The Science of Discworld III - Darwin's Watch tsod-3 Read online

  `Ah ... er, on a globe, the equator is an imaginary line around the middle,' said Ponder. `What happened was that the bulk of the technomancers and the priests got behind the ideas expressed in Darwin's book, because they gave everyone pretty much what they wanted. Quite of few of the technomancers had a strong belief in the god, and most of the brighter priests could see big flaws in the dogma. Together, they were a very large and influential force. The hard-line religionists and the unbending technomancers were marginalised. Out in the cold. Polarised, in fact.' This rather neat pun, although he said it himself, failed to get even a groan of acknowledgement, so he went on: `They didn't agree with the united group and they certainly didn't agree with one another. And, thus, happy compromise ruled. For well over sixty years.'

  `That's nice,' said the Lecturer in Recent Runes.

  `Er ... yes, sir, and then again, no,' said Ponder. `Technomancy doesn't work well in those circumstances. It can't make real progress by consensus. Hah, being led by a bunch of self-satisfied old men who are more interesting in big dinners than asking questions is a recipe for stagnation, anyone can see that.'

  The wizards nodded sagely.

  `Very true,' said Archchancellor Ridcully, narrowing his eyes. `That was an important point which needed to be made.'

  `Thank you, Archchancellor.'

  `And now it needs to be apologised for.'

  `Sorry, Archchancellor.'

  `Good. So, Mr Stibbons, what do-'

  There was a rattle from Hex's writing engine. The spidery arms wove across the paper and wrote:

  +++ The Chair of Indefinite Studies is correct +++ The wizards clustered round.

  `Right about what?' said Ponder.

  +++ Charles Darwin of Theology of Species was for much of his life a Rector in the Church of England, a sub-set of the British nation +++ the computer scrawled. +++ The chief function of the priests of that religion at the time was to further the arts of archaeology, local history, lepidoptery, botany, palaeontology, geology and the making of fireworks +++

  `Priests did that?' said the Dean. `What about the praying and so on?'

  +++ Some of them did that too, yes, although it was considered to be showing off. The God of the English did not require much in the way of sacrifice, only that people acted decently and kept the noise down. Being a priest in that church was a natural job for a young man of good breeding and education but no very specific talent. In the rural areas they had much free time. My calculations suggest that Theology of Species was the book that he was destined to write. In all the histories of third-level phase space, there is only one in which he writes The Origin of Species +++

  `Why is that?' said Ponder.

  +++ The explanation is complex +++

  `Well, out with it,' said Ridcully. `We're all sensible men here.'

  Another piece of paper slid off Hex's tray. It read: +++ Yes. That is the problem. You understand that every possibility of choice gives birth to a new universe in which that choice is manifest? +++

  `This is the Trousers of Time again, isn't it?' said Ridcully.

  +++ Yes. Except that every leg of the Trousers of Time branches into many other legs, and so do those legs and every following leg, until everywhere is full of legs, which often pass through one another or join up again +++

  `I think I'm losin' track,' said Ridcully.

  +++ Yes. Language is not good at this. Even mathematics gets lost.

  But a little story might work. I will tell you the story. It will be not completely inaccurate +++

  `Go ahead,' said Ridcully.

  +++ Imagine an unimaginably large number +++

  `Right. No problem there,' said Ridcully, after the wizards had consulted among themselves.

  +++ Very well +++ Hex wrote. +++ From the moment that the Roundworld universe was made, it began to split into almost identical copies of itself, billions of times a second. That unimaginably large number represents all possible Roundworld universes that there are +++

  `Do all these universes really exist?' said the Dean.

  +++ Impossible to prove. Assume that they do. In all those universes there are hardly any in which a man called Charles Darwin exists, takes a momentous ocean voyage, and writes a hugely influential book about the evolution of life on the planet. Nevertheless, that number is still unimaginably large +++

  `But imagined by a smaller imagination?' said Ridcully. `I mean, is it half as many as the other unimaginable number?'

  +++ No. It is unimaginably large. But compared to the first number, it is unimaginably small +++

  The wizards debated this in whispers.

  `Very well,' said Ridcully, at last. `Keep goin' and we'll kind of join in when we can.'

  +++ Even so, it is not so unimaginable as the number of universes in which the book was The Origin of Species. That number is quite strange and can only be imagined at all in very unusual circumstances +++

  `It's unimaginably larger?' said Ridcully.

  +++ just unimaginably unique. The number one. Gentlemen. All by itself. One is one and all alone. One. Yes. In third-level phase space there is only one history where he gets on the boat, completes the voyage, considers the findings and writes that book. All the other alternative Darwins either did not exist, did not stay on the boat, did not survive the journey, did not write any book at all or wrote, in a large number of cases, Theology of Species and entered the Church +++

  `Boat?' said Ponder. `What boat? What've boats got to do with it?'

  +++ I explained, in the successful timeline which led to humanity leaving the planet, Mr Darwin makes a significant voyage. It is one of nineteen pivotal events in the history of the species. It is almost as important as Joshua Goddelson leaving his house by the back door in 1734 +++

  `Who was he?' said Ponder. `I don't recall the name.'

  +++ A shoemaker living in Hamburg, Germany +++ wrote Hex.

  +++ Had he left his house by the front door that day, commercial nuclear fusion would not have been perfected 283 years later +++ `That was important, was it?' said Ridcully.

  +++ Vastly. Major technomancy +++

  `Did it need much in the way of shoes, then?' said Ridcully, mystified.

  +++ No. But the chain of causality, though complex, is clear +++ `How hard is it to get on this boat?' said the Dean. +++ In the case of Charles Darwin, very hard +++ `Where did it go?'

  +++ It sailed from England to England. But there were crucial stops along the way. Even in those histories where he did embark on the boat, he did not complete the voyage and complete The Origin of Species in every case but one +++

  `Just one version of history, you say,' said Ponder Stibbons. `Do you know why?'

  +++ Yes. It is the one where you intervene +++ `But we haven't intervened,' said Ridcully.

  +++ In a primitive subjective sense this is the case. However, you are going to will have already soon +++ Hex wrote.

  `What? And I am not a primitive subject, Mr Hex!'

  +++ I am sorry. It is hard to convey five-dimensional ideas in a language evolved to scream defiance at the monkeys in the next tree +++

  The wizards looked at one another.

  `Getting a man on a ship can't be hard, surely?' said the Dean.

  `Is it dangerous in Darwin's time?' said Rincewind.

  +++ Inevitably. The centre of the Globe is an inferno, humanity is protected from being fried alive by nothing more than a skin of air and magnetic forces, and the chance of an asteroid strike is ever present +++

  `I think Rincewind was referring to more immediate concerns,' said Ridcully.

  +++ Understood. The major city you must visit has many squalid areas and open sewers. The river bisecting it is noxious. Your destination could be considered a high-crime drainage ditch in a dangerous and dirty world +++

  `Pretty much like here, you mean?'

  +++ The similarity is noticeable, yes +++

  The writing arms stopped moving. Bits of Hex rattled and shook. The ants ceased their purposefu
l scurrying and began to mill about aimlessly in their glass tubing. Hex appeared to have something on his mind.

  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 +++

  6. 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.

  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 cliche here is the `grandfather paradox', which goes back to Rene 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 cliche, 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 hands[14] 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 res
pectable[15] 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[16].

  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[17], and that the tortoise is the fastest animal on the Disc[18]. 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.