A recent paper suggests a fundamental limit on the chaos in physical systems.
Lubos wrote an easy to read introduction to the main idea.
I think this might be interesting for Scott and everybody else interested in (quantum)computing. If one considers a Turing machine sensitive to initial conditions (i.e. the input string) or if one considers a (quantum)computer simulating chaotic systems, the conjecture seems to imply a limit on computability.
Or think about a device which measures the position x of the butterfly wings, sends the result to a computer, which calculates a function f(x) to determine its output. The conjecture seems to suggest a limit on the functions the computer can calculate in a finite amount of time.
Is it correct to read the result as "the number N of different internal states any computer can reach after a time T is bounded by ewT where w is a fundamental constant"?