Tuesday, June 19, 2012

#1100: doing the details, hacking the unconscious.

after writing out details on paper at home, this morning,
        mulling over them while walking to the bus,
                and realising, while on the bus, what needed to be done ..

.. i started LaTeχing like a fiend in the office.

i like the results now.

it's never clear to me whether the work is sufficiently hard, in the sense that i've proven something worth proving.  still, the results fit together, and they do address something i've wanted to understand for a while.  my hope is that they explain something ..
.. maybe even to someone else!  a boy can still dream, right?

as i've hinted at before, i've essentially turned someone else's theorem into a tautology .. though not exactly [0].  so the real novelty here, if any, is a human one: i was brave (read: foolhardy) enough to think that it was actually possible, and gotten lucky in spite of it.

regarding part of the process: yesterday i had this out-of-the-ordinary, peripheral thought that i've seen this pattern before, used it somehow and an old idea might fit ..

.. but i suppressed it, deciding to delay the heavy thinking until "tomorrow," meaning today.  as for my reasons:
  1. i think more carefully in the mornings .. and oddly enough, sometimes it's when i'm uncaffeinated.  sometimes i suspect that, not being completely awake, i can trick myself into doing work: a kind of marshmellow test, if you will.

  2. i want to be able to sleep well at night.  odds are that if i worked at it right away, then i would be tired by nightfall, wouldn't get the details right, and be bothered about it over a fitful night of sleep .. only to wake up unready for real work. [1]

  3. i think i was also trying to hack my unconscious toolbox, by pushing the thoughts out of the forefront of my awareness.  sometimes i wonder, to what extent, my conscious mind ever really does my mathematics for me.
if anything, i can't remember anything "notable" i've proven in a single day, and i don't want to start now.  once i do that and once i know it works, then i'll be obliged to do so every time .. just to convince myself that i'm not as lazy as i could be.

strange: sometimes the only reason why i'm not lazy is because of my compulsions.  maybe this is just a very mild instance of a supposed interplay between creativity and .. well, madness.

in other news, this is my 1100th post on this blog; it still astounds me how much i have to complain about mathematics, after 7 1/2 years. (-:

[0] it's more like a weak converse, and a full converse in a special case.  it's still bothering me that i haven't got a complete tautology .. but maybe it'll work as an open problem and spark some interest.  who knows?  stranger things have happened, like someone actually taking the time and effort to improve on my work.

[1] talking this over with colleagues, apparently i'm far from the only one who is aware of this.

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