education, as shown by Veldhuis especially, produced a kind of cultural literacy, including expertise in the literary heritage47 and, according to Høyrup, advanced mathematical practice. It’s in the scribal classroom, the eduba to use the Sumerian word, that knowledge is produced, preserved, accumulated, circulated, and appropriated, following Renn’s discussion, in order to advance cuneiform culture. On the other hand, the acquisition of functional and technical literacy – the gateway into specific aspects of cuneiform culture – is less well known. Neither were probably acquired in the classroom in the same way that scholarly literacy was, relying instead on other means, such as an apprenticeship.48 Identifying these kinds of learning environments is more difficult because the texts are often difficult for the modern readers to distinguish from real world practice. Here lays another problem addressed by the current work. While Veldhuis can suggest a wide functional literacy, the scribal 46

Renn (2019, 56–57). Veldhuis (2011, 82–83). 48 Robson (2008, 52–53). 47

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education as visible to us today aimed at scholarly literacy and identity creation, even if there are certainly aspects to this education that are necessary for functional literacy.49 However, with less certainty, these alternative learning environments have been suggested. For instance, Kraus in 1959 identified some Old Babylonian letters as student practice based on the appearance of duplicates or near duplicates.50 Educational texts could also resemble economic documents. This is shown very well by Foster, who was able to describe the education of Sargonic era bureaucrats in the city of Girsu by examining economic archives.51 Foster described several features that distinguish student practice: overly elegant tablets, exceedingly large script, lines written in the wrong direction, informality—including the omission of date formulas, and even doodles on the texts themselves. The mathematical curriculum consisted of exercises in measurement, extremely large values, and even building plans or surveys. Foster is not alone in identifying seemingly economic documents as student practice. Dunham, examining YBC 9819, proposes that this Ur III period text concerning bricks for the temple of Šara is in fact an educational text. ‘…it is a very carefully and neatly written tablet’, writes Dunham, ‘Even the signs for the sub-total and grand total are carefully drawn. While brick amounts are detailed as to what architectural part they were destined for, no responsible officials are mentioned and there is no date.’52 Englund takes this further, showing that some Ur III texts that resemble administrative texts were probably student practice because of their oddly rounded numbers and the multiplicity of duplicates.53 Such practice in a professional environment is not unheard of during the Old Babylonian period. Middeke-Conlin notes that two seemingly economic texts, BM 85,211 and BM 85,238 which date to Samsu-iluna year 7, were in fact student exercises.54 The reasons for this are the repetition between these texts, the clear use of what is called sexagesimal place value notation (SPVN) in calculation (see Chap. 3 for SPVN), and numerous obvious mistakes using SPVN. It’s often difficult to identify such texts, however, and even when they are identified their use as external representations of knowledge remain suspect because they resemble real-world situations. As Veldhuis points out, “they use the same formulary, the same conventions, and the same format as real documents because that is exactly their point: to train the student how to do it properly.”55 Rarity is also the 49

Veldhuis (2011, 86). Kraus (1959). 51 Foster (1982, 238–41). Foster states concerning student practice texts from Sargonic Girsu, ‘while this richness of learner’s material could mean that a “scribal school” was maintained at the building in which the tablets were found (…), it could just as well mean that some youngsters were educated in scribal schools “on the job,” picking up the necessary literate arts as they worked.’ (Ibid., 238). 52 Dunham (1982, 238–41). 53 Englund (2004, 39, text 4 and note 22). 54 Middeke-Conlin (2020a, 208–211). Both texts describe volumes to be excavated in an undisclosed canal excavation project. 55 Veldhuis (2011, 85). 50

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norm because, as student practice, they were not kept but often destroyed. At the same time, as external representations of knowledge, these tablets must have been identifiable to the practitioners who transmitted functional and technical literacy as suggested above. Thus, in each case, there were reasons to believe texts that seemed to express real-world situations were in fact the result of student practice. In Chap. 5, the case is built that 19 tablets, previously identified as administrative texts, can be described as external representations of knowledge and were used to perpetuate a kind of technical literacy to the next generation of scribes. As such, they present a rarity in Assyriology: they provide a relatively firm case for how technical literacy was acquired, as well as evidence for education in a small municipality during the Old Babylonian period, the small city of Lagaba. This leaves only functional literacy, a hypothesis of which is formulated in Chap. 6. Indeed, Chap. 6 concludes this work by concisely localizing technical and functional literacy alongside scholarly literacy. This brief proposes a global examination of knowledge, literacy, and education. It asks, “how was knowledge transmitted to learners in the Old Babylonian period?” In answer, it will trace student practice, exploring the very basic knowledge presented at the outset of the scribal curriculum; how knowledge changed during this period and place; and the variety of formal, erudite education throughout Babylonia. Next, it will offer an explanation of the places where technical literacy was acquired. Finally, it will advance a hypothesis on functional literacy. Functional, technical, and scholarly literacy were pursued in a variety of settings. This means the pursuit of each by the modern researcher requires a variety of techniques. The reader will see this. Chapters 2–4 will present a different method to pursue scholarly literacy than is seen in Chap. 5, while the conclusion necessarily presents a hypothesis on technical and functional literacy. Each discussion is also related. Chapters 2–4 must come before Chap. 5 because it forms a scholarly backdrop in which technical literacy was embedded. Both discussions, in turn, help contextualize and therefore must precede a hypothesis on functional literacy. The goal of this work is to offer a new method to the study of education and literacy. It incorporates and expands on the concepts of literacy presented by Veldhuis and Høyrup and the framework of knowledge and change espoused by Renn, among others. This work presents, then, methods to explore the acquisition and perpetuation of knowledge in its entirety within an ancient society.

References Boivin, Odette. 2022. The Kingdom of Babylon and the Kingdom of the Sealand. In The Oxford History of the Ancient Near East Volume II: From the End of the Third Millennium BC to the Fall of Babylon, ed. Karen Radner, Nadine Moeller, and Daniel T. Potts, 566–655. New York: Oxford University Press. Brown, David. 2000. Mesopotamian Planetary Astronomy-Astrology. Cuneiform Monographs 12. Groningen: STYX Publications.

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Charpin, Dominique. 1999. Review of Pientka, Rosel. 1998. Die spätaltbabylonische Zeit, Abiešuh bis Samsuditana: Quellen, Jahresdaten, Geschichte. Münster: Rhema. Archiv Für ˘ Orientforschung 46: 322–324. Charpin, Dominique. 2003. Hammu-rabi de Babylon. Paris: Presses Universitaires de France. Charpin, Dominique. 2004a. Tiel 1: Histoire politique du Proche-Orient Amorrite (2002–1595). In Mesopotamien: Die altbabylonische Zeit, ed. Dietz Otto Edzard, Dominique Charpin, and Marten Stol, 23–480. Frieburg and Göttingen: Universitätsverlag, Vandenhoeck and Ruprecht. Charpin, Dominique. 2004b. Lire et écrire en Mésopotamie: une affaire de spécialistes? Comptes rendus de l’Académie des Inscriptions et Belles Lettres 148e année: 481–501. Charpin, Dominique. 2008. Lire et écrire à Babylone. Paris: Presses Universitaires de France. Charpin, Dominique (ed.). 2009. ARCHIBAB: Babylonian archives (20th–17th centuries B.C.). Accessed 23 August 2022. http://www.archibab.fr/. Delnero, Paul. 2010a. Sumerian extract tablets and scribal education. Journal of Cuneiform Studies 62: 53–70. Delnero, Paul. 2010b. Sumerian literary catalogues and the scribal curriculum. Zeitschrift Für Assyriologie Und Vorderasiatische Archäologie 100: 32–55. Dunham, Sally. 1982. Bricks for the temples of Šara and Ninurra. Revue D’assyriologie Et D’archéologie Orientale 76: 27–41. Englund, Robert K. 2004. Banks in banning. In Von Sumer nach Ebla und zurück. Festschrift Giovanni Pettinato zum 27. September 1999 gewidmet von Freunden, Kollegen und Schülern, ed. Hartmut Waetzoldt, Heidelberger Studien zum alten Orient 9, 35–44. Heidelberg: Heidelberger Orientverlag. Fitzgerald, M. 2002. The Rulers of Larsa. Ph.D., Near Eastern Languages and Civilizations, Yale University. Foster, Benjamin R. 1982. Education of a Bureaucrat in Sargonic Sumer. Archiv Orientalni 50: 238–241. Gadotti, Alhena, and Alexander Kleinerman. 2021. Elementary Education in Early Second Millennium BCE Babylonia. Cornell University Studies in Assyriology and Sumerology 42. University Park: Eisenbrauns. Garfinkle, Steven J. 2022. The Kingdom of Ur. In The Oxford History of the Ancient Near East Volume II: From the End of the Third Millennium BC to the Fall of Babylon, ed. Karen Radner, Nadine Moeller, and Daniel T. Potts, 121–189. New York: Oxford University Press. Guichard, Michaël. 2014. Un traité d’alliance entre Larsa, Uruk et Ešnunna contre Sabium de Babylone. Semitica 56: 9–34. Horsnell, Malcolm John Albert. 1999. The Year-Names of the First Dynasty of Babylon. 2 vols. Hamilton: McMaster University Press. Høyrup, Jens. 1991. Mathematics and early state formation, or the Janus face of early Mesopotamian mathematics: bureaucratic tool and expression of scribal professional autonomy (revised contribution to the symposium Mathematics and the State). Filosofi og videnskabsteori på Roskilde universitetscenter. 3.række, Preprints og reprints. Roskilde: Roskilde Universitet. Høyrup, Jens. 1996. “Changing Trends in the Historiography of Mesopotamian Mathematics: An Insider’s View.” History of Science 34: 1–32. Høyrup, Jens. 2011. Mesopotamian calculation: background and contrast to greek mathematics. In IX Congresso della Società Italiana di Storia della Matematica, Genova, 12 November 2011. Kraus, Fritz R. 1959. Briefschreibübungen im altbabylonischen Schulunterricht. Jaarbericht Ex Oriente Lux 16: 16–39. Lafont, Bertrand. 1995. La chute des rois d’Ur et la fin des archives dans les grands centres administratifs de leur empire. Revue D’assyriologie Et D’archéologie Orientale 89: 3–13. Lion, Brigitte, and Eleanor Robson. 2005. Quelques Textes Scolaires Paléo-babyloniens Rédigés par des Femmes. Journal of Cuneiform Studies 57: 37–54. Michalowski, Piotr. 2011. The Correspondence of the Kings of Ur: An Epistolary History of an Ancient Mesopotamian Kingdom. Winona Lakes: Eisenbrauns.

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1 Introduction

Middeke-Conlin, Robert. 2020a. The Making of a Scribe: Errors, Mistakes, and Rounding Numbers in the Old Babylonian Kingdom of Larsa. Why the Sciences of the Ancient World Matter 4. Cham: Springer. Middeke-Conlin, Robert. 2020b. “Connecting a disconnect can evidence for a scribal education be found in a professional setting during the old Babylonian Period?” In Mathematics, Administrative and Economic Activities in Ancient Worlds, ed. Karine Chemla and Cécile Michel, Why the sciences of the Ancient World Matter 5, 435–462. Cham: Springer. Pientka, Rosel. 1998. Die spätaltbabylonische Zeit, Abiešuh bis Samsuditana: Quellen, Jahresdaten, ˘ Geschichte. Münster: Rhema. Proust, Christine. 2007. Tablettes mathématiques de Nippur. Istanbul: IFEA, De Boccard. Renn, Jürgen. 2019. The Evolution of Knowledge: Rethinking Science for the Anthropocene. Oxford: Princeton University Press. Robson, Eleanor. 2001. The Tablet House: A Scribal School in Old Babylonian Nippur. Revue D’assyriologie Et D’archéologie Orientale 95: 39–66. Robson, Eleanor. 2003. “Tables and tabular formatting in Sumer, Babylonia, and Assyria, 250050 BCE.” In The History of Mathematical Tables: from Sumer to Spreadsheets, ed. Martin Campbell-Kelly, Mary Croarken, Raymond Flood, and Eleanor Robson, 18–47. Oxford:: Oxford University Press. Robson, Eleanor. 2004. “Accounting for Change; The Development of Tabular Book-keeping in Early Mesopotamia.” In Creating Economic Order: Record-keeping, Standardization, and the Development of Accounting in the Ancient Near East, ed. Michael Hudson and Cornelia Wunsch. International Scholars Conference on Ancient Near Eastern Economies, 107–144. Bethesda: CDL Press. Rochberg, Francesca. 2004. The Heavenly Writing: Divination, Horoscopy, and Astronomy in Mesopotamian Culture. Cambridge: Cambridge University Press. Robson, Eleanor. 2008. Mathematics in Ancient Iraq: A Social History. Princeton: Princeton University Press. Sallaberger, Walter and Ingo Schrakamp. 2015. Philological data for a historical chronology of Mesopotamia in the 3rd Millennium. In History & Philology, ed. Walter Sallaberger and Ingo Schrakamp. Associated Regional Chronologies for the Ancient Near East and the Eastern Mediterranean 3, 1–136. Turnhout: Brepols. Sigrist, Marcel. 1988. Isin Year Names. Institute of Archaeology Publications Assyriological Series II. Berrien Springs: Andrews University Press. Sigrist, Marcel. 1990. Larsa Year Names. Institute of Archaeology Publications Assyriological Series III. Berrien Springs: Andrews University Press. Tinney, Steve. 1999. On the curricular setting of Sumerian literature. Iraq 61: 159–172. Van De Mieroop, M. 2005. King Hammurabi of Babylon: A Biography. Oxford: Blackwell Publishing. Veldhuis, Niek. 1997. Elementary Education at Nippur, The Lists of Trees and Wooden Objects. Ph.D., University of Groningen. Veldhuis, Niek. 2011. Levels of literacy. In The Oxford Handbook of Cuneiform Culture, ed. Karen Radner and Eleanor Robson, 68–89. Oxford: Oxford University Press. Veldhuis, Niek. 2014. History of the Cuneiform Lexical Tradition. Guides to the Mesopotamian Textual Record 6. Münster: Ugarit Verlag. Wagensonner, Klaus. 2019. Larsa Schools: A Palaeographic Journey. In Proceedings of the Workshop organised at the 64th Rencontre Assyriologique Internationale, Innsbruck 2018, ed. Jana Mynáˇrová Elena Devecchi, and Gerfrid G.W. Müller, Current Research in Cuneiform Palaeography 2, 41–86. Gladbeck: PeWe-Verlag. Wagensonner, Klaus. 2022. The Middle East after the Fall of Ur: Isin and Larsa. In The Oxford history of the Ancient Near East Volume II: From the End of the Third Millennium BC to the Fall of Babylon, ed. Karen Radner, Nadine Moeller, and Daniel T. Potts, 190–309. New York: Oxford University Press. Wilcke, Claus. 2000. Wer las und schrieb in Babylonien und Assyrien: Überlegungen zur Literalität im Alten Zweistromland. Sitzungsberichte der Bayerischen Akademie der Wissenschaft en Philosophisch-historische Klasse 2000/6. München: Verlag der Bayerischen Akademie der Wissenschaften.

Chapter 2

At the Eduba

Abstract This chapter focuses on topics from the eduba or “tablet house”. This chapter introduces the two primary themes of the formal scribal education: lexicography, used to translate the colloquial Akkadian language into the now dead and venerable Sumerian language, and mathematics, including metrology and numbers. This chapter briefly introducing the complexities of the cuneiform writing system as well as basic numeracy for those unfamiliar with cuneiform culture. Formal education begins to take shape, starting with the very elementary education in which tablets and writing were introduced and then a second level of education in which thematic and metrological lists were employed. A kind of educational structure emerges, informed by the art of translation explored during a more advanced phase of the elementary education. In this chapter, the reader becomes aware of the issues encountered by the ancient scribes as they extended cuneiform culture to the next generation. Keywords Lexicography · Translation · Numeracy · Education

The scribal education of the Old Babylonian period extant at Nippur and elsewhere was designed to impart the practical and esoteric knowledge necessary to engage in the world of the Mesopotamian elite. This education did not impart a mere functional or technical literacy. Instead, it imbued the student scribe with a kind of scholarly literacy composed of knowledge from an ancient heritage that harkened back to the very beginnings of writing in the fourth millennium. It was not aimed at the practical alone but pushed further to the very formation of scribal identity.1 This education took two main tracks over an elementary and advanced education: the lexical and the numerical. Such is said in the texts themselves. For instance, the literary composition, “The dialogue between an examiner and a scribe”, lines 36–38, states,2

1 2

Veldhuis (2011, 82–83). Translation from Vanstiphout (1997, 593).

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. Middeke-Conlin, Knowledge, Literacy, and Elementary Education in the Old Babylonian Period, SpringerBriefs in History of Science and Technology, https://doi.org/10.1007/978-3-031-45226-0_2

15

16

2 At the Eduba Having been at school for the required period, I am now an expert in Sumerian, in the scribal art, in interpretation, and in budgeting. I can even speak Sumerian.

Here the student’s education prepared him to be an expert in interpretation (literally “reading tablets”) as well as in budgeting, or more properly calculation and accounting. The student even boasts of his Sumerian. This was the erudite scribe of the Old Babylonian period, deft in the scribal arts of reading and calculating, complete with the ability to translate to and from Sumerian. But this scribe’s education takes some explanation. This chapter will begin to discuss scholarly education in the Old Babylonian period by exploring lexicality and metrology. It lays the groundwork for Chap. 3, which discuses changes that distinguished the Old Babylonian period from the prior Ur III period, and then a discussion of the modalities of this education—the external representations of knowledge and education in general throughout Babylonia—in Chap. 4. Focus is on elementary education. The scribal education presented both language and numbers. Sumerian, at least by the Old Babylonian period, was a dead language.3 It was no longer spoken at home but was now a cultural language with an ancient and venerable written tradition. Instead, the language of discourse was probably Akkadian. A Sumerian-Akkadian bilingualism existed in this environment.4 At the same time metrology had developed over the prior millennium to express capacity, weight, area and volume, and length. Numbers, too, had evolved over this period, both aiding in representing these metrological systems as well as to account for discrete numbers.5 Thus, the scribal education presented the cuneiform script, the ability to translate between two languages, and the ability to manipulate metrological and numerical values. To help understand this, it will help to understand the nature of the cuneiform script and translation (Sect. 2.1), and then metrology and numeracy (Sect. 2.2).

2.1 Signs and Lexicality To start with, most cuneiform signs are polyvalent, that is, they have more than one reading: either a syllable, called a syllabogram today, a word or logogram, or some other linguistic element.6 With syllabograms, groups of phonemes, vowels (V) and consonants (C), come together to form a syllable. Clusters occur like CVC, CV, VC, or even just V. The Akkadian verb il-la-ak, translated ‘he went’, is a word made up of VC and CV syllabograms. Such syllabograms represent sounds, but the same sound may be represented by multiple signs. The sound /il/ for instance is represented by 3

Sallaberger (2004), Michalowski (2006). Crisostomo (2019, 9–15). 5 Powell 1987–1990. 6 Following Civil (2020, 98–103), which provides good explanations of cuneiform signs, as well as Huenergard (2000, 68–74), which offers a very good introduction to the writing system from an Akkadian perspective. 4

2.1 Signs and Lexicality

17

no less than six signs throughout the life of cuneiform script. Such homophonous signs are distinguished by either an accent and subscript numbers (il, íl, ìl, il4 , etc.), or just subscript numbers (il, il2 , il3 , il4 , etc.) in many works today. Here subscript numbers alone are used. Logograms, on the other hand, typically represent entire words. Thus, the word gˆ en is the perfective form of the verb ‘to go’ while du is the imperfective form. Both forms are represented by the same sign, DU, which points to the polyphony of Sumerian signs. Such polyphony can be high, creating serious problems for the ancient and modern translator. The sign DU, for instance, could also stand for gub, ‘to stand’, and tum2 , ‘to place’. Only context can inform on the proper reading. In this work, caps are used to signify an uncertain reading, in this case DU. In text editions and text quotations, the Sumerian logographic reading of a sign, when known, will be signified with spaced letters following Assyriological conventions, while in paragraphs and tables Sumerian readings will simply be written in unspaced roman letters following Springer Nature style guidelines. For instance, the reader will see the Sumerian verb tum2 , ‘to place’, for the cuneiform sign DU. Akkadian readings will be represented by italics, such as the verb il-la-ak mentioned above. Polyphony is partially overcome by the appearance of phonetic glosses, signs that appear before or after a logogram to specify pronunciation. For instance, DUak is to be read as the Akkadian illak, ‘he goes’. On the other hand, gˆ a2 gˆ arar specifies that the sign is to be read gˆ ar, ‘to put’ and not, for instance, nig2 , ‘thing’. Phonetic compliments will always appear in superscript in this work. A further method to overcome polyphony is the use of classifiers (often called determinatives), unpronounced elements used to specify the semantic group of a noun (trees, plants, vessels, etc.).7 Classifiers can also appear before or after a noun, but never a verb. For instance, the sign gˆ eš, ‘wood, tree’, often appears before wooden objects or trees in Sumerian: gˆ eš banšur, ‘table’, or gˆ eš eren, ‘cedar’. Occasionally, common classifiers are shortened. This is the case with the sign ‘dingir’, which is shortened to ‘d’ when used to classify a divine name, such as in d utu, the Sumerian name of the sun-god Šamaš. Classifiers will always appear in superscript in this work. Finally, morphograms are used to represent a grammatical element in Sumerian.8 These are an intermediary between logograms and syllabograms in that they represent syllables but have a meaning in and of themselves. For instance, the modal prefix, he2 -, ha-, or hu- (depending on the vowel of the following syllable) can appear before ˘ ˘ a˘ Sumerian verb and all verbal elements to signify the subjunctive. These elements appear on lexical lists, to greater or lesser degrees, from the development of writing in the fourth millennium BCE through the Old Babylonian period, and into the late periods.9 For instance, texts like the list for trees and woods

7

For a list of these classifiers, see Edzard (2003, 9–10). Morphograms are discussed in Civil (2020, 100) and have not been fully accepted by Sumerologists. 9 For a history of lexical lists, see Veldhuis (2014). 8

18

2 At the Eduba

appear in the fourth millennium,10 through the Early Dynastic period (ca. 2900–2350 BCE), into the Old Babylonian period,11 and beyond. Throughout their lives, lexical lists played a vital role in preserving and fostering scribal culture.12 However, during the third millennium, the lexical lists became ossified, presenting little value to the scribal upbringing.13 With the Old Babylonian period, the lexical lists as a genre had gone through a massive transformation resulting in a significant development in education. Old lists changed while new lists were authored for deployment as a tool in the scribal education. These changes perhaps resulted from the rise of a new class of gentlemen and entrepreneurs, the aw¯ılum, an elite that required a community of practice fostered by the educational institution of the day, the scribal school or eduba.14 The Old Babylonian curriculum varied in detail from teacher to teacher,15 but some broad trends can be outlined.16 Before word lists were learned, the student was taught how to mold a tablet and then how to use a stylus. One learned how to produce the basic vertical stroke, the DIŠ sign , and then the horizontal stroke, the AŠ sign . This is seen directly on tablets , and finally an oblique stroke, the U sign where students repeat these signs over and over again.17 Lexical education began with basic sign lists, on which students practiced the writing of more complex signs, such as the syllable Alphabets A and B, as well as the syllabary, Tu-Ta-Ti, so named after its first sign sequence.18 Syllable Alphabet B lists meaningless combinations of two or three signs per line, introducing new signs every three or four lines. Repetition is important with this list, in which the student writes the same sign over and over again. Thus, combinations like that seen on the tablet N 5147 occur19 : 10

Ibid., 41–2. Ibid., 82–85. 12 Cf. Englund et al. (1993) and Nissen et al. (2004) for the archaic texts and then Englund (1998, 88– 89) for their preservation into the Early Dynastic period, as well as Civil (1987) for the production of new texts in the Early Dynastic period. 13 The lexical tradition of the fourth and third millennium is summed up well in Veldhuis (2014, 27–138). 14 See Chap. 1 here for this. These reforms and changes are well summed up in ibid., 202–225, especially 223–225. For a specific, well-developed example of the transformation and utility of a lexical text, see Linder (2021). 15 Robson (2001). 16 What follows relies heavily on Veldhuis’ research, especially Veldhuis (1997, 2014). For variety in education, see Sect. 4.2 here. 17 For examples of such texts from Nippur, see Tinney (1998). 18 Veldhuis (2014, 144). 19 Veldhuis (1997, 42). 11

2.1 Signs and Lexicality

19

AA AAA A KU A KU KU ME ME ME ME A PAP PAP PAP A MAŠ MAŠ The total composition consisted of several hundred lines, although the ending is not fully standardized. A shortened version of this alphabet is called Syllable Alphabet A. Signs in both compositions tend to be oversized, affording students the space needed to understand and explore the nuances of each sign.20 Syllable alphabet B was used primarily in Nippur, while Syllable Alphabet A was used more frequently everywhere else in Babylonia during the Old Babylonian period.21 In the composition Tu-Ta-Ti, each line begins with a single vertical wedge (DIŠ). Signs are introduced one by one followed by their triplet. Thus, the first two sets of this composition are22 : DIŠ

tu

DIŠ

ta

DIŠ

ti

DIŠ

tu-ta-ti

DIŠ

nu

DIŠ

na

DIŠ

ni

DIŠ

nu-na-ni

At Nippur there is a standard composition of 117 lines consisting of 29 triplets in total as well as a final doxology, ‘d nisaba za3 -mi2 ’ or “praise to Nisaba”. This composition introduces signs based on syllabic value, not shape or meaning, and therefor presents signs as an aspect of a writing system, cuneiform, not any specific language.23 The practice of sign elements, signs, and syllables made up the initial phase of the scribal education. These were followed by a list of names in both Sumerian and Akkadian. The names list was vital to the composition of letters and administrative texts24 because it introduced students to irregular orthographies and sign values that 20

Veldhuis (2014, 145–147). Ibid., 145–46. 22 Following ibid., 147. 23 Ibid., 147–148. 24 These are summed up in ibid., 148–49. 21

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2 At the Eduba

differed from other words. Because many names were Akkadian, this list presented the student with numerous Akkadian words and verbal phrases. The thematic list Ura followed the list of names.25 The name of this list, Ura, has been variously called ‘Ur5 -ra’ or ‘HAR-ra = hubullu’ after its middle Babylonian and first millennium versions, which begin with a˘ section on business expressions (ur5 -ra translates into “loan”). However, the Old Babylonian forerunner to this list began with gˆ iš taškaran, “boxwood”. The section on business was added later. Continuity was strong, however, so that the name Ura is kept by many Assyriologists.26 The Nippur version of Ura contained about 3600 words divided into six parts of between 507 (part 3) and 707 (part 1) entries. The list commenced with a section devoted to trees and wooden objects. This was followed by the second part devoted to crafts, raw materials, and manufactured items. The third part presented animals, both domestic and wild, as well as cuts of meat. The fourth part listed the natural world, including stones and stone objects, plants, fish and birds, and then fibers and clothing. The fifth listed geographical names, including the names of fields, cities, waters, stars, and ropes. Finally, the sixth part delved into food and drinks.27 Ura in the Old Babylonian period listed only Sumerian words, but these were probably accompanied by their Akkadian translations in the classroom, which were learned by heart: “The students had to know the Akkadian equivalents in order to understand Sumerian vocabulary—writing the Akkadian down, however, did not add to the value of the exercise.”28 Orality was an integral part of this and other lists. Ura was organized vertically, with entry following entry. Like the basic syllabaries, repetition was vital to the presentation of Ura. Entire entries were repeated, confirming that different Akkadian translations orally accompanied the Sumerian list. Main nouns were repeated along with different qualifiers to be repeated again in different sections. Entire passages were repeated for inclusion in other sections.29 The section dealing with leather bags (kuš dug3 -gan) is emblematic of this (Fig. 2.1).30 Such repetition would remain a vital part of the lexical education throughout the elementary education. More advanced lexical lists, the so-called acrographic word lists and advanced sign lists, were learned next. These included the list Ea/Aa, the list of professionals Lu, the lists izi, kagal, and nigga, in which explicit bilingualism occurs, as well as the advanced sign list diri. In this phase of the education, students became familiar with hermeneutic systems of resemblances that permeated cuneiform writing and lexical scholarship.31 This phase is often called the advanced lexical education. The advanced lexical education began with the list Ea/Aa. The name Ea is derived from the first line of its 1st millennium version. However, in the Old Babylonian period 25

See ibid., 149–157 as well as below in this volume for the thematic list Ura. Ibid., 149. 27 Ibid., 150. 28 Ibid., 151. 29 Ibid., 151–153. 30 CBS 11392 reverse iii 5–12, following Ibid., 153. 31 Cavigneaux (1976), Rochberg (2016), Van de Mieroop (2015), and Crisostomo (2019). 26

2.1 Signs and Lexicality

21

Fig. 2.1 Incipit of Ura (tablet CBS 11392)

it commenced with Aa as presented below. The purpose of this text was to explain the meaning of simple Sumerian signs. The same sign might be listed several times, preceded by its different Sumerian vocal glosses so that, for instance with A, the following initial four lines appear: a2

A

ia

A

du-ru

A

e

A

The sign A originally had five glosses. This was followed by more complex signs. The first sign perhaps represents an exclamation like “Ahh!”, while ‘ia’ represents the locative nominative grammatical morpheme; ‘du-ru’, the gloss for the reading ‘duru5 ’, conveyed the meaning “wet”; and ‘e’, the vocal for the reading ‘e4 ’, gave the meaning “water”.32 Two further formats existed, listing only the signs (one column format) or a three column format listing the Sumerian gloss, followed by the sign itself, followed by the Akkadian gloss. Old Babylonian Lu is often called Lu = ša for its bilingual incipit ‘lu2 ša’ (man = he). The list introduced words related to titles, functions, and professions, including words of which the primary relation was graphic or thematic analogy.33 Whether this text was outwardly bilingual or not, like Old Babylonian Ura it was probably conceptualized as bilingual and orality was an integral part of this list. Again, Akkadian translations were learned by heart.34 Indeed, some sections were organized by their often-implicit Akkadian gloss.35 However, unlike Ura, which is

32

Veldhuis (2014, 178–79). Crisostomo (2019, 83). 34 Veldhuis (2014, 159–61). 35 Crisostomo (2019, 83–84). 33

22

2 At the Eduba

arranged thematically, Lu adds entries based on both thematic and graphic associations.36 Lu contains several similar features to the acrographic lists, especially Izi, including thematic and graphic associations as well as proximity in the curriculum.37 Izi, “fire,” with over 140 exemplars, was probably one of the most copied lists in the advanced lexical education.38 Composed of two tablets comprising about 1025 entries it represents the longest of the acrographic lists. These lists are called acrographic because, The order of the entries is frequently arranged graphically, by common (often initial) sign (acrographic), and/or thematically, with occasional interpolations based on other associations. Such associations in Izi’s structure are based on analogies, recognizable by trained scribes.39

Thus, with Old Babylonian Izi entries such as those found in the section on the sign HUR appear, as illustrated in Fig. 2.2.40 Akkadian glosses precede the Sumerian ˘ UR, which is transliterated variously as ‘mur’, ‘ur ’, ‘kin ’, or ‘ara ’. Note sign H 5 2 3 ˘ not all entries for HUR are preceded by an Akkadian gloss. Orality, again, also that was an integral part of this ˘text. Old Babylonian Kagal, also an acrographic list, is divided into three sections: a section on building with qualities similar to a thematic list (233 lines), on words that begin with the sign A (275 lines), and then words that ˆ (34 lines).41 Nigga is the most rigorously organized of the start with the sign GIŠ acrographic lists. It is divided into six sections of around one hundred lines, each devoted to the signs GAR, ŠU, SA, BAL, GU2 , and KI respectively.42 The advanced sign list Diri presented the student with compound signs, that is, combinations of two or more graphemes that make up one syllabic unit. Thus ˆ the components UD.DU are the elements of e3 , ‘to ascend’; ŠU.GAR.TUR.LA 2 are the elements of tukum, “if”; and SI.A are the components of the sign dirig, meaning “to exceed, surpass.”43 This “syllabary” was used to teach an aspiring scribe the pronunciation of complex compound signs, the formation principle of “compoundness”, and associated Akkadian lexemes.44 The common format of this list was its Sumerian vocal gloss followed by the complex sign, followed by the Akkadian translation, as illustrated by the first line, di-ri

36

SI.A

wa-at-ru-um

Civil et al. (1969, 25). Veldhuis (2014, 162). 38 Crisostomo (2019, 12). 39 Ibid., 10. 40 N 3796 + N 3885 rev. 12–29, transliteration and translation presented in Veldhuis (2014, 166– 168). 41 Veldhuis (2014, 171–72), Crisostomo (2019, 84–85). 42 Veldhuis (2014, 174–175), Crisostomo (2019, 85–88). 43 Linder (2021, 120). 44 Linder loc cit. 37

2.1 Signs and Lexicality

23

Fig. 2.2 Incipit of list Izi (tablet N 3796 + N 3885)

The third column listing the Akkadian translation is almost always present.45 These advanced lexical lists were organized along a vertical axis, with one entry following the next. Most lists, such as the incipit of the list Ea/Aa presented above, were almost exclusively presented as unilingual, exhibiting only this vertical listing and then associated signs. Some scribes wrote glosses to these signs and their associated Sumerian words in the language of discourse of the day, Akkadian. This was illustrated above with an incipit of the list Izi, where it preceded the Sumerian word, and then in Diri, where it only appeared after the Sumerian gloss and then sign. These explanatory glosses occurred along a horizontal axis to render a “metatexual commentary to a given entry”.46 When glosses are not explicitly present, oral commentary probably delivered similar glosses so that such metatextual commentary permeated these lists. Thus, the lexical lists in the advanced lexical education, both sign lists and acrographic lists, can be understood as a form of “proto-commentary” in which the relationships between entries acted as hermeneutic tools that aided the

45 46

Veldhuis (2014, 182–83). Crisostomo (2019, 11).

