Imagined Civilizations: China, the West, and Their First Encounter

5. Tracing Practices Purloined by the Three Pillars

Chapter 5 Tracing Practices Purloined by the Three Pillars “ TATTERED SANDALS,” regrettably, was all that remained of Chinese mathematics, which could just as well be discarded because Western mathematics was in every respect superior—or at least so claimed Xu Guangqi  (1562–1633) in his preface to the Guide to Calculation in the Unified Script (Tong wen suan zhi !, 1613).1 The Guide to Calculation was purported to be a translation of Western mathematics, taken from Christoph Clavius’s (1538–1612) Epitome arithmeticae practicae (1583),2 together with some problems from Chinese mathematics that, clearly designated as such, were included to demonstrate the alleged superiority of Western mathematics. Xu, Li Zhizao  (1565–1630), and Yang Tingyun  (1557–1627), who collectively are often referred to as the “Three Pillars” (san da zhushi  ) of Catholicism in Ming China, each wrote a preface for the Guide to Calculation denouncing contemporary Chinese mathematics while promoting the superiority of Western mathematics. This chapter will show that the most difficult problems in their “translation” were purloined—without comparison, without analysis, without criticism, and without any mention of the source—from the very Chinese mathematical treatises Xu denigrated. In particular, the problems purloined by the Three Pillars and their collaborators, problems that were known in imperial China as fangcheng $ (sometimes translated as matrices or “rectangular arrays”), or what we 1 Tong wen suan zhi  [Guide to calculation in the unified script], in Zhongguo kexue jishu dianji tonghui: Shuxue juan   / [Comprehensive collection of the classics of Chinese science and technology: Mathematics volumes] (Zhengzhou: Henan jiaoyu chubanshe  2, 1993), hereinafter ZKJDT. Authorship is attributed to Matteo Ricci (1552–1610) and Li Zhizao  (1565–1630). For an analysis of the Guide to Calculation, see Takeda Kusuo  , Dōbunzanshi no seiritsu  [Inception of the Guide to Calculation in the Unified Script] (Tokyo: Iwanami Shoten ., 1954). For a recent study of the transmission of Western Learning into China, see Ahn Daeok  , Minmatsu Seiyō kagaku tōdenshi: “Tengaku shokan” kihen no kenkyū & :  6  [History of the transmission of Western science to the East in the late Ming: Research on the Qibian of the Tianxue chuhan] (Tokyo: Chisen Shokan ., 2007). 2 Christoph Clavius, SJ (1538–1612), Christophori Clavii Bambergensis e Societate Iesv epitome arithmetica practicae (Romae: Ex Typographia Dominici Basae, 1583). 131 132 5 Tracing Practices Purloined by the Three Pillars would now call linear algebra, are arguably the most advanced and recognizably “modern” mathematics in the Guide to Calculation. These problems were copied into chapter 5 of the second volume (tong bian  ), without any indication that they were from contemporary Chinese treatises. These problems were then provided a new name, the title of the chapter, “Method for addition, subtraction, and multiplication of heterogeneous [elements]” (za he jiao cheng fa  ). Chinese readers of the Guide to Calculation could not have known that Clavius’s Epitome contains no similar problems, but later Chinese commentators added notes remarking that similar problems could be found in Chinese works. That nineteen fangcheng problems were purloined from the very Chinese mathematical texts denounced by Xu as “tattered sandals” suggests that Xu, Li, Yang, and their collaborators did not themselves believe the assertions they presented in their prefaces extolling the superiority of mathematics from “the West.” Yet Xu’s pronouncements have seemed so persuasive that his claims have been, at least until recently, accepted for the most part by historians—Chinese and Western alike—as fact. We should instead critically analyze the self-serving statements in their prefaces as propaganda designed to promote “Western Learning” (Xi xue ), and together with it, their own careers in the imperial bureaucracy. More broadly, in this chapter I argue that extant mathematical treatises from this period should be viewed as epiphenomenal, preserving only fragments of mathematical practices: whereas the previous chapter of this book focused on extant mathematical treatises from the Song, Yuan, and Ming dynasties, this chapter will explore mathematical practices of imperial China by reconstructing those practices from extant mathematical treatises. More specifically, from extant mathematical treatises—which were written, compiled, circulated, and preserved by the literate elite—I reconstruct fangcheng mathematical practices. The earliest extant written records of these practices are recorded in Chinese mathematical treatises dating from the first century CE; these mathematical practices continued to be recorded in Chinese mathematical treatises throughout the imperial period. I argue that in general the literate elites who compiled mathematical treatises often had little more than a rudimentary understanding of the mathematical practices they recorded, especially for practices...