The Babylonian World - Historia Antigua

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— Mathematics, metrology and professional numeracy — one Shamash-etir, could easily have expressed the first fraction sexagesimally as 0;16 40 [= 3 ⁄18] of a day if he wanted: he was the chief priest of the Resh temple and was later to tutor Anu-belshunu’s son Anu-aba-uter extensively in mathematical astronomy. But in this context he – and all other scribes of prebendary contracts – made a contextual, social choice against the sexagesimal system and in favour of Greek-style expression. Shamash-etir’s notation hints that his priestly circle’s legal contracts and scholarly writing were now a tiny cuneiform island in a sea of alphabetic Greek and Aramaic; it is no wonder that his protégé Anu-aba-uter is the last Babylonian mathematician known to us. CONCLUSIONS Babylonian mathematics underwent many changes in the millennia of its history, but those changes cannot be fully understood – or sometimes even identified – if viewed from a mathematical standpoint alone. Terminology, methods, metrologies, notations all adapted to changing social needs and interests as well as intellectual ones, while shaping and challenging the ideas of the individuals and groups who created and used them. It is often assumed that Otto Neugebauer left nothing more to be said about Babylonian mathematics. On the contrary: its very Babylonian-ness is only now beginning to be explored. NOTES 1 Sexagesimal numbers are transcribed with spaces separating the sexagesimal places and a semicolon marking the boundary between integers and fractions. For example, 112;15 represents 1 × 60 + 12 + 15/60, or 72 1 ⁄4. 2 Eduba dialogue 3, lines 19–27: Vanstiphout (1997: 589). 3 Lipit-Eshtar hymn B, lines 23–24: Black et al. (1998–2006: 2.5.5.2). 4 The other tablets from the house belonged to later inhabitants, most notably Iqisha of the Ekur-zakir family (later fourth century BCE). BIBLIOGRAPHY Beaulieu, P.-A. 2000. ‘The descendants of Sîn-leqi-unninni’, in J. Marzahn and H. Neumann (eds), Assyriologica et Semitica: Festschrift für Joachim Oelsner. (Alter Orient und Altes Testament, 252), Münster: Ugarit-Verlag, 1–16. Black, J.A. et al. 1998–2006. The Electronic Text Corpus of Sumerian Literature. University of Oxford. http://etcsl.orinst.ox.ac.uk. Cavigneaux, A., 1981. Textes scolaires du temple de Nabû sˇa H ˘ arê (Texts from Babylon, 1), Baghdad: State Organization of Antiquities and Heritage. Cocquerillat, D. 1965. ‘Les calculs practiques sur les fractions à l’époque séleucide’, Bibliotheca Orientalis 22, 239–42. Foster, B.R. and E. Robson 2004. ‘A new look at the Sargonic mathematical corpus’, Zeitschrift für Assyriologie 94, 1–15. Friberg, J. 1990. ‘Mathematik’, in D.O. Edzard (ed.), Reallexikon der Assyriologie und vorderasiatischen Archäologie, vol. 7. Berlin/New York: de Gruyter, 531–585. –––– 1997. ‘Seed and reeds continued: another metro-mathematical topic text from Late Babylonian Uruk’, Baghdader Mitteilungen 28, 251–365. –––– 1997–98, ‘Round and almost round numbers in proto-literate metro-mathematical field texts’, Archiv für Orientforschung 44–45, 1–58. 429
— Eleanor Robson — –––– 1999. ‘A Late Babylonian factorisation algorithm for the computation of reciprocals of manyplace regular sexagesimal numbers’, Baghdader Mitteilungen 30, 139–161. –––– 2000. ‘Mathematics at Ur in the Old Babylonian period’, Revue d’Assyriologie 94, 97–188. –––– 2001. ‘Bricks and mud in metro-mathematical cuneiform texts’, in J. Høyrup and P. Damerow (eds), Changing views on ancient Near Eastern mathematics (Berliner Beiträge zum Vorderen Orient, 19), Berlin: Dietrich Reimer, 61–154. –––– et al. 1990. ‘Seed and reeds: a metro-mathematical topic text from Late Babylonian Uruk’, Baghdader Mitteilungen 21, 483–557. George, A.R. 1993. Babylonian topographical texts (Orientalia Lovaniensia Analecta, 40), Leuven: Peeters. Gesche, P.D. 2000. Schulunterricht in Babylonien im ersten Jahrtausend v. Chr. (Alter Orient und Altes Testament, 275), Münster: Ugarit-Verlag. Høyrup, J. 1990. ‘Algebra and naive geometry. An investigation of some basic aspects of Old Babylonian mathematical thought’, Altorientalische Forschungen 17, 27–69, 262–354. –––– 2002. Lengths, widths, surfaces: a portrait of Old Babylonian algebra and its kin, Berlin and New York: Springer. –––– and P. Damerow (eds) 