However, I was thinking of Joy as the analogue of an untenured faculty member. Certainly, any department that would grant tenure to Joy with his current record would immediately discredit itself.

So maybe the best policy would be for organizations like FQXi to have both “provisional members” and “tenured members,” and in order to move from the former category to the latter, you’d have to demonstrate an ability to produce work that’s original, interesting, and sane.

I wonder if you’ve thought the implications through, Scott?
I haven’t checked their statutes, but I’d be surprised if the National Academy of Sciences or the Royal Society have any procedure for revoking membership because of publishing incorrect papers, however provocatively or trivially wrong. And while I’m not certain about MIT, I’m pretty sure Cambridge also has no clear procedure for dismissing a tenured faculty member on such grounds. (If I understand our rules right, sacking any tenured university officer would require, among other things, a vote by the entire university.)

Of course, the membership selection for FQXi is rather less rigorous, and you can argue it’s a different case. But all these more venerable institutions seem to manage pretty well, even though a few of their members do indeed sometimes publish junk. Maybe that’s just (a small) part of the price of academic freedom? You can — I would — argue that FQXi should have a quality filter for the work it publicizes. But lobbying to exclude people seems to me to be going too far.

Not really. The best theory we have about nature is called “standard model” and it is known to be inconsistent at very high energies. (But it works really well at energies we can reach.)

I should confess, what appeals to me personally about complexity theory is precisely that it seems somewhere “between math and physics” on the scale of aprioricity! I.e., our models of computation aren’t sensitive to the mass of this or that muon, but they are sensitive to extremely basic features of the world like whether it’s deterministic or probabilistic, classical or quantum—and that’s exactly how I like it!

Short answer: the models of computation that we study in complexity theory (P, BPP, BQP, etc.) are all rigorously-definable mathematically—you can explain any of them to a mathematician who neither knows nor cares about physics. And the great open problems like P vs. NP, BPP vs. BQP, etc. are purely mathematical in character.

On the other hand, the motivation for studying these particular models and questions does appeal to facts about physics. With classical computation, the appeal to physics was implicit: that is, people just assumed that of course a bit has a definite “0″ or “1″ value, even if no one measures the bit, and they defined their mathematical models of computation accordingly. With quantum computation, the appeal to physics is explicit: the whole goal was to define a model of computation that takes quantum mechanics into account.

Now, from a sufficiently advanced perspective, even complexity classes like BQP might well seem motivated a priori to us. We’d say, “well, of course quantum mechanics is one of the most basic mathematical possibilities one needs to consider! that’s obvious, and would be, even if our universe happened to be classical, and experiments had never shown quantum behavior at all!”

On the other hand, the fact remains that mathematicians didn’t discover quantum mechanics through a priori reasoning; instead it was forced on the world by the physicists. So at present, I’d say that BQP is indeed a well-defined mathematical object, but that most (not all) of the interest in studying this object ultimately traces back to experimental discoveries in physics.