Epstein Secrets

rats exploring a space and Selz’s path sequences of computer screen dot quenches produced by clicking on them with a computer mouse. A precursor of Kolmogorov’s ergodicity was the earlier ergodicity of Ludwig Boltzmann. This describes a suitably partitioned system such that equivalent values come from quant

of Science, Essential Writings of Henri Poincare’ Stephen Jay Gould, Modern Library, Random House, N.Y. 2001 From Being to Becoming, /lya Prigogine, Freeman, San Francisco, 1980 The Development of Mathematics, E. 7. Bell, McGraw Hill, N.Y. 1945 Deterministic Chaos, An Introduction, Heinz, George Schuste

nd was previously a student of Andrei Nikolaevic Kolmogorov, the Russian guru of many of the Twentieth Century’s world- class Russian mathematicians. Kolmogorov axiomatized the field of probability and, more relevantly, initiated the theory of statistical descriptions, the ergodic theory, of nonlinear dynamic

ianity. C-S. Lewis. MacMillan, N.Y. 1952. Sacred Geometry. Miranda Lundy. Walker, N.Y. 1998. Fractals, Form, Chance and Dimension, B.B. Mandelbrot, Freeman, San Francisco, 1977. Non-Euclidean Geometry, H.S.M. Coxeter, University of Toronto Press, Toronto, 1957. Fundamentals of Mathematics, Vol. |. H. B

e had the same entropy. His answer was no, that —3(1/3 In (1/3)) = 1.098 > -2(1/2 In (1/2) = 0.6931 loge and in computer relevant logz, 1.5850 > 1.0 (Kolmogorov, 1959). Entropy increases with possibility. Nonlinear differential equations representing brain-relevant expanding dynamical systems replace Shannon

elbrot, B.B. (1975) Les Objets Fractals:Forme, Hasard et Dimension. Flammarion. Paris Mandelbrot, B.B. (1977) Fractals; Form, Chance and Dimension. Freeman. N.Y. Mandelbrot, B.B. (1977) Fractals: Form, Chance and Dimension, Freeman. San Francisco Mandell, A.J. (1983) From intermittency to transitivity