SIXTEEN

FREE WON'T

What is the biggest source of danger for any organism? Predators? Natural disasters? Fellow organisms of the same species, who constitute the most direct compe­tition for everything? Sibling rivals, who compete even in the same family, the same nest? No. The biggest danger is the future.

If you've survived until now, then your past and present offer no dangers, or at least no new dangers. That time you broke your leg and it didn't heal very well left you vulnerable to lions, but the attack is still going to come, if at all, in the future. You can't do anything to change your past - unless you're a wizard - but you can do something to change your future. In fact, everything you do changes your future, in the sense that the nebulous space of future possibilities starts to crystallise out into the one future that actually happens. If you are a wizard, able to visit the past and change that, too, you still have to think about how a range of possibilities crystallises out into just one. You still march forward into your own personal future along your own personal timeline; it's just that, when seen from the perspective of con­ventional history, that timeline zigzags a lot.

We are committed to a view of ourselves as creatures that exist in time, not just in an ever-changing present. That is why we are fasci­nated by stories of time travel. And by stories about the future. We have established elaborate methods to foretell the future, and find our­selves at the mercy of deep-seated concepts such as Destiny and Free Will, which relate to our place in time and our ability to change the future - or not. However, we have an ambivalent attitude to the future. In most respects, we think that it is pre-determined, usually by factors beyond our control. Otherwise, how could it be predicted? Most sci­entific theories of the universe are deterministic: the laws give rise to only one possible future.

To be sure, quantum mechanics involves unavoidable elements of chance, at least according to the orthodox attitude of nearly all physi­cists, but quantum uncertainty fuzzes out and 'decoheres' as we move from the microscopic world to the macroscopic one, so on a human scale nearly everything that matters is again deterministic from the physical point of view. That doesn't mean that we know ahead of time what's going to happen, though. We have seen that two features of the workings of natural laws, chaos and complexity, imply that deter­ministic systems need not be predictable in any practical sense. But when we start to think about ourselves, we are utterly certain that we are not deterministic at all. We have free will, we can make choices. We can choose when to get out of bed, what to eat for breakfast, whether or not to put the radio on and listen to the news.

We're not so certain that animals have free will. Do cats and dogs make choices? Or are they merely responding to innate and unchange­able 'drives'? When it comes to simpler organisms like amoebas, we find it difficult to conceive of them choosing between alternatives; though when we watch them through a microscope, we get a strong feeling that they know what they're doing. We're happy to believe that this feeling is an illusion, a silly piece of anthropomorphism, invest­ing human qualities in a tiny bag of biochemicals; no doubt the amoeba is responding, deterministically, to chemical gradients in its environment. But it doesn't look deterministic because of the afore­mentioned get-outs, chaos and complexity. In contrast, when we make a choice, we have the overwhelming impression that we could have chosen to do something else. If that wasn't possible, then it wasn't really a choice.

We therefore model ourselves as free agents making choice after choice against the background of a complex and chaotic world. We are aware that any threat to our existence - or anything desirable - will come from the future, and that the free choices we make now can and will affect how that future turns out. If only we could foresee the future, we could work out the best choices, and make the future hap­pen the way we would like, and not the way the lions would like. Our intelligence gives us the ability to construct mental models of the future, mostly simple extrapolations of patterns that we have noticed in the past. Our extelligence collects these models, and welds them together into religious prophecies, scientific laws, ideologies, social imperatives ... We are time-binding animals, whose every action is constrained not just by the past and present, but also by our own antic­ipations of the future. We know that we can't predict the future very accurately, but a prediction that works only some of the time is, we feel, better than none. So we tell ourselves and each other stories about the future, and we use those stories to run our lives.

Those stories form part of the extelligence, and they interact with other elements in it, such as science and religion, to create a strong emotional attachment to belief systems or technology that can help us navigate into that uncertain future. Or claim to do so, and can con­vince us that the claim is valid, even if it's not. In many religions, enormous respect is paid to prophets, people so wise, or so in tune with the deity, that they know what the future will bring. The priests gain respect by predicting eclipses and the turn of the seasons. Scientists gain rather less respect by predicting the movements of the planets, and (less effectively) tomorrow's weather. Whoever controls the future controls human destiny.

Destiny. That's a strange concept in a creature that believes it has free will. If you can control the future, then the future cannot be fixed. If it is not fixed, then there is no such thing as destiny. Unless, per­haps, the future converges on the same events, whatever you do. There are many stories with this theme, of which the most famous is 'Appointment in Samara' (parodied in The Colour of Magic), when a man's efforts to escape Death only bring him to the very place where Death is waiting.

We entertain contradictory beliefs about the future. That's not such a surprise: we're not the most logically consistent of creatures. We tend to apply logic locally, within narrow limits, and when it suits us. We're very bad at applying it globally, setting one of our cherished beliefs up against another and looking for the inconsistencies. But we are especially inconsistent when it comes to dealing with the future.

Paradoxically, free will is the last thing you want if you're tribal. You're caught in the matrix of 'Everything that isn't mandatory is forbidden', and there is simply no room for free will. On the one hand, such an existence is very secure; but on the other, punishments and rewards are just as mandatory as everything else if your sins are found out. Your personal responsibility is only to obey the rules.

You can still tell yourself stories about the future, but they involve very narrow choices. 'Shall I attend the ritual meal tonight and leave early to say my evening prayers, or shall I stay for the communal prayers like everybody else?' Even in a tribal system, a lot of cheating goes on, because we're human. 'Well, now ... If I leave early, then I can drop by Fatima's tent, and my wives won't know about it ...'

Plenty of sins are possible, even in a tribal society, and in reality ones that survive allow a little flexibility. If, say, you forget to fast on the Holy Day and someone sees you eating, and you genuinely thought it was tomorrow, or an enemy told you that it was tomorrow, or you had been made to think it was tomorrow because an enemy had cast a curse upon you ... then some skilful pleading might miti­gate your punishment.

The natural and attractive option is always to blame others; it is unbearable to know that you have brought the punishment upon your­self. If you can't see how anyone else can be blamed for material reasons, then blame them for cursing you. Blame Fatima for being attractive and willing, blame an enemy who lied to you. 'Luck' is not available as a concept in a tribal society, because Allah knows every­thing, Jehovah is omniscient: the natural response is fatalistic acceptance of whatever they throw your way. If you are to attain heaven, so be it; if your fate is to be flung into the everlasting fires, then that is the Will of God, to which you are subservient. The best you can do, as a peasant-level tribesman, is to find out what is in store for you, what is Written in the Book.

Maybe you don't really want to know what's in the Book, but mon­key curiosity overcomes fear, and in any case you can't change what's Written and it might just be nice. So you go to the old lady in the for­est who can read tealeaves, or (today) to the iridologist or the spiritualist medium. And all of these alleged ways to foresee the future have a very revealing common feature. They interpret the small-and-contingent into the large-and-important.

Just like the Roman general spilling the guts of a ram on to the ground before the battle, so that the small-and-complicated can mir­ror a forthcoming battle that will be large-and-complicated, tealeaves and hand-lines are small-and-complicated, and 'must' therefore encode your complicated future. The kind of magic that is being invoked here is an unexpressed homology, which on some level we all believe in because we use it all the time. The stories that we construct in our minds are small-and-complicated, and they really do mirror the large-and-complicated things that happen to us. The Concise Lexicon of the Occult lists 93 methods of divination, from aeromancy (divination by the shapes of clouds) to xylomancy (divination by the shapes of twigs). All but four of them employ the small-and-complicated to predict the large-and-complicated; their materials include salt, barley, wind, wax, lead, onion sprouts (that one's called 'cromniomancy'), laughter, blood, fish guts, flames, pearls, and the noises made by mice ('myomancy'). The other four involve invoking spirits, calling up demons, or talking to gods.

To many tribal innocents, other people sometimes seem to have access to different little stories that they can make relevant to your life, like 'Your fate is written on your hand' or 'The dead communi­cate with me and they know all'. So people of that inclination can convince you, with a bit of flummery, that they know your future, and they can produce convincing large stories which you interpret as your fate.

There is a deep paradox in our attitude to personal free will. We want to know what the future will be in order to make a free choice that protects us against it. So we think of the future of everything outside us as being deterministic, which is why the gypsy or the medium or the dead can know what it is going to be. Nevertheless, we think of our own future as involving free choices. Our free will lets us choose to consult the gypsy, who then convinces us that we have no choice: for example, that the life-line on our palm determines when we will die. So our actions betray a deep-seated belief that the laws of the universe apply to everything except us.

The biggest wholesale business that preys on our convictions and con­fusions about free will in a powerful and often cruel universe, is astrology. Astrologers claim authority from Ancient Egypt, from Paracelsus and Dee, from Ancient Wisdom of all kinds including the Hindu Vedas and other Eastern literature. Let us review the appeal of astrology in the light of narrativium.

Astrologers have an immense following, and they have managed to pick up on both tribal and barbarian stories. They have the counter-scientific story for the civilised culture, able to attract both the tribal and barbarian aspects of our foolishness. They really do believe that the future, for each of us, is influenced by our time of birth. They time it to the second.

What seems to be important to them is against which starry back­ground (the Zodiac) we view the planets in our own solar system. As we move from intra-uterine life to the hands of the midwife, doctor, partner, our lives are determined from then on by astral forces. This strange belief is supported by so many people, who turn to the 'Your Stars' pages first in their daily newspaper, that we should seek some explanation within our 'story' framework. What is the story of our futures that is implicit in the control of our lives by the positions of the stars? As opposed, say, to the medical staff who, at the time of our birth, probably had more gravitational influence upon us than the planet Jupiter was having?

Well, the stars are obviously very numinous, powerful. They're up there wheeling over us. At least, they were when we were shepherds, staying out all night, but most civilised folk now don't know why the Moon changes its shape, let alone why or where the pole star is. Yes, all right, you do, and it's not surprising. Others don't, and don't think what they don't know is worth knowing.

They have a vague feel for a few of the constellations, especially the Big Dipper (or Great Bear), but they don't know that those stars are not near to each other, but merely appear to be in that formation when viewed from Earth, and then only for a short time, astronomi­cally speaking. Most people don't entertain astronomical thoughts, so why are the stars so heavily involved in our most potent stories? Perhaps because, in our nursery stories, the celestial sphere gives a context, a primitive animistic one in which Moon and Sun take pro­tagonist parts? We don't find that persuasive. Perhaps it is because the power of the stars entered our cultural stories back in the time when everyone could see the clear night sky, and has hung on. Or perhaps it is the jargon of the Zodiac-mongers, with their gypsy fortune-teller use of language to give received certainty to the most nebulous of prophecies. We've never heard anyone say, after reading the news­paper's astrology columns, 'Right, then, they're totally wrong today, no more astrology for me!'

There are others playing the same card, from Pyramidologists to Ancient Astronaut promoters to Flying Saucers Will Save Us visionar­ies to Rosicrucians. Regular UFO enthusiasts and Loch Ness monster photographers are much less dangerous. We focus on the prophets: those who, like followers of Nostradamus's prophecies or astrology, must believe that all the little contingencies add up to a grand pattern of the human future and that Fate rules us all.

This is the tribal interpretation of the feeling of free will: it is an illusion, for God already knows our futures. Kismet (the word comes from the Turkish 'qismet' and Arabic 'qisma') rules. Moreover - a neat twist that gives power over people as well as their money - whether you will be a beetle or a king in the next turn of the cosmic wheel is determined by the balance that you have achieved in this life. This is equally out of your control, in practice, but you can escape to an inner life, making it as far as possible irrelevant to the vicissitudes that attack your outer self, and thereby avoid beetlehood in your next incarnation.

That apparent escape again depends on our ability to construct sto­ries about our future. Here, our future divides, with the soul taking one direction under our own control and freed from the control of powerful others, while the body is manifestly bowed by slavery, star­vation, or torture. Hundreds of millions have found comfort in that apparent control of their futures, following the story of their spiritual selves and denying the pains of the material self.

In the Buddhist literature and practice, something close to that tran­scendence seems to be achievable. If you believe in fate, or the nearby concept of karma, then wisdom can consist only in foreseeing events, training your spiritual self to accept what happens, and teaching oth­ers to do the same. Some authority will provide your map of material events, but your destiny cannot be avoided by fighting it. Your only option is to lead a disciplined spiritual life, guided by stories of pre­vious successes in this quest, notably the Buddha, and to entertain hopes of leaving the Wheel of Life altogether, to exist as a spiritual presence with all ties to the material severed.

This nirvanic view of heaven is not for those who enjoy the mate­rial ride too much to want to get off the bus. And the paradoxical nature of the prophetic predictions - of all prophetic predictions - is disturbing. There is no way at all that a deterministic Earth can be accommodated by today's view of what planets are like, and most of today's more sophisticated religions have no room for an immanent God, tinkering with each life, and its context, to achieve its destiny. Those that do have room for immanence encounter real problems with modern technology, whose basis lies in ways-of-the-universe mod­elled by science, not by djinns or the whim of a deity or deities. And although we may, with Fredric Brown, be amused that when the djinni that worked the electric light and the radio came out on strike, the steam-power genies came out in sympathy, we enjoy this animistic fantasy as fuel for Murphy's Law and nice Disneyesque animations. We don't buy any of it for real causality.

