[HN Gopher] Scientists find an effective solution for the three-...
___________________________________________________________________
Scientists find an effective solution for the three-body problem
Author : olvy0
Score : 291 points
Date : 2021-08-14 06:22 UTC (16 hours ago)
(HTM) web link (phys.technion.ac.il)
(TXT) w3m dump (phys.technion.ac.il)
| antognini wrote:
| 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 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 wrote:
| I don't get it. Is it just meant to be funny or is there a
| deeper message?
| dandelany wrote:
| 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."
| antognini wrote:
| 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. :)
| arvidkahl wrote:
| I 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 wrote:
| https://youtu.be/_eRRab36XLI
| jareklupinski wrote:
| if you have trouble telling your friends from your foes at a
| distance
|
| buy binoculars
| [deleted]
| snowAbstraction wrote:
| The 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 wrote:
| Trust me, mathematicians do not sit in libraries.
| archibaldJ wrote:
| they walk and wander around ;)
|
| https://jorgenveisdal.medium.com/the-mathematical-nomad-
| paul...
|
| https://medium.com/@vovakuzmenkov/poincares-
| creativity-8e31d...
| maxwells-daemon wrote:
| Fond memories of running into my math professor walking
| around campus at 3am...
| lmilcin wrote:
| I 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 wrote:
| I 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 ;)
| joaorico wrote:
| Alain Connes, Fields medalist, talks about going on walks
| while reading math books in a particular way (and on how
| a mathematician works and should read a book) [0]:
|
| "To understand any subject, above all, a mathematician
| SHOULD NOT pick up a book and read it.
|
| It is the worst error!
|
| No, a mathematician needs to look in a book, and to read
| it backwards. Then, he sees the statement of a theorem.
| And, well, he goes for a walk. And, above all, he does
| not look at the book.
|
| He says, "How the hell could I prove this?"
|
| He goes for his walk, he takes two hours ... He comes
| back and he has thought about how he would have proved
| it. He looks at the book. The proof is 10 pages long. 99%
| of the proof, pff, doesn't matter.
|
| Tak!, here's the idea!
|
| But this idea, on paper, it looks the same as everything
| else that is written. But there is a place, where this
| little thing is written, that will immediately translate
| in his brain through a complete change of mental image
| that will make the proof.
|
| So, this is how we operate. Well, at least some of us.
| Math is not learned in a book, it cannot be read from a
| book. There is something active about it, tremendously
| active.
|
| [...]
|
| It's a personal, individual work."
|
| [0] https://www.youtube.com/watch?v=9qlqVEUgdgo
| yarky wrote:
| Walking helps thinking, that is a well known fact, which
| I also learned from a mathematician who kept sharing in
| class how many problems he solved while walking his dog.
| He would always start his phrases with "while I was
| walking my dog I realized ...".
|
| There seems to be a lot of research on this topic btw.
| todd8 wrote:
| I had one famous professor, Gian-Carlo Rota, whose office
| was covered in stacks of books and journals; I believe
| that he was an editor of an AMS publication at the time.
| The next year I had a professor for a class in non-
| commutative ring theory (I sadly can't remember his name
| off the top of my head; I do remember that he was a
| pleasant and brilliant person.), his office was like a
| monk's room. There was a desk upon which rested a single
| sheet of paper with a yellow wooden pencil.
| thinkski wrote:
| 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?
| remram wrote:
| You can only do that with some error, e.g. your simulation
| needs some time step that controls the tradeoff between
| computational resources used and accuracy of the results. For
| any fixed time step, after enough time your simulation will
| completely diverge from reality.
| nine_k wrote:
| On top of theoretically computable, but highly divergent /
| unstable functions mentioned nearby, there are fully
| deterministic (non-random, pure) but non-computable functions.
| The simplest example is a function that answers whether a given
| Turing machine would stop.
| reedf1 wrote:
| Chaos is the _extreme_ dependence on initial conditions. The
| three body problem is significantly more _chaotic_ than a two
| body problem. Welcome to chaos theory!
| HWR_14 wrote:
| 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.
| argvargc wrote:
| 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.
