| Nope. Can I suggest you read Penrose again with a little more critical thought. There are problems it is possible to prove are not computable. But can you prove that human beings can solve them? Tessellation of the infinite plane? Please demonstrate a person that can solve this (i.e. not that they have a > 99.9% chance of being able to do it, or that you can show they can start out pretty successfully and you assume they'll always stay ahead of the game). Bear in mind when working out if a computer can solve a given problem (i.e. is it mathematically computable), we're not trying to work out if it can ever solve it, or even if it can solve it in infinitely many cases, or even in an arbitrarily high proportion of cases. We're working out if it can be proven that it is (not) guaranteed to find a correct solution in all cases. There's just no way to make those judgements of a human being. So instead, mathematical analysis of computation is compared against intuition arguments from the evidence that human beings have good, reliable strategies for solving some of them. Unsurprisingly, the brain comes off pretty well in that comparison! Penrose was big on handwaving and appeal to quantum magic, but not very good on the specific arguments to back up his claim. I found this article to be a huge bag of misconceptions about AI, computation, and the actual claims of AI professionals. As an argument against hyperbolic media mischaracterisation, it might be reasonable. But like Penrose, it manages a long and condescending argument from intuition that fails to take seriously the actual claims being made. [Edit: for clarity and spelling] |
Penrose himself would seem to be a demonstration that there is at least one person, IIRC.
Is your argument that uncomputable really just means no guaranteed success, and that just because some human can get a solution to an uncomputable problem doesn't mean that it isn't following a set of algorithms?