2001. Changing views on ancient Near Eastern mathematics (Berliner Beiträge zum Vorderen Orient, 19), Berlin. Hunger, H. 1976. Spätbabylonische Texte aus Uruk, I (Ausgrabungen der Deutschen Forschungsgemeinschaft in Uruk-Warka. Endberichte, 9), Berlin: Mann. Melville, D. 2002. ‘Ration computations at Fara: multiplication or repeated addition’, in J.M. Steele and A. Imhausen (eds), Under one sky: mathematics and astronomy in the ancient Near East (Alter Orient und Altes Testament, 297), Münster: Ugarit-Verlag, 237–252. Nemet-Nejat, K. 1982. Late Babylonian field plans in the British Museum (Studia Pohl Series Maior, 11), Rome: Pontifical Biblical Institute. Neugebauer, O. 1935–37. Mathematische Keilschrift-Texte, I–III (Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik, A3), Berlin: Springer. –––– 1948. The exact sciences in antiquity, Princeton: Princeton University Press. –––– and A.J. Sachs 1945. Mathematical cuneiform texts (American Oriental Series, 29), New Haven: American Oriental Society. Nissen, H., P. Damerow, and R.K. Englund 1993. Archaic bookkeeping: early writing and techniques of administration in the Ancient Near East. Chicago: Chicago University Press. Oelsner, J. 2001. ‘HS 201 – eine Reziprokentabelle der Ur III-Zeit’, in J. Høyrup and P. Damerow (eds), Changing views on ancient Near Eastern mathematics (Berliner Beiträge zum Vorderen Orient, 19), Berlin: Dietrich Reimer, 53–59. Pearce, L.E. and L.T. Doty 2000. ‘The activities of Anu-bēlsˇunu, Seleucid scribe’, in J. Marzahn and H. Neumann (eds), Assyriologica et Semitica: Festschrift für Joachim Oelsner (Alter Orient und Altes Testament, 252), Münster: Ugarit-Verlag, 331–342. Powell, M.A. 1976. ‘The antecedents of Old Babylonian place notation and the early history of Babylonian mathematics’, Historia Mathematica 3, 417–439. –––– 1990. ‘Maße und Gewichte’, in D.O. Edzard (ed.), Reallexikon der Assyriologie und vorderasiatischen Archäologie 7, Berlin and New York: Walter de Gruyter, 457–530. Robson, E. 1999. Mesopotamian mathematics, 2100–1600 BC: technical constants in bureaucracy and education (Oxford Editions of Cuneiform Texts, 14), Oxford: Clarendon Press. –––– 2001a. ‘Neither Sherlock Holmes nor Babylon: a reassessment of Plimpton 322’, Historia Mathematica 28, 167–206. –––– 2001b, ‘The tablet house: a scribal school in Old Babylonian Nippur’, Revue d’Assyriologie 95, 39–67. –––– 2002. ‘More than metrology: mathematics education in an Old Babylonian scribal school’, in J.M. Steele and A. Imhausen (eds), Under one sky: mathematics and astronomy in the ancient Near East (Alter Orient und Altes Testament, 297), Münster: Ugarit-Verlag, 325–365. 430
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THE BABYLONIAN WORLD As the layers
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THE BABYLONIAN WORLD Edited by Gwe
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* Translation is on p. 591. Lebensa
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— Contents — 11 Food and drink
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ILLUSTRATIONS FIGURES 2.1 Sustaini
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— Illustrations — 10.7 Portrait
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CONTRIBUTORS Tzvi Abusch is Rose B
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— Contributors — Dominique Coll
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— Contributors — Frans van Kopp
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— Contributors — Eleanor Robson
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CHAPTER ONE INTRODUCTION Gwendolyn
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— Introduction — mid-second mil
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— Introduction — that ‘belong
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— Introduction — persisted in t
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— Introduction — who, at differ
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CHAPTER TWO THE WORLD OF BABYLONIAN
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— The world of Babylonian country
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CHAPTER THREE LAND AND LAND USE The
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— Land and land use — past cons
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— Land and land use — Figure 3.
