# What is a space? Computations in emergent algebras and the front end visual system

@article{Buliga2010WhatIA, title={What is a space? Computations in emergent algebras and the front end visual system}, author={Marius Buliga}, journal={ArXiv}, year={2010}, volume={abs/1009.5028} }

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.

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#### 4 Citations

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#### References

SHOWING 1-10 OF 38 REFERENCES

The brain a geometry engine

- Psychology, Medicine
- Psychological research
- 1990

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 of… Expand

Harnessing Vision for Computation

- Computer Science, Medicine
- Perception
- 2008

New techniques are described for building ‘ visual circuits’ using wire, NOT, OR, and AND gates in a visual modality such that the visual system acts as ‘visual hardware’ computing the circuit, and generating a resultant perception which is the output. Expand

Knots as processes: a new kind of invariant

- Mathematics, Computer Science
- ArXiv
- 2010

We exhibit an encoding of knots into processes in the {\pi}-calculus such that knots are ambient isotopic if and only their encodings are weakly bisimilar.

Braided spaces with dilations and sub-riemannian symmetric spaces

- Mathematics
- 2010

Braided sets which are also spaces with dilations are presented and explored in this paper, in the general frame of emergent algebras arxiv:0907.1520. Examples of such spaces are the sub-riemannian… Expand

Dilatation structures in sub-riemannian geometry

- Mathematics
- 2007

Based on the notion of dilatation structure arXiv:math/0608536, we give an intrinsic treatment to sub-riemannian geometry, started in the paper arXiv:0706.3644 .
Here we prove that regular… Expand

Emergent algebras as generalizations of differentiable algebras, with applications

- Mathematics
- 2009

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 with… Expand

The Quantum Theory

- Physics
- Nature
- 1928

IN a lecture on the quantum theory it might be thought fitting to commence with a clear explanation of the purpose, nature, and scope of the subject; but an attempt to answer briefly the question,… Expand

Dilatation structures I. Fundamentals

- Mathematics
- 2006

A dilatation structure is a concept in between a group and a differential structure. In this article we study fundamental properties of dilatation structures on metric spaces. This is a part of a… Expand

Tangent bundles to sub-Riemannian groups

- Mathematics
- 2003

This paper is about non-Euclidean analysis on Lie groups endowed with left invariant distributions, seen as sub-Riemannian manifolds.
This is a an updated version, which will be modified according… Expand

Carnot-Carathéodory spaces seen from within

- Physics
- 1996

Let V be a smooth manifold where we distinguish a subset H in the set of all piecewise smooth curves c in V. We assume that H is defined by a local condition on curves, i.e. if c is divided into… Expand