Steven D'Aprano wrote:
one minute the grenade is sitting there, stable as can be, the next it's an expanding cloud of gas and metal fragments.
I'm not sure that counts as "discontinuous" in the mathematical sense. If you were to film the grenade exploding and play it back slowly enough, the process would actually look fairly smooth. Mathematically, it's possible for a system to exhibit chaotic behaviour (so that you can't tell exactly when the grenade is going to go off) even though all the equations describing its behaviour are smooth and continuous.
My money is on the universe being fundamentally discontinuous.
That's quite likely true. Quantum mechanics doesn't actually predict discrete behaviour -- the mathematics deals with continuously-changing state functions. It's only the interpretation of those functions (as determining the probabilities of finding the system in one of a discrete set of states) that introduces discontinuities. So it seems quite plausible that the continuous functions are just approximations of some underlying discrete process. The trick will be figuring out how such a process can work without running afoul of the various theorems concerning the non-existince of hidden variable theories... -- Greg -- http://mail.python.org/mailman/listinfo/python-list