Some problem being too chaotic or computationally expensive to perform is a completely different thing that claiming something supernatural. And there is hardly any reason for computers to be confined to silicon digital logic, using coprocessors is a standard procedure, so whatever element if any which exhibits hypercomputation (which is highly doubtful as the universe barely even reaches even a small fraction of the possibilities of turing machines let alone beyond them) or otherwise more efficient classical computation, we can isolate the element and use it as a chip.
replyTo be clear the limitation here isn't silicon logic, it's theoretical logic (specifically general recursive functions). It sure seems like any possible computation can be expressed as a general recursive function, but that's a scientific thesis, not a mathematical theorem. As we have yet to formalize "define a physical system" it is possible that this task isn't actually expressible in 21st century mathematical logic. I suppose some custom hardware which doesn't use logic at all might help, but then Gödel's theorem wouldn't apply at all. (Likewise with modal logic.)
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