Epstein Secrets

1864 Steriade, M., McCarley, R.W. (1990) Brainstem Control of Wakefulness and Sleep. Plenum. N.Y. 289 HOUSE_OVERSIGHT_013789 Stillwell, J. (1985) Poincare’s Papers on Fuchsian Groups. Springer-Verlag, N.Y. pp 1-50 Stockbridge,L.L., French,A.S. (1989) Characterization of a calcium-activated potassium ch

ormly divergent (and convergent), “hyperbolic” chaotic systems, such as brain systems, behave in Euclidean space, an intuitive similarity about which Poincare experienced his famous vacation bus trip epiphany (Stillwell, 1985). It should also be noted that encoding neural spike trains in one dimension for s

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

context of mathematical epistemology, the instantaneous images of a geometer contrast with the labored sequential logic of the mathematical analyst. Poincare’ claimed that inclinations toward one or the other of these two cognitive styles and their associated mathematical tools arise from different kinds o

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

blished a model of it through internal reconstructions of sequential sensory experiences that_accompanied our exploratory movements. A world. It was Poincare’s habit to topologize the dynamics of motion in mathematical problems that lacked analytic solutions. In this way, simple algebraic operations repla

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