Science of Discworld III

by Terry Pratchett

  Then one writing arm dipped its pen into the ink and wrote, slowly:

  +++ There is an additional problem. It is not clear to me why Darwin did not write Origin somewhere in the multiple universes without your forthcoming assistance +++

  ‘We haven’t decided that we will—’ Ridcully began.

  +++ But you are going to have done +++

  ‘Well, probably—’

  +++ Across the entire phase space of this world Charles Darwin did many things. He became an expert watchmaker. He ran a pottery factory. In many worlds he was a country priest. In others, he was a geologist. In yet others, he did make the important voyage and, as a result wrote Theology of Species. In some he began to write The Origin of Species only to give up. Only in one timeline was Origin published. This should not be possible. I detect … +++

  +++ I detect … +++

  The wizards waited politely.

  ‘Yes?’ said Ponder.

  The single pen moved across the paper.

  +++ MALIGNITY +++

  1 Phase space, in a given context, is the space of everything that might have happened, not just what did. See The Science of Discworld.

  SIX

  BORROWED TIME

  THE EVER-BRANCHING LEGS OF the Trousers of Time are a metaphor (unless you are a quantum physicist, in which case they represent a certain mathematical view of reality) for the many paths that history might have taken if events had been slightly different. Later, we’ll think about all those legs, but for now, we restrict attention to one trouser. One timeline. What exactly is time?

  We know what it is on Discworld. ‘Time’, states The New Discworld Companion, ‘is one of the Discworld’s most secretive anthropomorphic personifications. It is hazarded that time is female (she waits for no man) but she has never been seen in the mundane worlds, having always gone somewhere else just a moment before. In her chronophonic castle, made up of endless glass rooms, she does at, er, times, materialise into a tall woman with dark hair, wearing a long red-and-black dress.’

  Tick.

  Even Discworld has trouble with time. In Roundworld it’s worse. There was a time (there we go) when space and time were considered to be totally different things. Space had, or was, extension – it sort of spread itself around, and you could move through it at will. Within reason, maybe 20 miles (30km) a day on a good horse if the tracks weren’t too muddy and the highwaymen weren’t too obtrusive.

  Tick.

  Time, in contrast, moved of its own volition and took you along with it. Time just passed, at a fixed speed of one hour per hour, always in the direction of the future. The past had already happened, the present was happening right now – oops, gone already – and the future had yet to happen, but by jingo, it would, you mark my words, when it was good and ready.

  Tick.

  You could choose where you went in space, but you couldn’t choose when you went in time. You couldn’t visit the past to find out what had really happened, or visit the future to find out what fate had in store for you; you just had to wait and find out. So time was completely different from space. Space was three-dimensional, with three independent directions: left/right, back/forward, up/down. Time just was.

  Tick.

  Then along came Einstein, and time started to get mixed up with space. Time-like directions were still different from space-like ones, in some ways, but you could mix them up a bit. You could borrow time here and pay it back somewhere else. Even so, you couldn’t head off into the future and find yourself back in your own past. That would be time travel, which played no part in physics.

  Ti—

  What science abhors, the arts crave. Time travel may be a physical impossibility, but it is a wonderful narrative device for writers, because it allows the story to move to past, present, or future, at will. Of course you don’t need a time machine to do that – the flashback is a standard literary device. But it’s fun (and respectful to narrativium) to have some kind of rationale that fits into the story itself. Victorian writers liked to use dreams; a good example is Charles Dickens’s A Christmas Carol of 1843, with its ghosts of Christmas past, present, and yet-to-come. There is even a literary subgenre of ‘timeslip romances’, some of them really quite steamy. The French ones.

  Time travel causes problems if you treat it as more than just a literary device. When allied to free will, it leads to paradoxes. The ultimate cliché here is the ‘grandfather paradox’, which goes back to René Barjavel’s story Le Voyageur Imprudent. You go back in time and kill your grandfather, but because your father is then not born, neither are you, so you can’t go back to kill him … Quite why it’s always your grandfather isn’t clear (except as a sign that it’s a cliché, a low-bred form of narrativium). Killing your father or mother would have the same paradoxical consequences. And so might the slaughter of a Cretaceous butterfly, as in Ray Bradbury’s 1952 short story ‘A Sound of Thunder’, in which a butterfly’s accidental demise at the hands1 of an unwitting time traveller changes present-day politics for the worse.

