Archive for August, 2015

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.

Science Fiction Round 47: Asteroid Stories

Earlier this year, I got a recommendation to read Joan Vinge’s Heaven Chronicles, since it had been given a review as “the best asteroid story ever written”.  I haven’t read every asteroid-themed science fiction story ever written, and what is “best” is not well-defined.  But the stories were a pretty good read.

I’ll be focusing on the setting and world-building, rather than the detailed plot, but some spoilers do show up in the following.

Cover of the "Heaven Chronicles" Paperback.

This scene does appear in the book.  Kind of.  The attacking ships in the actual story are chemical rockets that were never designed to be flown in atmosphere (i.e. no wings or streamlining), and they use missiles rather than whatever makes those beams.  At least the gas giant Discus looks more or less right.


The events of the two stories in the Heaven Chronicles book, “Legacy” and “The Outcasts of Heaven Belt”, take place in a many-centuries-distant future, in a planetary system around a star that has been named Heaven.  Although there is a fair bit of backstory to “Outcasts” takes place at another planetary system called Morningside, there isn’t any detailed discussion of what motivated humans to colonize space or of what has happened in the solar system – mentions of Earth are limited to characters reading books from “the Old World”.

Human settlement in the Heaven system focused on an asteroid belt around the star – the Heaven Belt.  This makes sense given the setup of the system: Two inner terrestrial planets, one of which is too hot to live on and one of which is only somewhat more habitable than Mars (there is just enough oxygen from local biology that you wouldn’t suffocate in the first couple of hours).  If you’re in the business of traveling across interstellar space, a resource-rich asteroid belt is perhaps more attractive than not-very-enjoyable planets.  Further out from Heaven, humans also settle the moons of Discus; a large gas giant; and asteroids in Discus’ leading and trailing Trojan Points.  With all of these resources, in conveniently-shallow gravity wells, the Heaven Belt became extremely populous and technologically adept – and it was well-known for being so among the various other human colonies.

Then, for reasons not thoroughly explained in the book, there was a war around Heaven.  Rocks were run into one another; habitats were blown to vacuum; and the resulting destruction of hardware and interruption of supply chains caused nearly-total collapse of civilization around Heaven.  All of the action of the book takes place more than a century After The End, when there are three main factions of survivors:

  • Lansing – formerly the capital of the entire Heaven Belt.  Kept a population going only because it had large enough parks and gardens under transparent shells.  No longer has infrastructure or technical skill to provide reliable radiation shielding, and the rock is starting to run short of water…
  • The Demarchy – a loosely-governed direct democracy, spread across one of Discus’ Trojan points, which retains the most technical skill (e.g. reliable nuclear-electric-propulsion).
  • The Grand Harmony – a totalitarian state covering Discus’s rings and moons.  Only has chemical rockets, which it supplies by mining ice from the moons.

The three factions are fighting with one another; for salvage from the Belt, for what technological hardware the Demarchy is able to manufacture, for ice and refined fuel and water and air from the Grand Harmony.  Then the starship Ranger arrives from Morningside, with orders to trade with the wealthy Heaven Belt.

Plot ensues.

A Couple of Cool Bits of The Setting

1. These stories respect orbital mechanics.  The large distances between the Trojan clouds and Discus, and the large and variable distances between both and the different rock piles of the Belt are key aspects of the plot.  Vinge worked out the relative travel times assuming constant-thrust rockets and minimal orbital motion while the ships are en route, which isn’t perfect, but it’s good to have a story that recognizes how big and constantly-shifting planetary systems are.  And it’s also nice that the lightspeed limit is carefully respected, both for communications and for Ranger traveling several lightyears.

2. In post-war Heaven, there are very few non-human animals.  Life-support is expensive, and it is hard to maintain a stable population of more than one species.  We see people pay extremely large sums for a pet chameleon and a tank of goldfish; and the crew of Ranger briefly poses as a party from Lansing that has traveled to the Demarchy to trade a cat for years’ worth of water and fuel.  Correspondingly, food around Heaven is vegetarian – lots of sealed containers of pasta, tofu, and soymilk on Demarchy ships.  We don’t see the fish breeder or the vitamin-supplement bacterial vats, but I’m willing to allow Vinge to hide those in corners.

3. Advocacy of gender equality.  The societies of the factions at Heaven are pretty horrifically sexist, and this is portrayed as the bad thing that it is.  And Captain Betha Torgussen of the Ranger is well-motivated and complex character who has no patience for sexist nonsense.

A Couple of Holes In The Worldbuilding

1. Dry Trojan Asteroids.  A lot of the conflicts between the different factions at Heaven are based around the Demarchy having a near-monopoly on nuclear technology (Lansing has a few nuclear-electric ships, which leak unhealthy amounts of radiation), while the icy moons of Discus give the Grand Harmony a near-monopoly on water and other volatiles.  The problem with this?  In the solar system, the larger objects in both the outer asteroid belt and the Jupiter Trojans contain a great deal of water.

