Mathematical and Graphical Reasoning with Shi-graphs in Early China

In contrast to Western causal thinking, early Chinese thinking is often characterized as associative and thereby criticized as ambiguous and pre-logical. Contra this traditional view, this paper firstly argues that the early Chinese thinking can be clearly grasped in terms of analyzing its underlying logic and structure. In fact, a large number of mathematical and hemerological texts found in recent years provide us two important clues for the central claim of this study, that are numbers and images. Secondly, instead of considering the images in question as artificial signs for practical purposes or symbolic pictures with allegorical meanings, I argue that they are actually various models of natural or scientifically relevant objects (such as the returning cycle of the sun or that of the music tones), yet downscalingly demonstrated into two dimensional images. Normally there are three steps for inventing this kind of pictorial model, i.e., considering particular things as mathematical objects, searching for their periodicity and projecting it as an image, the process of which represents a mathematical and graphical reasoning crucial for the formation of early Chinese associative thought. Thirdly, I argue that the shi-graphs（ “式图” ）, the most popular tools used for divination in the folk society in early China, are also representations of Chinese mathematical and graphical reasoning, although with simplifications and transformations of the above pictorial models. Besides, shi-graphs extend and expand the domain of correlative things and are important for the fixation of this correlative thinking among ordinary people.