22 ms·
Scientists find an effective solution for the three-body problem
- f6v 5y agoAre Trisolarians happy now?
- bpodgursky 5y agoYes, they are throwing a party in Australia. Everyone is invited.
- numpad0 5y agoDoes that mean we finally get to know how they look like?
- midrus 5y agoI always imagined them as some kind of "plants", given how they're described to replicate/combine and how they're dried up and stored and later rehydrated...
- MaanuAir 5y agoIn The Redemption of Time, Baoshu offers his view. It’s “only” a fan fiction, albeit approved by Liu Cixin. It nonetheless gives a nice — and as expected — unexpected description of them.
- bhay 5y agoFor me, I pictured them as the water aliens from Futurama's "My Three Suns".
- krdl 5y agoDaleks with a strobe light on top.
- Borrible 5y agoHere you go: https://www.mentalfloss.com/article/56755/16-amazing-facts-about-sea-monkeys https://www.mentalfloss.com/article/56755/16-amazing-facts-a...
- taneq 5y agoI just got to that bit, fun times.
- rootusrootus 5y agoAs someone who just finished the first book in the trilogy and started on the second book yesterday, this is the comment I came here to see.
- paraknight 5y agoSend it over to Trisolaris!
- reedf1 5y agoMuch to my pedantic horror upon reading, they don't need the solution to a three body problem, but a four body problem!
- guerrilla 5y agoYou sure about that? The fourth body, being so small, can't really effect the motion of the other three; however if you have the evolution of the first three then you can determine the motion of the fourth.
- kragen 5y agoBecause three-body systems are chaotic, the fourth body can affect the motion of the other three, however small it is.
- im3w1l 5y agoDoes this mean that you could you use a three body system as a measurement device?
- simonh 5y agoNot really because they're already so chaotic you couldn't be sure what divergences from simulation were inherent and which were due to external perturbation.
- kragen 5y agoI'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.
- howenterprisey 5y agoIs it just me, or do the graphs (page 12 and onward) not match up too well? Note that I totally don't know what I'm looking at.
- isoprophlex 5y agoWeren't there already several solutions known? Wikipedia seems to think so. I find it hard to see if there's anything here that makes this different from the several cases mentioned on wikipedia. The linked paper was too dense for me, sadly... https://en.m.wikipedia.org/wiki/Three-body_problem https://en.m.wikipedia.org/wiki/Three-body_problem
- em-bee 5y agothe wikipedia page lists several solutions for special cases and a general solution, which is unusable. the article talks about an effective solution, which would mark a major step forward.
- cyberpsybin 5y agoIt's an already solved problem given you set the initial conditions.
- forgotpwd16 5y agoI guess this is downvoted because the initial conditions allude to numerical integration which isn't considered a proper "solution". Nevertheless, indeed the three-body (as well the n-body albeit with restrictions) has an analytic solution in form of power series. When people say it doesn't have one they mean in a closed-form. The research here isn't a solution (it doesn't allow one to find the exact state of the bodies at some specific later time) but rather a stochastic predictor of the behavior of the system.
- tgv 5y agoBut a power series is not what I'd call effective, which is what the headline stresses. It's also another type of solution (a probabilistic one).
- deleted 5y ago[deleted]
- thinkski 5y agoWhen 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?
- ordu 5y agoThey 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.
- Aeolun 5y agoHuh? 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.
- deleted 5y ago[deleted]
- colechristensen 5y agoThe 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 thought might happen before the nudge means anything at all, and a common occurrence is one of the bodies being ejected.
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- antonzabirko 5y agoWhy is this impactful? Isnt this already established that you can predict random walks with probability?
- forgotpwd16 5y agoProbably its application in the specific problem.
- mypastself 5y agoNow if only we could find a way around the sophon block.
- Borrible 5y agoThats easy, a sophon is just a quantum mechanical plot hole that evaporates instantanely with measurement. Just look very closely.
- nsoonhui 5y agoComing from a non-physics background, I would like to know how would this help us in predicting the future trajectory of a three-body system? How does it improve over the current solution techniques?
- ko27 5y agoHow good are we at predicting three body movement today with our computers? This is the question I could never find an answer too. Can we do it real time, or few years into the future? Can we do it accurately, to an arbitrary precision? Or is it always fuzzy with statistical outcomes?
