Allen Knutson, a mathematician at the University of California at Berkeley, keeps five balls aloft in an intricate pattern. Knutson often juggles in class to demonstrate the basic premise of discrete mathematics: One input (or throw) will inevitably yield one output (or falling ball).
Allen Knutson’s office is a mess. There’s a unicycle with a flat tire in the corner, and a Bongo Board beside that, and a bunch of stuffed lizards crawling amid heaps of papers and books. The computer monitor is face down and unplugged on the desk. But Knutson, a 35-year-old tenured mathematics professor at the University of California at Berkeley, is completely focused on the challenge at hand. Long-haired, bearded, and wispy, with a quiet, otherworldly presence, he coolly recites a number sequence while juggling four balls in the air: “6-6-1-5-1-5-6-6-1-5-1-5-6-6-1-5-1-5 . . .”
Knutson is an authority on algebraic combinatorics, which involves, among other things, the counting of intersecting lines in multidimensional spaces. The number sequence he’s uttering would be familiar to anyone who knows siteswap, a mathematical language that describes juggling routines. Siteswap codifies motion by assigning each throw a number. A 3 is a throw that goes about chin high and stays aloft for roughly three beats of time; most novices toss ever-repeating 3s while learning to juggle three balls. A 6 is an over-the-head toss that stays in the air about twice as long as a 3, and so on. Odd-number throws are passed from one hand to another. Evens are both tossed and caught by the same hand. A 2 is a held ball, and a 0 denotes an empty hand.
