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JGWeissman comments on Hardened Problems Make Brittle Models - Less Wrong
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I did not intend to dispute the stability of orbits. I mean to point out that the stability is a nice property of the territory, and it is only a nice property of the map because it is a property of the territory. Generally, we should not let our desire that maps have nice mathematical properties override our desire that the map reflects the territory. If the territory has discontinuities at corner cases, the map should reflect it, even though we like continuous functions.
More to the point, there are a variety of systems where the territory displays a degree of sensitive dependence on initial conditions at some scale that makes a stable map impossible.
In fact, on astronomical time scales the dynamics of the solar system (or generally, any multi-body gravitational system) displays such behaviors.