Hello from Athens, Georgia!

In Athens today, and will be going to Atlanta tomorrow to talk about cubic fields. A couple random observations:

- Athens seems like a really nice place. Definitely small, but certainly appealing. We walked around downtown a little bit -- it looked pleasantly chaotic, there were other people around, and the beer was good. (And tonight, I have insisted on a trip to the 40 Watt Club.)

- The University of Georgia has a lot of regrettably ugly buildings. I did some work in the science library, and they had all sorts of signs and posters which looked like they would be more at home in a middle school library than in somewhere professionals go to do research.

- I like the mood in the department. For one thing, it has more than the usual share of women -some math departments I have been to have been really, really male. I've gotten into some serious math conversations, but I don't get the insular vibe that I've gotten at some places.

- I've heard echoes of one of my frustrations as a postdoc: You enjoy a wonderful environment, and you're loving life, but you know full well you don't get to stay forever. Goes with the territory I guess.

- I got grilled during my talk. Some people hate that, but I'm always quite pleased when people ask me a ton of questions. Even if one of them is to politely inform me that no, $O_K \otimes Z$ is not an integral domain.

- My host has been extraordinarily polite. I knew him from grad school, but not all that well. He has taken considerable pains to show me around, without being overbearing. I'm moving to South Carolina in the fall, so I will have the opportunity to reciprocate!

- I think every city anywhere in the South has somewhere named Five Points.

Why Chinese mothers are(n't) superior.

I have no opinion on Chinese mothers themselves. But I definitely have an opinion on this essay, "Why Chinese Mothers Are Superior".

Her argument hinges on this point:

"What Chinese parents understand is that nothing is fun until you're good at it."

Is she right? Well, let me think about some things I've enjoyed in my own life:

Math: I enjoy it, and I enjoy it because I'm good at it.

Karate: I took karate lessons for ten years. I've earned a black belt, and I solidly enjoyed it. I seem to be making her point for her.

Improv comedy, cooking, chess, guitar, piano, blues dancing, sea kayaking, mountain climbing, bridge, ...: Here I feel that I can shoot down her point with some conviction.

But even then, I have to notice that she's right about a couple of things. In the first place, I enjoyed these things the most when I succeeded. When my fellow students and I pulled off a five-minute skit in improv lessons, or when I played some little piano piece with actual two-part harmony. So I enjoyed these things because I got a little good at them.

But beyond that, all of these activities are things I could get good at, with a lot more effort along the same lines. I enjoy chess precisely because I'm improving, and because I know it would never stop rewarding my efforts. But I enjoy it now, and that wouldn't change if I played my last game tonight.

Let me go one step further:

Math. I said I'm good at it. But actually, by the standards of the company I keep, I'm only good at analytic number theory. (And, if I compare myself to Sound, ..., but let's not go there.) Ravi Vakil advises graduate students to go to research seminars outside their seminar area. And I'm pretty sure he's right.

Now, I'm never going to get good at, say, algebraic geometry unless I take a serious amount of effort away from my other work. Does that mean I shouldn't go to algebraic geometry seminars? I think it doesn't. Ravi's idea is that, although I might not understand most of what is going on, seeing a different perspective on things helps get my internal wheels churning, improves my sense of creativity, imperceptibly teaches me how to do my own work just a little bit better.

And so it is with school plays, sleepovers, and instruments other than the piano and the violin. These things are of value, and of value that you can't always see.

Less Wrong?

So here is something interesting that has surprised me in San Francisco: It is common for people (i.e., roommates) to give each other rides to and from the airport.

Now why is this surprising? Because we have safe, efficient, clean public transportation (BART) that goes straight to the airport terminal. I know of friends living close to the BART line who've given or received rides.

And my first reaction was: To ask for or accept a ride... isn't this a bit irrational? To impose on others, or to allow others to impose on you, for something that's easily done alone?

So I was reading the interesting blog Less Wrong. The masthead declares that the blog is "devoted to refining the art of human rationality". The following problem ("Newcomb's Problem") appeared in one of their posts:

A superintelligence from another galaxy, whom we shall call Omega, comes to Earth and sets about playing a strange little game. In this game, Omega selects a human being, sets down two boxes in front of them, and flies away.

Box A is transparent and contains a thousand dollars.
Box B is opaque, and contains either a million dollars, or nothing.

You can take both boxes, or take only box B.

And the twist is that Omega has put a million dollars in box B iff Omega has predicted that you will take only box B.

Omega has been correct on each of 100 observed occasions so far - everyone who took both boxes has found box B empty and received only a thousand dollars; everyone who took only box B has found B containing a million dollars. (We assume that box A vanishes in a puff of smoke if you take only box B; no one else can take box A afterward.)

Before you make your choice, Omega has flown off and moved on to its next game. Box B is already empty or already full.

Omega drops two boxes on the ground in front of you and flies off.

Do you take both boxes, or only box B?

"Obviously", you should take both boxes. Omega has already flown off.

The Less Wrong blog post launches into a long discussion of rational behavior, even discussing Bayesian probability and whatnot. The blog seems to take it for granted that better decisions are made by people who understand Bayes' theorem than people who don't. But I think that most mathematicians would take both boxes, and most non-mathematicians would take only Box B. And get the million dollars.

In my opinion, the interesting thing about this example is how contrived it isn't. Suppose that your goal in life is to lead as rewarding of a life as possible, and you approach this rationally. Then you start thinking about how to optimize your time, and how to get the most of every day, and so on. Surely you wouldn't give anyone a ride to the airport.

And yet, I've developed a great admiration for people who give each other rides, whose sense of efficiency is trumped by a sense of companionship and consideration for others, and who don't ever try to optimize anything. These are the people who leave Box A on the ground. After all, as they know from experience, if you do, you get a million dollars.

And indeed you do. I understand Bayes' Theorem, which may put me at a disadvantage. But I've learned that it's often right to be more wrong.

No longer a blog for things to be.

Hello everyone! For the new year I'm rebooting my blog -- taking it totally public (i.e., putting a link on my Facebook page) and rededicating it to my original intention: talking about the interesting and beautiful things I see, hear, and experience every day. I've had this blog for about two years now, but it got a bit repetitive and stale, and I feel like starting over.

Don't have too much to say now... was up late last night at a fabulous blues dancing party! And so I'm too tired now to put a coherent sentence together. But watch this space.