The day started at 7:30 am, way too fucking early. I seem to have forgotten to bring shampoo, so I stole someone else's while taking a shower. I finally got to breakfast on time, though, so I was able to get a good seat and amuse cute women with my witty banter. I confess that the reason I enjoy meeting new people so much is that they haven't heard any of my jokes yet. It's even better if they are of the type that think lines like "The most amazing thing about reality is that it updates in realtime" are clever.
Two of the talks today I found interesting in that they were absolutely normal. I have easily been to hundreds, if not thousands, of mathematics talks exactly like them. The researcher generalizes some known theorem or definition in a slightly obscure way, plays around with it a bit, and comes up with a couple of propositions which he or she calls theorems (as my friend Manish would say, "Theorem inflation! Theorem inflation!). The material is decently presented, but at too fast of a speed for the audience to really care about it. The work implies nothing, and leads nowhere.
It may be that such talks are the unavoidable byproduct of the process of mathematical research, that no matter what field you are in there will be ten mediocre talks for every brilliant one. But that doesn't mean I have to like it.
Joe O'Rourke gave the 10:30 am talk on computational geometry. I typed up the lecture notes to this one; they are reproduced below. My transcription is considerably cleaner than what was actually presented: why is it that computer scientists think that giving a talk consists of simply reading a series of overhead slides with a bunch of bullet points on them?
My early afternoon consisted of writing up said transcription. My late afternoon consisted of listening to a talk (given by a computer scientist), the whole substance of which was: "I wrote a bunch of functions in Mathematica." I do not mean to unduly harsh on computer scientists -- many of my close friends are computer scientists (hi curtis!) -- but you must admit that it is disturbing for a field to have such low standards for that fundamental unit of science, "results good enough to give a talk about."
Before dinner I went tot the Smith College bookstore and bought a Beatles tape for $8 (Rock & Roll, vol.2), two books on chess openings for $3 each, Eric Dexler's "Engines of Creation" for $3, and a noteboke for $2. Dinner conversation was unusually good: I convinced two high school teachers to include fractals in their geometry ciriculums, explained how it was possible to be a vegetarian without eating vegetables, and found out from my analyst neighbor why operator theory isn't about operators. Heck, I was even able to use my "What kind of math do you study? I'm an analyst. Freudian or Jungian?" line.
After dinner, Don Caspar gave a deeply disturbing talk about crystalography. It's hard to explain why I felt so very unnerved by his lecture, but I'll give it a shot: Modern mathematicians, by philosophy and by their cultural education, are brought up to believe that math has no applications. This belief may come as a shock to those of you who look through science books and see nothing but equation after equation of mathematics, but let me add that what mathematicians mean by mathematics is not what everyone else means by mathematics. When a mathematician speaks of mathematics, she means deep mathematics, nontrivial mathematics, real mathematics. Only in the most theoretical of theoretical physics would a mathematician expect to find real mathematics. To give an analogy, it's one thing to say that an investor asks his stock broker to buy a stock in English, and another thing entirely to find in such a request beautifully written drama at the level of Shakespear.
So Don Caspar gave an hour and a half long talk on how the symmetries of polyhedron -- which has been deep mathematics ever since the Pythagoreans -- matter in crystals, and matter in nature. It blew my mind. And not only that; they also occur in viruses. I'm not sure about you, but I've always had a mental picture of a virus being green and wet and squishy with lots of little tentacles sticking out. Viruses (or at least the viruses which Don showed us) looked nothing like that. They looked like soccer balls, geodesic domes, and icosahedron. It was like Plato and Buckminster Fulley were invading your body in a Borg ship saying "Resistance is futile. You will be assimilated." So I was flipping out over that when finally Don put up a slide of a more traditional looking virus -- one that sort of looked with a kite, complete with tail. But as I was mentally readjusting, the very next slide had these viruses interlocking with each other so as to tile a sphere, with, get this, the tails fitting into the neighboring viruses in a symmetry pattern. It was like straight out of an Escher print; heck, it was more like an Escher print than most Escher prints.
So, all in all, the talk left me with a very postmodern feeling. You know, like Derrida talking about the familiar being more alien than the alien precisely because it is so familiar. That kind of stuff. I'm beginning to think that the only acceptible form of realism in art these days is surrealism.
The last talk of the day was by Heidi Burgiel on why you can't win at Tetris. Way cool talk. She proved that if the computer gives you a sequence of 240 alternating left and right S shapes, then you are screwed, no matter how you place them. And since such a sequence appears with probability one in any sufficiently long Tetris game ...