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The mathematics of canal construction in the kingdoms of Larsa and Babylon

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Abstract

Mathematical texts describing canal construction and maintenance abound in ancient Mesopotamia, where irrigation was vital to crop production. Indeed, this land’s survival was dependent upon irrigated agriculture. Intensification required new canals, which required the mobilization of significant resources. Old canals required maintenance, or they would silt up. This required planning and so surveyors and administrators needed to learn mathematical processes involved in planning and maintaining irrigation works. This paper examines these mathematical processes. It explores both mathematical texts from the Old Babylonian period (the beginning of the second millennium BCE in southern Iraq), as well as mathematical processes witnessed in administrative texts that deal with irrigation and excavation. It will be seen how well mathematical texts reflected administrative practice when it comes to canal maintenance.

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Notes

  1. See the appendix here for a catalog of mathematical texts.

  2. See Nemet-Nejat 1993: 35–43 and 46–54. Nemet-Nejat’s work, as its title proclaims, shows how cuneiform mathematical texts reflected every-day life.

  3. Described by Høyrup (2011: 6) as ‘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’.

  4. Categorization is based on terms found in the texts themselves. Thus, the Sumerian word ‘id2’ is used to denote canals. ‘pa5-sig’ is employed by the ancient authors and practitioners to describe a smaller canal or subsidiary canal, while the Sumerian word ‘ki-la’ describes a trench or reservoir.

  5. The word ‘actor’ is used here as a neutral term to describe a person that is responsible for calculation with the understanding that this may not be the text’s author.

  6. For Ni 18, see Proust (2007): 193 for translation and ibid pl. 1 for the text’s copy.

  7. See Damerow (2016) for the development of this system in Mesopotamia during the late third and early second millennium BCE, as well as its advantages over previous systems to compute area and volume.

  8. While formally the same, depth was treated numerically as different from length measurement values, with its own transformations to and from SPVN.

  9. For a complete reconstruction of a composite metrological table at Nippur, see Proust (2007): 311–315. For their appearance and use in the scribal curriculum at Nippur, see ibid 97–117.

  10. For these tables in the elementary education at Nippur, see Proust (2007): 117–14. For a composite list of these tables, see ibid 316–323.

  11. Robson (1999: 97) rightly, but tentatively, suggests these numbers are work assignments. Friberg (2000: 122–127) establishes a firmer link to canal excavation, showing their plausible relationship to numerous mathematical texts, especially YBC 4666 problems 9–10 and YBC 7164 problem 1. (Ibid 126–27. See also the appendix here for these texts).

  12. This seems to be a reference to what is called the surveyor’s formula by modern Assyriologists. This formula is clearly used in lines 6, 8, 10 of the obverse, and lines 8′ and 12′ of the reverse. In these lines, lengths in columns 2 and 3 are probably appended together and then divided in half to produce an average of the two sides. (Middeke-Conlin 2020: 8.3.4, esp. Table 8.17).

  13. For this text, see Middeke-Conlin (2018).

  14. YBC 12273 will be published in Middeke-Conlin forthcoming as text 22.

  15. If Namīram-šarur is the same person as or a relative of Namram-šarur, brother of Lamassatum in HS 2197: 7 (dated Rīm-Sîn year 45) and father of Suḫḫuntum in HS 2246 (dated to Samsu-iluna year 13) then he was probably active around the city of Nippur.

  16. For the centesimal system, see Proust 2002.

  17. See Middeke-Conlin (2020): Sect. 8.3 and appendix 1 for Riftin (1937) no 116.

  18. Robson (2014): SVJAD 117 [Tabular account], https://oracc.museum.upenn.edu/obta/P412628/html. Accessed 30 June 2018.

  19. Robson (2014): BM 016391 (unpublished) [Tabular account], https://oracc.museum.upenn.edu/obta/P412463/html. Accessed 30 June 2018.

Abbreviations

Ashm:

Museum siglum, Ashmolean Museum, Oxford

BM:

Museum siglum of the British Museum, London

CBS:

Museum siglum of the University Museum in Philadelphia

CDLI:

Cuneiform Digital Library Initiative (https://cdli.ucla.edu/)

Erm:

Museum siglum, State Hermitage Museum, St. Petersburg

HS:

Tablet siglum of the Hilprecht Collection, Jena

IM:

Museum siglum of the Iraq Museum, Baghdad

MAH:

Museum siglum, Musée d’Art et d’Histoire, Geneva.

MCT:

Neugebauer and Sachs 1945

MKT:

Neugebauer 1935–37

NBC:

Museum siglum, Nies Babylonian collection

TMB:

Thureau-Dangin 1938

TMS:

Bruins and Rutten 1961

U:

Find siglum, Ur

UET 6/2:

Gadd and Kramer 1966

VAT:

Museum siglum, Vorderasiatisches Museum, Berlin

YBC:

Museum siglum, Yale Babylonian collection

References

  • Al-Rawi FNH, Friberg J (2016) New mathematical cuneiform texts, sources and studies in the history of mathematics and physical sciences. Springer, Cham

    Google Scholar 

  • Bruins EM, Rutten M (1961) Textes mathématiques de Suse, Mémoires de la Mission archéologique en Iran 34. P. Geuthner, Paris

    Google Scholar 

  • Civil M (1994) the farmer's instructions: a sumerian agricultural manual, Aula Orientalis Supplementa 5. Editorial AUSA, Sabadell – Barcelona

