Abstract
This chapter offers an analysis of the segmentation of texts into lists of mathematical problems written on clay tablets during the Old Babylonian period (early second millennium BCE). The study focuses on mathematical series texts , that is, long lists of statements written on several numbered tablets. Two aspects are considered: material segmentation (sections, columns, tablets…) and textual segmentation (statements, groups of statements), as well as the relationship between these two aspects. It is shown that the analysis of parts of text may be a powerful tool for the reconstruction of the entire series and for detecting the operations on texts which produced the series.
The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant Agreement No. 269804.
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Notes
- 1.
I published this text in Proust (2009).
- 2.
Neugebauer already observed this phenomenon (Neugebauer 1935–1937: I, 433, Note 12a).
- 3.
As observed by Julie Lefebvre in her commentaries on the present paper (SAW seminar July 2013), ‘It seems that “im-šu” have somewhat the same status as “alinéa” in French: sometimes it only refers to a material phenomenon, a blank space generated by an indentation ; sometimes it means the textual content (in legal texts, “alinéa 15”, for example).’
- 4.
It seems that this is the meaning of ‘im-šu’ in Lines 7 and 10 of the literary text published by Kramer under the title Schooldays (Kramer 1949). Kramer translates ‘im-šu’ as ‘hand copy’: ‘(In) the afternoon, my hand copies were prepared for me […] I spoke to my father of my hand copies’ (kin-sig im-šu-mu ma-an-gub-bu-uš […] ad-da-mu im-šu-mu KA in-an-dug4-ma) (Kramer 1949: 201, 205). However, in his commentary, Kramer refers to the translation ‘section’ adopted by Neugebauer and Sachs: ‘In Line 7, ‘im-šu’ is to be rendered as “section” or “paragraph ” according to Neugebauer and Sachs' [Mathematical Cuneiform Text] 125.’ (Kramer 1949: 214).
- 5.
I follow Neugebauer (1935–1937) in Mathematische Keilschrifttexte I–III (in German: Abschnitte), and Neugebauer and Sachs in Mathematical Cuneiform Text. Thureau-Dangin tentatively translated ‘im-šu’ as ‘case’ (Thureau-Dangin 1938: 148, Note 1). However, the French word ‘case’ (box in English) refers to material segmentation only.
- 6.
- 7.
For a detailed analysis of the procedures in sets of problems, see Proust (forthcoming).
- 8.
The ninda is a unit of length of about 6 m.
- 9.
The complete list is provided in Proust (2012: 150–151, Table C). In this publication, I labeled the tablets containing mathematical series text as S1, S2, … S20.
- 10.
Neugebauer, in his chapter on ‘serientexte’ (Neugebauer 1935–1937: I, 387, Chap. VII), supposed that series tablets come from Kiš: ‘All texts discussed in this chapter come from the antiquities market. The two Berlin tablets (VAT 7528 and 7537) were purchased in Paris from Géjou and were probably inventoried between 1911 and 1912. In this purchase were also texts that, according to indications given by the merchant, came from Kish or localities in the immediate vicinity of Kish.’ (Alle in diesem Kapitel behandelten Texte stammen aus dem Antikenhandel. Die beiden Berliner Tafeln (VAT 7528 und 7537) sind von Gejou in Paris gekauft und vermutlich zwischen 1911 und 1912 inventarisiert worden. In diesem Kauf befinden sich auch Texte, die nach der Angabe des Händlers aus Kiš oder Orten unmittelbar bei Kiš stammen). Friberg considered that the provenience of tablets containing series text is more probably to be located in southern Mesopotamia, more precisely in Ur. He distinguished two different sub-groups among tablets containing series text: a group Sa and a group Sb, the latter only including the two tablets kept at the Oriental Institute of Chicago A 24194 and A 24195 (Friberg 2000: 172).
- 11.
- 12.
1 eše GAN is 6 GAN, that is, 6 times the area of a 10 ninda-side square, about 3600 m².
- 13.
Indeed, 10 is the product of 30, the length, by 20, the width, in floating sexagesimal place value notation. See Proust (2013) for more explanation on sexagesimal place value notation and floating multiplication.
- 14.
However, the scribe(s) who wrote the other known tablets which probably contain super-series, A 24194 and A 24195, seem not to have attempted to end each single series text exactly at the end of a column, or at the end of the obverse or at the end of the tablet (Proust 2015: 310–311).
- 15.
From the twenty known series texts, I excluded the three super-series (see Sect. 3.3.2); YBC 4714, because the type of tablet and the structure of the text are different; YBC 4696, whose colophon does not contain a serial number; YBC 4708 and YBC 4673, which deal with bricks, VAT 7528, which deals with canals; and YBC 4698, which deals with economic topics (see Middeke-Conlin and Proust 2014). Note that in the following, to facilitate the use of Table 3.6, I designate the tablets by the publication numbers S1, … S14 that I have used in previous articles.
- 16.
The tablets containing more than 200 statements are the three known ‘super-series’ tablets (YBC 4668, A 24194 and A 24195), which do not appear in Table 3.6, even if they deal with fields.
- 17.
Neugebauer stresses that YBC 4695 and YBC 4711 probably belong to the same series. (Neugebauer 1935–1937: I, 385).
Abbreviations
- MCT::
-
Neugebauer, et al. 1945
- MKT::
-
Neugebauer 1935–1937
- TMB::
-
Thureau-Dangin 1938
Bibliography
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Appendix
Appendix
AO 9071, copy published in Proust (2009: 177, 179)
Primary Sources
Museum numberCDLI number | Publication | |
|---|---|---|
A 24194 | P254383 | MCT: 107 |
A 24195 | P254384 | MCT: 119 |
AO 9071 | P254392 | Proust (2009) |
AO 9072 | P416818 | Proust (2009) |
VAT 7537 | P254933 | MKT: I, 466; TMB: 207 |
YBC 4657P254982 | MCT: 66 | |
YBC 4662 | P254983 | MCT: 66 |
YBC 4663 | P254984 | MCT: 66 |
YBC 4668 | P254986 | MKT: I, 420; TMB: 162 |
YBC 4695 | P255007 | MKT: I, 501; TMB: 214 |
YBC 4697 | P255009 | MKT: I, 485; TMB: 214 |
YBC 4709 | P255016 | MKT: I, 412; TMB: 155 |
YBC 4710 | P255017 | MKT: I, 402; TMB: 148 |
YBC 4711 | P255018 | MKT: I, 503; TMB: 214 |
YBC 4712 | P255019 | MKT: I, 420; TMB: 176 |
YBC 4713 | P255020 | MKT: I, 421; TMB: 162 |
YBC 4715 | P255022 | MKT: I, 478; TMB: 190 |
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Proust, C. (2018). Segmentation of Texts in Old Babylonian Mathematics. In: Bretelle-Establet, F., Schmitt, S. (eds) Pieces and Parts in Scientific Texts. Why the Sciences of the Ancient World Matter, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-319-78467-0_3
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