Relation of Origins of Primitive Chaos

TL;DR

This paper explores the mathematical relationship between the origins of primitive chaos, specifically nondegenerate Peano continua and Cantor sets, using topology to understand fundamental scientific concepts like causality and predictability.

Contribution

It introduces a topological analysis of the origins of primitive chaos, revealing new insights into the relation between key mathematical structures and fundamental scientific principles.

Findings

Relation between Peano continuum and Cantor set clarified

Emergence of concepts like whole-part relation and coarse graining

Implications for understanding causality and predictability

Abstract

A new concept, primitive chaos, was proposed, as a concept closely related to the fundamental problems of sciences themselves such as determinism, causality, free will, predictability, and time asymmetry [{\em J. Phys. Soc. Jpn.} {\bf 2014}, {\em 83}, 1401]. This concept is literally a primitive chaos in such a sense that it leads to the characteristic properties of the conventional chaos under natural conditions. Then, two contrast concepts, nondegenerate Peano continuum and Cantor set, are known as the origins of the primitive chaos. In this study, the relation of these origins is investigated with the aid of a mathematical method, topology. Then, we can see the emergence of interesting concepts such as the relation of whole and part, and coarse graining, which imply the essence of our intrinsic recognition for phenomena.