Joseph Needham brought light to this kind of confusion. He pointed out, in the introduction to his truly gigantic History of Science in China, that the reason why China never developed science as the West knows it is that they never espoused monotheism. In polytheistic philoso­phies, it isn't very sensible to search for the cause of something, like a thunderstorm, say: you're liable to get a very contingent answer involving several incidents in the love lives of the gods, and an expla­nation of the provenance of thunderbolts that verges on the ridiculous. Monotheists, however, by which we mean someone like Abraham, to whom we shall return later, reckon that God had a consistent set of ideas and causalities in mind when he set the universe up. One set of ideas. If you expect your one God to be consistent, then it's worth asking how those causalities relate to each other: for example, 'black clouds and rain will be associated with thunderstorms when ..." what­ever. The monotheist can predict the weather, even if rather badly. But the polytheist needs a theopsychologist and a precise account of what the gods are up to at the moment. She needs to know whether a tiff between two gods will result in a thunderstorm. So scientific causality is compatible with God-causality, but not with gods-causal­ity.

Monotheists, moreover, have a built-in intolerance. The position that there is only one truth, only one avenue to the one God, sets each monotheistic religion in opposition to all others. There is no room for manoeuvre, no way to tolerate the manifest errors of people who believe in some other god. So monotheism laid the foundation for the Inquisition, and for intemperate Christianity through the ages from the crusades through to African and Polynesian missionaries. 'I have the story, and it is the only one' is characteristic of many cults, all of them intolerant.

Faiths, of course, do get along. But they get along because of the hammering they have taken at the hands of science, material devel­opment and better education. They get along because of wise people within them who recognise the commonality of humanity. Where there are too few wise people, you get Northern Ireland. If you are lucky.

If the future is not fixed, but malleable, and we can predict the effects of our present behaviour, however badly, then predicting the future can be self-defeating. And that can even be the reason for predicting it.

Most of the Biblical prophets seem, like many science-fiction authors today, to be warning against what might happen if we go on as we are doing. So they succeed when their prophecy is not correct, because people heed it and change their actions. We can understand that; even though the prophecy didn't come true, we can all see that it might have done: it has given us a better idea of the phase space that the future of our culture lives in.

What about the gypsy who prophesies that a tall dark man will come into your life, thus making you receptive to all those future tall dark men? (if tall dark men interest you, of course; it's up to you.) This could be a self-fulfilling prophecy, the opposite of the stories told by Biblical prophets. It's a story that the recipient is sympathetic to, wants to happen.

There are said to be only seven basic story plots, so perhaps our minds are much less varied than we think, so that the newspaper astrologer and the fortune-teller are navigating a much smaller phase space of human experience than we thought. This would account for so many people feeling that the predictions show deep insight.

But when astronomers predict the future, and get it right, people are, paradoxically, much less impressed. When they predict eclipses correctly, every time, this seems less meaningful than the astrologers nearly getting many people right, sometimes. Remember Y2K, the prophecy that planes would fall out of the sky soon after the year 2000 dawned and your toaster wouldn't work? That prophecy cost the world several billion dollars in work to avert the problem - and it didn't hap­pen. A waste of time, then? Not at all. It didn't happen because people took precautions. If they hadn't done, the cost would have been much higher. It was a Biblical prophecy: 'If this goes on ...' And, lo, the mul­titude heeded.

This recursive dependence of prophecy upon people's responses to it, unlike most of the other kinds of thing that we say, relates back to our facility with our own made-up little futures, the stories that we tell ourselves. They confirm us in our identities. It is no wonder that when someone - an astrologer or Nostradamus, say - pokes his fin­ger into this mental place where we live, and inserts some of his own stories, we want to believe him. His stories are more exciting than ours. We wouldn't have thought, going down the stairs to get a train to work, 'I wonder if I'm going to meet a tall dark guy today?' But once it's been put into our minds, we smile at all the dark men, even some quite short ones. And so our lives are changed (perhaps in quite major ways, if you are a man doing the smiling) as are the stories that we ourselves proposed for our futures.

This way that we react, fairly predictably, to what the world throws at us, casts doubt on our otherwise unshakeable belief that we get to choose what we do. Do we truly possess free will? Or are we like the amoeba, drifting this way and that, propelled by the dynamic of a phase space that cannot be perceived from outside?

In Figments of Reality we included a chapter with the title 'We wanted to have a chapter on free will but we decided not to, so here it is'. There we examined such issues as whether, in a world without genuine free will, it would be fair to blame a person for their actions. We conclude that in a world without genuine free will, there might not be any choice: they would get blamed anyway because the pos­sibility of them not being blamed did not exist.

We won't go over that ground in detail, but we do want to sum­marise the main thrust of the argument. We start by observing that there is no effective scientific test for free will. You can't run the uni­verse again, with everything exactly as it was, and see if a different choice can be made second time round. Moreover, there seems to be no room in the laws of physics for genuine free will. Quantum inde­terminacy, seized on so readily by many philosophers and scientists as a catch-all explanation of 'consciousness', is the wrong kind of thing altogether: random unpredictability is not the same as choosing between clear alternatives.

There are many ways in which the known laws of physics could offer an illusion of free will, for example by exploiting chaos or emer­gence, but there is no way to set up a system that could make different choices even though every particle in the universe, including those making up the system, is in the same state on both occasions.

Add to this one rather interesting aspect of human social behaviour: although we feel as if we have free will, we don't act as if we believe that anybody else has. When somebody does something uncharac­teristic, 'not like them', we don't say 'Oh, Fred is exercising his free will. He's been a lot happier since he smiled at the tall, dark stranger.' We say 'What the devil has got into Fred?' Only when we find a rea­son for his actions, an explanation not involving the exercise of free will (like drunkenness, or 'doing it for a bet') do we feel satisfied.

All of this suggests that our minds do not actually make choices: they make judgements. Those judgements reveal not what we have chosen, but what kind of mind we possess. 'Well, I never would have guessed,' we say, and feel we've learned something that we can use in future dealings with that person.

So what about that strong feeling that we get, of making a choice? That's not what we're doing, it's what it feels like to us when we're doing it, just as that vivid grey quale of the visual system is not actu­ally out there on the elephant, but an added decoration that exists in our heads. 'Choosing' is what our minds feel like from inside when they're judging between alternatives. Free will is not a real attribute of human beings at all: it is merely the quale of judgement.

SEVENTEEN

FREEDOM OF INFORMATION

People believed that elves could look like anything they wanted to, but this was, strictly speaking, wrong. Elves looked the same all the time (rather dull and grey, with large eyes, rather similar to bushbabies without the charm) but they could, without effort, cause others to see them differently.

Currently the Queen looked like a fashionable lady of the time, in black lace, sparkling here and there with diamonds. Only with a hand over one eye and extreme concentration could even a trained wizard dimly see the true nature of the elf, and even then his eye would water alarmingly.

Nevertheless, the wizards stood up when she entered. There's such a thing as courtesy, after all.

'Welcome to my world, gentlemen,' said the Queen, sitting down. Behind her, a couple of guards took up station either side of the door. 'Ours!' snarled the Dean. 'It's our world!'

'Let us continue to disagree, shall we?' said the Queen brightly. 'You may have constructed it, but it's our world now.'

'We have iron, you know,' said Ridcully. 'Would you like some tea, by the way? Foul stuff made without actual tea.'

'Much good may it do you. No, thank you,' said the Queen. 'Please note that my guards are human. So is your host. The Dean looks angry. 'You intend to fight here? When you have no magic? Be serious, gen­tlemen. You should be grateful, after all. This is a world without narrativium. Your strange humans were monkeys without stories. They did not know how the world was supposed to go. We gave them stories, and made them people.'

'You gave them gods and monsters,' said Ridcully. 'Stuff that stops people thinking straight. Superstitions. Demons. Unicorns. Bogeymen.'

'You have bogeymen on your world, don't you?' said the Queen.

'Yes, we do. But outside, where we can get at 'em. They ain't sto­ries. When you can see 'em, they don't have any power.'

'Like unicorns,' said the Lecturer in Recent Runes. 'When you meet one, you find out it's just a big sweaty horse. Looks nice, smells horsey.'

'And it's magical,' said the Queen, her eyes gleaming.

'Yes, but that's just another thing about it,' said Ridcully. 'Big, sweaty, magical. There's nothing mysterious about it. You just learn the rules.'

'But surely you should be pleased!' said the Queen, her eyes say­ing that she knew they weren't and was glad of it. 'Everyone here thinks this world is just like yours! Many people even believe that it is flat!'

'Yes, but back home they'd be right,' said Ridcully. 'Here they're just ignorant.'

'Well, there is not a single thing you can do about it,' said the Queen. 'This is our world, Mister Wizard. It's all stories. The religions here ... amazing! And the beliefs ... wonderful! The crop is bountiful, the harvest is rewarding. Do you know that more people believe in magic here than they do on your world?'

'We don't have to believe in it. It works!' snapped Ridcully.

'They believe in it here, and it doesn't,' said the Queen. 'And thus they believe in it even more, while ceasing to believe in themselves. Isn't it astonishing?'

She stood up. Most of the wizards went to stand up, too, and one or two of them got all the way. Misogynists to a man, the wizards were therefore always punctiliously polite to ladies.

Here, you are just rather fussy old men,' she said. 'But we under­stand this world and we have had time to cultivate it. We like it. You can't take us away. Your humans need us. We are part of their world now.'

'This world, madam, has about another thousand years before all life is wiped out,' said Ridcully.

'Then there are other worlds,' said the Queen, lightly.

'That's all you have to say?'

'What else is there? Worlds begin and end,' said the Queen. 'That is how the universe works. That is the great circle of existence.'

'The great circle of existence, madam, can eat my underwear!' said Ridcully.

'Fine words,' said the Queen. 'You are good at concealing your true thoughts from me, but I can also see them in your face, nevertheless. You think you can still fight us and win. You have forgotten that there is no narrativium in this world. It does not know how stories should go. Here, the third son of a king is probably just a useless weak prince. Here, there are no heroes, only degrees of villainy. An old lady gath­ering wood in the forest is just an old lady and not, as in your world, almost certainly a witch. Oh, there is a belief in witches. But a witch here is merely a method of ridding society of burdensome old ladies and an inexpensive way of keeping the fire going all night. Here, gen­tlemen, good does not ultimately triumph at the expense of a few bruises and a non-threatening shoulder wound. Here, evil is generally defeated by a more organised kind of evil. My world, gentlemen. Not yours. Good day to you.'

And then she was gone.

The wizards sat down again. Outside, the carriage rattled away.

'Quite well spoken for an elf, I thought,' said the Lecturer in Recent Runes. 'Good turn of phrase.'

And that's it? said Ridcully. 'We can't do anything?'

'We don't have any magic, sir,' said Ponder.

'But we do know everythin' is goin' to turn out all right, though, don't we?' said Ridcully. 'We know that people get off the planet before the next big wallop, right? We saw the evidence. Right?'

Ponder sighed.

'Yes, sir. But it might not happen. It's like the Shell Midden people.'

'They didn t happen?'

'Not ... here, sir,' said Ponder.

'Ah. And you're goin' to say "it's because of quantum" at some point?' 'I hadn't intended to, sir, but you're on the right lines.'

'So ... when we left them, did they pop out of existence?'

'No, sir. We did.'

'Oh. Well, so long as someone did ...' said Ridcully. Any thoughts, gentlemen?'

'We could go to the pub again?' said the Lecturer in Recent Runes, hopefully.

'No,' said Ridcully. 'This is serious.'

'So am I.'

'I don't see what we can do,' said the Dean. 'The humans here needed the elves to tinker with their heads. When we stopped that, we got the Shell Midden people. When we didn't stop it, we got peo­ple like Dee, head half full of rubbish.'

'I know someone who'd be right at home with this problem,' said Ridcully, thoughtfully. 'Mister Stibbons, we would be able to get back home now, wouldn't we? Just to send a semaphore message?'

'Yes, sir, but there's no need for that. Hex can do that directly,' said Ponder, before he could stop himself.

'How?' said Ridcully.

'I ... er ... connected him up to the semaphore just after you left, sir. Er ... it was just a matter of pulleys and things. Er ... I installed a little set of repeater arms on the roof of the High Energy Magic Building. Er ... and employed a gargoyle to do the watching, and we needed one anyway, because the pigeons up there have really got too numerous ... er ...'

'So Hex can send and receive messages?' said Ridcully.

'Yes, sir. All the time. Er ...'

'But that costs a fortune! Is it coming out of your budget, man?'

'Er, no, sir, because it's actually quite cheap, er ... it's free, actually ..." Ponder went for broke. 'Hex worked out the codes, you see. The gargoyles up on the big tower don't bother about where the signals are coming from, they just notice the codes, so, er, Hex started by adding the codes for the Assassins' Guild or the Fools' Guilds to the messages and, er, they probably didn't notice the extra amount on their bills because they're using the clacks all the time these days-'

'So ... we're stealing? said Ridcully.

'Well, er, yes, sir, in a way, but it's hard to know exactly what. Last month Hex worked out the semaphore company's own codes so his messages travel as part of their internal signalling, sir. No one gets billed for that.'

'This is very disturbing news, Stibbons,' said Ridcully sternly.

