In your previous comment, you seemed to have no problem grasping what I mean by "can computers think?" - namely (and for the last time): "can computers emulate the full range of human thinking?", i.e. "is human thinking computational?". My point is that this is an open, and furthermore fascinating question, not at all boring. There are arguments on each side, and no conclusive evidence which can settle the question. Even in this last comment of yours you seem to understand this, because you again ask for hard evidence for non-computational aspects of human cognition, but then in the last paragraph you again regress to your complaint of "what are we even arguing about?". I'm guessing you realize you're repeating yourself so try to throw in everything you can think of to make yourself feel like you've won the argument or something. But it's dishonest and disrespectful.

And yes, you are right about the fact that we can imagine ways a physical system could provably be shown to be going beyond the limits of classical or even quantum computation. "Look we can solve the halting problem" comes close to the core of the problem, but think a bit what that would entail. (It's obvious to me you never thought deeply about these issues.) The halting problem by definition cannot have a formal answer: there cannot be some mathematical equation or procedure which given a turing machine decides, in bounded time, whether that machine ultimately stops or not. This is exactly what Alan Turing showed, so what you are naively asking for is impossible. But this in now way proves that physical processes are computational. It is easy to imagine deterministic systems which are non-computable.

So, the only way one could conceivably "solve the halting problem", is to solve it for certain machines and classes of machines, one at a time. But since a human life is finite, this could never happen in practice. But if you look at the whole of humanity together and more specifically their mathematical output over centuries as one cognitive activity, it would seem that yes, we can indeed solve the halting problem. I.e. so far we haven't encountered any hurdles so intimidating that we just couldn't clear them or at least begin to clear them. This is, in fact one of Penrose's arguments in his books. It's clearly and necessarily (because of Turing's theorem) not an airtight argument and there are many counter-arguments and counter-counter-arguments and so on, you'd have to get in the weeds to actually have a somewhat informed opinion on this matter. To me it definitely moves the needle towards the idea that there must be a noncomputational aspect to human cognition, but that's in addition to other clues, like pondering certain creative experiences or the phenomenon of intuition - a form of apparently direct seeing into the nature of things which Penrose also discusses, as does the other book I mentioned in another comment on this page. One of the most mind bending examples being Ramanujan's insights which seemed to arrive to him, often in dreams, fully-formed and without proof or justification even from some future mathematical century.

In conclusion, may I remark that I hope I'm talking to a teeneger, somewhat overexcited, petulant and overconfident, but bright and with the capacity to change and growth nonetheless. I only answered in the hopes that this is the case, since the alternative is too depressing to contemplate. Look up these clues I left you. ChatGPT makes it so easy these days, as long as you're open to have your dogmas questioned. But I personally am signing off from this conversation now, so know that whatever you might rashly mash together on your keyboard in anger will be akin to that proverbial tree falling in a forest empty of listening subjects. Wishing you all the best otherwise.

PS: machines can totally smerve! :)