January 10th, 2012

(no subject)

I got off on the wrong foot with my proof attempt yesterday by stupidly thinking I could dodge diagonalization by computable approximation; I guess the thing I had read somewhere was the (not computably realizable) fact that if you keep taking the smallest theory (i.e. Turing machine) consistent with the data so far, and which terminates on all inputs so far (that being the noncomputable part), you'll eventually be always right.

Here's another thought, though: choose up front a sound proof system P that has a terminating proof-checking procedure. On the nth step, start enumerating P-provably terminating Turing machines and running them on inputs 0..n-1. As soon as you get a g that is consistent with f(0)..f(n-1), guess g(n) as your prediction of f(n). As long as f is P-provably terminating, you'll eventually always make guesses consistent with it. The moral of diagonalizing here is that the guessing procedure itself can't possibly be P-provably terminating, right?

(no subject)

Things going on lately that aren't math:
Last night went to "Brooklyn Boulders" with , which was interesting. The climbing area was quite big but a bit crowded, and my shoes felt painfully tight. Dunno if my feet have swole up in the last couple years since last I climbed, or just my tolerance for footsqueezing has gone down, or if the rubber shrinks with time, or what. I grumped out of climbing very much, but I discovered they had a slackline which turned out to be fascinating. By the end of the evening I was able to take about two steps before falling off, at a rate of one out of every couple dozen attempts, which felt like great success.

Tonight had dinner with K at kesté down on Bleecker. Really tasty pizza (we split a Prosciutto) and an amazing panna cotta with blueberry sauce.