Epstein Secrets

e impressions of others can arise quickly and from only a few data points of observation. In the late 1960’s, University of California mathematician, Rufus Bowen, proved the now famous shadow theorem. This says that in dynamical states of hyperbolicity, directly observable on the screen in computer simulations

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

1968), the French mathematicians, Rene Thom (1972) and David Ruelle (1978) and the U.C. Berkeley mathematicians, Steve Smale (1967) and his student, Rufus Bowen (1975), and their associates who gathered together these and other related computational discoveries and embedded them in a qualitative theory of non

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

y, R.M. (1990) Nonlinear forcasting as a way of distinguishing chaos from measurement error in time series. Nature 344:734-741. Sullivan, D. (1979) Rufus Bowen. Publ. Math. |.H.E.S. 50:255 Szeto, H.H., Cheng, P.Y., Decena, J.A., Cheng, Y., Wu, D., Dwyer, G. (1992) Fractal properties in fetal breathing dynam

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