Thursday, July 11, 2013

à la pοincaré: the 4-hour day.

tuesday, 9 july 2013 @ 11:44 EEST:

my new plan: i'll concentrate on being as productive as i can, but specifically during the hours that i know that i am usually productive (even if it means that i am working far fewer hours than i usually do).

this includes first thing in the morning ..
today was already productive:
i constructed a whole class of counter-examples!

.. and probably late afternoon into early evening, just before i usually go running or join friends for climbing, actually.

odd: why would the "bookend" times be the most productive?

maybe i should also keep a "journal" of what i did during those hours, and how long it took? this is in reaction to how ineffective my to-do lists are: they are always overloaded and i can never check everything off, which eventually gets depressing.

the tricky thing is how to be productive in the hours in between. one possibility is that if i'm going to waste time, then i may as well enjoy myself, like reading novels or blogging or taking photos of the city, but another possibility is to fill it with drudgery, such as writing a review for this article that is 4 months late .. etc.

on the other hand, maybe a few hours of real work is enough; i mean if it was good enough for poincare .. [0]

wednesday, 10 july 2013 @ 08:38 EEST:

ups and downs again:
two days ago i knew what worked .. or at least, i thought i did;

yesterday i was convinced that a colleague's "conjecture" [1] is false and even had a rough proof in mind,

but just now i found a gap in my argument,
so i'll spend today working on a patch.
despite having been privately wrong [2] this has been a pretty exciting week, mathematically speaking. the uncertainty of it all is .. not intoxicating, but like a high. not knowing what exactly is true is all the more motivation to figuring out what it could be .. especially if it keeps on switching, due to increased effort.

so work is fun again and i can obsess about it with new abandon.

[0] to be fair, i wonder what poincare would consider "work." my guess is that the man had high standards, so a lot of things he wouldn't consider work, i would!

[1] i like to reserve the word 'conjecture' for those unproven claims that are particularly nontrivial .. and no, i don't have a definition of nontrivial, but just a sufficient condition: if, by telling someone related to your field of the basic notions, by stating the problem, and by showing why it is hard or what it would imply, that that someone become interested, then it's nontrivial.

[2] 'privately wrong' is doing something stupid in the privacy of your own workspace. 'publicly wrong' is having many people know about it. i've been both, and the former is very, very much preferable to the latter.

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