| ordu wrote:
| 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.
| simonh wrote:
| It's got nothing to do with perturbations from additional
| small bodies, the problem is exactly mathematically
| calculating the outcome for exactly three bodies within
| reasonable time frames even if you assume perfect ideal
| knowledge about the system. It turns out this is
| excruciatingly hard.
|
| The n-body problem where you add further bodies, even very
| small ones, is even harder.
| mjburgess wrote:
| Random doesnt mean non-deterministic anyway.
|
| X is random with respect to Y, if knowing Y makes no
| difference to your predicting that X.
|
| QM systems are _indeterminate_ , they are random in the above
| sense /because/ they are indeterminate. But that isnt what
| random means.
| elcomet wrote:
| What you're describing is not randomness, it's
| independence.
|
| It's hard to define randomness. I think non-determinism is
| better than your definition.
| ninkendo wrote:
| The motion isn't deterministic if free will exists. Launching
| a rocket into space decreases earth's rotation speed ever so
| slightly, which will have a small impact on the moon's
| trajectory due to tidal interactions, and so on.
| athrowaway3z wrote:
| Please define 'free will' before using it in a sentence
| about determinism.
| thaumasiotes wrote:
| If that was a requirement, discussions of determinism
| would sound awfully one-sided. ;p
| mxxc wrote:
| that case is beyond scope of the three body problem
| martincmartin wrote:
| There are those who believe determinism is not only
| compatible with free will, but required for free will.
|
| https://en.wikipedia.org/wiki/Compatibilism
| Aeolun wrote:
| Huh? 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.
| sasaf5 wrote:
| Better stated, the 2-body problem can be solved with a
| finite number of standard operations, i.e. a closed-form
| expression. This solution does not exist for the 3-body
| problem.
| evanb wrote:
| This is not a requirement for a system to lack chaos, nor
| is it a metric by which we can judge if a system DOES
| have chaos.
| aaaaaaaaaaab wrote:
| No. A small error in the initial conditions of a 2-body
| system produces a small error in the result. In case of a
| 3-body system, a small error will result in drastically
| different outcomes. The phase space of a 2-body system is
| nice and smooth, but a 3-body system's is more like a
| fractal.
| [deleted]
| colechristensen wrote:
| 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 thought
| might happen before the nudge means anything at all, and a
| common occurrence is one of the bodies being ejected.
| onlyrealcuzzo wrote:
| > 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.
|
| How does this even work? Where is a place in the universe
| where there are only two bodies?? Where would the nudge
| come from if not from a third body?! A ghost?
| mannerheim wrote:
| You're taking it too literally. The 'nudge' means a
| change in initial conditions, and could result e.g. from
| measurement uncertainty, not necessarily a literal nudge.
|
| It also doesn't necessarily matter that much if there are
| more than two bodies, if the gravitational influence of
| other bodies is small enough, then you can model as a two
| body problem.
| mokus wrote:
| The "nudge" can also come up even with exact starting
| information. When you calculate the next step and round
| it to the nearest nanometer, you've just nudged the
| system by enough to eventually make your prediction
| worthless in the 3-body case.
| colechristensen wrote:
| You do an accounting of the nearby massive objects and
| their distances from each other, pairs of objects within
| certain bounds of mass and distance can be treated like
| there are only those two objects in the universe with the
| understanding that there will be a small error because of
| outside influences. It's an approximation, but in the
| right circumstances a very good one.
|
| Each planet and the sun can be done like this, ignoring
| all of the other planets. Each moon and its planet can be
| considered a two body system ignoring the rest of the
| moons.
|
| If you just randomly generated a bunch of massive bodies
| and pressed play, you would have few 2 body systems and a
| lot of chaos, but that's a problem that solves itself as
| the chaos results in either collisions or ejections.
| mynegation wrote:
| The relative magnitude of interactions is important. The
| article specifically mentioned triple star system as an
| example. Solar system is of course many body, but (a) it
| has already settled into (sort of) stable configuration
| (b) there is one massive body and everything else
| revolves around it. Yes, massive bodies like gas giants
| have noticeable affect on other bodies, but due to the
| distances they tend to be in the stable territory.
