Complexity and Emergent Properties

Abstract

Consider billiards: the billiard balls travel in nice straight lines, bouncing off the cushions with geometric precision, striking other balls and sending them in predictable directions, obeying Newton’s laws, only restricted by energy loss through friction and imperfect cushions. Introducing spin increases the complexity of the game, as the reaction with the surface can result in curved paths. The game of pool introduces the “absorbing state” of Markov analysis: the pocket. The ball that enters the gravity field of the pocket may fall and be out of play. If the ball does not fall, its trajectory will be changed in a complex way. At the beginning of the game, the balls are racked in an array. The array is struck by the cue ball, sending all the balls around the table. Because the array is not perfectly formed and the cue ball placement and trajectory are not the same each time, the resulting trajectories are not repeatable: a simple geometric game actually involves complexity and chaos theory.