早期中国思维中的数理、图理与式图—以北大秦简《鲁久次问数于陈起》为中心
Mathematical and Graphical Reasoning with Shi-graphs in Early China
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摘要: 与西方因果思维相对，早期中国思维常被称为关联性思维，其特点常被认为是模糊的和前逻辑的。但实际上，早期中国最初一些核心要素的关联，有其自身逻辑和底层架构。近年来大量出土的数术文献，为我们指示出理解这种逻辑和架构的两个关键要素，即数与图像。过去认为早期中国与数有关的图像要么是为实际功用而创作的符号系统，要么是有寓意性的象征图像；但与此相反，它们（如三方三圆图、七衡六间图、十二律周期图）是关于实在的或自然的模型（如太阳回归周期的模型、音律回归周期的模型），背后有复杂的数理知识，只是被降维呈现在了二维图像上。在对事物的模型化和图像化过程中，将事物看作数学对象、寻找周期性并将其投射为图像，是其典型思维过程。民间占卜用的式图与基于数理知识的模型化图像有相同的思维，式图扩大了整个关联系统，对关联观念的固定化有重要作用。对于秦简《鲁久次问数于陈起》所指示出的任何早期中国思维特征的总结，都是放在与各种其他出土材料和相关传世文献，甚至是与其他文明的对比中进行的，因而绝非个例。Abstract: 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.
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Key words:
- correlative thinking /
- numbers /
- cyclicity /
- pictorial /
- model /
- shi-graphs
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五音 音名① 管子法② 十二律 音名 吕氏法③ 宫81 C1 81×4/3=108 黄钟81 C1 81×2/3=54 徵108 G 108×2/3=72 林钟54 G1 54×4/3=72 商72 D1 144×4/3=96 太簇72 D1 72×2/3=48 羽96 A 96×2/3=64 南吕48 A1 48×4/3=64 角64 E 姑洗64 E1 64×2/3≈42.67取42 应钟42 B1 42×4/3=57 蕤宾57 #F1 57×4/3=76 大吕76 #C1 76×2/3≈50.67取51 夷则51 #G1 51×4/3=68 夹钟68 #D1 68×2/3≈45.33取45 毋射45 #A1 45×4/3=60 中吕60 F1 60 
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