| stavros wrote:
| > a common occurrence is one of the bodies being ejected.
|
| So the problem eventually solves itself?
| motoboi wrote:
| Well, not if the ejected body contains you.
| TheOtherHobbes wrote:
| Being ejected from your model is unquestionably a
| solution of sorts, although it does Raise Questions.
| dnautics wrote:
| 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"?
| RhysU wrote:
| This is sometimes called "infinite sensitivity to initial
| conditions" or "deterministic chaos".
| bsf_ wrote:
| In principle - yes. Except that we can change our frame of
| reference, and treat the two body problem as a pseudo one
| body problem (the lab frame becomes the center of mass of
| one of the bodies). One cannot do this for the three body
| problem, which gives us at best a pseudo two body problem.
| alephu5 wrote:
| For a two-body problem the discrepancies between your model
| and reality increase gradually with time, but it's still
| possible to predict eclipses decades in advance with a
| precise albeit imperfect measurement of initial conditions.
|
| With a three-body problem any slight shift causes a wildly
| different trajectory, bearing no resemblance to the
| original so your measurements of the initial condition have
| to be perfect.
| ekianjo wrote:
| arent eclipses three body problems?
| nwatson wrote:
| For all practical purposes eclipses are two two-body
| problems ... Sun vs Earth-Moon pair, and Earth vs Moon.
| The scale of the Sun is so vastly larger and distances so
| great from sun to earth there's no need to do 3-body.
|
| If the three had roughly the same mass would be different
| story.
| Grustaf wrote:
| No that's not it. The two body problem has a closed,
| analytical solution, the three body one doesn't, so you
| need to simulate it. It's a fundamentally different
| approach.
| l332mn wrote:
| 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.
| Grustaf wrote:
| 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.
| chestervonwinch wrote:
| > 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
| johncolanduoni wrote:
| There are iterative methods/systems that stabilize over
| time. For example, symplectic integrators on tame
| problems oscillate lightly around the true energy of the
| system over time. The issue here is the properties of the
| underlying problem, not the set of solution methods.
| extropy wrote:
| Both of you are correct.
| Grustaf wrote:
| No, the fundamental difference is that the two-body problem
| can be solved analytically, you can write down a formula.
| For three bodies and up you only have numerical solutions,
| simulations, and they will break down over time.
| user-the-name wrote:
| That is not the issue. There are many problems that do
| not have analytical solutions, but can be approximated
| numerically to any precision you would like.
|
| The issue with the three-body problem is that it is
| chaotic, meaning any error will eventually grow to take
| over the entire solution, making prediction impossible,
| even in theory. Every chaotic system lacks an analytical
| solution, but not every system without an analytical
| solution is chaotic.
| bottled_poe wrote:
| I think this is accurate and I don't understand why you
| are being downvoted.
| phreeza wrote:
| 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.
| MontyCarloHall wrote:
| Conversely, there are also extremely simple closed-form
| recurrence relations that exhibit chaotic behavior, e.g.
| the logistic map.
| acjohnson55 wrote:
| Would a linear-feedback shift register be an example of a
| recurrence relation that exhibits chaotic behavior?
| phreeza wrote:
| True but a recurrence relationship is not the same as a
| closed form solution. The differential equation for a
| three body problem is also very simple.
| MontyCarloHall wrote:
| Of course. My point was just that you can evaluate a
| recurrence relation exactly (i.e. with zero numerical
| error) and still get chaotic behavior. OP's mistaken
| point was that the three body problem's chaos arises
| solely from numerical error during simulation, which is
| untrue.
| Grustaf wrote:
| 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.
| phreeza wrote:
| 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.
| Grustaf wrote:
| 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.
| kergonath wrote:
| I think the issue was more with "random" than with
| "unpredictable".
| deltasixeight wrote:
| >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 wrote:
| No. We know there is a deterministic solution, even if we
| can't calculate it.
| deltasixeight wrote:
| 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.
| spekcular wrote:
| 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://si
| tes.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. "
| deltasixeight wrote:
| 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.
