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.


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 ..


.. 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.


fragments of angry candy said...

Hope your talk went well! Actually, I'm sure it did. But sorry that I didn't go; I meant to, but got distracted during tea (which I went to to make sure I would know when 4:00 would roll around...)

janus said...

No problem, Jo. I think I had an audience of two this time around, but it was much fun because we could stop whenever we wanted and stare at the board, bother each other with questions and whatnot.

I like to think of it as mathematical slumber-party.


God, that's a weird thing to say. But no matter! The talk went well, I didn't say too many false things, and the audience was mildly entertained by the discussion, I think.

No worries about missing the talk. After all, I think I've missed all the talks that Alan has ever given at UM. (Mind you, that's not very exciting, because he's given just one, as far as I know.)