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Scientific Sources and Teaching Contexts Throughout History: Problems and Perspectives pp 69–94Cite as

Does a Master Always Write for His Students? Some Evidence from Old Babylonian Scribal Schools

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Part of the book series: Boston Studies in the Philosophy and History of Science ((BSPS,volume 301))

Abstract

Cuneiform mathematical texts from the Old Babylonian (period early second millennium BCE) are the result of the activities of scribal schools and, in this sense, emanate incontestably from a “teaching context”. Thus, mathematical texts are generally considered as evidence of pedagogical activity, meaning they are assumed to have been written either by students or for students. My goal is to show the simplistic nature of such a narrow alternative. Three groups of texts are examined to show that an elementary school text was not always puerile; that a text written for teaching could at the same time serve other purposes and that a text written by a master did not always have an educative objective. The contrasting analysis of these three groups thus allows me to highlight the contextual diversity of both the production and the usage of the texts, all of which nevertheless deriving from scribal schools

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Notes

  1. 1.

    Note on the dates: All the dates given in this chapter are Before the Common Era. The dating follows “middle chronology”, according to which the dates of Hammurabi’s reign are 1792–1750. This chronology, although contested (Gasche et al. 1998), is the most widely used by historians of the Ancient Near East. Note on the sources: the information on the tablets quoted in this chapter (physical description, references, photographs, copies, transliterations, translations) are available on the Cuneiform Digital Library Initiative website (CDLI http://cdli.ucla.edu). The statistics come from the CDLI website database, completed by data from my own database which includes unpublished tablets. To April 2013, the CDLI has identified about 1940 mathematical tablets, which represents a relatively complete inventory of mathematical sources known today. We must, however, add to this total further unpublished tablets kept at the Oriental Institute of the University of Chicago (approximately 200 school tablets from Nippur), and those unearthed at Mari (140 school tablets), so a total approaching 2,300 tablets. Of these, approximately 1900 date from the Old Babylonian period.

  2. 2.

    Neugebauer and Sachs (1945, 1).

  3. 3.

    Veldhuis (1997), Robson (2001, 2002), Friberg (2000), and Proust (2007, 2008b).

  4. 4.

    Neugebauer (1935–1937), Neugebauer and Sachs (1945), Thureau-Dangin (1936), Goetze (1951), Bruins and Rutten (1961), and Gonçalves (forthcoming) who provides a complete bibliography on Diyala’s material.

  5. 5.

    This general context of mathematics is recognized since long time: “[Problem texts] are school products intended to illustrate the rules for dealing with problems which are properly called ‘algebraic’.”(Neugebauer and Sachs 1945, 1).

  6. 6.

    In (Bernard and Proust 2008) there are comments on the various contexts through the evocation of the history of reciprocal tables-texts that have passed through millennia without great modification, but whose use has changed considerably over time.

  7. 7.

    I think this is the case for the interpretations that were given for texts such as CBS 1215, which deals with the inversion method of regular numbers, Plimpton 322, which deals with Pythagorean triples, or series texts (see Britton et al. 2011; Proust 2012).

  8. 8.

    For an up to date presentation of the debate and for related bibliography, see (Michalowski 2012). I rely on Michalowski’s analysis, who stresses the diversity of teaching situations.

  9. 9.

    Tanret (2002).

  10. 10.

    Charpin (1986, 420–486).

  11. 11.

    Michel (2008).

  12. 12.

    See the bibliography given in footnote 3.

  13. 13.

    Hilprecht (1906).

  14. 14.

    Veldhuis (1997).

  15. 15.

    Several authors have drawn attention to the fact that the literary texts used for training did not objectively reflect the reality of schools but rather reflected the ideology particular to the scribal milieu of Nippur (Michalowski 1987, 63; George 2005). Some literary texts, however, contain many details on the school curriculum that are confirmed by independently obtained data, and are therefore valuable sources of information.

  16. 16.

    Vanstiphout (1979).

  17. 17.

    This method consists in analyzing the text, not in isolation, but as an element in a collection of documents found at a precise archaeological locus. See on this subject (Veenhof 1986).

  18. 18.

    The best documented of the scribal schools at Nippur is “House F”, whose contents were analyzed by (Robson 2001).

  19. 19.

    These tablets are for the large part published (Proust 2007, 2008b; Robson 2001) or are on the way to being published.

  20. 20.

    For more details, see (Veldhuis 1997; Robson 2001; Proust 2007, 2008b).

  21. 21.

    A detailed description of the metrological lists and tables, as well as place value notation can be found in (Proust 2009b). An important feature of cuneiform sexagesimal place value notation is the fact that no mark indicates the order of magnitude of numbers, or, in other words, that the notation is “floating”.

