Wednesday, September 12, 2007

That Old Narrative

I am reconsidering a narrative I once thought about writing: an otherwise completely ordinary (and generally untalented) math graduate student stumbles upon a brilliant result that he otherwise doesn't understand--he realizes it's brilliant, but doesn't know how he thought of it, and knows he will never discover anything like it again. I am considering what the fiction of the result will be, and come up with something about a statement of meaning, M, and its self-referential equivalent, M', and showing that there exists a perfect isomorphism between any space made up of M's and the space made up of its equivalent self-referential M-primes. Then I am considering if there actually might be something in that, when I dimly recall some other result that where if I have two functions that are "onto" from one space to the other and vice versa, I can construct an isomorphism. Or something like that, anyway.