24 Table 2.1 Additional lexical texts

2 At the Eduba

I. Text name

II. Text content

Ugumu

Body parts list

Ki-ulutinbiše

Phrasebook of legal expressions

Nippur God List

List of deities

Lu-azlag

List of human beings

Saˆg

Acrographic list

aspiring scribe in producing a contextually correct interpretation.47 In this environment, “polyvalency and polysemy wove analogy and resemblance into the fundamentals of cuneiform literacy.”48 Habituation was the key to producing an hermeneutic system of resemblances that afforded advanced knowledge in writing and bilingualism. In this way, analogical hermeneutics became scribal habit by means of the advanced lexical education.49 Beyond the lexical lists just presented, additional texts could be memorized. For instance, there are several lexical lists and phrasebooks at Nippur that could serve to round out the advanced lexical education (Table 2.1). Similar to the lists Lu, Izi, Kagal, and Nigga, the body part list Ugumu (for ‘ugugˆ u10 ’, “my crown”) appears as both a unilingual Sumerian list and a bilingual list. Lu-azlag, like Diri, was almost always copied in its bilingual format.50 The lexical lists were followed by proverbs and then model contracts. Building on the same pedagogical principles as those of the advanced lexical education, the proverb collections served to present Sumerian grammatical structure, affording practice in sentence composition and introducing the aspiring scribe to the elements of Sumerian grammar.51 The model contracts introduced the student to realistic contracts, incorporating some technical vocabulary encountered in the prior lexical education while further inculcating students with Sumerian sentence structure. However, in contrast to actual contracts, witnesses and date formulas are omitted in the model contracts.52 Through the proverbs and model contracts, students contextualized the rare lexical terms they encountered in the prior education phase.53 Similar to the lexical lists, organization of both proverbs and contracts foster repetition and habituation, aiding memorization and application of texts and key concepts.54 All of this led to the advanced education in which the Sumerian literary corpus was

47

Frahm (2011, 12–19), Delnero (2016, 127–131). Crisostomo (2019, 143). 49 Ibid., 10. 50 Veldhuis (2014, 208). 51 Ibid., 204, 209–211. See also Taylor (2005, 18–24). 52 Spada (2014, 2). 53 Crisostomo (2019, 70–71). 54 Veldhuis (2014, 209–11), Spada (2014, 2) states of the model contracts, “The repetitive character of these texts is useful for explaining and drilling the Sumerian sentences and formulas.” 48

2.2 Numbers and Metrology

25

studied, “a vast array of hymns to gods and kings, narrative texts (heroic as well as mythological), and light-hearted compositions.”55

2.2 Numbers and Metrology This very short survey showed that much went into the lexical education of a scribe. While much ink has been spilled over the lexical tradition, of equal importance was the mathematical tradition. Old Babylonian metrology and mathematics are often difficult to understand for the expert and non-expert alike. This is in part because there were numerous metrological and numerical systems employed to express value. By the Old Babylonian period, these systems had been codified into four metrological systems and two primary numerical systems. Metrology consisted of a system to express capacity measurements, weight measurements, area and volume measurements, and length measurements. Numeracy also consisted of a system to count discrete numbers and larger capacity and weight measurement values, system S (for sexagesimal), and then a system to account for larger surface and volume measurement values, system G (for the sign GANA).56 The metrological lists were learned early in the scribal curriculum, along with the lexical lists discussed above. Items such as silver are accounted for using a system of weight which is summed up as follows: gu ←×60− mana ←×60− gin ←×180− sˇ e In this illustration, 1 gu is made up of 60 mana while 60 gin make up 1 mana and 180 še populate each gin. 1 gu is roughly 30 kg in our modern metric system.57 Grain, or properly speaking barley, and beer are accounted for using a capacity system in which 1 gur is composed of 5 bariga. 6 ban of 10 sila apiece composed each bariga. Every sila is then composed of 60 gin, which is also used to express lower values with the weight system: Gin are again made up of 180 še: gur ←×5− bariga ←×6− ban ←×10− sila←×60 − gin ←×180− sˇ e

55

Veldhuis (2011, 84). Pages 82–86 of Veldhuis (2011) sums up the structure of the curriculum. See especially Ibid., 83 Table 4.1, for a concise image of this curriculum. See Tinney (1999, 2011) for the literary corpus in the context of the scribal curriculum. 56 For more on metrology and numbers, see Chambon (2021), Proust (2009), and Powell ( 1987– 1990). 57 This illustration and the following ones organize units of measure hierarchically from right to left using a method originally developed in Friberg (1993). The smallest units appear at the right, the largest unites are located at the left. A left facing arrow that encloses a multiplication (←×n–) is used to present the factors that separate units of measure. Friberg’s method has the advantage of illustrating units in the same relative positions they appear in the texts of the Old Babylonian period while succinctly illustrating granularity, from fine to coarse.

26

2 At the Eduba

One sila is about the size of one liter in our modern metric system. System S was employed to count objects like reed bundles, as well as to count units of measure at and above gu weight and gur capacity: sˇ ar -gal sˇ u nu-tag ←×60− sˇ ar -gal ←×6− sˇ ar ’u ←×10 − sˇ ar ←×6− geˇs ’u ←×10− geˇs ←×6− u ←×10− unit/item counted This sexagesimal system was composed of an additive decimal structure. The numbers 1 through 9 are represented by the ‘diš’ sign to account for counted items, or the ‘aš’ sign for gu-weight or gur-capacity. Tens are expressed by up to five ‘u’ signs. ‘diš’ or ‘aš’ signs are added to ‘u’ signs in order to represent the numbers 1 through 59. To denote 60, a larger vertical sign is used, ‘geš2 ’, translated as geš here. Above these are units of geš’u (10 × 60), sar (602 ), sar’u (10 × 602 ), šar-gal (603 ), and šar-gal šu nu-tag (604 ).58 Area and volume were treated somewhat differently. First, their lower units were accounted for using sar measurement values: iku←×100 −sar ←×60− gin ←×180− sˇ e Here 100 sar are in one iku measurement value. Sar measurement values, like sila with capacity and mana with weight, are subdivided into 60 gin, which are in turn subdivided into 180 še measurement values. One sar is approximately 36 m2 or 16 m3 . Above sar, area measurement values were quantified using the numerical system G (for the sign GANA or GAN2 , a lexeme designating these as fields or area). While based on an additive structure, system G is only partially sexagesimal. sˇ ar -gal sˇ u nu-tag ←×60− sˇ ar -gal ←×6− sˇ ar ’u ←×10− sˇ ar ←×6− bur ’u ←×10− bur ←×3− eˇs e ←×6− a sˇ ←×2− ubu Like system S, the ‘aš’ sign is used to quantify its lowest full unit, the iku. One ubu is one half of an iku or the equivalent of 50 sar. Area and volume were computed out of length measurements, danna ←×30− USˇ ←×60− ninda ←×12− ku sˇ ←×30− sˇ usi In this system, 1 ninda comes to be about 6 m. 1 sar area was conceptualized as a square with sides of 1 ninda, while 1 sar volume was conceptualized as 1 sar area multiplied by 1 kuš height so that it could be understood as a prism with a base

58 However, it’s also quite possible this final unit, šar-gal šu nu-tag, was simply a comment on the system, stating that the upper unit, understood as šar-gal, could not be repeated. See Chambon and Robson (2011) for this.

2.2 Numbers and Metrology

27

of 1 sar.59 In the same way, 1 gin area multiplied by 1 kuš height produces 1 gin volume—a prism with a base of 1 gin area. Such connections, made by computation, can be called bridges. The metrological and numerical values were in many cases already ancient by the Old Babylonian period. For instance, the capacity system mentioned above appears in written documents around 3000 BCE, while the system of gur consisting of 5 bariga and 300 sila was probably implemented in the Sargonic period (late twentyfourth and twenty-third centuries BCE).60 The iku, eše, and bur of the area system were even older, having already been in use since the proto-literate period of the 4th millennium, while the remainder of the system had formed by the early dynastic period (c. 2900–2340 BCE).61 The weight system is one of the youngest systems but with some precursors in the Early Dynastic period. However, the gu measure itself is decidedly old. The weight system was heavily affected by the same Sargonic reforms as the capacity system, when a link was provided between the two so that 2 mana was the weight of 1 sila of water.62 Connections like this, that are based on the physical properties of measurement values and therefore do not require any computation are called alignments here. Additional alignments in this system can be summed up as,63 • Capacity, weight, area: – sila, mana, and sar are all divided into 60s of gin. • Volume and capacity: – a cube with 6 šusi edge has a capacity of 1 sila; – 1 gin volume has a capacity of 1 gur; – 1 sar volume has a capacity of 1 × 60 gur. These kinds of alignments were one basis for calculating disparate items, like a capacity of barley by a weight in silver to produce the value of barley in silver. By the Old Babylonian Period scholars had developed metrological lists that explored these dissimilar systems.64 The metrological lists were learned early in the 59

See Powell ( 1987–1990) for a more in-depth discussion of these systems. Area calculation is found on Ibid., 479, while volume is found on ibid., 490. 60 Ibid., 493. 61 Friberg (2007, 116). 62 Powell ( 1987–1990, 493) states of this, “Introduction of the Akkad gur is associated with a rationalization of the metrological system, which seems to consist primarily of the following: (1) abandonment of such archaic phenomena as distinct norms for liquid versus dry capacity and distinct minas to weigh wool or cloth versus metal; (2) establishment of a rational relationship between the mina and the sila (probably 2 minas of water = 1 sila); (3) introduction of the volume s/šar defined as 60 gur of capacity; (4) introduction of a new gur composed of 5 bariga to provide the basis for these linkages. General adjustment of norms probably accompanied this reform, but direct evidence is lacking.” 63 As summed up in Middeke-Conlin (2020, 28). 64 Metrological lists are not new in the Old Babylonian period. By the late-Uruk period lists of area measurements begin to appear, for instance. (Nissen et al. 1993, 2004) Moreover, the development

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2 At the Eduba

course of the scribal curriculum, after the students explored the construction of signs and syllables. At Nippur, they consisted of about 620 items: around 180 items in the list of capacities, 170 with weights, 110 with area and volume, and 160 with length and height.65 The student began by memorizing the metrological list of capacities at the same time as they memorized the names list and thematic lists. This was followed by the list of weight as they began memorizing their second thematic list, and then area and volume as they finished their thematic lists. Around halfway through the acrographic and advanced sign lists they finished memorizing the list of lengths.66 An incipit of the beginning of the metrological list of capacity from Nippur reads as follows67 : 1(d i š)

gin2

1(d i š) 1/3

gin2

1(d i š) 1/2

gin2

1(d i š) 5/6

gin2

1(d i š) 2/3

gin2

2(d i š)

gin2

2(d i š) 1/3

gin2

2(d i š) 1/2

gin2

2(d i š) 2/3

gin2

2(d i š) 5/6

gin2

3(d i š)

gin2

4(d i š)

gin2

5(d i š)

gin2

6(d i š)

gin2

še

A few things can be noted from this list. First, there are three distinct parts to the metrological value: A numerical value consisting of an integer number or a fractional value, a measurement unit, read as gin2 and translated gin, and then a lexeme, še or ‘barley’, signifying the nature of the quantified item. Not all measurements values fit so neatly into these three parts. For instance, later in the list measurement values like the ban measurement values appear. Such measurement values seem to combine the numerical value and the measurement unit into one grapheme: “1(ban2 ) še” which we translate to ‘1 ban barley’. Here 1(ban2 ) signifies both number and measurement followed by the lexeme, ‘še’, denoting barley measurements.68 of these lists, and in some instances tables, can be traced as tools in calculation through the third millennium (Friberg 2007, 147–153; Lecompte 2020; Proust 2020). For these tables, see Chap. 3. 65 Proust (2007, 99). 66 See ibid., 150–57, especially 151–52 where the mathematical curriculum is first laid out and connected with the lexical education as outlined above. Proust’s data is summarized in ibid., 255– 262. 67 See Proust (2009, §8.1). 68 For more on this, see Proust (2009) and Chambon (2021).

2.2 Numbers and Metrology Table 2.2 Common fraction signs

29

Fraction

Sign

1/3 1/2 2/3 5/6

Fractions were important in expressing numerical values, whether independently or as parts of metrological values. Four common signs developed to express factional values: 1/3, 1/2, 2/3, and 5/6 (Table 2.2). These signs account for most fractional values found in the texts. However, they are not the only means to write a fraction. Outside of these four signs, factions were written igi n-number-gal2 , such as igi 4(diš)-gal2 , translated here as ‘one-4th ’.69 The lists instilled in the students a concept of what made up a metrological value. At the same time, they instilled in the scribe an upper and lower limit of value. Thus, capacity, weight, and area /volume all had a lower limit of 1/2 še and an upper limit of šar-gal or šar-gal šu nu-tag.70 This alludes to a related concept instilled with the metrological lists: a concept of granularity or the detail produced by a measurement value. Less granularity here described a decrease in fineness and increase in coarseness. Thus, 2 gin barley is of less granularity than 1 gin barley because it is more coarse and less fine. By listing measurement values on a vertical axis in order of decreasing granularity, metrological lists presented the relationship each measurement value had with all other measurement values within this system. At the same time, different measurement values could be appended together on the metrological lists to produce and illustrate finer granularity71 : 1(b a n 2 ) še 1(b a n 2 ) 1(d i š) s i l a 3 1(b a n 2 ) 2(d i š) s i l a 3 1(b a n 2 ) 3(d i š) s i l a 3 1(b a n 2 ) 4(d i š) s i l a 3 1(b a n 2 ) 5(d i š) s i l a 3 1(b a n 2 ) 6(d i š) s i l a 3 1(b a n 2 ) 7(d i š) s i l a 3 69

Following Middeke-Conlin (2020, 29–30). For the lower limit, see Ibid., 162–69. For the upper limit, see Chambon and Robson (2011) for the different interpretations. 71 Proust (2009, §8.1). 70

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2 At the Eduba 1(b a n 2 ) 9(d i š) s i l a 3 1(b a n 2 ) 8(d i š) s i l a 3 2(b a n 2 ) š e

Here granularity decreases between 1 and 2 ban—an increase in coarseness. However, at the same time, sila measurement values are appended to 1 ban measurement values to produce finer granularity of individual measurements between 1 and 2 ban.72 This kind of repetition is similar to the addition of qualifiers to words, such as the example provided with ‘kuš dug3 -gan’, “leather bags” in the list Ura. In the case of the metrological lists, this repetition aided in retention and simultaneously illustrated how the metrological systems worked globally. It’s clear from these lists that repetition and habituation were important means to assist in memorization and implementation. With gin measurement values, the author repeated fractions of values—1/3, 1/2, 2/3, and 5/6 gin twice. More often the same numerical values will appear over and over again, each time associated with a different measurement unit. This is similar to the repetition of entries seen with the lexical lists. Indeed, the entire gin section of the list of capacities is repeated almost verbatim in the weight list—the only parts lacking in the weight list are fractions of 2 gin. This is reminiscent of the repetition of signs and Sumerian words in the lexical tradition as described above. There are, then, similarities in the presentation of the thematic lexical lists and the metrological lists memorized at the same time.73 This is only to be expected: they were often part of the same education and produced in a similar intellectual environment. These form the topics of the next two chapters, starting with the intellectual environment in Chap. 3 and moving to the educational environment in Chap. 4.

References Cavigneaux, Antoine. 1976. Die sumerisch-akkadischen Zeichenlisten: Überlieferungs-Problems. Ph.D. Thesis, Ludwig-Maximilians Universität München. Chambon, Grégory. 2021. Écrire et (se) représenter les nombres en Mésopotamie. PASIPHAE : Rivista Di Filologia e Antichità Egee 15: 63–82. Chambon, Grégory., and Eleanor Robson. 2011. Untouchable or unrepeatable? The upper end of the Old Babylonian metrological systems for capacity and area. Iraq 73: 127–147. Civil, Miguel, R.D. Biggs, Hans Gustav Güterbock, and Hans-Jörg Nissen. 1969. The series l´u = sˇa and related texts. Materialien zum Sumerischen Lexikon 12. Roma: Pontificio Istituto biblico. Civil, Miguel. 1987. The Early History of HAR-RA: The Ebla Link. In Ebla 1975–1985 : dieci anni di studi linguistici e filologici : atti del convegno internazionale (Napoli, 9–11 ottobre 1985), ed. Luigi Cagni, 135–158. Napoli: Istituto universitario orientale, Dipartimento di studi asiatici. Civil, Miguel. 2020. Esbós de gramàtica sumèria/An Outline of Sumerian Grammar. Barcino Monographica Orientalia 14. Barcelona: Edicions de la Universitat de Barcelona. 72

See Middeke-Conlin (2020, 163–164) for granularity in the Old Babylonian metrological systems. These similarities are remarked on by Crisostomo (2019, 92) who already notes that metrological lists (and tables, see below) and thematic lists function similarly.

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References

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Crisostomo, C. Jay. 2019. Translation as Scholarship: Language, Writing, and Bilingual Education in Ancient Babylonia. Studies in Ancient Near Eastern Records 22. Berlin: De Gruyter. Delnero, Paul. 2016. Literature and Identity in Mesopotamia during the Old Babylonian Period. In Problems of Canonicity and Identity Formation in Ancient Egypt and Mesopotamia, ed. Kim Ryholt and Gojko Barjamovic, 19–50. Copenhagen: Museum Tusculanum Press and CNI Publications. Edzard, Dietz Otto. 2003. Sumerian Grammar. Handbuch der Orientalistik 71. Leiden: Brill. Englund, Robert K. 1998. Texts from the Late Uruk period. In Mesopotamien: Späturuk-Zeit und Frühdynastische Zeit, ed. Josef Bauer, Robert K. Englund, and Manfred Krebernik, 15–233. Freiburg and Göttingen: Universitätsverlag, Vandenhoeck and Ruprecht. Englund, Robert K., Hans-Jörg Nissen, and Peter Damerow. 1993. Die lexikalischen Listen der archaischen Texte aus Uruk. Archaische Texte aus Uruk 3. Berlin Gebr. Mann. Frahm, Eckart. 2011. Babylonian and Assyrian Text Commentaries. Origins of Interpretation. Guides to the Mesopotamian Textual Record 5. Münster: Ugarit-Verlag. Friberg, Jöran. 1993. On the structure of cuneiform metrological table texts from the 1st millennium. In Die Rolle der Astronomie in Kulturen Mesopotamiens, ed. Hannes D. Glater, 383–405. Graz: RM Druck-und Verlagsgesellschaft. Friberg, Jöran. 2007. A remarkable collection of Babylonian mathematical texts: Manuscripts in the Schøyen collection: Cuneiform texts. Ed. J.Z. Buchwald, J. Lutzen, and J. Hogendijk. Sources and Studies in the History of Mathematics and Physical Sciences 1. New York: Springer. Huenergard, J. 2000. A Grammar of Akkadian. Harvard Semitic Museum Studies 45. Winona Lake: Eisenbrauns. Lecompte, Camille. 2020. The measurement of fields during the Pre-sargonic Period. In Mathematics, Administrative and Economic Activities in Ancient Worlds, ed. Karine Chemla, and Cécile Michel, Why the Sciences of the Ancient World Matter 5, 283–344. Cham: Springer. Linder, Nadia. 2021. Continuity in change: Lexicon and hermeneutic system of the Old Babylonian Diri “Oxford” in the light of the archaic and early dynastic lexical material. In Signs—Sounds— Semantics—Nature and Transformation of Writing in the Ancient Near East, ed. Gabriel Gösta, Karenleigh Overmann, and Annick Payne, Wiener Offene Orientalistik 13, 117–159. Münster: Ugarit-Verlag. Michalowski, Piotr. 2006. The lives of the Sumerian language. In Margins of Writing, Origins of Cultures, ed. Seth L. Sanders, Oriental Institute Seminars 2, 159–184. Chicago: Oriental Institute of the University of Chicago. Middeke-Conlin, Robert. 2020. The Making of a Scribe: Errors, Mistakes, and Rounding Numbers in the Old Babylonian Kngdom of Larsa. Why the Sciences of the Ancient World Matter 4. Cham: Springer. Nissen, Hans J., Peter Damerow, and Robert K. Englund. 1993. Archaic bookkeeping: Early writing and techniques of economic administration in the ancient Near East. Chicago: University of Chicago Press. Nissen, Hans J., Peter Damerow, and Robert K. Englund. 2004. Informationsverarbeitung vor 5000 Jahren: frühe Schrift und Techniken der Wirtschaftsverwaltung im alten Vorderen Orient. Berlin: Verlag Franzbecker. Powell, Marvin A. 1987–1990. Maße und Gewichte. In Reallexikon der Assyriologie und vorderasiatischen Archäologie 7, ed. Erich Ebeling, Dietz O. Edzard, and Bruno Meissner, 457–530. Berlin: Walter de Gruyter. Proust, Christine. 2007. Tablettes mathématiques de Nippur. Istanbul: IFEA, De Boccard. Proust, Christine. 2009. Numerical and metrological graphemes: From cuneiform to transliteration. Cuneiform Digital Library Journal 2009 (001). http://cdli.ucla.edu/pubs/cdlj/2009/cdlj2009_ 001.html. Proust, Christine. 2020. Early-dynastic tables from Southern Mesopotamia, or the multiple facets of the quantification of surfaces. In Mathematics, Administrative and Economic Activities in Ancient Worlds, ed. Karine Chemla and Cécile Michel, Why the Sciences of the Ancient World Matter 5, 345–395. Cham: Springer.

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Robson, Eleanor. 2001. The tablet house: A scribal school in Old Babylonian Nippur. Revue D’assyriologie Et D’archéologie Orientale 95: 39–66. Rochberg, Francesca. 2016. Before Nature: Cuneiform Knowledge and the History of Science. Chicago and London: University of Chicago Press. Sallaberger, Walter. 2004. Das Ende des Sumerischen. Tod und Nachleben einer altmesopotamischen Sprache. In Sprachtod und Sprachgeburt, ed. Peter Schrijver and Peter-Arnold Mumm, 108–140. Bremen: Hempen Verlag. Spada, Gabriella. 2014. Two Old Babylonian model contracts. Cuneiform Digital Library Journal 2014 (002). https://cdli.mpiwg-berlin.mpg.de/articles/cdlj/2014-2. Taylor, Jon. 2005. The Sumerian proverb collections. Revue D’assyriologie Et D’archéologie Orientale 99: 13–38. Tinney, Steve. 1998. Texts, Tablets, and Teaching. Scribal Education in Nippur and Ur. Expedition. The Magazine of the University of Pennsylvania Museum of Archaeology and Anthropology 40 (2): 40–50. Tinney, Steve. 1999. On the curricular setting of Sumerian literature. Iraq 61: 159–172. Tinney, Steve. 2011. Tablets of schools and scholars: A Portrait of the Old Babylonian corpus. In The Oxford Handbook of Cuneiform Culture, ed. Karen Radner and Eleanor Robson, 577–596. Oxford: Oxford University Press. Van De Mieroop, Marc. 2015. Philosophy before the Greeks: The pursuit of truth in ancient Babylonia. Princeton: Princeton University Press. Vanstiphout, Herman L.J. 1997. School dialogues. In The Context of Scripture I: Canonical Compositions from the Biblical World, ed. William W. Hallo, 588–593. Leiden: E.J. Brill. Veldhuis, Niek. 1997. Elementary education at Nippur, the lists of trees and wooden objects. Ph.D., University of Groningen. Veldhuis, Niek. 2011. Levels of literacy. In The Oxford Handbook of Cuneiform Culture, ed. Karen Radner and Eleanor Robson, 68–89. Oxford: Oxford University Press. Veldhuis, Niek. 2014. History of the Cuneiform Lexical Tradition. Guides to the Mesopotamian Textual Record 6. Münster: Ugarit Verlag.

Chapter 3

The Old Babylonian Shift

Abstract The Old Babylonian period was marked by a major shift in knowledge. New lexical lists appeared in the scribal curriculum while a new system of quantification emerged, seemingly overnight—the so-called Sexagesimal Place Value Notation. These major developments in education appeared with changes in formatting as well as changes in sign and number shape. Education developed to accommodate these changes as well, adding new metrological and numerical tables that were employed in the scribal curriculum at the same time as the new advanced lexical lists were learned. The abrupt appearance of change is stunning to many observers, and deceptive: change did not occur overnight but was the result of long-term developments that took place over the prior century. While we often lack evidence for these developments, a concrete example of epistemic change over time does exist with the numeric tables of reciprocals. This shows the Old Babylonian shift was not some kind of revolution in knowledge but part of a long processes that resulted in the latest iteration of the vibrant cuneiform culture. Keywords Calculation · Tabular formatting · Writing · Epistemic change

The metrological lists and lexical lists appear in a backdrop of substantial intellectual change. Already, we saw a variety of new lexical and literary texts incorporated into the scribal education. This was part of a broadening of literary and lexical genres that is representative of a series of innovations that fundamentally changed cuneiform culture during and after the Old Babylonian period. In addition to changes to the lexical tradition, this period is marked by the advent of personal letters,1 omens, and mathematical problem texts, among others.2 There were also changes in format, changes in numerical notation, and changes in handwriting.3 The following 1

As opposed to the bureaucratic letters that existed prior to the Old Babylonian period. Veldhuis (2011, 72). 3 This follows and adds to Veldhuis’s discussion, where it is stated, “In the history of cuneiform writing and literacy the Old Babylonian period introduced many novelties and there is good reason 2

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. Middeke-Conlin, Knowledge, Literacy, and Elementary Education in the Old Babylonian Period, SpringerBriefs in History of Science and Technology, https://doi.org/10.1007/978-3-031-45226-0_3

33

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3 The Old Babylonian Shift

explores these developments, starting with sexagesimal place value notation (SPVN, Sect. 3.1), moving to changes in format with a discussion of tabular formatting (Sect. 3.2), changes in writing and numerical notations (Sect. 3.3), and then an example of developing change (Sect. 3.4). These changes were not top-down reforms. There is no evidence that some singular government imposed these changes on its population. Nor can they be described as a kind of “revolution” in knowledge.4 Instead, these were the results of scholars and practitioners interacting with each other over a long period of development, but this must be shown. First, it would be good to understand what this change looked like. In so doing, the intellectual environment in which lexical and metrological lists were exploited will become salient.

3.1 Sexagesimal Place Value Notation A good place to start this investigation of change is SPVN. SPVN is a sexagesimal system of numbers. Unlike the modern name implies, it is not a place value system. Like System S, it exploits an additive decimal structure in which ones, represented by the ‘diš’ sign, and tens, represented by the ‘u’ sign, are appended together to form a sexagesimal number, 1 through 59. Strings of these sexagesimal numbers are written on mathematical texts, sexagesimal components that appear one after another at varying lengths. In this work, SPVN is transliterated using diš and u signs and translated using Arabic numerals. A colon separates sexagesimal components from each other to represent the sexagesimal nature of the system. Thus, transliterated 3(u) 6(diš) 4(u) would be translated 36:40.5 An interesting aspect of SPVN is its distinct lack of any null marker like our modern ‘zero’ within, between, or after sexagesimal components. Lack of a null marker is significant because it shows the system was not employed to store mathematical content. For one thing, it could not represent magnitude. Instead, SPVN was a floating system, so to speak, that was largely limited to calculation. The number 36:40, for instance, could represent 36:40, 36:0:40, 36:0:0:40, 36:40:0, and so on.

to suggest that in this period the role of writing and literacy changed fundamentally. In the present context we may discuss three such changes: new genres; new formats; and a new writing style” (Ibid., 72). 4 See Kuhn (1962) for the concept of “scientific revolution”. 5 Transliteration here is not the common method to transliterate SPVN. Normally, transliteration and translation look the same so that 3(u) 6(diš) 4(u) would be transliterated 36:40 and translated the same. Significance of transliteration conventions becomes important later in this chapter, in Sect. 3.3, where normalization becomes important; Sect.3.4, when the date of a text renders the intended signs themselves uncertain; and then Chap. 5 especially when the very nature of the texts calls into question the intended system. Here, then, transliteration is more basic and less interpretive out of necessity. For more on transliteration and translation conventions, see most recently Chemla et al. (2022: 731–35).

3.1 Sexagesimal Place Value Notation

35

Fig. 3.1 Ni 18 edition and interpretation

Use of SPVN in the Old Babylonian period was limited to multiplication and multiplication by a number’s reciprocal to produce a division. It was never used to carry out a purely additive operation. When additive operations do occur, they are only part of a larger, multiplicative procedure. SPVN only very rarely appears on texts outside of those produced in an academic setting because its purpose was limited to calculation, while economic texts focus on the inputs and results of these calculations.6 SPVN allowed scribes and other professionals to efficiently multiply using dissimilar metrological systems, such as multiplying an amount of grain expressed using capacity measurement values by a price in silver expressed in weight measurement values to produce the total grain value in weight silver. To do this the scribe would transform each measurement value into an SPVN number before multiplication, carry out calculation using multiplication, and then transform the SPVN number into a measurement value after multiplication. Transformation and calculation are illustrated particularly well with a student’s exercise from the Old Babylonian city of Nippur, Ni 18 (Fig. 3.1). This text presents the calculation of an area out of two similar lengths.7 In Fig. 3.1 and elsewhere, a right facing arrow indicates the direction of the transformation. The length measurement value listed in the first line of the lower right-hand corner, 1/3 kuš 3 šusi, transforms into 2:10. This is multiplied by itself in the upper left-hand corner to mistakenly produce 4:26:40 instead of the expected 4:41:40. Two signs, ‘2(u)’ and ‘6(diš)’, make up the SPVN component ‘26’, instead of the expected ‘4(u) 1(diš)’ for ‘41.’ This shows that the product is a lapse in multiplication and not in writing. The production of a mistake in 6

See Middeke-Conlin (2020a, 114–117) for a discussion of SPVN in Old Babylonian economic texts. 7 Ni 18 was originally published in Proust (2007, 193) (translation) and pl. 1 (copy).

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3 The Old Babylonian Shift

multiplication illustrates that this text is probably not the product of a teacher. Instead, a student who was learning the scribal art carried out multiplication himself. In the lower right-hand corner, the incorrect SPVN product, rather than the expected SPVN product, was transformed into a measurement value. 4:41:40 should transform into 14 še 1/12th še, rather than the stated transformation. This proves that transformation was performed by the student. The author of Ni 18 is not recording the answer from another tablet or recitation but produced the answer himself. A final mistake occurs with transformation: we expect 13 še one-3rd še from the stated 4:26:40, but instead see 13 še one-4th še. This final mistake shows that transformation was a difficult skill that the aspiring scribe had to practice.8 Ni 18 shows that both transformation to and from SPVN as well as multiplication using SPVN were skills learned in scribal schools.9 Numerical tools were memorized to facilitate multiplication in SPVN. At the same time as students began memorizing the advanced sign list Ea/Aa, students also began memorizing the numerical tables, starting with reciprocals, moving to multiplication tables, and then a table of squares, square roots, and cubed roots.10 Numerical training began with the study of the table of reciprocals.11 These numbers were considered vital to computation using SPVN because division did not exist yet as a distinct mathematical procedure. Instead, scribes multiplied by a number’s reciprocal to produce the same. Figure 3.2 illustrates the Old Babylonian table of reciprocals from Nippur.12 This table presents reciprocal pairs, written ‘igi n gal2 -bi y’, translated here “the reciprocal of n is y”. Thus, “the reciprocal of 2 is 30”, means that 2 multiplied by 30 is 1.13 In many cases texts are plainer, starting with the first two lines of the full text, but then listing the number in one column and its reciprocal in the next column as illustrated in Fig. 3.3. Movement is from left to right and is reversable. The table also moves vertically, starting with 1, then 2, and so on to 1, marking a complete sexagesimal cycle, before moving on to 1:4, and 1:21.

8

For more on this transformation, see Middeke-Conlin (2020a, 162–169). For more on the pedagogical function of this and similar tablets, see De Varent (2022). Summarizing the didactic tasks on Ni 18, De Varent states (p. 49): “In summary, this tablet allows us to encounter new sub-tasks, compared to previous tablets. Providing a correspondence for 1 kuš 3 šusi is done by interpolation, in two steps, and involves paying attention to the position of the number obtained in SPVN (positioning). The use of non-elementary multiplication involving an algorithm was also not encountered in tablets 1 and 2. Providing a correspondence for the number 4:41:40 in SPVN is done by a two-step interpolation and involves the circulation from one cycle to the preceding one, based on the sexagesimal positions (positioning). This implies a risk of error, which is new in our selection.” 10 Proust (2007, 118) for Nippur. Proust notes that the first three, reciprocals, multiplication tables, and squares, are assembled in this order on the tablet Ni 2733, as well as HS 202a and HS 209. 11 The following relies on ibid., 118–125. 12 See ibid., 120 for this table. 13 This is only one possible translation. For additional translations and interpretations of these sentences, see ibid., 118–19. 9

3.1 Sexagesimal Place Value Notation

37

Fig. 3.2 The Old Babylonian table of reciprocals

Fig. 3.3 Incipit of abbreviated reciprocal table

All numbers on these tables were what may be called regular numbers. That is, each number multiplied by itself, produces SPVN 1. Several numbers did not have so easily defined reciprocals. Numbers such as 7, 11, 13, and 14 may be called non-regular numbers. In so far as the Old Babylonian scribe was concerned, these numbers did not have a reciprocal with a finite number of sexagesimal places and

38

3 The Old Babylonian Shift

therefore were defined as “igi-nu”, “no reciprocal”. The problem revolved around the necessity to work with a finite number of sexagesimal components that could be written down. While the calculation of a non-regular number’s reciprocal resulted in a periodical sexagesimal number, there is neither evidence that the Old Babylonian scribe had a concept of periodicity, nor a differentiation between periodical and nonperiodical sexagesimal developments (that is, rational and irrational numbers), nor an interest in pursuing either concept. Instead, the Old Babylonian scribe sought approximations, often truncating a sexagesimal reciprocal to a usable component or rounding to a regular number.14 Most of the numbers found on the reciprocal tables also appear as “head numbers” in the Old Babylonian mathematical tables.15 The head numbers served to define each table, from 50 to 1:15 in descending order as follows: 50→45→44:26:40→40→36→30→25→24→22:30→20→18→16:40→16→15→12:30 →12→10→9→8:20→8→7:30→7:12→7→6:40→6→5→4:30→4→3:45→3:20 →3→2:30→2:24→2→1:40→1:30→1:20→1:15

The head numbers are somewhat enigmatic because it’s uncertain why they were chosen. Only fourteen multiplication tables were necessary for any calculation: the tables for the multiples 1 through 10, then 20, 30, 40, and 50.16 However, in the Old Babylonian period, at Nippur and elsewhere, aspiring scribes memorized 38 multiplication tables. Six more tables were useful in doubling operations: 22:30 is half of 45, 12:30 is half of 25, the number 7:12 is the reciprocal of 8:20, which is 2:5 multiplied by 22 , and finally half of 9 is 4:30.17 Doubling exercises were one of several common tropes from the more advanced mathematical curriculum, for which the multiplication tables seem well designed to prepare the student.18 As Robson sums up, “the set of multipliers appears to have been assembled because it gives good coverage of the numbers most likely to be used by scribes in their everyday arithmetical work.”19 Figure 3.4 offers an example of a multiplication table with the head number 4. Multiplication tables, like the reciprocal tables and the lexical lists, are organized vertically, listing one number after another in a list-like manner. Like the reciprocal table, there is also a horizontal axis on which calculation moves to the right, however calculation is not reversible. Like the tables of reciprocals, these tables also had abbreviated forms that highlight this movement (Fig. 3.5). 14

For this, see Høyrup (2002, 297–298) for a discussion of irrational and rational non-regular numbers and Middeke-Conlin (2020a, 195–197 and 231–233) for the approximating non-regular numbers. 15 The use of reciprocal and multiplication tables are treated as tasks in calculation most recently by De Varent (2022). 16 Proust (2007, 130). 17 Ibid., 131. 18 For doubling exercises and other geometric suites, see Proust (2007, 176–181). See Friberg (2007, 87–97) for more examples of how the multiplication tables prepared students for mathematical practice. 19 Robson (2001, 196).

3.1 Sexagesimal Place Value Notation Fig. 3.4 Edition of the table of multiplication on YBC 11,92420

Fig. 3.5 Incipit of abbreviated multiplication table

20

For YBC 11,924, see Robson (2004a, 15–16).