  Another celebrated time paradox is the cumulative audience paradox. Certain events, the standard one being the Crucifixion, are so endowed with narrativium that any self-respecting time tourist will insist on seeing them. The inevitable consequence is that anyone who visits the Crucifixion will find Christ surrounded by thousands, if not millions, of time travellers. A third is the perpetual investment paradox. Put your money in a bank account in 1955, take it out in 2005, with accumulated interest, then take it back to 1955 and put it in again … Be careful to use something like gold, not notes – notes from 2005 won’t be valid in 1955. Robert Silverberg’s Up the Line is about the Time Service, a force of time police whose job is to prevent such paradoxes from getting out of hand. A similar theme occurs in Isaac Asimov’s The End of Eternity.

  An entire class of paradoxes arises from time loops, closed loops of causality in which events only get started because someone comes from the future to initiate them. For example, the easiest way for today’s humanity to get hold of a time machine is if someone is presented with one by a time traveller from the far future, when such machines have already been invented. He or she then reverse engineers the machine to find out how it works, and these principles later form the basis for the future invention of the machine. Two classic stories of this type are Robert Heinlein’s ‘By His Bootstraps’ and ‘All you Zombies’, the second being noteworthy for a protagonist who becomes his own father and his own mother (via a sex change). David Gerrold took this idea to extremes in The Man Who Folded Himself.

  Science-fiction authors are divided on whether time paradoxes always neatly unwrap themselves to produce consistent results, or whether it is genuinely possible, in their fictional setting, to change the past or the present. (No one worries much about changing the future, mind you, presumably because ‘free will’ amounts to precisely that. We all change the future, from what it might have been to what it actually becomes, thousands of times every day. Or so we fondly imagine.) So some authors write of attempts to kill your grandfather that, by some neat twist, bring you into existence anyway. For example, your true father was not his son at all, but a man he killed. By mistakenly eliminating the wrong grandfather, you ensure that your true father survives to sire you. Others, like Asimov and Silverberg, set up entire organisations dedicated to making sure that the past, hence the present, remains intact. Which may or may not work.

  The paradoxes associated with time travel are part of the subject’s fascination, but they do rather point towards the conclusion that time travel is a logical impossibility, let alone a physical one. So we are happy to allow the wizards of Unseen University, whose world runs on magic, the facility to wander at will up and down the Roundworld timeline, switching history from one parallel universe to another, trying to get Charles Darwin – or somebody – to write That Book. The wizards live in Discworld, they operate outside Roundworld constraints. But we don’t really imagine that Roundworld people could do the same,
without external assistance, using only Roundworld science.

  Strangely, many scientists at the frontiers of today’s physics don’t agree. To them, time travel has become an entirely respectable2 research topic, paradoxes notwithstanding. It seems that there is nothing in the ‘laws’ of physics, as we currently understand them, that forbids time travel. The paradoxes are apparent rather than real; they can be ‘resolved’ without violating physical law, as we will see in Chapter 8. That may be a flaw in today’s physics, as Stephen Hawking maintains; his ‘chronology protection conjecture’ states that as yet unknown physical laws conspire to shut down any time machine just before it gets assembled – a built-in cosmological time cop.

  On the other hand, the possibility of time travel may be a profound statement about the universe. We probably won’t know for sure until we get to tackle the issue using tomorrow’s physics. And it’s worth remarking that we don’t really understand time, let alone how to travel through it.

