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Scientists find an effective solution for the three-body problem

phys.technion.ac.il

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Re: Scientists find an effective solution for the three-body problem

#101

Post by mannerheim »

onlyrealcuzzo wrote: post #99
colechristensen wrote: post #26

Earlier quoted context omitted.

The question is what happens with a small perturbation and how does it "grow". For a two body problem, you nudge one of the bodies and it is forever off by a small amount, but your predictions into infinity require only a small adjustment to compensate. For a three body problem you nudge one of the bodies and only for a very short time do your previous predictions stay true, the change amplifies until nothing you tho…

> For a two body problem, you nudge one of the bodies and it is forever off by a small amount, but your predictions into infinity require only a small adjustment to compensate. How does this even work? Where is a place in the universe where there are only two bodies?? Where would the nudge come from if not from a third body?! A ghost?

You're taking it too literally. The 'nudge' means a change in initial conditions, and could result e.g. from measurement uncertainty, not necessarily a literal nudge.

It also doesn't necessarily matter that much if there are more than two bodies, if the gravitational influence of other bodies is small enough, then you can model as a two body problem.

Re: Scientists find an effective solution for the three-body problem

#102

Post by mynegation »

onlyrealcuzzo wrote: post #99
colechristensen wrote: post #26

Earlier quoted context omitted.

The question is what happens with a small perturbation and how does it "grow". For a two body problem, you nudge one of the bodies and it is forever off by a small amount, but your predictions into infinity require only a small adjustment to compensate. For a three body problem you nudge one of the bodies and only for a very short time do your previous predictions stay true, the change amplifies until nothing you tho…

> For a two body problem, you nudge one of the bodies and it is forever off by a small amount, but your predictions into infinity require only a small adjustment to compensate. How does this even work? Where is a place in the universe where there are only two bodies?? Where would the nudge come from if not from a third body?! A ghost?

The relative magnitude of interactions is important. The article specifically mentioned triple star system as an example. Solar system is of course many body, but (a) it has already settled into (sort of) stable configuration (b) there is one massive body and everything else revolves around it. Yes, massive bodies like gas giants have noticeable affect on other bodies, but due to the distances they tend to be in the stable territory.

Re: Scientists find an effective solution for the three-body problem

#103

Post by TuringNYC »

mwcampbell wrote: post #83
paraknight wrote: post #3

Send it over to Trisolaris!

Practically speaking though, wouldn't the Trisolarans still want to leave their home planet for one that didn't have chaotic eras?

I'm sure they want to, but fitting into an electron-sized spaceship, under their current technology would be an issue.

Re: Scientists find an effective solution for the three-body problem

#104

Post by tgv »

forgotpwd16 wrote: post #23
cyberpsybin wrote: post #9

It's an already solved problem given you set the initial conditions.

I guess this is downvoted because the initial conditions allude to numerical integration which isn't considered a proper "solution". Nevertheless, indeed the three-body (as well the n-body albeit with restrictions) has an analytic solution in form of power series. When people say it doesn't have one they mean in a closed-form. The research here isn't a solution (it doesn't allow one to find the exact state of the bod…

But a power series is not what I'd call effective, which is what the headline stresses. It's also another type of solution (a probabilistic one).

Re: Scientists find an effective solution for the three-body problem

#106

Post by nsizx »

graderjs wrote: post #95

Fun to watch HN trying to solve the three-body problem in the comment thread.

People shouldn't be allowed to ask questions or make uneducated guesses to explore and understand the problem and satisfy their curiosity. We should ask you for permission first.

Re: Scientists find an effective solution for the three-body problem

#107

Post by nine_k »

thinkski wrote: post #13

When they say motions of three bodies are random and unpredictable, I assume they mean not able to be modeled with a closed form equation? Seems like the motions would still be entirely deterministic — could still predict the locations of the bodies computationally, given your computer computes faster than reality (at least for a reality with only 3 bodies), no?

On top of theoretically computable, but highly divergent / unstable functions mentioned nearby, there are fully deterministic (non-random, pure) but non-computable functions. The simplest example is a function that answers whether a given Turing machine would stop.

Re: Scientists find an effective solution for the three-body problem

#108

Post by simonh »

ordu wrote: post #14
thinkski wrote: post #13

When they say motions of three bodies are random and unpredictable, I assume they mean not able to be modeled with a closed form equation? Seems like the motions would still be entirely deterministic — could still predict the locations of the bodies computationally, given your computer computes faster than reality (at least for a reality with only 3 bodies), no?

They would be deterministic. But they are unpredictable. Minuscule fluctuations (coming from influence of some much smaller bodies, that are not in the model, or approximations in calculations) can lead to dramatic differences in the outcome. So theoretically speaking, they are deterministic, but practically they are unpredictable.

It's got nothing to do with perturbations from additional small bodies, the problem is exactly mathematically calculating the outcome for exactly three bodies within reasonable time frames even if you assume perfect ideal knowledge about the system. It turns out this is excruciatingly hard.

The n-body problem where you add further bodies, even very small ones, is even harder.

Re: Scientists find an effective solution for the three-body problem

#109

Post by [deleted] »

nsizx wrote: post #106
graderjs wrote: post #95

Fun to watch HN trying to solve the three-body problem in the comment thread.

People shouldn't be allowed to ask questions or make uneducated guesses to explore and understand the problem and satisfy their curiosity. We should ask you for permission first.

[deleted]

Re: Scientists find an effective solution for the three-body problem

#110

Post by robot_no_419 »

nsizx wrote: post #106
graderjs wrote: post #95

Fun to watch HN trying to solve the three-body problem in the comment thread.

People shouldn't be allowed to ask questions or make uneducated guesses to explore and understand the problem and satisfy their curiosity. We should ask you for permission first.

I'd even go so far to say that plenty people on these forums have the required knowledge in physics, mathematics, and computer science to make meaningful contributions to this conversation. This is not beyond the realm of every day people, it's a pretty accessible problem for many.
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