| kergonath wrote:
| > 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.
|
| We can prove that something has some properties even if
| we don't know everything about it. Newton's second law in
| a many-body system is (in the case of Newtonian gravity)
| basically a system of independent second-order ODEs. We
| know a thing or two about these beasts.
|
| Anyway, let me try something (without LaTeX, so I
| apologise in advance for the notation).
|
| Let's think about a many-body system (following Newtonian
| mechanics, and interacting via Newtonian gravity) from
| the point of view of its positions-velocities phase
| space. The solution is not deterministic if there are
| points (i.e., sets of positions and velocities for all
| the particles) that are part of at least two
| trajectories.
|
| Let's assume we are looking at such a point. The forces F
| and all their derivatives dF/dr are the same along all
| trajectories, because they depend only on the positions
| (which are identical). The velocities and the positions
| are the same because it is the same point in the phase
| space.
|
| The third derivatives of the positions w.r.t time are
| also identical (d^3r/dt^3 = 1/m dF/dt, and dF/dt = dF/dr
| dr/dt, and the dr/dt are identical).
|
| You can go on to the n-th derivative, n being arbitrary
| large (d^4 r/dt^4 is a function of only dF/dr, dr/dt, d^2
| r/dt^2 and d^2 F/dr^2, all of which are identical along
| both trajectories, etc).
|
| So, it means that both trajectories have the same
| position in the phase space, and all their derivatives
| are identical, i.e., both trajectories are identical. So
| it is deterministic (there is no point in the phase space
| that belongs to more than one trajectory).
|
| It is somewhat related to Liouville's theorem.
| spekcular wrote:
| "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."
|
| Why would it be necessary to have a closed form solution
| to know that the solution is deterministic? By the first
| reference in my previous comment, two identical initial
| conditions lead to identical time evolutions. That is
| literally the definition of determinism.
| deltasixeight wrote:
| No look at my wording more carefully. You are
| misinterpreting it. I said we don't know if a "closed
| form solution" is deterministic because we don't even
| know if there is a "closed form solution."
|
| I also said that you CAN prove determinism to me by
| finding a closed form solution that is deterministic. I
| never said you needed to nor did I say that was the only
| way.
|
| Your examples are for special cases. Can you prove it to
| me that for N-bodies and all possible initial conditions
| that all solutions are deterministic?
| robocat wrote:
| Unfortunately your aggressiveness and rudeness make your
| comment of lower quality than the one you are answering -
| read https://news.ycombinator.com/newsguidelines.html to
| see what site rules you are breaking as well. Betting
| doesn't make your argument truer, it only points to your
| own irrationality.
|
| Disclaimer: I am no mathematician nor physicist.
|
| However the intuition is that any set of equations must
| be deterministic, unless they refer to a non-
| deterministic function like random(x).
|
| Should you wish to argue that the three body problem can
| generate true randomness, I think it is your
| responsibility to refer to links that support your
| argument. I would expect an argument to refer to
| mathematical concepts and have nothing to do with the
| three body problem in particular. I suspect it verges on
| tautological that if you can define equations then it is
| deterministic.
| deltasixeight wrote:
| >Unfortunately your aggressiveness and rudeness make your
| comment of lower quality than the one you are answering -
| read https://news.ycombinator.com/newsguidelines.html to
| see what site rules you are breaking as well. Betting
| doesn't make your argument truer, it only points to your
| own irrationality.
|
| Did you not notice the person who replied to me literally
| just commented a single sentence and left it at that?
| It's called an unsubstantiated comment and it is also
| addressed int the rules you link here:
| https://news.ycombinator.com/newsguidelines.html
|
| I simply made a bet. There's no aggression here. I like
| to back up my claims with more seriousness rather then
| single line comments. Also claiming my post is rude and
| aggressive when it isn't is in itself rude. I just make
| claims and I offer to back up my claim with money. Why? I
| would offer a proof but no proof is known because my
| answer is: We don't know.
