Contenu du sommaire : Sous les nombres, le monde : Matériaux pour l'histoire culturelle du nombre en Chine ancienne

Use of Numerals in Shang Inscriptions Redouane Djamouri 's paper makes a detailed analysis of the role of numerals in the grammar of archaic Chinese language. He puts forward a hypothesis according to which the formation of the system of numbers was closely connected with, and in a sense determined by, the grammatical function of numerals. His paper contains several corrections of the materials published by previous authors on the earliest written forms of numerals on oracle bones.

Number and Operation, Warp and Weft of Mathematical Reality Karine Chemla proposes a new interpretation of the meaning of the word shu, "number", based on several fragments of Liu Hui' s (fl.+263) commentaries on the mathematical treatise Jiu zhang suan shu. She suggests that the commentator consciously used the polyvalency of certain terms, which permitted him to apply the same general procedures to numbers as well as to algorithms. This allows her to suggest a hypothesis on general description of procedures in mathematics at that time.

Alexeï Volkov' s paper treats the problem of the finiteness of numbers formulated in the IIIrd century (?) treatise Shu shu ji yi by Xu Yue, and commented in the VIth century by Zhen Luan. The author suggests that the treatise may have been used in the framework of debates on the Buddhist notion of reincarnation. A reference to a theoretical construction which allowed one to obtain numbers as large as desired (similar to that of Archimedes' Sand-Reckoner) is discussed, as well as the role of the counting devices in establishing a general notion of number.

Role and meaning of numbers in Daoist cosmology and alchemy Isabelle Robinet supplies the reader with a considerable amount of data concerning the use of numbers in texts from the Dao zang. She shows how the numbers were used symbolically and demonstrates how arithmetical operations (representation as a sum or a product of several addends or factors) allowed numbers to connect ritual and alchemical practices with Daoist cosmology in its temporal and spatial aspects.

John Major's paper is devoted to the relationship between the calendar and the musical scale, and contains a complete translation of the excerpt from the Huainanzi (chapter 3) concerning the calculation of the lengths of standard pitchpipes. He also discusses the role played by so-called "cosmograph" or "cosmic board" (shi) in establishing correspondences between several series of calendrical data and astronomical phenomena.

Hans Ulrich Vogel' s paper is on the imbedding of symbolic correlations into the system of standard measures done in the beginning of the first century A.D. by Liu Xin. He discusses in detail chapter 21 of the Han shu devoted to the system of measures, weights and capacities which leads to the construction of a cosmology based on strict numerical correspondences.

Geoffrey E.R. Lloyd's paper compares the topics treated by the authors in this issue on Chinese notions of number with similar topics in ancient Greece. The author is mainly based on Greek treatises of philosophy, astronomy and mathematics and also stresses the social aspects of "the science of numbers" in Greece and China.