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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

#191

Post by [deleted] »

prairiedogg wrote: post #132
jjcdtunb wrote: post #125

Earlier quoted context omitted.

> 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…

> No, it's that if you DON'T work hard, you WON'T get it. Depends on how much you start with.

[deleted]

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

#192

Post by kergonath »

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…

> No, it's that if you DON'T work hard, you WON'T get it.

There are plenty of born-rich counter examples. New-rich counter examples as well (see Bitcoin millionaires). Frankly, this is just as false as the other one.

Never mind the fact that “working hard” depends quite a lot on the beholder. For example, I would challenge a lot of those self-declared gritty, hard-working ideologists (such as Bezos and quite a few armchair billionaires) to live a year as a minimum-wage single mother in a city.

In any case, there are lots more hard-working poor than hard-working rich, regardless of how you define hardness. So it’s about as valuable as “all the winners played the lottery”, i.e., amusing to say but not really a good way of living.

Anyway, my feeling is that successive people are very good at gaslighting the others to justify their wealth, and that America has a workaholism problem.

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

#193

Post by kergonath »

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.

I think the issue was more with “random” than with “unpredictable”.

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

#194

Post by kergonath »

deltasixeight wrote: post #170

>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…

We can have these problems simply with classical mechanics’ equations of motion (Newton, Lagrange, Hamilton, whatever). These equations are deterministic, there is no doubt about this. We just don’t have an analytical form.

We know that exactly the same initial conditions will lead to the exact same trajectory. What we also know is that the tiniest error will make the trajectories diverge exponentially. It is still deterministic.

AFAICT, their random walk idea is not in the trajectories themselves, but in the sampling of the possible trajectories to assign them a statistical weight, a bit like we do commonly in statistical Physics.

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

#195

Post by [deleted] »

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.

[deleted]

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

#196

Post by deltasixeight »

spekcular wrote: post #190
deltasixeight wrote: post #186

Earlier quoted context omitted.

Prove it. I guarantee you 100% you don't know how and you can't ever prove it. You are completely and utterly wrong and you don't know what you're talking about. That is a fact. In fact I'm willing to put money on it. $1000 over venmo to you, a random stranger. You down? Give me a formal and correct proof that if a solution exists and that it is deterministic and I swear I'll venmo $1000 to whatever address you wish.…

You think Newtonian physics is non-deterministic? I haven't checked but I think existence and uniqueness for the classical three body problem likely follows from standard theorems on ODEs. If you can articulate why this is not the case, please do. edit: Yes, see section 2.1 of this term paper: https://sites.math.washington.edu/~morrow/336_13/papers/pete... . In fact, more is known: the solution exists and is analytic…

I didn't say that.

For the three body problem we don't know the closed form solution under Newtonian physics. So if we don't know it, then a closed solution may not even exist. If we don't know whether a closed form solution exists then how can we even know if it's deterministic.

You can prove determinism by finding me a solution that's closed and deterministic.

My answer is the same as stated: we don't know, and that the claim that we do know, is completely wrong.

>In fact, more is known: the solution exists and is analytic

These are special cases, under special conditions. A general solution is not actually known. We don't know. We are only assuming that it's deterministic. Also the solution you provided is analytic not closed.

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

#197

Post by deltasixeight »

kergonath wrote: post #194
deltasixeight wrote: post #170

>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…

We can have these problems simply with classical mechanics’ equations of motion (Newton, Lagrange, Hamilton, whatever). These equations are deterministic, there is no doubt about this. We just don’t have an analytical form. We know that exactly the same initial conditions will lead to the exact same trajectory. What we also know is that the tiniest error will make the trajectories diverge exponentially. It is still d…

>We know that exactly the same initial conditions will lead to the exact same trajectory.

Do we have a proof of this? Or is it that we just assume this?

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

#198

Post by im3w1l »

kragen wrote: post #188
im3w1l wrote: post #52

Earlier quoted context omitted.

Does this mean that you could you use a three body system as a measurement device?

I'm not sure. Measurement devices are designed to be very sensitive to some things and very insensitive to others; for example, you want a clock to be sensitive to how much time has passed but not what the temperature or air pressure are; you want a thermometer to be sensitive to the temperature but not how much time has passed or the air pressure; and you want a barometer to be sensitive to the air pressure but not…

> very sensitive to some things and very insensitive to others

Wow, phrased like that it sure sounds obvious, and yet somehow I never thought about it.

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

#199

Post by robocat »

bigfudge wrote: post #147
jjcdtunb wrote: post #125

Earlier quoted context omitted.

> 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.

It makes perfect sense to have an irrational belief in hard work.

You are likely to have more success if you believe in work. Certainly believing that 100% of outcomes is luck seems like a bad strategy.

At the level of a society then average beliefs matter. I find some less successful countries seem to obsess over the role of external influences, fate, god, and chance.

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

#200

Post by ThinBold »

While the tone sounds like a university webpage advertising its scholars' results, this does seem to be an interesting viewpoint. (Unless similar viewpoints have been proposed before.)

This also reminds me of the QR iteration, where you loose track of the matrix entries very quickly (after 2 or 3 steps into the iteration), but in the end the diagonal does converge to the eigenvalues.

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