'Yes, sir,' said Ponder, looking at his feet.

'I feel I must ask you a rather difficult and worrying question: is it likely that anyone will find out?'

'Oh, no, sir. It's impossible to trace.'

'Impossible?'

'Yes, sir. Every week Hex sends a message to company headquar­ters readjusting the total of messages sent, sir. Anyway, there's so many I don't think anyone checks.'

'Oh? Well, that's all right then,' said Ridcully. 'It never really hap­pens, and no one can find out it's us in any case. Can we send all our messages that way?'

"Well, technically yes, sir, but I think that might be abusing the-'

'We are academics, Stibbons,' said the Dean. 'And information should be allowed to flow freely.'

'Exactly,' said the Lecturer in Recent Runes. 'An untrammelled flow of information is essential to a progressive society. This is the age of the semaphore, after all.'

'Obviously it flows to us,' said Ridcully.

'Oh, certainly,' said the Dean. 'We don't want it flowing away from us. We're talking about flow here, not spread.'

'You wanted a message sent?' said Ponder, before the wizards got too deeply into this.

'And we really don't have to pay?' said Ridcully.

Ponder sighed. 'No, sir.'

'Jolly good,' said the Archchancellor. 'Have this one sent to the king­dom of Lancre, will you? They've only got one clacks tower. Got your notebook? Message begins:

"To Mistress Esmerelda Weatherwax. How are you? I am fine. An inter­esting problem has arisen ..."

EIGHTEEN

BIT FROM IT

A semaphore is a simple and time-honoured example of a digital communication system. It encodes letters of the alphabet using the positions of flags, lights, or something similar. In 1795 George Murray invented a version that is close to the system currently used in Discworld: a set of six shutters that could be opened or closed, thus giving 64 different 'codes', more than enough for the entire alphabet, numbers 0 to 10 and some 'special' codes. The system was further developed but ceased to be cutting-edge technology when the electric telegraph heralded the wired age. The Discworld semaphore (or 'clacks') has been taken much further, with mighty trunk route towers carrying bank after bank of shutters, aided by lamps after dark, and streaming messages bi-directionally across the continent. It is a pretty accurate 'evolution' of the technology: if we too had failed to harness steam and electricity, we might well be using something like it ...

There is enough capacity on that system even to handle pictures - seriously. Convert the picture to a 64 x 64 grid of little squares that can be black, white or four shades of grey, and then read the grid from left to right and top to bottom like a book. It's just a matter of infor­mation, a few clever clerks to work out some compression algorithms, and a man with a shallow box holding 4,096 wooden blocks, their six sides being, yes, black, white and four shades of grey. It'll take them a while to reassemble the pictures, but clerks are cheap.

Digital messages are the backbone of the Information Age, which is the name we currently give to the one we're living in, in the belief that we know a lot more than anyone else, ever. Discworld is com­parably proud of being in the Semaphore Age, the Age of the Clacks. But what, exactly, is information?

When you send a message, you are normally expected to pay for it - because if you don't, then whoever is doing the work of transmit­ting that message for you will object. It is this feature of messages that has got Ridcully worried, since he is wedded to the idea that acade­mics travel free.

Cost is one way to measure things, but it depends on complicated market forces. What, for example, if there's a sale on? The scientific-concept of 'information' is a measure of how much message you're sending. In human affairs, it seems to be a fairly universal principle that for any given medium, longer messages cost more than short ones. At the back of the human mind, then, lurks a deep-seated belief that messages can be quantified: they have a size. The size of a message tells you 'how much information' it contains.

Is 'information' the same as 'story'? No. A story does convey infor­mation, but that's probably the least interesting thing about stories. Most information doesn't constitute a story. Think of a telephone direc­tory: lots of information, strong cast, but a bit weak on narrative. What counts in a story is its meaning. And that's a very different concept from information.

We are proud that we live in the Information Age. We do, and that's the trouble. If we ever get to the Meaning Age, we'll finally understand where we went wrong.

Information is not a thing, but a concept. However, the human ten­dency to reify concepts into things has led many scientists to treat information as if it is genuinely real. And some physicists are start­ing to wonder whether the universe, too, might be made from information.

How did this viewpoint come about, and how sensible is it?

Humanity acquired the ability to quantify information in 1948, when the mathematician-turned-engineer Claude Shannon found a way to define how much information is contained in a message - he pre­ferred the term signal - sent from a transmitter to a receiver using some kind of code. By a signal, Shannon meant a series of binary dig­its ('bits', 0 and 1) of the kind that is ubiquitous in modern computers and communication devices, and in Murray's semaphore. By a code, he meant a specific procedure that transforms an original signal into another one. The simplest code is the trivial 'leave it alone'; more sophisticated codes can be used to detect or even correct transmis­sion errors. In the engineering applications, codes are a central issue, but for our purposes here we can ignore them and assume the mes­sage is sent 'in plain'.

Shannon's information measure puts a number to the extent to which our uncertainty about the bits that make up a signal is reduced by what we receive. In the simplest case, where the message is a string of 0s and 1s and every choice is equally likely, the amount of infor­mation in a message is entirely straightforward: it is the total number of binary digits. Each digit that we receive reduces our uncertainty about that particular digit (is it 0 or 1?) to certainty ('it's a 1', say) but tells us nothing about the others, so we have received one bit of infor­mation. Do this a thousand times and we have received a thousand bits of information. Easy.

The point of view here is that of a communications engineer, and the unstated assumption is that we are interested in the bit-by-bit con­tent of the signal, not in its meaning. So the message 111111111111111 contains 15 bits of information, and so does the message 111001101101011. But Shannon's concept of information is not the only possible one. More recently, Gregory Chaitin has pointed out that you can quantify the extent to which a signal contains patterns. The way to do this is to focus not on the size of the message, but on the size of a computer program, or algorithm, that can generate it. For instance, the first of the above messages can be created by the algo­rithm 'every digit is a 1'. But there is no simple way to describe the second message, other than to write it down bit by bit. So these two messages have the same Shannon information content, but from Chaitin's point of view the second contains far more 'algorithmic infor­mation' than the first.

Another way to say this is that Chaitin's concept focuses on the extent to which the message is 'compressible'. If a short program can generate a long message, then we can transmit the program instead of the message and save time and money. Such a program 'com­presses' the message. When your computer takes a big graphics file - a photograph, say - and turns it into a much smaller file in JPEG for­mat, it has used a standard algorithm to compress the information in the original file. This is possible because photographs contain numer­ous patterns: lots of repetitions of blue pixels for the sky, for instance. The more incompressible a signal is, the more information in Chaitin's sense it contains. And the way to compress a signal is to describe the patterns that make it up. This implies that incompressible signals are random, have no pattern, yet contain the most information. In one way this is reasonable: when each successive bit is maximally unpre­dictable, you learn more from knowing what it is. If the signal reads 111111111111111 then there is no great surprise if the next bit turns out to be 1; but if the signal reads 111001101101011 (which we obtained by tossing a coin 15 times) then there is no obvious guess for the next bit.

Both measures of information are useful in the design of electronic technology. Shannon information governs the time it takes to transmit a signal somewhere else; Chaitin information tells you whether there's a clever way to compress the signal first, and transmit something smaller. At least, it would do if you could calculate it, but one of the features of Chaitin's theory is that it is impossible to calculate the amount of algorithmic information in a message - and he can prove it. The wizards would approve of this twist.

'Information' is therefore a useful concept, but it is curious that 'To be or not to be' contains the same Shannon information as, and less Chaitin information than, 'xyQGRlfryu&d°/oskOwc'. The reason for this disparity is that information is not the same thing as meaning. That's fascinating. What really matters to people is the meaning of a mes­sage, not its bit-count, but mathematicians have been unable to quantify meaning. So far.

And that brings us back to stories, which are messages that convey meaning. The moral is that we should not confuse a story with 'infor­mation'. The elves gave humanity stories, but they didn't give them any information. In fact, the stories people came up with included things like werewolves, which don't even exist on Roundworld. No information there - at least, apart from what it might tell you about the human imagination.

Most people, scientists in particular, are happiest with a concept when they can put a number to it. Anything else, they feel, is too vague to be useful. 'Information' is a number, so that comfortable feeling of pre­cision slips in without anyone noticing that it might be spurious. Two sciences that have gone a long way down this slippery path are biol­ogy and physics.

The discovery of the linear molecular structure of DNA has given evolutionary biology a seductive metaphor for the complexity of organ­isms and how they evolve, namely: the genome of an organism represents the information that is required to construct it. The origin of this metaphor is Francis Crick and James Watson's epic discovery that an organism's DNA consists of 'code words' in the four molecu­lar 'letters' A C T G, which, you'll recall, are the initials of the four possible 'bases'. This description led to the inevitable metaphor that the genome contains information about the corresponding organism. Indeed, the genome is widely described as 'containing the informa­tion needed to produce' an organism.

The easy target here is the word 'the'. There are innumerable rea­sons why a developing organism's DNA does not determine the organism. These non-genomic influences on development are col­lectively known as 'epigenetics', and they range from subtle chemical tagging of DNA to the investment of parental care. The hard target is 'information'. Certainly, the genome includes information in some sense: currently an enormous international effort is being devoted to listing that information for the human genome, and also for other organisms such as rice, yeast, and the nematode worm Caenorhabditis elegans. But notice how easily we slip into cavalier attitudes, for here the word 'information' refers to the human mind as receiver, not to the developing organism. The Human Genome Project informs us, not organisms.

This flawed metaphor leads to the equally flawed conclusion that the genome explains the complexity of an organism in terms of the amount of information in its DNA code. Humans are complicated because they have a long genome that carries a lot of information; nematodes are less complicated because their genome is shorter. However, this seductive idea can't be true. For example, the Shannon information content of the human genome is smaller by several orders of magnitude than the quantity of information needed to describe the wiring of the neurons in the human brain. How can we be more com­plex than the information that describes us? And some amoebas have much longer genomes than ours, which takes us down several pegs as well as casting even more doubt on DNA as information.

Underlying the widespread belief that DNA complexity explains organism complexity (even though it clearly doesn't) are two assump­tions, two scientific stories that we tell ourselves. The first story is DNA as Blueprint, in which the genome is represented not just as an impor­tant source of control and guidance over biological development, but as the information needed to determine an organism. The second is DNA as Message, the 'Book of Life' metaphor.

Both stories oversimplify a beautifully complex interactive system. DNA as Blueprint says that the genome is a molecular 'map' of an organism. DNA as Message says that an organism can pass that map to the next generation by 'sending' the appropriate information.

Both of these are wrong, although they're quite good science fic­tion - or, at least, interestingly bad science fiction with good special effects.

If there is a 'receiver' for the DNA 'message' it is not the next gen­eration of the organism, which does not even exist at the time the 'message' is being 'sent', but the ribosome, which is the molecular machine that turns DNA sequences (in a protein-coding gene) into protein. The ribosome is an essential part of the coding system; it functions as an 'adapter', changing the sequence information along the DNA into an amino acid sequence in proteins. Every cell contains many ribosomes: we say 'the' because they are all identical. The metaphor of DNA as information has become almost universal, yet virtually nobody has suggested that the ribosome must be a vast repository of information. The structure of the ribosome is now known in high detail, and there is no sign of obvious 'information-bearing' structure like that in DNA. The ribosome seems to be a fixed machine. So where has the information gone? Nowhere. That's the wrong question.

The root of these misunderstandings lies in a lack of attention to context. Science is very strong on content, but it has a habit of ignor­ing 'external' constraints on the systems being studied. Context is an important but neglected feature of information. It is so easy to focus on the combinatorial clarity of the message and to ignore the messy, complicated processes carried out by the receiver when it decodes the message. Context is crucial to the interpretation of messages: to their meaning. In his book The User Illusion Tor Norretranders intro­duced the term exformation to capture the role of the context, and Douglas Hofstadter made the same general point in Godel, Escher, Bach. Observe how, in the next chapter, the otherwise incompre­hensible message 'THEOSTRY' becomes obvious when context is taken into account.

Instead of thinking about a DNA 'blueprint' encoding an organism, it's easier to think of a CD encoding music. Biological development is like a CD that contains instructions for building a new CD-player. You can't 'read' those instructions without already having one. If mean­ing does not depend upon context, then the code on the CD should have an invariant meaning, one that is independent of the player. Does it, though?

Compare two extremes: a 'standard' player that maps the digital code on the CD to music in the manner intended by the design engi­neers, and a jukebox. With a normal jukebox, the only message that you send is some money and a button-push; yet in the context of the jukebox these are interpreted as a specific several minutes' worth of music. In principle, any numerical code can 'mean' any piece of music you wish; it just depends on how the jukebox is set up, that is, on the exformation associated with the jukebox's design. Now consider a jukebox that reacts to a CD not by playing the tune that's encoded on it, as a series of bits, but by interpreting that code as a number, and then playing some other CD to which that number has been assigned. For instance, suppose that a recording of Beethoven's Fifth Symphony starts, in digital form, with 11001. That's the number 25 in binary. So the jukebox reads the CD as '25', and looks for CD number 25, which we'll assume is a recording of Charlie Parker playing jazz. On the other hand, elsewhere in the jukebox is CD number 973, which actually is Beethoven's Fifth Symphony. Then a CD of Beethoven's Fifth can be 'read' in two totally different ways: as a 'pointer' to Charlie Parker, or as Beethoven's Fifth Symphony itself (triggered by whichever CDs start with 973 in binary). Two contexts, two interpretations, two meanings, two results.

