「算數書」初探

On the Suan Shu Shu: A Preliminary Study

本文對迄今已知中國最古老的數學文本《算數書》(不晚於公元前186年)進行初步的考察。通過它與《九章算術》的比較，我們發現《算數書》至少在著述體例、知識分類判準以及算法表徵等三方面，都不如前書。儘管如此，在《算數書》的映照下，被認為同時代現身的《九章算術》，卻可以放在更恰當的脈絡中加以觀察。譬如說吧，《九章算術》的『術曰』，中不含論證之面向，顯示它的作者只對純粹的實用演算感興趣。相反地，《算數書》的作者卻在一些『術曰』中保留了『故』或『因而』等連接詞，其目的顯然是『論述』算法而不只是『描述』它們而已。誠然，《算數書》中的算法表徵，應該反映了一個事實，那就是：西漢早期的某些數學家如何受到先秦對論證極有興趣的墨家與名家之影響。相反地，由於《九章算術》的著述只關注數學知識的如何使用，因此，這一部中國古代數學經典深受儒家治國之教條所支配，是一個很難抗拒的結論。

This article is to explore, if only preliminarily, the Suan Shu Shu (算數書) of no later than 186 B.C., the oldest mathematical text written on bamboo was ever discovered in China so far. By comparison with the Jiu Zhang Suan Shu (九章算數， Nine Chapters on Mathematical Art), the Suan Shu Shu is inferior in at least the following aspects, namely, format of exposition (著述體例), criterion of knowledge classification (知識分類判準), as well as presentation of algorithms (算法表徵). Nevertheless, it is in the light of the text, the Jiu Zhang Suan Shu, presumably made its first appearance in the same period, might be observed in a more appropriate context. For example, the authors of the Jiu Zhang Suan Shu provided no reasoning in its algorithms -- an aspect pointing to their sole interest in practical calculation. On the other hand, the authors of the Suan Shu Shu offered syntactical connectives like "Gu" (故) and "Yin Er" (因而) in order to make a conclusive argument. Indeed, the representation of algorithms given in the Suan Shu Shu may well reflect just how early former Han mathematicians were influenced by the pre-Qin period thinkers (like the Mohists and sophists) in terms of their interests in argumentation. On the contrary, due to that the writing of the Jiu Zhang Suan Shu might have primarily concerned with practical use of mathematical knowledge, one cannot resist to conclude that the classic of the history of Chinese mathematics was basically devoted to Confucian concern with state bureaucratic management.