Astronomy and Mathematics in Ancient China: The Zhou Bi Suan Jing (review)

Reviews 367 Christopher Cullen. Astronomy and Mathematics in Ancient China: The Zhou Bi Suan Jing. Cambridge: Cambridge University Press, 1996. xiv, 241 pp. Hardcover $69.95, 1SBN 0-521-55089-0. Although the potential readership for this text is perhaps not large, that in no way detracts from its value. It is in all respects an exemplary piece ofwork, produced by Cambridge University Press in a very pleasing format. For this reason I would not hesitate to recommend it to students contemplating work on Chinese materials , even if they were not specializing in the history ofChinese astronomy. Students ofthe history of mathematics and science more generally will also find the book interesting and accessible. For Cullen has succeeded, where many others have not, in providing a work that is not only clear, concise, and readable but also carefully prepared and extremely thorough. He has indeed fulfilled his goal of giving the reader without specialized knowledge an outline understanding ofthe place of astronomy in the culture of China's early imperial period. In his preface, Cullen disclaims deployment of any very sophisticated methodology , reporting that half the effort required was ofthe "old-fashioned philological and text-critical variety." His three other guiding principles are ones that in recent years have increasingly come to characterize the work ofhistorians of science and mathematics, but which were often not observed in earlier histories of either Western or Chinese science and mathematics. Cullen gives a particularly clear statement of these principles, without becoming entangled in philosophical issues ofinterpretation: (1) to try to reconstruct the thought and practice of ancient authors from their writings rather than take for granted that modern categories will apply, while recognizing that such a reconstruction can never be fully attained and that one can never wholly refrain from imposing modern categories; (2) to begin by assuming that the various things people did in the past made sense to them as part of a more or less systematic approach to the tasks diey were addressing, even though it might in the end turn out to be the case that they had the usual human capacities for confusion and/or self-delusion; and (3) to try not to draw boundaries that may not have seemed at all solid at the time, or to force on the past issues that had not yet occurred to anybody. Certainly Cullen's work should serve to recommend to others the fruitfulness oftaking these guiding principles as their own. The translation ofthe Zhou Bi Suan Jing (MfQWKE) itselfoccupies onlyjust© 1997 by University over thirty pages. In the remainder of the book Cullen provides a much-needed ofHawai'i Pressbackground context to the work. The Zhou Bi (UW, The Gnomon ofthe Zhou [dynasty], or as some have translated the tide, TheArithmetical Classic ofthe Gnomon and the CircularPaths ofHeaven) is a collection ofancient Chinese texts on 368 China Review International: Vol. 4, No. 2, Fall 1997 astronomy and mathematics traditionally reputed to have been written during the Western Zhou dynasty (about 1100 b.c.) but now thought to have been assembled during the first century b.c. under the Western Han. Cullen argues that it is as a product of the Han age, with its changes in astronomical theory and practice, that the Zhou Bi can best be understood. As with many ancient Chinese texts, precise dating is problematic. Cullen deals with these problems in his third chapter, where the origins of the work and probable dates for its various parts are discussed . He suggests that the text contains a clearly identifiable core of closely related material, the later portions ofwhich cannot be earlier than the first century b.c. The collection had not reached the imperial library by around 5 b.c., but it seems that similar material was available by a.d. 18 and there are strong signs of the book's existence around a.d. 200. Much of the text of the Zhou Bi consists of calculations of the dimensions of the cosmos using observations of the shadow cast by a vertical pole gnomon. The cosmographical model on the basis ofwhich the calculations are made is the gai tian WlK theory according to which an umbrella-like...