something wrong, something right, and neither very promising.

it's been a frustrating 6 days.

i spent the first 4 days trying to prove something, aware of what shouldn't work in the proof .. due to known facts and non-examples .. and i couldn't prove it.

worse yet, it's because the argument is incomplete. as of 2 days ago, i had no more ideas or inspiration to fill the gap. so i don't know if the argument is wrong, either.

after these many [1] years in graduate school, i've learned not to feel that bad about being wrong or entertaining a stupid idea ..

more accurately, i would call it an emotional callous

.. but to be wrong and not to have learned anything .. ye gods, that's frustrating. it's like having a mild conspiracy theory stuck in your thoughts, and not knowing if you are indeed a crackpot or not.

i wonder, if only on a practical level, whether that explains why some conspiracy theorists are crazy .. that it's not the crackpot theory that drives them mad, but the uncertainty which does.

as for the other 2 days, i may have actually proved something, but the argument of proof doesn't look right.

you see, it's not my theorem. a few months ago i read a particular theorem in a paper from 1999 or 2000, and i couldn't understand the proof.

so i tried to cut up the author's argument into claims, and prove those. some i could prove and some i couldn't, so i thought of other claims which would make sense ..

.. but having let this take a life of its own, my current proof has noticeable difference from the author's proof.

so yes, i've had better weeks. \:

[1] and yes, i'm griping. i know that plenty of you have taken longer to finish your own ph.d.'s and that i have no basis to gripe about time.

for the record, i am griping about something else.