ABSTRACT
In ancient times, the education of a scholar included three domains, and art was one of them. Of the six arts, mathematics [shù 數, “number”] was one. For mathematics [shù 數] pervades all aspects of art just as earth is in the central position among the five elements [with wood, fire, metal and water]. All that can be seen or heard, all that has shape or form – they cannot be described or denoted without mathematics. Even what cannot be seen or heard, what is outside the physical universe, what took place tens of thousands of generations ago or is still to come, we cannot estimate or assess without the use of mathematics [shù 數]. To study what is and what will be, or anything that follows the laws of nature, we need mathematics [shù 數]. Human wisdom, however amazing, needs to work with addition, subtraction, multiplication and division. Human cunning, however profound, cannot obfuscate the results of calculation. This special profession does not lie. Through training, the mind becomes exceptionally agile; when versed in the knowledge, practice brings ingenuity. This knowledge anchors the mind to the real and the concrete, so that superficiality and arrogance will dissipate. It helps the intelligence to become active, so that one can understand and deal with the flux of change. Matters as miniscule as rice and salt, or as important as the latitudes and longitudes of the globe, depend on it. The legendary Yu 禹 [reigned, according to tradition, 2205-2197 BCE] depended on the compass and the carpenter’s square to restore the land during the deluge. The Duke of Zhou 周公 [d. 1105 BCE] observed the sky and made his measurements using the zhōubi 周髀 method [the right-angled triangle theory, known as
Pythagoras’s Theorem in the West].57 Who would say that the study of calculation methods is a trivial matter and an obstacle to the pursuit of more meaningful goals and aspirations? It is surely a better occupation than gambling or playing chess. Since the decline of ancient teaching [in mathematics], the concrete application of this art can no longer be seen. Scholars of the Anding School58 sought to revive the tradition, but what remains now is a mere shell of that tradition of study. In today’s world, a scholar with just a little knowledge of the canons would consider it a shame to be seen holding a measuring instrument or compass or a carpenter’s square. Even those who are as talented as the poet Cao Zhi曹植 [192-232] have no idea of the origins of rule and measure. Consequently, both in the management of the rivers and drainage, and in astronomy and the calendar, mistakes abound and the livelihood of the people has been badly affected. What a lamentable state!
