Mathematical beauty and assorted updates

Wooo!

So, gf and I are going to Rhythm & Jews tonight, to a 57th Street art thingy on Saturday, and then later that night to contra. Wooooooooo

Last night I went to see The Last 90 Minutes in the Life of Nikola Tesla at UT, which was absolutely outstandingawesomelulzy. (For your amusement: There were five Teslas. Two, including the most prominent one, were played by females.) It was entertaining, thoughtful, and well-executed, though there were a few occasional points at which it occasionally hit a bit closer to home than I'd've liked. Anyway, it was fantastic excitingness.

Since I feel obligated not to simply recapitulate events here, here's something new and interesting. This year my Analysis class has been in the IBL format, which means that we get statements of theorems, definitions, and exercises, and the students work their way through them, proving everything from start to finish with a bare minimum of input from the instructor and no textbooks. I have been quoted describing this class as "as good as sex."

Our final "unit" was everything I could've asked for. It's deeper than any continuous mathematics I have yet encountered, it involved building up a gorgeous and rich framework and letting the result simply fall out, and oh dear it was the most exciting thing evar!

Throughout the year the one continuous theme from my math and CS classes has been building up linear algebra to a height that I couldn't have appreciated, much less imagined, a year ago. The richness of the concepts of eigenstuff were the culmination of Laci Babai's Discrete class, Quantum introduced the concept of tensors and exploited it and eigenstuff gloriously, and finally Analysis has introduced me to a fully pure, well-formed concept of tensors, tensor spaces, and has built on top of the complete development of tensors an even richer collection of tools to work with.

It is almost an aside that from the sizable collection of resources we've created that some of the most powerful theorems of analysis fall out easily. It's such that one can progress if and only if one understands the definitions, understands how everything fits together, and once one has that understanding things fall out easily. It's beautiful and gorgeous and requires a lot of effort simply to wrap your head around things.

In pure mathematics, it is simply a requirement that you can devote a lot of thought to wrapping your head around a very detailed, sophisticated definition and reach a correct intuitive understanding. High school mathematics had a fair amount of this, but it was primarily algorithmic: learn to apply methods to obtain results, as opposed to understanding at a very deep, intuitive level what it was you were working with.

The job of a mathematics student, quite simply, is to grok.

Also, a bonus cutesyanecdote if you read this whole thing! I was going to go get some dinner, and I gave gf a few goodbye spins, because, y'know, we dance, and I like spinning people, and she tells me:

"Louis, one of these days you're going to sweep me off my feet."

There was really only one way to respond.

"Absolutely."

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theater and excitement

Facts learned (or reestablished) yesterday:

UChicago theater is excellent. In fact, theater in general is excellent. In point of fact, since I started considering the problems involved, the objectives of theater, the particular challenges, and so on, maybe two years ago, my respect for the field has steadily risen. A Breckie dude I massively respect directed one, woo! The plays were...superbly interesting, to an extent nothing less than I would've expected from the UofC.

There's no better way to say this: playing with tied-up people is fun for all parties. 'Nuff said.

I ought to cultivate a few more dance partners willing to lead me, as opposed to the other way around. I do almost exclusively dance with ladies, typically because I empathize so much better with women, so I can, say, pick up on when they're dizzy, when they'd actually rather swing than spin, when they want more momentum, when they're running out of energy.

I'm a very aggressive dancer -- I never hold back my energy, I love momentum and speed and spinning and especially moving my partner even faster than myself -- and I've learned, for instance, to always ask just before a dance whether or not my partner gets dizzy. Being able to pick up on a partner's cues is damn useful.

It took me several tries, and at least one person yelling at me, to figure out the headspace for a follower. You have to be much physically looser, ready for another dancer to do any of a variety of things. That's substantially different from leading, where the goal is to make anticipating your own next move easy for your partner, which requires steadiness and a firm grip.

It still takes me at least a minute to change my headspace from leading to following, simply because I have to put my mind in a position where my first reaction to a firm grip is to let it control me. I also haven't learned to control my aggressiveness when I'm following, which -- given how much I like spinning -- tends to result in draining considerably more of my energy in a single dance. My movements are also considerably less smooth as a follower, but that's more an issue of practice than anything else -- that, and the reality that I'm tall enough to make spinning me difficult.

I dance because I love making people happy, and I lead because when I dance with a skilled partner, I can usually succeed in giving them a fast, exhilarating dance, modulo the energy of the band and the song. When I follow, it becomes about how much I'm enjoying myself, rather than about how exhilarated I can make my partner. There's a fair bit to think about here -- I absolutely adore thrilling a good dancer, so clearly as a leader I'm getting something out of it; that much is evident from how much I adore a good partner. When I follow, what is the headspace to appreciate that? To know that my skill, to spin and whirl and bend as fast as they can move me, encourages and excites my partner?

Of the things I need to learn, learning new headspaces is perhaps what I care most about.