What is the three-body problem anyway?
What is the three-body problem anyway?
Netflix’s highly anticipated 3 Body Problem hit our screens in March amid a fanfare of publicity. But what is the scientific problem both the series is named for?
The long awaited western adaptation of Liu Cixin’s epic Sci-Fi trilogy hit our screens last week amid a fanfare of publicity. The literary trilogy on which The 3 Body Problem series is based, known as the Remembrance of Earth’s Past (of which The three-body problem is the first book), count Barak Obama and George RR Martin among a long list of dedicated fans. Showrunners David Benioff and DB Weiss (of Game of Thrones fame) were acutely aware from the start that they had a lot to live up to. The first series, featuring significant divergences from the books, has thus far divided critics. The original trilogy belongs to the hard SF subgenre of science fiction, characterised by the authors’ attention to scientific detail. The adaptation, you may be pleased to hear, is softer but still crammed with scientific ideas.
The TV series focusses on a group of five 30-somethings, known as the “Oxford Five”, who all studied under the same professor at the University of Oxford. Some of the five have gone on to become scientists themselves (a post-doctoral physics researcher, a founder and chief scientific officer of a nano-tech company, and a theoretical physics academic), one has become a school physics teacher and another is now a snack-food entrepreneur. Scientific credentials abound.
The crux of the story is that members of an alien race (the Trisolarans or San-Ti Ren) are headed to Earth in order to colonise it. Through intergalactic communication, the travellers are attempting to intimidate scientists here on Earth in order to slow down our rapid technological advancement, thus making us easier to conquer. They employ all sorts of advanced technologies to soften Earth up for the taking.
But why are they so hell-bent on coming and taking over our planet in the first place? This is where the three-body problem comes in. Bodies, in this context, is a scientific byword for planets, moons, suns or any other massive astronomical object. The extra-terrestrials’ home planet is situated in a solar system with not one, but three suns (hence their name in the English translation of the book – the Trisolarans). This three-sun system can be highly unstable, making conditions extremely difficult for the majority of life on the planet, hence the desire to travel across the universe in order to inhabit our relatively stable solar system.
The motion of two bodies under gravity is a well-studied problem. In our seemingly straightforward solar system, the earth’s rotation around the sun can be modelled as a two body system with a regular orbiting period lasting roughly 365.24 days – one solar year. Similarly the moon rotates around the Earth approximately every 27.3 days – another stable, effective-two-body system.
Way back in 1687, in his famous scientific treatise Principia Mathematica, Sir Isaac Newton gave us his Universal Law of Gravitation – describing the gravitational forces exerted by one body on another. He was even able to solve the resulting equations for a two-body system exactly. This meant that Newton, armed with his two-body solution, could, in theory, predict the positions of the planets, moons and comets of the solar system way into the future.
But Newton didn’t know about chaos. Newton’s two-body solution was only ever an approximation to the real solar system. In general, the influence of the smaller bodies on the larger cannot be completely ignored. Instead of a two-body problem, our solar system instead comprises what is known as an n-body problem. Such problems cannot be solved, in general, using traditional mathematical techniques to give a nice closed-form solution. Worse than that, the trajectories predicted by such systems allow for chaos.
In the mathematical sense (as opposed to the commonly understood usage to mean disarray and disorganisation), chaos is often characterised by what mathematicians refer to as sensitive dependence on initial conditions. As I argue in How to Expect the Unexpected – my recent book about predicting the future - this means that the behaviour of two otherwise identical chaotic systems, initiated with an extremely similar (but not exactly identical) initial set-up, will eventually diverge from each other if we watch their evolution for long enough.
Although the laws Newton devised (and, more recently, the theory of general relativity for more accurate calculations) can indeed be used to give seemingly accurate predictions of the future configuration of our solar system, the motions of these celestial bodies are actually chaotic. This planetary chaos, however, only becomes apparent on relatively long timescales – a chaos-horizon of the order of tens to hundreds of millions of years. Knowing the current positions of the planets to a good degree of precision will allow us to predict their positions accurately for a few million years, but eventually, after a long time, a planet might be found on completely the opposite side of the solar system to where today’s calculations would locate it. This isn’t because of any randomness in the dynamics of the planets – their motion is well described by Newton’s laws – but a result of the fact that the motion of three or more celestial bodies can be a chaotic system.
So while the equations governing the motion of two bodies can be solved exactly and the observed motion will stay close to the predicted solutions, even in the absence of precise initial data, the motion of more than two bodies can be subject to chaos and inherent unpredictability. The simplest such set up exhibiting these properties is a three-body system. The three bodies of the TV series are the three relatively massive suns of the trisolar system – the original home of the interstellar refugees known in the series as the San Ti Ren (which means “Three-body people” in Mandarin). The motion of the suns (and the planets subject to their gravity) is inherently chaotic. The planets in the system could be swallowed up by one of the suns or spat out of the system all together.
To communicate this somewhat complex scientific idea to the audience, the members of the focal Oxford Five group of scientists play a virtual reality video game. Different levels of the ultra-realistic game see the participants pitched into different historical human civilisations that are all seemingly subject to the whims of a trisolar system. As the game progresses, some of history’s more famous scientists take on the challenge of informing that level’s civilisations’ ‘leaders’ (ranging from Pope Gregory to Kubla Kahn) how long periods of relative stability will last for and how long the intervening chaotic periods will endure. One scene sees Isaac Newton team up with Alan Turing to solve Newton’s Universal Law of Gravitation on a human realisation of one of Turing’s computing machines.
[Watch Jin, one of the Oxford Five, trying to convince Pope Gregory of her three body theory in a ‘middle-ages’ level of the VR video game].
Sadly, for Newton and Turing, their resulting predictions are off the mark, which leads to their, and the entire simulated civilisation’s, abrupt end. Appreciating that the San-Ti will never have much luck with predicting (and even less chance of controlling) the chaotic trajectories their planet is subject to, the Oxford Five gamers eventually come to the conclusion that the San-Ti themselves have already reached – that the San-Ti must abandon their planet in order to save their people.
Through the VR game scenarios, we come to realise that the titular three-body problem of the Netflix series – the chaotic nature of the unsolvable mathematical conundrum of the trisolar system - is the very reason why the San-Ti have left their home planet to restart their civilisation on Earth. The three body problem is, then, the root cause of all the drama that subsequently plays out throughout the rest of the series (and potentially the next two series the show’s creators have planned). How it all pans out: the destiny of the Oxford Five; the future of civilisation on Earth as we know it; the survival of the San-Ti; – you’ll have to watch the series to find out.
This is adapted from my BBC Future article.
Interesting article, I had no idea about this problem of the three bodies, I had not even imagined it, I am reading it more carefully because in stellar fields I did not imagine that this problem could occur.
Good article, to understand more about the cosmos.
It's not a bad show, aside from the fact there's not actually much science in it, the "genius" Oxford physicists look and act more like instagram influencers than scientists, and the "once in a generation" astrophysicist of the group rarely says anything that a mildly curious undergrad couldn't parrot (and which I heard myself, more or less, 20+ years ago)..but it's not really about science, more like how terrible the cultural revolution was, which is good for a western audience, since most people are ignorant of Chinese history and how insane it's been.