about that miscalculation ..

as mentioned in a recent post edit, yesterday i miscalculated an integral [1] and spent an entire weekend in self-delusion. other than puzzled confusion as to why that special case wouldn't generalise, it was a rather pleasant weekend.

i suppose it's another shred of evidence for the case of pessimism.

after all, moments of happiness and other positive synchronicities lie in an exceptional set of measure zero, and almost surely, things never work out as you'd like.

so at last count, i have .. let's see: zero (0) research results to report, which isn't very many at all. [2]

as an interesting contrast, this is also the same number of results that a non-mathematician, working a regular job and earning a median-level income, would have.

having arrived at this conclusion, i decided that since i was being just as unproductive as if i weren't doing any mathematics, i might as well not work at all and have a bit of fun instead.

so last night i watched two episodes of a medical drama on the FOX channel called "House" with my flatmate, then met with more friends at a local bar (leopold bros, for those who know), and after the bar closed down, we walked over to a friend's house, ordered pizza, and played many marvelous games of foozball.

so today i sat down and thought about the problem and its parts:

• what i thought was true (but isn't),
  
• what, if true, i could use to prove something,
  
• what i didn't know, but would narrow down this ever-increasing list of things to know and not to know,
  

and in the end, the only thing left was a simple observation i made, when working out that ill-fated miscalculation. it's my last lead, a small lead ..

.. but it's still a lead.

the mystery endures, and it's geometric in nature: i don't know enough about group actions and high-dimensional hyperbolic geometry, but i'll need to learn enough and to know enough, otherwise the trail will turn cold and i''ll have to face that dark abyss of mathematician's block -- terrible cousin to writer's block, and more terrible, i'd say.

it's going to be a long few months, i fear.

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[1] to be entirely accurate, it was more like an infinite number of integrals .. countably infinite, in fact.

also, i didn't actually calculate them, either; i was doing the analyst thing and trying to bound them.

[2] depressingly enough, this isn't the lowest possible number, either.

a few months ago in a discussion with the advisor, we realised that my "proof" wasn't actually a proof, making it a day where i had minus one (-1) research results to report.