Chapter 7: Mechanisms in Programs and Nature

Section 5: The Intrinsic Generation of Randomness

Repeatably random experiments

Over the years, I have asked many experimental scientists about repeatability in seemingly random data, and in almost all cases they have told me that they have never looked for such a thing. But in a few cases they say that in fact on thinking about it they remember various forms of repeatability.

Examples where I have seen evidence of repeatable randomness as a function of time in published experimental data include temperature differences in thermal convection in closed cells of liquid helium, reaction rates in oxidation of carbon monoxide on catalytic surfaces, and output voltages from firings of excited single nerve cells. Typically there are quite long periods of time where the behavior is rather accurately repeatable—even though it may wiggle tens or hundreds in a seemingly random way—interspersed with jumps of some kind. In most cases the only credible models seem to be ones based on intrinsic randomness generation. But insofar as there is any definite model, it is inevitable that looking in sufficient detail at sufficiently many components of the system will reveal regularities associated with the underlying mechanism.

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From Stephen Wolfram: A New Kind of Science [citation]