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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

#181

Post by spaetzleesser »

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 don't know who is learning from their parents that if you work hard you'll get rich."

I read that line a lot from successful people: "I have achieved X. IF I can achieve it, you can too. Let me explain how. "

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

#182

Post by jareklupinski »

konschubert wrote: post #174
antognini wrote: post #159

Here is a link to the arXiv version of the paper: https://arxiv.org/abs/2011.00010 Incidentally, I used to work in dynamics and Hagai is great to work with. To give you a sense of him, I went to a conference on dynamics that he organized about six years ago, and he opened it with the following story: Many years ago, the philosopher Nasreddin was on his farm looking out into the distance and saw some people approachin…

I don't get it. Is it just meant to be funny or is there a deeper message?

if you have trouble telling your friends from your foes at a distance

buy binoculars

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

#183

Post by argvargc »

HWR_14 wrote: post #126
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?

As I understand it, "random and unpredictable" means impossible to measure the initial state in sufficient precision and/or computationally impossible to calculate in a reasonable amount of time. The actual underlying math is deterministic.

It seems the problem is often mis-stated - there is no calculation problem, the problem is in adequately defining/sampling the initial data.

It's maybe similar to predicting the weather - we can have all the perfect equations in the world for fluid dynamics and heat flow etc, but until we have system-invisible temperature and humidity sensors for every square millimetre of atmosphere and earth volume, we won't be able to predict the weather very accurately or very far ahead.

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

#184

Post by dandelany »

konschubert wrote: post #174
antognini wrote: post #159

Here is a link to the arXiv version of the paper: https://arxiv.org/abs/2011.00010 Incidentally, I used to work in dynamics and Hagai is great to work with. To give you a sense of him, I went to a conference on dynamics that he organized about six years ago, and he opened it with the following story: Many years ago, the philosopher Nasreddin was on his farm looking out into the distance and saw some people approachin…

I don't get it. Is it just meant to be funny or is there a deeper message?

Here’s my reading of it: when speaking about dynamical systems with several interdependent moving parts, humans are fond of asking “why” questions and looking for simple narratives in such systems where satisfying answers may not exist.

For example, imagine a three-body planetary system which exists in a pseudo-stable configuration for millions of years, until suddenly one of the planets gets slung off on a wild orbit and ejected from the system. A layman might be inclined to ask, “whoa, that’s weird, why did that happen?!” while the physicist will reply “All I can say is that planet A is where it is because of planets B & C, and B & C are where they are because of A.”

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

#185

Post by antognini »

dandelany wrote: post #184
konschubert wrote: post #174

Earlier quoted context omitted.

I don't get it. Is it just meant to be funny or is there a deeper message?

Here’s my reading of it: when speaking about dynamical systems with several interdependent moving parts, humans are fond of asking “why” questions and looking for simple narratives in such systems where satisfying answers may not exist. For example, imagine a three-body planetary system which exists in a pseudo-stable configuration for millions of years, until suddenly one of the planets gets slung off on a wild orbi…

I like that! The way I interpreted it when hearing it at the conference he was saying that we were all here at the conference because he had organized it, but he was there because we were all there to talk about our research. But the great thing about a good parable is that there are endless interpretations. :)

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

#186

Post by deltasixeight »

konschubert wrote: post #175
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…

No. We know there is a deterministic solution, even if we can't calculate it.

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. Can you do the same? No, you can't.

If not then I'm right. We don't KNOW whether it's deterministic because our BEST model is probabilistic.

We really should raise the stakes and seriousness of HN comments to prevent random uneducated people who really don't know anything from posting random comments. Like come on... HN is better than reddit but some random set of "rules" against unsubstantiated comments doesn't stop people like this guy from posting unsubstantiated comments.

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

#187

Post by graderjs »

krisoft wrote: post #121
graderjs wrote: post #119

Earlier quoted context omitted.

> Asking questions and providing answers to ones best abilities dude, they're not trying to do that there they're just trying to one up each other. Just like you're trying to do with this comment. It's the hn ape brain mind.

True! And that is why I wrote “If that was your true intention…” Thank you for quoting it! ——- Looks like you completely changed your comment. Not cool. I’m going to leave mine as it is. This is no way to behave in a discussion. Have a good day.

Haha, yes and you're behaving morally: projecting your shit under someone else's stuff as a fake excuse to attack them? That's the 'no way to behave'

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

#188

Post by kragen »

im3w1l wrote: post #52
kragen wrote: post #11

Earlier quoted context omitted.

Because three-body systems are chaotic, the fourth body can affect the motion of the other three, however small it is.

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 the temperature or how much time has passed.

It's easy to make a device that's sensitive to all three, like a glass jar partly full of water, upside down in a bowl of water, resting on a bed of gravel in the bottom of the bowl, so that some air is trapped inside the jar. The water level inside the glass jar will go up when the air pressure goes up and down when the air pressure goes down. But it will also go down when the temperature goes down and up when the temperature goes up, because the trapped air will expand and contract. And over time water will evaporate from the bowl, reducing the water level outside the jar, so over time the water level inside the jar will go down.

Usually metrology involves either reducing or eliminating these extra influences (a mercury barometer works the same way as the device described above, but is much less sensitive to temperature because it doesn't have any trapped air; and it's less sensitive to time because mercury evaporates very slowly, and the level of the mercury outside the tube is very low) or balancing them against one another so they precisely cancel out. Chaotic metrology would seem to require a different approach.

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

#189

Post by Supermancho »

simonh wrote: post #155
fahadkhan wrote: post #153

Earlier quoted context omitted.

> There's this characiture of American culture and the idea of our meritocracy But earlier > if I work hard and have a little luck, I'll get by. A little more luck and I'll be successful. A little less, and I might need to rely on my family or community. This isn't a meritocracy that you are describing

Sure it is. Hard work weights probability in your favour and gives you more opportunities. Surely that's the best anyone can ever hope for? Do you have a system in mind that makes guarantees?

A meritocracy isn't about guarantees, other than ranking is by performance not externalities. By most definitions, a meritocracy is impractical, granted. In a real-world sense, the socio-economic status of every individual on earth is primarily governed by luck/circumstance. Not to say there aren't exceptions, but there has to be an inordinate amount of "merit" AND luck to overcome the initial state, statistically. To whit, a human lifetime is more complex and complicated to navigate, than the 3 body problem.

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

#190

Post by spekcular »

deltasixeight wrote: post #186
konschubert wrote: post #175

Earlier quoted context omitted.

No. We know there is a deterministic solution, even if we can't calculate it.

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. From Wikipedia: "However, in 1912 the Finnish mathematician Karl Fritiof Sundman proved that there exists an analytic solution to the three-body problem in the form of a power series in terms of powers of t1/3. This series converges for all real t, except for initial conditions corresponding to zero angular momentum. In practice, the latter restriction is insignificant since initial conditions with zero angular momentum are rare, having Lebesgue measure zero. "

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