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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

#141

Post by dnautics »

stavros wrote: post #46
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…

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

Yes, but but also the problem really is: "given some initial condition space, can we estimate the likelihood of ejection (how many conditions in the condition space eject) in X timeframe"?

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

#142

Post by PragmaticPulp »

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…

> 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.

Well said. I think the common misconception comes from reducing these wisdoms into aphorisms that are short, but easily misunderstood. Any adult who has lived more than a few years in the real world quickly understands that hard work doesn’t guarantee success, but that success isn’t going to fall in your lap without putting in work.

The online discourse has become particularly bad, with the pendulum swinging between extremes of “You can do anything if you follow your dreams” to the opposite of “Nothing you do matters because it’s all blind luck”.

The latter, cynical mindset has become particularly popular as a way of dismissing or downplaying the success of others. I can’t count how many times I’ve heard people try to attribute Jeff Bezo’s success to that one time he was lucky enough to receive a loan from his family. Yes, it was a lucky break, but it should be obvious that something like receiving a loan from one’s family doesn’t automatically predispose someone to lucking into building a trillion dollar company. Yet there’s a growing contingent of people who want to believe that Jeff Bezos tripped and fell and landed in the founder seat of a successful company by pure luck.

I think the truth is that a lot of people, especially younger people still finding their way, are insecure about their own success or place in life. It can be extremely comforting to surround yourself with explanations that nothing is actually within your control or that others’ success or happiness is the result of randomness. I think this is why we see the oft-repeated trope (on HN especially) that people who post happy photos on social media must actually be secretly sad and miserable behind the scenes: It’s a convenient excuse to downplay the happiness and success of others.

Ignore the extremes. Accept that success isn’t guaranteed. Know that luck is a factor, but it’s not the only factor. Hard work is your lever to maximize the cards you’ve been dealt. We’re all dealt different cards, but it still comes down to your own actions in leveraging the hand you’ve been dealt.

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

#143

Post by phreeza »

Grustaf wrote: post #88
phreeza wrote: post #59

Earlier quoted context omitted.

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.

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.

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

#144

Post by chestervonwinch »

Grustaf wrote: post #72
l332mn wrote: post #45

Earlier quoted context omitted.

That's not really the issue. The three body problem does have an analytical solution in the form of a power series, but the problem is that it converges so slowly to be of any practical use.

It is though, if you don’t have a closed form solution you need to use an iterative process to calculate the positions, meaning errors will accrue over time. For a closed form solution that wouldn’t be the case. Thanks for mentioning the existence of an analytical solution at all though, I wasn't aware of that.

> meaning errors will accrue over time

This is not universally true. Error behavior is a function of the particular problem, the algorithm used to approximate its solution, and the properties of input data. A large subtopic of numerical analysis is concerned with this kind of stuff. See [1] or [2] to get a flavor.

[1]: https://en.wikipedia.org/wiki/Numerical_stability

[2]: https://en.wikipedia.org/wiki/Lax_equivalence_theorem

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

#145

Post by hippari »

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…

Lots of classes function are infeasible to compute, but they're deterministic nevertheless. The whole universe might not have enough computational power to give you the answers.

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

#146

Post by PragmaticPulp »

hippari wrote: post #145
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…

Lots of classes function are infeasible to compute, but they're deterministic nevertheless. The whole universe might not have enough computational power to give you the answers.

> Lots of classes function are infeasible to compute, but they're deterministic nevertheless.

Exactly, and it also depends on the timescale and precision you're looking for.

It should be obvious that planets in our own solar system aren't showing up at unpredictable locations after a few years, even though our solar system has significantly more than 3 bodies in orbit.

The chaotic behavior in these systems shows up eventually but it's a mistake to think that it's chaotic from the start. We can, and do, predict these systems quite accurately around the starting conditions and time.

The philosophical mistake in the OP's comment is equating a hands-off chaotic system (n-body problem) with a system that has many feedback loops (a person's life). Planets orbiting in space can't take action to change their trajectories. Humans navigating their lives can and do take actions to change their trajectories.

Humans can make moves to correct their own course. Planets cannot. Equating the two is a misunderstanding of personal agency.

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

#147

Post by bigfudge »

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…

Interestingly though, when asked Americans rate luck as much less important in financial success than other cultures. Euro countries in particular are more comfortable attributing a higher fraction of their success to luck than those in the US. And by asked I mean a reasonable well designed study… I can’t find the ref just now but will post if I do when home again.

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

#148

Post by Borrible »

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…

>but when I was asked in a Job interview I always attribute to "luck" more than anything else

Reframe that to recognizing potential and realizing it with great success.

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

#149

Post by m3kw9 »

hippari wrote: post #145
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…

Lots of classes function are infeasible to compute, but they're deterministic nevertheless. The whole universe might not have enough computational power to give you the answers.

If you think about it, the universe did compute the answer it just takes time to get there.

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

#150

Post by m3kw9 »

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?

If you freeze each point in time , isn’t the next minute step deterministic? Every time you freeze, you would have all the motion vectors to calculate the next moment, if you expand that using a lot of computation power, ca you solve it that way?
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