[reappear]

But Feynman's point is: "Maybe not." We already know a computer-in-the-world can compute the fine-structure constant, in much the same way it computes its own temperature and fan speed. (I don't know enough physics to be at all sure the previous statement is true or even meaningful.) If you wanted to gauge how powerful a computer-in-the-world could be, or how powerful a computer-the-world's-in could be, you'd want to know whether a Turing machine could output the fine-structure constant, too, just as though it were pi or e or the first zero of a Bessel function.

[jessriedel]

Oh, I understand that we hope (and probably expect) that the fine-structure constant will turn out to be some mathematically well defined number derivable from an underlying theory. But that doesn't mean it's out of place on a list of integers which are interesting for purely mathematical reasons.