Good points. I just wanted to draw attention to the idea that Turing Machine is just one way of doing "computing". Whatever is proven about Turing Machines is proven about Turing Machines, not about all mechanical devices, like quantum computers, and "light-computers", in general.
I'm wondering is there a universal definition of "computing"? Saying that "Conmputing is what Turing Machines do" somehow seems circular. :-)
Well, Turing machines are supposed to be that definition. The Church-Turing thesis still hasn't been shown to be false. Proving something of Turing machines that doesn't hold for one of those classes of devices would mean refuting it. Basically we'd need to find some problem that, memory not being an issue, one class of computer can solve in finite time while another can't solve in any finite amount of time.
I'm wondering is there a universal definition of "computing"? Saying that "Conmputing is what Turing Machines do" somehow seems circular. :-)