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

ns of probability), we notice that /og70(0.5) = 0.693147 and /og70(0.25) = 1.386294 and that 0.693147 + 0.693147 = 1.386294. The dot-dash choices of Morse code machines, the go, no-go gates of transistors, the open versus closed ion channel-mediated neuronal membrane discharge and the left, right spins

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

mical system, such as nerve membrane equations as above, or in the aggregate, the middle layer of a completely connected neural network, can encode, Morse code-like, messages (Paulus et al, 1989). Bifurcations in Biologically Relevant Dynamical Systems Bifurcations, “splitting into (two) branches,” ar

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

ence not distance preserving ) representation of a difficult to characterize system of “geodesics on surfaces of negative curvature” (Hadamard, 1898; Morse, 1917; Morse and Hedlund, 1938). Geodesics here are the shortest lines in this curved, non-Euclidean space in which nearby lines spread apart and far