Physics “proofs”
Fortunately, I had just finished a good dinner before I read this. Otherwise I would have gone through the roof:
His response chilled me: “maybe it’s time mathematics started accepting string theory proofs as valid.”
This is from the mouth of a mathematics grad student who did his undergraduate physics. I might make various kind arguments. I could make some statement about forging ahead and filling in the gaps if the way proved useful.
I won’t.
Instead, I will call deny the student the title of mathematician, for he is ignorant of his heritage. Mathematics underwent a great formalization during the end of the 19th century and beginning of the 20th. The great framework erected during the 18th and early 19th century on “physics proofs” (for that is the origin of that standard of proof) kept falling to pieces, and the mathematics community undertook to try to fix the structural deficencies.
The problems turned out to be huge, and yielded whole fields of mathematics. Cantor’s set paradoxes led down a path that gave us Lebesgue integration (which lets us define integrals on any measurable space), Hilbert’s program, and Gödel’s theorems.
Fractal geometry sprang from the same abyss and provides the operating principle in place of analytic functions when systems become scale invariant — which happens surprisingly often.
Physics proofs consist of empirical techniques, a set of intuitive shortcuts that seem to work in a number of common cases. The history of mathematics provides us with one overwhelming empirical principle governing physics proofs: don’t layer them more than one or two deep or you’ll see oceans as infinitesimal drops, and you may well drown.
madhadron :: Feb.05.2007 :: Uncategorized :: 3 Comments »
3 Responses to “Physics “proofs””
My immediate response was much the same. I told him that if I were to take a postdoc in St. Petersburg I’d learn to speak Russian, so if he wants his Ph.D. from the department he was in he’d better learn to speak math.
I wouldn’t deny him the title quite yet, though. He hadn’t yet passed his quals, and beyond that there will be actual research to be done. He had come to a department under the seeming impression that it was big in string theory, when the last people who did anything close had decided there wasn’t any “there” there years ago. What they are is academically disciplined, and won’t let him get a doctorate from them without severely changing his tune.
Hoo boy, I hope Lubos isn’t reading this….
If his quals are still ahead, then he still has a lot of particularly nasty counterexamples to come to grips with. They’ll probably sober him up a bit. It will be good for him.
As for Lubos, I’m a biologist these days. String theorists have no bearing on my existence. When I do math and physics in the evenings for my own diversion, it’s generally not particle physics, so they don’t even impinge upon me there.