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Chapitre D'ouvrage Année : 2022

Place-Value Notations in the Ur III Period: Marginal Numbers in Administrative Texts

Xiaoli Ouyang
  • Fonction : Auteur
Christine Proust

Résumé

The use of sexagesimal place value notation (hereafter SPVN) is one of the most striking features of cuneiform mathematics. The earliest attestations of a systematic use of SPVN in cuneiform sources are found in a small set of mathematical texts dated to the Ur III period (ca. 2112 to 2004 BCE). Besides this mathematical corpus, traces of numbers written in positional notations have been found in some Ur III administrative texts. Just a few dozen tablets, among tens of thousands of known Ur III administrative documents, exhibit such numbers noted in positional notation. Moreover, such numbers noted in positional notation appear almost only as a kind of graffiti in the margins. This chapter focuses on these scanty 'marginal numbers'. Marginal numbers in Ur III administrative texts testify to diverse practices with positional notations and sexagesimal factors in an administrative context, and, in this way, exemplify different 'cultures of computation and quantification' in the Ur III period. Through a close analysis of the positional notations found in Ur III administrative texts, we detect a diversity of graphical systems for what was considered until now as a uniform notion of SPVN. We show that these graphical systems vary according to the operations (multiplication, reciprocal, addition, subtraction), the contexts (administrative or mathematical), and the archaeological sites considered in this study (Umma, Girsu, Puzriš-Dagan, Nippur). Our goal is to show that this diversity of notations reflects different computational methods.
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Dates et versions

hal-04003095 , version 1 (23-02-2023)

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Xiaoli Ouyang, Christine Proust. Place-Value Notations in the Ur III Period: Marginal Numbers in Administrative Texts. Cultures of Computation and Quantification in the Ancient World, 6, Springer International Publishing, pp.267-356, 2022, Why the Sciences of the Ancient World Matter, ⟨10.1007/978-3-030-98361-1_5⟩. ⟨hal-04003095⟩
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