"the best laid plans .."

yesterday afternoon i told my flatmate alan that i was writing off the whole weekend: no mathematics! since a week's worth of work went to $hit, i thought it was the right time for a short break, and he thought it was a good idea, too.

earlier tonight, alan tells me that my idea was so good that, in fact, he used it himself. after trying and failing to understand a preprint of this recent work, he decided to cut his losses and take sunday off, just like i said that i would.

nodding nervously, i admitted to him that my plan didn't quite work out.

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yesterday was fine, and i enjoyed myself immensely: i played basketball, drank plenty of coffee, wrote pieces and ideas for short stories in my journal, bought a collection of short stories of Hemingway's from the sidewalk guy,

(ann arbor natives will know whom i mean:
think state street, near the theater)

.. and even read an actual (non-math) book!

then sunday came around, i woke up, couldn't think of what to do, and went to the corner coffeehouse out of habit. i had also brought my bookbag out of habit, and forgot that Hemingway collection at the apartment. the counter had already sold out the day's quota of newspapers, and i had nothing to read; had i left the coffeehouse to fetch the Hemingway, i would have reneged on my free coffee refill privileges ..

.. and i'd be damned if i ever willingly do that! you can take the boy out of the mathematics department, but .. q:

anyways, realising the impasse of the situation, i gave up, fished out my work notes, and sought to understand where precisely my "proof" went wrong. a few basic implications hit me, and i realised, again, how truly stupid my error was.

then, remembering that taxes were due tomorrow and not trusting the wireless networks near the apartment, i marched to the department and e-file on their computers. on the way there, i had a new idea.

diligently i filed my taxes, and then tested out the idea. it doesn't quite work, but it's a new lead, and it might lead to something that may work. only time will tell.

i might think a little about it tomorrow before starting on this new topic. it's the "conformally natural" planar extension of Douady and Earle: a wholly different creature from these harmonic extensions.

at the very least, there's some hope now.