|
| >Should you wish to argue that the three body problem can
| generate true randomness, I think it is your
| responsibility to refer to links that support your
| argument
|
| Except this is not my wish and I never stated such. My
| statement is that we don't know if it's deterministic. My
| offer is that I put money on the fact we don't have any
| definitive proof we do know.
|
| >However the intuition is that any set of equations must
| be deterministic,
|
| Intuition is just hand waving. There is nothing
| definitive here I'm sorry. My offer stands to the first
| person that can give me a proof, $1000. That includes you
| even though I found the first paragraph of your post
| dishonest and rude. You called me irrational, that's
| practically an insult and a flagrant violation of the
| rules. I did no such violation.
|
| What's going on here is not that I'm violating the rules.
| But that you're biased. You disagree with me so your bias
| senses aggression and violations of rules on my side even
| though I did no such thing. In fact your bias blinds you
| to your own violation. You called me irrational. Might as
| well call me stupid. Same personal insult just disguised
| with smarter wording.
| kergonath wrote:
| 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.
| deltasixeight wrote:
| >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?
| [deleted]
| bo0tzz wrote:
| While we can simulate three (or more) bodies' gravitational
| interaction, the chaoticness means that any error in initial
| state, no matter how small, will be hugely amplified. This
| makes long-term predictions untractable
| ineptech wrote:
| 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.
| m3kw9 wrote:
| 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?
| akomtu wrote:
| The initial conditions are usually known up to a small epsilon
| in practice. I guess this initial error grows exponentially
| with time, hence "unpredictability".
| DiogenesKynikos wrote:
| This exponential increase in error is described by the
| Lyapunov exponent of the system:
| https://en.wikipedia.org/wiki/Lyapunov_exponent
| mxxc wrote:
| there is no closed form, like you say, and the additional
| complexity is around ergodicity, i.e. solutions that start
| close to each other might end up very far from each other after
| a certain point. this is also an issue with computer
| simulations as the error might accumulate and push solutions
| away. in practice, given the amount of cosmological
| computations people do on a daily basis, including those for
| satellites and rockets, this might not necessarily be that big
| of an issue, but i don't work with that stuff on a daily basis.
| bad_username wrote:
| There are cases in classical mechanics that fail to be
| deterministic.
|
| https://physics.stackexchange.com/questions/403574/what-situ...
| cankut_orakcal wrote:
| Please 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.
| nsoonhui wrote:
| Coming 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?
| ksec wrote:
| 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
| 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
| jjcdtunb wrote:
| > 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
| hard work, but you have to have a lot more of it to get rich
| and you still might squander it if you didn't earn it because
| you won't know what to do with it if you get it by pure chance
|
| You can have hard work without luck, too, like most of the
| folks in flyover country have. They know they aren't getting
| rich, they're just trying to get by.
|
| But you can't have real success without both hard work and
| luck. You might win the lottery with just luck, but you won't
| wind up running a successful enterprise.
|
| I don't know who is learning from their parents that if you
| work hard you'll get rich. Mine taught me that 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. That's what they're for.
|
| There's this characiture of American culture and the idea of
| our meritocracy that I see represented here and in media and it
| doesn't ring true to me -- I would be interested to know if the
| people who think luck is the only necessary component for
| success are Coastal or Flyover, and how much luck they've had
|
| I know for myself, I've needed both work and luck. Without the
| work, I never would've been in a position to take the
| opportunities offered by luck.
| prairiedogg wrote:
| > No, it's that if you DON'T work hard, you WON'T get it.
|
| Depends on how much you start with.
| [deleted]
| godelski wrote:
| 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
| PragmaticPulp wrote:
| > 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.
| WalterBright wrote:
| > 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.
|
| On the other hand, accepting responsibility for results is
| empowering, because it means one can be successful.
|
| I don't see anything happy about deciding one is a hapless
| victim of others.
| smolder wrote:
| The comfort in shifting your locus of control outward
| comes from relieving the shame of failure, not from being
| an overall positive experience. In fact, it's common for
| people to both take credit for their successes while
| blaming their failures on external factors to relieve the
| shame.
| WalterBright wrote:
| Blaming failure on others or external factors doesn't
| lead to success. It leads to bitterness and resentment.
