4 ms·
I'm not sure what you mean. The n-body problem has no analytical solution in general. You have to simulate. The author is suggesting that assumptions you make (
by andbberger 7y ago
I'm not sure what you mean. The n-body problem has no analytical solution in general. You have to simulate. The author is suggesting that assumptions you make (such as representing the earth moon system as a point mass at their CoM) in order to make simulation feasible might lead to a catastrophic divergence from reality over time.
This is all a consequence of n-body dynamics being chaotic [1]
https://en.wikipedia.org/wiki/Chaos_theory https://en.wikipedia.org/wiki/Chaos_theory
- philwelch 7y agoI don't know a lot about physics, but I do know a little bit about computer science, and it seems to me that--barring some crazy breakthrough in computation--any simulation accurate enough to overcome the chaotic nature of this problem may very well be fundamentally impossible. That in itself would be a pretty fascinating result.
- andbberger 7y agoThe problem isn't the fidelity of the simulation persay, it's that chaotic systems are quite literally infinitely sensitive to initial conditions.
- philwelch 7y agoSure; the possible result that the physical universe is fundamentally uncomputable is the result I find interesting.
- andbberger 7y agoThat is _not_ the result though. This has nothing to do with computability. It's about the behavior of a certain pervasive class of dynamical systems.
- philwelch 7y agoOkay, I’m missing something then.
- ryanthedev 7y agoMeh. The axiom of choice is well documented. Each initial set of conditions would create a unquie system. Look at Banach–Tarski paradox
- andbberger 7y agoWhat does this have to do with the axiom of choice?
- ryanthedev 7y agoYou implied the issue is the infinite set of initial conditions. All systems are based off the initial set of conditions. The axiom of choice. The issue is the degrees of freedom introduced with more dimensions...