39

40

3 The Old Babylonian Shift

At Nippur, multiplication tables were memorized at the same time as the advanced sign and acrographic lists were being memorized and were preceded by memorizing reciprocal tables. The multiplication tables were memorized in decreasing order based on their head numbers. Thus, the multiplication table of 50 was memorized before the table of 45, which was memorized before the table of 44:26:40 and so on.21 Memorization of numerical tables continued with the tables of squares, just as students concluded memorizing the acrographic lists. Square roots and cubed roots were memorized just as students began memorizing their proverbs and model contracts at Nippur. Shortly after, students began practicing basic mathematical exercises such as the calculation of squares from length measurements presented in Fig. 3.1.22 Transformation was vital to calculation with SPVN, but, as shown with Fig. 3.1, it was a difficult process that required practice. It’s possible the Old Babylonian scribes saw transformation as something akin to a mathematical operation when calculating using SPVN.23 These transformations were facilitated by memorizing metrological tables such as those illustrated in Fig. 3.6.24 Metrological values appear on the left of the tablet while SPVN transformations of these measurement values appear on the right. Similar to the metrological lists, the metrological tables present an upper and a lower limit to metrological value, while granularity is illustrated by means of the linear order of metrological values. While granularity decreased, associated SPVN numbers moved from 1 through 59 and back to 1 again in a constant cycle. This is illustrated right away in Fig. 3.6 with the first six numbers: Granularity decreases from 1/2 še to 1 še, 1 1/2 še, 2 še, 2 1/2 še, and then 3 še. At the same time SPVN numbers move cyclically from 10 to 20, 30, 40, and 50, to return to 1. Between 3 še and 1 gin, representing an increase in coarseness, another SPVN cycle occurs. Like with lists, metrological values are appended to each other to produce finer granularity of individual measurements. This is especially seen in Fig. 3.6 when 10 še is appended to one-6th gin and 5 še is appended to one-4th gin. At the same time SPVN 3:20 is appended to 10 and 1:40 is appended to 15 to produce the SPVN transformations of 13:20 and 15:40 respectively—an increase in SPVN digits. While students practiced constructing measurement value, they practiced construction of SPVN numbers. This practice reinforced a link between measurement value and SPVN number—the transformation that was so important and so difficult to master.25 Such practice introduced students to SPVN and connected these SPVN numbers to 21

Proust (2007, 147). Ibid., 152. 23 For a discussion of SPVN and transformation as a mathematical process, see Middeke-Conlin (2022), especially 386–388. For discussion of it as a learned task, see De Varent (2022, 43–46). For the metrological lists and calculation, see Middeke-Conlin (2020b). The latter two build on concepts presented in Proust (2007, 244–251). 24 For Ashm 1923–410, see Robson (2004a, 22–23). For HS 242 from Nippur, see Hilprecht (1906, pl 21) (no. 32) and Proust (2008, pl 18) (no. 26). 25 The production of value and SPVN numbers in metrological lists is examined in Middeke-Conlin (2020a, 162–64). 22

3.1 Sexagesimal Place Value Notation

41

Fig. 3.6 Metrological table of weight on HS 242 and Ashm 1923–410

specific measurement values.26 The example of 3 še transforms to 1 in SPVN shows that transformation does not necessarily produce a one-to-one movement between 26

Proust states as much, pointing out concerning metrological tables, that ‘The issue of the respective pedagogical function of metrological lists and tables has not been exhaustively described. (…) Whatever their precise role in the curriculum may have been, metrological tables provided future scribes with two fundamental notions that are new in relation to the lists: the sexagesimal

42

3 The Old Babylonian Shift

metrological value and SPVN number. Metrological values were constructed first, over a thousand-year period, while the SPVN numbers were associated with these values sometime by the Old Babylonian period, perhaps during or just prior to the Ur III period.27 One needed familiarity with the metrological lists to truly understand the art of transformation. This was an advanced skill and so metrological tables were memorized in an advanced phase of elementary education. As scribes were in the process of memorizing acrographic lists, in particular when they were memorizing the list Izi, scribes also began memorizing the metrological table for capacity. Memorizing the capacity table was roughly concurrent with the memorization of the metrological list of lengths as well and was followed by the memorization of the table for weight, area and volume, length, and then a new table for height.28 Again, repetition was vital to memorizing lists. Again, organization techniques foster repetition like those witnessed with metrological lists as well as the thematic and acrographic lists: repetition of numerical values with metrological units, repetition of entire sections of the tables (especially gin measurement values), and appending measurement values to measurement values to increase fineness. This time, however, the appending could result in more associated SPVN digits. Habituation, a result of such repetition, afforded implementation into mathematical practice.

3.2 The Tabular Format With this change in computation came an increase in the use of the tabular format. This format is not an invention of the Old Babylonian scribes. For instance, five tables for square and rectangular areas have come down to us from the Early Dynastic period sites of Šuruppak, Zabalam, and Adab.29 A couple of texts take on a tabular format in the Ur III period, probably either student practice or initial drafts.30 If the latter, place value notation and a correspondence between the measurement values and these positional numbers.’ (Proust 2009, Sect. 4.1). 27 See below, Sect. 3.4 for this. 28 See Proust (2007, 144–156, 255–262, and 267–276), especially pages 152, 263 and Tableau 5 on p. 273. Crisostomo (2019, 192–194) supports and refines Proust’s findings, stating that, “Table P is never reviewed on the reverse of an Izi exemplar. It is probable, then, that metrological tables C and P and Izi were studied more or less concurrently. A student might begin learning Izi, even completing Izi I, and then begin learning these particular tables. Sometime before finishing Izi II, the student would review the metrological lists and tables.” (Ibid., 193) While Proust sees the metrological tables as commencing with capacity around the memorization of thematic lists are winding down, her data affords the potential that, in the majority of cases, memorization of metrological lists commenced around the memorization of Izi. See especially Proust (2007, 272–273) for this data. 29 These tablets are, by location, VAT 12,593 (Šuruppak), MS 3047 (Šuruppak? ), Feliu (2012) (Zabalam? ), CUNES 50–08-001 (Zabalam? ), and A 681 (Adab? ). See Proust (2020) for a recent study of these texts. 30 Robson (2004b, 118–9), discussing Ashm 1910–759 (published as TAD 42 and appearing in MKT I: 82; Grégoire (1996, pl. 17).

3.2 The Tabular Format

43

this alludes to the interesting possibility that drafts, taking on a tabular format, were common in the Ur III period—perhaps using some kind of writing board.31 If the former, this would mark elusive evidence for scribal formation in the Ur III period.32 In any event, tabular formatting took off in the Old Babylonian period, becoming an acceptable format for presenting administrative and economic data.33 Early, in Old Babylonian Nippur alone, over 420 administrative texts in one archive, the šattukku archive, took a tabular format.34 By the reign of R¯ım-Sîn of Larsa and then Hammurabi of Babylon, the tabular format was used to plan irrigation works35 and administer land use.36 The tabular format also took a new role in education, appearing as a means to illustrate a link between metrological values and SPVN numbers, numerical relationships such as the multiplication tables witnessed above, or basic mathematical practice. This latter is especially well represented in texts from the city of Ur, where numerical exercises were written down using a tabular format, devoid of any stated problem. See Sect. 4.2.2 for this. There is a link between tabular layout and mathematical reasoning witnessed in both the mathematical tradition and in administrative texts.37 Prior to the Old Babylonian period texts were almost exclusively arranged in a prosaic format. In a prosaic format, information moves in a linear, prose-like list. In contrast, a tabular format separates data along at least two axes. Here we speak of a formal table, which utilizes horizontal and vertical rulings to separate information categories, as well as an informal table, which separates information categories by spatial arrangement alone. Tables can also be headed, that is, when the information in each column are described in a statement, typically above it or at the column’s ‘head’, or they can lack this and be called unheaded tables.38 The numerical and metrological tables mentioned above are unheaded, informal tables. In each table, information moves along two axes, while calculation moves along one axis. For instance, with the metrological tables, transformation occurs along one axis in which granularity decreases. Corresponding SPVN cycles change along a second axis as seen in Fig. 3.7. In Fig. 3.7, linear movement between measurement values and SPVN cycles occurs along vertical axis 2 while a two-way calculation, transformation, occurs horizontally along axis 1.39 31

Robson (2008). Education, is suggested but in no way confirmed by the appearance of conspicuously round numbers, while as shown in Sect. 4.3, the appearance of a dates on these texts do not preclude their educational utility. 33 Robson ( 2004b, 119). 34 See Sigrist (1984) for this archive. More recently Brisch has taken up this archive with the intent of a full publication. See most recently Brisch (2017). 35 Middeke-Conlin (2020c). 36 This is especially seen in the texts used to administer land in the kingdom of Larsa after Hammurabi’s conquest. See Fiette (2018) for a comprehensive study of these texts and the administration of land, especially his Annexe (pp. 325–363). 37 Middeke-Conlin Forthcoming. 38 These definitions follow Robson (2004b, 116). 39 This is presented in Middeke-Conlin Forthcoming. 32

44

3 The Old Babylonian Shift

Fig. 3.7 Arrangement of data in metrological tables

With multiplication tables movement is again along two axes (Fig. 3.8). Axis 1 moves horizontally while axis 2 moves vertically in these tables as well. In axis 1, the head number or multiplicand is an initial data point. Multipliers occur after these numbers on the table, followed by the product. Only the first line states the multiplicand, while the remaining lines omit this number. Thus, calculation is linear in one direction. Movement occurs along a second axis in a linear manner as well. Multipliers and their related products are presented based on their relative location within SPVN cycles moving in a list-like manner. Finally, with the reciprocal tables (Fig. 3.9) there are, again, two axes of movement and, again, only one axis of calculation. Calculation, that is reciprocal extraction, occurs horizontally in the first axis. Each number appears on the left of the table, each reciprocal appears on the right of the table. Reciprocal extraction can occur in both directions on these tables so that, like the metrological tables, it’s possible to suggest a reversable calculation. The second axis appears on a vertical plane as a means to arrange data. Like multiplication tables, movement along axis two in the reciprocal tables is in a linear, list-like manner based on each number’s appearance in their respective SPVN cycles.

3.2 The Tabular Format

45

Fig. 3.8 Arrangement of data in multiplication tables

Each of these is a table because data is arranged along multiple axes while information is clearly separated spatially. Calculation occurs along a horizontal axis while the vertical axis serves to arrange data in a linear manner without calculation. Underlying these linear arrangements are decreased granularity between measurement values in the metrological tables, and SPVN cyclical arrangements in the metrological and numerical tables. A similar, horizontal movement of activity as well as a logical, vertical arrangement of this activity unify lexical lists and the mathematical tables. The lexical lists arrange translation horizontally, explicitly when glosses are present and implicitly when glosses are provided orally, while mathematical texts arrange calculation horizontally. Connection between these individual points of activity is made vertically and based on logic local to each tradition: theme, sign shape, or sound in the lexical tradition and the arrangement of metrological or numerical relationships in the mathematical tradition. Medium is important at this point. In many cases glosses do not appear on lexical texts but instead are implicit, they were presented orally. Tabular mathematical texts represent activity on a physical horizontal axis similar to lexical translation represented orally with occasional written glosses. Tabular arrangement in the metrological and numerical tables is used to physically embody an otherwise oral arrangement. Layout makes explicit connection without necessary recourse to orality. At the same time, orality in the lexical tradition, spoken glosses to present meaning, is just as powerful in establishing connection as the tabular arrangement in the mathematical tradition. The quasi-oral lexical list and tabular mathematical list

46

3 The Old Babylonian Shift

Fig. 3.9 Arrangement of data in reciprocal tables

represent a similar method of reasoning; medium is the primary difference, perhaps because mathematics was perceived physically. Physicality is embodied in the cutand-paste geometry that takes firm shape in the Old Babylonian Period.40 More importantly, Babylonian mathematics is emblematic of an abacus culture in which numbers would be arranged physically in rows and columns for manipulation.41 A physical, tabular format would be intuitive in this environment. The lexical tradition was an embodiment of orality so that oral format of translation was intuitive. A kind of reasoning begins to appear, codified by the Old Babylonians, a reasoning that permeates translation and mathematics. This reasoning is made explicit with the tabular format but is implicit with the lexical lists when translation is safely assumed and especially when glosses are stated. In this reasoning, activity is representable as a horizontal motion while unity is applied vertically. 40 41

Høyrup (2002). Proust (2000), Netz (2002), Middeke-Conlin (2020a, 121–138).

3.3 Signs and Numbers

47

Table 3.1 Normalized and non-normalized numbers Number 4

Normalized

Non-normalized

7 8 9 40

or

50

or

3.3 Signs and Numbers Change permeated the most basic aspects of cuneiform writing as well: The shapes of numbers and signs. While SPVN was being developed and tabular formatting explored, scribes were experimenting with the shape of numbers. During the Old Babylonian period, what modern Assyriologists call “normalized numbers” begin to appear in texts along with “non-normalized numbers”.42 Non-normalized numbers are an older form of writing, a cumulative-positional system of expression in which wedges appear in up to two rows of up to five wedges. In this mode of representation, 9(diš) appears as an upper row of five wedges and a lower row of four wedges, while 4(diš) appears as two rows of two wedges each. These numbers often enumerate value in economic texts. Normalized numbers are a later development, typically used to express SPVN numbers, but later in the Old Babylonian period it occasionally enumerates value within economic texts. In this mode of numerical expression, numbers appear in up to three rows of three wedges. For instance, ‘9(diš)’ appears as three rows of three wedges, while 4(diš) appears as one upper row of three wedges and one wedge in a lower row. The distinction between non-normalized and normalized is visible with the numbers 4, 7, 8, 9, 40, and 50 as expressed with clusters of the wedge signs diš, geš2 , aš, and u. Table 3.1 illustrates this distinction. To illustrate the extent of normalization, a superscript ‘n’ will appear next to numbers that attest to normalization from this point in the work. The advent of normalized numbers reflects a move to more rapid recognition of numbers, against the more formal, established non-normalized numbers. This hypothesis relies on the three-by-three layout of wedges in normalized numbers and the human ability to appreciate small quantities. Very small quantities, from one though three, occasionally four, are perceptually salient. A scribe could look at a set of wedges and know it was three or occasionally four without need to count. This ability is called subitization. Any quantity greater than the subitization range needs to be counted.43 Thus, a scribe could recognize three or four wedges, but anything above needed to be counted. The arrangement of wedges into subitizable groups, that is rows and columns of up to three wedges, may have been a move 42 43

Following a distinction made in Oelsner (2001, esp. 54). This is well described in Overmann (2019, 15–16).

48

3 The Old Babylonian Shift

to facilitate easier recognition of numbers. A skilled scribe could see normalized numbers four through nine and know the intended statement. One could see 40 and 50 and know the same. The scribes of this period experimented with layout and came up with the optimal arrangement of numbers to express meaning. This would have been an initial move from the cumulative-positional system of third millennium cuneiform numbers towards a symbolic positional notation—a kind of proto-symbolic number.44 Through habituation, the skilled scribe, like the skilled Assyriologist today, could probably look at normalized 7 and normalized 9 and know that seven and nine wedges were written without need to count. However, the leap to symbolic notation was not made at this time; there was still recourse to count some or all wedges by the less skilled.45 This change in the shape of numbers occurred along with a general change in the shape of signs. By the Old Babylonian period a kind of cursive script appears. Prior to the Old Babylonian period, in the Ur III period, signs appear as a semimonumental script. In most instances this script is difficult to distinguish from monumental scripts.46 The cursive script that appears in the Old Babylonian period, however, was much more simplified, presenting an abbreviation to the very basic form necessary to convey meaning. At the same time, writing is much more crowded than in the Ur III period. This abbreviation betrays a preference to ease of writing. The development of a cursive indicates a more utilitarian approach (one that puts less emphasis on writing as a symbol of power) but at the same time requires a more intimate familiarity with written texts, a type of literacy that can do away with the kind of tiny details that used to clearly distinguish one sign from another in earlier phases of writing. The introduction of a cursive in the Old Babylonian period may be understood as indicative of a wider availability of functional literacy in the Old Babylonian period.47

At the same time a monumental form of writing similar to Ur III writing continued to exist in the Old Babylonian period. Monumental inscriptions from the Old Babylonian period and later tended to archaize sign forms for prestige. Scribes had the choice between the extent of their cursive hand and the formality of their hand.48 Table 3.2 provides illustrations of the semi-monumental form common in the Ur III period, the monumental form common to the Old Babylonian period, and one cursive form of the signs AN, DU, and ŠEŠ.49 One can wonder why this change to cursive did not occur in the highly bureaucratized kingdom of Ur. The Ur III period is very well documented, with tens if not hundreds of thousands of administrative texts representing a highly intrusive bureaucratic apparatus. Yet even with the numerous, formulaic administrative texts there 44

Symbolic notation as compared with cuneiform numbers is discussed in Overmann (2019, 201– 206). However, Overmann does not go so far as to call this kind of notation “proto-symbolic”. 45 As is stated by Overmann (2019, 204), who goes further to state that such “cyphered forms like 4, 7, and 9 would ultimately develop, but well after the cuneiform era had ended.” 46 Veldhuis (2012, 12). 47 Veldhuis (2011, 72). 48 Veldhuis (2012, 12). 49 Forms from Labat (1988) and Mittermayer (2006).

3.4 Change

49

Table 3.2 Ur III and Old Babylonian sign forms Sign

Ur III

Old Babylonian Monumental

Old Babylonian Cursive

AN DU ŠEŠ

was no tendency towards the cursive writing seen in the Old Babylonian period. The same can be said of normalized and non-normalized numbers. When the very rare normalized number appears on an Ur III administrative document, it is at the margin, detached from the text itself.50 This is perhaps because writing was a representation of officialdom in the Ur III period, whereas it was much more democratized in the Old Babylonian period, affording a greater variety and simplification of sign shape as well as a tendency towards crowding and unclear sign boundaries. This innovation benefited those who had to write a greater volume of texts.51 While numbers became easier to read, texts themselves were becoming easier to write. Perhaps both can be seen as part of a rapid democratization of literacy, a literacy that developed and altered writing in order to accommodate a large influx of persons able to participate more intensively in the economy.

3.4 Change While the influx of participants may have been rapid, all of these changes did not appear overnight. They were the latest developments in long-term shifts that took place prior to or during the Ur III period and into the Old Babylonian transition. These changes can be difficult, if not impossible, to chart in a textual record that is often broken. The advent of new lexical lists, for instance, seem to appear out of nowhere. The same can be said for many of the mathematical texts. However, we do see traces of changes. The reciprocal tables, for instance, illustrate the development of all three changes highlighted in this chapter: the development of SPVN, the shift from prosaic to tabular formatting, and paleographic change. Reciprocal tables are not new to the Old Babylonian period. In fact, the development of these tables, the advent of SPVN, and the introduction of normalized numbers can be traced from the Ur III period, into the Old Babylonian transition, through the early Old Babylonian period, until they appear as mature tables in the

50 51

Ouyang and Proust (2022). Veldhuis (2012, 12 and 2011, 71).

50

3 The Old Babylonian Shift

middle of the Old Babylonian period.52 Firm evidence for the use of SPVN starts in the Ur III period. Around the time that place value notations show up on the margins of some administrative documents,53 several tables of reciprocals appear: HS 201 and Ist Ni 374 from Nippur ; Ist L 7375, Ist L 9006, and Ist L 9008 from Girsu; and SM 2685 of uncertain provenance.54 These tables are described in Table 3.3 here.55 Table 3.3, like all tables in this section, serves to sum up the reciprocal tables. Organization is by provenance and then tablet number in the first two rows. In the next row the number of columns used to present each text and whether they appear on one side or both sides of the tablet are stated. The condition of each tablet is described next, followed by the first and then last entry in each text in transliteration, or a reconstruction of these entries. Finally, the entry and then number formats are summed up in the last two rows. HS 201 lists integer numbers followed by the sign “igi”, “reciprocal”, and then each number’s reciprocal when available to the scribe. Ist Ni 374 lists the sign “igi”, followed by each integer number and its reciprocal. While the obverse is largely lost, Ist L 7375 clearly listed integer numbers and then their reciprocal. In all three texts, when the number is non-regular, the word “nu”, meaning “no” or “does not exist”, appears. In all three tables, numbers are non-normalized. These texts are found on well-crafted tablets that exhibit a fine hand. However, there is little uniformity between the texts. They are, in all likelihood, the work of scholars, not students, who are working out these tables and SPVN calculation in general.56 The representation of numbers on the tablet SM 2685 deserves particular attention in this regard.57 SM 2685 cannot be attributed to a particular scribal center. In this text, each integer number is preceded by the sign “igi” and followed by the signs “gal2 bi”, while each row concludes with either the number’s reciprocal or approximate reciprocal. Like the prior three tablets, numbers are non-normalized. However, with SM 2685 numbers occur with fraction signs, 1/3, 1/2, 2/3, and 5/6, as illustrated 52

This has been done by several authors on which this discussion relies, including most recently Oelsner (2001), Robson (2003/2004), Proust (2008, 19–21), Friberg (2009, § 4), Friberg and al-Rawi (2016, 487–518), and then Ouyang and Proust (2022). 53 See Ouyang and Proust (2022) for this phenomenon. See also ibid., 269–71 for the possible antecedents of SPVN well before the Ur III period. 54 HS 201 appears in Oelsner (2001, 56–57 (transliteration and commentary), 58 (photo), and 59 (copy). Ist Ni 374 is published in Proust 2007, 125–128 and pl. 1. Ist L 7375 is mislabelled Ist. T 7375 in MKT 1: 10. It appears first in Delaporte 1911. Ist L 9006 and Ist L 9008, are discussed by Proust 2008, 19 and then Friberg and al-Rawi (2016, 506). SM 2685 is published in Friberg and al-Rawi (2016, 487–490). For these texts, see Friberg 2007, 356; Friberg 2009, 4.2.1.; and especially Friberg and al-Rawi (2016, 499). 55 The first line of SM 2685 is based on Friberg and al-Rawi’s reconstruction (Friberg and al-Rawi 2016, 488–489). The final line of Ist Ni 374 is according to Friberg and al-Rawi (2016, 518) and based on Proust’s copy (2007, pl 1). 56 See Proust 2008, 20–21. 57 Discussion follows edition of the SM 2685 in Friberg and Al-Rawi (2016, 487–490).

Ist Ni 374

SM 2685

1 column, 2 sides

Tablet number

Columns

[igi 1(diš) 4(u) 3(u)] 6(diš) / [igi 2(diš) 5(diš) 2(u) 8(diš)] 4(u) 8(diš)

igi n n' ; igi n nu

igi 1(diš/geš2 ) 2(u) 1(diš) gal2 -bi 2/3[…]

igi n-gal2 -bi n'

Non-normalized

Last lines

Entry format

Number format

Damaged

Non-normalized

[1(diš/geš2 )-da igi 2(diš)] / [gal2 -b]i 3(u)

Damaged

[igi 1(diš) 1(u) 2(diš)-gal2 -bi 5(u)]

Condition

First line

2 columns, 2 sides

Nippur

Uncertain

Provenance

Table 3.3 Reciprocal tables from the Ur III period

Non-normalized

n igi n' ; n igi nu

3(u) 1(diš) igi nu/3(u) 2(diš) igi 1(diš) 5(u) 2(diš) 30

[1(diš/geš2 )]-da igi 2(diš) / [g]al2 -bi 3(u)

Damaged

2 columns, 1 side

HS 201

Non-normalized, fractions

n igi n' ; n igi nu

1(diš) la2 1(diš) igi nu/ 1(diš) igi 1(diš)

2(diš) [igi 3(u)]

Damaged

2 columns, 2 sides

Ist L 7375

Girsu

Non-normalized

n igi n' ; n igi nu

broken

2(diš) igi 3(u)

Damaged

2 columns

Ist L 9006

Non-normalized

n igi n' ; n igi nu

broken

broken

Fragments

2 columns

Ist L 9008

3.4 Change 51

52

3 The Old Babylonian Shift

Fig. 3.10 Incipit of SM 2685

in the accompanying incipit (Fig. 3.10). Thus, there appear statements like, “igi1(u) 2/3-gal2 -bi 5(diš) 1/2 7(diš) 1/2”, in line 29' . This translates to “the reciprocal of 10 2/3 is 5 1/2 7 1/2”, which can be understood as “the reciprocal of 10:40 is 5:37:30” when transformation into mature SPVN is applied.58 The approximate reciprocal of 7, which is a non-regular number, is probably defined as 8 1/2 4 in line 21' , or 8:34 when transformation into mature SPVN is applied.59 While value relative to the whole is defined with this statement by means of fractional values, a certain amount of abstraction is obtained in these texts in that they are not constrained by any metrological value.60 These tables, then, exhibit an early development of SPVN and show innovation in how numbers were conceived in terms of mathematical processes: they were no longer conceived as necessarily connected to one or several specific metrological or numerical systems. Intermediate tables, probably dating to the transition from the Ur III to the Old Babylonian period and then the Early Old Babylonian period, also exist (Table 3.4). These tables express the beginning of a shift to normalized numbers on the numerical tables as well as a change in the shape of tablets. For instance, Erm 14,645, BM 106425, and Ist L 9007 + 9005, perhaps dated to late in the Ur III, period bear witness to the advent of the normalized number “40”.61 In all three texts, the number 40 is written in both non-normalized and normalized forms. Normalized 40 consistently appears in the reciprocal column of all entries of both texts, while normalized 50 appears in the reciprocal column on BM 106425 and Ist L 9007 + 9005.62 All other

58

This is according to Friberg and al-Rawi (2016, 489–490). The exact reciprocal is uncertain because of a break in the text, but Friberg and al-Rawi’s restoration is quite likely. Friberg and al-Rawi note that 7 multiplied by 8 1/2 4 would produce 59 1/2 28. (Friberg and al-Rawi 2016, 490). 60 This is highlighted by Friberg and al-Rawi (2016, 510). 61 For Erm 14,645, see Friberg 2009, Fig. 8. BM 106425 was published together with the reciprocal table BM 106444 in Robson 2003/2004. Both texts were attributed by her to the Ur III period. For Ist L 9007 + 9005, see Friberg and al-Rawi (2016, 504). BM 106444 is published in Robson 2003/ 2004, 356. 62 Note that, as Friberg and al-Rawi point out, “a difference between the two tables of reciprocals is that the line 1(60).da 2/3 40 in RA 12, 197 has no counterpart in BM 106425, which instead begins with the line [1(60)].da igi.2.gál 30.” (Friberg and al-Rawi 2016, 503). 59

3.4 Change

53

Table 3.4 Reciprocal tables from the Ur III period transition into the Old Babylonian period Provenance

Umma

Tablet number

BM 106444

Girsu

Uncertain

Ist L 9007 + 9005 Erm 14,645

BM 106425

Columns

1 column, 2 sides

1 column, 2 sides 2 columns

1 column, 2 sides

Condition

good

good

Worn

First line

1(diš/geš2 )-da igi 1(diš/geš2 )-da igi broken 2(diš) gal2 -bi 3(u) 2(diš) gal2 -bi 3(u)

[1(diš/geš2 )]-da igi 2(diš) gal2 -bi 3(u)

Last lines

igi 2(diš) 5(diš)-bi igi 1(diš) 2(u) broken 1(diš)-bi 4(u)n 2(u) 8(diš) 4(u) 8(diš) 4(diš) 2(u) 6(diš) 4(u)n

igi 1(diš) 2(u) 1(diš) 4(u)n 4(diš) 2(u) 6(diš) 4(u)n

Entry format

igi n-bi n'

Number format Non-normalized, fractions

Fragments

igi n-bi n'

n igi n'

igi n n'

Mixed (normalized 40 and 50, reciprocal column)

Mixed (normalized 40 and 50, reciprocal column)

Mixed (normalized 40, reciprocal column)

numbers are non-normalized. Moreover, with both BM 106444 and BM 106425, additional entries appear, similar to SM 2685, including two fractional values: i g i 7 1/2-b i

8

And i g i 8-b i

71/2

When normalized numbers are limited to the reciprocal column, it may be assumed that the tabular format did not represent calculation in both directions, only one direction: from the integer number to its reciprocal. BM 106425 probably appears late in the Ur III period, when normalized numbers are beginning to appear in mathematical texts themselves, not on the margins, but while fractions can still appear to provide a value relative to the whole number. The appearance of fractions shows that SPVN as a system for calculation itself was still being worked out. Perhaps numbers were still associated with value and so transformation was an imperfect concept at this point. By the transition into the Old Babylonian period a movement toward normalizing numbers in mathematical texts began to take shape. At the same time, SPVN as a concept was evolving and transformation as a procedure was being debated. RA 12, 197, MS 3874, Ist Ni 10,235 + 2854, and SM 2574 perhaps date to early in the Old Babylonian period (Table 3.5).63 All texts exhibit intensified use 63

RA 12, 197 was published by Scheil 1915, who first points to the variant form of 40 in this text. MS 3874 appears in Friberg 2007, 69. Ist Ni 10,235 + 2854 is published in Proust 2007, pl 48. Finally, SM 2574 is presented in Friberg and al-Rawi (2016, 500–502).

54

3 The Old Babylonian Shift

Table 3.5 Reciprocal tables from the Early Old Babylonian period Period

OB transitional

Provenance

Uncertain

Nippur

Uncertain

Tablet number

RA 12, 197

MS 3874

Ist Ni 10,235 + 3854

SM 2574

Columns

1 column, 2 sides

1 column, 2 sides

1 column, 2 sides

1 column, 2 sides

Condition

good

Lower broken

Fragments

Worn edges

First lines

1(diš/geš2 )-da 2/3 4(u) / šu-ri-bi 3(u)

1(diš/geš2 )-da-am3 2/3-bi [1(diš/geš2 )-da 2/3] 4(u) [-am3] / šu-ri-bi 3(u)-am3 4(u) / šu-ri-bi 3(u)-am3

1(diš/geš2 )-da 2/3 4(u)n / šu-ri-bi 3(u)-am3

Last lines

igi 1(diš) 2(u) 1 gal2 -bi 4(u)n 4(diš) 2(u) 6(diš) 4(u)n / igi-gal2 1(diš/ geš2 )-da-kam

igi 1(diš) 2(u) 1(diš) gal2 -bi Broken 4(u)n 4(diš) 2(u) 6(diš) 4(u)n / im-gid2 -da še20 -ep-d EN.ZU

1(diš) 2(u) 1 igi-gal2 -bi [4(u) 4(diš) 2(u) 6(diš) 4(u)]

Entry format

igi n-gal2 -bi n'

igi n-gal2 -bi n'

igi n-gal2 -bi n'

n igi-gal2 -bi n'

Number format

Mixed (normalized 40, reciprocal column)

Mixed (normalized 40 and 50, reciprocal column, number column broken)

Mixed (normalized 4, 40, and 50, reciprocal column, number column broken)

mixed (normalized 4, 8, 9, 40, 50, both columns)

Early Old Babylonian

of normalized numbers. Thus, in RA 12, 197 normalized 40 appears in the same way as it does during the Ur III period transition. However, in each text, no fractions appear, suggesting all value was detached from SPVN and transformation was a firmer concept. Normalization is limited to the reciprocal column so that reciprocal extraction is still one way. With MS 3874, however, both 40 and 50 appear in normalized forms on the reciprocal side. Unfortunately, the tablet is broken where 40 and 50 are expected as part of integer numbers so that it’s uncertain if it extends to all parts of the tablet. While Ist Ni 10,235 + 2854 is in fragments, what is extant shows increased use of normalized numbers: the numbers, 4, 40, and 50 appear in three different reciprocal numbers. In these three tablets, dated to the Old Babylonian transition, the initial statement is limited to non-normalized numbers even in the reciprocal column. With SM 2574, dated to the early Old Babylonian period, non-normalized and normalized numbers appear in both columns. Normalization also appears in the initial row. The mixture of normalized and non-normalized numbers in SM 2574 is especially interesting for the purposes of this study (Table 3.6). The number 7 only appears in its non-normalized form, while the numbers 9 and 40 only appear in their normalized forms. The numbers 4 and 8, however, show a mix between normalized and nonnormalized, with non-normalized numbers appearing more towards the beginning of the text and normalized numbers appearing towards the end of the text, with exceptions. This suggests the author of SM 2574 was exploring both SPVN and whether or how to write normalized numbers in mathematical texts.

3.4 Change

55

Table 3.6 Normalized and non-normalized numbers by line in SM 2574 Number

Normalized (by line)

Non-normalized (by line)

4

25

4, 11, 15, 17

7

7, 16

8

13, 23

9

8

40

1, 8, 12, 20, 21, 22, 23, 25?

50

19, 24, 25

7

SM 2574 has roughly the same layout as the mature reciprocal tables, while more normalized numbers appear in this text than the previous texts dated to the Ur III and transitional periods. However, SM 2574 shows some unusual features compared to the mature Old Babylonian tables of reciprocals, as well as the other three Old Babylonian transitional tables of reciprocals. For instance, while RA 12,197, MS 3874, and Ist Ni 10,235 + 3854 list entries as ‘igi-number-gal2 -bi’, the phrase ‘igigal2 -bi’ appears after each integer number in SM 2574. In addition, “-kam” appears at the end of each statement rather than the enclitic copula ‘-am3 ’, translated “is” here.64 ‘-kam’ describes a genitive relationship governed by the copula. An early Old Babylonian partial reciprocal extraction text, CBS 10,201, shows similar archaic tendencies, such as the appearance of ‘igi-gal2 -bi’.65 However, unlike SM 2574, all numbers in this incipit are normalized. Perhaps in both texts, the appearance of ‘igigal2 -bi’ between a number and its reciprocal served to underline that movement was in both directions. This would mean that reciprocal extraction can move in both directions on the reciprocal tables after the transition into the early Old Babylonian period was completed. It’s difficult to tell whether a list is more advanced or of a later date based on numbers alone. The shape of the tablet and entry format, among other aspects, must all be taken together. While the early Old Babylonian tables of reciprocals show an increasing tendency towards the highly standardized later Old Babylonian texts compared to their Ur III and Ur III transitional counterparts, it’s also clear that multiple scholars with their own opinions were exploring the expression and function of SPVN, deciding when to normalize numbers, and how the texts themselves should look.

64

As noted by Friberg and al-Rawi, “kam” is typically a determinative after ordinal numbers (Friberg and al-Rawi 2016, 501). However, see Middeke-Conlin 2020a, 34 for the appearance of “-kam” attached to ordinal numbers used to express a quantity of days. 65 CBS 10,201 is published in Hilprecht 1906 as text 25, with a new copy of the text in Friberg and al-Rawi (2016, 501). As Friberg and al-Rawi state, SM 2574 and CBS 10,201 are exceptional. Citing MKT 1: 4–9 and MCT: 32–37, they note that there are no other extant examples of this phenomenon in the textual record from Mesopotamia. ‘igi’ and ‘gal2 -bi’ typically appear on opposite sides of the number. This leads them to the conclusion that both texts are from an intermediate stage in the development of the table of reciprocals. (Friberg and al-Rawi 2016, 501).