    Google Scholar 

  • Clevenstine E (2015) MAH 15886 + 16295, a Rim-Sin tabular account in Geneva. Cuneiform Digital Library Notes 2015:009

    Google Scholar 

  • Damerow P (2016) Chapter 3: the impact of notation systems: from the practical knowledge of surveyors to babylonian geometry. In: Schemmel M (ed) Spatial thinking and external representation: towards a historical epistemology of space. Edition Open Access, Berlin, pp 93–119

    Google Scholar 

  • Friberg J (1993) On the structure of cuneiform metrological table texts from the -1st millennium. In: Glater HD (ed) Die Rolle der Astronomie in Kulturen Mesopotamiens. RM Druck-und Verlagsgesellschaft, Graz, pp 383–405

    Google Scholar 

  • Friberg J (2000) Mathematics at Ur in the Old Babylonian period. Revue d'assyriologie 94:97–188

    Google Scholar 

  • Gadd CJ, Kramer SN (1966) Literary and religious texts: second part, Ur excavation: texts. London/Philadelphia: Publications of the Joint expedition of the British Museum and of the Museum of the University of Pennsylvania to Mesopotamia.

  • Gonçalves C (2015) Mathematical tablets from Tell Harmal, sources and studies in the history of mathematics and physical sciences. Springer, New York, London

    Google Scholar 

  • Høyrup J (2002) Lengths, widths, surfaces: a portrait of Old Babylonian algebra and its kin. Springer, New York

    Book  Google Scholar 

  • Høyrup J (2011) Mesopotamian calculation: background and contrast to Greek mathematics. IX Congresso della Società Italiana di Storia della Matematica, Genova, 12 November 2011.

  • Hunt R (1988) Hydraulic management in southern mesopotamia in sumerian times: some observations. Bulletin on Sumerian Agriculture 4:189–205

    Google Scholar 

  • Middeke-Conlin R (2018) Estimation and observation: a study of two old Babylonian tabular administrative documents. In: Cavigneaux A, Attinger C, Mittermayer C, Novak M (eds) Text and image: Proceedings of the 61e Rencontre Assyriologique Internationale, Geneva and Bern, 22–26 July 2015. Peeters Publishers, Leuven, pp 281–291

  • Middeke-Conlin R (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. Springer, Cham

    Book  Google Scholar 

  • Middeke-Conlin R. Forthcoming. Old Babylonian texts dealing with area, volume, and bricks: texts from the Babylonian collection. New Haven: Yale University Press.

  • Nemet-Nejat KR (1993) Cuneiform mathematical texts as a reflection of everyday life in Mesopotamia, American Oriental Series 75. American Oriental Society, New Haven

    Google Scholar 

  • Neugebauer O (1935–37) Mathematische Keilschrifttexte. 3 vols, Quellen und Studien zur Geschichte der Mathematik Astronomie und Physik. Springer, Berlin

  • Neugebauer O, Sachs AJ (1945) Mathematical cuneiform texts, American oriental studies 29. American Oriental Society, New Haven

    Google Scholar 

  • Powell MA (1988) Evidence for agriculture and waterworks in babylonian mathematical texts. Bulletin on Sumerian Agriculture 4:161–172

    Google Scholar 

  • Proust C (2002) Numération centesimal de position à Mari. In: Charpin D, Durand J-M (eds) Florilegium Marianum 6: Recueil d'études à la mémoire d'André Parrot. Société pour l'étude du Proche-orient ancient, Paris, pp 513–516

    Google Scholar 

  • Proust C (2007) Tablettes mathématiques de Nippur. IFEA, De Boccard, Istanbul

    Google Scholar 

  • Reculeau H (2018) Florilegium marianum XVI. L’agriculture irriguée à Mari : essai d’histoire des techniques. Mémoires de N.A.B.U. 21. Paris: Société pour l’Étude du Proche-Orient Ancien SEPOA

  • Riftin AP (1937) Staro-vavilonskie iuridicheskie i administrativnye dokumenty v sobraniiakh SSSR. Izd-vo Akademii nauk SSSR, Moscow

    Google Scholar 

  • Robson E (1999) Mesopotamian mathematics 2100–1600 BC: technical constants in bureaucracy and education, Oxford editions of cuneiform texts 14. Clarendon Press, Oxford

    Google Scholar 

  • Robson E (2014) Old Babylonian tabular accounts. https://oracc.museum.upenn.edu/obta/. Accessed June 30, 2018.

  • Rost S (2017) Water management in Mesopotamia from the sixth till the first millennium BC. WIREs Water 4:e1230

    Article  Google Scholar 

  • Thureau-Dangin F (1938) Textes mathématiques babyloniens, Ex Oriente Lux, vol 1. E. J. Brill, Leiden

    Google Scholar 

  • Vaiman, A.A. 1961. Sumero-vavilonskaya matematika, III-I tysyaceletiya do n.e. (Sumero-Babylonian mathematics, third to first, B.C.). Moscow.

  • Walters S (1970) Water for Larsa: an old Babylonian archive dealing with irrigation, Yale Near Eastern Researches 4. Yale University Press, New Haven

    Google Scholar 

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  1. Department of Cross-Cultural and Regional Studies, University of Copenhagen, Berlin, Denmark

    Robert Middeke-Conlin

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Appendix

Appendix

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Table 12 Catalogue of mathematical texts on irrigation and excavation
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Middeke-Conlin, R. The mathematics of canal construction in the kingdoms of Larsa and Babylon. Water Hist 12, 105–128 (2020). https://doi.org/10.1007/s12685-020-00243-7

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