  Although (apparently) the laws of physics do not forbid time travel, it turns out that they do make it very difficult. One theoretical scheme for achieving that goal, which involves towing black holes around very fast, requires rather more energy than is contained in the entire universe. This is a bit of a bummer, and it does seem to rule out the typical science fiction time machine, about the size of a car.3

  The most extensive descriptions of Discworld time are found in Thief of Time. The ingredients for this novel include a member of the Guild of Clockmakers, Jeremy Clockson, who is determined to make a completely accurate clock. However, he is up against a theoretical barrier, the paradoxes of the Ephebian philosopher Xeno, which are first mentioned in Pyramids. A Roundworld philosopher with an oddly similar name, Zeno of Elea, born around 490 BC, stated four paradoxes about the relation between space, time and motion. He is Xeno’s Roundworld counterpart, and his paradoxes bear a curious resemblance to the Ephebian philosopher’s. Xeno proved by logic alone that an arrow cannot hit a running man,4 and that the tortoise is the fastest animal on the Disc.5 He combined both in one experiment, by shooting an arrow at a tortoise that was racing against a hare. The arrow hit the hare by mistake, and the tortoise won, which proved that he was right. In Pyramids, Xeno describes the thinking behind this experiment.

  ‘’s quite simple,’ said Xeno. ‘Look, let’s say this olive stone is an arrow and this, and this –’ he cast around aimlessly – ‘and this stunned seagull is the tortoise, right? Now, when you fire the arrow it goes from here to the seag— the tortoise, am I right?’

  ‘I suppose so, but—’

  ‘But, by this time, the seagu— the tortoise has moved on a bit, hasn’t he? Am I right?’

  ‘I suppose so,’ said Teppic, helplessly. Xeno gave him a look of triumph.

  ‘So the arrow has to go a bit further, doesn’t it, to where the tortoise is now. Meanwhile the tortoise has flow— moved on, not much, I’ll grant you, but it doesn’t have to be much. Am I right? So the arrow has a bit further to go, but the point is that by the time it gets to where the tortoise is now the tortoise isn’t there. So if the tortoise keeps moving, the arrow will never hit it. It’ll keep getting closer and closer, but it’ll never hit it. QED.’

  Zeno has a similar set-up, though he garbles it into two paradoxes. The first, called the Dichotomy, states that motion is impossible, because before you can get anywhere, you have to get halfway, and before you can get there, you have to get halfway to that, and so on for ever … so you have to co infinitely many things to get started, which is silly. The second, Achilles and the Tortoise, is pretty much the paradox enunciated by Xeno, but with the hare replaced by the Greek hero Achilles. Achilles runs faster than the tortoise – face it, anyone can run faster than a tortoise – but he starts a bit behind, and can never catch up because whenever he reaches the place where the tortoise was, it’s moved on a bit. Like the ambiguous puzuma, by the time you get to it, it’s not there. The third paradox says that a moving arrow isn’t moving. Time must be divided into successive instants, and at each instant the arrow occupies a definite position, so it must be at rest. If it’s always at rest, it can’t move. The fourth of Zeno’s paradoxes, the Moving Rows (or Stadium), is more technical to describe, but it boils down to this. Suppose three bodies are level with each other, and in the smallest instant of time one moves the smallest possible distance to the right, while the other moves the smallest possible distance to the left. Then those two bodies have moved apart by twice the smallest distance, taking the smallest instant of time to do that. So when they were just the smallest distance apart, halfway to their final destinations, time must have changed by half the smallest possible instant of time. Which would be smaller, which is crazy.

  There is a serious intent to Zeno’s paradoxes, and a reason why there are four of them. The Greek philosophers of Roundworld antiquity were arguing whether space and time were discrete, made up of indivisible tiny units, or continuous – infinitely divisible. Zeno’s four paradoxes neatly dispose of all four combinations of continuous/discrete for space with continuous/discrete for time, neatly stuffing everyone else’s theories, which is how you make your mark in philosophical circles. For instance, the Moving Rows paradox shows that having both space and time discrete is contradictory.

  Zeno’s paradoxes still show up today in some areas of theoretical physics and mathematics, although Achilles and the Tortoise can be dealt with by agreeing that if space and time are both continuous, then infinitely many things can (indeed must) happen in a finite time. The Arrow paradox can be resolved by noting that in the general mathematical treatment of classical mechanics, known as Hamiltonian mechanics after the great (and drunken) Irish mathematician Sir William Rowan Hamilton, the state of a body is given by two quantities, not one. As well as position it also has momentum, a disguised version of velocity. The two are related by the body’s motion, but they are conceptually distinct. All you see is position; momentum is observable only through its effect on the subsequent positions. A body in a given position with zero momentum is not moving at that instant, and so will not go anywhere, whereas one in the same position with non-zero momentum – which appears identical – is moving, even though instantaneously it stays in the same place.