56

3 The Old Babylonian Shift

The other numerical tables, such as tables of multiplication, show similar tendencies. Ist Ni 5173, an Ur III or early Old Babylonian numeric table on which the traces of a reciprocal table appear with multiplication tables, is emblematic: numbers are mixed. 4, 7, and 8 are non-normalized, 9 appears both normalized and nonnormalized, while 40 and 50 appear normalized. A similar phenomenon occurs in Ist Ni 2208, an Ur III or early Old Babylonia multiplication table of 7 in which numbers appear as a similar mix of non-normalized and normalized. These texts were probably not the work of students but of masters and may be considered a part of the ongoing experimentation with SPVN in mathematical texts.66 In addition, some texts of professional practice—administrative texts—from the Ur III period show clear examples of normalized numbers to represent a kind of partial-SPVN and SPVN. These numbers, located at the margins of the texts, such as tablet edges, offer traces of mathematical practice and transformation in advance of calculation. The marginal location suggests they were not part of the text itself, but a crutch of some form, whether necessary notes or calculation aids.67 For our purposes, the appearance of partial-SPVN and SPVN on the margins of texts from the Ur III period hints at the origin of this system, as well as a debate among practitioners on the utility and proper appearance of this tool as a calculation aid, further underlining its early appearance and incremental development. In any event, tools were being developed in the Ur III period, tools such as the tables of reciprocals and the multiplication tables mentioned and discussed here. This experimentation went on through the Ur III/Old Babylonian transition into the early Old Babylonian period. Through this period SPVN was being developed, the shape of tablets and entry formats were being refined, and the shape of numbers was being decided. Two-way movement on the reciprocal tables would only appear late, when the transition into the Old Babylonian period was completed. It’s in this period, perhaps quite early on, that transformation of numbers to and from SPVN as a mathematical process was debated and refined by the scribes who were developing and exploring this number system. These scholars explored whether and how value would be defined within calculation, and how SPVN would be represented in texts. Normalization would not appear fully developed in mathematical texts for some time yet. The result of this experimentation would be the creation of highly standardized education texts, including standard, relatively uniform metrological and numerical lists and tables that would be memorized by students in an early phase of their education. The development of the reciprocal tables is emblematic of scholarly literacy. This development offers an image of the generative ambiguity mentioned in Chap. 1. External representations of knowledge are, in this instance, employed as clear agents of change used to develop a powerful tool necessary for the employment of SPVN. At the same time, they offer evidence for the tribulations surrounding the development 66

Ist Ni 5173 and Ist Ni 2208 appear in Proust (2007, pl. 31 and 3) respectively. Discussion of these texts appears on ibid., 134. 67 For a comprehensive study of place value notation on administrative texts from the Ur III period, see Ouyang and Proust (2022).

References

57

of this numerical system during the Ur III period and through the Old Babylonian transition. In this period, it was by no means certain whether and how SPVN would look and act on mathematical texts. The ramifications of SPVN as a mathematical tool were not yet fully salient. This is clear with the use of fractions early in the development of these texts. By the middle of the Old Babylonian period, the reciprocal tables were employed as a means to stabilize and transmit knowledge to future generations. At that time, external representations of knowledge like the reciprocal tables served to transmit the scribal art and its new dependence on SPVN for calculation as well as the use of cursive script, new lexical lists, and new literary genres to the next generations of scholars and scribes.

References Brisch, Nicole. 2017. To Eat Like a God: Religion and Economy in Old Babylonian Nippur. In At the Dawn of History: Ancient Near Eastern Studies in Honour of J. N. Postgate, edited by Ya˘gmur Heffron, Adam Stone, and Martin Worthington, 43–53. Winona Lakes, Indiana: Eisenbrauns. Chemla, Karine, Agathe Keller, and Christine Proust, eds. 2022. Cultures of Computation and Quantification in the Ancient World: Numbers, Measurements, and Operations in Documents from Mesopotamia, China and south Asia. Why the Sciences of the Ancient World Matter 6. Cham: Springer. Crisostomo, C. Jay. 2019. Translation as Scholarship: Language, Writing, and Bilingual Education in Ancient Babylonia. Studies in Ancient Near Eastern Records 22. Berlin: De Gruyter. De Varent, Charlotte. 2022. Small numerical variations in a set of similar problems from Nippur on the area of the square. Historia Mathematica 58: 35–70 Delaporte, Louis-Joseph. 1911. Document mathématique de l’époque des rois d’Our. Revue D’assyriologie Et D’archéologie Orientale 8: 131–133. Feliu, Lluís. 2012. A new Early Dynastic IIIb metro-mathematical tablet of area measures from Zabalum. Altorientalische Forschungen 39: 218–225. Fiette, Baptiste. 2018. Le palais, la terre et les hommes: La gestion du domaine royal de Larsa d’après les archives de Šamaš-hazir. ARCHIBAB 3, Mémoíres de N.A.B.U. 20. Paris: Société pour l’Étude du Proche-Orient Ancient. Friberg, Jöran. 2007. A remarkable collection of Babylonian mathematical texts: Manuscripts in the Schøyen collection: Cuneiform texts, ed. by J.Z. Buchwald, J. Lutzen, J. Hogendijk. Sources and Studies in the History of Mathematics and Physical Sciences 1. New York: Springer. Friberg, Jöran. 2009. A geometric algorithm with solutions to quadratic equations in a Sumerian Juridical Document from Ur III Umma. Cuneiform Digital Library Journal 2009 (003). http:// cdli.ucla.edu/pubs/cdlj/2009/cdlj2009_003.html. Friberg, Jöran, and Farouk al-Rawi. 2016. New Mathematical Cuneiform Texts. Sources and Studies in the History of Mathematics and Physical Sciences. Cham: Springer. Grégoire, Jean Pierre. 1996. Archives Administratives et Inscriptions Cunéiformes: Ashmolean Museum, Bodleian Collection, Oxford 1. Paris: Librairie Paul Geuthner. Hilprecht, Hermann. 1906. Mathematical, Metrological, and Chronological Tablets from the Temple Library of Nippur, ed. H.V. Hilprecht. Series A: Cuneiform Texts 10, part 1. Philadelphia: Department of Archaeology, University of Pennsylvania. Høyrup, Jens. 2002. Lengths, Widths, Surfaces: A portrait of Old Babylonian Algebra and Its Kin. New York: Springer. Kuhn, Thomas S. 1962. The Structure of Scientific Revolutions. Chicago: University of Chicago Press.

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Labat, René. 1988. Manuel d’épigraphie Akkadien (Signes, Syllabair, Idéogrammes, 6th ed. Paris: Librairie Paul Geuthner. Langdon, Stephen. 1911. Tablets from the Archives of Drehem, with a complete account of the origin of the Sumerian Calendar, Translation, Commentary and 23 Plates. Paris: Librairie Paul Geuthner. Middeke-Conlin, Robert. 2020a. The Making of a Scribe: Errors, mistakes, and rounding numbers in the Old Babylonian kingdom of Larsa. Why the Sciences of the Ancient World Matter 4. Cham: Springer. Middeke-Conlin, Robert. 2020b. Connecting a disconnect can evidence for a scribal education be found in a professional setting during the Old Babylonian Period? In Mathematics, Administrative and Economic Activities in Ancient Worlds, ed. Karine Chemla and Cécile Michel, Why the Sciences of the Ancient World Matter 5, 435–462. Cham: Springer. Middeke-Conlin, Robert. 2020c. Planning a canal maintenance project in the kingdoms of Larsa and Babylon. Water History 12: 105–128. Middeke-Conlin, Robert. 2022. The Nazbalum in Old Babylonian Mesopotamia: An absolute number or an administrative tool? In Cultures of Computation and Quantification in the Ancient World: Numbers, Measurements and Operations in Documents from Mesopotamia, China, and South Asia, ed. Karine Chemla, Agathe Keller, and Christine Proust, Why the Sciences of the Ancient World Matter 6, 357–397. Cham: Springer. Middeke-Conlin, Robert. Forthcoming. Tabular administrative texts as a reflection of mathematical reasoning. In Practices of Reasoning in the Mathematical Sciences. Cham: Springer. Mittermayer, Catherine. 2006. Altbabylonische Zeichenliste: der sumerisch-literarischen Texte. Orbus Biblicus et Orientalis Sonderband. Fribourg, Göttingen: Academic Press Fribourg, Vandenhoeck & Ruprecht. Netz, Reviel. 2002. Counter culture: Towards a history of greek numeracy. History of Science 40: 321–352. Neugebauer, Otto. 1935. Mathematische Keilschrifttexte I. Quellen und Studien zur Geschichte der Mathematik Astronomie und Physik. Berlin: Julius Springer. Neugebauer, Otto, and Abraham J. Sachs. 1945. Mathematical Cuneiform Texts. American Oriental Series 29. New Haven: American Oriental Series and American Schools of Oriental Research. Oelsner, Joachim. 2001. HS 201—Eine Rexiprokentabelle der Ur III-Zeit. In Changing Views on Ancient Near Eastern Mathematics, ed. Jens. Høyrup and Peter. Damerow, 53–60. Berlin: Deitrich Reimer Verlag. Ouyang, Xiaoli, and Christine Proust. 2022. Place-value notations in the Ur III period: Marginal numbers in administrative texts. In Cultures of Computation and Quantification in the Ancient World: Numbers, Measurements and Operations in Documents from Mesopotamia, China, and South Asia, ed. Karine Chemla, Agathe Keller, and Christine Proust, Why the sciences of the Ancient World Matter 6, 267–356. Cham: Springer Nature. Overmann, Karenleigh A. 2019. The Material Origin of numbers: Insights from the Archaeology of the Ancient Near East. Gorgias Studies in the Ancient Near East 14. Piscataway: Gorgias Press LLC. Proust, Christine. 2000. La multiplication babylonienne: La part non écrite du calcul. Revue D’histoire Des Mathématiques 6: 293–303. Proust, Christine. 2007. Tablettes mathématiques de Nippur. Istanbul: IFEA, De Boccard. Proust, Christine. 2008. Tablettes mathématiques de la collection Hilprecht. Leipzig: Harrassowitz. Proust, Christine. 2009. Numerical and metrological graphemes: From cuneiform to transliteration. Cuneiform Digital Library Journal 2009 (001). http://cdli.ucla.edu/pubs/cdlj/2009/cdlj2009_ 001.html. Proust, Christine. 2020. Early-dynastic tables from Southern Mesopotamia, or the multiple facets of the quantification of surfaces. In Mathematics, Administrative and Economic Activities in Ancient Worlds, ed. Karine Chemla and Cécile Michel, Why the Sciences of the Ancient World Matter 5, 345–395. Cham: Springer.

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Robson, Eleanor. 2001. Neither Sherlock Holmes nor Babylon: A reassessment of plimpton 322. Historia Mathematica 28: 167–206. Robson, Eleanor. 2003/2004. Reviewed of J. Høyrup and P. Damerow (Hrsg.), Changing Views on Ancient Near Eastern Mathematics. XVI + 316 pp. Berlin, Dietrich Reimer Verlag, 2001 (= Berliner Beiträge zum Vorderen Orient 19). Archiv für Orientforschung 50: 356–362. Robson, Eleanor. 2004a. Mathematical cuneiform tablets in the Ashmolean Museum, Oxford. SCIAMVS–Sources and Commentaries in Exact Sciences 5: 3–65. Robson, Eleanor. 2004b. Accounting for change; the development of tabular book-keeping in Early Mesopotamia. In Creating Economic Order: Record-Keeping, Standardization, and the Development of Accounting in the Ancient Near East, ed. M. Hudson and C. Wunsch, International Scholars Conference on Ancient Near Eastern Economies, 107–144. Bethesda: CDL Press. Robson, Eleanor. 2008. Mathematics in Ancient Iraq: a Social History. Princeton: Princeton University Press. Scheil, Vincent. 1915. Notules. Revue D’assyriologie Et D’archéologie Orientale 12: 193–201. Sigrist, Marcel. 1984. Les Sattukku dans l’Eshumesha durant la Priode d’Isin et Larsa. Bibliotheca Mesopotamica 11. Malibu: Undena Publications. Veldhuis, Niek. 2011. Levels of literacy. In The Oxford Handbook of Cuneiform Culture, ed. Karen Radner and Eleanor Robson, 68–89. Oxford: Oxford University Press. Veldhuis, Niek. 2012. Cuneiform: Changes and developments. In The Shape of Script: How and Why Writing Systems Change, ed. Stephen D. Houston, 3–23. Santa Fe: School for Advanced Research Press.

Chapter 4

Variety and Uniformity

Abstract The document enters discussion with this chapter. This chapter presents a variety of tablet types and their modes of employment in the scribal education that marked scholarly literacy. Education at multiple scribal centers —Nippur, Ur, Larsa, Uruk, Isin, Babylon, Kiš, and Sippar—are reconstructed by exploiting this tablet typology and then the texts presented in Chaps. 2 and 3. Variety is shown in the curricula between these centers. A concrete example of this variety is presented next. By the end of the chapter, a uniform knowledge economy becomes apparent, but in this unity there is clear space for variety. This variety amid unity is emblematic of the Old Babylonia period and suggestive of technical literacy acquired even while pursuing the more scholarly literacy. Keywords Document · Curriculum · Metatext · Scholarly literacy

The knowledge systems just described were perpetuated throughout Babylonia by different iterations of a similar economy. Certainly, by the middle of the Old Babylonian period, scholarly literacy was achieved via memorization of lexical, metrological, and numerical lists and tables. Thus, lexical lists and sign lists were learned in tandem with metrological lists and then metrological and numerical tables of similar design. Presentation was made using similar mediums—tablets that appear in similar shapes and variety throughout Mesopotamia. However, these similar media are deployed in different ways between scribal centers. What follows is a discussion of tablet types and their employment in education throughout Babylonia. Discussion starts with the tablet types used to inculcate learners (Sect. 4.1), then a comparison of the syllabi of eight cities as evidenced by these tablets (Sect. 4.2), and finally a concrete example of the diversity witnessed on the very tablet types exploited in presenting these educations (Sect. 4.3).

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. Middeke-Conlin, Knowledge, Literacy, and Elementary Education in the Old Babylonian Period, SpringerBriefs in History of Science and Technology, https://doi.org/10.1007/978-3-031-45226-0_4

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62

4 Variety and Uniformity

4.1 The Document By the Old Babylonian period cuneiform culture was perpetuated using various tablet types. For instance, Ni 18, is labelled a type IV tablet ; AshM 1923–410, HS 242, and YBC 11,924 are labelled type III tablets; and CBS 11,392, N 3796 + N 3885, and N 5147 are labelled a type II tablets according to a typology developed by Miguel Civil.1 According to Civil, there are four distinct tablet types on which educational or academic texts from the city of Nippur were written. He conveniently named these tablets type I, II, III, and IV.2 Two additional tablet types, type M and type S, as well as prisms are described by Tinney.3 These tablet types and the texts written on them, that is to say the document, are the external representations of knowledge as described in chapter one. Each was used for a different purpose in developing and transmitting knowledge to the next generation of erudite practitioners.4 Type IV tablets are either round or square shaped and are small enough to hold in one hand. These tablets were employed throughout the scribal education. They often present only a few lines of a text, whether lexical, mathematical, or literary compositions.5 They appear throughout Babylonia during this period, but the form and content of type IV tablets differ from place to place. For instance, focusing on mathematical exercises, texts at Nippur, such as Ni 18 presented in Fig. 3.1, are often written on a square tablet, feature problems and answers inscribed on the lower right-hand corner with computation in SPVN in the upper left-hand corner. At Ur, these tablets are typically round. Numerical exercises, presented in tabular format devoid of stated problems, often appear on the reverse while proverbs appear on the obverse.6 A text from Larsa published by Robson is also round, in this case with a trapezoidal diagram on the obverse and many partially erased numbers in SPVN on the reverse.7 Type III tablets are small, elongated tablets on which extracts of larger compositions are found, typically about eight to fifteen lines of text.8 Figure 3.6 presents translations of Ashm 1923–410 and HS 242, on which extracts of the metrological table of weight appears, while Fig. 3.4 presents YBC 11924, on which is found an extract of the multiplication tables.9 These tablets were often produced by students who were reviewing texts they had already memorized.

1

See Sect. 3.1 above for these texts. Civil (1995, 2308). 3 Tinney (1999, 160). 4 Proust (2007, 90, 163) for these tablet types in the mathematical tradition at Nippur. 5 For this, see especially Charpin (1986, 449–452), Veldhuis (1997, 38–40), Friberg (2000, 99), and Proust (2007, 163). 6 For these tablets, see Robson (1999, 245–72) and Friberg (2000). 7 Ashm 1922–168. For this text, see Robson (2004, 18–9). 8 For these tablets, see Veldhuis (1997a, b, 38) and Proust (2007, 88). 9 For the places of these tablets in the scribal education at Larsa, see Middeke-Conlin (2020, 37–38). These tables highlight that similar lists were memorized throughout Babylonia. 2

4.1 The Document

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The texts reviewed with type III tablets were initially memorized using type II tablets. Type II tablets were an innovation of the Old Babylonian period.10 The teacher would write a text’s extract on the left third or half of the obverse of these tablets. The student would copy this extract on the remainder of the obverse, scraping off and rewriting this copy multiple times. On the tablet’s reverse the student would write out an unrelated text learned prior to the text on the obverse. For instance, on the obverse of N 3796 + N 3885 the student is memorizing an incipit of the metrological table of capacity, while on the reverse, presented in Fig. 2.2, the student is writing from memory an incipit of the acrographic list Izi. This correlation between the obverse and reverse allowed modern researchers to reconstruct the order of the elementary curricula at Nippur and elsewhere during the Old Babylonian period.11 Texts memorized by aspiring scribes using type II tablets and practiced using type III tablets could range from basic sign and vocabulary lists to more advanced model contracts and then literary extracts. In so far as mathematics is concerned, the components of metrology and calculation were learned by the young pupil via these texts. Indeed, the lexical and metrological lists presented in Chap. 2 as well as the mathematical tables discussed in Chap. 3 were practiced with type III tablets. It has been hypothesized that some form of commentary accompanied the wrote learning witnessed by these lists and tables, the kind of oral commentary that connects theory and practice to make coursework useful in a professional environment.12 The teacher probably explained when each sign learned by writing sign lists would be employed, gave definitions of the vocabulary learned by writing out the lexical lists, or expounded on measurement practice when the student was writing out the metrological lists and tables. As discussed above (Sect. 3.2), tabular formatting may have been a visible expression of some of this oral commentary. Finally, large, multi-columned tablets, type I tablets, as well as prisms, that were inscribed with hundreds of lines of texts making up entire compositions, may have been used as a kind of examination, testing the pupil on knowledge memorized in the course of his or her education.13 Prisms are often marked by a subscript stating the number of faces.14 Type M tablets are multi-columned texts—between two and five columns. These may contain extracts, entire compositions, or several compositions and, where possible, they may also give a numeric sub-script indicating the number of columns per side. Type S tablets, on the other hand, resemble large type III tablets. 10

Civil (1995). This was done by Veldhuis (1997) for the lexical tradition at Nippur and then Proust (2007) for the mathematical tradition at Nippur. For type II tablets at Nippur, see Veldhuis (1997, 35–6). Veldhuis states of these texts, ‘The reverse exercise of a type II tablet was generally a repetition of a school text previously studied. That this was the case may be concluded from an analysis of obverse/reverse correlations. Nippur type II tablets carrying an extract from a thematic list on the obverse often carry an elementary exercise on the reverse. Advanced exercises such as proverbs or model contracts on the obverse often go with a thematic list on the reverse. This corresponds to a rough curricular order: elementary exercises—thematic lists—advanced exercises.’ (Ibid., 35). 12 Civil (2009), Michalowski (2012, 48), and Middeke-Conlin (2020, 170–171). 13 Veldhuis (1997, 31). 14 Tinney (1999, 160). 11

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They are typically taller than they are wide but can be nearly square shaped. They often only carry extracts from compositions—around 40–60 lines—or the entirety of shorter compositions. However, some type S tablets contain upwards of 100 lines of text and some carry multiple compositions.15 Both type M and type S tablets were typically used exclusively in the advanced scribal education16 or by experts in the craft: the texts used to develop reciprocal tables discussed earlier (Sect. 3.4) were prior iterations of type M and S tablets. These tablets and the texts they held were seldom meant to be kept. As Robson points out, “Old Babylonian school tablets were essentially ephemera, created to aid and demonstrate recall, destined almost immediately for the recycling bin.”17 Production was utilitarian, meant to extend the scribal craft. A quality of these tablets is their near indestructibility, which led to their incorporation, in some instances, in building materiel: in house foundations, floors, and wall fillings. This recycling served, in effect, to preserve them to the modern day.18 Some tablets were kept, especially type I tablets, type M tablets, and Prisms, on which significant compositions appeared. This is because these tablets were not simply used to present knowledge to the next generation. As Proust notes, anticipating Renn’s “generative ambiguity” of external representations of knowledge, “school tablets” do not mean “school texts.” Metrological texts were written on very different types of tablets according to the place, the time, or the milieu: we often find brief extracts on round tablets, as in the schools of Mari or Ur, but sometimes whole series appear on great prisms or tablets. For example, the prism AO 8865, perhaps from Larsa, is probably not an exercise performed by a young pupil, but rather the work of an experienced scribe. Metrological lists and tables fulfil not only a pedagogical function, but also a normative one. They are the “white papers” of the scribes.19

These tablets were used to produce new knowledge, stabilize this knowledge, and then transmit it to successive generations. If they were kept, this was because they had some intrinsic value; perhaps they reflected a new knowledge. Or, perhaps they were useful as a kind of reference: an example of a specific curriculum’s makeup, for example. Finally, a tablet could reflect a point of pride such as the completion of a kind of “test”.

15

All three tablet types are discussed in Tinney (1999, 160). Proust (2007, 90). 17 Robson (2008, 124). 18 Proust (2019, 2). 19 Proust (2009, §7.3). 16

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4.2 Educations Whatever the case, these tablets reflect the various scribal curricula throughout Babylonia. Most of our knowledge of the Old Babylonian scholarly education comes from Nippur in central Babylonia, which was the religious and intellectual capital of Babylonia of the time. Certainly, what’s been discussed to this point reflects the Nippur curriculum. However, evidence for education comes from all over Babylonia. We turn now to education in these different centers. In southern Babylonia evidence is found for Ur, Larsa, and Uruk. For central Babylonia education at Isin is mentioned. In northern Babylonia, evidence is drawn from Babylon itself, Kiš, and late Old Babylonian Sippar. However, for comparison we will sum up the scholarly scribal curriculum at Nippur in central Babylonia first.

4.2.1 Nippur At Nippur, elementary education can be divided into four levels (Fig. 4.1).20 A first level of education was the basic introduction to tablets and signs. It is at this point that students learned to form tablets, practiced imprinting cuneiform wedges, and memorized basic signs. The basic practices necessary for any written literacy were learned at this point. This was followed by a second level in which thematic content was memorized in the lexical tradition and metrological content was memorized in the mathematical tradition. The metrological lists functioned in a similar manner as the thematic lists in that they present one topic after another: capacity with one list, weight with the next, and so on.21 The only difference seems to be the time it took to memorize these lists: memorization of the metrological lists concluded about halfway through the third level of elementary education. Thus, these thematic lexical and metrological lists were memorized concurrently, by and large. The third level commenced with the advanced sign lists in the lexical tradition and the introduction to SPVN in the mathematical tradition. The study of advanced 20

Basic division into levels follows Veldhuis (2014, 205–207) while the mathematical tradition is largely based on Proust (2007, 152, Fig. 9, and 255–262) with changes. Here we incorporate the mathematical tradition better into Veldhuis’ synopsis, which changes things slightly. First, the names list is included with texts Veldhuis associates with level 2 (Veldhuis 2014, 206). This is because the names list was memorized around the same time as the capacity list was memorized suggesting that these lists inaugurate a secondary level of the elementary curriculum. This leads to the second and greatest change: metrological training begins with Veldhuis’ level 2 and not with level 3. Proust convincingly presents the memorization of the capacity list at the same time as the names list (Proust 2007, 255–262). Proust’s interpretation was confirmed to an extent by Crisostomo (2019, 192–194). However, Crisostomo found that metrological tables were probably memorized around the same time as the acrographic list Izi was memorized, pushing the general memorization of metrological tables back to the conclusion of the memorization of the metrological lists. 21 Crisostomo (2019, 92).

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Fig. 4.1 Summary of Nippur scribal curriculum

lexical lists began with the bilingual list Ea/Aa and then the list of professions Lu. With the advanced lists come an increased presence of written Akkadian. Students began their training in SPVN with the memorization of the numerical table of reciprocals, followed by their multiplication tables and so on, concluding with roots. At the same time as students were memorizing the acrographic list Izi, they began memorizing metrological tables, starting with the table of capacity. These tables were only memorized when metrology was well developed and after SPVN had been introduced. Crisostomo sees analogical hermeneutics as fundamental to the advanced lexical education and cuneiform culture in general.22 While it may be difficult to see the training in SPVN in the same light, the fact that this training begins at the same time as the advanced lexical training suggests that the Old Babylonian teachers saw a similarity in the two themes. The numerical tables taken one after the other renders the feeling of a thematic nature. However, taken together they represent a kind of reasoning that allows an actor to multiply dissimilar information, transforming metrological values into SPVN numbers, multiplying these numbers to produce a new product, and then transforming them into a wholly new metrological value. 22

Crisostomo (2019, 14).

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This can be seen as a production of knowledge similar to, although certainly not the same as, the analogical hermeneutics espoused by Crisostomo. For one thing, we should not see the transformation of metrological values into SPVN numbers as a kind of translation. Transformation is a mathematical process while translation is a linguistic process. In a similar vein, numbers and language are dissociated in the brain. Language is processed in the prefrontal cortex while numbers are processed in the intraparietal sulcus.23 However, to the Old Babylonians, the third level of the elementary education provided a similar function: it inculcated the student with the building blocks of both mathematical reasoning and analogical hermeneutical theory. As seen in Sect. 3.2, the lexical lists and mathematical tables presented these in a similar manner using different media. Lexicality and mathematics were the twin pillars of Old Babylonian Cuneiform Culture, founded on the document as presented in Sect. 4.1. These building blocks were assembled in a fourth level of elementary education, a liminal phase of the education; still part of the elementary education, but it prepared the student for advanced practice. This level commenced with the memorization of proverbs in the lexical tradition, when the student scribe learned basic grammatical structures, and moved onto model contracts, when technical vocabulary and sentence structures were reinforced. Basic exercises in the mathematical tradition occurred around this time, after the metrological table for heights and the numerical tables of roots were memorized.24 With the conclusion of the fourth level, the student scribe would enter the advanced level of education where literary texts were memorized and when advanced mathematical practice occurred. Tablet types I through IV were used to varying degrees at all levels of elementary education at Nippur, but with type II predominant. For instance, in level 1, dedicated to basic literacy, and in levels 2 and 3 of the lexical and grammatical tradition, the overwhelming majority of tablets are type II tablets.25 A similar situation existed in the mathematical tradition. Tablet types I–III appear, but the overwhelming majority of tablets are type II tablets.26 Things change with level 4, in which variation appears based on content. In the mathematical tradition, for instance, type IV tablets are used almost exclusively, serving as a medium for more advanced mathematical practice.27 On the other hand, model contracts memorized in level 4 of the elementary education appear on types I through III tablets and prisms, especially type II tablets, while I am not aware of a single model contract from Nippur written on a type IV tablet.28 In the advanced literary education, type II and IV tablets are limited to the very first 23

See Overmann (2019, 46–64). Proust (2007, 150) suggests that the table for height was an extension of the series of metrological tables, while the table square and cubic roots formed an autonomous series. 25 As summed up by Veldhuis 1999. 26 Proust (2007, 153–57 and 68–69) (Annex 3.1). 27 Proust (2007, 164). 28 See especially Spada (2014, 1 fn. 6) for a list of published model contracts as well as Spada (2018) for additional model contracts from Nippur. Note that Spada (2018) publishes three prisms, one type I tablet, two of uncertain typology, and then five type II tablets. 24

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attempts at copying a literary composition.29 Advanced mathematical practice drops type II tablets altogether. Practice is limited to type IV, S, and M tablets.30 Both shifts, starting in level 4 and moving to the advanced education, betray a shift from focus on memorization to focus on skill building. This is, by and large, the situation at Nippur. However, within Nippur, there could be multiple schools because findspots were not recorded within this city for most tablets. Where excavators indicated findspots, the image changes slightly. In House F, for instance, the syllabary Tu-Ta-Ti is not present.31 The instructor’s whim is seen when the metrological table of capacity was introduced to students: in one instance, it was introduced early, just before memorizing the advanced sign lists Lu. In other instances, practice and memorization continued through the introduction of proverbs and model contracts. As Proust states, “leur étude se poursuit pendant tout le cursus lexical”.32

4.2.2 Ur At Ur, tablets excavated in two houses, No. 1 Broad Street and No. 7 Quiet Street, evidence education.33 While tablets in No 1 Broad street were found in-situ, proving their unity as a single curriculum, the tablets from No 7 Quiet Street were found reused to pave the floor so that it’s unclear whether or not they were part of the same curriculum.34 At No. 7 Quiet Street, there are numerous round type IV tablets, including mathematical tables and lexical lists. About 20 tablets contain literary content that were copied as part of an advanced education.35 At No. 1 Broad Street, documents suggest the early elementary curriculum at Ur was remarkably similar to that witnessed at Nippur, in particular House F. There are extracts from the syllabaries, including Syllable Alphabet B, the thematic lists, and advanced lists such as the professions list Lu.36 One multiplication table was also found in No. 1 Broad Street. Beyond No. 1 Broad Street, and beyond No. 1 Quiet Street as well, at a third site, the dump site SM, at least five fragments of multiplication tables were found. Two additional type I tablets lack an excavation 29

Veldhuis (2014, 212). Proust (2007, 163). 31 Ibid., 213 citing Robson (2001). 32 Proust (2007, 261). Proust is summing up her data concerning the introduction and sequence of metrological tables. However, while there is an exemplar of the capacity list on the reverse of a type II tablet containing Lu, the majority of examples appear on the acrographic list Izi, supporting Crisostomo’s assertion. 33 For a summary of these texts, see Charpin (1986, 30–34 and 432–33). See also Delnero (2012, 64–66) for discussion of these finds. 34 Charpin (1986, 485). 35 Delnero (2012, 64). 36 Ibid., 65. 30

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number. On one of the type I tablets a metrological table of length is found, while the other holds length and height tables.37 More advanced elementary practice is represented by proverbs as well as extracts from debates found on round type IV tablets. On the reverse of the proverb tablets, basic mathematical exercises appear. This is reminiscent of the curriculum at Nippur, where proverbs and basic mathematical exercises occur in level 4 of elementary education. However, the basic mathematical exercises are very different between the two centers. The exercises at Ur appear as purely numerical exercises carried out using a tabular format. They probably referred to extant problems local to the Old Babylonian period with changes based on the instructor’s whim.38 The advanced education at Ur is markedly different from that seen at Nippur. At Ur, literary texts are locally focused to a greater extent, such as on the moon God Nanna/ Sîn, Ur’s titular deity.39 Literary compositions were probably learned in a different order between the two sites.40 Akkadian appears more often as well.41 Finally, while there are often more mistakes, the technical quality of the compositions are greater at Ur than at Nippur.42 Advanced mathematics consisted of inheritance divisions in a geometric progression, calculation with “funny numbers”, equal-partitioned trapezoids, sides of square prisms or cubes, and then brick metrology.43 Summing up education at Ur, when extant, the early elementary curriculum was similar to that witnessed at Nippur. Similar syllabaries served to introduce the student to the cuneiform script. In so far as the lexical tradition is concerned, Ur presented content from levels 2 through 4 of the elementary education. In so far as mathematics is concerned, texts at Ur were representative of level 3 at Nippur, but level 4 texts— especially basic mathematical exercises—are very different. Moreover, at Ur, much of the evidence for the elementary education is found on round type IV tablets, also a notable difference from the educations witnessed at Nippur. Differences became even more stark with the advanced education.

4.2.3 Larsa While the tablets ar Nippur and Ur were, by and large, the result of scientific excavations, the evidence from Larsa, northwest of Ur, were often illicitly excavated in the course of the late nineteenth and early twentieth centuries. However, when legal excavations began in 1933 by Andre Parrot,44 over 200 tablets were dug up, including 37

Friberg (2000, 154–57). This is illustrated by Friberg concerning the texts from Ur (Friberg 2000). 39 Delnero (2016). 40 Delnero (2011, 145–46). 41 Tinney (1999, 167), Delnero (2016). 42 Delnero (2016). 43 Friberg (2000, 146). 44 The modern history of Larsa is summed up in Middeke-Conlin (2020, 9–10). 38

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those from the so-called maison du scribe of the Old Babylonian period. In this house, around seventy school texts were excavated. These included personal name lists, thematic lists, multiplication tables, and other exercises that have yet to be fully published.45 Many additional texts made it to collections via the antiquities markets early in the twentieth century, including much evidence for the mathematical education at Larsa. These tablet types ranged from three type I tablets and two Prisms on which entire compositions were impressed, two very broken type II tablets, numerous type III tablets, and then one type IV tablet.46 These tablets offer ample evidence for levels 2, 3, and possibly level 4, of the elementary mathematical education as witnessed at Nippur. Level 2 is evident with the type II tablets from Larsa. While only two exemplars have been published, their content is significant for our purposes.47 These tablets from Larsa show that the thematic list of trees and wooden objects, Ura 1, was memorized after the list of capacity was introduced. One can speculate from this that capacities were introduced around the same time as a names list was introduced, before the thematic list Ura was introduced just as it was at Nippur. Much more evidence exists for level 3, although the exact order is difficult to state with certainty. Numerous tables of multiplication have been found on type III tablets, as well as a table of roots. Metrological tables of weight and area have also appeared on type III tablets. The remains of entire multiplication series and tables of squares, square roots, and cube roots have been found on several type I tablets. Metrological tables of length and height have appeared together with tables of squares, square roots, and cube roots. All of this suggests that much of level 3 at Nippur was certainly learned at Larsa as well. The multiplication tables were probably preceded by reciprocal tables just as they were at Nippur. These were followed by the tables of squares and roots. At some point, metrological tables were introduced, probably starting with capacity and then moving to the table of weight, area and volume, length, and then height. The content of these metrological tables differed slightly from that at Nippur and then Ur, but their overall nature remained the same.48 The names of two students are known from the colophons on the numerical tables (see Sect. 4.3 for these colophons), B¯el¯anum and Sîn-apil-Urim. One tablet dates to R¯ım-Sîn of Larsa’s 4th year in power (1819 BCE). Divergence from the Nippur curriculum is visible from the very limited evidence of level 4, just as at Ur. Level 4 is represented by one sole type IV tablet on which a diagram of a trapezoidal figure appears on the obverse and the traces of numerical practice appears on the reverse. One can speculate that the problem introduced with this diagram was the division of a field into three unequal parts.49 Finally, one tablet presents a mathematical problem and associated diagram. The problem on the tablet asks and explains how to find the length and area of a triangle out of the slope of 45

Delnero (2012, 82). See Robson (2004, 10–27) and Middeke-Conlin (2020, 35–41) for these tablets. 47 See Robson (2004, 23–24) for these texts. 48 Middeke-Conlin (2020, 41–57). 49 Robson (2004, 18–19). 46

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the hypotenuse and furrow lengths. This tablet is related to four or five other tablets on which incantations in Elamite and Akkadian appear.50 Thus, the late elementary education consisted of geometric exercises that prepared the student for more advanced geometric exercises in the advanced education. Instead of or in conjunction with Sumerian literature, the student learned Elamite and Akkadian incantations in the advanced education. At Larsa the majority of published curriculum deals with mathematics, although the unpublished curriculum offers potential for a robust lexical education as well. What is available of the elementary mathematical curriculum is similar to that at Nippur and Ur, although certainly not the same. However, advanced elementary mathematical practice diverged between Nippur, Ur, and Larsa.

