Archive for the ‘Three Body’ Category

Science Fiction Round 48: Three-Body Problems

I recently read the English translation of the best-selling science fiction novel 三体Sān Tǐ / “Three Body”, by 刘慈欣 / Liú Cíxīn / Cixin Liu, with thanks to the accomplished writer and translator Ken Liu.  The English version is styled “The Three-Body Problem”.  I enjoyed Cixin Liu’s storytelling, but I have opinions about his world-building.   A film adaptation of Three Body is slated to be released in the middle of next year (July 2016), so this seemed like a good time for a review of the book.

A note on spoilers: Three Body is the first book in a trilogy, and was originally published in 2006.  The sequels 黑暗森林 / Hēi’àn sēnlín / “Dark Forest” and 死神永生 / Sǐshén yǒngshēng / “Death’s End” were originally published in 2008 and 2010; English-language versions are scheduled for release soon.  Since my ability to read hanzi is extremely limited, I haven’t yet read the sequels myself and won’t spoil them.  But the following will spoil much of the plot of Three Body.

Cover of the original 2008 Mandarin edition. Cover art evokes the background of the Cultural Revolution, as well as alien technology.

Cover of the 2008 Mandarin edition of “Three Body”. Cover art evokes the Cultural Revolution, as well as alien technology.

Cover of the 2014 English edition. Art here is intended to evoke three-body dynamics, and also features a representation of an alien pyramidal building.

Cover of the 2014 English edition. Art here is intended to evoke three-body dynamics, and also features a virtual representation of an alien pyramidal building.

The Story

Liu tells a complex story; shifting deftly between China during the Cultural Revolution, Beijing twenty minutes into the future, and virtual-reality representations of an alien world – among other places.  The narrative is non-linear, with events in the past gradually revealed as characters in the future learn about them.  It’s an effective style.  Unscrambling the timeline, here’s what happens in Three Body:

In the late 1960’s / early 1970’s, at the height of the Cultural Revolution, the Chinese military sponsors a technology-development program that among other things quietly engages in an extensive SETI project – both passively searching for extraterrestrial radio signals and actively transmitting high-power radio beams at a large number of stars, from a facility in the Greater Khingan Mountains.  One of the astronomers assigned to this project, Ye Wenjie, is a primary character to the story.

Ye is the daughter of a professor at Tsinghua University who was beaten to death by members of the Red Guards for allegedly being a reactionary.  Ye herself is exiled to the SETI project compound, as an alternative to being imprisoned for objecting to environmental destruction caused by parts of the Third Front Movement.  Something more than eight years after starting to transmit high-power radio signals into space, Ye receives a reply, from an alien astronomer of a species and culture humans later call the Trisolarians.  As you may be able to tell from the response time, the Trisolarians are based at Alpha Centauri.

The reply is a warning from a Trisolarian dissident.  It warns that if humans continue to contact the Trisolarians, they will conquer Earth.  The Trisolarians occupy a planet around Alpha Cen in a chaotic orbit.  They seek more stable environments, and would plan to occupy Earth to do so – by sending a fleet that would be a few hundred years in route.  Ye decides that humanity’s inflicting of violence upon the environment and upon one another means that the Trisolarians would do a better job running things here, and sends out another message offering to help them.  Over the next few decades, she and a well-funded group of fellow self-declared agents for the invasion establish covert scrambled communication with the Trisolarians, to avoid other humans knowing what is happening.

The Trisolarians seek to disrupt human technological innovation, to minimize resistance to their invasion fleet when it arrives in 450 years.  They send both information to Ye’s group and artificial-intelligence emissaries, with orders to interfere with particle physics experiments and other advanced research to scramble their results.  This interference extends to massive gaslighting of scientists, and then to several murders.  Their activities eventually arouse the interest of a multi-national military intelligence coalition.  Aided by a materials scientist from Beijing and a scary chain-smoking old former-covert-ops soldier turned cop, the coalition takes down Ye’s group and learns of the pending invasion.  The Trisolarians are not amused; and will still arrive to try and destroy humanity in 450 years (setting up the plot for the sequels).

Plot Holes

The technologies that the Trisolarians use to interfere with scientists on Earth from 4.37 lightyears away are both physically impossible and such that anyone who could use them would not need to bother with conquering Earth in the first place.  Nor would they need a strong radio beacon coming off Earth to know that the planet is here and has life on it (we can do that now).

This is a fairly pervasive problem with Three Body.  Liu will encounter some part of his plot that requires a solution to a problem, but that solution doesn’t make any sense in terms of the next part of the plot.  Rachel suggests that he could have avoided some of these plot holes by being less specific.  e.g. He has a character realize that the Trisolarians are messing up the data recorded by satellites monitoring the cosmic microwave background in the 21st century – but one of the satellites he specifically names is COBE, which stopped taking data in 1993.

