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I assume you're alluding to N-body problem? https://en.wikipedia.org/wiki/N-body_problem https://en.wikipedia.org/wiki/N-body_problem
by d33 9y ago
I assume you're alluding to N-body problem?
https://en.wikipedia.org/wiki/N-body_problem https://en.wikipedia.org/wiki/N-body_problem
- jdc0589 9y agothat....and the assumption that general idea that we know everything we know to engineer a stable solar system with 416 plants is kind of hilarious.
- unit91 9y agoExactly
- Parcissons 9y agoMy assumption is that this simulation did for example not contian liquid planetary cores- who if repeatetly beeing subject to gravity fluctuations - would start to resonate- basically resulting in a sort of lava tide to shake the planets apart over time.
- marcosdumay 9y agoI assume he is alluding to how a simulation of finite precision can not prove anything about a chaotic system. And yes, that the N-body problem is chaotic.
- tgb 9y agoI 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 http://ww2.ii.uj.edu.pl/~kapela/papers/nosym.pdf
- saalweachter 9y agoWell, 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.
- marcosdumay 9y agoOrbits 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.