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

@article{Buliga2011ComputingWS,
title={Computing with space: a tangle formalism for chora and difference},
author={Marius Buliga},
journal={ArXiv},
year={2011},
volume={abs/1103.6007}
}
• Marius Buliga
• Published 2011
• Computer Science, Physics, Mathematics, Biology
• ArXiv
What is space computing,simulation, or understanding? Converging from several sources, this seems to be something more primitive than what is meant nowadays 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… Expand

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#### References

SHOWING 1-10 OF 31 REFERENCES
More than discrete or continuous: a bird's view
I try to give mathematical evidence to the following equivalence, which is based on ideas from Plato (Timaeus): reality emerges from a more primitive, non-geometrical, reality in the same way as the brain construct the image of reality, starting from intensive properties. Expand
A NON-ARISTOTELIAN SYSTEM AND ITS NECESSITY FOR RIGOUR IN MATHEMATICS AND PHYSICS
A very extensive literature shows that the problems of ‘infinity’ pervade human psycho-logical reactions, starting from the lowest stage of human development up to the present and that without someExpand
Conservative logic
• 1982
Conservative logic is a comprehensive model of computation which explicitly reflects a number of fundamental principles of physics, such as the reversibility of the dynamical laws and theExpand
What is a space? Computations in emergent algebras and the front end visual system
With the help of link diagrams with decorated crossings, I explain computations in emergent algebras, introduced in arXiv:0907.1520, as the kind of computations done in the front end visual system.
The brain a geometry engine
SummaryAccording to Kant, spacetime is a form of the mind. If so, the brain must be a geometry engine. This idea is taken seriously, and consequently the implementation of space and time in terms ofExpand
An Algorithmic Definition of the Axial Map
• Computer Science
• 2005
It is proposed that the analytical power of the axial map in empirical studies derives from the efficient representation of key properties of the spatial configuration that it captures. Expand
From insect vision to robot vision
• Biology
• 1992
The understanding of some invertebrate sensory-motor systems has now reached a level able to provide valuable design hints and this approach brings into prominence the mutual constraints in the designs of a sensory and a motor system, in both living and non-living ambulatory creatures. Expand
Emergent algebras as generalizations of differentiable algebras, with applications
We propose a generalization of differentiable algebras, where the underlying differential structure is replaced by a uniform idempotent right quasigroup (irq). Algebraically, irqs are related withExpand
RACKS AND LINKS IN CODIMENSION TWO
• Mathematics
• 1992
A rack, which is the algebraic distillation of two of the Reidemeister moves, is a set with a binary operation such that right multiplication is an automorphism. Any codimension two link has aExpand
Chord diagram invariants of tangles and graphs
• Mathematics
• 1998
The notion of a chord diagram emerged from Vassiliev's work Vas90], Vas92] (see also Gusarov Gus91], Gus94] and Bar-Natan BN91], BN95]). Slightly later, Kontsevich Kon93] deened an invariant ofExpand