A few nights ago I found out that my idea concerning a research problem doesn't work. Worse yet, it's the sort of error which occurs late at night when you're excited and really want it to work .. but in the light of day it's painfully obvious that it can't possibly work and you become ashamed that you even thought of it.
But it would have been such a nice idea .. you would have just computed this and piggy-back'ed on that paper .. there would still be much to do, but at least it would then be tenable ..
Bah. Argh. Hmph.
Back to square one, I guess.
It feels like something fundamental is missing from the context of the problem .. just a nagging feeling that I can't seem to shake. The best way I can describe this are those moments when you remember something and it's on the tip of your tongue, but you can't remember the exact word.
It's something like that, except that I'm not remembering but discovering .. more like solving a crime. A mechanism is missing, I can feel it and imagine it somewhat, but I don't know what it is.
Curses! I should be finishing the particulars to my talk, or planning out how to approach a potential advisor .. something. As much as I love pursuing this problem, I have to set it aside because other things must come first.
Business before pleasure, and all that.
This is what I mean: in my mind this is not thesis work, but an idle curiosity of some small importance. It should be set aside if I want to get anything done as a graduate student.
Showing posts with label Σ:newyears. Show all posts
Showing posts with label Σ:newyears. Show all posts
Wednesday, February 02, 2005
Exorcising the Inner Demons .. Part 2 of 3.
Tomorrow's Part II of my talk. I really hope that I don't overtime again; I can only imagine what a pain in the neck it causes the people who bother listening to me.
Nothing gives the same scale of paranoia as giving a mathematical talk, I'd wager. Irrationally I believe that some heckler will inevitably find a rather deep error, and then this huge Vaudeville-style cane will come out of nowhere and drag me away from the blackboard, while the audience looks on ang laughs.
[re-reads]
My god. I actually wrote that. Er .. moving on ..
I must say, though, that this paranoia can be rather helpful. I've been far more careful with my reading and perspective on proofs, though my explanations still feel painfully vague .. but they are getting less vague!
I'm improving my understanding of the Be11aiche and Gr0mov articles, if only through the help of reading Montgomery. Differential geometry is a tricky subject; sometimes it feels like the study of "What do do if you're not in Rn" .. (;
In particular, reading and rereading these articles feels like retracing footsteps of intellectual giants. You can tell the improvements made over time, and the increasing sophistication and abstraction.1 It's not as severe from Newton's theories to Einstein's, but it does give a sense of history, and gives hope that something little you can do might lead to a greater whole someday.
At least some good comes out of this. Better yet, maybe the audience actually finds this interesting ..
[chuckles]
.. well, a guy can dream .. (;
1 More and more I sense that how one learns is extremely important, and by that, I'll emphasize the order of learning and the level of sophistication. To imagine a C-C space, I have to imagine a Carnot group (the Heisenberg group in particular) and to understand that, I imagine a Riemannian manifold, and before that, a surface in space with arrows on it.
Abstraction is hard. I wonder how anyone, most of all the algebraic geometers, get by with it.
Nothing gives the same scale of paranoia as giving a mathematical talk, I'd wager. Irrationally I believe that some heckler will inevitably find a rather deep error, and then this huge Vaudeville-style cane will come out of nowhere and drag me away from the blackboard, while the audience looks on ang laughs.
[re-reads]
My god. I actually wrote that. Er .. moving on ..
I must say, though, that this paranoia can be rather helpful. I've been far more careful with my reading and perspective on proofs, though my explanations still feel painfully vague .. but they are getting less vague!
I'm improving my understanding of the Be11aiche and Gr0mov articles, if only through the help of reading Montgomery. Differential geometry is a tricky subject; sometimes it feels like the study of "What do do if you're not in Rn" .. (;
In particular, reading and rereading these articles feels like retracing footsteps of intellectual giants. You can tell the improvements made over time, and the increasing sophistication and abstraction.1 It's not as severe from Newton's theories to Einstein's, but it does give a sense of history, and gives hope that something little you can do might lead to a greater whole someday.
At least some good comes out of this. Better yet, maybe the audience actually finds this interesting ..
[chuckles]
.. well, a guy can dream .. (;
1 More and more I sense that how one learns is extremely important, and by that, I'll emphasize the order of learning and the level of sophistication. To imagine a C-C space, I have to imagine a Carnot group (the Heisenberg group in particular) and to understand that, I imagine a Riemannian manifold, and before that, a surface in space with arrows on it.
Abstraction is hard. I wonder how anyone, most of all the algebraic geometers, get by with it.
Exorcising the Inner Demons .. Part 1 of 3.
I should quickly secure a thesis advisor, and soon. I would have secured an advisor by now, were it not for the fact that I am a gutless coward.
Argh.
More and more I'm inclined to believe that it's not how you ask that is important, but that you ask at all -- though it still seems better that I talk to said person regulary, then ask at a later day. It would be somewhat strange to ask "Will you be my advisor?" unexpectedly and out of the blue. Ideally, one asks in hopes of a "Yes" answer, and hence it is better to ask when confident of such an answer.
But what am I supposed to talk about? I don't know anything -- anything interesting or deep, or have any good ideas, at any rate -- so what can I say?
Part of me worries -- not only about obtaining a thesis advisor, though that is troublesome enough -- but what it means to be someone's student.
Does that mean that I must set aside the idle interests and curiosities that I've collected over the years, and focus all my energies into the coming Prelim Exam and to do research solely towards my dissertation? What if I want to attend a conference, if only to learn something that's not strongly related to my thesis topic?
It's silly to think that one must give up one's curiosities, because that is what makes us mathematicians. But then I remember: after this term I'll have three years left. That's not a very long time to get it all done .. and what if my first thesis topic doesn't pan out, and I have to start again? The curiosities will be the first to go, if ever there is a problem with time.
Perhaps I'm just afraid of making choices: from now on I'll work with this professor and I will study these things. Those other ideas are very interesting, but I don't have time to study that now. There's work to be done first.
I don't know. Maybe I'm just being silly or paranoid or both.
Argh.
More and more I'm inclined to believe that it's not how you ask that is important, but that you ask at all -- though it still seems better that I talk to said person regulary, then ask at a later day. It would be somewhat strange to ask "Will you be my advisor?" unexpectedly and out of the blue. Ideally, one asks in hopes of a "Yes" answer, and hence it is better to ask when confident of such an answer.
But what am I supposed to talk about? I don't know anything -- anything interesting or deep, or have any good ideas, at any rate -- so what can I say?
Part of me worries -- not only about obtaining a thesis advisor, though that is troublesome enough -- but what it means to be someone's student.
Does that mean that I must set aside the idle interests and curiosities that I've collected over the years, and focus all my energies into the coming Prelim Exam and to do research solely towards my dissertation? What if I want to attend a conference, if only to learn something that's not strongly related to my thesis topic?
It's silly to think that one must give up one's curiosities, because that is what makes us mathematicians. But then I remember: after this term I'll have three years left. That's not a very long time to get it all done .. and what if my first thesis topic doesn't pan out, and I have to start again? The curiosities will be the first to go, if ever there is a problem with time.
Perhaps I'm just afraid of making choices: from now on I'll work with this professor and I will study these things. Those other ideas are very interesting, but I don't have time to study that now. There's work to be done first.
I don't know. Maybe I'm just being silly or paranoid or both.
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