On 15 Jul 99, at 13:08, Ron Kean wrote:
> On Thu, 15 Jul 1999 12:56:18 +0100 Rob Harris Cen-IT
> <Rob.Harris@bournemouth.gov.uk> writes:
> >> >A system with a load of variables that we can't track at this tech
> >>> >level is>> >not "unpredictable", it is "very hard to predict", if
> you want to >be>> >correct.
> >Does anyone know about the principle of true uncertainty? Often when I
> >>discuss determinism and causality with people, they pull out the old
> >"Quantum uncertainty" thing. I don't know what this is, or if it really
> >>describes true uncertainty (i.e. truly spontaneous occurrences).
> >doubt it. >Ron, can you expand the uncertainty detail at all? Anyone
[Good quick summary of uncertainty with a quick brush of entropy]
> So the precise initial conditions needed to make a prediction cannot be
> obtained, given the uncertainty principle.
The sensitivity of a system to initial conditions is expressed by the Lyapunov exponent. You can look at it (backwards) as a way of saying how finely you have to measure initial conditions to predict the state of the system at some future time. Even in "simple" systems like a driven pendulum, the divergence can be dramatic, and you can say that there is a time horizon T beyond which you would have needed subatomic precision at time 0 to predict the state of motion.
Basically, we're not living in Euclidean space (or in Kansas any more, Toto -- with apologies to any Kansans, or for that matter, Oz-phobes on the list :-).