As Chaitin put it, “God not only plays dice in quantum mechanics and nonlinear dynamics, but even in elementary number theory.” Among its lessons were these: Most numbers are random. Yet very few of them can be proved random. A chaotic stream of information may yet hide a simple algorithm. Working backward from the chaos to the algorithm may be impossible. Kolmogorov-Chaitin (KC) complexity is to mathematics what entropy is to thermodynamics: the antidote to perfection. Just as we can have no perpetual-motion machines, there can be no complete formal axiomatic systems. Some mathematical facts
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