Remarks on the Mathematics and Philosophy of Space-time in Early Imperial China

Résumé En

This paper addresses two contradictory axioms of sinology: that (1) Chinese thought is unique in recognising the interconnectedness of space and time, and that (2) Chinese astronomy is a ‘calendar science’ dealing uniquely with the latter. These propositions cannot both be true, and a brief examination of the workings of li 曆 will reveal how neither is. In short, time is a function of the spatial displacement of celestial objects, and vice versa, their correlation being bound by natural velocities. In as much as ‘astronomy’ is the mathematical study of these velocities, the difference between astronomical cultures is not space vs time but the apparatus by which one transforms the one into the other. What little is unique about the Chinese case is the mathematical culture informing this operation: li rests upon sets of integer constants (shu 數), which Sivin (1969, 13) invites us to think of as cogs in a ‘gear-train’; functionally, however, the procedures (shu 術) reveal these to be lü 率, a mundane element of suan 算 presented in terms of grain-conversion. Examining how methods for converting between rice and beans were extended to time and space, we will consider commentators’ Changes-like reflections upon the metaphysics of lü, supplying actor’s categories where observer’s categories fall short of explaining how Chinese astronomy worked. In the conclusion, we will reflect upon the difference here between philosophical reflections and the contents of practice, asking why it is that the quantitative study of time and space is written out of the history of ‘Chinese thought’, ‘cosmology’ and shushu 數術.