It’s a bit of an odd feeling to be reading a novel and stumble upon yourself as a character. Well, at least a well-disguised version of yourself. The novel is Victor Snaith’s The Yukiad, and the character is a large Scotsman named Pans who tugs at his earrings when he becomes agitated. I am neither Scottish, nor earringed, nor particularly large, but I suspect that Pans, viewed through the haze of poetic license, is I.
When we meet Pans, he is hovering over a glass contraption—a perpetual motion machine, really—consisting of a circular tube containing several colored beads, which travel around the tube, some clockwise, some counterclockwise, all at the same speed, bouncing off each other in perfectly elastic collisions whenever they collide. Pans is currently tugging at his earrings so hard as to cause some concern for the integrity of his earlobes, as he ponders the following question:
But wull tha’ aver gut bark to weer tha’s started, at a’, at a’?
Well, okay, maybe I’m not Pans. Maybe I’m the character Sherloch Humes, a “trim but rather wrinkled gentleman in worsteds”, who calculates for Pans’s benefit that “the configuration of beads is guaranteed to have exactly replicated itself by the year two thousand and nineteen”. I believe that I am the inspiration for one of these characters and that the mathematician Leonid Vaserstein (who is neither Scottish nor wrinkled) is the inspiration for the other, and here is why:
Many years ago, for reasons I can no longer remember, Vaserstein and I posed ourselves the following question: Suppose several point particles, all of different colors, are located on a circle, with some traveling clockwise and others counterclockwise, all at the same speed. Whenever two particles collide, they instantly bounce off each other and proceed in the opposite of their original directions, still at the same speed. Take a snapshot of this system at, say, 12PM. Must there be some time in the future when another snapshot of the system will look identical? In other words, does the history of the system repeat itself?
As I said, I can no longer remember how we came up with this question, but I do remember that it triggered a vigorous discussion. We were riding in a car at the time, myself in the passenger seat and Vaserstein in the rear. Victor Snaith, who some years later was to write The Yukiad, was driving.
The solution—which I’m pretty sure Vaserstein contributed more to than I did—is beautiful and elegant and crystal clear once you see it. Do you see it?