today was the weekly meeting with the advisor, and short as it was, i think it went as well as can be expected. rather, it went as well as one could expect out of my first week of reading a new paper [1] ..
.. which means that one should have few expectations, if any. i follow that same rule, myself. q:
but enough self-recrimination: it certainly went well, because my efforts are now sharpened towards more specific goals. after a bounty of good ideas from the advisor [2], there is much work to do in these next few weeks, and when this matter of 2-dimensional homeomorphism extensions is resolved, there remains the big lingering problem whose solution will (hopefully) form the body of a dissertation.
there's something soothing about having work to do [3], which is a bit like having a (temporary) purpose in life.
earlier today i started wondering (read: worrying) about the nature of research, and i despaired about ever having any good and fruitful research ideas of my own.
sure, i have ideas, but are they any good?
will they lead to anything of passing interest?
will i be able to carry through any of them, even if they are interesting?
as a larger question, how does one obtain a "vision?" how does one think towards a cohesive body of knowledge which explains some abstract phenomenon, rather than merely dabbling and proving what lemmata or theorems which can be done with a few clever tricks?
in mathematics, i listen and less often, i understand. i follow this or that line of reasoning, and with a little twist i can conjure up something of slight novelty but of same spirit ..
.. but i've never created anything. i've left no contributions to the body of knowledge from which i've so consistently borrowed and occasionally earned. in the simplistic words of ayn rand [4], thus far in my life i've been a "second-hander."
somewhat fittingly, i never resolved that line of questioning, but merely forgot it. later i left the office with friends to see a film, stay for a Q&A session with the director, and then off for a pleasant dinner.
[1] it's the one by Douady and Earle, concerning "conformally natural" extensions of circle homeomorphisms.
[2] trust me; the ideas aren't mine, as much as i'd like to them to be.
[3] as opposed to not getting any work done; the difference lies in at which point one obtains the workload. "having work to do" means that you haven't done the work yet, and there is potential in all possibilities; "not getting any work done" means that you've tried and tried and nothing seems to work.
[4] i'm referring to one of the several hundred pages of the book, the fountainhead. for the record, it's not worth reading; if i could trade the time it took to read those pages for a better choice of pages, i would, and i'd probably have chosen Dostoevsky as its replacement.
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