The surprising fact that science works at all is a strong indication that our universe is mechanical.
In other words, it is trivial to produce fully unpredictable results from a deterministic machine. (It is also possible to recover deterministic behavior down to an arbitrarily small epsilon from a probabilistic machine, which is how our computers work.)
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Ok, so the fundamentals of physics are deterministic, but they produce apparently random behavior. I like this; proving it is the problem.
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I don't see how this is a problem? From within a system, the best truth is never the ground truth, but the set of theories that can explain all observations. There does not need to be any proof beyond showing that it can work.
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