4.2.4 Uruk At Uruk, there is greater divergence between elementary curriculums than between Nippur, Ur, and Larsa, although it’s clear they are part of the same tradition. Type II and IV tablets prevail at Uruk, demonstrating preference for basic memorization. Within the so-called “Scherbenlock” were a wide range of texts found on seventythree round type IV tablets and twenty-one type II tablets that allow a cursory reconstruction of the order of the scribal curriculum.51 While it is by no means certain, Cavigneaux suggests these make up a coherent corpus of texts based on prosopography, chronology, and similarities in content of administrative texts.52 The group of texts date from between R¯ım-Sîn’s 32nd and 34th years in power (1791–1789 BCE) and probably originally belonged to a priestly family. The tablets are mostly populated by lexical and literary texts, along with other school texts. Only one lexical composition, Syllable Alphabet A, can be certainly identified among the type IV tablets. The remaining lexical compositions may be a gods list, a professions list similar to Lu, and a thematic list or grammatical paradigm such as an early version of Ura I and II.53 In addition, about thirty type IV tablets contain excerpts from literary compositions. The type II tablets, in contrast to the curriculum at Nippur, contain only texts from early in the scribal curriculum or later. Four of twenty-one identifiable type II tablets from Uruk contain Syllable Alphabet A while five contain model contracts.54 Some kind of elementary sign list also appears, perhaps supplanting the list Tu-Ta-Ti from Nippur.55 The gods list is rare at Nippur but at Uruk this list seems to supplant the 50

Robson (2004, 24–27). For these texts, see Cavigneaux (1996). For a reconstruction of the curriculum, see Veldhuis (1997/1998). See also Oelsner (2014). 52 Cavigneaux (1996). 53 Veldhuis (1997/1998, 360). 54 Ibid., 362. 55 Veldhuis (2014, 214). 51

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Fig. 4.2 Comparison of lexical curricula at Uruk and Nippur

name list as the earliest thematic list in the curriculum: four examples of the gods list appear while only one personal name list appears.56 This was probably acceptable because much of the name list involved theophoric elements to personal names. The gods list and personal names lists were probably followed by extracts from Ura, then advanced lexical lists like the body part list Ugumu, the sign list Ea, the acrographic list Kagal, and then the sign and acrographic list Lu. Finally, model contracts were followed by a selection of hymns making up the end of the elementary education and leading to the advanced education populated by literary texts.57 Figure 4.2 sums up the extant lexical curriculum at Uruk and compares it to the lexical curricula at Nippur. The distribution of elementary education texts on type II and type IV tablets is similar: over representation of lists early and late in the scribal education but still representative of levels 1 through 4 of the Nippur lexical tradition. There is very little with regards to mathematical practice at Uruk. However, one multiplication table58 suggests the existence of basic numeric practice, coinciding with level 3 of the curriculum at Nippur, and perhaps alludes to the existence of metrological practice, 56

Veldhuis (1997/1998, 362) sums these lists up. Veldhuis (2014, 214). 58 Cavigneaux (1996, 105). 57

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both lists and tables. Summing up elementary education at Uruk, Veldhuis states, “One possible interpretation of this distribution of the available lexical material is that, compared to Nippur the Uruk school made a short-cut from the elementary to the literary phase of education. It only treated the absolutely necessary.”59 Focus was on content and professional practice geared towards the education of a priest in Uruk.

4.2.5 Isin Education at Isin is well-attested but poorly studied. Numerous educational tablets were found in several spots over 11 excavations that took place between 1973 and 1989.60 In particular, a house excavated in the 1st and 2nd season yielded about two hundred tablets including school tablets as well as a room that was probably used for tablet preparation.61 Tablets in the section labelled the Nord-Abschnitt, or north section, found in the fourth, fifth, and sixth seasons, were mostly dated between Samsu-Iluna’s first through 29th year in power.62 A house excavated in the seventh and eighth season in the Nordost-Abschnitt, or northeast section, unearthed more school tablets mostly from this period as well.63 Finally, further school tablets were excavated in the ninth through eleventh campaigns in buildings of the SüdostAbschnitt, or southeast section.64 The tablets themselves are often varying sized fragments of type I tablets on which large elementary lexical and mathematical texts are written. Type II tablets appear, suggesting practice in memorization, while several type III tablets exist, also evidence for memorization. These include one with a colophon labelling it a long tablet, specifying a personal name, and a date to month and day: a table of reciprocals was written by Imgur-Sîn on the 10th day of a month, the name of which is unfortunately broken.65 Numerous type IV tablets present exercises throughout the education. All four levels of elementary education witnessed at Nippur appear in Isin, to greater and lesser extents. This elementary education is summarized in Fig. 4.3. Gray in Fig. 4.3 states texts, extant at Nippur, that are not extant at Isin nor replaced by any alternative. Lack of a text does not preclude its existence at Isin or elsewhere, only its absence from excavated and studied material. Thus, representative of level 1, an example of the Syllable Alphabet A was unearthed in the Nord-Abscnitt. 59

Cavigneaux loc cit. Edzard and Wilcke (1977), Walker and Wilcke (1981), Wilcke (1987), Krebernik (1992), and Sommerfeld (1992). These tablets have been catalogued and copied in Wilcke et al. (2018). 61 Edzard and Wilcke (1977, 44), Postgate (1975, 58). 62 Walker and Wilcke (1981, 91–102), Postgate (1976). 63 Wilcke (1987, 93–112). 64 Krebernik (1992), and Sommerfeld (1992). 65 IB 1211 (ABAW 143, 208). See Walker and Wilcke (1981, 92–93). 60

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Fig. 4.3 Summary of elementary scribal curriculum at Isin

Much greater evidence for the second level of lexical education is also found, especially in the Nordost-Abschnitt where exemplars of a gods list, personal names list and then parts 1, 2, 4, and 6 of Ura where unearthed. In the Nord-, Nordost-, and Sudost-Abschnitt comes evidence for level 3 with the discovery of the advanced sign list Ea/Aa (Nord- and Sudost-Abschnitt) and Lu (Nordost-Abschnitt) as well as an exemplar of Izi (Nordost-Abschnitt). The fourth level of elementary lexical education is witnessed by model contracts found in the Nordost-Abschnitt. An exemplar of the Syllable Vocabulary A, a text which associates the entries found on the Syllable Alphabet A with Akkadian words, along with a creation myth, was found in the Nord-Abschnitt. In each center, advanced education is witnessed by numerous literary finds.66 Mathematical education is primarily seen in the Nord- and Nordost-Abschnitt. A list of capacity and lengths, representative of the second elementary mathematical level, are found in the Nordost-Abschnitt. The beginning of the third mathematical level is seen with a table of reciprocals found in the Nord-Abschnitt, and then multiplication tables found in both areas, as well as tables of squares in both areas. A mistake occurs on one type I tablet from the Nord-Abschnitt. On this tablet, every product of the multiplication table for 36 are incorrect.67 This suggest the text was 66 67

See Delnero (2012, 76–77) for a summary of the literary texts found in Isin. Walker and Wilcke (1981, 93), referring to ABAW 143, 201 (IB 864).

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produced by a student, perhaps a kind of test. A metrological table of heights was found in the Nord-Abschnitt. Thus, levels 2 and 3 of the mathematical education are also attested at Isin, albeit to a lesser degree. An innovation occurs at Isin as well: several round type IV tablets appear with administrative exercises on them.68 These tablets give the impression of real-world administrative practice. Appearance on type IV tablets within the educational context of the Nord-Abschnitt render it probable that these are examples of student practice. Thus, education is similar to that witnessed at Nippur, but with variants. For instance, the Syllable Alphabet A appears, rather than the Syllable Alphabet B. The God list appears as well as the personal name list. Most striking is the appearance of clearly educational tablets in multiple sites throughout Isin, suggesting this erudite education was locally available to multiple communities within Isin. Interestingly, part of this education consisted of practice in the construction of administrative tablets. Much more study needs to be done on education in Isin.

4.2.6 Babylon Education at Babylon is well documented, but the elementary education is poorly studies.69 An assemblage of about 450 texts was found in one house, perhaps belonging to Marduk-n¯as.ir, the “overseer of students” (ugula dumu-meš e2 -dubba-a in Sumerian and wakil m¯ari b¯ıt .tuppim in Akkadian). Among the tablets were 19 tablets with lexical lists or sign lists as well as 38 square or round type IV tablets. Among these texts is the Weidner Gods List, a list of deities similar to the Nippur Gods List of the level 2 lexical curriculum.70 Advanced education is seen in numerous curricular literary texts.71

4.2.7 Kiš One hundred and twenty-four exercise tablets are distributed over several sights at Kiš, showing that multiple scholastic environments existed in this Old Babylonian municipality: 23 school tablets were excavated at Uhaimir, also called mound Z, or ancient Kiš proper, while an additional 15 tablets probably come from this mound. 52 school tablets were excavated at another mound, Ingharra or mound E, the ancient municipality of Hursaˆg-kalama. Another 7 tablets that lack provenance probably ˘ come from this mound as well. An additional 2 tablets from Ingharra, mound W 68

Edzard and Wilcke (1977, 87). The tablets are, ABAW 143, 202 (IB 431), IB 474, ABAW 143, 224 (IB 573), and ABAW 143, 246 (IB 582a) and ABAW 143, 543 (IB 582b). 69 For this city, see Pedersén (2005, 17–68), especially 19–37 and Pedersén (2011). 70 See Veldhuis (2014, 200–201) for this list. 71 See especially Delnero (2012), 80 for a discussion of these texts.

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this time, and then 27 tablets of uncertain origin, are attributed to the area of Kiš as well. The school tablets excavated in these locations were found with numerous administrative texts, but the dating of these texts is difficult because dates range from the reign of Sin-muballit (1812–1793 BCE) to the reign of Ammi-ditana (1683–1647 BCE).72 Texts from Uhaimir were found in two primary locations: near the Ziggurat and in the ruins of a house. A relatively complete lexical education is evident by the firmly provenanced texts from this site. Three exemplars of the personal name list appear on type III tablets. On a type II tablet an extract of Ura 1 appears on the obverse with an excerpt of Ea on the reverse. Another type III tablet shows an excerpt of Ura 1 as well, while a third very broken text may show more of Ura 1. Ea, usually part of the advanced lexical training, is clearly memorized before Ura 1. Level 3 is seen with a tablet flake on which Izi appears. The level 4 lexical education is seen in several type IV tablets with some kind of sentence construction practice. In so far as mathematics is concerned, there is a portion of the standard metrological table of weights on the reverse of a type I or II tablet. A multiplication table appears on a type III tablet. Finally, a calculation performed on a type IV tablet gives evidence of level 4 mathematical practice. Thus, the final three stages of the elementary mathematical education are represented at this location. The advanced curriculum is different from that witnessed in Nippur. While there is typical curricular Sumerian literature at this site, Uhaimir also yields practice in Akkadian letter writing.73 Several tablets that are insecurely attributed to this mound help to round out the curriculum, including two exemplars of Syllable Alphabet A that are representative of Level 1 education in the northern tradition. Unfortunately, it’s difficult to state whether these tablets are type I, II, or III. Level 2 lexical and mathematical practice is seen on a type II tablet on which the metrological list of area appears on the reverse and Ura 1 on the obverse, suggesting area measurement values were learned before Ura. A type III tablet on which a reciprocal table appears shows level 3 mathematical practice. A type IV tablet on which an elementary Sumerian sentence is constructed affords evidence of Level 4 lexical training. Finally, Akkadian letters appear on three type III or S tablets.74 Thus, all levels of education witnessed at Nippur are represented at Uhaimir as well, but with notable differences in ordering, and with the addition of Akkadian letter writing to the curriculum. While present, levels 1 and 2 are poorly represented here. Moreover, we do not see proverbs and model contracts, but instead basic sentence construction of an unknown variety at Uhaimir. All four levels appear at Ingharra, near Uhaimir, as well. This time they are better represented. Seven extracts of syllable Alphabet A appears on type I, II, and IV tablets or tablet fragments, while three extracts of Syllabary A appear on type I and II tablets, offering evidence for level 1 education. Evidence for level 2 is also 72

See Ohgama and Robson (2010) for education in and around Kiš. See also Delnero (2012, 73–75) for a summary of this city’s education. 73 This site is summed up in Ohgama and Robson (2010, 213). 74 Ibid., 216.

4.2 Educations

77

extensive. Two type IV tablets witness personal name exercises. Ura 1 appears on a type IV and type III tablet, Ura 2 on one type I or II fragment, Ura 4 on one type IV and three type I tablets, while Ura 6 is seen on the reverse of a type II tablet. Level 4 lexical education is extensive as well. Ea is seen on a type I tablet and the reverse of a type II tablet. Izi and Saˆg, a list typical of northern Babylonia,75 appear on a type II tablet. Level III mathematical education is seen with a multiplication table and a metrological table, both found on type III tablets. Level 4 mathematical practice is seen with a diagram found on a type IV tablet. Advanced education lacks Akkadian letter writing but instead offers a more complete repertoire of Sumerian curricular literary texts.76 Additional tablets appear without relatively certain provenance. For instance, in addition to what has already been noted at or near Kiš, there is an extract of Ura 3 on a type I tablet, the profession list Lu, verbal paradigms with Akkadian translations, tables of squares, numerous examples of literature in a Sumerian dialect called Emesal, as well as a syllabic Sumerian literary text.77 From all of this, curricula come into view that, while in many ways drawn from that witnessed at Nippur, had a very different purpose (Fig. 4.4). Tablet types and use are similar between Kiš and Nippur: type II, III, and IV tablets used in levels 1 through 3 express extended practice in memorization, while type III and IV tablets used during and after level 4 also show more advanced grammatical and mathematical practice. Type I tablets suggest a possibility of testing. At both Kiš sites, Syllable Alphabet A was used, reflective of the northern tradition, along with Syllabary A at Ingharra. We do not have evidence for any other basic writing practice. Levels 2 through 4 are well attested, though level 2 is less well attested at Uhaimir than at Ingharra. Both Uhaimir and Ingharra ordered exercises differently than at Nippur. For instance, the list of area seems to have been learned before Ura 1, suggesting either a different ordering of lexical lists, or a different order of metrological lists. Ea also appears to have been out of order, before Ura 1 was memorized. Together this suggest that Ura 1 was memorized towards the end of the thematic lists, rather than the beginning. The order of the remaining lists is uncertain. Perhaps advanced lexical training, level 3, began while level 2 was concluding. Ea/Aa appeared first, followed by Lu, then Izi, followed by Sag. It’s uncertain if additional lexical practice from Nippur occurred. However, at some point, verbal paradigms were memorized along with their Akkadian translations, possibly following Saˆg. Level 3 mathematical practice also took place, with both numerical and metrological tables memorized as at Nippur, and with no reason to assume ordering was different. Level 4 was different from the Nippur curriculum. Rather than proverbs and model contracts, the students practiced Sumerian sentence structures from an unknown source. While calculation practice appears to have been in line with the mathematical tradition, diagrams were also produced, similar to Larsa. The advanced education was also different. While both sites witnessed advanced, curricular Sumerian literature 75

See Veldhuis (2014, 175) for Saˆg. Ohgama and Robson (2010, 224). 77 Ibid., 225–229. 76

78

4 Variety and Uniformity

Fig. 4.4 Summary of scribal curriculum at Kiš

as at Nippur, at Uhaimir Akkadian letter writing occurred. Moreover, at some site Emesal was practiced, as well as syllabic Sumerian.

4.2.8 Sippar The evidence of education at Sippar was excavated from the house of Ur-Utu, son of the Chief Lamentation singer Inana-mansum. This house was destroyed in a fire, which preserved the tablets. The archive is firmly dated to late in the Old Babylonian period, between Ammi-ditana year 30 to Ammi-s.aduqa year 17, or 1654–1630 BCE.78 Education was of a single person, probably Ur-Utu.79 This education is well represented, showing evidence for levels 1 and 2 from Nippur, with regional variations typical to the north, and professional practice not seen in any of the larger regional centers except Isin (Fig. 4.5). 78 79

Dating and provenance are discussed in Tanret (2002, 3–22). Tanret (2011, 276).

4.2 Educations

79

Fig. 4.5 Comparison of elementary curricula at Sippar and Nippur

Exercises in basic writing occurred in the house of Ur-Utu; the practice in tablet construction and sign elements witnessed at Nippur.80 This was followed by Syllable Alphabet A81 and then Syllabary A,82 concluding the first level of education at Sippar. Level 2 began with personal names.83 Next came the Sippar Phrasebook, a collection of legal terms that incorporated Ura 1 and 2 common to the Middle Babylonian period (c. 1595–1155 BCE), and then concluded, as far as is evident, with the remainder of Ura.84 One text is perhaps an extract of Lu or Diri, offering evidence for level 3 in the lexical tradition.85 Several metrological tables also appear, including tables for capacity86 and weight.87 These all appear on type I, II, or III tablets showing focus on memorization. Along with the tablets just mentioned were numerous type IV tablets that present exercises throughout Ur-Utu’s academic upbringing.88 Thus, tablet 57, a metrological list of capacity showing the hand of an instructor on the obverse and student on the reverse, gives evidence of practice in basic numeracy.89 Lexical practice with personal names that are rare in Sippar, if they appear at all in this city, occurs in tablet 51.90 Advanced mathematical practice is seen with tablet 59, on which appears

80

Tanret (2002, 25–30, texts 1–5). Ibid., 31–50, texts 2, 6–15. 82 Ibid., 51–60, texts 8, 11, 16–22. 83 Ibid., 123–124, texts 65–66. See also text 51, pp 114–116. 84 Ibid., 61–99, texts 23–38. 85 Ibid., 73–75, text 30. 86 Ibid., 100–108, texts 42–45. 87 Ibid., 108–111, texts 45–47. 88 For these tablets, see Tanret (2002, 112–122). 89 See ibid., 118 for tablet 57. 90 Tablet 51 is presented on ibid., 114–116. 81

80

4 Variety and Uniformity

Fig. 4.6 Edition of MHET 3/1 2, 62

purely numerical exercises similar to those witnessed at Ur (see Sect. 4.2.2 above).91 Tablet 59, like many of the type IV tablets from Sippar, also shows signs of reuse.92 Economic or administrative practice appears on round type IV tablets from Sippar as well. Tablet 50 shows practice in writing letter introductions on the obverse and practice in constructing entries typical to economic texts concerning barley on the reverse. While broken, tablet 56 presents part of a contract on the obverse and practice calculating a field on the reverse. Finally, tablet 62 shows practice in writing entries for an economic text concerning fields (Fig. 4.6).93 These type IV tablets could easily be mistaken for memos or drafts when taken out of context, but when contextualized they prove themselves part of a young professional’s academic upbringing. The texts on the type IV tablets exhibit a distinct improvement in sign quality, showing the products of both a beginning student, who was practicing basic signs, and an advanced student who was carrying out advanced mathematical and administrative practice. At the same time, there is ample evidence for other tablet types used to present the more established scribal curriculum as witnessed at Nippur and elsewhere, from basic writing practice, then sign lists, thematic lists, and metrological lists and tables.94 Yet the type IV tablets are quite frequent—making up seventeen out of eighty-four exercise tablets, or 21.25% of the tablets excavated in one house.95 The type IV tablets were used both for exercises that supplemented the normal elementary education and then advanced mathematical and economic practice.96

91

See ibid., 118–119 for this tablet. Ibid., 119, see also ibid., 122 for reuse. 93 For discussion of tablet 50 (MHET 1/1, 67), see ibid., 113–114. Tablet 56 is discussed on ibid., 117–118. Tablet 62 is described on ibid., 119–120. 94 See ibid., 25–111 for these texts. Writing practice is discussed in Chap. 1 (ibid., 25–30), syllabaries in Chaps. 2 and 3 (31–60), thematic lists are mentioned in Chap. 4 (61–99), and then metrological tables are discussed in Chap. 5 (100–111). 95 Ibid., 112. For comparison, ninety percent of mathematical texts from Nippur come from the elementary phase of education (Proust 2007, 97). 96 As Tanret states, “Le fait qu’elles sont écrites aussi bien par des débutants que des apprentis fort avancés, montre qu’elles sont utilisées de pair avec les exercices sur d’autres formes de tablettes. Elles ne se situent donc pas à un moment précis du curriculum, mais pratiquement tout au long de celui-ci” (Tanret 2002, 121). 92

4.3 Metatextual Variety

81

Fig. 4.7 Colophon of type III tablet YBC 11924

As Tanret notes, these texts were all excavated from one house, hypothesizing that, “Un gala.mag fait former son fils et successeur, peut-être une naditum faitelle prodiguer un enseignement, à sa nièce.”97 At Sippar there is firm evidence of education outside of a school environment and within a household environment, a galamah or chief lamentation singer, that was designed to pass on erudite and ˘ knowledge to a successor of some kind, a kind of in-situ learning. professional

4.3 Metatextual Variety An interesting aspect of the scribal curriculum is the colophon on many a document, especially the dated colophon. This is particularly interesting because dated texts in general, whether dated to day, month, or year, often prescribe texts as economic records. Of the texts from later Old Babylonian Sippar just discussed, only two are dated, neither of which are necessarily student practice. Both texts date to Ammiditana’s 28th year in power. The first, which describes the location of a field, was written on month 9, day 20, while the second, of which only the date remains, was written in month 10 day 12. Tanret hypothesizes that they were produced before the construction of the house and were preserved during this phase, only to be thrown out with the student practice texts, their utility having lapsed with the utility of the student practice.98 Dates do appear, often with other metatextual data, on documents devoted to student practice. For instance, the colophon on YBC 11924 (Fig. 4.7),99 probably from the city of Larsa, dates this type III tablet written by a student named Sîn-apilUrim to the eleventh day of the sixth month of R¯ım-Sîn’s 4th regnal year (1819 BCE). At Isin, IB 1211, a type III tablet, specifies in the colophon that it was written by Imgur-Sîn on the 10th day of an uncertain month.100 A survey of all colophons and all metatextual data would be unwieldy and is unnecessary for the purposes of this study. A more focused survey will suffice to illustrate metatextual variety by scribal center and perhaps by instructor. Table 4.1 was produced with this in mind. It presents colophons found on tablets containing elementary mathematical texts. Table 4.1 is divided between tablets from Larsa in the south, 97

Ibid., 168. Tanret (2002, 7–8). 99 For YBC 11924, see Robson (2004, 15–16). 100 Published as ABAW 143, 208 (Walker and Wilcke 1981, 92–93). 98

82

4 Variety and Uniformity

Isin in central Babylonia, Kiš in northern Babylonia, and then unprovenanced tablets from throughout Babylonia during the Old Babylonian period. Museum numbers are stated in the initial column, followed by the abbreviated primary publication of each tablet, and then the remaining columns present the content of each tablet, especially the colophon: whether each tablet is self-described as a long tablet in the colophon (im-gid2 -da, the Sumerian name for type III tablets), the tablet type as discussed above (Sect. 4.1), if a personal name is found in the colophon, then date by day, month, and regnal year, and finally the content of each tablet. When xx appears, it implies a break, while—implies the omission of this part of a date formula. Only dated tablets appear on Table 4.1. At Larsa in the south, six out of a total of 13 tablets were found to have a date: One tablet is only dated to day, three are dated to month, while two tablets are dated to year.101 Five of the six texts are found on type III tablets, while the final dated text is found on a prism. The colophons on four out of six objects from Larsa self-describe themselves as long tablets and the product of one of two personal names. Three tablets and their texts bear the name of Sîn-apil-Urim102 and one of B¯el¯anum in the colophon. Two of these give a doxology praising Nisaba and Ea. These four tablets present multiplication tables. The fifth type III tablet, Ashm 1923–410, presents the sole text from this site to state day only, and is the only solely metrological table from Larsa to state a date at all. The quality of writing with this date is also the worst of all the tables, although the table of capacity is quite well written. It’s as if the date were an afterthought. Another metrological table, a table of lengths and then heights, also includes numerical practice: a table of square and cube roots. It presents a complete, well written date formula to Samsu-iluna of Babylon’s 1st year in power (1749 BCE, after Hammurabi conquered the kingdom), from month to day to year. All remaining date formulas are well formed. This is all significant. As shown above (Sect. 4.2.1), at Nippur at least, metrological tables were learned at the same time as numerical tables. The table of reciprocals was learned first, followed by multiplication tables. Students started memorizing multiplication tables with the table for 50 and continued through the table of 1:15. While memorizing multiplication tables, students began memorizing metrological tables, starting with capacity, moving to weight and then area and volume. They finished by memorizing metrological tables of length and then heights around the same time they were memorizing their square and cubed roots. Type III tablets, it will be recalled, were used to review already learned information. Prisms, as well as type I tablets, it will be recalled, were possibly a kind of test or other significant object. Dates of any kind do not appear on metrological lists, nor of tables of capacities, nor reciprocals. Not until both tables of weight measurement values were already memorized and halfway through the memorization of multiplication tables do dates 101

See Middeke-Conlin (2020, 34–58) for more on education from Larsa and the south, and especially 35–41 for a discussion of tablet types and dated student practice at Larsa. 102 This name appears in the colophon of a fifth text, Ashm 1924–472, which lacks a date and is therefore not included here.

Robson (2004, 13, 1)

Robson (2004, 14)

Robson (2004, 15)

MCT 023; Robson (2004, 15–16)

MKT 1, 69, Proust (2006)

ABAW 143, 208

Ashm 1922–178

Ashm 1924–447

Ashm 1924–451

YBC 11,924

AO 8865103

IB 1211

Yes?

Yes

Yes

Yes

Yes

Long tablet

Type III (fragment)

Prism

Type III

Type III

Type III

Type III

Type III

Tablet type

Imgur-Sîn

Sîn-apil-Urim

Sîn-apil-Urim

Sîn-apil-Urim

B¯el¯anum

Personal name

10.x.–

5.11.Samsu-iluna year 1

11.6.R¯ım-Sîn year 4

13.12.–

9.12.–

12.7.–

27.–.–

Date (day.month.year)

103 Proust 2005 casts doubts on this provenance. It is tentatively included here under Larsa with this caveat.

Isin

Robson (2004, 23, 10)

Publication

Ashm 1923–410

Larsa

Museum/ excavation number

Table 4.1 Dated mathematical student practice texts

Nisaba, Ayya

praise Nisaba

praise Nisaba, Ea

Doxology

(continued)

Table of reciprocals

Table of lengths, height, square roots, cube roots

× 4 (20 la2 1)

× 24 (20 la2 1)

× 24 (20 la2 1)

× 25

Table of weights

Content

4.3 Metatextual Variety 83

Type III Type III

MKT 1, 37; PRAK 1 (B 54, B 58

MKT 1, 39

Ist O 4438 + 4442

Ist O 4443

Sîn-…

NA

Sîn-…

Type III

MLC 1611

MS 3873/1

Type III

Type III

Yes

MS 3909/3

YBC 8617

Type S

MCT

Friberg (2007, 77)

MCT

MLC 646

Type III

Šep-Sîn

Friberg (2007, 75, 77)

BRM 4, 36; MKT 1, 54

VAT 8167

Type III

Inbi-ilišu

MKT 1, 36

VAT 1221

Ardum

Personal name

Type III

Yes

Yes

Friberg (2007: 69)

MKT 1, 36

MS 3874 Type III

Type III

Robson (2004), 29–30, 16

Ashm 1929–833

Uncertain findspot

Type III

Robson (2004, 28–9, 15)

Ashm 1924–590

Tablet type

Type I

Yes

Long tablet

Robson (2004, 35–37)

Publication

BM 96,949

Kiš

Museum/ excavation number

Table 4.1 (continued)

24.10.–

xx.8.xx

5.6 II.–

xx.12.Samsu-Iluna year X

(continued)

× 24 (20 la2 1)

× 25

× 30

× 40 (20 la2 1)

× 44:26:40, × 24

20.1.Samsu-Iluna year 23?

× 45

Reciprocal table

×8

× 24

× 2:24, ends in square and reciprocals of 2 and 30

Reciprocal table

Table of capacities

Content

× 44:26:40

Doxology

6.9.–

26.1.–

1.–.–

25.–.–

–.12.–

14+.11.–

8.4.–

8.9.Samsu-Iluna year 14

Date (day.month.year)

84 4 Variety and Uniformity

Yes

Yes

BRM 4, 38; MKT 1, 39

MLC 117

Type III

MCT 23

MKT 1, 42

NBC 7346

Type III

MCT 23

Friberg (2007, 76)

NBC 7701

MS 3967/1

VAT 15,375

Type III

MCT 23; Moore (1939, no. 94)

M 406

Type III

Yes Type III

Type III

Yes

Type III

MKT 1, 41

MKT 1, 41

LB 798

Type III

VAT 7892

Yes

Type III

Yes

MCT

MKT 1, 40

YBC 6769

VAT 7896

Type III Type III

Yes

MKT 1, 39

MCT

VAT 7895

YBC 6705

Type III

Type III Type III

Type III

MCT

Yes

Type III Type S

MKT 1, 39

YBC 11,138

Yes

Tablet type

NBC 7374

MCT

MS 2719

Long tablet

VAT 7858

Friberg (2007, 71)

Friberg (2007, 78)

MS 2708

Publication

Museum/ excavation number

Table 4.1 (continued)

Ili-ippalšam

Ešei-pani-AN

Ubarrum

Ubarrum

Anatum

Sinatum m¯ar S.illi-Nin…

Šamaš-muballit

Personal name

× 1:40 × 1:30 (20 la2 1)

× 2 (20 la2 1)

× 3:45

×5

×5

×6

×7

×8

×9

×9

× 10

× 10

× 15

× 16

× 18, × 16:40

× 18

Content

25.8.– ba-zal

Doxology

21.12 II? (iti diri). R¯ım-Sîn year 44

9.–.– ba-zal

20.10.–

18.–.–

21.7.Sumu-la-el year 29

6.8.–

10.8.xx

20.6.– ba-zal

25.6.–

17.7.–

25.9.Samsu-Iluna year 1

9.7.–

9.–.–

1.xx.Samsu-Iluna year X

14.12 II.–

28.8.– ba-zal

Date (day.month.year)

4.3 Metatextual Variety 85

86

4 Variety and Uniformity

appear on the mathematical tablets of Larsa. Students learned to write day first, after they memorized their table of weights. They learned to write months and days by the time they memorized the multiplication table of 25. By the time they were almost done memorizing their multiplication tables—after the multiplication table of 4 was memorized, they added year names to the colophons. Finally, a full, proper formula of day, month, and year appears on a prism with the final set of memorized tables: the table of lengths, heights, and cube roots. Perhaps one can suggest that, at Larsa, colophons, including dates, would only appear with texts of a more advanced stage in a student’s elementary mathematical education, after metrological lists were learned and during the memorization of metrological and numerical tables.104 Moving to Kiš in the heartland of Babylon, the information is less clear. Five tablets present dates out of 41 total.105 One type III tablet only dates to day and one only to month. Two more type III tablets date the texts to day and month. Finally, one type I tablet dates the text to day, month, and year: The text on BM 96,949 was written on the 8th day of the 9th month of Samsu-iluna’s 14th year in power (1736 BCE). The text on BM 96,949 also presents a well written, condensed version of the Old Babylonian list of capacities and is the only text from Kiš to state a personal name, Ardum.106 A reciprocal table appears with day and month at Kiš. However, on the colophon of a type III tablet with a multiplication table for the SPVN number 2:24, day and month also appear. Only the day is written in the colophon of a multiplication table for 8, while a month is written in the colophon to a multiplication table for 24. No date appears on metrological lists. From all this, a couple things can be said about dated mathematical practice at Kiš. First, full dates might only appear on significant school texts at Kiš, such as tests. Second, in so far as the mathematical curriculum is concerned, date formulas were practiced along with mathematical material earlier than they were at Larsa, just as students began memorizing metrological and numerical tables. Proust, in her thorough study of educations from Nippur, notes only two scholarly mathematical tablets on which a date was found at Nippur.107 The city of Ur did not yield dated elementary student practice at all. Dated mathematical practice could not be firmly attributed to any center beyond Larsa, Isin, and Kiš. However, there are at least 25 out of a total of 131 surveyed tablets that lack provenance on which dates appear in the colophon. These tablets confirm that, in so far as the mathematical tradition is concerned, dates appear after metrological lists had been memorized and as students are memorizing their metrological and numerical tables. 23 dates appear 104

See Middeke-Conlin (2020, 37–39) for this. See above for the ordering of multiplication tables in the Nippur curriculum. 105 Robson (2004, 42–43) notes 45 total mathematical texts from Old Babylonian Kiš. However, four of these texts are problem texts and not included in this study. 106 Robson suggests this name, assuming a spelling mistake: the author wrote hi-ri-du-um when ˘ 2004, 35) We he intended ar ! (IGI! + RI)-du-um, which is a name that appears at Sippar. (Robson tentatively follow Robson. 107 Proust (2007, 96).

4.3 Metatextual Variety

87

on type III tablets, which were used to review already learned information. Two dates appear on type S tablets, which were similar to type III tablets, but used in the advanced education. Taking the unprovenanced tablets together, students typically begin practicing construction of dates with their multiplication tables. Only one of these dates appears with a reciprocal table. On MS 3874 the colophon reads “long tablet of Šep-Sîn, day 1”.108 Three more texts, a multiplication table of 15, a multiplication table of 5, and then a multiplication table of 2, state only the day. Fourteen tablets, including one type M tablet, state day and month. The texts on these tablets range from the multiplication table of 45 to the multiplication table of 1:40. The tablets on which eight multiplication tables appear date to day and month and are self-described as long tablets, while seven of these include personal names. Finally, the texts of six tablets state year, starting with the multiplication table for 44:26:40 and moving to the multiplication table of 1:30. Only three of these tablets describe themselves as long tablets and include a personal name. One tablet is a type M tablet. Year names on these tablets are: Sumu-la-el’s 29th year in power at Babylon (1852 BCE), R¯ım-Sîn of Larsa’s 44th year in power (1779 BCE), and Samsu-iluna of Babylon years 1 and 23 (1749 and 1747 respectively). The two remaining date formulas are broken but probably date to Samsu-iluna as well. Outside of Babylonia, dated colophons also appear associated with similar content. This is the case for one type I tablet from Aššur that presented the entire series of multiplication tables,109 as well as four type III tablets from Mari on which multiplication tables were found.110 These were not included in the survey on Table 4.1 but are mentioned to demonstrate the universality of dating texts during the Old Babylonian period. This very limited survey evidenced at least three groups of educational tablets and texts with relatively firm provenance as well as a series of unprovenanced tablets and texts in which practice with date composition takes place. While far from conclusive, some initial statements can be made from this. Dates occur in greater and lesser frequency between scribal centers. At Larsa 46% of surveyed tablets exhibited some kind of date, a striking difference from Kiš, where only 12% of tablets exhibited dates, Isin only shows one tablet with a date. When it comes to unprovenanced tablets, 19% contain a date of some form. This is only to be expected because, as Proust notes, “chaque cite semble avoir utilisé des norms d’écriture qui lui sont propres.”111 The use of dates is more often associated with level 3 practice during the elementary phase of mathematical education. This is especially true of Larsa, where the extant dates show a progression in practice from simple day, to day and month, to day month and year, that occurred in a similar order to the memorization of metrological and numerical tables at Nippur. This would make sense—Nippur fell within 108

“im-gid2 -da Ši-ip-d EN.ZU / ud 1”. See MKT 1: 46–47. 110 Proust (2007, 88). A fifth type III tablet from Mari containing a metrological table of weight was undated. 111 Proust (2007, 96). 109

88

4 Variety and Uniformity

the kingdom of Larsa and had for much of the early Old Babylonian period, and so elementary education at Larsa may have reflected that at Nippur. At Kiš in the Babylonian heartland, the appearance of dates does not adhere so firmly to the memorization of metrological and numerical tables. The same can be said about the unprovenanced tablets, on which the texts do not exhibit an underlying order or progression. The only thing that can be said universally based on Table 4.1 is that dates appear with the memorization of the metrological and numerical tables, not metrological lists. It must be born in mind that the conclusions drawn here are based on very sparce data (except at Nippur). They rely on the silence of the textual record when it comes to metrological lists just as much as what is present in the metrological and numerical tables. Friberg, speaking only of the Schøyen collection, states that there are 154 different numeric tables, many of which remain unpublished.112 New data could change these results. For our purposes, dates do appear on tablets, along with texts that were certainly student practice. The tablet itself is important to understanding the dates presented in this survey: the tablet on which a date appeared, whether type I, III, S, etc., informed the ancient observer that these were not in any way administrative documents. This suggests that dates on student practice would only appear when the nature of the text was somehow obvious to the ancient observer. From this, we can posit that the dating of student practice texts was somewhat common. At the same time, dated or not, we do not expect these texts to be preserved in most places. The tablets on which these texts were written, like most tablets from the scribal curriculums, were never meant to be kept. These objects were utilitarian, produced to extend the scribal craft and then discarded. The external representations of knowledge visible throughout Babylonia reflect a somewhat universal, erudite knowledge economy. They were employed to expand, stabilize, and then transmit a specific knowledge system, cuneiform culture, to an intellectual class. Each scribal center presented a relatively uniform variety of texts using the same tablet types as were present throughout Babylonian, with relatively minor variations in shape. When extant, the very basic elementary education was similar. The second level of education is relatively stable as well: Thematic lists were commonly employed in this level, although there was fluctuation. By the third level of education differences between centers become apparent. These differences become more pronounced with the fourth level of the elementary education and then the advanced educations. Thus, while a relatively common curriculum, with modest variety, existed between centers, by level 3 each center employed different lexical texts. While mathematical practice is relatively stable in this third level of elementary education, variety is seen in the addition of colophons, which could include a doxology, personal names, and even date formulas. At level 4 there are pronounced differences in grammatical and mathematical exercises.