| thayne wrote:
| > I don't know who is learning from their parents that if you
| work hard you'll get rich
|
| Rich people. It's the result of survivor bias, "I worked hard
| and got rich, so if you work hard you can get rich too." And
| they discount the "luck". And it is reinforced by the fact
| that being born to wealthy, well connected parents is really
| luck.
| kergonath wrote:
| > 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.
| dclowd9901 wrote:
| 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.
| spaetzleesser wrote:
| "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. "
| fahadkhan wrote:
| > 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
| simonh wrote:
| 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?
| WalterBright wrote:
| Right. Successful people make their own luck.
| Supermancho wrote:
| 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.
| bigfudge wrote:
| 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.
| robocat wrote:
| 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.
| WalterBright wrote:
| > 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.
|
| Reminds me of when the CEO of GM said "What's good for
| General Motors is good for the country." Except he didn't say
| that. The press did a hatchet job on him by reporting it that
| way. The actual quote is "what was good for our country was
| good for General Motors, and vice versa."
|
| https://en.wikipedia.org/wiki/Charles_Erwin_Wilson#General_M.
| ..
| PaulDavisThe1st wrote:
| you think that making the "and vice versa" explicit ("...
| and what's good for General Motors is good for our
| country") is a hatchet job?
| WalterBright wrote:
| Leaving off crucial parts of the statement makes it a
| hatchet job.
|
| Just like if someone says "more or less" and the
| journalist leaves out the "or less".
| PaulDavisThe1st wrote:
| You believe that the first clause somehow balances the
| second?
|
| When this (partial) quote is used, it's generally in a
| context where the first clause is arguably irrelevant. I
| don't think it's like your "more or less" analogy. There
| are not many corporations that fail to benefit when the
| country does well, so the first clause is broadly agreed
| upon. The second clause, however, is controversial, and
| has implications that are quite independent of the first
| clause.
|
| "It will be sunny today, and tomorrow there will be snow"
| - if you hear this weather forecast at 13:00 on a sunny
| day, the first clause is close to information-free, but
| the second is very striking.
|
| So it is with the quote from the head of GM.
| WalterBright wrote:
| > You believe that the first clause somehow balances the
| second?
|
| It doesn't matter if I believe it or not. It's a hatchet
| job to selectively misquote people to pursue the
| journalist's agenda.
| sgregnt wrote:
| To me it is not surprising that an interviewer would not be
| satisfied if you attribute your success to luck alone. What can
| you contribute to a new work place if you rely purely on luck?
| It is important to identify how you were in a position to take
| advantage of the lucky circumstances that you had...
|
| My two cents: A well thought out design process tries to
| augment luck with a controlled progress: where you try to move
| towards your goals in a systematic, more controlled, way so the
| final outcome is less dependent on luck but more dependent on
| your ability to properly adjust and execute your design plan.
| It might be that luck was more important than the process in
| your case, but that hard to build on, and more importantly, to
| make any learnings for the future, it still good to analyze how
| the process could be made better, how you could better take
| advantage of the lucky circumstances you had.
| DiggyJohnson wrote:
| I 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.
| nathanvanfleet wrote:
| That's actually pretty interesting.
| wincy wrote:
| Ugh I think back to my server-first raid boss kills in wow,
| my giant space battles in EVE Online, my lasting relationship
| trauma from being "catfished" before it was even a word on
| Second Life, and wish I'd just gone to college or something
| instead of spending my teens and 20s playing MMOs. What a
| terrible trap these things are.
| bgroat wrote:
| Is there an email list where I can subscribe for information
| about this book/pre-order?
| DiggyJohnson wrote:
| 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.
| petercooper wrote:
| I would also be keen to follow progress on this when you
| reach such a point.
| ghoward wrote:
| I think it's great that you're not hyping it, and hope
| you don't until it's close to ready.
|
| That said, even though I am not an MMORPG player, I'd be
| interested in seeing it.
| PragmaticPulp wrote:
| > 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, simulating our own solar system with far more than 3
| bodies in play can be done with a high degree of accuracy to
| timescales far beyond our lifetimes.
