The wizards looked at him.
‘Er,’ he went on, ‘if you think a god is huge and powerful and everywhere, then it’s natural to be god-fearing. But if someone comes along and paints that god as a big bearded chap in the sky, it’s not going to be long before people say, don’t be silly, there can’t be a big bearded man on a cloud somewhere, let’s go and invent Logic’
‘Can’t there be gods here?’ said the Lecturer in Recent Runes. ‘We’ve got a mountaintop full of ’em at home.’
‘We’ve never detected deitygen in this universe,’ said Ponder thoughtfully.
‘But it’s said to be generated by intelligent creatures, just like cows generate marsh gas,’ said Ridcully.
‘In a universe based on magic, certainly,’ said Ponder. ‘This one is just based on bent space.’
‘Well, there’s been lots of wars, lots of deaths and I’d bet there’s lots of believers,’ said the Chair of Indefinite Studies, now looking extremely uncomfortable. ‘When thousands die for a god, you get a god. If someone is prepared to die for a god, you get a god.’
‘At home, yes. But does that work here?’ said Ponder.
The wizards sat in silence for a while.
‘Are we going to get into any sort of religious trouble for this?’ said the Dean.
‘None of us has been struck by lightning yet,’ said Ridcully.
‘True, true. I just wish there was a less, er, permanent test,’ said the Chair of Indefinite Studies. ‘Er … the dominant religion on this continent seems to be a family concern, somewhat similar to Old Omnianism.’
‘Big on smiting?’
‘Not lately. It’s gone very quiet vis-à-vis heavenly fire, widespread flooding and transmutation into food additives,’ said the Chair.
‘Don’t tell me,’ said Ridcully. ‘A public appearance, some simple moral precepts, and then apparent silence? Apart, that is, for millions of people arguing what “Do not steal” and “Don’t Commit Murder” actually mean?’
‘That’s right.’
‘Just like Omnianism, then,’ said the Archchancellor glumly. ‘Noisy religion, silent god. We must tread carefully, gentlemen.’
‘But I did point out that there is no perceptible trace whatsoever of any deities of any kind anywhere in this universe!’ said Ponder.
‘Yes, very puzzling,’ said Ridcully. ‘Nevertheless, we have no magical powers here and it pays to be careful.’
Ponder opened his mouth. He wanted to say: We know everything about this place! We’ve watched it happen! It’s all balls, spinning in curves. It’s matter bending space and space moving matter. Everything here is the result of a few simple rules! That’s all! It’s all just a matter of rules! It’s all … logical.
He wanted it to be logical. Discworld wasn’t logical. Some things happened on the whim of gods, some things happened because it was a good idea at the time, some things happened out of sheer randomness. But there was no logic – at least, no logic that Ponder approved of. He’d gone to the little town called Athens that Rincewind had talked about, in a sheet borrowed from Doctor Dee, and listened to men not entirely unlike the philosophers of Ephebe talking about logic, and it had made him want to burst into tears. They didn’t have to live in a place where things changed on a whim.
Everything ticked and tocked and turned for them like a great big machine. There were rules. Things stayed the same. The same reliable stars came up every night. Planets didn’t disappear because they’ve wandered too close to a flipper and been flicked far away from the sun.
No trouble, no complications. A few simple rules, a handful of elements … it was all so easy. Admittedly, he found it a little hard to work out exactly how you got from a few simple rules to, say, the sheen on mother-of-pearl or the common porcupine, but he was sure that you did. He wanted, intensely, to believe in a world where logic worked. It was a matter of faith.
He envied those philosophers. They nodded to their gods and then, by degrees, destroyed them.
And now he sighed.
‘We’ve done the best we can,’ he said. ‘Your plan, Rincewind?’
Rincewind stared at the glass sphere that was the current abode of Hex.
‘Hex, is this world ready for the William Shakespeare of whom we spoke?’
‘It is.’