Whether something is a message depends upon context, too: sender and receiver must agree upon a protocol for turning meanings into symbols and back again. Without this protocol a semaphore is just a few bits of wood that flap about. Tree branches are bits of wood that flap about, too, but no one ever tries to decode the message being transmitted by a tree. Tree rings - the growth rings that appear when you saw through the trunk, one ring per year - are a different matter. We have learned to 'decode' their 'message', about climate in the year 1066 and the like. A thick ring indicates a good year with lots of growth on the tree, probably warm and wet; a thin ring indicates a poor year, probably cold and dry. But the sequence of tree rings only became a message, only conveyed information, when we figured out the rules that link climate to tree growth. The tree didn't send its mes­sage to us.

In biological development the protocol that gives meaning to the DNA message is the laws of physics and chemistry. That is where the exformation resides. However, it is unlikely that exformation can be quantified. An organism's complexity is not determined by the num­ber of bases in its DNA sequence, but by the complexity of the actions initiated by those bases within the context of biological development. That is, by the meaning of the DNA 'message' when it is received by a finely tuned, up-and-running biochemical machine. This is where we gain an edge over those amoebas. Starting with an embryo that develops little flaps, and making a baby with those exquisite little hands, involves a series of processes that produce skeleton, muscles, skin, and so on. Each stage depends on the current state of the oth­ers, and all of them depend on contextual physical, biological, chemical and cultural processes.

A central concept in Shannon's information theory is something that he called entropy, which in this context is a measure of how statisti­cal patterns in a source of messages affect the amount of information that the messages can convey. If certain patterns of bits are more likely than others, then their presence conveys less information, because the uncertainty is reduced by a smaller amount. In English, for example, the letter 'E' is much more common than the letter 'Q'. So receiving an 'E' tells you less than receiving a 'Q'. Given a choice between 'E' and 'Q', your best bet is that you're going to receive an 'E'*. And you learn the most when your expectations are proved wrong. Shannon's entropy smooths out these statistical biases and provides a 'fair' mea­sure of information content.

In retrospect, it was a pity that he used the name 'entropy', because there is a longstanding concept in physics with the same name, nor­mally interpreted as 'disorder'. Its opposite, 'order', is usually identified with complexity. The context here is the branch of physics known as thermodynamics, which is a specific simplified model of a gas. In ther­modynamics, the molecules of a gas are modelled as 'hard spheres', tiny billiard balls. Occasionally balls collide, and when they do, they bounce off each other as if they are perfectly elastic. The Laws of Thermodynamics state that a large collection of such spheres will obey certain statistical regularities. In such a system, there are two forms of energy: mechanical energy and heat energy. The First Law states that the total energy of the system never changes. Heat energy can be trans­formed into mechanical energy, as it is in, say, a steam engine; conversely, mechanical energy can be transformed into heat. But the sum of the two is always the same. The Second Law states, in more precise terms (which we explain in a moment), that heat cannot be transferred from a cool body to a hotter one. And the Third Law states that there is a specific temperature below which the gas cannot go - 'absolute zero', which is around -273 degrees Celsius.

The most difficult - and the most interesting - of these laws is the Second. In more detail, it involves a quantity that is again called 'entropy', which is usually interpreted as 'disorder'. If the gas in a room is concentrated in one corner, for instance, this is a more ordered (that is, less disordered!) state than one in which it is distributed uniformly throughout the room. So when the gas is uni­formly distributed, its entropy is higher than when it is all in one corner. One formulation of the Second Law is that the amount of entropy in the universe always increases as time passes. Another way to say this is that the universe always becomes less ordered, or equivalently less complex, as time passes. According to this interpretation, the highly complex world of living creatures will inevitably become less complex, until the universe eventually runs out of steam and turns into a thin, lukewarm soup.

This property gives rise to one explanation for the 'arrow of time', the curious fact that it is easy to scramble an egg but impossible to unscramble one. Time flows in the direction of increasing entropy. So scrambling an egg makes the egg more disordered - that is, increases its entropy - which is in accordance with the Second Law. Unscrambling the egg makes it less disordered, and decreases energy, which conflicts with the Second Law. An egg is not a gas, mind you, but thermodynamics can be extended to solids and liquids, too.

At this point we encounter one of the big paradoxes of physics, a source of considerable confusion for a century or so. A different set of physical laws, Newton's laws of motion, predicts that scrambling an egg and unscrambling it are equally plausible physical events. More precisely, if any dynamic behaviour that is consistent with Newton's laws is run backwards in time, then the result is also consistent with Newton's laws. In short, Newton's laws are 'time-reversible'.

However, a thermodynamic gas is really just a mechanical system built from lots of tiny spheres. In this model, heat energy is just a spe­cial type of mechanical energy, in which the spheres vibrate but do not move en masse. So we can compare Newton's laws with the laws of thermodynamics. The First Law of Thermodynamics is simply a restatement of energy conservation in Newtonian mechanics, so the First Law does not contradict Newton's laws. Neither does the Third Law: absolute zero is just the temperature at which the spheres cease vibrating. The amount of vibration can never be less than zero.

Unfortunately, the Second Law of Thermodynamics behaves very differently. It contradicts Newton's laws. Specifically, it contradicts the property of time-reversibility. Our universe has a definite direction for its 'arrow of time', but a universe obeying Newton's laws has two dis­tinct arrows of time, one the opposite of the other. In our universe, scrambling eggs is easy and unscrambling them seems impossible. Therefore, according to Newton's laws, in a time-reversal of our uni­verse, unscrambling eggs is easy but scrambling them is impossible. But Newton's laws are the same in both universes, so they cannot pre­scribe a definite arrow of time.

Many suggestions have been made to resolve this discrepancy. The best mathematical one is that thermodynamics is an approximation, involving a 'coarse-graining' of the universe in which details on very fine scales are smeared out and ignored. In effect, the universe is divided into tiny boxes, each containing (say) several thousand gas molecules. The detailed motion inside such a box is ignored, and only the average state of its molecules is considered.

It's a bit like a picture on a computer screen. If you look at it from a distance, you can see cows and trees and all kinds of structure. But if you look sufficiently closely at a tree, all you see is one uniformly green square, or pixel. A real tree would still have detailed structure at this scale - leaves and twigs, say - but in the picture all this detail is smeared out into the same shade of green.

In this approximation, once 'order' has disappeared below the level of the coarse-graining, it can never come back. Once a pixel has been smeared, you can't unsmear it. In the real universe, though, it some­times can, because in the real universe the detailed motion inside the boxes is still going on, and a smeared-out average ignores that detail. So the model and the reality are different. Moreover, this modelling assumption treats forward and backward time asymmetrically. In for­ward time, once a molecule goes into a box, it can't escape. In contrast, in a time-reversal of this model it can escape from a box but it can never get in if it wasn't already inside that box to begin with.

This explanation makes it clear that the Second Law of Thermodynamics is not a genuine property of the universe, but merely a property of an approximate mathematical description. Whether the approximation is helpful or not thus depends on the context in which it is invoked, not on the content of the Second Law of Thermodynamics. And the approximation involved destroys any relation with Newton's laws, which are inextricably linked to that fine detail. Now, as we said, Shannon used the same word 'entropy' for his mea­sure of the structure introduced by statistical patterns in an information source. He did so because the mathematical formula for Shannon's entropy looks exactly the same as the formula for the thermodynamic concept. Except for a minus sign. So thermodynamic entropy looks like negative Shannon entropy: that is, thermodynamic entropy can be interpreted as 'missing information'. Many papers and books have been written exploiting this relationship - attributing the arrow of time to a gradual loss of information from the universe, for instance. After all, when you replace all that fine detail inside a box by a smeared-out average, you lose information about the fine detail. And once it's lost, you can't get it back. Bingo: time flows in the direction of informa­tion-loss.

However, the proposed relationship here is bogus. Yes, the formu­las look the same ... but they apply in very different, unrelated, contexts. In Einstein's famous formula relating mass and energy, the symbol c represents the speed of light. In Pythagoras's Theorem, the same letter represents one side of a right triangle. The letters are the same, but nobody expects to get sensible conclusions by identifying one side of a right triangle with the speed of light. The alleged rela­tionship between thermodynamic entropy and negative information isn't quite that silly, of course. Not quite.

As we've said, science is not a fixed body of 'facts', and there are disagreements. The relation between Shannon's entropy and thermo­dynamic entropy is one of them. Whether it is meaningful to view thermodynamic entropy as negative information has been a contro­versial issue for many years. The scientific disagreements rumble on, even today, and published, peer-reviewed papers by competent sci­entists flatly contradict each other.

What seems to have happened here is a confusion between a for­mal mathematical setting in which 'laws' of information and entropy can be stated, a series of physical intuitions about heuristic interpreta­tions of those concepts, and a failure to understand the role of context. Much is made of the resemblance between the formulas for entropy in information theory and thermodynamics, but little attention is paid to the context in which those formulas apply. This habit has led to some very sloppy thinking about some important issues in physics.

One important difference is that in thermodynamics, entropy is a quantity associated with a state of the gas, whereas in information the­ory it is defined for an information source: a system that generates entire collections of states ('messages'). Roughly speaking, a source is a phase space for successive bits of a message, and a message is a tra­jectory, a path, in that phase space. In contrast, a thermodynamic configuration of molecules is a point in phase space. A specific con­figuration of gas molecules has a thermodynamic entropy, but a specific message does not have a Shannon entropy. This fact alone should serve as a warning. And even in information theory, the infor­mation 'in' a message is not negative information-theoretic entropy. Indeed the entropy of the source remains unchanged, no matter how many messages it generates.

There is another puzzle associated with entropy in our universe. Astronomical observations do not fit well with the Second Law. On cosmological scales, our universe seems to have become more com­plex with the passage of time, not less complex. The matter in the universe started out in the Big Bang with a very smooth distribution, and has become more and more clumpy - more and more complex - with the passage of time. The entropy of the universe seems to have decreased considerably, not increased. Matter is now segregated on a huge range of scales: into rocks, asteroids, planets, stars, galaxies, galactic clusters, galactic superclusters and so on. Using the same metaphor as in thermodynamics, the distribution of matter in the uni­verse seems to be becoming increasingly ordered. This is puzzling since the Second Law tells us that a thermodynamic system should become increasingly disordered.

The cause of this clumping seems to be well established: it is grav­ity. A second time-reversibility paradox now rears its head. Einstein's field equations for gravitational systems are time-reversible. This means that if any solution of Einstein's field equations is time-reversed, it becomes an equally valid solution. Our own universe, run backwards in this manner, becomes a gravitational system that gets less and less clumpy as time passes - so getting less clumpy is just as valid, physi­cally, as getting more clumpy. Our universe, though, does only one of these things: more clumpy.

Paul Davies's view here is that 'as with all arrows of time, there is a puzzle about where the asymmetry comes in ... The asymmetry must therefore be traced to initial conditions'. What he means here is that even with time-reversible laws, you can get different behaviour by starting the system in a different way. If you start with an egg and stir it with a fork, then it scrambles. If you start with the scrambled egg, and very very carefully give each tiny particle of egg exactly the right push along precisely the opposite trajectory, then it will unscramble. The difference lies entirely in the initial state, not in the laws. Notice that 'stir with a fork' is a very general kind of initial condition: lots of different ways to stir will scramble the egg. In contrast, the initial con­dition for unscrambling an egg is extremely delicate and special.

In a way this is an attractive option. Our clumping universe is like an unscrambling egg: its increasing complexity is a consequence of very special initial conditions. Most 'ordinary' initial conditions would lead to a universe that isn't clumped - just as any reasonable kind of stirring leads to a scrambled egg. And observations strongly suggest that the universe's initial conditions at the time of the Big Bang were extremely smooth, whereas any 'ordinary' state of a gravitational sys­tem presumably should be clumped. So, in agreement with the suggestion just outlined, it seems that the initial conditions of the uni­verse must have been very special - an attractive proposition for those who believe that our universe is highly unusual, and ditto for our place within it.

From the Second Law to God in one easy step.

Roger Penrose has even quantified how special this initial state is, by comparing the thermodynamic entropy of the initial state with that of a hypothetical but plausible final state in which the universe has become a system of Black Holes. This final state shows an extreme degree of dumpiness - though not the ultimate degree, which would be a single giant Black Hole. The result is that the entropy of the initial state is about l0³⁰ times that of the hypothetical final state, mak­ing it extremely special. So special, in fact, that Penrose was led to introduce a new time-asymmetric law that forces the early universe to be exceptionally smooth.

Oh, how our stories mislead us ... There is another, much more rea­sonable, explanation. The key point is simple: gravitation is very different from thermodynamics. In a gas of buzzing molecules, the uni­form state - equal density everywhere - is stable. Confine all the gas into one small part of a room, let it go, and within a split second it's back to a uniform state. Gravity is exactly the opposite: uniform sys­tems of gravitating bodies are unstable. Differences smaller than any specific level of coarse-graining not only can 'bubble up' into macro­scopic differences as time passes, but do.

