If it's physically grounded then it would be computable by some machine, just not necessarily a Turing machine. For instance, a hypercomputer can solve the Halting problem for Turing machines. We just have to be clear about the kind of machine on which a problem is computable.
> 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.
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.
Consider 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.)
It depends on if the universe is fundamentally deterministic or not. Right now we don't have any way to see beyond the apparent randomness in quantum mechanics and we probably never will. This part of the universe might be completely non-computable to us, it's just random.
Randomness doesn't have any real impact on whether a problem is computable. Just model the distribution of the random variable. Non-deterministic Turing machines are a thing.
That's true. I suppose it comes down to what exactly is meant by "is computable". I don't think it was defined well enough, which I suppose is to be expected when discussing these topics that involve lots of hand-waving.
I interpreted it to mean that we can predict the outcome of it, you interpret it to mean that we can model it.
Either way, maybe it doesn't matter since the original proposal is that consciousness is a subjective experience and there isn't an obvious way to define how to programmatically create it i.e. compute it.
You probably mean probabilistic Turing machines. Non-deterministic automata in general don't involve randomness, and the results of their computation are considered to be deterministic despite the name.
And of course all TMs are just theoretical models. Non-deterministic Turing machine equivalents in particular don't physically exist and may be physically impossible.
But of course if there is indeed true randomness in nature that needs to be modelled, that same randomness can be used a source of true randomness for computation, and you can then build computation that does have stochastically determined results.
