Computing with space: a tangle formalism for chora and difference

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".