work frustrations.

it's been a frustrating day .. at least on the level of research.

none of my ideas are working and i can't seem to think of any new ones. the old, unusable ones recur and recur; each time it happens, i wonder if i've overlooked an important detail or insight that could solve the problem at hand.

each time, nothing useful comes out. i only realise that the idea has some flaw, that there is a little gap in my logic, or the number of lemmas and claims i need grow like heads on a hydra: i try to prove one, and two subcases arise from its place.

it even got to the point when i was backtracking through my previous work tonight, i thought a lemma my advisor and i proved was wrong, and it took me half- to a full hour to work out why it was true again. on the bright side, the proof is now about a dozen lines long, and barely a half-page.

i'm almost convinced that i have the wrong perspective, or that my tools are too primitive. for instance, i don't think i can "compute my way out of the problem."

it's also occurred to me that i haven't thought of many examples, and come to think of it, i don't have a very good picture of what is happening. the theorem we're after still seems quite plausible, but it is like a slippery eel: there's no place for a good grip.

it's late. i should quit for the day, wait until tomorrow, and try again. i should sit in my apartment and find some purpose for my non-work hours, which is frustratingly hard on its own.