‘And he exists?’
‘No. Two of his grandparents did not meet. His mother was never born.’
In his hollow voice, Hex recounted the sad history, in detail. The wizards took notes.
‘Right,’ said Ridcully, rubbing his hands together when Hex finished. ‘This at least is a simple problem. We shall need a length of string, a leather ball of some kind, and a large bunch of flowers …’
Later, Rincewind stared at the glass sphere that was the current abode of Hex.
‘Hex, now is this world ready for the William Shakespeare of whom we spoke?’
‘It is.’
‘And he exists?’
‘Violet Shakespeare exists. She married Josiah Slink at the age of sixteen. No plays have been written, but there have been eight children of which five have survived. Her rime is fully occupied.’
The wizards exchanged glances.
‘Perhaps if we offered to babysit?’ said Rincewind.
‘Too many problems,’ said Ridcully firmly. ‘Still it’s a change to have an easy one for once. We will need the probable date of conception, a stepladder and a gallon of black paint.’
Rincewind stared at the glass sphere that was the current abode of Hex.
‘Hex, is this world ready for the William Shakespeare of whom we spoke?’
‘It is.’
‘And he exists?’
‘He was born, but died at the age of 18 months. Details follow …’
The wizards listened. Ridcully looked thoughtful for a moment.
‘This will require some strong disinfectant,’ he said. ‘And a lot of carbolic soap.’
Rincewind stared at the glass sphere that was the current abode of Hex.
‘Hex, is this world ready for the William Shakespeare of whom we spoke?’
‘It is.’
‘And he exists?’
‘No. He was born, successfully survived several childhood illnesses, but was shot dead one night while poaching game at the age of thirteen. Details follow …’
‘Another easy one,’ said Ridcully, standing up. ‘We shall need … let me see … some drab clothing, a dark lantern and a very large cosh …’
Rincewind stared at the glass sphere that was the current abode of Hex.
‘Hex, is this world ready for the William Shakespeare of whom we spoke? Please?’
‘It is.’
‘And he exists?’
‘Yes.’
The wizards tried not to look hopeful. There had been too many false dawns in the last week.
‘Alive?’ said Rincewind. ‘Male? Sane? Not in the Americas? Not struck by a meteorite? Not left incapacitated by a hake during an unusual fall of fish? Or killed in a duel?’
‘No. At this moment he is in the tavern that you gentlemen frequent.’
‘Does he have all his arms and legs?’
‘Yes,’ said Hex. ‘And … Rincewind?’
‘Yes?’
‘As one of two unexpected collateral events to this latest interference, the potato has been brought to these shores.’
‘Hot damn!’
‘And Arthur J. Nightingale is a ploughman and never learned to write.’
‘Near miss there,’ said Ridcully.
TWENTY-EIGHT
WORLDS OF IF
THE WIZARDS HAVE DEVISED A SECRET WEAPON in their battle against the elves for the soul of Roundworld, and they are busily re-engineering history to make sure that their weapon gets invented. The weapon is one Will Shakespeare – Arthur J. Nightingale just can’t hack it. And they’re proceeding by trial and error, with a lot of both. Nonetheless, they gradually persuade the flow of history to converge, step by step, towa
rds their desired outcome.
Black paint? You may know this superstitious practice, but if not: painting the kitchen ceiling black is supposed to guarantee a boy.1 The wizards will try anything. To begin with. And if it doesn’t work, they’ll try something else, until eventually they get somewhere.
Why is it unreasonable to expect them to succeed in one go, but reasonable to expect them to achieve their objective by repeated refinements?
History is like that.
