The origin of universality: Making and invalidating a free category

Yukio Pegio Gunji*, Hideki Higashi

*この研究の対応する著者

研究成果: Article査読

4 被引用数 (Scopus)

抄録

We propose a model of evolutionary systems characterized by internal measurement, or endo-physics, that is based on a particular graph morphism. If we take an internal stance, we have to focus on the influence of the outside of the domain of choice. The outside of the domain is not explicitly expressed as a particular ensemble in advance, although a formal expression generally requires an explicit form of the outside as the possible forms. In our model, a system is expressed by a directed graph, and the time transition is expressed as a particular graph morphism referring to the outside of the domain of the morphism. Referring to the outside of the domain is expressed by dynamical decomposition and synthesis of the relationship between a graph and its possible forms expressed as an underlying free category. Because the transformations from a graph to a category and vice versa are expressed as two adjunctive functors, a graph morphism is defined by a sequence of the operation of a free functor and a special operator standing for invalidation of the operation of the free functor. Time development of this system can generate a particular universal structure like a limit and co-limit as a part of a directed graph, which stands for generation of a higher order. We also argue that the process toward the generation of a universal structure can reveal intermittency, and that an emergent boundary in pattern formation can be demonstrated by the generation of this universal structure. In addition, we discuss emergent computation such as the origin of primitive recursive functions through the origination of a universal structure.

本文言語English
ページ(範囲)283-313
ページ数31
ジャーナルPhysica D: Nonlinear Phenomena
156
3-4
DOI
出版ステータスPublished - 2001 8 15
外部発表はい

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 数理物理学
  • 凝縮系物理学
  • 応用数学

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