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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

#81

Post by mxxc »

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?

there is no closed form, like you say, and the additional complexity is around ergodicity, i.e. solutions that start close to each other might end up very far from each other after a certain point. this is also an issue with computer simulations as the error might accumulate and push solutions away. in practice, given the amount of cosmological computations people do on a daily basis, including those for satellites and rockets, this might not necessarily be that big of an issue, but i don't work with that stuff on a daily basis.

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

#82

Post by Borrible »

Barrin92 wrote: post #61
Borrible wrote: post #37

Earlier quoted context omitted.

Wasn't talking to them the whole problem in the first place?

yep I was about to say, first the UFOs and now this, turn the radio beacons off already

Not to say all the other signs of earth those seamonkey tea bag aliens craving for a better future missed with their superior technologies in Alpha Centauris immediate neighborhood.

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

#84

Post by thaumasiotes »

athrowaway3z wrote: post #79
ninkendo wrote: post #77

Earlier quoted context omitted.

The motion isn’t deterministic if free will exists. Launching a rocket into space decreases earth’s rotation speed ever so slightly, which will have a small impact on the moon’s trajectory due to tidal interactions, and so on.

Please define 'free will' before using it in a sentence about determinism.

If that was a requirement, discussions of determinism would sound awfully one-sided. ;p

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

#85

Post by TheOtherHobbes »

motoboi wrote: post #49
stavros wrote: post #46

Earlier quoted context omitted.

> a common occurrence is one of the bodies being ejected. So the problem eventually solves itself?

Well, not if the ejected body contains you.

Being ejected from your model is unquestionably a solution of sorts, although it does Raise Questions.

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

#86

Post by martincmartin »

ninkendo wrote: post #77
ordu wrote: post #14

Earlier quoted context omitted.

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.

The motion isn’t deterministic if free will exists. Launching a rocket into space decreases earth’s rotation speed ever so slightly, which will have a small impact on the moon’s trajectory due to tidal interactions, and so on.

There are those who believe determinism is not only compatible with free will, but required for free will.

https://en.wikipedia.org/wiki/Compatibilism

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

#87

Post by lmilcin »

snowAbstraction wrote: post #73

The photo of Professor Hagai Perets (Left) and Ph.D. student Yonadav Barry Ginat seems to have them in their native environment: the university's Science and Math library. If you zoom you'll see the Math and Science topics listed on the card for the book shelves behind them.

Trust me, mathematicians do not sit in libraries.

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

#88

Post by Grustaf »

phreeza wrote: post #59
Grustaf wrote: post #28

Earlier quoted context omitted.

No, the fundamental difference is that the two-body problem can be solved analytically, you can write down a formula. For three bodies and up you only have numerical solutions, simulations, and they will break down over time.

The problem is that a three-body system is inherently unstable/chaotic. So even if you run a numerical simulation with the same granularity for a two-body and a three-body system, the three-body simulation will degrade much faster than the two-body system. This is unrelated to the fact that there is a closed form solution, there are many stable, non-chaotic dynamical systems that don't have a closed form solution.

Well sure. But my point was that for two bodies you don’t need to simulate at all, you can just get the answer for any point in time.

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

#89

Post by evanb »

sasaf5 wrote: post #32
Aeolun wrote: post #19

Earlier quoted context omitted.

Huh? If this is the case, wouldn’t a 2 body problem also be practically impossible to calculate? I mean, you can certainly still predict to a certain (probably high) level of accuracy, but ultimately that motion is also influenced by factors outside your model.

Better stated, the 2-body problem can be solved with a finite number of standard operations, i.e. a closed-form expression. This solution does not exist for the 3-body problem.

This is not a requirement for a system to lack chaos, nor is it a metric by which we can judge if a system DOES have chaos.

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

#90

Post by wisty »

zelphirkalt wrote: post #58
aaaaaaaaaaab wrote: post #54

Earlier quoted context omitted.

It is a chaotic system. Arbitrary small deviations in the initial conditions will result in completely different outcomes. So your simulation will eventually diverge from reality as you cannot measure the initial conditions exactly.

Nitpick + a little more thought: Isn't it more correct to say, that initially slightly different conditions might (instead of "will") result in a very much different outcome? Does chaotic mean, that two states which only differ a little must result in vastly different outcomes? I wonder whether there could be states, which are very similar and some condition drives them to converge again. Or is such a thing impossibl…

Often yes. How often happens in practice will usually depend on the size of the solution space.

A chaotic system is pretty much a random number generator, and random number generators can spit out the same number (or nearby numbers) twice (otherwise they wouldn't be random).

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