an annoying splinter of an idea.

i had this research idea from last week, but sometimes i wish i hadn't thought of it.

you see, it doesn't work.

on the way to the airport last thursday, i worked out a simple example of a "measure-induced metric" on the unit interval, and that didn't work.

then again, i didn't expect it to work because it shouldn't; there are underlying reasons, and that later idea was meant to exploit those reasons.

so during the random moments i could muster over these holidays, i tried a more complicated example and hence: the idea that i mentioned earlier.

it not only fails to work, but it makes no sense; if i can finish one particular argument, then it will lead to a contradiction, and that's no good at all. it would mean that there is some undetected error in my work -- an error i can't quite understand, and that irritates me to no end.

i don't mind making errors; they're inevitable, and i've made my peace with that. but i can't stand making an error whose consequences are evident but whose source is secret.

it's like having a friend who knows a good riddle, knows that you don't know the answer, and won't tell you no matter how many times you ask ..

.. but perhaps i should focus on the positive. at least, everyone seems to tell me that.

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at any rate, my best guess is that by modifying the example, i've turned a purely metric condition into something .. sobolev, or more aptly, function-theoretic.

the end result looks like a variational problem and i don't quite know how to formulate it. it's almost as if the functional is "in the wrong place," but i can't make that precise ..

moreover, is it even worth formulating? the example was meant to generalise into a setting which hasn't enough structure for variational problems!

on the other hand, i'm curious to see if other perspectives will illuminate the situation.

if only by analogy, the modified example reminds me of .. something like elasticity in light of finite energy, and i'm tempted to ask the folks at syracuse if they've seen anything like it.

then again, it could be something simple or crackpot. i'd hate to waste their time .. that, and look like an idiot.

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usually such conundrums are worth even a little something, if only for the trouble they cause. however, i remain of the opinion that i might be better off without this idea.

at least, i would be less disturbed if the idea came in early january, when i'd be back in ann arbor and more inclined to work.

unhappily, it is still very late december, i am visiting family, and the holiday season hasn't yet passed.

my family are already of the opinion that i am a little crazy and "not quite right," and i'd rather not convince them any more of that.

inspiration .. or rather, motivated confusion .. strikes at such inopportune times!