The Science of Discworld II

by Terry Pratchett

  Agreed, this is not a sensible way to model the behaviour of a cat. But it does make it clear that the usual physicists’ rhetoric about quantum mechanics being ‘fundamental’ is at best true in a philosophical sense. It’s not fundamental to our understanding of the cat, although it might be fundamental to the cat.

  Despite these difficulties, cats generally manage to behave like cats, and in particular they discover their own futures by living them. Down on the philosophical level, again, this may be because the universe is a lot better at solving Schrödinger’s equation than we are, and because it doesn’t need a description of the quantum wavefunction of the cat: it’s already got the cat, which is its own quantum wavefunction from this point of view.

  Let’s accept that, even though it’s rather likely that the universe doesn’t propagate a cat into its future by applying anything that corresponds to Schrödinger’s equation. The equation is a human model, not the reality. But even if Schrödinger’s equation is what the universe ‘really’ does – and more so if it’s not – there’s no way that we limited humans can follow the ‘calculation’ step by step. There are too many steps. What interests us about cats occurs on the system level: things like purring, catching mice, drinking milk, getting stuck in the catflap. Schrödinger’s equation doesn’t help us understand those phenomena.

  When the logical chain that leads from an entity-level description of a complex system to system-level behaviour is far too complicated for any human being to follow it, that behaviour is said to be an emergent property of the complex system, or just to be ‘emergent’. A cat drinking milk is an emergent property of Schrödinger’s equation applied to the subatomic particles that make up the cat. And the milk, and the saucer … and the kitchen floor, and …

  One way to predict the future is to cheat. This method has many advantages. It works. You can test it, so that makes it scientific. Lots of people will believe the evidence of their own eyes, unaware that eyes tell lies and you’ll never catch a competent charlatan in the act of cheating.

  The wizards got Shakespeare right, aside – at a late stage – from the minor matter of sex. When it comes to a baby’s sex, the Grand Master of Foretelling the Future was ‘Prince Monolulu’. He was a West African who wore very impressive tribal gear and haunted (in a very material sense) the markets in the East End of London in the 1950s. Prince Monolulu would accost pregnant women with the cry ‘I will tell you the sex of your baby, money back guarantee!’ Many ladies fell for this ploy, and paid a shilling, then about a fiftieth of one week’s wages.

  Level One of the trick is that random guesses would guarantee the Prince 50 per cent of the money, but he was much more cunning than that. He improved the scheme to Level Two by writing the prophecy on a note, putting it into an envelope, and getting the sucker to sign across the seal. When it turned out that the anticipated John was really Joan, or Joan was John, the few who bothered to return to reclaim their money found that, on opening their envelope, it contained a correct prediction. They didn’t get their money back, because Prince Monolulu insisted that what was in the envelope was what he had originally told them; the sucker must have remembered it wrong. In reality, the envelope always contained the opposite prediction to the verbal one.

  History is a complex system; its entities are people, its rules of interaction are the complicated ways in which human beings behave towards each other. We don’t know enough sociology to write down effective rules at this entity level. But even if we did, the system-level phenomena, and the system-level rules that govern them, would almost certainly be emergent properties. So the rule that propagates the state of the entire system one step into the future is not something we can write down. It is an emergent dynamic.

  When the system-level dynamic is emergent, then even the system itself does not ‘know’ where it is going. The only way to find out is to let the system run and see what happens. You have to allow the system to make up its own future as it goes along. In principle only one future is possible, but there is no short cut that lets you predict what will happen before the system itself gets there and we all find out. This behaviour is typical of complex systems with emergent dynamics. In particular, it is typical of human history and of biological evolution. And cats.

