I've been thinking about P != NP lately. I think the recent advances in thermodynamics of computation give the insight to solve it. Basically, my thought is that if you can characterizes P and NP problems in terms of area (or more specifically, growth), you can apply physical constraints (notably C as the limit of the velocity by which information can propagate) to the problem. Oh goody! Now I can be a crank getting in way over my depth!