Tuesday, February 19, 2013

couldn't sleep .. (or: siege, part ii: early morning ambush)

// initially written ~ 7:30

odd. i startled awake this morning at 5:45 and couldn't get back to sleep. so i got up, tired, and started working ..

.. only to have everything fitting together, as if my choices for function spaces paid off and that there was no longer any fuss about what topologies to use, what structures were available.

with two lemmas or so proven, a good chunk of details worked out, the argument looks done .. well, not quite: i still need to look up some details about duality (with respect to Bochner integrals) but everything else looks intact. it's not even 7:30 and i feel like i've done a full day's thinking. i'm tired but i've just had two cups of coffee. the sun's risen, the snow is white, and the day's just begun ..
// added later @ 8:30

this is all very suspicious, of course. i'm waiting to find an obvious error when i'm better rested. maybe i should set this down for the rest of today and look at it again tomorrow.

as for some background, yesterday i felt constantly .. not interrupted, but apart from a few hours in the morning, there never seemed any significant chunk of time to work out the details: an early lunch with colleagues at 11:30, a finnish language class in another part of town, a meet-up with a friend for a sauna night .. that ended up being closed on mondays.

waking up today, i felt impelled to work everything out. maybe it's just my unconscious put into overdrive ..?

// updated: 20 feb 2013 @ 23:04

curiouser and curiouser: i don't see an obvious error yet.

i'm even trying to break up the argument into as many lemmas as possible .. if only to make sure that each proof, being short, is easy to check for correctness.

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