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Mathematics > Metric Geometry

arXiv:1103.6007 (math)
[Submitted on 30 Mar 2011 (v1), last revised 21 Apr 2011 (this version, v2)]

Title:Computing with space: a tangle formalism for chora and difference

Authors:Marius Buliga
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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".
Comments: 56 pages, added content and reorganized the paper, title changed, many figures
Subjects: Metric Geometry (math.MG); Logic in Computer Science (cs.LO); Neurons and Cognition (q-bio.NC)
Cite as: arXiv:1103.6007 [math.MG]
  (or arXiv:1103.6007v2 [math.MG] for this version)
  https://doi.org/10.48550/arXiv.1103.6007

Submission history

From: Marius Buliga [view email]
[v1] Wed, 30 Mar 2011 18:06:30 UTC (342 KB)
[v2] Thu, 21 Apr 2011 12:35:32 UTC (419 KB)
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