Here lies the big difference between gravity and thermodynamics. The thermodynamic model that best fits our universe is one in which differences dissipate by disappearing below the level of coarse-grain­ing as time marches forwards. The gravitic model that best fits our universe is one in which differences amplify by bubbling up from below the level of coarse-graining as time marches forwards. The rela­tion of these two scientific domains to coarse-graining is exactly opposite when the same arrow of time is used for both.

We can now give a completely different, and far more reasonable, explanation for the 'entropy gap' between the early and late universes, as observed by Penrose and credited by him to astonishingly unlikely initial conditions. It is actually an artefact of coarse-graining. Gravitational clumping bubbles up from a level of coarse-graining to which thermodynamic entropy is, by definition, insensitive. Therefore virtually any initial distribution of matter in the universe would lead to clumping. There's no need for something extraordinarily special.

The physical differences between gravitating systems and thermo­dynamic ones are straightforward: gravity is a long-range attractive force, whereas elastic collisions are short-range and repulsive. With such different force laws, it is hardly surprising that the behaviour should be so different. As an extreme case, imagine systems where gravity' is so short range that it has no effect unless particles collide, but then they stick together forever. Increasing dumpiness is obvious for such a force law.

The real universe is both gravitational and thermodynamic. In some contexts, the thermodynamic model is more appropriate and thermo­dynamics provides a good model. In other contexts, a gravitational model is more appropriate. There are yet other contexts: molecular chemistry involves different types of forces again. It is a mistake to shoehorn all natural phenomena into the thermodynamic approxima­tion or the gravitic approximation. It is especially dubious to expect both thermodynamic and gravitic approximations to work in the same context, when the way they respond to coarse-graining is diametri­cally opposite.

See? It's simple. Not magical at all ...

Perhaps it's a good idea to sum up our thinking here.

The 'laws' of thermodynamics, especially the celebrated Second Law, are statistically valid models of nature in a particular set of contexts. They are not universally valid truths about the universe, as the clump­ing of gravity demonstrates. It even seems plausible that a suitable measure of gravitational complexity, like thermodynamic entropy but different, might one day be defined - call it 'gravtropy', say. Then we might be able to deduce, mathematically, a 'second law of gravities', stating that the gravtropy of a gravitic system increases with time. For example, gravtropy might perhaps be the fractal dimension ('degree of intricacy') of the system.

Even though coarse-graining works in opposite ways for these two types of system, both 'second laws' - thermodynamic and gravitic - would correspond rather well to our own universe. The reason is that both laws are formulated to correspond to what we actually observe in our own universe. Nevertheless, despite this apparent concurrence, the two laws would apply to drastically different physical systems: one to gases, the other to systems of particles moving under gravity.

With these two examples of the misuse of information-theoretic and associated thermodynamic principles behind us, we can turn to the intriguing suggestion that the universe is made from information.

Ridcully suspected that Ponder Stibbons would invoke 'quantum' to explain anything really bizarre, like the disappearance of the Shell Midden People. The quantum world is bizarre, and this kind of invo­cation is always tempting. In an attempt to make sense of the quantum universe, several physicists have suggested founding all quantum phe­nomena (that is, everything) on the concept of information. John Archibald Wheeler coined the phrase 'It from Bit' to capture this idea. Briefly, every quantum object is characterised by a finite number of states. The spin of an electron, for instance, can either be up or down, a binary choice. The state of the universe is therefore a huge list of ups and downs and more sophisticated quantities of the same general kind: a very long binary message.

So far, this is a clever and (it turns out) useful way to formalise the mathematics of the quantum world. The next step is more controver­sial. All that really matters is that message, that list of bits. And what is a message? Information. Conclusion: the real stuff of the universe is raw information. Everything else is made from it according to quan­tum principles. Ponder would approve.

Information thereby takes its place in a small pantheon of similar concepts - velocity, energy, momentum - that have made the transi­tion from convenient mathematical fiction to reality. Physicists like to convert their technically most useful mathematical concepts into real things: like Discworld, they reify the abstract. It does no physical harm to 'project' the mathematics back into the universe like this, but it may do philosophical harm if you take the result literally. Thanks to a sim­ilar process, for example, entirely sane physicists today insist that our universe is merely one of trillions that coexist in a quantum super­position. In one of them you left your house this morning and were hit by a meteorite; in the one in which you're reading this book, that didn't happen. 'Oh, yes,' they urge: 'those other universes really do exist. We can do experiments to prove it.'

Not so.

Consistency with an experimental result is not a proof, not even a demonstration, that an explanation is valid. The 'many-worlds' con­cept, as it is called, is an interpretation of the experiments, within its own framework. But any experiment has many interpretations, not all of which can be 'how the universe really does it'. For example, all experiments can be interpreted as 'God made that happen', but those selfsame physicists would reject their experiment as a proof of the exis­tence of God. In that they are correct: it's just one interpretation. But then, so are a trillion coexisting universes.

Quantum states do superpose. Quantum universes can also super­pose. But separating them out into classical worlds in which real-life people do real-life things, and saying that those superpose, is non­sense. There isn't a quantum physicist anywhere in the world that can write down the quantum-mechanical description of a person. How, then, can they claim that their experiment (usually done with a cou­ple of electrons or photons) 'proves' that an alternate you was hit by a meteorite in another universe?

'Information' began its existence as a human construct, a concept that described certain processes in communication. This was 'bit from it', the abstraction of a metaphor from reality, rather than 'it from bit', the reconstruction of reality from the metaphor. The metaphor of infor­mation has since been extended far beyond its original bounds, often unwisely. Reifying information into the basic substance of the universe is probably even more unwise. Mathematically, it probably does no harm, but Reification Can Damage Your Philosophy.

NINETEEN

LETTER FROM LANCRE

Granny Weatherwax, known to all and not least to her­self as Discworld's most competent witch, was gathering wood in the forests of Lancre, high in the mountains and far from any university at all.

Wood gathering was a task fraught with danger for an old lady so attractive to narrativium. It was quite hard these days, when gathering firewood, to avoid third sons of kings, young swine­herds seeking their destiny and others whose unfolding adventure demanded that they be kind to an old lady who would with a cer­tainty turn out to be a witch, thus proving that smug virtue is its own reward.

There is only a limited number of times even a kindly disposed per­son wishes to be carried across a stream that they had, in fact, not particularly desired to cross. These days, she kept a pocket full of small stones and pine cones to discourage that kind of thing.

She heard the soft sound of hooves behind her and turned with a pine cone raised.

'I warn you, I'm fed up with you lads always on the ear'ole for three wishes-' she began.

Shawn Ogg, astride his official donkey, waved his hands desper­ately.

'It's me, Mistress Weatherwax! I wish you'd stop doing this!' 'See?' said Granny. 'You ain't havin' another two!' 'No, no, I've just come up to deliver this for you ... ' Shawn waved quite a thick wad of paper. 'What is it?'

'Tis a clacks for you, Mistress Weatherwax! It's only the third one we've ever had!' Shawn beamed at the thought of being so close to the cutting edge of technology.

'What's one of them things?' Granny demanded. 'It's like a letter that's taken to bits and sent through the air,' said Sean.

'By them towers I keep flyin' into?' 'That's right, Mistress Weatherwax.'

'They move 'em around at night, you know,' said Granny. She took the paper.

'Er ... I don't think they do ...' Shawn ventured. 'Oh, so I don't know how to fly a broomstick right, do I?' said Granny, her eyes glinting.

'Actually, yes, I've remembered,' said Shawn quickly. 'They move them around all the time. On carts. Big, big carts. They ...'

'Yes, yes,' said Granny, sitting on a stump. 'Be quiet now, I'm readin'

The forest went silent, except for the occasional shuffling of paper.

Finally, Granny Weatherwax finished. She sniffed. Birdsong came back into the forest.

'Silly old fools think they can't see the wood for the trees, and the trees are the wood,' she muttered. 'Cost a lot, does it, sendin' mes­sages like this?'

'That message,' said Shawn, in awe, 'cost more than 600 dollars! I counted the words! Wizards must be made of money!'

'Well, I ain't,' said the witch. 'How much is one word?'

'Five pence for the sending and five pence the first word,' said Shawn, promptly.

'Ah,' said Granny. She frowned in concentration, and her lips moved silently. 'I've never been one for numbers,' she said, 'but I reckon that comes to ... sixpence and one half-penny?'

Shawn knew his witches. It was best to give in right at the start.

'That's right,' he said.

'You have a pencil?' said Granny. Shawn handed it over. With great care, the witch printed some block capitals on the back of one of the pages, and gave it to him.

'That's all?' he said.

'Long question, short answer,' said Granny, as it if was some uni­versal truth. 'Was there anything else?'

Well, there might be the money, Shawn thought. But in her own localised way, Granny Weatherwax had an academic position in these matters. Witches took the view that they helped society in all kinds of ways which couldn't easily be explained but would become obvious if they stopped doing them, and that it was worth six pence and one half-penny not to find out what these were.

He didn't get his pencil back.

The hole into L-space was quite obvious now. It fascinated Dr.Dee, who was confidently expecting angels to come out of it, although all it had produced so far was an ape.

The wizards' automatic response to any problem was to see if there was a book about it. L-space was providing plenty of books. The dif­ficulty, however, was finding the ones that applied to the current history; when you potentially know everything, it's hard to find any­thing you want to know.

'So let's see where we are now, shall we?' said Ridcully, after a while. 'The last known books in this leg of the trousers of time are due to be written in-?'

'About a hundred years' time,' said the Lecturer in Recent Runes, looking at his notes. 'Just before the collapse of civilisation, such as it is. Then there's fire, famine, war ... all the usual stuff.'

'Hex says people here are back to living in villages when the aster­oid hits,' said Ponder. 'Things are rather better on one or two other continents, but no one even sees it coming.'

'There have been periods like it before,' said the Dean. 'But as far as we can tell, in the area where we are now there were always small isolated groups of people who preserved what books there were.'

'Ah. Our kind of people,' said Ridcully.

'Afraid not,' said the Dean. 'Religious.'

'Oh dear,' said Ridcully.

'It's hard to follow, but there appear to be about four main gods on this continent,' said the Dean. 'Loosely associated.'

'Big beards in the sky?' said Ridcully.

'A couple, yes.'

'Clearly a morphic memory of ourselves, then,' said Ridcully.

'It's hard to tell, with religions,' said the Dean. 'But at least they pre­served the idea that books were important and that reading and writing were more than just a skive for people too weedy to hack at one another with swords.'

'Any of these religious places still around?' said the Lecturer in Recent Runes. "Would it be useful to drop in, explain that we are, in fact, the creators of this universe, and put them right on a few points?'

There was silence. And then Ponder said, in his best talking-to-superiors voice: 'I believe, sir, that this world is no different from our own in its attitude to apparent human beings who turn up and say that they're a god.'

'We wouldn't get special treatment?'

'Not of the sort you have in mind, sir, no,' said Ponder. 'Besides, the places in this country appear to have been closed down by a recent monarch. I'm not sure I understand it all, but it appears to have been some kind of cost-cutting exercise.'

'Downsizing of redundant units, re-allocation of staff, that sort of thing?' said Ridcully.

'Yes, sir,' said Ponder. And a few murders, some torturing, that sort of thing.'

'But probably nothing, I'm sure, that couldn't be sorted out by get­ting everyone to go and run around in the woods shooting paint at one another,' said the Lecturer in Recent Runes, innocently.

'I shall ignore that, Runes,' said Ridcully. 'Now, gentlemen, we are supposed to be thinkers. We haven't got magic. We can be moved in time and space, according to Hex. And we've got big sticks. What can we do?'

'A message has arrived,' said Hex.

'From Lancre? That's quick!'

'Yes. The message is unsigned. It is: THEOSTRY'

Hex spelled it out. Ponder wrote it down in his notebook.

'What does that mean?' Ridcully looked up at his wizards.

'Looks a bit religious to me,' said the Dean. 'Rincewind? This sort of thing is right up your street, isn't it?'

Rincewind looked at the word. Really, when you came to think of it, his whole life was a crossword puzzle ...

'The clacks people charge by the word, don't they?' he said.

'Yes, it's scandalous,' said Ridcully. 'Five pence a word, on the long­distance trunk!'

'And this was sent back by an old woman in Lancre, where as far as I recall the chicken is the basic unit of currency?' said Rincewind. 'Not much money for fancy messages, then. It looks to me like a sim­ple anagram of ... THE STORY

'I think it means "change the story",' said Ponder, without looking up. At a saving of five pence.'

'We tried changing it!' said the Dean.

'Change it in a different way, perhaps? At a different time?' said Ponder. 'We've got L-space. We ought to be able to get some guidance from books written in different futures-'

'Ook!'

'I'm sorry, sir, but the library rules don't apply here!' said Ponder.

'Look at it this way, old chap,' said Ridcully, to the angry Librarian. 'The rules do of course apply here, everyone can see that, and we wouldn't dream of asking you to interfere with the nature of causality in the normal way of things. It's just that the nature of causality on this world is such that, if any libraries survive the next thousand years with­out being used for lighting fires or uncomfortable toilet paper, they're due to be destroyed in a fireball and/or entombed in ice. Dr Dee's wonderful books which you like so much, with their many delicate illustrations of completely useless magical circles and rather interest­ing mathematical cyphers, will go the way of the, the ...' He snapped his fingers. 'Someone give me the name of something that'll be going completely extinct,' he demanded.

