Measuring Fractal Dimension ?

[greg]

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