- amelius 5y agoThe system is chaotic so there is a strong dependence on the initial conditions. I suppose that if you don't know these precisely, then at some point even the best computer simulation can't help you much.
- db48x 5y agoWe can do it accurately, to any precision you care to pay for. Since n-body gravitation is a chaotic system, getting more precise predictions requires more precise measurements of the current state of the solar system. When it’s not possible to measure things more precisely, we instead run many simulations with small random perturbations in the current state, then classify the simulations to get probabilities.
- Y_Y 5y agoOne way to deal with these kinds of issues is to express your initial conditions as intervals (or even distributions) in the sense that you include the a range of possible values, rather than the most probable one (which is normally implicitly done). So if you measure the earth to be (6±1)e24 kg, then you work with something that looks like [5,7]e24 kg i.e. the segment of the number line corresponding to the possible physical realities that led to your measurement. You'll get a range of different outcomes in the end, and their relative probabilities given your priors. You can do this exactly for some systems, but usually you'll do some monte carlo and hope it's valid. This is similar to classical (linear) error propagation where you carry around an "uncertainty", but chaotic systems don't generally allow you to make the assumption of narrow Gaussians used there.
- aaaaaaaaaaab 5y agoIt 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.
- cankut_orakcal 5y agoPlease saw off the head of Mr. Cankut Orakcal. You can stop the coronavirus pandemic, the next 9/11 or financial crisis. Decapitate on sight as needed.
- justmedep 5y agoxxx
- CogitoCogito 5y agoWhy weren't they impressed?
- deleted 5y ago[deleted]
- snowAbstraction 5y agoThe 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.
- lmilcin 5y agoTrust me, mathematicians do not sit in libraries.
- archibaldJ 5y agothey walk and wander around ;) https://jorgenveisdal.medium.com/the-mathematical-nomad-paul-erd%C5%91s-3163b70a2863 https://jorgenveisdal.medium.com/the-mathematical-nomad-paul... https://medium.com/@vovakuzmenkov/poincares-creativity-8e31d5031529 https://medium.com/@vovakuzmenkov/poincares-creativity-8e31d...
- lmilcin 5y agoI am sure that there is at least one mathematician who likes to sit in libraries. But in general there is nothing for a mathematician to do in a library. It is not like you need access to large number of hard to get books. And if you need access to a book, you probably need a lot of time with that book. That is if you even need books at all. Even when I studied theoretical math I wouldn't use books at all. Problems tend to be easily formulated. Once I understood the problem I would walk around, lie on the couch, try stuff on the whiteboard or in my notepad, run experiments on Matlab, meet with friends to discuss the problem over coffee or beer and so on. I don't remember spending time in a library or hearing about anybody spending time in a library.
- archibaldJ 5y agoI was looking around but couldn't find the piece my prof sent me 5 years ago. It was a piece from a mathematician's diary about walking and coming up with proofs. There is something about a changing enviroment and being on the move that's very fascinating to me. I guess that one mathematician who likes to sit in libraries probably sits there just for sitting there ;)
- graderjs 5y agoFun to watch HN trying to solve the three-body problem in the comment thread.
- nsizx 5y agoPeople shouldn't be allowed to ask questions or make uneducated guesses to explore and understand the problem and satisfy their curiosity. We should ask you for permission first.
- deleted 5y ago[deleted]
- robot_no_419 5y agoI'd even go so far to say that plenty people on these forums have the required knowledge in physics, mathematics, and computer science to make meaningful contributions to this conversation. This is not beyond the realm of every day people, it's a pretty accessible problem for many.
- deleted 5y ago[deleted]
- graderjs 5y agoYou think that's there? There's no desire to control. It's fun to watch. Funny though that you projected your stuff onto it...
- krisoft 5y agoThat’s not what I see. I see people, many of whom are not experts in math or physics, discussing the topic. There are many smart questions, and there are also some which are less so. Your comment insinuates, but does not state, that this is wrong somehow. If that was your true intention then you are both smug and wrong. Science is not something you should put in a glass case, only to be handled by ordained priests in the appropriate manner. Asking questions and providing answers to ones best abilities is how it is best interacted with. If you know better, that is amazing. If you see wrong answers: correct them. If you see misleading questions: explain why they are so. Just don’t be smug, nothing ever got better by that.