'People,' said Rincewind.

There was silence.

Then the Librarian said: 'Ook ook.'

'He says he's just finding the books, okay?' said Rincewind. 'And he'll leave them in a pile and go out of the room and no one is to look at them while he's gone, because if they do he won't know about it, and if he coughs loudly before he comes back in that will only be because he's got a cough and not for any other reason, okay?'

TWENTY

SMALL GODS

'Religious,' said the Dean. 'Oh dear,' said Ridcully.

Discworld's wizardry is not terribly keen on religion. Given the history of the Discworld, this is not surpris­ing. One big problem is that on Discworld, gods are known to be real. We list a few later on, but we can set the scene with reference to the god of mayflies. In Reaper Man, an old mayfly is telling some youngsters about this god, as they hover just above the surface of a stream:

'... you were telling us about the Great Trout.'

'Ah. Yes. Right. The Trout. Well, you see, if you've been a good mayfly, zigzagging up and down properly-'

'-taking heed of your elders and betters-'

'- yes, and taking heed of your elders and betters, then eventually the Great Trout-'

Clop.

Clop.

'Yes?' said one of the younger mayflies.

There was no reply.

'The Great Trout what?' said another mayfly, nervously.

They looked down at a series of expanding concentric rings on the water.

'The holy sign!' said a mayfly. 'I remember being told about that! A Great Circle in the water! Thus shall be the sign of the Great Trout!'

Roundworld religions avoid the difficulty of gods that you can actually see, or meet or be eaten by: most of the world's current religions find it best to go the whole hog and locate their gods in a place that is not just outside Roundworld the planet, but outside Roundworld the uni­verse. This demonstrates admirable foresight, for regions impenetrable today may be a forest of tourist hotels tomorrow. When the sky was an unexplored and unfathomable realm, it was fashionable to locate gods in the sky, or on top of unscalable Mount Olympus, or in the halls of Valhalla, which amounts to much the same thing. But now all sig­nificant mountains have been climbed, people routinely fly across the Atlantic, five miles up, and reports of encounters with gods are few.

However, it turns out that when gods don't manifest themselves in physical form on an everyday basis, they acquire an impressive degree of ineffability. On Discworld, on the other hand, it is possible to run into gods in the street or even in the gutter. They also lounge around in Discworld's equivalent of Valhalla, known as Dunmanifestin, which is situated on top of Cori Celesti, a ten mile high spire of green ice and grey stone at the Disc's hub.

Because of the everyday presence of tangible gods, on Discworld there's no problem about belief in gods; it's more a matter of how much you disapprove of their lifestyle. On Roundworld, deities do not infest the highways and byways - or, if they do, they do so in such a subtle guise that the unbeliever does not notice them. It then becomes possible to have a serious debate about belief, because that's what most people's concept of God rests on.

We've already said that on Discworld everything is reified, and that's pretty much the case there with belief. Now B-space, the space of beliefs, is huge, because people have vivid and varied imaginations and can believe almost anything. Therefore G-space, the space of gods, is also huge. And on Discworld, phase spaces are reified. So the Discworld not only has gods: it is infested with them. There are at least 3,000 major gods on the Disc, and scarcely a week passes with­out the research theologians discovering more. Some use props like false noses to appear in religious chronicles under hundreds of dif­ferent names, which makes it difficult to keep count accurately. Among them are Cephut, the god of cutlery (Pyramids), Flatulus, god of the winds (Small Gods), Grune, the god of unseasonal fruit (ReaperMan), Hat, the vulture-headed god of unexpected guests (Pyramids), Offler, the crocodile god (Mort and Sourcery), Petulia, the goddess of nego­tiable affection (Small Gods), and Steikheigel, the god of isolated cow byres (Mort).

Then there are the minor gods. According to The Discworld Companion, 'There are billions of them, tiny bundles containing noth­ing more than a pinch of pure ego and some hunger'. What they hunger for, at least to start with, is human belief, because on Discworld the size and power of a god is proportional to how many people believe in him, her, or it. Things are much the same on Roundworld, in fact, because the influence and power of a religion are proportional to the number of its adherents. So the parallel is much closer than you might expect - which is what you should always expect with Discworld, because it has an uncanny ability to reflect and illuminate the human condition in Roundworld. Actually, it's not always human (or mayfly) belief that matters. According to Lords and Ladies-.

There were a number of gods in the mountains and forests of Lancre. One of them was known as Herne the Hunted. He was a god of the chase and the hunt. More or less.

Most gods are created and sustained by belief and hope. Hunters danced in animal skins and created gods of the chase, who tended to be hearty and boisterous with the tact of a tidal wave. But they are not the only gods of hunting. The prey has an occult voice too, as the blood pounds and the hounds bay. Herne was the god of the chased and the hunted and all small animals whose ultimate destiny is to be an abrupt damp squeak.

When discussing religious beliefs, there is always the danger of upset­ting people. The same goes when discussing football, of course, but people take their religion nearly as seriously. So let us begin by acknowledging, as we did towards the end of The Science of Discworld, that 'all religions are true, for a given value of true'. We have no wish to damage your beliefs, if you have them, or to damage your lack of beliefs if you don't. We don't mind if we cause you to modify your beliefs, though. That's your responsibility and your choice: don't blame us. But we're shortly going to have a go at science, and then we're going to have a go at art, so we don't think it's fair that religion should get away scot-free. Anyway, whatever your beliefs, religion is an essen­tial feature of the human condition, and it's one of the things that made us what we are. We have to examine it, and ask whether Discworld puts it in a new light.

If you are religious, and you want to feel comfortable about what we're saying, you can always assume that we're talking about all the other religions, but not yours. Some years ago, during Ecumenical Week, Rabbi Lionel Blue was giving the 'Thought for the Day' on BBC Radio 4, as part of a series on tolerance. He was the first speaker in the series, and he ended with a joke. 'They shouldn't have asked me to start the series,' he said, and then explained how the later speakers from other religions would differ from him, and how he would be tol­erant about that. 'After all,' he said, 'they worship God in their way ... whereas I worship Him in His.'

If you see that this is a joke, as the good rabbi did, but also under­stand that outside that cosy context this is not, in a multicultural world, a good way to think, let alone speak, then you're already getting to grips with the ambivalent role that religion has played in human his­tory. And with the mental twists and turns required to live in a multiculture.

The big problem with religion, for a dispassionate observer, has noth­ing to do with belief versus proof. If religion were susceptible to scientific-style proofs or disproofs, there wouldn't be a lot to argue about. No, the big problem is the disparity between individual human spirituality - the deep-seated feeling that we belong in this awesome universe - with the unmitigated disasters that organised, large-scale religions have at various times, including in all probability yesterday, inflicted on the planet and its people. This is upsetting. Religion ought to be a force for good, and mostly it is ... But when it isn't, it goes spectacularly and horribly wrong.

In both Pyramids and Small Gods, we see that the real problem in this connection is not religion as such, but priests. Priests have been known to seize upon the spiritual feelings of individuals and twist them into something terrible; the Quisition in Small Gods was hardly an invention. Sometimes it had been done for power, or for money. It's even been done because the priests really believe that this is what the god of choice wants them to do.

Again, on an individual level many priests (or equivalent) are per­fectly nice people who do many positive things, but collectively they can have some very negative effects. It is this mismatch that will form the core of our discussion, because it tells us interesting things about what it is to be human.

We are very tiny, fragile creatures inside a huge, uncontrollable uni­verse. Evolution has equipped us not just with eyes to see the universe, but minds to hold little models of it within us; that is, to tell ourselves stories about it.

We have learned, over the millennia, to exert more and more con­trol over our world, but we see evidence every day that our ability to control our own lives is extremely limited. In the past, disease, death, famine and ferocious animals were part of everyday existence. You could control when you planted your crops, but you couldn't control when the rains came, and you might just get jumped by a pride of lionesses while you were bending down to pull up weeds.

It is very uncomfortable to have to cope unaided with that kind of world, and many people still have to do so. Everyone feels much hap­pier if they believe that there are ways to control rain and lionesses.

Now, the human mind is an inveterate pattern-seeker, one that finds patterns even where none exist. Every week millions of perfectly sane people look for patterns in lottery numbers, oblivious to the absence of any meaningful structure in random numbers. So it's not really nec­essary for the belief in an ability to control rain or lionesses to correspond to an actual ability to do so. We all know that even when things are under control, they can still go wrong, so our faith in our beliefs seldom gets seriously challenged, whatever happens.

The idea that there is a Rain Goddess who decides when it will rain, or a Lion God who can either keep you safe from lion attacks or unleash them upon you, therefore has irresistible advantages. You can't control rain, and of course you can't control a Rain Goddess either, but, with the proper rituals, you can hope to influence her decisions. This is where the priesthood comes in, because they can act as an intermediary between everybody else and the gods. They can pre­scribe the appropriate rituals - and, like all good politicians, they can claim the credit when things work out and blame someone else when they go wrong. 'What, Henry was eaten by a lion? Well then, he must not have shown proper respect when making his daily sacrifice to the Lion God.' 'How do you know that?' 'Well, if he had shown proper respect, he wouldn't have been eaten.' Ally that to the priests' soon-acquired power to throw you to the earthly representatives of the Lion God if you disagree, and you can see that the Cult of the Lion God has an awful lot going for it.

People look at the universe around them, and they feel overawed. It's so big, so incomprehensible - yet it seems to dance to a tune. People who grow up in a culture - especially one with a lengthy his­tory and a well-developed set of techniques for making buildings, planting crops, hunting animals, building boats - immediately recog­nise that they are faced with something that is far greater than they are. Which immediately raises all the big philosophical questions: where did it come from, what's it for, why am I here? And so on.

Imagine how it must have seemed to Abraham, one of the found­ing fathers of Judaism. He was probably a shepherd, and he probably lived in and around Ur, one of the first true city-states. He was sur­rounded by the icons of simple-minded religions: gold-plated idols, masks, altars. He was wildly unimpressed by them. They were trivial things, small-minded. They did not begin to measure up to the awesomeness of the natural world, and its stunning power. Additionally, he was aware that 'something' much bigger than him was running that world. It knew when to plant crops and when to reap them, how to tell whether rain was on the way, how to build boats, how to breed sheep (well, he would have known that bit), how to have a prosper­ous life. Even more: it knew how to pass all this knowledge on to the next generation. Abraham knew that his own tiny intelligence was nothing compared to this majestic something. So he reified it, and gave it a name: Jehovah, which means 'that which is'. So far, so good, but then he made a simple but intellectually fatal error. He fell for the trap of 'ontic dumping'.

Nice phrase. What does it mean? Ontology is the study of knowl­edge. Not knowledge itself, just its study. One important way to firm up new knowledge is to invent new words. For instance, when you make an arrow, someone has to produce the sharp pointy thing that sits at its business end. They chip it from flint or cast it in bronze; either way, you can't go on forever referring to it as 'the sharp pointy thing on the end of an arrow'. So you cast around for a metaphor, and you remember that the thing that sits at the business end of a person or animal is called its head. So you invent the term 'arrow-head'.

You have now dumped the knowledge of what the flint or bronze gadget is into a name. We say 'dumped', because for most purposes you don't need to recall where the name came from. Arrowhead (no hyphen) has now become a thing in its own right, not a property pos­sessed in relation to an arrow.

The human mind is a storytelling device, a metaphor machine: ontic dumping comes naturally to creatures like us. It's how our language works, how our minds work. It's a trick we use to simplify things that would otherwise be incomprehensible. It is the linguistic analogue of a political hierarchy as a way for one person to control millions. As a side effect, ontically dumped words wallow in associations. We are seldom conscious of these, except when we occasionally stop and ask something like 'What on Earth does "gossamer" mean?' Then we rush off to the dictionary and discover that it probably (no one ever knows these things for sure) comes from 'goose summer'. What's that got to do with fine threads that float on the breeze? Well, in a summer when geese abound, a good summer, you find a lot of these fine spider-silk threads hanging in the air ...

Subconsciously, though, we are all too aware of the dark associa­tions several layers down in the ontic-dumping hierarchy. So words, which ought to be abstract labels, are smeared all over with their own (often irrelevant) stories.

Abraham, then, was overawed by 'that which is', and he ontically dumped it into a word, Jehovah. Which quickly became a thing, indeed, a person. That's another of our habits, personifying things. So Abraham made the tiny step from 'there is something outside us that is greater than ourselves' to 'there is someone outside us who is greater than ourselves'. He had looked on the burgeoning extelligence of his own culture, and before his eyes it turned into God.

And that made so much sense. It explained so much else. Instead of the world being like it was for reasons he couldn't understand - even though that greater something clearly understood it perfectly well - he now saw that the world was like that because God had made it that way. The rain fell not because some tawdry idol rain-god made it fall; Abraham was too smart to believe that. It fell because that awe­some God whose presence could be seen everywhere made it fall. And he, Abraham, couldn't hope to understand the Mind of God, so of course he couldn't predict when it would rain.

