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>I guess if the measure of "information richness" is based in compressibility of electrical activity ... is it surprising that it isn't higher in the chaotic ph
by scythe 5y ago
>I guess if the measure of "information richness" is based in compressibility of electrical activity ... is it surprising that it isn't higher in the chaotic phase? Why wouldn't one expect the chaotic system to produce as much or more random output?
Chaos can be highly regular. For example, the limiting case of the logistic map, x -> 4x - 4x^2, is chaotic, but also has an exact solution x[n] = sin^2(arcsin(sqrt(x[0])) * 2^n). It's not hard to see why this still obeys the usual properties of Lyapunov doubling etc, but a simple double exponential doesn't seem like the sort of thing that leads to consciousness! From an information-theoretic point of view, the nth bit of x[0] becomes relevant at roughly step n, which means there is a steady "trickle" of information into the system instead of the more complicated dynamics we expect of a "computational" system -- in fact, if we consider the binary expansion of (arcsin(sqrt(x[0]))/pi) we find that only a finite number of bits have an effect on the system's measurable properties at any time, and the effect is rather like scrolling steadily along an infinite tape of random bits.