  Biologists learned long ago not to trust evolutionary explanations in which the evolving organisms ‘knew’ what they were trying to achieve. Explanations like ‘the elephant evolved a long trunk in order to suck up water without bending down’. The objectionable item here is not the reason why the elephant’s trunk is long (though, of course, that can be debated): it is the phrase ‘in order to’. This endows elephants with evolutionary prescience, and suggests (wrongly) that they can somehow choose the direction in which they evolve. All this is obvious nonsense, so it’s not sensible to have a theory that attributes purpose to elephant evolution.

  Unfortunately, a dynamic looks remarkably like purpose. If elephant evolution follows a dynamic, then it looks as if the end result is predetermined, in which case the system ‘knows’ in advance what it ought to be doing. The individual elephants need not be conscious of their objective, but the system in some sense has to be. That would be a good argument against a dynamic description if the evolutionary dynamic for elephants was something we could prescribe ahead of time. However, if that dynamic is emergent, then the system itself, along with the elephants, can find out where it’s headed only by going there and discovering where it gets to.

  The same goes for history. Being able to put a name to a historical period only after it’s happened looks remarkably like what you’d observe if there is a historical dynamic, but it is emergent.

  This far into the discussion, it may seem that an emergent dynamic is no better than no dynamic at all. Our task now is to convince you that this is not so. The reason is that although an emergent dynamic cannot be deduced, in complete logical detail, from entity-level rules, it is still a dynamic. It has its own patterns and regularities, and it may be possible to work with those directly.

  Exactly this is going on when a historian says something like ‘Croesus the Unprepared was a rich but weak king who never maintained a sufficiently large army. It was therefore inevitable that his kingdom would be overrun by the neighbouring Pictogoths, and his treasury would be plundered’. This kind of story proposes a system-level rule, a historical pattern, which can sometimes be compelling. We can question how scientific such stories are, because it is always easy to be wise after the event. But in this case the story generalises: rich weak kings are asking to be invaded by mean, poor barbarians. And that’s a prediction, wisdom before the event, and as such it is scientifically testable.3

  The stories that evolutionary biologists tell are of the same kind, and they become science when they stop being Just-So Stories, justifications after the event, and become general principles that make predictions. These predictions are of a limited kind: ‘in these circumstances expect this behaviour’. They are not predictions of the type ‘On Tuesday at 7.43pm the first elephant trunk will evolve’. But this is what ‘prediction’ means in science: saying ahead of time that under certain conditions, certain things will happen. You don’t have to predict the timing of the experiment.

  An evolutionary example of this kind of pattern can be found in the co-evolution of ‘creodonts’, big cats like sabretooth tigers, and their ‘titanothere’ prey – large-hoofed mammals, often with huge horns. When it comes to improving performance for the big cats, the line of least resistance is to develop bigger teeth. Faced with that, the best response for the prey is to develop thicker skins and bigger horns. An evolutionary arms race now becomes pretty much unavoidable: the cats get bigger and bigger teeth, and the prey respond with thicker and thicker skins … to which the cats’ only response is even bigger teeth … and so it goes. An evolutionary arms race sets in, with both species trapped in a single strategy. The end result is that the cats’ teeth get so enormous that the poor animals can hardly move their heads, wh
ile the titanotheres’ skins, and multiple horns on nose and brow, and associated musculature, get so heavy that they find trouble dragging themselves across the plains. Both species promptly die out.

  This creodont-titanothere arms race has happened at least five times in evolutionary history, taking about five million years to run its course on each occasion. It is a striking example of an emergent pattern, and the fact that it plays out in exactly the same way over and over again confirms that there really is an underlying dynamic. In all likelihood it would be happening again, now, except for the arrival of humans, who have clobbered both the big cats and their slow prey.

