试论数学的文化奇观——兼谈文化和科学文化

摘要

广义的文化定义主要有＂总和说＂与＂模糊说＂两类。把＂总和说＂进一步扩展为＂超广义说＂,把＂模糊说＂修改为＂自创生说＂,将两者结合起来称做＂超广义自创生文化说＂。科学文化指科学本身以及科学与社会其他文化相互交融所形成的文化群类。数学文化指把自然、社会、思维等各个领域中的数量关系、空间形式、信息符号、能量运转、物质结构的哲理精蕴、艺术神采以其微妙深奥的规律化方式智慧地展现出来。数学的文化奇观的表现形式为深蕴的统一性、内增的复杂性、天成的艺术性和奇难的悬疑性等四个方面。%A broad definition of culture mainly includes the summation theory and the vagueness theory. The summation theory can be expanded into the super-generalization theory and the vagueness theory can be trans- formed into the autopoiesis theory. The two theories combined are called the cultural theory of super-generali- zation and autopoiesis. Scientific culture refers to science itself and the mixtures of science and other cultures. Mathematical culture shows the lawfulness of philosophy and artistry in quantitative relation, spatial form, information symbols, energy motion and physical structure of nature, human society and thought. Cultural wonder of mathematics is characterized by unity, complexity, artistry and suspense.