Ok, this was fascinating. From my stash of cool academic blogs..
"In my own field of complex systems theory, Stephen Wolfram has emphasized that there are simple computer programs, known as cellular automata, whose dynamics can be so inscrutable that there's no way to predict how they'll behave; the best you can do is simulate them on the computer, sit back, and watch how they unfold. Observation replaces insight. Mathematics becomes a spectator sport."
(Quoted in Marginal Revolution.)