|
| However, the n-body problem isn't a good analogy for your sense
| of personal agency anyway. You aren't a chunk of rock floating
| helplessly through space. You are a human being who can take
| action to influence your own trajectory. You can apply pressure
| and course correct in a feedback loop, unlike a planet hurling
| through the solar system.
|
| That doesn't mean you can influence everything, but it it does
| mean that it's wrong to assume that your life is chaotic or
| that nothing you do matters. (FWIW, The latter feeling is a
| very classic, and erroneous, thought pattern present in
| depressive disorders. Correcting that misconception is a core
| principle of CBT therapy).
|
| You are not a planet hurtling helplessly through space for
| billions of years. You're more like a satellite being launched
| optimistically into the right general area, but it still has to
| use the limited amount of thruster energy onboard to push
| itself into the right place. It doesn't always work exactly as
| planned, but not using the thrusters at all would assure
| failure.
| jvanderbot wrote:
| You are more like a ship than a bottle in the sea. And like a
| ship, require maintenance, helping hands, bravery, and a
| destination.
| function_seven wrote:
| I think you'd like Ted Chiang's short story "Anxiety is the
| Dizziness of Freedom"
|
| Touches on these themes and really made me think about the
| overlap of chaos and ("macro"?)determinism.
|
| https://onezero.medium.com/anxiety-is-the-dizziness-of-freed...
| hippari wrote:
| 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.
| m3kw9 wrote:
| If you think about it, the universe did compute the answer it
| just takes time to get there.
| PragmaticPulp wrote:
| > 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.
| WalterBright wrote:
| > if you work hard you will get it
|
| That's a misunderstanding. It's working hard _on the right
| things_. Working hard digging a hole then filling it up again
| will never lead to success.
|
| As for luck, the idea is to put yourself in a position where
| luck can find you. For example, you'll never meet the partner
| of your dreams by never leaving the house.
| Borrible wrote:
| >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.
| SubiculumCode wrote:
| 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.
| antonzabirko wrote:
| Why is this impactful? Isnt this already established that you can
| predict random walks with probability?
| forgotpwd16 wrote:
| Probably its application in the specific problem.
| ThinBold wrote:
| 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.
| graderjs wrote:
| Fun to watch HN trying to solve the three-body problem in the
| comment thread.
| krisoft wrote:
| That'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.
| graderjs wrote:
| > 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.
| krisoft wrote:
| 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.
| [deleted]
| graderjs wrote:
| 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'
| nsizx wrote:
| People 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]
| robot_no_419 wrote:
| I'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.
| graderjs wrote:
| You think that's there? There's no desire to control. It's
| fun to watch. Funny though that you projected your stuff onto
| it...
| [deleted]
| [deleted]
| justmedep wrote:
| xxx
| CogitoCogito wrote:
| Why weren't they impressed?
| [deleted]
| phkahler wrote:
| I'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.
| f6v wrote:
| Are Trisolarians happy now?
| rootusrootus wrote:
| As 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.
| bpodgursky wrote:
| Yes, they are throwing a party in Australia. Everyone is
| invited.
| taneq wrote:
| I just got to that bit, fun times.
| numpad0 wrote:
| Does that mean we finally get to know how they look like?
| Borrible wrote:
| Here you go:
|
| https://www.mentalfloss.com/article/56755/16-amazing-
| facts-a...
| MaanuAir wrote:
| In 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.
| midrus wrote:
| I 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...
| krdl wrote:
| Daleks with a strobe light on top.
| bhay wrote:
| For me, I pictured them as the water aliens from Futurama's
| "My Three Suns".
| paraknight wrote:
| Send it over to Trisolaris!
| Borrible wrote:
| Wasn't talking to them the whole problem in the first place?
| Barrin92 wrote:
| yep I was about to say, first the UFOs and now this, turn the
| radio beacons off already
| Borrible wrote:
| Not to say all the other signs of earth those seamonkey tea
| bag aliens craving for a better future missed with their
| superior technologies in Alpha Centauris immediate
| neighborhood.