112

Friberg (2007, 87).

References

89

This variety can only be expected: each student of each education was pursuing a different specialty. Thus, at Uruk the education seemed to focus on the education of priests while at late Old Babylonian Sippar the education was probably of a galamah or chief lamentation singer. Both educations were geared towards schol˘ arly literacy, but both were also geared towards educating a specific community or a specific profession—vestiges of the technical literacy mentioned in chapter 1. Differences in education are becoming apparent, especially when the external representations of knowledge are compared between each center, and these differences reflect professional practice. In exploring variety in a uniform knowledge economy, all three aspects of literacy are vital, while document literacy comes to the fore. Prose literacy in the form of lexical and grammatical practice shows greater variety in levels 3 and 4 of education, numeracy in the form of mathematical exercises witnesses significant differences in level 4. However, it’s the documents themselves where extensive variety is seen. The colophons on type I, III, and S tablets presented the elusive differences between centers in mathematical practice at the third level of elementary mathematical training. The type IV tablets employed in scribal schools throughout Babylonia showed incredible variety of practice between centers, both mathematical and grammatical. Indeed, a different type of practice begins to take shape with these educations: at both Isin and Sippar, student practice began to resemble real-world economic or administrative texts. Context and tablet shape, however, proved student practice of texts that may have been otherwise viewed as administrative work. Appearance in an educational milieu and on type IV tablets proved these texts were student practice in record keeping. Such practice is suggestive of the generative ambiguity witnessed already in the development of reciprocal tables. Here it is serving to stabilize knowledge by rendering scribal knowledge as transmitted in the scribal curriculum applicable to the real world. However, at both Isin and Sippar, evidence for these exercises is limited.

References Cavigneaux, Antoine. 1996. Uruk: Altbabylonische Texte aus dem Planquadrat PE XVI-4/5 nach Kopien von Adam Falkenstein Ausgrabung in Uruk-Warka Endberichte 23. Mainz: P. von Zabern. Charpin, Dominique. 1986. Le clergé d’Ur au siècle d’Hammurabi Genève: Droz. Civil, Miguel. 1995. Ancient Mesopotamian Lexicography. In Civilizations of the Ancient Near East 4, ed. J. Sasson, 2305–2314. New York: Charles Scribner’s Sons. Civil, Miguel. 2009. The Mesopotamian Lexical Lists: Authors and Commentators. In Reconstruyendo el Pasado Remoto. Estudios sobre el Próximo Oriente Antiguo en homenaje a Jorge R. Silva Castillo / Reconstructing a Distant Past: Ancient Near Eastern Essays in Tribute to Jorge R. Silva Castillo, ed. Diego A. Barreyra Fracaroli and Gregorio Del Olmo Lete, In Aula orientalis. Supplementa, 65–72. Sabadell and Barcelona: Editoral AUSA. Clay, Albert. 1923. Epics, Hymns, Omens and Other Texts. Babylonian Records in the Library of J. Pierpont Morgan 4. New Haven: Yale University Press. Crisostomo, C. Jay. 2019. Translation as Scholarship: Language, Writing, and Bilingual Education in Ancient Babylonia. Studies in Ancient Near Eastern Records 22. Berlin: De Gruyter.

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Delnero, Paul. 2011. ‘Inana and Ebih’ and the Scribal Tradition. In A Common Cultural Heritage: Studies on Mesopotamia and the˘Biblical World in Honor of Barry L. Eichler, edited by Grant Frame, Erle Leichty, Karen Sonik, Jeffrey H. Tigay, and Steve Tinney, 123–149. Bethesda: CDL Press. Delnero, Paul. 2012. The Textual Criticism of Sumerian Literature. Journal of Cuneiform Studies Supplemental Series 3. Boston: American School of Oriental Research. Delnero, Paul. 2016. Literature and Identity in Mesopotamia during the Old Babylonian Period. In Problems of Canonicity and Identity Formation in Ancient Egypt and Mesopotamia, ed. Kim Ryholt and Gojko Barjamovic, 19–50. Copenhagen: Museum Tusculanum Press and CNI Publications. Edzard, Dietz Otto and Claus Wilcke. 1977. Vorläufiger Bericht über die Inschriftenfunde 1973–74. In Isin-Iš¯an Bah.r¯ıy¯at I: Die Ergebnisse der Ausgrabungen 1973–1974, ed. by Barthel Hrouda, Abhandlungen der Bayerische Akademie der Wissenschaften 79, 83–91. München: Verlag der Bayerischen Akademie der Wissenschaften. Friberg, Jöran. 2000. Mathematics at Ur in the Old Babylonian period. Revue D’assyriologie Et D’archéologie Orientale 94: 97–188. Friberg, Jöran. 2007. A Remarkable Collection of Babylonian Mathematical Texts: Manuscripts in the Schoyen Collection: Cuneiform Texts, ed. J.Z. Buchwald, J. Lutzen, J. Hogendijk. Sources and Studies in the History of Mathematics and Physical Sciences 1. New York: Springer. Genouillac, Henri de. 1924; 1926. Premières recherches archéologiques à Kish.Fouilles françaises d’el-’Akymer. Mission d’Henri de Genouillac, 1911–1912. 2 vols. Paris: Librairie ancienne E. Champion. Krebernik, Manfred. 1992. "Die Textfunde der 9. Kampagne (1986)." In Isin-Iš¯an Bah.r¯ıy¯at IV: Die Ergebnisse der Ausgrabungen 1986–1989, ed. Barthel Hrouda, Abhandlungen der Bayerische Akademie der Wissenschaften 105, 102–144. München: Verlag der Bayerischen Akademie der Wissenschaften. Michalowski, Piotr. 2012. Literacy, Schooling and the Transmission of Knowledge in Early Mesopotamian Culture. In Theory and Practice of Knowledge Transfer. Studies in School Education in the Ancient Near East and Beyond, ed. Wolfert S. Van Egmond and Wilfred H. Van Soldt, 39–57. Leiden: Nederlands Instituut voor Het Nabije Oosten. Middeke-Conlin, Robert. 2020. The Making of a Scribe: Errors, mistakes, and rounding numbers in the Old Babylonian kingdom of Larsa. Why the Sciences of the Ancient World Matter 4. Cham: Springer. Moore, E.W. 1939. Neo-Babylonian Documents in the university of Michigan Collection. Ann Arbor: University of Michigan Press. Neugebauer, Otto. 1935. Mathematische Keilschrifttexte I. Quellen und Studien zur Geschichte der Mathematik Astronomie und Physik. Berlin: Julius Springer. Neugebauer, Otto and Abraham J. Sachs. 1945. Mathematical Cuneiform Texts. American Oriental Series 29. New Haven: American Oriental Series and American Schools of Oriental Research. Oelsner, Joachim. 2014. Bemerkungen zum Edubba’a in Uruk. In Babel und Bibel 8; Studies in Sumerian Language and Literature: Festschrift Joachim Krecher, ed Natalia Koslova, E. Vizirova, and Gabor Zólyomi, 423–436. Winona Lake: Eise.nbrauns. Ohgama, Naoko, and Eleanor Robson. 2010. Scribal Schooling in Old Babylonian Kish: The Evidence of the Oxford Tablets. In Your Praise is Sweet: A Memorial Volume for Jeremy Black from Students, Colleagues and Friends, ed. Eleanor Robson Heather, D. Baker, and Gábor. Zólyomi, 207–236. London: British Institute for the Study of Iraq. Overmann, Karenleigh A. 2019. The Material Origin of Numbers: Insights from the Archaeology of the Ancient Near East.Gorgias Studies in the Ancient Near East 14. Piscataway: Gorgias Press LLC. Pedersén, Olof. 2005. Archiv und Bibliotheken in Babylon: Die Tontafeln der Granbung Robert Koldeweys 1899–1917. Abhandlung der Deutschen Orient-Gesellschaft 25. Berlin: Saarländische Druckerie und Verlag.

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Pedersén, Olof. 2011. Excavated and Unexcavated Libraries in Baby Ion. In Babylon. Wissenskultur in Orient und Okzident, edited by Eva Cancik-Kirschbaum, Margarete van and and Joachim Marzahn Ess, TOPOI 1, 47–67. Berlin: Walter de Gruyter.Pientka, Rosel. 1998. Die spätaltbabylonische Zeit, Abiešuh bis Samsuditana: Quellen, Jahresdaten, Geschichte. Münster: ˘ Rhema. Postgate, Nicholas. 1975. Excavations in Iraq 1973–74. Iraq 37: 56–67. Postgate, Nicholas. 1976. Excavations in Iraq 1975. Iraq 38: 65–79. Proust, Christine. 2007. Tablettes mathématiques de Nippur. Istanbul: IFEA, De Boccard. Proust, Christine. 2009. Numerical and Metrological Graphemes: From Cuneiform to Transliteration. Cuneiform Digital Library Journal 2009 (001). http://cdli.ucla.edu/pubs/cdlj/2009/cdl j2009_001.html. Proust, Christine. 2019. Foundations of mathematics buried in school garbage (Southern Mesopotamia, early second millennium BCE). In Interfaces between Mathematical Practices and Mathematical Education, ed. Gert Schubring, 1–25. Cham: Springer. Robson, Eleanor. 1999 Mesopotamian Mathematics 2100–1600 BC: Technical Constants in Bureaucracy and Education. Oxford Editions of Cuneiform Texts 14. Oxford: Clarendon Press. Robson, Eleanor. 2001. The Tablet House: A Scribal School in Old Babylonian Nippur. Revue D’assyriologie Et D’archéologie Orientale 95: 39–66. Robson, Eleanor. 2004. Mathematical cuneiform tablets in the Ashmolean Museum, Oxford. SCIAMVS–Sources and Commentaries in Exact Sciences 5: 3–65. Robson, Eleanor. 2008. Mathematics in Ancient Iraq: A Social History. Princeton: Princeton University Press. Sommerfeld, Walter. 1992. "Die Inschriftenfunde der 10. und 11. Kampagne (1988 und 1989). In Isin-Iš¯an Bah.r¯ıy¯at IV: Die Ergebnisse der Ausgrabungen 1986–1989, edited by Barthel Hrouda, Abhandlungen der Bayerische Akademie der Wissenschaften 105, 144–164. München: Verlag der Bayerischen Akademie der Wissens.chaften. Spada, Gabriella. 2014. Two Old Babylonian Model Contracts. Cuneiform Digital Library Journal 2014 (002). https://cdli.mpiwg-berlin.mpg.de/articles/cdlj/2014-2. Spada, Gabriella. 2018. Sumerian Model Contracts from the Old Babylonian Period in the Hilprecht Collection Jena. Texte und Materialien der Hilprecht Collection 11. Wiesbaden: Harrassowitz Verlag. Tanret, Michel. 2002. Sippar-Amn¯anum: The Ur-Utu Archive 2. Per aspera ad astra. L’apprentissage du cunéiforme à Sippar-Amnanum pendant la période paléo-babylonienne tardive. Mesopotamian History and Environment 3. Gand: Université de Gand. Tanret, Michel. 2011. Learned, Rich, Famous, and Unhappy: Ur-Utu of Sippar. In The Oxford Handbook of Cuneiform Culture, ed. Karen Radner and Eleanor Robson, 270–287. Oxford: Oxford University Press. Tinney, Steve. 1999. On the curricular setting of Sumerian literature. Iraq 61: 159–172. Van Lerberghe, Karel and Gabriella Voet. 1991. Sippar-Amnânum: The Ur-Utu Archive 1: Transliterations, Translations, Comments. Mesopotamian History and Environment 1. Ghent: University of Ghent. Veldhuis, Niek. 1997. Elementary Education at Nippur, The Lists of Trees and Wooden Objects. Ph.D., University of Groningen. Veldhuis, Niek. 1997/1998. "Review of Cavigneaux, Antoine. 1996. Uruk: Altbabylonische Texte aus dem Planquadrat PE XVI-4/5 nach Kopien von Adam Falkenstein Ausgrabung in UrukWarka Endberichte 23. Mainz: P. von Zabern." Archiv für Orientforschung 44/45: 360–363. Veldhuis, Niek. 2014. History of the Cuneiform Lexical Tradition. Guides to the Mesopotamian Textual Record 6. Münster: Ugarit Verlag. Walker, Christopher Bromhead Fleming and Claus Wilcke. 1981. Preliminary report on the inscriptions autumn 1975, spring 1977, autumn 1978. Isin-Iš¯an Bah.r¯ıy¯at II: Die Ergebnisse der Ausgrabungen 1975–1978, ed. by Barthel Hrouda, Abhandlungen der Bayerische Akademie der Wissenschaften 87, 91–102. München: Verlag der Bayerischen Akademie der Wissenschaften.

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Wilcke, Claus. 1987. Die Inschriftenfunde der 7. und 8. Kampagnen (1983 und 1984). In IsinIš¯an Bah.r¯ıy¯at III: Die Ergebnisse der Ausgrabungen 1983–1984, ed. by Barthel Hrouda, Abhandlungen der Bayerische Akademie der Wissenschaften 94, 83–120. München: Verlag der Bayerischen Akademie der Wissenschaften. Wilcke, Claus (Editor), with copies by Dietz Otto Edzard and Christopher B.F. Walker, contribution by Stefan Odzuck, and introduction by Walter Sommerfeld. 2018. Keilschrifttexte aus Isin Iš¯an Bah.r¯ıy¯at : Ergebnisse der Ausgrabungen der Deutschen Forschungsgemeinschaft unter der Schirmherrschaft der Bayerischen Akademie der Wissenschaften. Abhandlungen der Bayerische Akademie der Wissenschaften 143. München: Bayerische Akademie der Wissenschaften.

Chapter 5

Stabilizing Knowledge

Abstract The study moves from the more universal scribal education marking scholarly literacy to a case study in technical literacy in this chapter. With this shift to technical literacy comes a shift in tone and method as well. This chapter focuses on the external representations of knowledge, their content and function, and uses nineteen tablets from Lagaba as an example. These nineteen tablets were previously identified as some kinds of administrative texts: drafts and memoranda. However, by studying these tablets, shape and content, it becomes clear they were produced in pursuit of education, and that they functioned to stabilize knowledge itself by transferring it from the purely scholastic to a professional environment. The knowledge acquired with the elementary scholarly education was prepared for an administrative reality using these tablets. It was contextualized with other kinds of knowledge for deployment outside of the knowledge economy and within the general economy. Keywords Learning by doing · Lagaba · Stabilized knowledge

The generative ambiguity suggested with Chap. 4 is evident in a group of 19 texts from the municipality of Lagaba (Table 5.1). These texts, when taken in isolation, give the impression that they are economic documents. They give the appearance of administering agricultural production and managing labor, silver and grain expenditures, among other things. However, the appearance of these texts on type IV tablets shows that, similar to tablets from Isin and Sippar, they are more likely the external representations of knowledge used in pursuit of an education. They offer evidence for the technical literacy that has been so elusive. They present an example of the generative ambiguity posed by external representations in stabilizing knowledge. This chapter focuses on these texts. Before exploring the texts’ contents (Sect. 5.3), it will help to contextualize these tablets a little more, in particular by introducing Lagaba (Sect. 5.1) and then introducing the tablets themselves (Sect. 5.2).

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. Middeke-Conlin, Knowledge, Literacy, and Elementary Education in the Old Babylonian Period, SpringerBriefs in History of Science and Technology, https://doi.org/10.1007/978-3-031-45226-0_5

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Table 5.1 Breakdown of tablets from Lagaba Round I. Museum number

II. Publication

III. Figure here

IV. Date

V. Archive

LB 1824

TLB 1, 132

Practice in accounting and numbers, list of reeds with total and subtraction

LB 1960

TLB 1, 125

Practice in accounting for barley production (gleaning). Sub-total and total

LB 1961

TLB 1, 136

Practice in accounting, possible total, much lost

LB 1967

TLB 1, 123

Practice in accounting, mathematical practice in silver to barley equivalency and barley interest

LB 1968

TLB 1, 124

Practice in constructing a balanced barley account

Uncertain

LB 1969

TLB 1, 129

Practice in Samsu-Iluna 23 accounting using a tabular format. Sub-total to column 1, incomplete

Imgur-edim-anna

LB 1970

TLB 1, 121

Practice in accounting, barley production with sub-total and total

Marduk-muballit. / Ili-u-Šamaš

LB 1971

TLB 1, 135

Practice in line construction, number production, and addition

Marduk-muballit. / Ili-u-Šamaš

Imgur-edim-anna

Samsu-Iluna 18

Ili-u-Šamaš / uncertain

Uncertain

Samsu-Iluna 3

Marduk-muballit. / Ili-u-Šamaš

(continued)

5 Stabilizing Knowledge

95

Table 5.1 (continued) Round I. Museum number

II. Publication

III. Figure here

IV. Date

V. Archive

LB 1972

TLB 1, 126

Basic accounting practice, list of numbers and associated personal names on the obverse, Lengths of furrows on the reverse

Marduk-muballit. / Ili-u-Šamaš

LB 1973

TLB 1, 134

Basic accounting practice, list of measurement values and personal names

Uncertain

LB 1975

TLB 1, 133

Practice in accounting, measuring and measurement vessels with sub-total and total

Uncertain

LB 1976

TLB 1, 128

Practice in accounting, barley production with sub-total and total

Uncertain

LB 1977

TLB 1, 131

Practice in line construction

Uncertain

LB 1979

TLB 1, 127

Practice in accounting, barley distributions, number of furrows mentioned

Marduk-muballit. / Ili-u-Šamaš

NBC 6286

Tammuz (1993, 228–230)

Practice in accounting. List of dates, barley, and silver. Scratchpad in tabular format on reverse

Uncertain

NBC 6288

Tammuz (1993, 230–231)

Basic practice in signs, numbers, and line production concerning barley and beer rations

Marduk-muballit. / Ili-u-Šamaš

NBC 8531

Tammuz (1996b, 127)

Practice in text structure; wood delivery

Uncertain

(continued)

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5 Stabilizing Knowledge

Table 5.1 (continued) Round I. Museum number

II. Publication

III. Figure here

IV. Date

V. Archive

Semi-rectangular LB 1963

TLB 1, 122

Accounting Samsu-Iluna 28 practice, administrative timekeeping and text compilation, receipts of beer over five consecutive months with total

Imgur-edim-anna

LB 1974

TLB 1, 130

Practice in line construction

Imgur-edim-anna?

5.1 Lagaba Lagaba is a somewhat enigmatic center. Several possible locations have been suggested for this site. Leemans, who first studied the texts from Lagaba, initially suggested that it was located in the southern part of Babylonia1 but later proposed a more northerly location near the city of Kutha.2 Frankena, challenging Leemans’ claim, located it near the city of Kiš.3 Gasche located it north of Nippur.4 Frayne, supporting Leemans, suggested it is on the Irnina canal near Kutha.5 Tammuz, in particular, suggested it must be near Kutha, stating that, ‘In the Old Babylonian Period Kutha was connected to the Euphrates by a canal. This canal was connected to the Euphrates about 15 km NNE to Babylon… Lagaba was located on the bank of this canal.’6 The latter is represented in the map found with Fig. 1.1. Whatever the case, Lagaba was certainly located in the kingdom of Babylon because the texts, when dated, state years late in the reign of king Hammurabi, around his 38th regnal year, and through his successor, Samsu-Iluna’s 30th regnal year, that is, between 1755 and 1720 BCE. After 1720 BCE, this center falls silent, part of a general trend in central Babylonia at the end of Samsu-iluna’s reign.7

1

Leemans (1952, 39). Leemans (1960, 2–5). 3 Frankena (1978, 33). 4 Gasche (1989, 126). 5 Frayne (1992, 16). 6 Tammuz (1996a, 24). Tammuz cites the text NBC 6287 and Gibson’s surveys of the area. See Gibson (1972, maps 1C and 5). 7 Boivin (2022, 625). See Sect. 1.1, above for more on Old Babylonian history. 2

5.2 The Texts

97

Debate over the city’s location alludes to an important point: the background of each text attributed to this city is unknown because they were all acquired on the antiquity market early in the last century. Thus, all evidence for life in this city, including education, necessarily comes from the textual record. The texts from this small city were first studied by Leemans in 1960.8 The focus of Leemans’ work were texts housed in Leiden. Letters from Lagaba were published by Frankena first9 and then Kraus.10 Texts in transliteration and translation housed in the Yale Babylonian Collection, both letters as well as economic texts, were examined by Tammuz in 1993 as part of his Ph.D. dissertation.11 Building on his predecessors’ studies, Tammuz focused on the construction of archives, in particular the archives of Mardukmuballit. and the familial archive of Imgur-edim-anna. Marduk-muballit. acted as the head of a bureaucratic archive that, among other things, oversaw barley on palace lands. Marduk-muballit.’s archive lasted from the end of the reign of Hammurabi and into the first few years of Samsu-iluna’s reign. Imgur-edim-anna was a local notable at Lagaba. His familial archive was chiefly active around years 28 and 29 of Samsu-Iluna, ending around the time that evidence itself waned at Lagaba and central Babylonia in general. Additional tablets and bullae have come to light since Tammuz’s dissertation. Dalley et al. published several economic texts connected to the Imgur-edim-anna family as well as a letter.12 In 2018, Siddall et al. published numerous tags attributed to Ili-u-Šamaš who worked with Marduk-muballit..13 Jacquet and Lacambre returned to these tags in 2020, adding additional details to the nature of Ili-u-Šamaš and the Marduk-muballit. archive. They make the important point that Ili-u-Šamaš was probably a brewer.14

5.2 The Texts Marduk-muballit., Ili-u-Šamaš, and the household of Imgur-edim-anna will all become important as we examine the nineteen tablets catalogued in Table 5.1. and especially in Chap. 6. These tablets were examined by Leemans and then Tammuz, who identified them as economic texts. Summing up his argument, Leemans states,

8

Leemans (1960). The archive was published in copy as (TLB 1). TLB 4 (Frankena 1965), Frankena (1968), and with further commentary to these letters provided after Frankena’s death (Frankena 1978). 10 Kraus (1985). 11 Tammuz (1993). Tammuz returned to these archives to more fully publish several texts in Tammuz (1996b) and then in his unpublished work, Texts from Lagaba. 12 Dalley et al. (2005). 13 Siddall et al. (2018). 14 Jacquet and Lacambre (2020, 23–27). 9

98

5 Stabilizing Knowledge The question arises whether these round tablets contain ordinary economic records or texts of a particular nature. Sometimes such tablets are regarded as schooltexts. But most of the present tablets evidently are not. For a number of them have the appearance of ordinary economic records and they are closely related to previous tablets… Remarkable differences with former tablets are that in the present tablets often big quantities of barley are booked, and that notwithstanding this feature most of the tablets are written in a very slovenly manner, with on the reverse or the edges signs which bear no traceable coherence at all. The impression which most of these tablets give is one of short notes, memoranda; a number of them is undated.15

Tammuz follows Leemans’ synopses, often describing round texts as drafts or memoranda. For instance, he describes NBC 6288 (Fig. 5.3) as ‘a draft that was erased and written over many times. The writer did not shape it very well and probably did not intend it to be kept as an archival document.’16 Table 5.1 catalogues the so-called ‘round tablets’ studied by Leemans and then Tammuz. However, it distinguishes between round and semi-rectangular tablets. See below for this. From there, tablets are organized by museum number in column I. Following this is the publication in which their copies can be found (Column II), content as it pertains to education (III), the regnal year written on the text when available (IV), and then archive to which I attributed each text (V). LB 1970 was on loan at the time of accession while LB 1973 is currently missing.17 Because these tablets form the basis of study on education at Lagaba, each remaining tablet, whether NBC or LB, was viewed in person or via image. Leemans published the texts found on the tablets housed in the Laigre Böhl collection in transliteration and translation in 1960 (Leemans) and then in copy in 1964 (TLB 1). However, Leemans was little concerned with the tablets on which these texts were written, publishing images of only two “round tablets”.18 As seen in Chap. 4, the tablet on which a text is written is vital to the study of knowledge, literacy, and education, offering among other things insights into the functions and utility of the text written on the tablet. This justified the production of illustrations of the tablets previously treated by Leemans in 1960 and 1964. An illustration of each so-called “round tablet” was produced to highlight the shape and characteristics of each tablet as well as the textual layout and sign shapes found on each tablet. The illustrations here supplement Leemans’ text copies but do not supplant them. An index of these illustrations by museum number can be found at the beginning of Sect. 5.4. With the illustrations the distinction between round and semi-rectangular tablets becomes apparent, as demonstrated by Figs. 5.1 and 5.2. Both figures offer illustrations of a similar tablet. The illustration of LB 1974 in Fig. 5.1 shows the shape of semi-rectangular tablets. Note for now the shape of the tablet: While LB 1974 is roughly rectangular, edges are rounded justifying the label, “semi-rectangular”. The 15

Leemans (1960, 26). Tammuz (1993, 231). 17 LB 1973 is described in the de Laigre Böhl collection’s database as round, which allows its tentative inclusion with the other round tablets. An image of LB 1970 was included in Leemans (1960), allowing certain inclusion with round tablets as well. 18 LB 1970 ((TLB 1), 121) and LB 1975 ((TLB 1) 133). See Figs. 5.15 and 5.7 here respectively. 16

5.2 The Texts

99

shape of semi-rectangular tablets separated them visually from the typical administrative texts from Lagaba and requires explanation. The shape of LB 1963 is similar to LB 1974, suggesting these two tablets belong together, perhaps the product of one singular author, a member of the Imgur-edim-anna family as I suggest in Table 5.1. However, this rounded shape is distinct from the remaining seventeen tablets, as illustrated by LB 1977 (Fig. 5.2). The round tablets are typical of the type IV tablets found in numerous centers throughout southern Mesopotamia at this time (see Sect. 4.1). If the shape of the semi-rectangular tablets rendered distinction from administrative tablets, these round tablets offered even greater disparity. Fig. 5.1 LB 1974

100

Fig. 5.2 LB 1977

Fig. 5.3 Edition of NBC 6288

5 Stabilizing Knowledge

5.3 Learning by Doing

101

There is a distinction within Leemans’ round tablets: there are smaller, semirectangular and larger round objects. Perhaps one can posit a distinction in the nature and purpose of the tablets. The round type IV tablets, similar to elsewhere in Babylonia at this time, were probably produced as a medium for educational texts. Similar to Isin and Sippar, at Lagaba, these educational texts mirrored economic texts. The tablet shape separated them from tablets used as a medium for actual administrative documents. This would have been obvious to anyone reading the texts. The semi-rectangular tablets are distinct from both varieties of tablets. They are perhaps the work of a student as well, but the shape signals a semi-official character. That is, the semi-rectangular tablets may have been employed as a means for the student to produce an actual administrative text but signaled to the owner of the archive—the teacher—that it was produced by the student. Under this hypothesis, the semi-rectangular tablets were educational in that they offered practice for the student scribe, but a practice that also yielded a useful document for the teacher. The large size and careful construction of the signs on LB 1974 suggests a less practiced scribe and supports this hypothesis. Finally, a word must be said about NBC 6288 (Fig. 5.3), which is poorly shaped. This also suggests a less experienced scribe, such as a student. However, While the tablet is poorly shaped, the rounded edges and layout of the text show it was intended as a round tablet, not the semi-rectangular tablets just described. Content, as will be discussed below, further betrays student practice. In any event, this tablet was certainly not kept as any official record, nor even as a scratchpad. With these caveats in mind, both varieties of tablets will be examined as educational objects in this work.

5.3 Learning by Doing Leemans’ suggestion that round tablets from Lagaba are probably part of some record keeping mechanism—his notes and memoranda—was intuitive at the time: while the medium, type IV tablets, suggested these were student practice tablets, the administrative character suggested otherwise to Leemans, who was writing in the 50’s and early 60’s. Indeed, distinguishing student practice from more permanent records can be difficult. Writing on the distinction between student practice tablets and reference or library tablets, Veldhuis states, “we have to recognize that we do not always know the difference and that in some cases the distinction is futile.”19 Yet in many cases such distinctions can be made. It is possible to suggest with relative certainty that a tablet, and the text written on it, is administrative or educational, and then library or practice. 19

Veldhuis (2014, 16).

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5 Stabilizing Knowledge

As shown in Chap. 1, there is both evidence for in-situ learning in Mesopotamia and evidence that the external representations of this in-situ learning could appear to us similar too, if not the same as, economic texts. However, in each case presented in Chap. 1, the substance, makeup, appearance, and even context of each text lent to the supposition that they were examples of student practice in a professional setting—a kind of ‘learning by doing’20 —and not the product of masters in pursuit of their professions. The implications of this are significant to the present project: our reconstruction of technical literacy will necessarily focus on record-keeping practice because the texts themselves emphasized record-keeping as a learning tool to present knowledge necessary to the scribal art. What follows, then, is a survey of knowledge as it was presented to the students and as it comes down to us today: as student practice in record-keeping. In so far as appearance is concerned, the use of round and semi-rectangular type IV tablets at Lagaba would signify to the ancient observer that their associated texts are student practice, similar to type I through III tablets described in Chap. 4. As Leemans stated, the texts are often poorly written. Leemans interpreted this as a rushed hand, but it is more likely that, similar to Old Akkadian Girsu and later Old Babylonian Sippar, the poor quality of writing is evidence for a less skilled hand, perhaps student practice. Student practice is especially suggested with NBC 6288 (Fig. 5.3),21 which is undated. As Tammuz observed, NBC 6288 had been erased and written over many times. This suggests a repetition in practice similar to that encountered with type IV tablets at Sippar. The poor shaping of the tablet, also noted by Tammuz, suggests that it was constructed by an inexperienced scribe. This is reinforced by the large but carefully constructed signs on the obverse, showing the inexperienced care one expects from a student scribe. NBC 6288 perhaps had four functions. First, lines 1 and 4 shows practice in writing basic number forms: the numbers ‘4(u)n ’ which is distinct from ‘4(diš)n ’, in line 1, and then the numbers 7(diš)n , 1(diš), and the number 1(u) 4(diš) in line 4. Second, line 1 also shows practice in the production of basic signs: ‘KAŠ’, ‘PA’, ‘TAB’, ‘KA’, and ‘NI’. No extant lexical list presents these signs in this order, calling into question the origin of this exercise. However, such practice in sign formation is similar to the very elementary syllabaries at Nippur and elsewhere. Third, lines 2 and 3 show the construction of proper entries in a list, similar to type IV tablets at Sippar. Here entries of barley and beer are accounted for using capacity measurement values. Finally, the appearance of sexagesimal numbers, perhaps SPVN, on the reverse implies some practice in numeracy.

20

Or when teachers present practical, real-world problems to students in order to encouraging and develop problem solving techniques. For a recent presentation of the ‘learning by doing’ approach to teaching, see DuFour et al. (2016). 21 For an image of this tablet, see its entry in the Cuneiform Digital Library Initiative, “NBC 06288 (P286246)”, https://cdli.mpiwg-berlin.mpg.de/artifacts/286246.

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Numerical practice in NBC 6288 is highly nuanced. This is evident by the two forms of ‘4(diš)’ seen in lines 1, 4, and 5. In lines 1 and 5, the number 4 is normalized, while in line 4, it is non-normalized. We see practice constructing different numeric forms as part and parcel with very basic sign practice. At this point the student is not learning calculation but instead how to write. While basic numeracy—the construction of numbers—is practiced on NBC 6288, this seems secondary to the text’s intent. Instead, the practice on this text focused more on sign construction and lexicography. Numeracy itself seems to be the focus of LB 1971 (Fig. 5.4). The obverse of the text shows five lines: in line 1 the ordinal number “1(u) 4(diš)n -kam” or “14th ” appears. This is followed by two lines that state capacity values ‘among X number gur’, followed by the total value in the fourth line and a personal name associated with these values. Perhaps the purpose of these lines was the construction of capacity values and then basic addition and subtraction of capacity values. The obverse concludes with a repetition of the ordinal, 14th. Interestingly, both examples of ‘4(diš)’ in lines 1 and 5 are normalized numbers. The reverse shows the traces of numerous numbers, typically normalized when visible, of which it is hard to conclude any relationships. One suspects this side was the result of practice in both forming numbers and calculating with numbers—a kind of student’s scratchpad during oral exercises. The appearance of numerous erasures on the obverse and reverse and additional, unrelated signs on the obverse suggest this tablet was reused. All of this encourages the supposition that LB 1971 is student practice in basic numeracy and line construction. NBC 6288 and LB 1971 present basic practice in lexicography, numeracy, and line construction. Two additional texts, LB 1974 and LB 1977, show further practice with line construction, but this time by more experienced students. Indeed, if the hypothesis presented in Sect. 5.2, concerning semi-rectangular tablets is accepted, then LB 1974 takes on a semi-official character—the student was tasked with producing an actual account, perhaps a line item to be added to another text later (see below for this). All these texts may represent an initial phase of learning with a goal similar to level 1 of the elementary education at Nippur and elsewhere: basic introduction to texts and writing. With NBC 6288 and LB 1971, the student is practicing basic sign and number forms and how these signs and numbers interact, both in the form of words and entries in texts and basic addition and subtraction. In LB 1977, the student is practicing how to construct text entries. In LB 1974 the student has mastered line construction and is entrusted, under supervision, with record keeping. Once he mastered this skill, the student would have begun to learn how to construct actual texts in a second level of education. This is seen with the next two texts. Lexical and numerical practice come together with LB 1972 (Fig. 5.5). Leemans is uncertain whether the text on the obverse and reverse of the tablet are related. Indeed, the number of furrows in line 1 of the reverse is not the total of the obverse, nor is it obviously related to the list on the rest of the reverse. The obverse witnesses practice in writing a simple list of numbers with associated personal names next to them, perhaps harvesters as Leemans suggested.22 The aspiring scribe has moved 22

Leemans (1960, 63).