  Notice that we’ve been calling these system-level patterns ‘stories’, and so they are. They have a narrative, a consistent internal logic; they have a beginning and an end. They are stories because they cannot be ‘reduced’ to an entity-level description; that would be more like an interminable soap opera. ‘Well, this electron bumped into that electron and the two of them got together and emitted a photon …’ repeated, with slight variations, a truly inconceivable number of times. One of the central questions about emergent dynamics is: what would happen if we ran the system again, in slightly different circumstances? Would the same patterns emerge, or would we see something completely different? If European history in the early twentieth century was rerun, but without Adolf Hitler, would World War II have happened anyway, by a different route? Or would it all have been sweetness and light? Historically, this is a crucial question. There is no doubting that Hitler was instrumental in starting World War II; the deeper question here is whether he was a product of the politics of the time, and in his absence someone else would have done much the same, or whether it was Hitler who moulded history and created a war when otherwise nothing would have happened.

  At risk of being controversial, we are inclined to the view that World War II was a pretty much inevitable consequence of the political situation in the 1930s, with Germany saddled with huge reparations for World War I, the trains not running on time … and Hitler was merely the medium through which the national will to war was expressed. But it’s not the answer that concerns us here: it is the nature of the question. It is a ‘what if’ question, and it is about historical phase space. It does not ask what happened; it asks what might have happened instead.

  This point is well understood on Discworld. In Lords and Ladies we find the following passage:

  There are indeed such things as parallel universes, although parallel is hardly the right word – universes swoop and spiral around one another like some mad weaving machine or a squadron of Yossarians4 with middle-ear trouble.

  And they branch. But, and this is important, not all the time. The universe doesn’t much care if you tread on a butterfly. There are plenty more butterflies. Gods might note the fall of a sparrow but they don’t make any effort to catch them.

  Shoot the dictator and prevent the war? But the dictator is merely the tip of the whole festering boil of social pus from which dictators emerge; shoot one and there’ll be another one along in a minute. Shoot him too? Why not shoot everyone and invade Poland? In fifty years’, thirty years’, ten years’ time the world will be very nearly back on its old course. History always has a great weight of inertia.

  Almost always …

  At circle time, when the walls between this and that are thinner, when there are all sorts of strange leakages … Ah, then choices are made, then the universe can be sent careening down a different leg of the well-known Trousers of Time.

  This kind of question can be asked of any dynamical system, emergent or not; but it takes on a special aspect when the dynamic ‘makes itself up as it goes along’. In a rerun, would it make up the same thing? Would it tell the same story? If so, that story is robust: it has a degree of inevitability, not just in some particular run of history, but in all of them.

  Science fiction writers explore historical phase space in ‘alternate5 universe’ stories, where one historical event is changed and the author develops possible consequences. Philip K. Dick’s The Man in the High Castle explores a history in which Germany won World War II. Harry Harrison’s West of Eden trilogy explores a world in which the K/T meteorite missed and the dinosaurs survived. Science writers also ask about historical phase space, especially in the context of evolution. The most celebrated example is Stephen Jay Gould’s Wonderful Life, which asks whether humans would arise again on Earth if evolution were to be run again. His answer, ‘no’, rests on a very literal interpretation of ‘human’. Harrison’s answer in West of Eden is that intelligent mosasaurs – contemporaries of the dinosaurs that had returned to the sea – would evolve, and play the same role on the evolutionary stage that humans have played in this world. (For plot reasons he also has genuine humans in his alternate universe, but the Yilané, the smart mosasaur descendants, were there first.)

  Where Gould sees divergence and massive changes brought about by chance events, Harrison sees convergence: same play, different actors. To Gould, a change of actor is significant; to Harrison, what matters is the play. Both have good arguments to present, but the main point is that they are tackling different questions.

  A second way in which science fiction writers explore alternative historical tracks is through the time travel story, and this brings us back to the wizards of Unseen University and their battle against the elves. There are two kinds of time travel story. In the first kind, the protagonists mainly use their ability to travel in time as a way of observing the past or future; a good example is the first significant time travel novel, H.G. Wells’s The Time Machine of 1895. The time machine is a vehicle for Wells to discuss the future of humanity, but his Time Traveller makes no real effort to change history. In contrast, the narrative theme of Robert Silverberg’s 1969 novel Up the Line is the paradoxes that arise if it is possible to travel into the past and change it. In this story, the Time Service does not set out to change the past; on the contrary, its prime objective is to preserve the past and avoid paradoxes, despite the activities of observers from the future, who are cataloguing the past by visiting it and seeing what actually happened.

