Original title: Geometrochemistry vs Soft Computing of Mendeleev's Brain
Authors: Gottvald, Aleš
Document type: Papers
Conference/Event: Mendel 2010 - International Conference on Soft Computing /16./, Brno (CZ), 2010-06-23 / 2010-06-25
Year: 2010
Language: eng
Abstract: The role of projective geometry in nature remains somewhat enigmatic for centuries. It is very strange indeed, as the projective geometry is the mother of all geometries with more restrictive symmetry groups, as clearly recognized yet by seminal insights of Felix Klein, Arthur Cayley, Paul Dirac and other eminent scientists. We usually imagine that Euclidean geometry is primary for the geometrization of our (nonrelativistic) spaces, and the Euclidean-Pythagorean metric is natural for measuring the distances in such a space. However, how to measure distances in spaces associated with statistical thermodynamics or quantum mechanics? We show that projective geometry and associated "geometrochemistry" is manifest in nature. In particular, it offers a novel soft-computing rationale for recovering basic structure of Mendeleev's periodic table of chemical elements, and elucidates some mysteries of brain information processing, including a new understanding of Artificial Neural Networks.
Keywords: artificial neural networks; brain information processing; cross-ratio; incidence structures; Law of Mass Action; Mendeleev periodic table; projective geometry
Project no.: CEZ:AV0Z20650511 (CEP)
Host item entry: Mendel 2010 - 16th International Conference on Soft Computing, ISBN 978-80-214-4120-0

Institution: Institute of Scientific Instruments AS ČR (web)
Document availability information: Fulltext is available at the institute of the Academy of Sciences.
Original record: http://hdl.handle.net/11104/0192068

Permalink: http://www.nusl.cz/ntk/nusl-42243


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