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Fig. 5.4 Edition of LB 1971

beyond writing individual entries among signs and is beginning to gain literacy in text formats with LB 1972. The nature of the reverse is very different from the obverse. The reverse seems to explore agricultural accounting. The reverse starts with a number of furrows, 28. This is followed by what appears to be a practice in basic addition. There are five numerical entries, ostensibly sixties and portions of sixties. Each entry has a space next to it; perhaps personal names or field names were intended to be next to these entries. Interestingly, the—word šu-ši, ‘sixties’, is also abbreviated to just ‘šu’ in lines 2, 3, and the total in line 7 of the reverse. Addition otherwise works as expected so that the values in lines 2 through 6 produce the total in line 7.

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105

The mathematical text BM 85,194 problem 7 can help explain the reverse of LB 1972.23 Problem 7 probably described the calculation of yields out of furrows. The setup lists 4 furrows in every 30 square gin or ½ sar land. For every bur of land, there is 8 danna length of furrows, which transforms into 4 in SPVN. If a similar relationship is seen in BM 85,194 as here, then the sixties in LB 1972 probably refer to lengths of furrows so that the total length can be suggested as 4 uš 1 ½ ninda length of furrows and an area of 1 ubu 11 ½ sar land. In any event, both furrows in line 1 and numbers in lines 2 through 6, as well as the total in line 7, all have to do with the field of Gula mentioned in line 8. This field is present in Ura 5, the list of geographical names discussed in Chap. 2. Fig. 5.5 Edition of LB 1972

23

BM 85194 was first published in CT 9, pl. 8–13 and then examined variously by Neugebauer (MKT I: 142–93), Thureau-Dangin (1938, 36), and then Powell (1984, 63–64).

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Notes Rev. 8 This is probably a shortened form of ‘a-ša 3 a-gar gu-la’ found on the Old Babylonian forerunner to Ura 5 from Nippur. See MSL 11: 98 and 130 for this.

Fig. 5.5 (continued)

Practice with LB 1972 explores aspects of agricultural record-keeping and accounting. Practice on the obverse is complete while the reverse is missing large portions of the text—the names or purposes associated with each furrow. Perhaps the obverse of this text is review: the author has already learned how to compile a list and is already familiar with the entries, signs, and words associated with this list. The reverse is new, however. The author is just beginning to learn how to account for furrows. This would explain why it is incomplete. Perhaps much of it was presented orally, or the student simply did not have time to complete it before practice moved on. Whatever the case, LB 1972 probably demonstrates two kinds of information: already learned knowledge on the obverse and new knowledge on the reverse. A slightly different phenomenon may occur with LB 1824 (Fig. 5.6). In this text, large quantities appear, Leemans’ “big quantities” that he associated with memoranda. However, similar to Sargonic Girsu, this could well be interpreted as student practice. Eight entries appear on the obverse of LB 1824 using normalized numbers in system S. On the reverse the total of these entries is written: one round šar or exactly 3600 in our base 10. This is followed by a personal name and a line item. On the obverse, signs are generally well formed but large, with additional strokes added to signs, such as is seen in the numbers in line five, as well as the occasional faint strokes. Quality on the reverse, on the other hand, is generally poorer. It is also clear the student erased parts of the reverse, suggesting either reuse—the student used the back as a scratchpad and then wrote the final lines, or a mistake—the student made a mistake in calculation and was forced to re-write parts of the reverse.

5.3 Learning by Doing

Fig. 5.6 Edition of LB 1824

107

108

Notes 1

5 Stabilizing Knowledge

An extra wedge appears above the sign AB, perhaps the author started writing LUM before he realized his mistake and wrote the remainder of AB.

4

An erasure occurs with the sign LI, as well as several faint or repeated wedges, suggesting difficulty forming this sign.

5

An additional, small wedge appears before the number 7(g e š2 ) and in the number 4(u). One suspects that the author accidentally made two strikes with the stylus when one was intended with each. The sign DINGIR is missing the vertical wedge, the AMAR element holds faint wedges and is written over an erasure, and an additional wedge in the UTU element occurs in the PN, all suggesting difficulty writing the theophoric element of the PN.

11

Leemans translates AŠ as “subtracted” and is unable to reconcile this with the remaining sentence, which he leaves untranslated. (Leemans 1960, 67.) Perhaps AŠ can be normalized as dili and takes on a partitive sense (tr. ‘each’), or is used to underline that this is a unique transaction (tr. ‘alone’). Reading ‘u4-gal-lim’ is tentative. For the Ugallum demon, see Frayne et al. 2021, 353–354.

Fig. 5.6 (continued)

The information presented on the obverse was already learned. Similar to LB 1972, the author had already mastered line construction. Perhaps he was writing out from the instructor’s dictation. Or perhaps he was copying information off smaller texts similar to LB 1977. However, the student author was left to his own devices to write the reverse. There, the exercise was to tabulate the total of reeds found on the obverse and then complete the accounting: insert the associated authority behind these reeds and any qualifier to the transaction. In carrying out his tabulation, the author probably used the reverse as a scratchpad first. Having completed his tabulation, he erased the reverse and wrote out his answer and then the remainder of the tablet over it. In any case, one gets the impression that the student is reinforcing the relationships between numbers as an exercise in accounting as well as practicing a newly introduced aspect of record-keeping. He has moved beyond the simple lists seen in LB 1972 to full accountings. Metrological practice is possibly observed with LB 1975 (Fig. 5.7).24 In this text different standard vessels are employed to qualify flour, such as the 3-ban standard 24

For a discussion of metrological practices in the Old Babylonian period, see Middeke-Conlin (2020a, 139–175).

5.3 Learning by Doing

Fig. 5.7 Edition of LB 1975

109

110

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Notes 2 3

5, 8

My translation “3-ban standard-vessel” follows Proust 2022. CAD Š III 99-100 describes šiqqu as a kind of fish sauce. However, šīqu C (ibid 102) is defined as a measure of capacity dating to the Old Babylonian period, among others. Here it is notably listed following the word ‘dug’, designating it as a jar or pot used to measure liquid capacity. For the kūtum vessel, see CAD K, 611-612, where it is described as “a container of clay or metal, rarely of wood” and attested in the Old Babylonian period with LB 1975, as well as in Elam (MDP 22 83: 4, wr. ku-di) and in Alalakh Wiseman 1953, no. 56: 16, 32, wr. ku-ut-ti, ku-ut-ta-a-at.” Black et. al. (2000, 171) translates this as a ““jug, can” for liquids”.

Fig. 5.7 (continued)

vessel in line 2 as well as at least two unusual standards: the š¯ıqim-jar in line 3 and the k¯utum-jug in line 5. Both are typically used as liquid capacity containers.25 A statement of remeasurement in lines 1 and 10 presents the possibility that measurement techniques were also being learned with LB 1975. If so, then the teacher in this case presented both the different standard vessels and measuring techniques as commentary that accompanied the production of this text, similar to that encountered already in the Old Babylonian scribal curriculum from Nippur and elsewhere. Finally, basic additions of metrological values are seen with the subtotal of line 6 and total of line 9. If this text does not merely represent a hypothetical exercise, then one gets the impression that this text resulted from an observation. The student was asked to observe and record what the instructor was doing. Thus, the student stated the activity in the first line, remeasurement. He then stated observed remeasurements in lines 2 through 8. Following this, he was told to tabulate the quantities of remeasured grain on the reverse and insert the place of remeasurement as a qualifier. Again, the student was learning how to produce a proper record with LB 1975. At the same time, the student was learning an important, hands-on aspect of the scribal art, namely measurement and remeasurement, the natures of different, sometimes rare 25

For recent, in-depth discussions of standard vessels, see Chambon (2011), de Boer (2013), and Proust (2022).

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vessels, and the significance of location, all accompanied by commentary. LB 1972, LB 1824, and LB 1975 probably represent a second phase of education at Lagaba, in which thematic elements were explored. This practice incorporated furrows and geographical practice in LB 1972, reeds and basic addition with LB 1824, and standard vessels and practices in LB 1975. This second phase tied basic, thematic content to record keeping practices. Following this phase was more difficult practice, tying mathematical processes with more complex record-keeping techniques. Such more advanced economic and mathematical practice is evidenced by LB 1967 (Fig. 5.8). The text presents practice in calculating equivalencies, that is, the assessment of one commodity in terms of another commodity, and in calculating interest.26 An equivalency is made in lines 1 through 3: An initial value in silver is stated in line 1. This is followed by the rate in barley per measure of silver in line 2, and then the equivalent value in capacity of barley in line 3. On the left edge of this text is written 26:36, which can be understood as a truncation of the SPVN transformation of the measurement value seen in line 1: 1/3 mana → 20 6 gin → 6 1/2 gin → 30 20 še → 6:40 10 + 6 + 30 + 6:40 = 26:36:40

Here the measurement value seen in line 3 is subdivided into values found on the standard capacity table discussed in Chap. 3 to better reflect transformation. The student-author omitted the final element of this number, ‘40’. This shows that the student learned to transform measurement values to and from SPVN and to carry out multiplication using SPVN. Interestingly, the barley equivalency to this silver is a rounded value: the author of this text probably rounded the expected value up to the stated value.27 The student is learning how to produce approximations, a very useful activity for a merchant-administrator at this time.28

26

The production of equivalencies is the topic of several problems and procedures found in mathematical texts, including statement 3 and possibly 4 of YBC 4698. For this text, see most recently Middeke-Conlin and Proust (2014) and Friberg and al-Rawi (2016, 421–446). Friberg and al-Rawi label them ‘combined market rate exercises’. 27 One can speculate that rounding was carried out in SPVN to simplify transformation from SPVN to measurement value: 5:10:27:46:40, which would transform into 1 geš 2 gur 2 ban 7 2/3 sila 20 še, was rounded up to 5:10:30, which transforms into 1 geš 2 gur 3 ban. 28 For an in-depth study concerning the importance of rounding and other approximations to scribal education and scribal culture, see Middeke-Conlin (2020a).

112

Fig. 5.8 Edition of LB 1967

5 Stabilizing Knowledge

5.3 Learning by Doing

Edge

113

An additional, faint wedge outlines the first of the lower vertical wedges of the lower row of the number 6(diš). The author seems to have struck this wedge twice when forming the number 6.

Fig. 5.8 (continued)

A second calculation appears after a ruling in lines 4 through 6, this time concerning the calculation of barley interest29 : 33 gur 1 bariga → 2:46 11 gur 2 ban → 55:20 55:20 × 3 = 2:46 2:46 × 20 = 55:20

Accrued barley interest is exactly one-third of the barley principal and is the standard barley interest of one-third the principal as witnessed in numerous texts, including mathematical texts.30 However, while LB 1967 pretends to mimic professional procedure, a total of accrued barley interest is never stated in the barley loan texts from Lagaba.31 This marks a deviation from standard procedure that further betrays this text’s educational character. This is evident in, for instance, NBC 8874, a real-world loan of ½ gin silver made by Marduk-muballit. to Ili-u-Šamaš (Fig. 5.9).32 In NBC 8874 the loan is made at “the established interest rate” while principal silver and accrued interest will be paid out at the delivery of harvest. No specific amount 29

Interest problems appear in multiple mathematical texts of the Old Babylonian period, such as VAT 8521 and VAT 8528. For these texts, see especially Muroi (1990, 29–34). For more on interest, see Middeke-Conlin and Proust (2014, §6 #1), and Friberg and al-Rawi (2016, 421–428). 30 See Middeke-Conlin and Proust op. cit. as well as Friberg and al-Rawi op. cit. 31 See Tammuz (1993), especially nos. 47–52 and 54–55, for the loan texts from Lagaba. 32 Edition of NBC 8874 is after Tammuz 1993, 306–307.

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Fig. 5.9 NBC 8874

of interest is applied to this loan because it is incomplete and will not be completed until it matures and is repaid. Then and only then will an interest be applied to the loan. More difficult record-keeping practice is seen with tablets like LB 1969 (Fig. 5.10), on which appears a text in tabular array. Columns are described in their headings as ‘expended’ in column 1, ‘received’ in column 2, ‘remainder’ in column 3, and ‘person’, or the individual to which each entry was allocated, in column 4. Capacity measurement values in column 1 are totaled. A subtraction of column 2 from column 1 was clearly intended with column 3. This subtraction was not completed, suggesting either a lack of skill in the learner, a lack of time in the academic environment, or that this exercise was completed orally. Further practice in record-keeping techniques, specifically practice in administrative timekeeping and text compilations, can be surmised with LB 1963 (Fig. 5.11). The importance of timekeeping to LB 1963 is seen in lines 1 through 5, in which the author of this text associates the names of months two through six with capacity measurements. The appearance of a date formula underlines the importance of administrative timekeeping to this text. These lines are followed by a sub-total in line 6, the receiving agent in line 7, and then the sender in line 8, showing practice in basic record-keeping. Line 9 suggests this tablet may also represent practice in compiling data from other documents, perhaps from actual economic texts. The author of LB 1963 may have compiled the text out of thirteen day, week, or month accounts, which would have been provided by the instructor or which the student would have produced in previous exercises. Such an exercise is perhaps seen with LB 1974 discussed above (Fig. 5.1). One can easily speculate that consolidating data found on disparate accounts into one account was an important but difficult skill for an aspiring scribe to learn for a simple reason: Record-keeping was conducted using

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115

clay tablets. Because clay dries, scribes had to be able to both keep track of old records and also to compile these old records into new, updated records.33 Fig. 5.10 Edition of LB 1969

33

For different record-keeping strategies, see Steinkeller (2003) and Hallo (2004).

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Notes 5, 6 column 1 A small winkelhaken follows each entry, what Leemans calls, ““checking” marks” (TLB 1, 79, n. 12, p. 23), 9, column 4 For the reading uš-ta-an-[ni-diĝir] as Uštaš[ni-ilim], see CAD Š1, 409 šanu A 6 b. 11 Signs on this line are illegible, partly due to the break above, partly because the line itself appears to have been used as a kind of scratchpad.

Fig. 5.10 (continued)

Finally, practice in record-keeping mimicked real life. This is as much seen with, for instance, LB 1960 (Fig. 5.12), the text on which is reminiscent of the economic texts on three other tablets from the archive of Marduk-muballit.: LB 1986, LB 1956, and LB 1843.34 All four texts mention gleanings of barley. However, unlike the other texts, LB 1960 is written with poorer quality signs, is more difficult to read, and the layout is confusing, all of which suggests a less skilled scribe. Layout is especially interesting: the author writes two additional lines horizontally over the right edge, proceeds to write two more lines over the left edge, and the date formula over the upper edge. This renders the impression that the scribe was unskilled in estimating the space needed to produce a text. 34

TLB 1, 95 through 97 respectively. These texts appear in transliteration and translation in Leemans (1960), 41–43.

5.3 Learning by Doing Fig. 5.11 Edition of LB 1963

117

118

Notes 1–5

6 10

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The month names on this text are glossed as months 2 through 6, rather than translating them as Aiaru, Simānu, Dumuzi, Abū, or Elūlu respectively. This is because, as Greengus already points out, while the Sumerian bara-za-gar series of month names was commonly used throughout Babylonia, the Akkadian names for these months are not necessarily derived from the Nisannu series (Greengus 1987, 209–29, especially 209–211, and Greengus 2001, 257–67, especially 257–259). For instance, in Sippar, the Akkadian translation of month 2 is gusisi, month 3 is qāti-ir itim, month 4 is elūnum, month 5 is Abum, and month 6 is tirum. This is different from that found in the Diyala valley and that found in the kingdom of Šamši-Adad. See Greengus 2001, 267, chart 1 for these month names. sila 3 is written over an erasure. ag 2 is written over an erasure.

Fig. 5.11 (continued)

The texts studied here were misidentified early on according to the evidence available at the time. When taken as a group and then examined as both objects and texts, it becomes clear that each tablet was the product of a kind of education into record keeping: Seventeen tablets are clearly type IV tablets used throughout Babylonia at this time for student exercises. Two semi-rectangular tablets clearly separate themselves from typical administrative practice; they are not the rectangular tablets typical for Lagaba. The tablet shape and content betray both a lack of experience, especially NBC 6288 and LB 1971 (Figs. 5.3 and 5.4 respectively), practice atypical to professional standards, such as LB 1960 and 1967 (Figs. 5.11 and 5.8), and the inexperienced care one expects with students learning an activity, such as NBC 6288 and LB 1974 (Figs. 5.2 and 5.3 respectively). Numbers, in particular, give the impression of student practice—unusually round numbers, repetitions, roundings, and so on. See, for instance, LB 1824, LB 1971, and LB 1967 (Figs. 5.6, 5.3, and 5.8 respectively). There are examples of clear lexical practice as well, as witnessed in NBC 6288 and LB 1972 (Figs. 5.3 and 5.5). Sometimes, entries clearly reflect the lexical texts, such as the appearance of the field of Gula in LB 1972: 8 and LB 1960: 16 (Figs. 5.5 and 5.12), which is also seen in Ura 5. Mistakes, aberrant sign forms, erasures, incomplete exercises, and so on are common to these texts. This list could go on ad nauseam. The clear impression that is given by these tablets and their associated texts is one of student practice in a professional environment.

5.3 Learning by Doing

Fig. 5.12 Edition of LB 1960

119

120

' '

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' ' ' ' ' ' ' ' ' ' '

Notes 15 -16 These lines are to the right of lines 10 and 11 on Leeman’s copy. On the tablet, they appear wrapping around the edge of the text horizontally. 16 For this field, see LB 1972 rev. 8. 17 -18 These lines appear on the left edge of the tablet vertically, circling the tablet itself, 17 The sign ‘TI’ is malformed and therefor the reading ‘su-t i-a’ is very tentative. 19 -20 These lines appear on the upper edge of the tablet, separated from the lines 17 -18 .

Fig. 5.12 (continued)

It is also clear that the tablets themselves were employed in two ways: as a means to transmit knowledge to the next generation of scribes through practice and in so doing to stabilize this knowledge in a professional environment. The type IV round and semi-rectangular tablets on which these exercises appear afforded an environment to practice the lexical, numerical, and documentary tasks necessary for a scribe without compromising professional standards. Type IV tablets were not easily mistaken for actual administrative documents. They were recognizable as the space necessary for a student scribe to practice his or her craft, to make mistakes, and to learn new (to the student) knowledge. The semi-rectangular tablets allowed a student to carry out his or her craft without compromising office standards because they showed the potential for error even if they were actual record-keeping documents. They advertised to the teacher that the author was inexperienced. At the same time, they allowed the author to interact in a professional capacity as a kind of apprentice.

5.4 Additional Tablet Illustrations

121

This is all the kind of ambiguity expected from external representations of knowledge. They can mimic the real world because they are meant to present knowledge necessary to interact in the real world. Such mimicry stabilized knowledge by applying it to the world of professional practice. It is not simply some abstract knowledge but instead applicable to the real world. At the same time the external representations of knowledge are quite obviously not the real world, or not fully part of the real world. They are liminal in this respect, a midway point between the theoretical world of the scholar and the practical world of the skilled professional. They are the interface, in this way, between the teacher and student or the current practitioner and future practitioner. They are witnesses to us of both the knowledge economy and the knowledge system idealized by this economy.

5.4 Additional Tablet Illustrations This section provides illustrations of the remaining so-called round tablets from the de Laigre Böhl collection. Tablets are organized by museum numbers. An index of tablets is provided, listing museum numbers, the publication in which Leemans’ original copies can be found, dimensions, and then the figure in which each illustration is presented. Dimensions are in millimeter. With round tablets they are by diameter and thickness. With semi-rectangular tablets, dimensions are by length by width by thickness (Table 5.2). Table 5.2 Index of tablets

Museum number Text copy

Dimensions

Location

LB 1824

TLB 1, 132 77 × 29.3

Fig. 5.6

LB 1960

TLB 1, 125 66 × 29.2

Fig. 5.12

LB 1961

TLB 1, 136 82.8 × 38

Fig. 5.13

LB 1963

TLB 1, 122 45.5 × 49.7 × 20.7 Fig. 5.11

LB 1967

TLB 1, 123 80 × 30.2

Fig. 5.8

LB 1968

TLB 1, 124 72.4 × 24

Fig. 5.14

LB 1969

TLB 1, 129 68 × 22.7

Fig. 5.10

LB 1970

TLB 1, 121 NA

Fig. 5.15

LB 1971

TLB 1, 135 56 × 19.7

Fig. 5.4

LB 1972

TLB 1, 126 56.4 × 20.5

Fig. 5.5

LB 1974

TLB 1, 130 43.7 × 46 × 26.4

Fig. 5.1

LB 1975

TLB 1, 133 64 × 23

Fig. 5.7

LB 1976

TLB 1, 128 77 × 26.3

Fig. 5.16

LB 1977

TLB 1, 131 57.2 × 25

Fig. 5.2

LB 1979

TLB 1, 127 71 × 29.5

Fig. 5.17

122

Fig. 5.13 LB 1961

5 Stabilizing Knowledge

5.4 Additional Tablet Illustrations

Fig. 5.14 LB 1968

123

124

Fig. 5.15 LB 1970

Fig. 5.16 LB 1976

5 Stabilizing Knowledge

5.4 Additional Tablet Illustrations

Fig. 5.16 (continued)

Fig. 5.17 LB 1979

125

126

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Fig. 5.17 (continued)

References Black, J., A. George, and N. Postgate. 2000. A Concise Dictionary of Akkadian. 2nd ed. SANTAG 5. Wiesbaden Harrassowitz Verlag. Boivin, Odette. 2022. The Kingdom of Babylon and the Kingdom of the Sealand. In The Oxford history of the Ancient Near East Volume II: From the End of the Third Millennium BC to the Fall of Babylon, ed. Karen Radner, Nadine Moeller, and Daniel T. Potts, 566–655. New York: Oxford University Press. British Museum. Department of Egyptian and Assyrian Antiquities. 1900. Cuneiform texts from Babylonian tablets, &c. in the British Museum. Part 9. London: Trustees of the British Museum. Civil, Miguel and Erica Reiner. 1974. The Series HAR-ra = hubullu: Tablets XX-XXIV. Materialien zum Sumerischen Lexikon 11. Roma: Pontificium Institutum Biblicum. Chambon, Grégory. 2011. Normes et pratiques : L’homme, la mesure et l’écriture en Mésopotamie I. Les mesures de capacité et de poids en Syrie Ancienne, d’Ébla a Émar. Berlin Beiträge zum Vorderen Orient 21. Gladbeck: PeWe-Verlag. Dalley, Stephanie with copies contributed by Eleanor Robson and Tina Breckwoldt. 2005. Old Babylonian Texts in the Ashmolean Museum. Oxford Editions of Cuneiform Texts 15. Oxford: Clarendon Press. de Boer, Rients. 2013. Measuring Barley with Šamaš in Old Babylonian Sippar. Akkadica 134: 103–116. DuFour, Richard, Rebecca DuFour, Robert Eaker, Thomas W. Many, and Mike Mattos. 2016. Learning by Doing: A Handbook for Professional Learning Communities at Work, 3rd ed. Bloomington: Solution Tree. Frankena, Rintje. 1965. Altbabylonische Briefe. Tabulae Cuneiformes a F. M. Th. de Liagre Bohl Collectae Conservatae 4. Leiden: Nederlands Institute Voor Het Nabije Oosten.

References

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Frankena, Rintje. 1968. Briefe aus der Leidener Sammlung. Ed. Fritz R. Kraus. Altbabyloniche Briefe in Umschrift und übersetzung 3. Leiden: E.J. Brill. Frankena, Rintje. 1978. Kommentar zu den Altbabvlonischen Briefen aus Lagaba und Anderen Orten. Studia ad Tabulas Cuneiformes Collectas a F. M. Th. de Liagre Bohl Pertinentia 4. Leiden: Nederlands Instituut voor het Nabije Oosten. Frayne, Douglas R. 1992. The Early Dynastic List of Geographical Names. American Oriental Series 75. New Haven: American Oriental Society. Frayne, Douglas R., and Johanna H. Stuckey, Stéphane Beaulieu (illustrator). 2021. A Handbook of Gods and Goddesses of the Ancient Near East: Three Thousand Deities of Anatolia, Syria, Israel, Sumer, Babylonia, Assyria, and Elam. University Park: Eisenbrauns. Friberg, Jöran, and Farouk al-Rawi. 2016. New Mathematical Cuneiform Texts. Sources and Studies in the History of Mathematics and Physical Sciences. Cham: Springer. Gasche, Hermann. 1989. La Babylonie du XVIIe siècle avant notre ère : approche archéologique, problèmes et perspectives. Mesopotamian History and Environment, Series 2, Memoirs 1. Ghent: The University of Ghent. Gibson, McGuire. 1972. The city and area of Kish. Miami: Field Research Projects. Greengus, Samuel. 1987. The Akkadian Calendar at Sippar. Journal of the American Oriental Society 107: 209–229. Greengus, Samuel. 2001. New evidence on the Old Babylonian Calendar and real estate documents from Sippar. Journal of the American Oriental Society 121: 257–267. Hallo, William W. 2004. Bookkeeping in the 21st Century BCE. In Creating Economic Order: Record-Keeping, Standardization and the Development of Accounting in the Ancient Near East, ed. Michael Hudson and Cornelia Wunsch, 89–106. Bethesda: CDL Press. Jacquet, Antoine and Denis Lacambre. 2020. New etiquettes from Lagaba concerning beer and by-products, and the placement of the year MU GIBIL. N.A.B.U. Nouvelles Assyríologíques Bréves et Utílítaíres (1 (mars)): 23–27. Kraus, Fritz R. 1985. Briefe aus kleineren westeuropäischen Sammlungen.Altbabylonische Briefe in Umschrift und übersetzung 10. Leiden: Brill. Leemans, Wilhelmus F. 1952. Ishtar of Lagaba and her Dress. Studia ad tabulas cuneiformes collectas a F. M. Th. de Liagre Böhl pertinentia 1 (1). Leiden: E .J. Brill. Leemans, Wilhelmus F. 1960. Legal and administrative documents of the time of Hammurabi and Samsuiluna (mainly from Lagaba). Studia ad tabulas cuneiformes collectas a F. ˘M. Th. de Liagre Böhl pertinentia 1 (3). Leiden: E. J. Brill. Leemans, Wilhelmus F. 1964. Old Babylonian legal and administrative documents. Tabulae Cuneiformes a F. M. Th. de Liagre Böhl Collectae: Old Babylonian 1. Leiden: Nederlands Instituut voor het Nabije Oosten. Middeke-Conlin, Robert. 2020a. The Making of a Scribe: Errors, mistakes, and rounding numbers in the Old Babylonian kingdom of Larsa. Why the Sciences of the Ancient World Matter 4. Cham: Springer. Middeke-Conlin, Robert. and Christine Proust. 2014. Interest, Price, and Profit: An Overview of Mathematical Economics in YBC 4698. Cuneiform Digital Library Journal 2014 (003). http:// cdli.ucla.edu/pubs/cdlj/2014/cdlj2014_003.html Muroi, Kazuo. 1990. Interest Calculation of Babylonian Mathematics: New Interpretations of VAT 8521 and VAT 8528. Historia Scientiarum 39: 29–34. Neugebauer, Otto. 1935. Mathematische Keilschrifttexte I. Quellen und Studien zur Geschichte der Mathematik Astronomie und Physik. Berlin: Julius Springer. Powell, Marvin A. 1984. Late Babylonian Surface Mensuration. Archiv Für Orientforschung 31: 32–66. Proust, Christine. 2022. Volume, brickage and capacity in Old Babylonian mathematical texts from southern Mesopotamia. In Cultures of Computation and Quantification in the Ancient World: Numbers, Measurements and Operations in Documents from Mesopotamia, China, and South Asia, ed. Karine Chemla, Agathe Keller, and Christine Proust, Why the sciences of the Ancient World Matter 6, 197–264. Cham: Springer.

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Scheil, Vincent. 1930. Actes juridiques susiens. Mémoires de la Délégation en Perse 22. Paris: Librairie Ernest Leroux. Siddall, Luis R., Wayne Horowitz, and Peter Zilberg. 2018. Old Babylonian clay bullae from Lagaba in the Australian Institute of Archaeology and other collections, buried History. The Journal of the Australian Institute of Archaeology 54: 11–14. Steinkeller, Piotr. 2003. Archival Practices at Babylonia in the Third Millennium. In Ancient Archives and Archival Traditions: Concepts of Record-Keeping in the Ancient World, ed. Maria Brosius, 37–58. Oxford: Oxford University Press. Tammuz, Oded. 1993. Archives from Lagaba. PhD.: Yale University. Tammuz, Oded. 1996a. The Location of Lagaba. Revue D’assyriologie Et D’archéologie Orientale 90: 19–25. Tammuz, Oded. 1996b. Two small archives from Lagaba. Revue D’assyriologie Et D’archéologie Orientale 90: 121–133. Thureau-Dangin, F. 1938. Textes mathématiques babyloniens. Ex Oriente Lux 1. Leiden: E. J. Brill. Veldhuis, Niek. 2014. History of the Cuneiform Lexical Tradition. Guides to the Mesopotamian Textual Record 6. Münster: Ugarit Verlag. Wiseman, Donald J. 1953. The Alalakh Tablets. London: The British Institute of Archaeology at Ankara.

Chapter 6

Outside the Eduba

Abstract This short chapter concludes this work by focuses on the place of technical literacy outside of the classroom and on localizing functional literacy. First, Sect. 6.1 focuses on technical literacy. Two educational environments in the city of Lagaba are proposed: the one a tutelage between one office-holder to the next, the other a home-school. A basic curriculum is outlined for these environments. Finally, a theory is proposed on technical literacy, suggesting each iteration is its own microeconomy mixing local and global knowledge (Sect. 6.2). From this theory we move onto functional literacy, which was derived from and emblematic of local knowledge propagated by the activities of the parents and community in general, derived from orality and action, and then extended in the classroom as available. Orality, important to generating scholarly and technical literacy, was particularly vital to the acquisition of functional literacy. Keywords Technical literacy · Functional literacy · Orality · Literacy levels

The external representations of knowledge served to expand knowledge, stabilize knowledge, and then insure its longevity through transmission. The tablets presented in Chap. 5 stabilized this knowledge by illustrating the applicability of cuneiform culture, as expressed by the prose, numeracy, and document, to an administrative environment. As tools to transmit this knowledge, they assured the longevity of this knowledge system. But where was this knowledge system acquired? Was it relegated to the classroom as we saw with the Eduba? Or could it be acquired elsewhere, perhaps an apprenticeship, or even at home? This concluding chapter attempts to answer these questions and in so doing to localize technical (Sect. 6.1) and functional literacy (Sect. 6.2). In so doing, we will explore what constituted literacy in this environment. We will see a distinction between local knowledge and global knowledge, as well as where education fits in each.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. Middeke-Conlin, Knowledge, Literacy, and Elementary Education in the Old Babylonian Period, SpringerBriefs in History of Science and Technology, https://doi.org/10.1007/978-3-031-45226-0_6

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6.1 Technical Literacy To start with, it will help to review what exactly was presented at Lagaba, and what is missing from our evidence. As seen in Chap. 5, there was lexical practice and practice in constructing short sentences or phrases. There was practice in the construction of basic numerical and measurement values, measurement techniques, basic addition and subtraction, accounting techniques, and then more advanced equivalencies and loan interest calculations using SPVN. Finally, there was practice in constructing texts reminiscent of real-world situations, with particular focus on land tenure as well as barley and barley products like beer. Administrative timekeeping was important to this practice in text construction. Oral commentary probably made up a significant part of a scribe’s education, bridging the gap between rote learning and professional procedure in a similar manner as is surmised for education in the major urban centers of Babylonia. To date, the nineteen tablets presented in Chap. 5 are the only evidence for education at Lagaba. However, Lagaba has not been scientifically excavated so that all texts studied from this municipality lack firm provenance. This means that, if they exist, some tablets were probably not properly attributed to Lagaba. Tablets like the type I, II, and III practice tablets often do not have a full colophon that could afford attribution to a specific environment. Thus, it is impossible at this point to state what additional texts accompanied these type IV tablets. However, at Isin and Sippar, both places where student practice could resemble economic or administrative texts, education included lexical, metrological, and numerical practice more typical of the erudite scribal curriculums witnessed throughout Babylonia at this time. At Sippar, 21.25% of tablets were type IV tablets employed to stabilize the knowledge memorized using type II and III tablets. From this we can speculate that, at Lagaba, the round and semi-rectangular type IV tablets served to reinforce and stabilize education introduced with other tablets and their corresponding texts. Type IV tablets probably did not stand alone at Lagaba. However, the extent of their employment against other practice cannot be speculated. Student practice at Lagaba probably started with texts from the traditional scribal curriculum outlined in Chaps. 2–4. Vestiges of the very beginnings of literacy, perhaps corresponding to level 1 elementary education at Nippur and elsewhere, is visible in texts like NBC 6288, LB 1971, and perhaps LB 1974 and LB 1977. Basic line construction and list formation is seen next, visible with LB 1972 and LB 1824. General themes, such as furrows and geography (LB 1972), reeds, and standard vessels, as well as basic mathematical processes like addition, subtraction, and measurement techniques were tied into the production of lists as documents in a second level of education. This level was perhaps tied to level 2 elementary practice discussed in Chap. 4. This is suggested with texts like LB 1972, LB 1824, and LB 1975. Finally, there was more difficult practice, including the production of difficult texts like a text in tabular array or a balanced account, or production of equivalencies and the calculation of interest—practice that required the use of SPVN in a higher level of education. See LB 1969, LB 1968, and LB 1967 for examples of these more

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advanced practices. This later level is difficult to apply to one distinct phase of the elementary education witnessed at Nippur and elsewhere. Perhaps, similar to Uruk, a kind of shortcut was taken to bridge earlier elementary and more advanced practice. In any event, a third level is suggested by the texts from Lagaba. Tammuz found two main archives in his study: an earlier archive, dated to the end of Hammurabi’s reign and the beginning of the reign of Samsu-iluna, that was governed by Marduk-muballit., and then a second archive dated to around Samsuiluna’s 28th and 29th years in power (1722–1721 BCE) that centered around the Imgur-edim-anna family. When texts are organized by archive and then date, at least three educational groups become apparent in Lagaba, as illustrated by Table 6.1. Working with Marduk-muballit. was a subordinate, Ili-u-Šamaš. Tammuz, describing this working relationship, states, ‘when Marduk-muballit was operating in Lagaba, he shared an “office” with his subordinate Ili-u-Šamaš… In Samsuiluna 19, Ili-uŠamaš continued to do exactly what he did under Marduk-muballit, only with no one to supervise his activity.’1 It seems that LB 1967, among other educational texts from late in the reign of Hammurabi and early in the reign of Samsu-iluna, were the product of Ili-u-Šamaš in so far as he was a young student to Marduk-muballit.. This is the first educational group. LB 1960, concerning barley gleanings, was probably produced under the guidance of Ili-u-Šamaš by his own young protégé just before or shortly after Ili-u-Šamaš had taken over full management of this bureau from Marduk-muballit.. This is the second educational group. Finally, a third educational group consisted of texts dated late in the reign of Samsu-iluna. This group was run by a member of the Imgur-edim-anna family. This is underlined by names found in this group, such as the name Ruttum, the daughter of Imgur-edim-anna, who appears in LB 1963. This text is perhaps the product of practice in this household environment, perhaps by one of the four grandchildren of Imgur-edim-anna.2 Education in Lagaba followed family and office, but not necessarily profession. That is to say, education took place in the household of Imgur-edim-anna and in the office of Marduk-muballit. as he administered palace resources. However, Iliu-Šamaš was probably a brewer by profession,3 while Marduk-muballit. probably was not. A survey of the texts shows that the activities of Ili-u-Šamaš make little mention of Marduk-muballit.,4 suggesting that these two did not share a craft. Beyond a shared office, there is little to connect Marduk-muballit. and Ili-u-Šamaš. Nor is there evidence for more than one student associated with Marduk-muballit.. Education was personal in this regard. It probably took place in the office of Marduk-muballit., perhaps to train one local professional, Ili-u-Šamaš, as a successor in the office.5 Because education transfers knowledge from one office holder to the next, and not 1

Tammuz (1993, 479). See ibid., 485 for a family tree. See Sect. 5.2 for the caveats to treating this text as the product of an educational environment. 3 Jacquet and Lacambre (2020, 24). 4 See, for instance, ibid., 25–26, Table 1. 5 Activity as a brewer would not preclude Ili-u-Šamaš from interacting with and overseeing palace resources. Nor were offices necessarily filled by a specific profession. For instance, multiple actors with varied careers worked to organize the shipment of barley to the city of Larsa late in the reign 2

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Table 6.1 Breakdown of texts from Lagaba by archive and date Museum number Month Day Year

Archive

NBC 6288

Marduk-muballit. / Ili-u-Šamaš Marduk-muballit. / Ili-u-Šamaš

LB 1971 LB 1972 LB 1967

4

20

Samsu-Iluna 3 (1747 BCE)

Marduk-muballit. / Ili-u-Šamaš Marduk-muballit. / Ili-u-Šamaš Marduk-muballit. / Ili-u-Šamaš

LB 1970

5

5

LB 1979

7

9

LB 1960

1

16

Marduk-muballit. / Ili-u-Šamaš Samsu-Iluna 18 (1732 BCE) Ili-u-Šamaš / uncertain student

12

14

Samsu-Iluna 23 (1727 BCE) Imgur-edim-anna

LB 1824 LB 1969 LB 1963 LB 1974

Imgur-edim-anna Samsu-Iluna 28 (1722 BCE) Imgur-edim-anna Imgur-edim-anna?

one craftsperson to the next, the word “tutelage” is a better fit than “apprenticeship” when describing this educational environment. The office holder transfers only a part of his knowledge to the student, scribal knowledge associated with his office. The brewer’s trade came from elsewhere. As education at Lagaba begins to take shape, it must be asked, from where these exercises were derived? The texts LB 1967, LB 1960, as well as NBC 6288 can help answer this inquiry. LB 1967 was probably produced in Samsu-Iluna’s 3rd regnal year under the authority of Marduk-muballit.. As stated above (Sect. 5.1), Marduk-muballit. was head of a bureaucratic archive that, among other things, oversaw barley on palace lands. This would explain the focus on barley equivalencies and barley interest in LB 1967. In fact, there are numerous examples of texts dealing with barley loans from Marduk-muballit.’s archive.6 LB 1960, on the other hand, was produced fifteen years later, in Samsu-Iluna’s eighteenth regnal year (1732 BCE). This text could be connected to three economic texts dated to Samsu-Iluna year 3 (1747 BCE), that is LB 1968, LB 1956, and LB 1843. All four texts deal with the gleaning of barley. While LB 1960 is probably student practice, the other three older texts describe real-world activity concerning fields managed by Marduk-muballit.. As noted earlier, lexical practice on NBC 6288 could not be linked to any academic list, calling into question the source material used by the instructors. Focus on real world activities, especially underlined by the content of LB 1967 as well as the similarity between the student practice text LB 1960 and actual economic texts, suggests that the subject matter presented on the round and semi-rectangular type IV tablets was, by and of Warad-Sîn and early in the reign of R¯ım-Sîn. See Breckwoldt (1995/1996, 71), for this. A similar situation of skilled craftsmen and merchants acting on the palace’s behalf can be suggested for the current archive as well. A brewer would certainly have had a vested interest in the maintenance of the barley supply, and, in so far as he acted as a merchant, a brewer would need an education in record-keeping as well. 6 See Tammuz (1993, nos. 47–52 and 54–55).

