> Every time somebody tries to point to an example of a “topic that is
> beyond the reach of science”, it seems to get knocked over eventually.

Generate a sequence of "random" bits from your favorite physical source
(radioactive decay, quantum entanglement, or whatever).  Is the sequence
really algorithmically random (like in Kolmogorov randomness)?  This is
scientifically unknowable.  To check the randomness you have to solve
the halting problem.
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