We have used Abraham here as a placeholder. Choose your religion, choose your founder, adapt the story to fit. We're not saying that we know that the birth of Judaism happened the way we've just explained. That was just a story, probably no more true than Winnie-the-Pooh and the honey. But just as Pooh in the rabbit-hole teaches us about greed, so Abraham's ontic dumping points to a plausible route whereby sane, sensitive people can be led from their own private spir­itual feelings to reify a natural process into an unfathomable Being.

This reification has had many positive consequences. People take notice of the wishes of unfathomable, all-powerful Beings. Religious teachings often lay down guidelines (laws, commandments) for accept­able behaviour towards other people. To be sure, there are many disagreements between the different religions, or between sects within a given religion, about points of fine detail. And there are some quite substantial areas of disagreement, such as the recommended treatment of women, or to what extent basic rights should be extended to the infidel. On the whole, however, there is a strong consensus in such teachings, for example an almost universal condemnation of theft and murder. Virtually all religions reinforce a very similar consensus of what constitutes 'good' behaviour, perhaps because it is this consen­sus that has survived the test of time. In terms of the barbarian/tribal distinction, it is a tribal consensus, reinforced by tribal methods such as ritual, but none the worse for that.

Many people find inspiration in their religion, and it helps instil a sense of belonging. It enhances their feeling of what an awesome place the universe is. It helps them cope with disasters. With exceptions, mainly related to specific circumstances such as war, most religions preach that love is good and hatred is bad. And throughout history, ordinary people have made huge sacrifices, often of their own lives, on that basis.

This kind of behaviour, generally referred to as altruism, has caused evolutionary biologists a great deal of head-scratching. First, we'll sum­marise how they have thought about the problem and what kinds of conclusion they have reached. Then we'll consider an alternative approach, originally motivated by religious considerations, which looks to us to be far more promising.

At first sight, altruism is not a problem. If two organisms cooperate, by which in this context we here mean that each is willing to risk its life to help the other, then both stand to gain. Natural selection favours such an advantage, and reinforces it. What more explanation is needed?

Quite a lot, unfortunately. A standard reflex in evolutionary biology is to ask whether such a situation is stable - whether it will persist if some organisms adopt other strategies. What happens, for example, if most organisms cooperate, but a few decide to cheat? If the cheats prosper, then it is better to become a cheat than to cooperate, and the strategy of cooperation is unstable and will die out. Using the meth­ods of mid-twentieth-century genetics, the approach pioneered by Ronald Aylmer Fisher, you can do the sums and work out the cir­cumstances in which altruism is an evolutionarily stable strategy. The answer is that it all depends upon whom you cooperate with, whose life you risk your own to save. The closer kin they are to you, the more genes they share with you, so the more worthwhile it is for you to risk your own safety. This analysis leads to conclusions like 'It is worth jumping into a lake to save your sister, but not to save your aunt.' And certainly not to save a stranger.

That's the genetic orthodoxy, and like most orthodoxies, it is believed by the orthodox. On the other hand, though: if someone has fallen into a lake, people do not ask 'Excuse me, sir, but how closely related are you to me? Are you, by any chance, a close relative?' before diving in to rescue them. If they are the sort of people who dive in, they do so whoever has fallen into the lake. If not, they don't. Mostly. A clear exception arises when a child falls in; even if they can't swim its par­ent is then very likely indeed to plunge in to the rescue, but probably would not do so for someone else's child, and even less so for an adult. So the genetic orthodoxy does have a certain amount going for it.

Not much, though. Fisher's mathematics is rather old-fashioned, and it rests on a big - and very shaky - modelling simplification. It rep­resents a species by its gene-pool, where all that matters is the proportion of organisms that possess a given gene. Instead of com­paring different strategies that might be adopted by an organism, it works out what strategy is best 'on average'. And inasmuch as indi­vidual organisms are represented within its framework at all, which they are only as contributors to the gene-pool, it views competition between organisms as a direct 'me versus thee' choice. A bird that eats seeds is up against a bird that eats worms in a head-to-head struggle for survival, like two tennis-players ... and may the best bird win.

This is a bean-counting analysis performed with a bean-counting mentality. The bird with the most beans (energy from seeds or worms, say) survives; the other does not.

From a complex system viewpoint, evolution isn't like that at all. Organisms may sometimes compete directly - two birds tugging at the same worm, for instance. Or two baby birds in the nest, where direct competition can be fierce and fatal. But mostly the competition is indi­rect - so indirect that 'compete' just isn't the right word. Each individual bird either survives, or not, against the background of everything else, including the other birds. Birds A and B do not go head-to-head. They compete against each other only in the sense that we choose to com­pare how A does with how B does, and declare one of them to be more successful.

It's like two teenagers taking driving tests. Maybe one of them is in the UK and the other is in the USA. If one passes and the other fails, then we can declare the one who has passed to be the 'winner'. But the two teenagers don't even know they are competing, for the very good reason that they're not. The success or failure of one has no effect on the success or failure of the other. Nevertheless, one gets to drive a car, and the other doesn't.

The driving-test system works that way, and it doesn't matter that the American test is easier to pass than the British one (as we can attest from personal experience). Evolutionary 'competition' mostly works like the driving test, but with the added complication that just occa­sionally it really is more like a tennis match.

From this point of view, evolution is a complex system, with organ­isms as entities. Which organisms survive to reproduce, and which do not, are system-level properties. They depend as much on context (American driving test versus British) as on the internal features of the individuals. The survival of a species is an emergent feature of the whole system, and no simple short-cut computation can predict it. In particular, computations based on the frequencies of genes in the gene-pool can't predict it, and the alleged explanation of altruism by gene-frequencies is unconvincing.

Why, then, does altruism arise? An intriguing answer was given by Randolph Nesse in the magazine Science and Spirit in 1999. In a word, his answer is 'overcommitment'. And it is a refreshing and much-needed alternative to bean-counting.

We have said more than once that humans are time-binders. We run our lives not just on what is happening now, but on what we think will happen in the future. This makes it possible for us to commit our­selves to a future action. 'If you fall sick, I will look after you.' 'If an enemy attacks you, I will come to your aid.' Commitment strategies change the face of 'competition' completely. An example is the strat­egy of 'mutual assured destruction' as a deterrent for nuclear war: 'If you attack me with nuclear weapons, I will use mine to destroy your country completely.' Even if one country has many more nuclear weapons, which on a bean-counting basis means that it will 'win', the commitment strategy means that it can't.

If two people, tribes or nations make a pact, and agree to commit support to each other, then they are both strengthened, and their sur­vival prospects increase. (Provided it's a sensible pact. We leave you to invent scenarios where what we've just said is wrong.) Ah, yes, that's all very well, but can you trust the other to keep to the agreement? We have evolved some quite effective methods for deciding whether or not to trust someone. At the simplest level, we watch what they do and compare it to what they say. We can also try to find out how they have behaved in similar circumstances before. As long as we can get such decisions right most of the time, they offer a substantial survival advantage. They improve how well we do, against the background of everything else. Comparison with others is irrelevant.

From a bean-counter's point of view, the 'correct' strategy in such circumstances is to count how many beans you gain by committing yourself, compare that to how many you gain by cheating, and see which pile of beans is biggest. From Nesse's point of view, that approach doesn't amount to a hill of beans. The whole calculation can be sidestepped, at a stroke, by the strategy of overcommitment. 'Stuff the beans: I guarantee that I will commit myself to you, no matter what. And you can trust me, because I will prove to you, and keep proving it every day that we live, that I am committed at that level.' Overcommitment beats the bean-counters hands down. While they're trying to compare 142 beans with 143, overcommitment has wiped the floor with them.

Nesse suggests that such strategies have had a decisive effect in shaping our extelligence (though he doesn't use that word):

Commitment strategies give rise to complexities that may be a selec­tive force that has shaped human intelligence. This is why human psychology and relationships are so hard to fathom. Perhaps a better understanding of the deep roots of commitment will illuminate the relationships between reason and emotion, and biology and belief.

Or, to put it another way: perhaps that's what gave us an edge over the Neanderthals. Though it would be difficult to find a scientific test for such a suggestion.

When humans overcommit in this manner, we call it 'love'. There is far more to love than the simple scenario just outlined, of course, but one feature is common to both: love counts not the cost. It doesn't care about who gets the most beans. And by refusing to play the bean-counters' game, it wins outright. Which is a very religious, spiritual and uplifting message. And sound evolutionary sense. What more could we ask?

Quite a bit, actually, because now it all starts to get nasty. The reasons, however, are admirable. Every culture needs its own Make-a-Human kit, to build into the next generation the kind of mind that will keep the culture going - and, recursively, ensure that the next generation does the same for the one that comes after that. Rituals fit very read­ily into such a kit, because it is easy to distinguish Us from Them by the rituals that We follow but They don't. It is also an excellent test of a child's willingness to obey cultural norms by insisting that they carry out some perfectly ordinary task in an unnecessarily prescribed and elaborate manner.

Now, however, the priesthood has got its ideological toe in the cultural doorway. Rituals need someone to organise them, and to elaborate them. Every bureaucracy builds itself an empire by creating unnecessary tasks and then finding people to carry them out. A crucial task here is to ensure that members of the tribe or village or nation really do obey the norms and carry out the rituals. There has to be some sanction to make sure that they do, even if they're free-thinking types who'd rather not. Because everything is founded on an ontically dumped concept, reference to reality has to be replaced by belief. The less testable a human belief is, the more strongly we tend to hold on to it. Deep down we recognise that although not being testable means that disbelievers can't prove we're wrong, it also means that we can't prove we're right. Since we know that we are, that sets up a tremendous tension.

Now the atrocities begin. Religion slides over the edge of sanity, and the result is horrors like the Spanish Inquisition. Think about it for a moment. The priesthood of a religion whose central tenet was universal love and brotherhood systematically inflicted appalling tor­tures, sick and disgusting things, on innocent people who merely happened to disagree about minor items of belief. This is a massive contradiction and it demands explanation. Were the Inquisitors evil people who knowingly did evil things?

Small Gods, one of the most profound and philosophical of the Discworld novels, examines the role of belief in religions, and Discworld undergoes its own version of the Spanish Inquisition. One twist is that on Discworld, there is no lack of gods; however, few of them have any great significance:

There are billions of gods in the world. They swarm as thick as her­ring roe. Most of them are too small to see and never get worshipped, at least by anything bigger than bacteria, who never say their prayers and don't demand much in the way of miracles.

They are the small gods, the spirits of places where two ant trails cross, the gods of microclimates down between the grass roots. And most of them stay that way.

Because what they lack is belief.

Small Gods is the story of one rather larger god, the Great God Om, who manifests himself to a novice monk called Brutha, in the Citadel at the heart of the city of Kom in the lands between the deserts of Klatch and the jungles of Howondaland.

Brutha's attitude to religion is a very personal one. He runs his own life by it. In contrast, Deacon Vorbis believes that the role of religion is to run everybody else's life. Vorbis is head of the Quisition, whose role is 'to do all those things that needed to be done and which other people would rather not do'. Nobody ever interrupts Vorbis to ask what he is thinking about, because they are scared stiff that the answer will be 'You'.

The Great God's manifestation takes the form of a small tortoise. Brutha finds this hard to believe:

I've seen the Great God Om ... and he isn't tortoise-shaped. He comes as an eagle, or a lion, or a mighty bull. There's a statue in the Great Temple. It's seven cubits high. It's got bronze on it and everything. It's trampling infidels. You can't trample infidels when you're a tortoise.

Om's power has waned because of a lack of belief. He tests his strength by silently cursing a beetle, but it makes no difference and the insect plods away unperturbed. He curses a melon unto the eighth generation, but with no evident effect. He inflicts a plague of boils on it, but all it does is sit there, slowly ripening. He vows that when he returns to his rightful state, the Tribes of Beetle and Melons will regret not responding. For on Discworld, the size of a god is determined by the strength, and amount, of belief in him (or her, or it). Om's church had become so corrupt and powerful that the fearful belief of the com­mon people had been transferred to the church itself - it's very easy to believe in a red-hot poker - and only Brutha, simple soul, still truly believes. No god ever dies, because there is always some tiny pocket of belief remaining somewhere in the world, but a tortoise is pretty much as low as you can get.

Brutha is going to become the Eighth Prophet of Om. (His grand­mother would have made it two generations before, but she was a woman, and narrative imperative forbids female prophets.) Vorbis's job is to ensure that all Omnians remain true to the teachings of the Great God Om, which is to say, they do what Vorbis tells them. The presence on the Discworld of the god itself, causing changes to all the old teachings and generally making trouble, is not greatly to Vorbis's taste. Neither is the presence of a genuine prophet. Vorbis is faced with the inquisitor's spiritual dilemma, and resolves it in the time-hon­oured manner of the Spanish Inquisition (which, basically, is to tell oneself that torturing people is fine because it's for their own good, in the long run).

Brutha has a much simpler vision of Omnianism: it is something for individuals to live by. Vorbis shows Brutha a new instrument that he has had made: an iron turtle upon which a man or woman can be spreadeagled, with a firebox inside. The time it takes for the iron to heat up will give them plenty of time to reflect on their heresies. In a flash of prophecy, Brutha realises that its first victim will be himself. And in due course, he finds himself chained to it, and uncomfortably warm, with Vorbis watching over him, gloating. Then the Great God Om intervenes, dropped from the talons of an eagle.