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— Land and land use — December.
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— Land and land use — districts
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— Land and land use — however,
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— Land and land use — BIBLIOGRA
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— Land and land use — ---- 2001
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— Agricultural techniques — Fig
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— Agricultural techniques — Fig
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— Agricultural techniques — Oth
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— Agricultural techniques — wit
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— Agricultural techniques — The
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— Agricultural techniques — Pet
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— Urban form in the first millenn
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CHAPTER SIX ARCHITECTURE IN THE OLD
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— Architecture in the Old Babylon
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CHAPTER SEVEN BABYLONIAN SEALS 1 D
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— Babylonian seals — (a) (b) (c
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— Babylonian seals — Figure 7.6
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— Babylonian seals — ruler he s
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1 1 — Babylonian seals — An ext
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1 1 — Babylonian seals — Figure
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— Babylonian seals — mostly cor
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— Babylonian seals — MacGinnis,
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— Babylonian sources of exotic ra
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CHAPTER NINE CLOTH IN THE BABYLONIA
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— Cloth in the Babylonian World
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CHAPTER TEN THE BABYLONIAN VISUAL I
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— The Babylonian visual image —
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sˇūkil akalu sˇiqi kurunnu eris
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— Food and drink in Babylonia —
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PART III ECONOMIC LIFE 185
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— Johannes Renger — stands in c
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— Johannes Renger — eventually
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— Johannes Renger — fertility o
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— Johannes Renger — utensils ma
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— Johannes Renger — BIBLIOGRAPH
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CHAPTER THIRTEEN THE OLD BABYLONIAN
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— Anne Goddeeris — of the craft
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— Anne Goddeeris — silver could
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— Anne Goddeeris — waves during
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— Anne Goddeeris — SOME CHARACT
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— Anne Goddeeris — could consis
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CHAPTER FOURTEEN ASPECTS OF SOCIETY
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— Frans van Koppen — its territ
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— Frans van Koppen — Figure 14.
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— Frans van Koppen — The durati
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— Frans van Koppen — for many b
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— Frans van Koppen — provincial
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— Frans van Koppen — BIBLIOGRAP
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CHAPTER FIFTEEN THE BABYLONIAN ECON
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— Michael Jursa — cereal farmin
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— Michael Jursa — were determin
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— Michael Jursa — main point of
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— Michael Jursa — Given these b
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— Michael Jursa — of Joannès 2
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CHAPTER SIXTEEN THE EGIBI FAMILY C
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— Cornelia Wunsch — aside every
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— Cornelia Wunsch — of a hired
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— Cornelia Wunsch — Figure 16.1
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— Cornelia Wunsch — qa = 3600 n
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— Cornelia Wunsch — The committ
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PART IV SOCIETY AND POLITICS 249
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— Petr Charvát — Figure 17.1 S
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— Petr Charvát — In warfare th
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— Petr Charvát — Early Dynasti
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— Petr Charvát — their obligat
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— Petr Charvát — NOTES 1 Coope
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— Petr Charvát — 97 On them cf
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— Petr Charvát — Rehm, Ellen 2
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— Walther Sallaberger — Figure
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— Walther Sallaberger — Babylon
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— Walther Sallaberger — (Maul 2
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— Walther Sallaberger — of good
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— Walther Sallaberger — the bes
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CHAPTER NINETEEN POWER, ECONOMY AND
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— Gebhard J. Selz — Figure 19.1
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— Gebhard J. Selz — influence o
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— Gebhard J. Selz — Mesopotamia
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— Gebhard J. Selz — and loan. N
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— Gebhard J. Selz — distrust in
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CHAPTER TWENTY ARAMEANS AND CHALDEA
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— Frederick Mario Fales — and c
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— Frederick Mario Fales — level
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— Frederick Mario Fales — Figur
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— Frederick Mario Fales — Babyl