But several of the inconsistent things Liu has happen can’t be resolved without breaking his plot.  An example: Some readers may have noted that Alpha Cen is not visible from the Greater Khingan Mountains – like all of China north of the Yangtze, the mountains are too far north for Alpha Cen to be above the horizon.  For the transmissions to reach Alpha Cen, Liu has Ye bounce them off of the Sun.  Solar radar is a thing that is done to study the plasma in the Sun’s corona, but the real Sun is neither a perfect radio mirror nor an amplifier.  It can’t be used to make a signal transmitted from northern China detectable at Alpha Cen.  And even if it were, that wouldn’t make it possible for a message from Alpha Cen to be received in the Greater Khingans – and Liu doesn’t invoke any bouncing on that set of signals.  It is as though the mountain range is arbitrarily relocated 2000 km southward or northward depending on the part of the story.

There are a few other such things in the book.  For the rest of this review, I’m going to focus on just one particularly prominent inconsistency: how Three Body treats the three-body problem.


The three body problem in Newtonian dynamics refers to the relative motion of three point masses under the influence of gravity.  In contrast to the two-body case, there is no closed-form solution to this problem.  Liu notes this explicitly, appropriately referencing Sundman’s series solution and the various numerical integration methods that perform much more efficiently in practice.

In the story, a subfaction of the humans aware of the Trisolarians futilely tries to find better ways of solving the three-body problem, in the hope of enabling the Trisolarians to predict the chaotic variations in their planet’s climate – so that they won’t invade Earth.  I was a bit surprised that Liu did not mention the work of the Chinese-American mathematician Qiudong Wang, who developed a generalization of Sundman’s results to any number of point masses, in this part of the story.  That the mathematicians in the story fail is appropriate, but there is a more serious problem. The Trisolarian’s planet and its system do not reflect how three-body dynamics actually works.

The Trisolar system consists of three stars, on chaotic and constantly-shifting mutual orbits that have apparently been stably bound for the last several billion years – with the planet being caught up in its own entirely unpredictable orbit around them (so technically this is a four body problem).  The problem with this?

In real life, Alpha Cen, like all other triple and higher-orbit star systems more than a few tens of millions years old, is a hierarchical binary system.  Alpha Cen A and B are in a mutual elliptical orbit; which is only extremely slightly perturbed by the presence of Alpha Cen C / Proxima two light-months away.  Triple- and higher-order multiple systems that aren’t in stable hierarchical states rapidly end up in two end states: a collision between stars and, much more commonly, with at least one of the stars being ejected from the system completely at high speed.  The type case for this is the Trapezium group in the Orion Nebula, a group of young stars which has ejected several different members over the past two million years.  So the Trisolar stellar system cannot exist for any length of time.

Similarly, planets on orbits within multiple star systems that aren’t in regions where the chaotic evolution of their orbits is tightly limited are not stable for billions of years.  Part of this is because the N-body problem is inadequate as a description of planetary motion.  Stars aren’t point masses.  Planets aren’t point masses.  Gravity follows the rules of general relativity, not exactly the same as Newton’s model.  Passing stars, the galaxy, and interstellar gas clouds introduce perturbations.  Even radiation pressure forces push planets around significantly over thousands of years.  Smaller bodies get perturbed more rapidly.

Liu acknowledges this: the Trisolarian’s planet once passed close enough to a star to be tidally disrupted, pulling off a satellite.  But given how actual multi-body systems work, anything that does one such pass will nearly always either be ejected completely or do more than one such pass.  And then it either gets destroyed or goes through the same process yet again until it is no more.  The Trisolarian’s planet can’t exist for any length of time either.

This is not to say that you can’t have a planet in a triple star system.  We know of planets near double stars, triple stars, and even quadruple stars.  There have even been reports of a planet at the real-life Alpha Cen – although those have not been confirmed.  All of these planets have one of two properties: they either orbit close in to one star, or around a double star at a distance large compared to the separation between the two stars.  For example, in the quadruple-star case of PlanetHunters1: there are two pairs of binary stars orbiting over 1000 AU from one another, while the planet orbits one of the pairs with a 138.3-day orbital period as compared to the 20-day orbital period of those two stars relative to one another.  It is true that the orbits of planets in multi-star systems are perturbed by the additional stars, as are their climates.  Which such planets are potentially habitable is currently argued.  Planets on habitable orbits around each of Alpha Cen A and B may be stable, even though the two stars get as close together as the Sun and Saturn once every 79.91 years.

So if there were a habitable planet around Alpha Cen, it would not have the large orbital and climate variations that are necessary to the plot of Three Body.

Alas for Liu’s story.  It is well-written and entertaining, but it has plot holes the size of a planetary system.


If I parse this release correctly, by the first half of 2012 Three Body had sold about 40 million units in the Chinese-language markets and presumably has sold quite a few more copies since then.  For comparison, that’s equal to or somewhat more than the number of copies the first Hunger Games book has sold in the English-language markets.  That’s a big audience for science fiction.  And it explains the studio’s investing 200 million CNY / 33 million USD or so into producing the movie adaptation of Three Body.