It may be possible to have icy moons around a gas giant and for that gas giant to have non-icy Trojan clouds with some pattern of planetary migration in the early history of a planetary system, with the icy small bodies originally in the system getting scattered out.  I would have to do a bunch of detailed dynamical simulations to say.  So I’m not sure what I should think of Vinge’s choice here.

2. Morningside.  This place, seen only in the backstory for the Ranger’s crew, is a tidally-locked habitable planet around a red dwarf star.  Planets in the nominal habitable zones of low-mass stars are indeed expected to become tidally locked.  What isn’t clear is if such planets will be habitable – even in the ring right on the starward side of the terminator, where the Morningsiders live.  I can’t really fault Vinge on this one, given that she was writing circa. 1980 and scientists are still arguing about it now.

3. Interstellar Radio.  The crew of Ranger had originally planned to go to a third stellar system, to help a struggling colony there.  When they got a radio call over lightyears that things were doing better there, they changed their plan and launched from Morningside towards Heaven – planning to trade with the wealthy Heaven Belt for useful high-tech gear and come back to Morningside.

See the problem?  Morningside has communication with several different human colonies, as it should, and obviously knows about human presence in the Heaven system.  But they haven’t had any recent communication from Heaven – since well before the war, and the distances are such that signals sent from Heaven long after the war would have reached Morningside before the ship left.  Perhaps it makes sense that interstellar communications would not have been maintained during the collapse at Heaven.  But the fact of Heaven’s having dropped off of the interstellar radio network means that the Morningsiders should know that something very bad may have happened at Heaven, and should not necessarily expect a peaceful and wealthy culture to be waiting for them.

I don’t think this last bit makes the stories Vinge wanted to tell unsalvageable.  But the Ranger‘s crew should have been a bit more cautious and a bit less taken by surprise when The Grand Harmony started attacking them.

Science Fiction Round 46: Homestuck

2015/08/02 Leave a comment

Homestuck is a notable and popular webcomic.  (Here’s the TVTropes page, which may help explaining… stuff.)

It is very complicated.  So complicated, I don’t think I can even do a plot summary justice at this point.  (It’s also very long, and despite having been reading it for over a month, I still haven’t gone through the entire archive.)

I quote the comic:


If you enjoy complex plot, time travel, significant meta, as well as clever flash graphics and rampant destruction of the fourth wall, you may find this comic fun.

(Although, I should add that some parts may not be a good idea for someone who’s epileptic and reacts to flashing lights.)

There are spoilers below, of course, but… there’s so much complexity that if you start reading from the beginning, I suspect that it will be hard to figure out how stuff is spoiled.

This is a thing from Homestuck. From earlier in the story, so it's less of a spoiler. Nonetheless, I'm not even going to bother explaining, beyond yes, those are meteors, and I'm not even sure whether that's supposed to be Skaia in the middle, or just the teleport out thing.

This is a thing from Homestuck.
From earlier in the story, so it’s less of a spoiler.
Nonetheless, I’m not even going to bother explaining, beyond yes, those are meteors, and I’m not even sure whether that’s supposed to be Skaia in the middle, or just the teleport out thing.


These go up to eleven, and then some.

Video game mechanics that impact reality are only the start.  Teleportation and time travel show up fairly early on, even if you don’t initially realize that they’re there.  Then come the aliens, who were actually there all along, and the parallel realities, and universes spawning universes in turn.

As I said, it’s complicated.

That being said, the comic does try to be consistent.  For instance, there is some primary reality that must happen.  Time travel thus either invokes stable time-loops, which are self-consistent (and well planned in the context of the story), or result in “doomed” time-lines, in which all ends in failure, and thus cannot be “real.”

And then… the Great Retcon happens.  (That’s not a term in the story, but the name seems appropriate.)  The primary timeline is overwritten in a way that was previously thought impossible, touching on events far, far earlier in the story, changing them in subtle ways, to prevent a terrible distaster later on.

The one character who initially attempts to explain that mess uses only one word:


Although, I will note that there is one good indicator of “shenanigans” or wibbley-wobbley time travel stuff incoming: If too many important characters die, there’s probably going to be a reset or a jump back from the failed timeline.

Naturally, this is filled with way too much nonsense (including various back-and-forth as to whether magic is real) to even think about trying to treat it as if it had some basis in science.

At least light-speed limits get a nod in passing while all the laws of reality as we know it are warped beyond recognition.

Scale of Epic

The scale of epic spins like a top, whirling from childhood troubles and birthday parties to multiverse spanning doom and back again.

For the most part, the story does a good job of taking you along for the ride.  However, some of the low-epic items — teenage angsting and silly little pointless jokes — get to be a little too much in some sections.

An Explanation for the Human Aliens

At least, sort of.

This includes the rumored trolls, as well as the cherubs that appear later in the story.

In this case, the “human alien” trolls came first.  They created our universe in a way that it essentially inherited its trait from ours, result in our planet being populated by bizarre hornless trolls with monochromatic blood.  There are also some cultural things we borrow from the trolls, such as cotton candy, which are explained in this way.

As for the cherubs, well… let’s just not even get started.