Computing with space: a tangle formalism for chora and difference

TL;DR

This paper explores the concept of space as a fundamental form of computation, using tangle formalism inspired by philosophical ideas and previous mathematical work, with potential applications in understanding visual systems and cybernetics.

Contribution

It introduces a novel formalism using tangle diagrams to model space and transformations, bridging philosophical notions with mathematical structures.

Findings

Proposes a tangle formalism for space computation

Links space, map, and territory through this formalism

Suggests applications in visual system understanding

Abstract

What is space computing, simulation, or understanding? Converging from several sources, this seems to be something more primitive than what is usually meant by computation, something that was along with us since antiquity (the word "choros", "chora", denotes "space" or "place" and is seemingly the most mysterious notion from Plato, described in Timaeus 48e - 53c) which has to do with cybernetics and with the understanding of the front end visual system. It may have some unexpected applications, also. Here, inspired by Bateson (see Supplementary Material), I explore from the mathematical side the point of view that there is no difference between the map and the territory, but instead the transformation of one into another can be understood by using a formalism of tangle diagrams. This paper continues arXiv:1009.5028 "What is a space? Computations in emergent algebras and the front end visual system" and the arXiv:1007.2362 "Introduction to metric spaces with dilations".