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Strilanc comments on Estimating the kolmogorov complexity of the known laws of physics? - Less Wrong
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You're confusing chaos with incomputability. Chaos has to do with mixing, error amplification, and imperfect initial conditions. Incomputability has to do with abstract problems and whether or not they can solved by computers.
In any case, even if the standard model was an approximation of truly Turing-incomputable physics laws... I still want to know what its Kolmogorov complexity is.