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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

#161

Post by ineptech »

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?

Edward Lorenz summarized chaotic behavior as: "When the present determines the future, but the approximate present does not approximately determine the future."

So yes, you could predict the locations computationally to an arbitrary point in the future if you knew their starting locations and velocities with perfect precision; but in practice of course you cannot know anything's position with perfect precision, so your simulation would become inaccurate relatively quickly.

edit to add: and I believe that what this paper discusses is not a solution to the above, but rather a way of getting around it by modeling some types of three-body behavior as if it were truly random, rather than chaotically deterministic.

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

#162

Post by dclowd9901 »

jjcdtunb wrote: post #125
ksec wrote: post #111

This may be a Rant, or an unpopular opinion. Life is strange. As if God is reminding me something. It was only yesterday Overthinking [1] was submitted on HN. A little over 10 years ago many of my friends and colleagues told me to stop overthinking about things. It was causing me some stress and depression because when you start doing analysis many level deep the only conclusion is any small variance will simply caus…

> Americanism ( which also spreads to non-Americans working inside American companies ) views on the world suggest if you work hard you will get it. America is a big place. I'm seventh generation American, with a patriotic family. I wasn't raised to believe that if you work hard you WILL get it. No, it's that if you DON'T work hard, you WON'T get it. You see, success is hard work + luck. You can have luck without har…

My parents’ attitudes are very much more oriented toward hard work becoming success and that if you haven’t gotten what you wanted, it’s because you haven’t tried hard enough yet.

In a way, they’re right. I’d love a 911 GT3, and I could almost certainly get one, if only for a short period of time, and with the benefit of armed robbery.

There’s a lot of things I’ve “chosen” to consider instead of putting everything aside to chase a dream. In more concrete terms, anyone can have anything they want, but what you have to give up for it matters. And that’s something I think my parents and people like them don’t think about. Not everyone has the emotional construction, or even the ability to give up aspects of their life to achieve what they want. I think a large part of “luck” is when the time comes to make a hard decision like that, some fortunate circumstance made swallowing that pill a bit easier.

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

#163

Post by SubiculumCode »

ksec wrote: post #111

This may be a Rant, or an unpopular opinion. Life is strange. As if God is reminding me something. It was only yesterday Overthinking [1] was submitted on HN. A little over 10 years ago many of my friends and colleagues told me to stop overthinking about things. It was causing me some stress and depression because when you start doing analysis many level deep the only conclusion is any small variance will simply caus…

A rain drop forms in the sky and begins to fall. What path it takes, no one knows, but that it lands, we can surely assume.

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

#165

Post by godelski »

jjcdtunb wrote: post #125
ksec wrote: post #111

This may be a Rant, or an unpopular opinion. Life is strange. As if God is reminding me something. It was only yesterday Overthinking [1] was submitted on HN. A little over 10 years ago many of my friends and colleagues told me to stop overthinking about things. It was causing me some stress and depression because when you start doing analysis many level deep the only conclusion is any small variance will simply caus…

> Americanism ( which also spreads to non-Americans working inside American companies ) views on the world suggest if you work hard you will get it. America is a big place. I'm seventh generation American, with a patriotic family. I wasn't raised to believe that if you work hard you WILL get it. No, it's that if you DON'T work hard, you WON'T get it. You see, success is hard work + luck. You can have luck without har…

There's a saying: the harder I work, the luckier I get.

I read this as the harder you work the more you're able to take advantage of lucky moments. But those lucky moments still need to happen for you to take advantage of them. I think a lot of people don't like to admit that luck had anything to do with it because we have a culture that often suggests that it's luck or work but not some combination. While there are cases on the extreme ends of the spectrum I'm willing to bet that the vast majority are from a combination of hard work and high luck.

Veritasium did a (pretty obvious) simulation that showed those on the top end up having both high luck and hard work.[0] I think this should make sense to most people given how the simulation was run.

[0] https://youtu.be/3LopI4YeC4I

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

#167

Post by jvanderbot »

PragmaticPulp wrote: post #151
ksec wrote: post #111

This may be a Rant, or an unpopular opinion. Life is strange. As if God is reminding me something. It was only yesterday Overthinking [1] was submitted on HN. A little over 10 years ago many of my friends and colleagues told me to stop overthinking about things. It was causing me some stress and depression because when you start doing analysis many level deep the only conclusion is any small variance will simply caus…

> It was causing me some stress and depression because when you start doing analysis many level deep the only conclusion is any small variance will simply cause Chaos. With n-body simulation problems, we don’t actually observe immediate chaotic behavior following small perturbations. In fact, we can readily simulate these systems with considerable accuracy if we want to spend the compute resources. For example, simul…

You are more like a ship than a bottle in the sea. And like a ship, require maintenance, helping hands, bravery, and a destination.

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

#168

Post by Grustaf »

phreeza wrote: post #143
Grustaf wrote: post #88

Earlier quoted context omitted.

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.

The need for numerical simulations is completely unrelated to the predictability and/or stability of the system. If you have a Lyapunov exponent smaller than 0 everywhere, errors don't accumulate and you can simulate numerically for as long as you like.

It's not unrelated, but the implication only goes in one direction. If you have a closed form solution, that implies that you can model it completely forever, but sure the opposite is not true.

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

#169

Post by petercooper »

DiggyJohnson wrote: post #127
bgroat wrote: post #115

Earlier quoted context omitted.

Is there an email list where I can subscribe for information about this book/pre-order?

Not yet, but I'll start thinking about it. I've never talked to anyone about it other than close friends, I probably should share more as progress continues.

I would also be keen to follow progress on this when you reach such a point.

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

#170

Post by deltasixeight »

>So theoretically speaking, they are deterministic, but practically they are unpredictable.

The three body problem is REFERING to the ideal case where only a perfect model is considered. Within this model we don't even know the math to calculate it. So, in short, we lack a "deterministic theory" about this problem at all.

What's going on here is an assumption. We assume that an idealistic scenario will always produce the same result. But we don't actually know because we don't even have a proper model. From a certain angle what this paper is kind of saying is that this assumption is WRONG and that the underlying model of the ideal case of the three body problem IS probabilistic.

I'm not a math/physics guy but the fact that this "theory" involves probability seems sort of like the same initial cop out that came with quantum theory. It's like we can't explain mathematically why a particle behaves this way but it seems to be obeying a probability so let's make probability the basis of the theory! Problem Solved!

Men are by probability more likely to join engineering than women. Because of this probability should we make up a theory called "The fundamental theory of men and women joining engineering" that is described by a probability equation? OR is it better to find an underlying more "deterministic" explanation for why this occurs?

It may sound like I'm denigrating the probabilistic path here, but really theories like this usually only come about when it's basically impossible to come up with a deterministic version. And technically speaking we can never actually know whether the foundations of the universe are probabilistic or deterministic.

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