| pkdpic_y9k wrote:
| They're gonna feel so silly when they get all the way here to
| kill us and realize we solved their silly little problem and
| they have to turn right back around and go home. The looks on
| their translucent non-existent face things...
| WJW wrote:
| We should probably get started on an analytical problem to
| the whole dark forest problem thing too.
| mwcampbell wrote:
| Practically speaking though, wouldn't the Trisolarans still
| want to leave their home planet for one that didn't have
| chaotic eras?
| TuringNYC wrote:
| I'm sure they want to, but fitting into an electron-sized
| spaceship, under their current technology would be an issue.
| reedf1 wrote:
| Much to my pedantic horror upon reading, they don't need the
| solution to a three body problem, but a four body problem!
| [deleted]
| mastersummoner wrote:
| Well, did we ever learn whether there were other planets in
| the system? It's been a minute and it's slipping my mind.
|
| I really loved the entire trilogy though. Each book had a
| very different vibe and addressed a completely different
| topic/problem.
| SonicScrub wrote:
| It's been a while since I've read it, but I seem to recall
| that there were other planets, but they either got ejected
| from the system, or fell into one of the stars.
| guerrilla wrote:
| You 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 wrote:
| Because three-body systems are chaotic, the fourth body
| _can_ affect the motion of the other three, however small
| it is.
| im3w1l wrote:
| Does this mean that you could you use a three body system
| as a measurement device?
| kragen wrote:
| 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.
| im3w1l wrote:
| > 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.
| simonh wrote:
| Not 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.
| forgotpwd16 wrote:
| Not sure what the discussion is about, but the restricted
| approximation only works for "insignificant" masses (e.g. a
| moon if talking about two big planets and a star). And even
| then for "short" time periods (a few million years). In
| larger scales even that mass will (I assume you've heard of
| the butterfly effect) play role.
| thomasz wrote:
| https://en.wikipedia.org/wiki/The_Three-
| Body_Problem_(novel)
| guerrilla wrote:
| tl;dr three suns, one planet
| mypastself wrote:
| Now if only we could find a way around the sophon block.
| Borrible wrote:
| Thats easy, a sophon is just a quantum mechanical plot hole
| that evaporates instantanely with measurement.
|
| Just look very closely.
| howenterprisey wrote:
| Is 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.
| ko27 wrote:
| How 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?
| db48x wrote:
| We 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 wrote:
| One 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 wrote:
| It 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.
| zelphirkalt wrote:
| Nitpick + a little more thought: Isn't it more correct to
| say, that initially slightly different conditions might
| (instead of "will") result in a very much different outcome?
| Does chaotic mean, that two states which only differ a little
| must result in vastly different outcomes? I wonder whether
| there could be states, which are very similar and some
| condition drives them to converge again. Or is such a thing
| impossible?
| aaaaaaaaaaab wrote:
| Indeed, there can be islands of stability in the phase
| space of chaotical systems.
| wisty wrote:
| Often yes. How often happens in practice will usually
| depend on the size of the solution space.
|
| A chaotic system is pretty much a random number generator,
| and random number generators can spit out the same number
| (or nearby numbers) twice (otherwise they wouldn't be
| random).
| jjgreen wrote:
| Not to answer your question, but you may be interested to
| know that chaotic systems can often be effectively
| controlled by small perturbations:
| https://en.wikipedia.org/wiki/Control_of_chaos
| [deleted]
| dekhn wrote:
| we can simulate the solar system to very high accuracy a few
| hundred years into the future.
|
| https://www.nature.com/articles/nphys728
| amelius wrote:
| The 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.
| anonymousiam wrote:
| Apparently also solved by AI less than two years ago.
|
| https://www.livescience.com/ai-solves-three-body-problem-fas...
| isoprophlex wrote:
| Weren'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
| em-bee wrote:
| the 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 wrote:
| It's an already solved problem given you set the initial
| conditions.
| forgotpwd16 wrote:
| I 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 wrote:
| But 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).
| thayne wrote:
| > 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 wrote:
| It's true even with arbitrarily good measurements when you get
| to the level of quantum mechanics.
| amluto wrote:
| If 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.
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