I'll say a little more about the mathematics of contra dancing at a later date. My role as an invited speaker at the meeting was to keep everyone awake after the Saturday luncheon with a keynote presentation on how randomness arises in the gambling world, the amusement park, and elsewhere. I had a chance to give a preview of some of the topics in my upcoming book The Jungles of Randomness . The casino setting gave me an excuse to consider some of the details of how both electronic and mechanical slot machines work, particularly how they create the illusion of chance. That meant talking about the sensitive dependence on initial conditions that characterizes chaos and on the vagaries of random-number generators.
Dice also represent an intriguing case of the interplay between randomness and physical laws.
At the Horizon, I finally got a good look at real casino dice, which differ in crucial ways from those sold in novelty stores and with many board games. According to gambling expert John Scarne, casino dice are made by hand, each cube typically 0.75 inch wide and precisely sawed from a rod of cellulose or some other plastic. Pits are drilled about 0.017 inch deep into the faces of a cube, and the recesses are then filled in with paint of the same weight as the plastic that has been drilled out. The transparent dice are then buffed and polished. The edges are generally perfectly square and sharp.