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I believe you're underestimating the state-of-the-art. See [1], for example, which claims a method for saying that a sufficiently good numerical solution implies an exact periodic solution close by. (I doubt that the author of the original article did anything like this.)

[1] http://ww2.ii.uj.edu.pl/~kapela/papers/nosym.pdf

Well, that's the question - is his 416-planet system chaotic? Do perturbtions get amplified or do they get pushed back to the stable configuration?

Of course, when you're talking about a civilization building 416 equal-mass planets equally spaced in 8 counter-rotating orbits, worrying about how stable they are is kind of silly; as long as they're "mostly" stable the maintenance of monitoring and tweaking their orbits for a billion years would presumably both be feasible and cheap compared to the initial construction.

Orbits on a N-body system are chaotic if N > 2. Always.

That said, the longer you simulate those orbits, the more certainty you have that they are stable. But you will never get a mathematical proof, because only symbolic math can ever prove things in a chaotic system, finite precision math can only deal with statistic degrees of certainty.

there's nothing that prevents nbody to be solvable with certain starting conditions.

https://en.wikipedia.org/wiki/N-body_problem#n-body_choreogr...

...as long as nothing hits the system, right? I don't know much about astrophysics, but this sounds logical:

https://news.ycombinator.com/item?id=14767295

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.

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.

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

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.

he said stable, not robust

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