There are certain physical processes that naturally seek configurations that optimize some metric, usually minimizing potential energy. I'm very interested in understanding their dynamics, because I think they may help elucidate the physical underpinnings of the origin of life and evolution. The simplest example of optimization is probably the hanging chain. Analytically, the calculus of variations can be used to prove that this shape is a hyperbolic cosine (known as a *catenary*). However, think about the physical dynamics for a second; suppose I pick up a chain fixed at two points and let go. It can't hang freely until it dissipates the potential energy it gained when I lifted it. This dissipation takes a few different forms: friction between links in the chain, sound, and air resistance are probably the main three. In spite of the fact that these interactions are pretty complex and can be wildly different across experiments, somehow the chain always arrives at the same final shape. The calculus of variations simply tells us what happens to the chain; it does not explain why, or how. The reason is probably statistical: something like "vastly more paths in phase space lead to the chain assuming that shape than any other." I wonder if these processes have a combinatorial interpretation, and if so, whether such a method can be applied to understanding life. It's abundantly clear that, in a process reminiscent of the settling of the chain, evolution explores some space of states while optimizing some energy metric. However, tools like calculus seem to be insufficient to explain this behavior, possibly because the optima found by evolution depend on discrete structures unsuited to a continuous treatment.