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large, derived directly from the experience and records of the instructor. However, the appearance of the field of Gula in LB 1972 and LB 1960 suggests familiarity with the lexical tradition taught at Nippur and elsewhere. This is not limited to Mardukmuballit. and Ili-u-Šamaš. LB 1963 of the Imgur-edim-anna family was probably compiled out of day, week, or month accounts that the instructor provided, or were composed by the student. Curriculum in Lagaba was to a significant degree derived from real world situations, directly from or based on situations encountered by the instructors—the ‘learning by doing’ mentioned early in Sect. 5.3. However, it’s also clear that this practice, to greater or lesser degree, must have drawn on the lexical and mathematical traditions typical of the erudite educations taught at Nippur and elsewhere. Practice in these texts focused on utility. All environments were designed to inculcate students with the ability to produce administrative or economic documents. With the semi-rectangular tablets both practice and utility come to the fore. For instance, LB 1963 is one of two semi-rectangular objects with a semi-official character marking an actual administrative document produced by an inexperienced student-scribe. Such practice would have afforded a kind of ‘assistant’ status to the pupil, allowing the pupil to carry out student practice while at the same time producing real administrative documents. The utility of these documents was limited, however. The semirectangular shape of the tablets advertised the inexperience of the student-assistant to the instructor. It prescribed caution because a student might make a mistake. The teacher still had to look at the tablet after it was written to assure both the success of the exercise and the utility of the administrative document.

6.2 Localizing Functional Literacy The environments just described produced technical literacies as described in Chap. 1. Students were inculcated with the technical jargon necessary for land management and the merchant-brewer, in the case of Marduk-muballit. and Ili-u-Šamaš, and the household activities of local notables in the case of the Imgur-edim-anna family. Subsets of lexicon with associated special meanings are combined with special calculation techniques and documentation practices in these educations. For instance, in LB 1975 specialized vocabulary associated with different standard vessels are tied to measurement techniques and record-keeping practices. This is technical literacy, a special subset of a knowledge system, perpetuated via a specific education, tutelage in an office or in a home. Each education can be understood as a specific microeconomy, in every way as vital to the extension of cuneiform culture as the erudite, scholarly literacy propagated in the scribal schools of Nippur and elsewhere in the Old Babylonian period. This education stabilized knowledge by applying it to dayto-day record keeping practices, extending this knowledge in an efficient way to the next generation of scribes, a way that did not threaten these day-to-day records. Thus, local technical literacy was generated in an educational environment within an office

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or home just as the vestiges for this technical literacy were seen in the more formal schoolings of the eduba, and even the more erudite apprenticeship at Sippar late in the Old Babylonian period. The knowledge economies of the Old Babylonian period were highly developed. Scholarly literacy was transmitted to the next generation of erudite scribes in the eduba, an institution designed to initiate the learner into the ancient and venerable cuneiform culture. While this institution differed from place to place, with a different iteration designed by each individual teacher, the basic shape of the education it provided was similar: four levels of elementary education introduced the student to the cuneiform script and then presented him or her with the tools necessary to translate the common Akkadian dialects into the ancient Sumerian language, as well as to carry out calculation using both the numerous, ancient metrological systems and the novel sexagesimal place value notation. At Nippur and elsewhere, external representations of knowledge used as aids to indoctrinate cuneiform culture were already well-codified. This codification, as was shown with the table of reciprocals, took place over the Ur III and early Old Babylonian periods. The codified knowledge produced a culture of “humanism”, to quote Høyrup, which a scribe was suppose to possess if able to exert scribal abilities beyond what was practically necessary: writing and speaking the dead Sumerian language, knowing rare and occult meaning of cuneiform signs, etc. The texts which explain this ideal (texts studied in school and thus meant to inculcate professional ideology in future scribes) also mention mathematics, but give no particulars.7

Codified external representations of knowledge were a means to control access to a “globalized knowledge”.8 However, each iteration of the education system also served to transfer the knowledge necessary for day-to-day operations in professional environments, technical literacy as it were, to the next generation of scribes. The municipality of Lagaba served as a strong example of how a technical literacy took shape. Education at Lagaba is probably similar to that witnessed in Sippar and Isin. Practice in recordkeeping occurred on type IV tablets from all three centers in similar ways. Indeed, many of the same kinds of practice took place on type IV tablets at Lagaba and at Sippar. Even though education at Lagaba is exclusively represented by Type IV tablets, a full corpus of tablet types probably existed in this city, introducing the student to the very elementary scribal curriculum that existed throughout Babylonia at this time. Thus, one can imagine type II tablets introduced lexical, metrological, and numerical texts common to Babylonia. These were reviewed using type III tablets and then tested using type I tablets or prisms. The type IV tablets served to stabilize the knowledge presented via the other three tablet types in a way that mimicked real world situations the students might encounter in everyday life. This seems to be a purpose of type IV tablets in general throughout Babylonia: to stabilize knowledge 7

Høyrup (2012, 8). “Knowledge no longer bound to local contexts and hence, in principle, capable of participating in globalization processes” (Renn 2019, 430).

8

6.2 Localizing Functional Literacy

135

via practice local to all levels of the scribal curriculum. Oral discourse giving sound to signs, technique to calculation, and meaning to education was vital to this education at all levels. Orality was probably vital to present a technical literacy at Lagaba. There, the extent of the scribal curriculum’s basis on the codified knowledge witnessed by types I–III tablets at Nippur and elsewhere is unclear. Did these tablets represent the entire education? Or did education include some or all of the lexical and mathematic lists and tables witnessed in the elementary education? The extant external representations of knowledge, the type IV tablets, suggest the latter. They drew from real-world situations, what may be called “local knowledge”,9 that is partially represented in the thematic lists. Education at Lagaba seems to go beyond these lists, however. This is perhaps the nature of technical literacy—it is an expression of local knowledge, to greater and lesser extents. However, there are traces of the more globalized knowledge with technical literacy as well, such as SPVN. Instead of initiating the future scribe into the “humanism” visible in the scholarly eduba, education at Lagaba passed on knowledge pertinent to an office or familial practice to young protégés. Local knowledge may be representative of functional literacy as well, and this literacy may have its origins in the household. Research into the impact of the home learning environments reveals the importance of the home environment on the development of basic literacy and numeracy in young children.10 Informal activities, such as shared reading or the measuring of ingredients while cooking, as well as formal activities aimed at instructing a child have both been shown to positively affect literacy and numeracy outcomes, starting with very young children in early toddlerhood.11 While it is difficult to see parents reading cuneiform texts in controlled or uncontrolled environments to the toddlers of Babylonia, it is quite probable that education began in the home. Exposure to numeracy related contents at early toddlerhood, for instance, “may help children to gain understanding of quantity manipulation without the deliberate instruction of a symbolic number system.”12 It must be born in mind as well that the home environment of Mesopotamia, “was not just a place for food preparation, eating, sleeping and raising children. It could also be a place for storage, small-scale production, such as pottery and textiles, or administrative tasks.”13 The home was the economic center of the family and so a place where the child would encounter much economic activity from which to learn. In addition, as seen throughout this work, orality holds a complex relationship with writing.14 In this vein, we can imagine vocabulary building exercises occurred with recitations of myths or legends common to the household or community. Younger children accompanying parents outside of the home environment would further gain 9

“Knowledge emergent from and dependent on the specific experiences of locally definable groups (cultures, societies, communities)” (Renn op. cit.). 10 Cf. Mol and Bus (2011), Silver et al. (2020), Salminen et al. (2021), among others. 11 Salminen et al. (2021). 12 Ibid., 14. 13 Collins (2013, 353). 14 See Zinn (2021) for more on orality and literacy.

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such literacy skills through interactions within the broader community—observing and participating in activities such as purchasing goods at a market or witnessing cultic activities.15 These would be further iterations of the local knowledge mentioned above, a tapestry of knowledge exhibited by the communities of Babylonia. Here we alter the definition of functional literacy described in Sect. 1.2. Very basic functional literacy was based on orality and numeracy inculcated at home and then within the community in general. This functional literacy would be very broad because it was attainable within any household and community. One can speculate further that some basic education may have been available to wealthier members of the community at the eduba or in the workshops in which cuneiform writing was employed. Here I suggest the very basic first level of education could have been broadly available, to greater or lesser degrees. The young learned to produce tablets, write signs, and then the sounds and sometimes meanings these signs represented— all the information necessary to write the Akkadian language. At the same time students learned more concisely measurement values and numbers necessary to carry out day-to-day activities between professions. Orality was important in all of this. Sound and meaning were provided through oral glosses and discourse, just as it was in inculcating technical and scholarly literacy. This would be the broad functional literacy suggested in Babylonian. In the middle of the Old Babylonian period, there is evidence for three intertwined iterations of a general Babylonian knowledge economy: a knowledge economy typical of the eduba in which external representations of global knowledge had been codified, an economy based on local and technical knowledge that was rarified by the codified global knowledge, and a knowledge economy derived from household and communal knowledge, perhaps incorporating the codified, global knowledge in certain instances. These are the scholarly, technical, and functional literacies discussed at the outset of this work. All three varieties of literacy probably incorporated, to greater or lesser extents, global knowledge transmitted through codified external representations of knowledge designed for the scholarly literacy. Scholarly literacy was aimed at the production of an educated, humanistic elite. It did in many instances instill in students some technical knowledge, but its aim was primarily the creation of an erudite elite. While the document was vital in representing this literacy, student practice focused on the prose and on the numeracy. Technical literacy could also produce erudition. However, its aim was the functions of a craftsperson or other professional in a literate culture. In this technical literacy, practice with the document was just as important as the prose or the numeracy. Attaining functional literacy only involved global knowledge for interaction with members of the literate society. In this, the oral document was just as vital as, if not more vital than, the physical document as an external representation of knowledge. The current study lends support to Eleanor Robson’s assertion, citing Jean Lave and Etienne Wenger, that learning best occurs “in the social and professional context to which it pertains, through interaction and collaboration with competent

15

Delnero (2021) shows that orality and oral performance were vital parts of written ritual laments.

References

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practitioners, rather than through abstract, decontextualized classrooms.”16 Robson speaks of practice at the earliest stages of writing in the late fourth millennium BCE, but the current discussion extends her assertion to the early second millennium. For this reason, knowledge was not uniform in Babylonia. Instead, there was a tapestry of local knowledge exhibited by the small communities throughout Babylonia from which the more global, humanistic knowledge visible in the scholarly community emerged.

References Breckwoldt, Tina. 1995/1996. Management of Grain Storage in Old Babylonian Larsa. Archiv für Orientforschung 42/43: 64–88. Collins, Paul. 2013. Everyday life in Sumer. In The Sumerian World, ed. Harriet Crawford, 345–358. London: Routledge. Delnero, Paul. 2021. Texts before Texts: Orality, Writing, and the Transmission of Sumerian Laments. In Oral et écrit dans l’Antiquité orientale: les processus de rédaction et d’édition: Actes du colloque organisé par le Collège de France, Paris, les 26 et 27 mai 2016, ed. Thomas Römer, Hervé Gonzalez, Lionel Marti, and Jan Rückl, 23–52. Leuven: Peeters. Høyrup, Jens. 2012. A hypothetical history of Old Babylonian mathematics: places, passages, stages, development. Max-Planck-Institut für Wissenschaftsgeschichte. Preprint 436: 1–20 Jacquet, Antoine, and Denis Lacambre. 2020. New etiquettes from Lagaba concerning beer and by-products, and the placement of the year MU GIBIL. N.A.B.U. Nouvelles Assyríologíques Bréves et Utílítaíres (1 (mars)): 23–27. Lave, Jean, and Etienne Wenger. 1991. Situated Learning: Legitimate Peripheral Participation. Cambridge: Cambridge University Press. Mol, Suzanne E., and Adriane G. Bus. 2011. To read or not to read: A meta-analysis of print exposure from infancy to early adulthood. Psychological Bulletin 137: 267–296. Renn, Jürgen. 2019. The Evolution of Knowledge: Rethinking Science for the Anthropocene. Princeton and Oxford: Princeton University Press. Robson, Eleanor. 2008. Mathematics in Ancient Iraq: A Social History. Princeton: Princeton University Press. Salminen, Jenni, Daria Khanolainen, Tuire Koponen, Minna Torppa, and Marja-Kristiina Lerkkanen. 2021. Development of numeracy and literacy skills in early childhood—A longitudinal study on the roles of home environment and familial risk for reading and math difficulties. Frontiers in Education 6: 725337. https://www.frontiersin.org/articles/10.3389/feduc.2021.725 337/full Silver, Alex M., Leanne Elliott, Adwoa Imbeah, and Melissa E. Libertus. 2020. Understanding the unique contributions of home numeracy, inhibitory control, the approximate number system, and spontaneous focusing on number for children’s math abilities. Mathematical Thinking and Learning 22: 296–311. Tammuz, Oded. 1993. Archives from Lagaba. PhD.: Yale University. Zinn, Katharina. 2021. Collective literacy, knowledge systems and memory: blurring the lines between orality and literacy in ancient Egypt. In Exchange of Knowledge Between Literate Cultures, University of Copenhagen, 19–21 July 2021. https://ccrs.ku.dk/research-data/exc hange-of-knowledge-between-literate-cultures-presentations/

16

Robson (2008, 52), Lave and Wenger (1991).

Tablet Index

A A 681, 42 AO 8865, 64, 83 Ashm 1910-759, 42 Ashm 1922-178, 83 Ashm 1923-410, 40, 41, 62, 82, 83 Ashm 1924-447, 83 Ashm 1924-451, 83 Ashm 1924-590, 84 Ashm 1929-833, 84 B BM 106425, 52, 53 BM 106444, 52, 53 BM 85194, 105 BM 85211, 11 BM 85238, 11 BM 96949, 84, 86 C CBS 10201, 55 CBS 11392, 20, 21, 62 CUNES 50-08-001, 42 E Erm 14645, 52, 53 F Feliu 2012, 42 H HS 201, 50, 51

HS 202a, 36 HS 209, 36 HS 242, 40, 41, 62

I IB 1211, 73, 81, 83 Ist L 7375, 50, 51 Ist L 9006, 50, 51 Ist L 9007+9005, 52, 53 Ist L 9008, 50, 51 Ist Ni 10235+3854, 54, 55 Ist Ni 2208, 56 Ist Ni 374, 50, 51 Ist Ni 5173, 56 Ist O 4438+4442, 84 Ist O 4443, 84

L LB 1824, 94, 106, 107, 111, 118, 121, 130, 132 LB 1843, 132 LB 1956, 132 LB 1960, 94, 116, 118, 119, 121, 131, 132 LB 1961, 94, 121, 122 LB 1963, 96, 99, 114, 117, 121, 131–133 LB 1967, 94, 111–113, 118, 121, 130–132 LB 1968, 94, 121, 123, 130, 132 LB 1969, 94, 114, 115, 121, 130, 132 LB 1970, 94, 98, 121, 124, 132 LB 1971, 94, 103, 104, 118, 121, 130, 132 LB 1972, 95, 103, 105, 106, 108, 111, 118, 121, 130, 132, 133 LB 1973, 95, 98

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. Middeke-Conlin, Knowledge, Literacy, and Elementary Education in the Old Babylonian Period, SpringerBriefs in History of Science and Technology, https://doi.org/10.1007/978-3-031-45226-0

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140 LB 1974, 96, 98, 99, 101, 103, 114, 118, 121, 130, 132 LB 1975, 95, 98, 108–110, 121, 130, 133 LB 1976, 95, 121, 124 LB 1977, 95, 99, 100, 103, 108, 121, 130 LB 1979, 95, 121, 125, 132 LB 798, 85

Tablet Index NBC 8531, 95 NBC 8874, 113, 114 Ni 18, 35, 36, 62 Ni 2733, 36

R RA 12, 197, 52–55

M M 406, 85 MHET 3/1 2, 62, 80 MLC 117, 85 MLC 1611, 84 MLC 646, 84 MS 2708, 85 MS 2719, 85 MS 3047, 42 MS 3873/1, 84 MS 3874, 53–55, 84, 87 MS 3909/3, 84 MS 3967/1, 85

V VAT 1221, 84 VAT 12593, 42 VAT 15375, 85 VAT 7858, 85 VAT 7892, 85 VAT 7895, 85 VAT 7896, 85 VAT 8167, 84 VAT 8521, 113 VAT 8528, 113

N N 3796 + N 3885, 22, 23, 62, 63 N 5147, 18, 62 NBC 6286, 95 NBC 6288, 95, 98, 100–103, 118, 130, 132 NBC 7346, 85 NBC 7374, 85 NBC 7701, 85

Y YBC 11138, 85 YBC 11924, 39, 62, 81, 83 YBC 4698, 111 YBC 6705, 85 YBC 6769, 85 YBC 8617, 84 YBC 9819, 11

General Index

A Abacus culture, 46 Acrographic list, 20, 22, 23, 40, 42, 63, 65, 66, 68, 72 Adab, 42 Addition, 30, 76, 88, 94, 103, 104, 111, 130 Administrative practice, 75, 80, 118 Administrative timekeeping, 96, 114 Advanced education, 10, 15, 24, 68, 69, 71, 72, 74, 77, 87 Advanced lexical education, 20, 22–24, 66 Advanced literary education, 67 Advanced mathematical curriculum, 38 Advanced sign list, 20, 22, 28, 36, 65, 68, 74 Agricultural accounting, 104 Agricultural record-keeping, 106 Akkadian letter writing, 76–78 Analogical hermeneutics, 24, 66 Anatum, 85 Apprenticeship, 10, 129, 132, 134 Approximations, 38, 111 Archaize, 48 Ardum, 84, 86 Area, 16, 25–29, 35, 42, 70, 76, 77, 82, 96, 105 Aššur, 87 Aw¯ılum, 7, 18

B Babylon, 4–6, 43, 61, 65, 75, 82, 86, 87, 96 B¯el¯anum, 70, 82, 83

C Capacity, 16, 25–29, 35, 42, 63, 65, 66, 68, 70, 74, 79, 82, 102, 103, 110, 111, 114, 120 Codified knowledge, 134, 135 Colophon, 70, 73, 81, 82, 86–89, 130 Commentary, 23, 50, 63, 97, 110, 111, 130 Compoundness, 22 Cubed roots, 36, 40, 82 Cuneiform culture, 6, 9, 10, 15, 33, 62, 66, 67, 88, 129, 133, 134 Cuneiform script, 16, 17, 69, 134 Cuneiform writing, 6, 7, 15, 20, 33, 47, 136 Cursive, 48, 57

D Debates, 69 Democratization, 49 Diagram, 62, 70, 77 Dictation, 108 Diri, 22–24, 79 Division of a field, 70 Document literacy, 10, 89 Doxology, 19, 82, 88

E Ea/Aa, 20, 23, 36, 66, 74, 77 Early Dynastic period, 18, 27, 42 Early Old Babylonian period, 52 Economic documents, 11, 93, 133 Economic practice, 80 Economic texts, 8, 11, 35, 47, 80, 97, 101, 102, 114, 116, 132 Eduba, 10, 15, 18, 129, 134–136

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. Middeke-Conlin, Knowledge, Literacy, and Elementary Education in the Old Babylonian Period, SpringerBriefs in History of Science and Technology, https://doi.org/10.1007/978-3-031-45226-0

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142 Elementary curriculum, 65, 68, 69, 71 Elementary education, 15, 16, 20, 42, 65, 67, 69, 71–73, 75, 80, 88, 103, 130, 134, 135 Elementary mathematical education, 70, 76, 86 Emesal, 77, 78 Epistemic change, 2, 10, 33 Equivalencies, 111, 130, 132 Ešei-pani-AN, 85 Euphrates, 5, 96 Explanatory glosses, 23 External representation, 9–12, 16, 57, 62, 64, 88, 89, 93, 102, 121, 129, 134–136

F Field of Gula, 105, 118, 133 Formal table, 43 Fractions, 29, 30, 51, 53, 54, 57 Functional literacy, 2, 6, 10, 12, 48, 129, 136 Funny numbers, 69 Furrows, 71, 95, 103, 105, 106, 111, 130

G Generative ambiguity, 9, 56, 64, 89, 93 Geometric exercises, 71 Geometric progression, 69 Girsu, 4, 11, 50, 51, 53, 102, 106 Globalized knowledge, 134, 135 Global knowledge, 129, 136 Gods list, 71, 74 Granularity, 25, 29, 30, 40, 43, 45

H Habituation, 24, 30, 42, 48 HAR-ra =hubullu, see Ura ˘ Head numbers, 38, 40 Height, 26, 28, 42, 67, 69, 70, 83 Home learning environments, 135 House F, 68 Humanism, 7, 134, 135 Hursaˆg-kalama, 75 ˘ Hymns, 25, 72

I Ili-ippalšam, 85 Ili-u-Šamaš, 94, 95, 97, 113, 131–133 im-gid2 -da, 54, 82, 87

General Index Imgur-edim-anna, 94, 96, 97, 99, 131–133 Imgur-Sîn, 73, 81, 83 Inana-mansum, 78 Inbi-ilišu, 84 Incantations, 71 Informal table, 43 Ingharra, 75–77 Inheritance divisions, 69 In-situ learning, 81, 102 Interest, 38, 94, 111, 113, 130, 132 Intraparietal sulcus, 67 Irnina canal, 96 Irrational numbers, 38 Isin, 1, 4, 5, 61, 65, 73–75, 78, 81–83, 86, 87, 89, 93, 101, 130, 134 Izi, 20, 22–24, 42, 63, 65, 66, 68, 74, 76, 77 K Kagal, 20, 22, 24, 72 Kingdom of Babylon, 96 Kingdom of Larsa, 4, 88 Kingdom of Ur, 2, 7, 48 Kiš, 1, 4, 61, 65, 75–78, 82, 84, 86–88, 96 Ki-ulutinbiše, 24 Knowledge economy, 9, 61, 88, 89, 93, 121, 136 Knowledge system, 1, 2, 9, 61, 88, 121, 129, 133 Knowledge transmission, 9, 10 Kutha, 96 L Lagaba, 2, 12, 93, 94, 96–99, 101, 102, 111, 113, 118, 129–132, 134, 135 Larsa, 1, 4, 5, 43, 61, 62, 64, 65, 69–71, 77, 81–83, 86, 87, 131 Layout, 45, 116 Learning by doing, 102, 133 Length, 16, 25, 26, 28, 35, 40, 42, 69, 70, 82, 105, 121 Lexical curriculum, 72, 75 Lexical education, 20, 24, 25, 28, 71, 74, 76, 77 Lexicality, 1, 2, 16, 67 Lexical list, 8, 17, 18, 20, 23–25, 30, 33, 38, 45, 46, 49, 57, 61, 63, 66–68, 72, 75, 77 Lexical text, 8, 24, 45, 88, 118 Lexical tradition, 8, 10, 18, 25, 30, 33, 45, 63, 65, 67, 69, 72, 79, 133 Lexicography, 8, 15, 103 Library tablets, 101

General Index Line construction, 94–96, 103, 108, 130 List formation, 130 Literacy, 1, 2, 6–10, 12, 15, 24, 33, 48, 49, 56, 61, 65, 67, 89, 93, 98, 102, 104, 129, 130, 133–136 Literary compositions, 69 Loan, 20, 98, 113, 130, 132 Local knowledge, 129, 135–137 Lu, 20, 21, 24, 66, 68, 71, 72, 74, 77, 79 Lu-azlag, 24 Lu=ša, see Lu

M Maison du scribe, 70 Marduk-muballit., 94, 95, 97, 113, 116, 131–133 Marduk-n¯as.ir, 75 Mari, 5, 64, 87 Mathematical curriculum, 11, 28, 71, 86 Mathematical tradition, 8, 25, 43, 45, 62, 63, 65, 67, 77, 86 Mathematics, 1, 7, 8, 15, 25, 46, 63, 67, 69, 71, 76, 134 Measurements value, 28 Measurement techniques, 110, 130, 133 Measurement unit, 28, 30 Measuring techniques, 110 Medium, 45 Metatextual data, 81 Metrological list, 8, 15, 25, 27–30, 33, 34, 40–42, 61, 63, 65, 76, 77, 79, 80, 82, 86, 88 Metrological practice, 72 Metrological systems, 16, 25, 27, 30, 35, 134 Metrological table, 40–45, 62, 63, 65–70, 75–77, 79, 80, 82, 87 Metrological value, 28, 29, 40, 42, 52, 66 Metrology, 8, 15, 16, 25, 63, 66, 69 Model contracts, 24, 40, 63, 67, 68, 71, 74, 76, 77 Monumental, 48 Mound E, 75 Mound W, 75 Multiplication table, 36, 38–40, 43–45, 56, 62, 66, 68, 70, 72, 74, 76, 77, 82, 86, 87

N Name list, 19, 28, 65, 70, 72, 74–76 Nigga, 20, 22, 24

143 Nippur, 1, 4, 9, 15, 18–20, 24, 28, 35, 36, 38, 40, 43, 50, 51, 54, 61–63, 65–73, 75–80, 82, 86–88, 96, 102, 103, 110, 130, 133–135 Nippur God List, 24 Non-normalized number, 47, 49, 54, 55 Non-regular number, 37, 38 Nord-Abschnitt, 73–75 Nordost-Abschnitt, 73, 74 Normalization, 34, 47, 54, 56 Normalized number, 47, 49, 52–56, 103, 106 No. 1 Broad Street, 68 No. 7 Quiet Street, 68 Numeracy, 2, 10, 15, 16, 79, 89, 102, 103, 129, 135, 136 Numerical exercises, 43, 69, 80 Numerical table, 8, 33, 36, 40, 45, 52, 56, 61, 66, 67, 70, 82, 86–88 Numerical value, 28 Numeric practice, 72

O Old Babylonian period, 1, 2, 4, 6–12, 15–17, 19, 20, 25, 27, 33, 35, 38, 42, 43, 47–49, 52–57, 61–63, 69, 70, 78, 82, 87, 88, 108, 113, 133, 134, 136 Old Babylonian transition, 49, 54, 56, 57 Oral document, 136 Orality, 20–22, 45, 129, 135, 136 Overseer of students, 75

P Periodicity, 38 Prefrontal cortex, 67 Prisms, 63, 64, 70, 82 Professional practice, 7, 56, 73, 78, 89, 121 Prosaic format, 43 Prose, 1, 10, 43, 129, 136 Prose literacy, 10, 89 Proverbs, 24, 40, 62, 63, 67–69, 76, 77

R Rational numbers, 27, 38 Reciprocal extraction, 44, 54, 55 Reciprocal table, 37, 38, 40, 44, 46, 49, 50, 52, 55, 56, 64, 70, 76, 86, 87, 89 Record-keeping practice, 102, 114 Regular number, 37 Remeasurement, 110 Repetition, 11, 20, 24, 30, 42, 63, 102, 103

144 Revolution, 33, 34 Rounded value, 111 Round tablets, 64, 98, 99, 101, 121 Ruttum, 131

S Saˆg, 24, 77 Šamaš-muballit, 85 Sargonic period, 27 Sargonic reforms, 27 Šattukku archive, 43 Scherbenlock, 71 Scholarly literacy, 2, 6, 7, 10, 12, 15, 61, 133, 134, 136 School texts, 64, 70, 71, 86 Scratchpad, 101, 103, 106, 108 Scribal culture, 18, 111 Scribal curriculum, 1, 9, 10, 12, 25, 28, 33, 65, 66, 71, 74, 78, 80, 81, 89, 110, 130, 134, 135 Scribal education, 1, 6, 11, 15, 16, 18, 19, 33, 61, 62, 64, 72, 93, 111 Scribal school, 1, 11, 18 Semi-monumental, 48 Semi-rectangular tablets, 98, 101, 103, 118, 120, 121, 133 Šep-Sîn, 84 Sexagesimal cycle, 36 Sexagesimal place value notation, 11, 33, 34, 42, 134 Sexagesimal system, 26, 34 Sign forms, 48, 49, 118 S.illi-Nin, 85 Sîn-apil-Urim, 70, 81–83 Sinatum m¯ar, 85 Sippar, 1, 4, 61, 65, 78–81, 86, 89, 93, 101, 102, 130, 134 Sippar Phrasebook, 79 SM 2574, 53–55 SM 2685, 50–53 Square roots, 36, 40, 70, 83 Stabilized knowledge, 121, 133 Stabilize knowledge, 9, 89, 93, 129, 134 Stabilizing knowledge, 93 Standard vessels, 108, 110, 111, 130, 133 Student practice tablets, 101 Subitization, 47 Subtraction, 94, 103, 114, 130 Südost-Abschnitt, 73 Sumerian-Akkadian bilingualism, 16 Sumerian literary corpus, 24 Sumerian literature, 71, 76, 77

General Index Šuruppak, 42 Syllabaries, 20, 68, 69, 80, 102 Syllabary A, 76, 77, 79 Syllabic Sumerian, 77, 78 Syllable Alphabet A, 19, 71, 73, 75–77, 79 Syllable Alphabet B, 18, 68, 75 Syllable Vocabulary A, 74 System G, 25, 26 System S, 25, 26, 34, 106

T Table of reciprocals, 36, 37, 55, 66, 73, 74, 82, 134 Tables of squares, 36, 40, 70, 74, 77 Tabular array, 114, 130 Tabular format, 8, 34, 42, 43, 46, 47, 49, 53, 62, 63, 69, 94, 95 Tabular layout, 43 Technical literacy, 2, 6, 7, 12, 61, 89, 93, 129, 133–136 Text compilations, 114 The dialogue between an examiner and a scribe, 15 The document, 1, 8, 9, 62, 67, 136 Thematic lists, 20, 22, 28, 30, 42, 63, 65, 68, 70–72, 77, 80, 135 Timekeeping, 114, 130 Transformation, 10, 18, 35, 36, 40, 42, 43, 52–54, 56, 67, 111 Trapezoid, 69, 70 Triangle, 5, 70 Truncation, 111 Tu-Ta-Ti, 18, 68, 71 Tutelage, 129, 132, 133 Type I tablets, 62–64, 67–70, 73, 74, 77, 82, 86, 87, 134 Type II tablets, 62, 63, 67, 68, 70, 71, 73, 76, 77, 134 Type III tablets, 62, 63, 70, 73, 76, 77, 81, 82, 86, 87, 134 Type IV tablets, 62, 67–73, 75–77, 79, 80, 89, 93, 99, 101, 102, 118, 120, 130, 132, 134, 135 Type M tablets, 63, 64, 87 Type S tablets, 63

U Ubarrum, 85 Ugumu, 24, 72 Uhaimir, 75–77 Umma, 53

General Index Ur, 1, 2, 4, 43, 49, 61, 62, 64, 65, 68–71, 79, 86 Ur5 -ra., see Ura Ura, 20, 21, 30, 70–72, 74, 76, 77, 79, 105, 118 Ur III kingdom, see kingdom of Ur Ur III period, 7, 11, 16, 42, 43, 48–50, 52–54, 56, 57 Ur III transitional, 55 Ur III writing, 48 Uruk, 1, 4, 5, 27, 61, 65, 71, 72, 89, 131 Ur-Utu, 78, 79

145 V Vocabulary building exercises, 135 Volume, 16, 25–29, 42, 49, 70, 82

W Weidner Gods List, 75 Weight, 16, 25–30, 35, 41, 42, 62, 65, 70, 79, 82, 87

Z Zabalam, 42