Geometrochemistry vs Soft Computing of Mendeleev's Brain

0352590 - ÚPT 2011 RIV CZ eng C - Konferenční příspěvek (zahraniční konf.)
Gottvald, Aleš
Geometrochemistry vs Soft Computing of Mendeleev's Brain.
Mendel 2010 - 16th International Conference on Soft Computing. Brno: Brno University of Technology, 2010, s. 558-564. ISBN 978-80-214-4120-0.
[Mendel 2010 - International Conference on Soft Computing /16./. Brno (CZ), 23.06.2010-25.06.2010]
Výzkumný záměr: CEZ:AV0Z20650511
Klíčová slova: projective geometry * Law of Mass Action * Mendeleev periodic table * brain information processing * artificial neural networks * cross-ratio * incidence structures
Kód oboru RIV: BD - Teorie informace

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.
Trvalý link: http://hdl.handle.net/11104/0192068