I hope that the ending of my previous “Diary” installment has not left anyone with the impression that mathematicians are a humorless lot. Far from it. There is a great deal of drollery at MSRI. Much of it is delicate and perhaps a little esoteric. The other day, for example, the number theorist Hendrik Lenstra defined a “smooth” number as one whose prime factors are all small, then added in a very stern tone, “So if you know what ‘small’ means, you now know what ‘smooth’ means.” Another famous number theorist, Carl Pomerance, remarked of log(log[n]) that “this function can be proved to diverge to infinity although it has never been observed doing so.” (You either get this or you don’t.) Some of the jokes, admittedly, are less dry. Why did Fermat write his proof in the butter? Because there wasn’t enough room in the margarine.
I have described MSRI as a kind of Platonic heaven. The only real concession to the sensuous world here is the presence of a concert grand piano in the foyer. Mathematicians are incurably musical. I suppose this deep affinity goes back to Pythagoras, who discovered the arithmetical basis of musical intervals. The sort of aesthetic reaction that pure mathematics evokes—a “chill in the spine” is the way mathematicians often describe it—is very similar to the pleasure afforded by abstract musical patterns.
The first question I was asked when I came here was: What instrument do you play? “The heckelphone!” I lied, beaming a bit. (The heckelphone was invented by Auguste Heckel around the time that Adolphe Sax invented the saxophone, but unlike the saxophone it never really took off. As very little music has been written for the heckelphone, claiming to play it is unlikely to get you yoked into a chamber group. I used to affect to play the sackbutt, but this is risky these days, what with all the interest in early music.)
There are frequent afternoon musicales at MSRI. The other day the formidable mathematician Noam Elkies played a series of his favorite fugues on the concert grand, beginning with Bach and ending up with some fugues of his own devising. Besides being the youngest professor ever to be tenured at Harvard, Elkies also performs his compositions with symphony orchestras to great acclaim. There is no God.
I bail out of the recital after a fugue or two and head off for a logic colloquium being given by a young Italian mathematical philosopher with the wonderfully musical name of Bacciagaluppi. He is talking about realistic interpretations of quantum mechanics.
I find one remark he makes utterly arresting. It has to do with the application of the Heisenberg Uncertainty Principle to music. The Heisenberg Uncertainty Principle says that the more you know about a particle’s position, the less you know about its momentum, and vice versa. This inescapable vagueness stems from the wavelike nature of particles in quantum physics. But a similar uncertainty relation holds mathematically for any wave system, including sound waves. In music, the uncertainty tradeoff is between a note’s pitch and its duration: The more precisely the note is localized in pitch space, the more delocalized it gets in time. This uncertainty is especially dramatic in the lower notes. “Therefore,” Bacciagaluppi concludes, “a fast jig on the lower register of an organ is not bad music—it is not music at all.”
In addition to the general passion for music here, there is also a strong and statistically anomalous interest in juggling. Happily, the mathematicians show no detectable interest in folk dancing.