  22. 22.

    See (Proust 2007, ch. 6 and 7).

  23. 23.

    Tablet UM 29-15-192 comes from Nippur and is kept in Philadelphia; it is published in (Neugebauer and Sachs 1984, 251).

  24. 24.

    This last interpretation, based on the idea that surface and volume calculations use unit conversions, is largely referred to in the publications on this subject. I have explained in detail the reasons for my disagreement with this interpretation in (Proust 2008a). A recent example where the surface exercises are explained, in an uncontextualized way, by the conversion of units is found in (Robson 2008, 8–12).

  25. 25.

    Proust (2005).

  26. 26.

    For a detailed analysis of the normative character of the metrological texts, see (Proust 2009b).

  27. 27.

    I use the term “erudite” here in contrast to “elementary school” (see the introduction of this chapter). This term refers to teaching texts destined for advanced student or pieces of pure erudition.

  28. 28.

    Goetze (1945).

  29. 29.

    Tinney (1998, 46, 1999).

  30. 30.

    Goetze (1945, 148).

  31. 31.

    It is assumed here that, by default, the work lasted 1 day: other texts lead to the belief that the work lasted 9 days (see YBC 4657 and YBC 4662 quoted later and Neugebauer and Sachs 1945, 74), and therefore the “number of workers” is in fact the number of workers × days (30 workers for 9 days).

  32. 32.

    I use standard font for the words translated from Sumerian ideograms, and italics for the words translated from Akkadian.

  33. 33.

    One can refer to the metrological tables in their entirety on the CDLI website (Proust 2009b). The arrows represent the “reading” of the tables, that is to say the correspondence established by the metrological tables. These are referred to, in brief, as follows: “table L” means the length measurement table, “table Lh ” means the height measurement table; “table S” means the surface measurement table; “table P” refers to the weight measurement table. For more details on the calculation of volumes (units, using the height table and surface tables for volumes), see (Proust 2008a).

  34. 34.

    The following equalities must be understood modulo a factor 60n, n any positive or negative integer.

  35. 35.

    The name comes from Jöran Friberg and from Jens Høyrup (2002, 8 including note 13).

  36. 36.

    The three texts are published together in the same section by Neugebauer and Sachs (1945, 66 ss.), who underline: “These three texts form a closely knit group.” (ibid, 73). However, the question of whether procedure texts derive from the catalogues (or vice versa) is not addressed in Neugebauer and Sachs 1945 nor indeed is the issue of the possible difference in function between procedure texts and catalogues.

  37. 37.

    For more details, see (Neugebauer and Sachs 1945, 74; Proust 2012).

  38. 38.

    Glassner (2009).

  39. 39.

    For the tablets at Yale and in Berlin see Neugebauer (1935–1937), I ch. 7 and III pp. 27–45; for those in Chicago, see Neugebauer and Sachs (1945), texts T and U; for those at the Louvre, see Proust (2009a).

  40. 40.

    I shall confine myself here to very general remarks about the series texts. Entering into the detail of the texts largely goes beyond the scope of this contribution. For more information, see (Proust 2009a, 2012).

  41. 41.

    TMS 7 and 16 (Høyrup 2002, 85, 181).

  42. 42.

    See for example sections #35 to 47 of the YBC 4668 series tablet (Neugebauer 1935–1937, I:455–6), which contain fourth degree problems, or sections #28 to 32 of YBC 4710 (Neugebauer 1935–1937, I:410–1), which contain fifth degree problems.

  43. 43.

    It is interesting to note that the function of the sets of parameters in the collections of problems is not always the same. See for example cases described by Alexei Volkov (ch. 9).

  44. 44.

    “the sophistication of many of the series texts – regarding mathematical substance as well as the pluridimensional variation of statements – shows them to belong to a more mature phase of scholastization than the Eshnunna corpus” (Høyrup 2002, 351).

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  1. Laboratoire SPHERE UMR 7219, CNRS & Université Paris Diderot, rue Thomas Mann 5, 75205, Paris, France

    Christine Proust

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    Alain Bernard

  2. Laboratoire SPHERE UMR 7219, Université Paris 7 - CNRS, Paris, France

    Christine Proust

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Proust, C. (2014). Does a Master Always Write for His Students? Some Evidence from Old Babylonian Scribal Schools. In: Bernard, A., Proust, C. (eds) Scientific Sources and Teaching Contexts Throughout History: Problems and Perspectives. Boston Studies in the Philosophy and History of Science, vol 301. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5122-4_4

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