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Comment by keymone | Hacker News Reader

2+2 is also not 4 when you change the base assumptions drastically.

obviously if another star smashes into planetary system - it won't survive, at least not in original form.

I think the problem gets into some chaos theory, the kind you see in weather prediction.

When the forecast says "60% chance of showers tomorrow", what he really means is that they ran a few billion simulations of the environment with very tiny perturbations of the initial conditions and in 60% of those simulations, it rained. In 40%, it didn't.

Tiny little changes in any variable in a chaotic system will, in the long run, lead to huge variations in outcomes.

This system with it's 416 planets has one outcome- perfect orbits constantly. But if you add a single 1 kg asteroid to the system, that would perturb everything ever so slightly. That slight change could result in the entire system chaotically coming apart from stability.

"stable" always comes with conditions, even if implicit. there's no need to add any asteroids - if any of those planets has tectonic activity, that will already introduce perturbations into gravity fields and cause a collapse eventually.

going off on a tangent here, since you mentioned weather prediction, chance of rain % or probability of precipitation (pop) are computed not only for probability of rain in a given area but also for area of location that will receive the rain if any at all, ie 60% here expresses combination of degree of confidence that rain will occur in an area and geographic coverage of that rain. more details on the wiki entry here - https://en.wikipedia.org/wiki/Probability_of_precipitation

The point is, if you perturb it by a small enough epsilon will it go back to the initial configuration or fall apart? Pencil standing on its tip kind of a deal.

in nbody terms - that is an additional condition so the problem would have to be solved separately. ask the author, i'm just a lurker here.

Yeah, my dad was always quick to remind me that 2 + 2 = 5 for large values of 2.

He said he came across that particular problem in a system which handled rounding numbers in a very suspect manner.

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