I don't understand the point at all. Mathematical theorems like godel's incompleteness theorem or the halting problem are applicable to everything including the human brain. If they were a limitation to developing general intelligence then human beings wouldn't have existed.
Are they? Are there any actual Turing machines? Doesn’t that require infinite memory? I don’t know of a single thing which actually has that, nor one that comes close.
> Godel's incompleteness theorem or the halting problem are applicable to everything including the human brain.
Maybe. That's if you assume that the universe is a conventional computer. Far from settled and the alternative isn't necessarily just "God does it" - it might be that the universe is a "computer-plus", with some processes that produce results not computable by Turing means. It would be strange, but so is quantum mechanics, so...