No, that is not true. Their intractability has absolutely nothing to do with the precision of measurement. Assume the initial condition with infinite precision and the further evolution of the system is still intractable. Ignoring the Heisenberg Uncertainty Principle for a moment and getting to the heart of chaos theory the problem is the production of information at a rate faster than any existant (and I believe, though I don't understand it well enough to give exact details) or fundamentally possible future system of mathematics can compensate for. Nonlinear systems (ie, essentially everything in existence) display chaos (extreme sensitivity to initial conditions, period-doubling, whatever you wish to call it) on every scale. Were the universe mathematics and mathematics alone, all things which are provably outside of the grasp of mathematics would also be non-existent. Such things, however, do exist.
While we may not be able to predict the location of a single molecule of air in a mere 10,000 years with a rough accuracy of a cubic femtometer, the universe does it. And our inability to predict it is not because we need a bigger computer. Our inability to predict it is because in order to predict it, we would have to simulate the entire universe and every single particle within it, and every interaction between all of them, to infinite (ehhh... maybe) precision. Which would have an information load exactly as big as the universe itself and increase entropy (which implies it takes as much time) as much as actual evolution of the entire universe over that course of time. To predict one molecule of air. And the universe does it for all the molecules of air. Along with all the other particles.
That's a very strange quote you did... did you honestly think that I meant the pronoun 'it' to mean 'predict'? I absolutely did not. The universe does it. It executes. It evolves along the pathway and 'calculates' (if you wish) the end result. A thing which no mathematics can, or will ever be able to, do.
If you are looking for the future position of a particle, the future position of that particle is by definition the result sought. I think I might not understand your meaning.
