5 ms·

Why should a complete simulation be possible? in fact there are plenty of things we can do that can't be simulated on a Turing machine. just one example the Bu

• mkl 2y ago
  Proving properties and computing values are quite different things, and proofs can absolutely be done on Turing machines, e.g. with proof assistants like Lean.
  • cowl 2y ago
    well you try feeding the Busy Beaver Problem with large N to lean then and see what comes out.
    • hcs 2y ago
      Do you think a machine proof of "BB(n) grows faster than any computable function" would require that?
      • cowl 2y ago
        no, see the problem is that the machine needs a well defined problem, and the "BB(n) grows faster than any defined problem" is well defined but you would not come up with an insight like that by executing the BB(n) function. that insight requires a leap out of the problem into a new area and then sure after it is defined as a new problem you enter again in the computability realm in a different dimension. But if the machine tries to come up with insight like that by executing the BB(n) function it will get stuck in infinite loops.
• dekhn 2y ago
  As long as you take the assumption that the universe is finite, follows a fixed set of laws, and is completely deterministic, then I think it follows (if not perfectly, then at least to a first order) that anything within the universe could be simulated using a theoretical computer, and you could also simulate a smaller universe on a real computer, although a real computer that simulated something of this complexity would be extremely hard to engineer. It's not entirely clear, though, that the universe is deterministic- our best experiments suggest there is some remaining and relevant nondeterminism. Turing machines, Goedel incompleteness, Busy Beaver Functions, and (probably) NP problems don't have any relevance to simulating complex phenomena or hard problems in biology.