  Got that?

  Anyway, we were talking about Thief of Time, and thanks to Xeno we’ve not yet got past see here. The main point is that Discworld time is malleable, so the laws of narrative imperative sometimes need a little help to make sure that the narrative does what the imperative says it should.

  Tick.

  Lady Myria LeJean is an Auditor of reality, who has temporarily assumed human form. Discworld is relentlessly animistic; virtually everything is conscious on some level, including basic physics. The Auditors police the laws of nature; they would very likely fine you for exceeding the speed of light. They normally take the form of small grey robes with a cowl – and nothing inside. They are the ultimate bureaucrats. LeJean points out to Jeremy that the perfect clock must be able to measure Xeno’s smallest unit of time. ‘It must exist, mustn’t it? Consider the present. It must have a length, because one end of it is connected to the past and the other is connected to the future, and if it didn’t have a length then the present couldn’t exist at all. There would be no time for it to be the present in.’

  Her views correspond rather closely to current theories of the psychology of the perception of time. Our brains perceive an ‘instant’ as an extended, though brief, period of time. This is analogous to the way discrete rods and cones in the retina seem to perceive individual points, but actually sample a small region of space. The brain accepts coarse-grained inputs and smooths them out.

  LeJean is explaining Xeno to Jeremy because she has a hidden agenda: if Jeremy succeeds in making the perfect clock, then time will stop. This will make the Auditors’ task as clerks of the universe much simpler, because humans are always moving things around, which makes it difficult to keep track of their locations in time and space.
>
  Tick.

  Near the Discworld Hub, in a high, green valley, lies the monastery of Oi Dong, where live the fighting monks of the order of Wen, otherwise known as History Monks. They have taken upon themselves the task of ensuring that the right history happens in the right order. The monks know what is right because they guard the History Books, which are not records of what did happen, but instructions for what should.

  A youngster named Ludd, a foundling brought up by the Thieves’ Guild, where he was an exceptionally talented student, has been recruited to the ranks of the History Monks and given the name Lobsang. The monks’ main technological aids are procrastinators, huge spinning machines that store and move time. With a procrastinator, you can borrow time and pay it back later. Lobsang wouldn’t dream of living on borrowed time, though – but if it wasn’t nailed down, he would almost certainly steal it. He can steal anything, and usually does. And, thanks to the procrastinators, time is not nailed down.

  If you haven’t got the joke by now, take another look at the title.

  LeJean’s plan works; Jeremy builds his clock.

  Ti—

  Time stops, which is what the Auditors wanted. Not only on Discworld: temporal stasis expands across the universe at the speed of light. Soon, everything will stop. The History Monks are powerless, for they, too, have stopped. Only Susan Sto Helit, Death’s granddaughter, can get time started again. And Ronnie Soak, who used to be Kaos, the Fifth Horseman of the Apocralypse, but left because of artistic disputes before they became famous … Fortunately, the Auditors like obeying rules, and DO NOT FEED THE ELEPHANT really perplexes them when there is no elephant to feed. Fatally, they also have a love–hate relationship with chocolate. They are living on stolen time.

  A procrastinator is a sort of time machine, but it moves time itself, instead of moving people through time. Moreover, it’s fact, not fiction, as is all of Discworld to those who live there. On Roundworld, the first fictional time machine, as opposed to dreams or narrative timeslip, seems to have been invented by Edward Mitchell, an editor for the New York Sun newspaper. In 1881 he published an anonymous story, ‘The Clock That Went Backward’, in his paper. The most celebrated time-travel gadget appears in Herbert George Wells’s novel The Time Machine of 1895, and this set a standard for all that followed. The novel tells of a Victorian inventor who builds a time machine and travels into the far future. There he finds that humanity has speciated into two distinct types – the nasty Morlocks, who live deep inside caverns, and the ethereal Eloi, who are preyed on by the Morlocks and are too indolent to do anything about it. Several movies, all fairly ghastly, have been based on the book.