Computer science on prediction and the edge of chaos

With the development of statistical mechanics, physicists became the first agent-based modellers. Since the scientists of the 19th century didn’t have super-computers, they couldn’t succumb to the curse of computing and had to come up with analytic treatments of their “agent-based models”. These analytic treatments were often not rigorous, and only a heuristic correspondence was established between the dynamics of macro-variables and the underlying microdynamical implementation. Right before lunch on the second day of the Natural Algorithms and the Sciences workshop, Joel Lebowitz sketched how — for some models — mathematical physicists still continue their quest to rigorously show that macrodynamics fatefully reproduce the aggregate behavior of the microstates. In this way, they continue to ask the question: “when can we trust our analytic theory and when do we have to simulate the agents?”