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> If it's physically grounded then it would be computable by some machine, just not necessarily a Turing machine. What makes you think that? The overwhelming m
by User23 2y ago
> If it's physically grounded then it would be computable by some machine, just not necessarily a Turing machine.
What makes you think that? The overwhelming majority of functions aren’t computable. The evidence suggests, if anything, that the universe is uncomputable and at best some isolatable well-measured specific phenomena can have approximations computed to some arbitrary but inexact precision.
- naasking 2y ago> What makes you think that? Because if it's physically grounded then you can build a physical analogue of it. > overwhelming majority of functions aren’t computable By Turing machines, not by any other type of machine. As I said, if hypercomputers exist then they can solve the Halting problem, which Turing machines cannot.
- lambdaone 2y agoConsider the set of functions that that map the reals onto other reals. Almost all of these functions are truly random, with no way of expressing them that does not require the storage of an infinite number of infinite strings. Not only is there no practical way of creating such a thing, most formulations of physics preclude any possibility of making one by placing finite limits of the amount of space or time accessible to us. (Not to mention that almost all reals are [Turing] uncomputable in their own right, but that's a more complex thing to demonstrate.)
- naasking 2y agoYou don't need to express or encode the reals if you've built a physical analogue that operates on those reals, that's the point.