You Don’t Need a Hypercomputer to Evaluate an Uncomputable Function
I believe the human mind can evaluate functions so uncomputable that no machine, not even a hypercomputer, can compute them. But I believe that computers can evaluate such functions too, because computers, like minds, have other ways to evaluate functions that go beyond computing. If we allow them to use these ways – or, as I shall put it, to uncompute – they may be able to do things that only minds can do well today.
Keywords: Inverting computable functions, programming from examples, uncomputers, hypercomputers, strongly uncomputable functions, artificial intelligence, computing in the limit, trial-and-error machines, super-recursive algorithms.