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Computing with space: a tangle formalism for chora and difference

Buliga, Marius (2011) Computing with space: a tangle formalism for chora and difference. [Preprint]

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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 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, 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.

Item Type:Preprint
Subjects:Neuroscience > Biophysics
Computer Science > Human Computer Interaction
Computer Science > Machine Vision
Philosophy > Philosophy of Mind
ID Code:7287
Deposited By: Buliga, Dr. Marius
Deposited On:02 May 2011 17:10
Last Modified:02 May 2011 17:10

References in Article

Select the SEEK icon to attempt to find the referenced article. If it does not appear to be in cogprints you will be forwarded to the paracite service. Poorly formated references will probably not work.

\bibitem{buligadil1} M. Buliga, Dilatation structures I. Fundamentals, {\it

J. Gen. Lie Theory Appl.}, {\bf 1} (2007), 2, 65-95.

\bibitem{buligadil2} M. Buliga, Infinitesimal affine geometry of metric spaces

endowed with a dilatation structure , {\it Houston Journal

of Math.} 36, 1 (2010), 91-136, \url{http://arxiv.org/abs/0804.0135}

\bibitem{buligasr} M. Buliga, Dilatation structures in sub-riemannian geometry,

in: Contemporary Geometry and Topology and Related Topics.

Cluj-Napoca, Cluj-Napoca, Cluj University Press (2008), 89-105

\bibitem{buligadil3} M. Buliga, A characterization of sub-riemannian spaces as length dilation

structures constructed via coherent projections, {\it Commun. Math. Anal.}

{\bf 11} (2011), No. 2, pp. 70-111, \\

\url{http://arxiv.org/abs/0810.5042}

\bibitem{buligairq} M. Buliga, Emergent algebras as generalizations of

differentiable algebras, with applications, (2009), \url{http://arxiv.org/abs/0907.1520}

\bibitem{buligabraided} M. Buliga, Braided spaces with dilations and sub-riemannian symmetric spaces, (2010),

\url{http://arxiv.org/abs/1005.5031}

\bibitem{buligafrontend} M. Buliga, What is a space? Computations in emergent algebras and the front end

visual system (2010), \url{http://arxiv.org/abs/1009.5028}

\bibitem{buligamore} M. Buliga, More than discrete or continuous: a bird's view

(2010), \url{http://arxiv.org/abs/arXiv:1011.4485}

\bibitem{buligaintro} M, Buliga, Introduction to metric spaces with dilations

(2010), \url{http://arxiv.org/abs/1007.2362}

\bibitem{buligagr} M. Buliga, Deformations of normed groupoids and differential calculus.

First part, (2009), \url{http://arxiv.org/abs/0911.1300}

\bibitem{buliga2} M. Buliga, Tangent bundles to sub-Riemannian groups, (2003), \\

\url{http://xxx.arxiv.org/abs/math.MG/0307342}

\bibitem{duzhin} S. Chmutov, S. Duzhin, J. Mostovoy, Introduction to Vassiliev

Knot Invariants, (2011), \\ \url{http://arxiv.org/abs/1103.5628}

\bibitem{connes} A. Connes, Sur la theorie non commutative de l'integration, in: Alg\'ebres d'Op\'erateurs, S\'eminaire sur les Alg\'ebres d'Op\'erateurs, Les Plans-sur-Bex, Suisse, 13-18 mars 1978, Lecture Notes in Mathematics 725, ed. by

A. Dold and B. Eckmann, Springer-Verlag 1079, p. 19-143

\bibitem{recent} L. van den Dries, I. Goldbring, Locally compact contractive local groups,

(2009), http://arxiv.org/abs/0909.4565

\bibitem{fly} N. Franceschini, J.M. Pichon, C. Blanes, From insect vision to

robot vision, {\it Phil. Trans.: Biological Sciences}, {\bf 337}, 1281 (1992),

Natural and Artificial Low-Level Seeing Systems, 283-294

\bibitem{fennrourke} R. Fenn, C. Rourke, Racks and Links in codimension two,

{\it J. Knot Theory Ramifications}, {\bf 1} (1992), no. 4, 343--406

\bibitem{hil1} Hillier B, Penn A (2004) Rejoinder to Carlo Ratti in Environment and

Planning B: Planning and Design 31 512-511 ISSN 0265 8135

\bibitem{joyce} D. Joyce, A classifying invariant of knots; the knot quandle,

{\it J. Pure Appl. Alg.}, {\bf 23} (1982), 37-65

\bibitem{kassel} C. Kassel, V. Turaev, Chord diagram invariants of tangles and

graphs, {\it Duke Math. J.}, {\bf 92} (1998), no. 3. 497-552

\bibitem{koen} J. Koenderink, The brain a geometry engine, {\it Psychol. Res.} {\bf 52} (1990), 122-127

\bibitem{koen2} J.. Koenderink, A. Kappers, A. van Doorn, Local Operations :The Embodiment of Geometry. Basic Research Series, (1992), 1-23

\bibitem{korzybski} A. Korzybski, A Non-Aristotelian System and its Necessity

for Rigour in Mathematics and Physics, a paper presented before the American

Mathematical Society at the New Orleans, Louisiana, meeting of the American

Association for the Advancement of Science, December 28, 1931.

Reprinted in Science and Sanity, 1933, p. 747-761.

\bibitem{meredith} L.G. Meredith, D.F. Snyder, Knots as processes: a new kind of

invariant, (2010) \\

\url{http://arxiv.org/abs/1009.2107}

\bibitem{metrology} JCGM 200:2008 International vocabulary of metrology - Basic

and general concepts and associated terms (VIM),

\url{http://www.bipm.org/utils/common/documents/jcgm/JCGM_200_2008.pdf}

\bibitem{pansu} P. Pansu, M\'etriques de Carnot-Carath\'eodory et

quasi-isom\'etries des espaces sym\'etriques de rang un, Ann. of Math., (2)

{\bf 129}, (1989), 1-60

\bibitem{plato} Plato, Timaeus 48e - 53c, \url{http://www.ellopos.net/elpenor/physis/plato-timaeus/space.asp}

\bibitem{siebert} E. Siebert, Contractive automorphisms on locally compact

groups, {\it Math. Z.}, 191, 73-90, (1986)

\bibitem{toffoli} E. Fredkin, T. Toffoli, Conservative logic, {\it Int. J. of Theoretical Physics}, {\bf 21} (1982), %no. 3-4, 219-253

\bibitem{hil2} Turner A, Hillier B, Penn A (2005) An algorithmic definition of the

axial map Environment and Planning B 32-3, 425-444

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