Calling out Zheng Xuan (127–200 CE) at the crossroads of ritual, maths, sport and classical commentary (version 2)

International audienceIt is Zheng Xuan 鄭玄 (127–200 CE), more than any other commentator, to whom we owe our current understanding of the Confucian Classics – Zheng Xuan, of course, and the subcommentators, Kong Yingda 孔穎達 (574–648 CE) and Jia Gongyan 賈公彥 (fl. 637 CE), responsible for canonising his readings in the early Tang (618–907 CE). Zheng Xuan made mistakes, however, and this chapter offers a case study on one of the more glaring examples: the calculation of physically impossible target geometries for the royal archery meet reputedly held in the Western Zhou (1045–771 BCE), the ‘Big Shoot’ (dashe 大射). In transforming the ambiguous language of the Classics into an elaborate maths problem with definite quantities, Zheng Xuan neglects to account for the targets being in three dimensions, his subcommentators entering to supply mathematical proofs to numbers that are flat wrong, in both senses of the word. It is not as if they could not have known, I argue, considering that the Big Shoot was living practice in their respective days, and as preeminent commentators like Zheng Xuan and Kong Yingda were equally trained in mathematics equipped to solve this very problem. Faced with this curious epistemic dissonance between exegesis, experience, and mathematical training, I offer that we might better understand the work of the Classical commentator as reconstructing abstract, ‘Platonic forms’ necessarily divorced from their reality and for which mathematics suggested itself as the perfect tool