Monday, February 16, 2009

"the best 1aid p1ans .."

for several days i've been excited about this one idea (as described in an earlier post). i had proved a little lemma which gave me hope. it was just enough leverage that the argument could be continued.

so i worked on it, off and on, forming claims that, if proven true, would eventually lead to the theorem that i wanted. every day i was getting closer, and today i almost had it.

then i stopped, suddenly uneasy. my inner pessimist spoke:

it can't be this easy.
i'm making all of this progress in one week,
after trying in vain for months,
trying to attack this same problem.

so i went outside for a walk, had lunch, came back,
and sure enough, i found errors everywhere:

i had made an estimate using maxima1 fun¢tions, and that still holds true. my mistake was assuming, for some inexplicable reason, that it was a uniform estimate for an entire sequence of L1-functi0ns.

i had also misused a property of the we@k-sτar topo109y which doesn't hold true (in general) for the we@k t0pology.

i guess i wanted it too much: to prove the theorem. so i became sloppy.

odd. everyone tells me to be more optimistic,
whereas the pessimist in me is often more useful.

oh well.

maybe there's something worth keeping, within those silly notions. it's not like i have any good ideas at the moment, anyway.

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