There is a dynamic to history, but we find out what that dynamic is only as the events concerned unfold. That’s why we can put a name to historical periods only after they’ve happened. That’s why the history monks on Discworld have to wander the Disc making sure that historical events that ought to happen do happen. They are the guardians of narrativium and they spread it around dispassionately to ensure that the whole world obeys its storyline. The history monks come into their own in Thief of Time. Using great spinning cylinders called Procrastinators, they borrow time from where it is not needed and repay it where it is:
According to the Second Scroll of Wen the Eternally Surprised, Wen the Eternally Surprised sawed the first procrastinator from a trunk of a wamwam tree, carved certain symbols on it, fitted it with a bronze spindle, and summoned the apprentice, Clodpool.
‘Ah, very nice, master,’ said Clodpool. ‘A prayer wheel, yes?’
‘No, this is nothing like as complex,’ said Wen. ‘It merely stores and moves time.’
‘That simple, eh?’
‘And now I shall test it,’ said Wen. He gave it a half-turn with his hand.
‘Ah, very nice, master,’ said Clodpool. ‘A prayer wheel, yes?’
‘No, this is nothing like as complex,’ said Wen. ‘It merely stores and moves time.’
‘That simple, eh?’
‘And now I shall test it,’ said Wen. He moved it a little less this time.
‘That simple, eh?’
‘And now I shall test it,’ said Wen. This time he twisted it gently to and fro.
‘That si-si-si That simple-ple, eh eheh simple, eh?’ said Clodpool.
‘And I have tested it,’ said Wen.
On Roundworld we don’t have history monks – or, at least, we’ve never caught anyone playing that role, but could we ever do so? – but we do have a kind of historical narrativium. We have a saying that ‘history repeats itself’ – the first time as comedy, the second time as tragedy, because the one thing we learn from history is that we never learn from history.
Roundworld history is like biological evolution: it obeys rules, but even so, it seems to make itself up as it goes along. In fact, it seems to make up its rules as it goes along. At first sight, that seems incompatible with the existence of a dynamic, because a dynamic is a rule that takes the system from its present state to the next one, a tiny instant into the future. Nonetheless, there must be a dynamic, otherwise historians would not be able to make sense of history, even after the event. Ditto evolutionary biology.
The solution to this conundrum lies in the strange nature of the historical dynamic. It is emergent. Emergence is one of the most important, but also the most puzzling, features of complex systems. And it is important for this book, because it is the existence of emergent dynamics that leads humans to tell stories. Briefly: if the dynamic wasn’t emergent, then we wouldn’t need to tell stories about the system, because we’d all be able to understand the system on its own terms. But when the dynamic is emergent, a simplified but evocative story is the best description that we can hope to find …
But now we’re getting ahead of our own story, so let’s back up a little and explain what we’re talking about.
A conventional dynamical system has an explicit, pre-stated phase space. That is, there exists a simple, precise description of everything that the system can possibly do, and in some sense this description is known in advance. In addition, there is a fixed rule, or rules, that takes the current state of the system and transforms it into the next state. For example, if we are trying to understand the solar system, from a classical point of view, then the phase space comprises all possible positions and velocities for the planets, moons, and other bodies, and the rules are a combination of Newton’s law of gravity and Newton’s laws of motion.
Such a system is deterministic: in principle, the future is entirely determined by the present. The reasoning is straightforward. Start with the present state and work out what it will be one time-step into the future by applying the rules. But we can now consider that state as the new ‘present’ state, and apply the rule again to find out what the system will be doing two time-steps into the future. Repeat again, and we know what will happen after three time-steps. Repeat a billion times, and the future is determined for the next billion time-steps.
This mathematical phenomenon led the eighteenth-century mathematician Pierre Simon de Laplace to a vivid image of a ‘vast intellect’ that could predict the entire future of every particle in the universe, once it was furnished with an exact description of all those particles at one instant. Laplace was aware that performing such a computation was far too difficult to be practical, and he was also aware of the difficulty, indeed the impossibility, of observing the state of every particle at the same moment. Despite these problems, his image helped to create an optimistic attitude about the predictability of the universe. Or, more accurately, of small enough bits of it. And for several centuries, science made huge inroads into making such predictions feasible. Today, we can predict the motion of the solar system billions of years in advance, and we can even predict the weather (fairly accurately) three whole days in advance, which is amazing. Seriously. Weather is a lot less predictable than the solar system.
Laplace’s hypothetical intellect was lampooned in Douglas Adams’s The Hitchhiker’s Guide to the Galaxy as Deep Thought, the supercomputer which took five million years to calculate the answer to the great question of life, the universe, and everything. The answer it got was 42. ‘Deep Thought’ is not so far away from ‘Vast Intellect’, although the name originates in the pornographic movie Deep Throat, whose title was the cover-name of a clandestine source in the Watergate scandal in which the presidency of Richard Nixon self-destructed (how soon people forget …).
One reason why Adams was able to poke fun at Laplace’s dream is that about forty years ago we learned that predicting the future of the universe, or even a small part of it, requires more than just a vast intellect. It requires absolutely exact initial data, correct to infinitely many decimal places. No error, however minuscule, can be tolerated. None. No marks for trying. Thanks to the phenomenon known as ‘chaos’, even the smallest error in determining the initial state of the universe can blow up exponentially fast, so that the predicted future quickly becomes wildly inaccurate. In practice, though, measuring anything to an accuracy of more than one part in a trillion, 12 decimal digits, is beyond the abilities of today’s science. So, for instance, although we can indeed predict the motion of the solar system billions of years in advance, we can’t predict it correctly. In fact, we have very little idea where Pluto will be, a hundred million years from now.
Ten million, on the other hand, is a cinch.
Chaos is just one of the practical reasons why it’s generally impossible to predict the future (and get it right). Here we’ll examine a rather different one: complexity. Chaos afflicts the prediction method, but complexity afflicts the rules. Chaos occurs because it is impossible to say in practice what the state of the system is, exactly. In a complex system, it may be impossible to say what the range of possible states of the system is, even approximately. Chaos throws a spanner in the works of the scientific prediction machine, but complexity turns that machine into a small cube of crumpled scrap metal.
We’ve already discussed the limitations of the Laplacian world-picture in the context of Kauffman’s theory of autonomous agents expanding into the space of the adjacent possible. Now we’ll take a closer look at how such expansions occur. We
’ll see that the Laplacian picture still has a role to play, but a less ambitious one.
A complex system consists of a number (usually large) of entities or agents, which interact with each other according to specific rules. This description makes it sound as though a complex system is just a dynamical system whose phase space has a huge number of dimensions, one or more per entity. This is correct, but the word ‘just’ is misleadingly dismissive. Dynamical systems with big phase spaces can do remarkable things, far more remarkable than what the solar system can do.
The new ingredient in complex systems is that the rules are ‘local’, stated on the level of the entities. In contrast, the interesting features of the system itself are global, stated on the level of the entire system. Even if we know the local rules for entities, it may not be possible – either in practice, or in principle – to deduce the dynamical rules of the system as a whole. The problem here is that the calculations involved may be intractable, either in the weak sense that they would take far too long to do, or in the strong sense that you can’t actually do them at all.
Suppose, for example, that you wanted to use the laws of quantum mechanics to predict the behaviour of a cat. If you take the problem seriously, the way to do this is to write down the ‘quantum wave-function’ of every single subatomic particle in the cat. Having done this, you apply a mathematical rule known as Schrödinger’s equation, which physicists tell us will predict the future state of the cat.2
However, no sensible physicist would attempt any such thing, because the wavefunction is far too complicated. The number of subatomic particles in a cat is enormous; even if you could measure their states precisely – which of course you can’t do anyway – the universe does not contain a sheet of paper big enough to list all the numbers. So the calculation can’t even get started, because in practical terms the present state of the cat is indescribable in the language of quantum wavefunctions. As for plugging the wavefunction into Schrödinger’s equation, well, forget it.
The Science of Discworld II Page 33