on research and moving targets.

this week starts the second week of my visit to spain.

i think it's going well. we're discussing a lot of problems, setting up projects, seeing which approaches make sense and which could be wishful thinking. two weeks isn't forever, you see;

it's good to plan what can be done later, on our own.

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regularly my colleagues have been asking me specific questions, to which i don't have any answers. this is completely natural, of course ..

.. it's not like they know the answer either,
.. but i still can't stand not knowing.

it reminds me of the film butch cassιdy and the sundance kid:

there's this one scene where the two main characters are practicing their shooting, and sundance is missing every shot.

when asked how he can hit anything, sundance starts walking to the doorway and simultaneously shooting .. only to hit the bullseye every time.

"I'm better when I move," he says.

research-wise, i don't think i've ever been able to solve an explicit problem when "standing still" .. that is, in one concentrated session.

(this includes dedicating a full 6 weeks to it and working on nothing else.)

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it almost always occurs by accident.

sometimes it's when i'm doing something else.
other times it's some time later after i've finally give up (usually at least a week).

either way it just dawns on me that two separate topics are related in exactly the way that i need them to relate .. at which point, it's not that i feel particularly happy that i hit the target. there's a base amount of amazement that it actually fits together, sure, but most of all i feel stupid that it took me that long!

that's not exactly how it works, though: it probably takes a while to absorb all the information, how everything connects logically, and to step sufficiently far away from it all in order to see the truly essential parts.

i guess seeing something "easy" after months of fruitless activity is just a little disarming to me ..

.. then again, even after the answer presents itself, there is usually a lot of technical work before the proof is fully rigorous.

so usually after the writeup, i feel slightly better .. that yes, it does take more than a lucky break to prove theorems.

if the result is worthwhile, then usually it requires quite a bit of hard work .. \-: