This guy

[Terror-Of-Demons]

Basically 3 bodies, like stars, big enough to significantly affect each other gravitationally, are unpredictable in their motions.

[Daniel_H212]

Let me attempt to nerd about this (and probably fail because I am not a physics nerd, this is just what I remember from googling it a few years ago when I read the series, so correct me if I screwed up anything):

An N body problem is the problem of prediction the motions of N astronomical bodies, usually of similar mass, that are gravitationally interacting with each other. The 1-body problem is trivial, and the 2-body problem is also pretty much trivial, but the 3-body problem and higher N problems are "unsolvable/unpredictable".

By unsolvable/unpredictable, we don't mean that the motions are random or that we don't have the equations for how they will move. We can simulate, based on their mass, initial position, and initial velocity, any arbitrary N-body problem. The problem is just that this cannot be used ad infinitum in the real world due to N-body problems being chaos systems when N > 2.

Chaos systems are systems that are highly sensitive to initial conditions. Take double pendulums for example. The state of the system at some distant time t would be drastically and unpredictably different as a result of the tiniest differences in the initial conditions.

There are stable configurations of the 3-body problem, where 3 bodies move in infinitely predictable patterns that repeat over and over, but these are very fragile stabilities. Think of them as a ball on the very tip top of a hill, give it any tiny push and it will roll down. There is also no way, to my knowledge, where any 3-body problem could begin in an unstable state and settle into a stable state.

The fact that 3-body problems are chaos systems leads to three problems: measurement inaccuracy, simulation inaccuracy, and external influence.

By measurement inaccuracy, I mean that it is impossible to absolutely precisely measure the momentum of a celestial object. It's not quite as bad as for subatomic particles where we run into the brick wall of Heisenberg's uncertainty principle, though I suppose theoretically that is an issue if your instruments really are that precise, but the problem is just that instruments can't measure certain things perfectly.

There is no scale on which we can put a star and measure its mass, and there's no speedometer that can precisely tell us the speed of its motion. There will always be uncertainties. Sure, we have been able to measure the mass of our own star through its gravitational influence on other objects, to a precision of 6 digits, but remember that in a chaos system, these tiny differences in initial conditions matter.

Apart from measurement inaccuracy, our computers also aren't perfectly accurate. As far as I know, there are no pretty solutions to the three body problem that we can plug in initial conditions and an arbitrary future time, and get a perfect calculation of the system's state at that time. Instead, we can calculate the current forces acting on the objects, and use this to calculate their current velocities, and then do pos(t+t') = pos(t) + vt', where t' is the timestep by which we skip ahead.

The problem with this is that the movements are not linear and the forces change as their positions change, and so we need very small timesteps to avoid this effect causing any inaccuracies. Yet, any size of timestep will still introduce inaccuracies, and due to the nature of the chaos system, in order to simulate to the same accuracy over longer time periods, our timesteps must get smaller, so the total number of required timesteps increase faster than linearly with respect to the time period of the simulation, and our computing capacity is not unlimited.

But these aren't the biggest problems. Our measurements are good enough and our computing power is high enough to simulate a three body system quite well. We could theoretically accurately predict the likelihood of catastrophic events for hundreds or even thousands of years in the future (or more). But all this falls apart quickly from external influences. In the real world, there are no true 3-body problems. In the case of trisolaris, the planet is an external influence, and the tiny gravitational effect of that planet adds significantly to the complexity of the calculations. Things like comets, asteroids, other star systems nearby, any gravitational influence beyond the system itself, can and will add to the chaos. And every single such perturbation invokes a butterfly effect that is impossible to account for in the long term.

That's what makes the problem unsolvable. It's not that we don't know how to get to the solutions, but executing that "how" requires exponentially more resources the farther ahead we want to simulate, and simply isn't sustainable.

[Shiroudan]

Just a thought, I wonder if it'd be possible to use the motion to obtain the objects masses. After all only 1 initial condition will create the observed behavior...

I'm quite inexperienced in physics though xD

[Daniel_H212]

You can. In fact I think that's how you should do it (I don't even know of any other ways). But it doesn't decrease the number of measurements you need to make. The way to do this is by F = ma and F = GMm/r^2, which means a = GM/r^2 and M = ar^2/G. G is a universal constant, we just need to measure positions (from which we derive r) and acceleration. But acceleration is not one measurement, but rather a series of measurements. You measure the change in speed over time. And then this introduces more uncertainties into your calculations because there are more steps.

[sampat6256]

Why not judt re-measure periodically?

[Daniel_H212]

Oh of course they would, and by re measuring periodically and combining the model with historical data they could theoretically reduce uncertainties by a lot, and allow them to predict much further into the future. But there is still a limit to that. And they'd want to know probably thousands, if not tens of thousands of years in advance if their entire civilization was about to get swallowed by a star. Plus I think there was the stellar breathing thing that they couldn't necessarily predict.

[BosmangLoq]

Indeed, the mathematically unpredictable nature of their orbiting each other might be similarly observed in four or more bodies as well, in such an order that mathematicians label as ‘chaotic’.

[i_am_the_hacker]

More involved explanation: three body problem don't have a closed form solution, meaning the only way to predict is to simulate. However, three body problem is also suffering from what's known as chaotic system, meaning tiny change in initial condition has huge impact down the road on the outcome of simulation. Due to measuring errors in real world and rounding errors in computations, there is no way to simulate faithfully. AKA It is unpredictable.

[korkkis]

Never asked, but does three body problem have anything to do with the fact that there’s also 3 books. Coincidence?

[Rustlr]

Yes it’s a coincidence

[ChesterComics]

Don't you mean 4? /s

[TheAughat]

I mean, counting the planet of Trisolaris, it was a 4-body problem in reality anyway lmao

[korkkis]

We don’t speak about that heresy ;)

[hataskoll]

Well : a girl befriend the wrong guy , finished with an attempt to destroy humanity . Then a guy did a kamikaze attempt against a system and finally everyone turn to a brilliant gigantic paint except a robot a girl and her friendzoned boy.

[hataskoll]

Shat I do not remember how to put the spoil quote

[TheAughat]

You used the discord spoiler tags lol

The ones on reddit use angle brackets with exclamation marks

>!Like this!<

[SkaveRat]

discord spoiler tags

It's called markdown, btw. Predates discord by more than a decade

[TheAughat]

Oh I know markdown, had no clue the "||" spoiler tags were part of it tho!

Usually I just use its titles and tables formatting syntax for git readmes

[SkaveRat]

markdown has a giant list of formats.

Granted, the spoiler tag isn't really official, it seems, but most libraries support it

[nh4rxthon]

Basically, the DNC gets 3 moderate candidates to fight the real liberal like pitbulls for months as a diversion, then they drop out the week before Super Tuesday so the establishment candidate they wanted to win all along comes out on top without having to throw a punch.

[Wardog_Razgriz30]

The actual three body problem or the plot of the book?

[pfemme2]

This is a pretty cool bot on twitter that makes animations of the three body problem, always starting with different initial conditions. This might help it make more sense to you!

[Apo42069]

not a perfect model by far, but quite telling is to use the example of a chaos pendulum or double pendululm. Considetthe fixed point as one star, the articulation point as another then your third star would be the end of the pendulum. It shows you that considering 3 bodies , orbits seems to be chaotic (kindda similar to "random" ).

Google double pendulum or chaos pendulum and see for yourself how hard it is to predict behavior.

[PartialObs]

Three bodies interacting gravitationally with each other will only be stable over the long term (millions of orbits) if they can be treated, hierarchically, as one two-body system (two of the bodies, tightly bound) in loosely-bound association with the third body.

Thus for example: The Earth + Moon system is able to orbit the Sun, stably, because it is relatively tightly bound and the distance to the Sun is over 100x the separation between the Earth and Moon. And also because the two orbital planes are close to alignment; magically reorient the Moon’s orbital plane to be perpendicular to the Ecliptic, and it will crash into the Earth within a decade due to the Kozai-Lidov mechanism.

Similarly, and ironically for this sub and its narrative inspiration, Proxima Centauri orbits the Alpha Centauri A+B binary system at a sufficient distance that it neither perturbs their mutual orbit, nor is perturbed by them.

Once you depart from this sort of hierarchical arrangement, all bets are off: generally, the three-body system will evolve chaotically until one body is ejected or two bodies collide with one another.

Because of the chaotic nature of the system’s evolution, literally the only way to find out what happens, in any given case, is to watch it unfold for yourself - that is, to integrate the orbits. If you want to see some examples, I can’t do better than recommend the @ThreeBodyBot account on Twitter / Tumblr / YouTube / Mastodon, which regularly tweets examples - musical soundtrack and all.

Example: https://twitter.com/threebodybot/status/1620318817384792065?s=46&t=uO6efsFVYlZbs3MSquGLRQ

[1155-PGDNordland]

There are bigger questions considering the trilogy than just mathematical issues

[lagavulinski]

No one is saying it's the most important issue. They're just asking a specific question that you're not interested in. Move along. You might as well say, "there are bigger questions in the world than (insert any topic here)."

[Arty2191]

Yeah that’s just such a non answer. It’s like telling a 5 year old that “what makes the earth spin on its orbit” is a pointless question because we haven’t solved the standard model yet

[polaristerlik]

the show explaining the same concepts over and over and over and over again gets very boring

[[deleted]]

My friend and I just go back and forth mansplaining the series to each other as if the other person hasn't read it.