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Mathematics in Ancient Iraq: A Social History

Princeton University Press
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Unless you have a significant interest in ancient civilizations and their mathematics, this book will be of little interest to you. The emphasis is much more on the social history than it is on mathematics. In many cases, in fact, one can argue that what is being described is not mathematics: some of the clay tablets describe the measurements of structures or farm fields and others are records of inventories.

A great deal of time is spent in setting the social context for the creation of the tablets, which is valuable if your interest is more on the social context for ancient mathematics. The time period covered is the fourth through first millennia BCE (Before the Common Era). With the exception of the fourth millennium, two chapters are dedicated to each millennium. Given that the count is progressing upward from the negative, the chapter titled “The Early Second Millennium” refers roughly to the years 2000 BCE to 1500 BCE.

Each chapter begins with a map of the Mesopotamian region with notes as to where the clay tablets discussed in the chapter were found as well as some historical context of the times. A list of all the tablets referenced is included in appendix B; they are organized based on the date assigned to their creation and the region where they were discovered.

This is mathematical history at its most difficult (from the perspective of the history). Reading it requires little in the way of mathematical knowledge but a lot of background knowledge of the history of the region. To truly appreciate the value of the book as a summary of the archeological record you must also have some idea of the amount of work that went into the recovery and study of the artifacts. From the physical effort of digging, through the cataloging and finally the translation, this book is truly the result of a great deal of labor.

Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, teaching college classes and co-editing The Journal of Recreational Mathematics. In his spare time, he reads about these things and helps his daughter in her lawn care business.


Date Received: 
Monday, November 17, 2008
Include In BLL Rating: 
Eleanor Robson
Publication Date: 
Charles Ashbacher


List of Figures xi
List of Tables xvii
Preface xxi
Acknowledgments xxv

Chapter One: Scope, Methods, Sources 1
1.1 The Subject: Ancient Iraq and Its Mathematics 1
1.2 The Artefacts: Assyriological and Mathematical Analysis 8
1.3 The Contexts: Textuality, Materiality, and Social History 17

Chapter Two: Before the Mid-Third Millennium 27
2.1 Background and Evidence 28
2.2 Quantitative Management and Emerging Statehood 33
2.3 Enumeration and Abstraction 40
2.4 Symmetry, Geometry, and Visual Culture 45
2.5 Conclusions 51

Chapter Three: The Later Third Millennium 54
3.1 Background and Evidence 55
3.2 Maps, Plans, and Itineraries: Visual and Textual Representations of Spatial Relationships 60
3.3 Accounting for Time and Labour: Approximation, Standardisation, Prediction 67
3.4 The Development of the Sexagesimal Place Value System (SPVS) 75
3.5 Conclusions 83

Chapter Four: The Early Second Millennium 85
4.1 Background and Evidence 86
4.2 Metrology, Multiplication, Memorisation: Elementary Mathematics Education 97
4.3 Words and Pictures, Reciprocals and Squares 106
4.4 Measurement, Justice, and the Ideology of Kingship 115
4.5 Conclusions 123

Chapter Five: Assyria 125
5.1 Background and Evidence 126
5.2 Palatial and Mercantile Numeracy in Early Assyria 129
5.3 Counting Heads, Marking Time: Quantifi cations in Royal Inscriptions and Records 136
5.4 Arû: Number Manipulation in Neo-Assyrian Scholarship 143
5.5 Conclusions 149

Chapter Six: The Later Second Millennium 151
6.1 Background and Evidence 151
6.2 Tabular Accounting in Southern Babylonia 157
6.3 Land Surveyors and Their Records in Northern Babylonia 166
6.4 Quantifi cation as Literary Device in the Epic of Gilgames 177
6.5 Conclusions 181

Chapter Seven: The Early First Millennium 183
7.1 Background and Evidence 184
7.2 Libraries and Schools: The Formalisation of the First-Millennium Scribal Curriculum 192
7.3 Home Economics: Numeracy in a Mid-First-Millennium Urban Household 198
7.4 Measuring Houses, Maintaining Professionalism 206
7.5 Conclusions 212

Chapter Eight: The Later First Millennium 214
8.1 Background and Evidence 215
8.2 Babylon: Mathematics in the Service of Astronomy? 220
8.3 Achaemenid Uruk: The Sangû-Ninurta and Ekur-z?kir Families 227
8.4 Seleucid Uruk: The Hunzû and Sîn-leqi-unninni Families 240
8.5 Conclusions 260

Chapter Nine: Epilogue 263
9.1 The Big Picture: Three Millennia of Mathematics in Ancient Iraq 263
9.2 Ancient Mathematics in the Modern World 268
9.3 Inside Ancient Mathematics: Translation, Representation, Interpretation 274
9.4 The Worlds of Ancient Mathematics: History, Society, Community 284
9.5 Conclusions 288

Appendix A: Metrological Systems 291
Appendix B: Published Mathematical Tablets 299
Notes 345
Bibliography 373
Index of Tablets 409
Subject Index 425

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Friday, December 12, 2008