Sure, just do something with Fourier transforms. Okay, it's not completely accurate, but most simulations aren't anyway.

In fact, I can simulate this in text form with no floating-point or number theory issues at all. Here's the simulation:

> For every 10^100 turns of the first gear, the last gear will move about one full turn.

Nope. Even if your physics engine could deal with the rotation of the first gear in one "unit", and batch the rotation of that gear a million times in a "super unit", then calculate a million "super units" each second, it would still take longer than the universe has been around, by 10^70 times, to complete one rotation of the final gear.

Only if you're okay with some sort of extreme fast-forward mechanism (which seems like cheating), since even if you turned the first gear once per CPU cycle you'd still be spending about 10^90 seconds to turn the last gear once. There's otherwise no problem with representing the state of the simulation itself; a googol only takes 333 bits to represent.