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Úvahy o vnitřních symetriích teorie pravděpodobnosti a možné roli Kleinovy kvartiky v základech fyziky
Gottvald, Aleš
Probability theory features as the internal symmetries of physical laws, acting in an intrinsically 6-dimensional hyperspace. Concerning symmetries, classical thermodynamics and Klein's Erlangen program involve the same underlying idea. Probability theory is an exceptional structure, closely linked to a unique Triality symmetry and other exceptional structures in nature (symmetric group S6, Platonic solids, (2, 3, 7)-triangular group and a correspondin tessellation of a hyperbolic space, exceptional Lie groups, etc.). Exponential mapping of statistical physics is associated with Klein's quartic curve, an extremal Hurwitz surface whose 168 automorphisms may be related to Standard model of particle physics and to a highly composite number (42) of special importance for fundamental physics.

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