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— Frederick Mario Fales — the w
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— Laura D. Steele — experiences
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— Laura D. Steele — Babylonian
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— Laura D. Steele — Figure 21.1
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— Laura D. Steele — Figure 21.2
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— Laura D. Steele — as large as
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— Laura D. Steele — Babylonian
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— Laura D. Steele — novel but l
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— Laura D. Steele — Dandamaev,
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— Laura D. Steele — ---- (1995b
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CHAPTER TWENTY-TWO THE ROLE AND FUN
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— The role and function of goddes
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— Inanna and Ishtar in the Babylo
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— The Babylonian god Marduk — E
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— The Babylonian god Marduk — i
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— The Babylonian god Marduk — T
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— The Babylonian god Marduk — t
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— The Babylonian god Marduk — 7
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— The Babylonian god Marduk — B
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CHAPTER TWENTY-FIVE DIVINATION CULT
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— Divination culture and the hand
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CHAPTER TWENTY-SIX WITCHCRAFT LITER
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— Witchcraft literature in Mesopo
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— Witchcraft literature in Mesopo
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Page 414 and 415: — Incantations within Akkadian me
Page 424 and 425: — Letters in the Amorite world
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Page 472 and 473: — Gilgamesh and the literature of
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Page 496 and 497: CHAPTER THIRTY-THREE LATE BABYLONIA
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— Late Babylonian intellectual li
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PART VII INTERNATIONAL RELATIONS Ba
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— David A. Warburton — both Egy
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— David A. Warburton — But thes
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Table 34.1 Middle Babylonian period
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— David A. Warburton — forces i
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— David A. Warburton — of Esarh
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— David A. Warburton — but such
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— David A. Warburton — contrast
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— David A. Warburton — set off
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— Trevor Bryce — Figure 35.1 Th
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— Trevor Bryce — in the region
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— Trevor Bryce — But for the re
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— Trevor Bryce — an acrimonious
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— Trevor Bryce — king Kashtilia
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— Trevor Bryce — Gasche, H., Ar
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— P. S. Vermaak — In our presen
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— P. S. Vermaak — The spelling
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— P. S. Vermaak — Nippur (moder
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— P. S. Vermaak — such as Ugari
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— P. S. Vermaak — Brown, S. (19
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— P. S. Vermaak — ---- and Vida
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— Hannes D. Galter — 2000 BCE,
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— Hannes D. Galter — The reason
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— Hannes D. Galter — Figure 37.
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— Hannes D. Galter — Figure 37.
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— Hannes D. Galter — Mesopotami
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— Hannes D. Galter — new lord o
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— Hannes D. Galter — ---- 2006
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— Baruch A. Levine — Biblical l
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— Baruch A. Levine — presented
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— Baruch A. Levine — Among othe
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— Baruch A. Levine — the word o
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— Baruch A. Levine — when the c
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— Baruch A. Levine — as coming
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— Baruch A. Levine — punishment
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— Baruch A. Levine — The prophe
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— Baruch A. Levine — Habakkuk
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— Baruch A. Levine — The same c
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CHAPTER THIRTY-NINE THE PERSIAN EMP
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— Amélie Kuhrt — Figure 39.1 D
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— Amélie Kuhrt — Memphis, in L
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— Amélie Kuhrt — by Jews. Neig
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— Amélie Kuhrt — by the king,
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— Amélie Kuhrt — dress, elabor
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— Amélie Kuhrt — The one autho
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— Amélie Kuhrt — C. Waerzegger
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ancestor cult 270, 281 Andarig 401
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cuneiform: tablets 1, 54; writing 9
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gift exchange 272-3, 491, 511 Gilga
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leaching 57-8 lead 127 leeks 46 len
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omens 253, 299, 303, 361-71, 373, 3
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soil 55; cultivation 57; improvemen
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Zabalam 18, 268 Zagros mountains 12
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