“Only because of our conversation on the bench in Central Park I was able to understand … [that] given is an actually infinite system of points (the actual infinity is worth stressing because nothing will make sense on a finite no matter how large model),” noted Ulam, who then sketched out how he and von Neumann had hypothesized the evolution of Turing-complete (or “universal”) cellular automata within a digital universe of communicating memory cells. The definitions had to be made mathematically precise:
