The Science in the Context of Culture Euclid’s Elements and the Chiu Chang Suan Shu («Nachala» Evklida I «Czyu Chjan Suan' Shu»)

Abstract:     
This book covers two main issues. The first is the problem of connection between the style of scientific thinking, basic approaches to solving different problems within some scientific domain and the type of culture which the scientist belong to. The second issue relates to the eastern types of rationality, the peculiarities of the eastern science and philosophy.

As the material for these items the author uses two mathematical texts: Euclid’s Elements and the Chiu Chang Suan Shu (Mathematics in nine books). The former appear to be the outcome of Greek mathematics, the latter – of Chinese. The first point is that one of the key features of polis as economical, political and social system was straight opposition between the free and the slaves, which had the ontological foundation. The slaves were asserted to have been born to perform rough physical work, the free – to lead and occupy the intellectual activity. Due to these attitudes the contemplation of ideal structures was supposed much more perfect than creation or transformation of material objects. It entailed the key features of ancient Greek mathematics. First of all, it is a self-sufficient entity and its laws have nothing in common with that of the material world. These attitudes define the place of Aristotelian logic as the base for creating chains of mathematical statements.

The world structure in Chinese philosophy is crucially different. The Chinese had no ideal world like Plato’s world of ideas and the key point there was the isomorphism between different domains of reality: physical world, society, man. This isomorphism was expressed in the complicated system of correspondences between these domains: five elements (tree, fire, earth, metal, water) – five tastes – five colors – five kinds of activity – five divine emperors and the like. The important base for this isomorphism was the notion of tsi (the world pneuma), which was supposed to penetrate in the all domains of the world.

This attitude was realized in Chinese (and later in Japanese) mathematics. The main way of mathematical reasoning there appears to have been reasoning by analogy, for instance, between figures on plain and in space. As a variation of such a way of thinking one can mark out the method of demonstration by examples which replaced the precise proof in Greek mathematics. Thus, the author of “Mathematics in nine books” calculates the volume of pyramid in this way.

Keywords: Greek mathematics, Chinese mathematics, culture, way of thinking, context

JEL Classification: C00,

Accepted Paper Series