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> This system is completely stable—I double-checked with computer simulations. I would think that's a hilarious joke if the author didn't seem so serious.
by unit91 9y ago
> This system is completely stable—I double-checked with computer simulations.
I would think that's a hilarious joke if the author didn't seem so serious.
- d33 9y agoI 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.
- keymone 9y agothere's nothing that prevents nbody to be solvable with certain starting conditions. https://en.wikipedia.org/wiki/N-body_problem#n-body_choreography https://en.wikipedia.org/wiki/N-body_problem#n-body_choreogr...
- d33 9y ago...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 https://news.ycombinator.com/item?id=14767295
- keymone 9y ago2+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.
- ithinkso 9y agoThe 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.
- keymone 9y agoin 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.
- mabbo 9y agoI 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.
- archgoon 9y agoTo the point, it's unknown if our current solar system is stable. https://en.wikipedia.org/wiki/Stability_of_the_Solar_System https://en.wikipedia.org/wiki/Stability_of_the_Solar_System https://www.ias.edu/ideas/2011/tremaine-solar-system https://www.ias.edu/ideas/2011/tremaine-solar-system
- dsr_ 9y agoStability is an unobtainable goal if you don't put a particular timespan on it. 5-6 billion years is probably just fine.
- JoeAltmaier 9y agoSounds fair. Outside perturbations are probably likely in that timeframe.
- yummybear 9y agoUntil an extra solar asteroid entered the system and wiped out 200 civilizations, and sent the rest hurdling into intergalactic space.