  The classic time travel paradox is ‘what if I went back and killed my grandfather?’ The logic of the situation, of course, is that with granddad dead, you wouldn’t have been born, so you wouldn’t be able to go back and kill him, so he’d have lived, so you would have been born … All attempts to resolve this self-contradictory causal loop are cheats: perhaps granddad dies, but you get born anyway with different grandparents, but then it wasn’t really granddad that you killed. In the ‘many worlds’ interpretation of quantum mechanics, the causal logic of the universe holds together provided the grandfather that gets killed was in a different parallel universe from that of the killer. But then he wasn’t your real granddad, either, just a parallel version in some other universe.

  A slightly more subtle time paradox is the Cumulative Audience Paradox. If people in the future have access to time machines, then they are bound to want to go back and witness all of the great historical events, like the crucifixion. But we know, from existing descriptions of these events, that they did not happen in front of crowds of thousands of visitors from the future. So where were they? This is a temporal analogue of the Fermi Paradox6 about intelligent aliens: if they’re all over the galaxy, then why aren’t they here? Why haven’t they visited us? Other time paradoxes are used as essential plot elements in Robert A. Heinlein’s short stories ‘By his bootstraps’ and ‘All you zombies’. In the latter, a time-traveller manages to be his own father, son, and – via a sex change – mother. When asked where he comes from, he replies that he knows exactly where he comes from. The big puzzle is: where does everybody else come from? This idea is taken to serious extremes by David Gerrold in The Man Who Folded Himself.

  Over the last few decades, serious physicists have started thinking about the possibility of time travel and the resolution of any associated paradoxes. Their work is a tribute to narrative imperativ
e on Roundworld. The reason they are asking such questions is no doubt that as children they read stories like those of Wells, Silverberg, Heinlein and Gerrold. When they became professional physicists, the stories bubbled up from their subconscious, and they began to take the idea seriously – not as a practical engineering issue, but as a theoretical challenge.

  Do the laws of physics permit time travel, or not? You’d expect the answer to be ‘no’, but the remarkable consequence of the theorists’ research is that it is ‘yes’. A working time machine is still a long way off, and it may be that we’re missing some basic physical principle that would change the answer to ‘no’, but the fact is that today’s accepted frontier physics does not forbid time travel. It even offers a few scenarios in which it could occur.

  The context for such research is general relativity, in which the continuum of space and time can be distorted by gravity. Or, more accurately, in which gravity is caused by such distortions, ‘curved spacetime’. In place of a time machine, the physicists look for a ‘closed timelike curve’. Such a curve corresponds to an object that travels into the future and ends up in its own past, and so becomes trapped in a closed ‘time loop’.

  The best known way to generate a closed timelike curve is to use a wormhole. A wormhole is a short-cut through space, obtained by fusing a Black Hole to its time-reversal, a White Hole. Just as Black Holes suck in anything that comes near them, White Holes spit things out. A wormhole sucks things in at its black end and spits them out at its white end. Of itself, a wormhole is more a matter-transmitter than a time machine, but it becomes a time machine when allied to the famous Twin Paradox. In relativity, time slows down for objects moving at very high speeds. So if one member of a pair of twins heads out to a distant star at very high speed, and then returns, she will have aged less than the other twin who stayed at home. Suppose that the travelling twin takes with her the white end of a wormhole, while her sister keeps the black end. Then when the travelling twin returns, the white end is younger than the black end: the exit from the wormhole lies in the past of the entrance. So anything that is sucked into the black end is spat out in its own past. Because the white end is now right next to the black one – the twin has come back home – the object can hop across to the Black Hole and go round and round this closed loop in spacetime, tracing a closed timelike curve.