Mathematics in Ancient Iraq: A Social History by Eleanor Robson (PDF)

Description

This monumental book traces the origins and development of mathematics in the ancient Middle East, from its earliest beginnings in the fourth millennium BCE to the end of indigenous intellectual culture in the second century BCE when cuneiform writing was gradually abandoned. Eleanor Robson offers a history like no other, examining ancient mathematics within its broader social, political, economic, and religious contexts, and showing that mathematics was not just an abstract discipline for elites but a key component in ordering society and understanding the world. The region of modern-day Iraq is uniquely rich in evidence for ancient mathematics because its prehistoric inhabitants wrote on clay tablets, many hundreds of thousands of which have been archaeologically excavated, deciphered, and translated. Drawing from these and a wealth of other textual and archaeological evidence, Robson gives an extraordinarily detailed picture of how mathematical ideas and practices were conceived, used, and taught during this period. She challenges the prevailing view that they were merely the simplistic precursors of classical Greek mathematics, and explains how the prevailing view came to be. Robson reveals the true sophistication and beauty of ancient Middle Eastern mathematics as it evolved over three thousand years, from the earliest beginnings of recorded accounting to complex mathematical astronomy. Every chapter provides detailed information on sources, and the book includes an appendix on all mathematical cuneiform tablets published before 2007.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐For any one interested in serious research on the subject of Cuneiform, this book is a must read. It is clear, concise, and informative. Although it could be a text book, it does not read like one. I have used it as a reference numerous times and keep it at hand.

⭐”From about 6000 BCE, long before writing, Neolithic villagers used simple geometric counters in clay and stone to record exchange transactions, funded by agricultural surpluses. As societies and economies grew in size and complexity, ever more strain was placed on trust and memory. By the late fourth millennium the intricacies of institutional management necessitated both an increasing numerical sophistication and the invention of written signs for the commodities, agents, and actions involved in controlling them.” (27) “Mesopotamian city states had implemented an extensible and powerful literate technology for the quantitative control and management of their assets and labour force. In doing so, they had created in parallel a new social class—in Uruk called the umbisag ‘accountant/scribe’—who was neither economically productive nor political powerful, but whose role was to manage the primary producers on the elite’s behalf.” (40)”It was the … state bureaucracy in which the scribes were embedded that … drove the need for … the sexagesimal place value system … by imposing increasingly high calculational standards on its functionaries through the demand for complex annual balanced accounts.” (83) This went hand in hand with “centrally imposed reforms of weights and measures throughout the third millennium” (84). “None of these newly invented units of measure was recorded with compound metrological numerals, but always written as numbers recorded according to the discrete notation system followed by a separate sign for the metrological unit,” (76) unlike the earliest sources, where, “while there was a single word for ‘ten’,” “there was no single numeral but different signs for ‘ten-discrete-objects’, ‘ten-units-of-grain’, and ‘ten-units-of-land'” (33).”In the early Old Babylonian period [c. 1850 BCE], elementary scribal training underwent a revolution … in which emphasis was more on the ability to manipulate imaginary lines and areas in almost algebraic ways than on the ability to count livestock or calculate work rates.” (86) “Topics range from apparently abstract ‘naive-geometrical algebra’, via plane geometry, to practical pretexts for setting a problem—whether agricultural labour, land inheritance, or metrological conversions. Even the most abstract problems may be dressed up with ‘practical’ scenarios.” (89)This was “a style of mathematics that encapsulated the principles of … justice” on which the society was based; “in solving abstruse puzzles about measured space, the true scribe demonstrated his or her technical capability … for upholding justice and maintaining social and political stability on behalf of king and god” (266).As one scribe put it: “When I go to divide a plot, I can divide it; when I go to apportion a field, I can apportion the pieces, so that when wronged men have a quarrel I soothe their hearts … Brother will be at peace with brother.” (122)”The Sumerian word for justice was nig-si-sa, literally ‘straightness, equality, squareness’, Akkadian misarum ‘means of making straight’. The royal regalia of justice were the measuring rod and rope … In [this] light … Old Babylonian mathematics, with its twin preoccupation of land and labour management on the one hand and cut-and-paste geometrical algebra on the other, becomes truly comprehensible.” (123-124)This tradition effectively came to an end with “the collapse of the Old Babylonian kingdom in c. 1600 BCE” (151), though “traces of Old Babylonian mathematical learning lingered on long after the political ideology that it supported had disappeared” (181). “Evidence suggests that mathematics … was still a vital component of Babylonian intellectual life” (151) for a while, but ultimately a massive decline followed. “In the first half of the first millennium we find a low level of mathematical sophistication in school, consumer, and professional contexts.” (212)”Mathematics and mathematical astronomy were central components of the last flowering of cuneiform culture.” (261) “From the mid-seventh century [BCE] onwards, … compilers of eclipse records and astronomical diaries had begun to think in terms of divine quantification. … Apparently random events of great ominous significance were observed, quantified, and recorded in the hope that numerical patterns could be detected amongst them. The ultimate aim was to understand the will of the gods, to ensure that they were propitiated and would act benignly to the king and humanity. Thus in later Babylonia mathematics became a priestly concern.” (268)These priests “comprised a tiny number of individuals from a restricted social circle, intermarrying, working closely together to train each successive generation, and highly valuing privacy and secrecy” (261-262). “Their sole aim was to uphold the belief systems and religious practices of ancient times.” “In this context [they] developed increasingly mathematically sophisticated means to ensure the calendrical accuracy of their rituals.” (262)

⭐Except to say; if ever I have encountered a book that not only explained what the author knew, but would explain it to the reader plainly and completely; this is it. I stand in awe of the power of this work, it is without a doubt something that belongs on the bookshelf of every maven of history – Biblical and otherwise. But for this person it fit the bill beyond expectation. The detail, the trail we are lead upon – which you can dive in anywhere and it will draw you into the whole – is complex but simplified by the step by step understanding illustrated in each chapter. I, just to be experimental read the summation material first, and knew immediately this was a book to drink in small sips and then in deep draughts. A book that can be re-read without exhaustion. To the textual archaeologists out there – get this book.

⭐Der Band ist zum einen ein Referenzwerk, das die wichtigsten mathematischen Tontafeln aus Mesopotamien aufzählt, den Übersetzer, den geographischen Ursprung und die zugehörige Literaturquelle angibt. Der Band umfasst daher eine sehr umfangreiche Mathematik-Bibliographie über Mesopotamien (34 Seiten!). Zum anderen bietet der Band eine ausführliche Beschreibung der Schriftanfänge, der Tontafeln aus Assur, Sumer, Altbabylon und Neubabylon. Viele bekannte Tontafeln werden vorgestellt, aber nur einige mathematische Probleme behandelt. Sehr umfangreich und anschaulich sind die Beschreibungen der Ausgrabungen: Es werden teilweise Bibliotheken aus Uruk rekonstruiert und Verbindungen zwischen den Schreibern hergestellt. So findet man ein Soziogramm der Familie bzw. Schule des neubabylonischen Schreibers Sin-leqi-unninni, der akkadische und assyrische Epen in dem berühmten Gilgamesh-Epos vereinigt hat. Gute Englisch-Kenntnisse werden empfohlen.

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⭐written by THE expert on Mesopotamian mathematics, Eleanor Robson. The author succeeded brillantly in not giving an overview but in diving deep into the culture of ancient Iraq so that mathematical developments are viewed in their historical and cultural context. For quite some time I thought that the writings of Otto Neugebauer were the last and definite word but I learned with pleasure that Robson was able to add a multitude of recent research results. This is simply a brillant book on the early history in mathematics.

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