数学与物理关系中数学空间的哲学特征

Philosophical Features of Mathematical Space in the Relationship Between Mathematics and Physics

与物理学史上5个重大物理理论相关的5个数学空间,在本体、认识与方法上也表现出有规律的哲学特征:在欧几里得空间中,本体、认识与方法之间是一种分立关系;在黎曼流形、希尔伯特空间、纤维丛与卡-丘空间中,本体、认识与方法之间分别都有交集,并且这种交集依次在增大,即从部分相交到大部分相交再到渐进融合。

Associated with five landmark theories in the history of physics, there are five mathematical spaces in mathematics, which display regular philosophical features ontologically, epistemologically and methodologically. In Euclidean space, the ontology, epistemology and methodology are discrete. In Riemann manifold, Hilbert space, fiber bundle and Calabi-Yau manifold, the ontology, epistemology and methodology overlap respectively, and their overlaps increase successively： from partly overlap to mostly overlap, and then to gradual integration.