Saturday, October 04, 2008

reluctant workday; thoughts on a research shift.

i'm short on motivation today. this morning i woke up late, around 10:15am [1], and i told myself that i would work for a few hours in exchange for my morning cup of coffee.

a fair trade: i ended up thinking about something i was asked to think about, over an email from last night ..

.. so yes, sometimes i do take requests,
but it depends from whom ..

.. and i got as far as i could [2] without cracking open one particular book: hirs¢h's differentia1 t0polo9y. it's a good book, but like i said: i can't seem to work today.

two further thoughts come to mind:
  1. i blame this lassitude on yesterday and the day before: thursday i was driven to finish this manuscript, and i did. on friday night i was also up late -- until 2am -- reading a printout of that manuscript and jotting down comments, in efforts to have something tolerable by monday.

    so perhaps my mathematical battery's gone dead and needs a recharge.

  2. this looks to be a transition in my mathematical life.

    i've spent the last two years of my life studying one particular topic -- derivati0ns and ¢urrents on metri¢ spaces -- and maybe i'll write a paper or two about some of the more interesting thoughts i've had; maybe more, if i'm lucky.

    now i'm in a new research group and they think differently. different topics have importance, such as s0bo1ev spaces in various contexts. i once told a friend of mine to think about sobo1ev spaces as a tool and not as a primary object of study -- he was thinking about giving a talk on the subject -- but i think i will change my mind now. i've always been fond of those function spaces, but now, with new company, i think i will study them again with renewed curiosity.

    perhaps, back then, i was simply asking the wrong questions, or i didn't have the right perspective.
strange, how a place makes you rethink who you are. i never thought of myself as a "ge0metric" person, but now i seem more inclined in that direction than say, ana1ysis of PDE.

[1] some years ago, i would have called that waking up early. odd how things change when one gets older!

[2] i thought of an idea, then realised its weakness, then realised that i was needlessly adhering to one way of doing things. so i came up with a different idea, and over lunch, realised that i was thinking too 2-dimensionally and relying too much on my illustrations. i think this second idea might work; if worse comes to worse, i'll see if i can find something in hirs¢h.

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