Sunday, October 04, 2009

a day, back in the life.

in terms of research, i may have to learn patience again-- discipline, too.

all day yesterday i worked on a problem,
off and on, but more off than on.

i blame it on the fact that yesterday was saturday, the first one after weeks of grant-writing. it's hard to focus.

i also blame the grant-writing process.

in a short span of time i came up with a host of research ideas. if successful, it would take me a few years to enact all of them.

realistically i know that i cannot accomplish them all at once, but that doesn't mean that i don't want to.

anyway, yesterday was full of breaks and distractions.

in the morning i re-read the outline of a strategy that i wrote the day before. then i recalled a lemma that i remembered from a book. not having the book on hand, though, i proved it just to be sure.

then i jotted down an idea -- maybe i could write it as a variational problem -- and after working out a few lines, i dismissed it as out of hand.

then i checked my email, read the news from several websites, and went on flickr to look for new desktop wallpapers.

after a while i felt unproductive and lazy enough to return to my workbook.

forget highfalutin ideas; just work out an easy special case. do something.

so i did.
no, that's too easy. what about ..?

and so it went, on and on. more cases followed, coalesced into something good and general, and then ..

wait. i wanted a single function out of this, didn't i? then why is this a vector field ..?!?

dejected, i went and read more news online,
then went lurking at a few online maths communities,
answered a question about compacτness [1],
felt better, made lunch, then took a nap.

sometimes a nap is a good excuse to wake up and make a fresh cup of coffee. by then i felt good enough to return to the workbook.

i had meant to flip immediately to the next blank page, but the pages were hard to separate with only one hand [2]. the first page of that day's worknotes appeared and something caught my eye ..

i'm an idiot. why didn't i do this first?
anyone would have done this first. it's obvious ..

.. and yes, it works.

two steps of the strategy are now complete, but a few steps remain. those would have to wait until i learn more about this one theory that i've learned from hearsay [3] and when i reach the maths library again, on campus.

closing the notebook, i saw that it would get dark soon. where did i leave those running shoes again? ..

[1] it didn't sound like a homework problem and therefore warranted an answer. even if it were someone's homework, i gave a metrιc toρological answer to a hιlbert space problem: illuminating but mostly useless.

[2] the other was holding a cup of coffee.

[3] for experts out there, i mean abstract dirιchlet forms. admittedly, i'd never thought i'd actually use them, but they seem exactly the right fit.

No comments: