There are people who insist that the halting problem "proves" that machines will never be able to think. That this means they don't understand the difference between writing down (or generating a proof of) the halting problem and the implications of the halting problem, does not stop them from using it.
I don't know that I agree that computation is a variety of thinking. It's certainly influenced by thinking, but I think of thinking as more the thing you do before, after, and in-between the computation, not the actual computation itself.