- deleted 5y ago[deleted]
- ksec 5y agoThis 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 cause Chaos. I look it up on the internet and that was the first time I learn about three body problem, Chaos theory, and the much more widely known butterfly effect. I wish I was taught about this in school or told a lot sooner. To me it is much more about life than it is to maths or physics. Where everything could start out as deterministic, and yet the small difference made end results unpredictable. Over time it also evolved or taught me another concept, many many things or solutions in the world are somehow counter-intuitive. Then I had a few successful project under my belt, but when I was asked in a Job interview I always attribute to "luck" more than anything else. Which happens to be a word HR and many people hate. Americanism ( which also spreads to non-Americans working inside American companies ) views on the world suggest if you work hard you will get it. I wish that was the case, but there were hundreds if not thousands of known moving parts. And possibly thousands of other unknown unknown. It worked. We worked hard. And it worked. It was everyone involved and lots of luck. I was only a small part of it. I am sure those who interview me are all pretty smart. May be they should try to solve the three body problem. [1] https://news.ycombinator.com/item?id=28158435 https://news.ycombinator.com/item?id=28158435
- DiggyJohnson 5y agoI agree. I’m writing a book about why people play MMORPGs, and you just got at the heart of (part of one of my) theses.
- bgroat 5y agoIs there an email list where I can subscribe for information about this book/pre-order?
- DiggyJohnson 5y agoNot 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.
- thayne 5y ago> one cannot simply specify the system evolution over long time-scales. While practically true, this isn't technically correct. If you knew the masses, velocities, and location with infinite precision and could perform all operations with infinite precision, (also assuming no external interaction and quantum mechanics doesn't come into it), you could know the state of the system for long time periods. The problem is we can't measure things that accurately.
- beervirus 5y agoIt’s true even with arbitrarily good measurements when you get to the level of quantum mechanics.
- amluto 5y agoIf you know the initial wave function (which you can’t measure, but you could in principal choose and set up three bodies accordingly), then quantum mechanics is deterministic. If you throw the standard model in, you get a mess, though.
- antognini 5y agoHere is a link to the arXiv version of the paper: https://arxiv.org/abs/2011.00010 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 approaching. He had heard that there were bandits in the area and became afraid that they would come, beat him, and steal all his things. So Nasreddin ran away. As he ran, he came to a graveyard, and there he found an open grave. In case the bandits followed him, he decided to take off all his clothes, get in the grave, and pretend to be dead. It turned out that the men were not bandits, but were Nasreddin's friends. They saw him run off and wondered where he was going and so followed him. As they were walking through the graveyard, they came upon the open grave and saw Nasreddin lying there naked. So they asked him, "Nasreddin, why are you lying in this grave with all your clothes off?" Nasreddin opened his eyes and saw it was his friends, and replied, "My friends, there are some questions which have no answers. All I can tell you is that I am here because of you, and you are here because of me."
- konschubert 5y agoI don't get it. Is it just meant to be funny or is there a deeper message?
- arvidkahl 5y agoI think this might be about the interdependency of these actions. Both lead to each other. None would happen without the other. Wrapped in a funny story.
- OnlineGladiator 5y agohttps://youtu.be/_eRRab36XLI https://youtu.be/_eRRab36XLI
- jareklupinski 5y agoif you have trouble telling your friends from your foes at a distance buy binoculars
- anonymousiam 5y agoApparently also solved by AI less than two years ago. https://www.livescience.com/ai-solves-three-body-problem-fast.html https://www.livescience.com/ai-solves-three-body-problem-fas...
- deltasixeight 5y ago>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.
- konschubert 5y agoNo. We know there is a deterministic solution, even if we can't calculate it.
- deltasixeight 5y agoProve 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.
- phkahler 5y agoI'd like to see this extended slightly to give a half-life based on the masses or similar. Another interesting 3-body problem is the quarks in a proton or neutron. These can be critically stable with the resulting magnetic field adding more stability. But physics as a field has truly abandoned all mechanical models in favor or purely statistical ones.
- ThinBold 5y agoWhile 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.
- timoth3y 5y agoPopular belief, and This paper, imply that the three-body problem is unsolvable. The authors mention Poincaré's work demonstrating this. However, they don't mention Sundman's work in the early 1900's proving that the n-body problem can be solved as a converging power-series. Sundman's solution is correct, but the series converges very slowly and is impractical. Since an analytic solution was found over 100 years ago, why are we still debating whether one exists?
- PostThisTooFast 5y agoThe solution? Don't get involved in three-ways. Someone always gets jealous.