A Brief Discussion on Information Geometry
信息几何浅论

摘要

信息几何研究信息系统拓扑场频率场波时间场空间场弈法运算的几何规律。信息系统拓扑空间生维现象：信息系 统拓扑时间场空间场，群码场与全码场自然力级集场力弈法运算宇称偏恒场形成多级平行多元信息系统拓扑场时间场 空间场生维场、相交场、交换场、复杂有序生物场。利用调查法、信息法、系统法、数学分析法、逻辑推理法研究了 信息系统拓扑场时间场空间生维、相交及交换现象。级集力场群码场与全码场平衡场是宇称对称场、守恒场、混沌场。 级集力场群码场与全码场宇称偏恒场是生维场、生物场。基本粒子场、星系场、生物场来源于级集场、平行场、多元 信息系统拓扑空间场生维、相交及交换。遁集系统（微观）生维场、相交场、交换场形成基本粒子场。玄集系统（宏 观）生维场、相交场、交换场形成星系场。智集系统（中观）生维场、相交场、交换场形成生物场。

Abstract

 Information geometry studies the geometric laws of game-theoretic operations involving the topological field, frequency field, wave field, time field, and spatial field of information systems. The phenomenon of dimension generation in the topological space of information systems refers to the formation of multilevel parallel and multiple information system topological fields, time fields, spatial fields, dimension-generating fields, intersecting fields, exchange fields, and complex ordered biological fields through parity partial-conservation field operations of the natural-force level-set field, group-code field, and full-code field within the topological time field and spatial field of information systems. This paper applies investigation methods, information methods, systems methods, mathematical analysis, and logical reasoning to study the phenomena of dimension generation, intersection, and exchange in the topological field, time field, and spatial field of information systems. The equilibrium fields of the level-set force field, group-code field, and full-code field are parity-symmetric fields, conserved fields, and chaotic fields. The parity partial-conservation fields of the level-set force field, group-code field, and full-code field are dimension-generating fields and biological fields. Elementary particle fields, galaxy fields, and biological fields originate from dimension generation, intersection, and exchange in level-set fields, parallel fields, and multiple information system topological spatial fields. Dimension-generating fields, intersecting fields, and exchange fields in the Dun-set system at the microscopic level form elementary particle fields. Dimension-generating fields, intersecting fields, and exchange fields in the Xuan-set system at the macroscopic level form galaxy fields. Dimension-generating fields, intersecting fields, and exchange fields in the Zhi-set system at the mesoscopic level form biological fields.