One or two people, who had been watching Vorbis closely, said later that there was just time for his expression to change before two pounds of tortoise, travelling at three metres per second, hit him between the eyes.

It was a revelation.

And that does something to people watching. For a start, they believe with all their heart.

The Great God Om now is truly great. He rises over the Temple, a bil­lowing cloud shaped like eagle-headed men, bulls, golden horns, all tangled and fused into one another. Four bolts of fire whir out of the cloud and burst the chains that fastened Brutha to the iron turtle. The Great God declares Brutha to be Prophet of Prophets.

The Great God gives Brutha the opportunity to make some Commandments. The Prophet declines, having decided that 'You should do things because they're right. Not because gods say so. They might say something different another time'. And he tells Om that there will be no Commandments unless the god agrees to obey them, too.

Which is a new thought, for a god. Small Gods has many wise words to say about religion and belief, and it makes the point that in their own terms the Inquisitors believe they are doing good. Fyodor Dostoyevsky's The Brothers Karamazov has a scene in which the Grand Inquisitor encounters Christ, and explains his point of view, including why Christ's renewed message of univer­sal love couldn't have come at a worse time and will only cause trouble. Just as the presence of Brutha, a genuine prophet, was not at all to the liking of Deacon Vorbis.

The Spanish Inquisitors' justification of their actions was philo­sophically convoluted. The purpose of their tortures was straightforward: it was to save a sinner from eternal damnation. The tortures of Hell would be far worse than anything that the Inquisitors could inflict in this world, and they would never stop. So of course they were justified in using any means whatsoever to save the poor soul from destruction. They therefore believed that their actions were justified, and in accordance with Christian principles. Not to act would have been to leave the person concerned in danger of the terrible fires of Hell.

Yes, but what if they were wrong in this belief? This is the convo­luted bit. They weren't quite sure about their religious position. What were the rules? If they failed to convert one tortured heretic, would the Inquisitors burn forever? If they converted one heretic, would their souls be guaranteed a place in Heaven? The Inquisitors believed that by inflicting pain and terror without knowing the rules, they risked their own mortal souls. If they were wrong, it was they who would be immersed in the eternal flames. But they were willing to risk this enormous spiritual danger, to take upon themselves all of the consequences of their actions, should they turn out to be wrong. See how incredibly magnanimous they were being, even as they burned people alive and hacked them limb from limb with red-hot knives ...

Clearly something is wrong. Dostoyevsky solves his own narrative problem by having Christ respond the way his own teachings would lead him to: he kisses the Inquisitor. This is an answer, of a kind, but it doesn't satisfy our analytical instincts. There is a logical flaw in the Inquisitors' position: what is it?

It's very simple. They have thought about what happens if their belief that their actions are justified is wrong - but only within the frame of their religion. They have not asked themselves what their position would be if their religious beliefs are false, if there is no Hell, no eternal damnation, no fire and brimstone. Then their justification would fall to bits.

Of course, if their religion is wrong, then its doctrine of brotherly love could also be wrong. It doesn't have to be: some parts might be fine, others nonsense. But to the Inquisitors it is all of one piece, it stands or falls as a whole. If they are wrong about their religion, then there is no sin, no God, and they can cheerfully torture people if they want to. It really is a nasty philosophical trap.

This is the kind of thing that happens when a big, powerful priest­hood latches on to what started as one person's awe at the universe. It is what happens when people construct elaborate verbal traps for themselves, trip over the logic, and fall headlong into them. It is where Holy Wars come from, where neighbour can inflict atrocity on neigh­bour merely because this otherwise reasonable person goes to a church with a round tower instead of a square one. It is the attitude that Jonathan Swift caricatured in Gulliver's Travels, with the conflict between the big-endians and the little-endians, over which end of an egg to slice into when eating it. It is, perhaps, why so many people today are turning to unorthodox cults in an effort to find a home for their own spirituality. But cults run the same risk as the Inquisition. The only safe home for one's personal spirituality is oneself.

TWENTY-ONE

THE NEW SCIENTIST

These was something called, as far as Ponder could work out, psyence. All his expertise as a reader of invisible writings was needed to get a grip on this idea - L-space was very hazy about the future of this world. 'As far as I can tell,' he reported, 'it's a way of mak­ing up stories that work. It's a way of finding things out and thinking about them ... psy-ence, you see? "Psy" means "mind" and "ence" means, er, esness. It works on Roundworld in the way magic does at home.'

'Useful stuff, then,' said Ridcully. Anyone doing it?' 'Hex is going to try to take us to what appear to be practical exam­ples of it,' said Ponder.

'Time travel again?' said the Dean. The white circle appeared on the floor ... ... and on the sand, and vanished. The wizards looked around.

'All right, then,' said Ponder. 'So ... dry climate, evidence of agri­culture, fields of crops, irrigation ditches, naked man turning a handle, man staring at us, man screaming and running away ...'

Rincewind stepped down into the ditch and inspected the pipe-like device the man had been turning.

'It's just a water-lifting screw,' he announced. 'I've seen a lot of them. You turn the handle, water is screwed out of the ditch, goes up the thread inside and spills out of the top. The screw makes a sort of line of travelling buckets inside the tube. There's nothing special about it. It's just basic ... stuff.'

'Not psyence, then?' said Ridcully.

'You tell me, sir,' said Rincewind.

'Psyence is quite a difficult concept,' said Ponder. 'But I think per­haps tinkering with this thing to make it more efficient might be psyence?'

'Sounds like engineering,' said the Lecturer in Recent Runes. 'That's where you try and make it in different ways to see if any of them are better.'

'The Librarian did turn up one book, very grudgingly,' said Ponder, pulling it out of his pocket.

It was called Basic Science for Schools, pub.1920.

'They've spelt it wrong,' said Ridcully.

'And it's not very helpful,' said Ponder. 'There's quite a lot of what looks like alchemy. You know, mixing stuff up to see what happens.'

'Is that all it is, then?' said the Archchancellor, leafing through the book. 'Hold on, hold on. Alchemy is, at bottom, all about the alchemist. His books tell him all the stuff he's got to do in order make things work - what to wear, when to wear it, that sort of thing. It's very personal.'

'And?' said the Lecturer in Recent Runes.

'Hark at this,' said Ridcully. 'There's no invocations, nothing to tell you what to wear or what phase of the moon it should be. Nothing important. It just says here "A clean beaker was taken. To this was added 20 grammes" - whatever they are - "of copper sulphate" ...' He stopped.

'Well?' said the Lecturer in Recent Runes.

'Well, who did the taking? Who added the stuff? What's going on here?'

'Perhaps it's trying to say that it doesn't matter who does it?' said Ponder. He'd already glanced at the book, and felt that the perfectly ordinary ignorance he'd had just before opening it had been multi­plied several times by page ten.

'Anyone can do it?' shouted Ridcully. 'Science is incredibly impor­tant but anyone can do it? And what's this?'

He held the book open for all to see, his finger pointing at an illustration. It showed a drawing of an eye, side on, to one side of the apparatus.

'Perhaps it's a God of Science?' Rincewind suggested. 'Watching to see who keeps taking things?'

'So ... science is done by anyone,' said Ridcully, 'and most of the equipment is stolen and it's all watched by a giant eyeball?'

As one wizard, they looked around, guiltily.

'There's just us,' said Ponder.

'Then this isn't science,' said Ridcully. 'No giant eyeball visible. Anyway, we can see it isn't science. It's just engineering. Any bright lad could have built it. It's obvious how it works.'

'How does it work?' said Rincewind.

'Very simply,' said Ridcully. The screw goes round and round and the water comes out here.'

'Hex?' said Ponder, and held out his hand. A large volume appeared in it. It was slim, full of colourful pictures, and entitled Great Moments in Science. It hadn't escaped his notice that when Hex or the Librarian wanted to explain something to the wizards they used a children's book.

He flicked through the passages. Big pictures, big writing.

'Ah,' he said. 'Archimedes invented this. He was a philosopher. He's also famous because one day, when he got into his bath, it overflowed. It says here this gave him an idea-'

'Buy a bigger bath?' said the Dean.

'Philosophers are always having ideas in the bath,' said Ridcully. 'All right, if we've got nothing else to go on ...'

'Gentlemen, please?' pleaded Ponder. 'Hex, take us to Archimedes. Oh, and give me a towel.'

'Nice place,' said the Dean, as the wizards sat on the sea wall, staring out at the wine-dark sea. 'I can feel the sea air doing me good. Anyone got more wine?'

It had been quite an interesting day. But, Ponder asked, had it been science? There was a pile of books beside him. Hex had been busy.

'Must have been science,' said Ridcully. 'King gave your man a prob­lem. How to tell if the crown was all gold. He was thinking about it. Water sloshed out of bath. He leaped out, we handed him a towel, and then he worked out that ... what was it?'

'The apparent loss of weight of a body totally or partially immersed in a liquid is equal to the weight of the liquid it displaces,' said Ponder.

'Right. And he sees it doesn't just work with bodies, it works with crowns, too. A few tests, and bingo, science,' said Ridcully. 'Science is just working things out. And paying attention. And hoping there's someone around to dry you off.'

'I'm not ... exactly sure that's all there is to it,' said Ponder. 'I've been doing some reading and even people who do science don't seem clear about what it is. Look at Archimedes, for example. Is a bright idea enough? Is it science if you just solve problems? Is that science, or what you get before you have science?'

'Your book of Great Moments calls him a scienter,' Ridcully pointed.

'Scientist,' Ponder corrected him. 'But I'm not sure about that, either. I mean, that sort of thing happens a lot. People always like to believe that what they're doing has been hallowed by history. Supposing men found out how to fly. They'd probably say "Early experimenters with man-powered flight included Gudrun the Idiot, who leaped off the clock tower in Pseudopolis after soaking his trousers in dew and glu­ing swan feathers to his shirt" when in fact he wasn't an early aviator-'

'-he was a late idiot?' said Rincewind.

'Exactly. It's like with wizards, Archchancellor. You can't just call yourself a wizard. Other wizards have to agree that you're a wizard.'

'So you can't have just one scientist, but you can have two?'

'It appears so, Archchancellor.'

Ridcully lit his pipe. 'Well, mildly entertaining though it is to watch philosophers having a bath, can we simply ask Hex to find us a sci­entist who is definitely a scientist and who is regarded by other scientists as a scientist? Then all we have to do is find out if what he's doing is any use to us. We don't want to be all day at this, Stibbons.'

'Yes, sir. Hex, we-'

They were in a cellar. It was quite large, which was just as well because several of the wizards fell over upon landing. When they had picked themselves up and all found the right hat, they saw ...

... something familiar.

'Mr Stibbons?' said Ridcully.

'I don't understand ...' muttered Ponder. But it really was an alchem­ical laboratory. It smelled like one. Moreover, it looked like one. There were the big heavy retorts, the crucibles, the fire ...

'We know what alchemists are, Mr Stibbons.'

'Yes, er, I'm sorry, sir, something seems to have gone wrong ...' Ponder held out his hand. 'Book, please, Hex.'

A small volume appeared.

'"Great Men Of Science No.2",' Ponder read. 'Er ... if I can just take a quick look inside, Archchancellor ...'

'I don't think that will be necessary,' said the Dean, who had picked up a manuscript that was on the table. 'Listen to this, gentlemen: "... The spirit of this earth is y^e fire in w^ch Pontanus digests his feculent matter, the blood of infants in w^ch y^e 0 & 2) bath themselves, the unclean green Lion w^ch, saith Ripley, is y* means of joyning y^e tinc­tures of 0 and 3), the broth w^ch Medea poured on y^e two serpents, the Venus by meditation of w^ch 0 vulgar and the $ of 7 eagles saith Philalethes must be decocted ..." yada yada yada.'

He thumped the manuscript on to the table.

'Genuine alchemical gibberish,' he said, 'and I don't like the sound of it. What's "feculent" mean? Do we dare find out? I think not.'

'Er ... the man who apparently lived here is described as a giant amongst scientists ...' muttered Ponder, leafing though the booklet.

'Really?' said Ridcully, with a dismissive sniff. 'Hex, please take us to a scientist. We don't mind where he is. Not some dabbler. We want someone who embodies the very essence of science.'

Ponder sighed, and dropped the booklet on to the ground.

The wizards vanished.

For a moment the book lay on the floorboards, front cover upwards showing its title: Great Men of Science No. 2: Sir Isaac Newton. Then it, too, vanished.

There was a thunderstorm grumbling in the distance, and black clouds hung over the sea. The wizards were back on a beach again. Why is it always beaches?' said Rincewind.

'Edges,' said Ridcully. 'Things happen on the edges.'

They had been happening here. At first glance the place looked like a shipyard that had launched its last ship. Large wooden constructions, most of them in disrepair, littered the sand. There were a few shacks, too, also with that hopeless look of things abandoned. There was noth­ing but desolation.

And an oppressive, silence. A few sea birds cried and flew away, but that only left the world to the sound of waves and the footfalls of the wizards as they approached the shacks.

At which point, another sound became apparent. It was a rhythmi­cal cracking, a khss ... khss ... khss behind which it was just possible to hear voices raised in song; the singers sounded as if they were far away and at the bottom of a tin bath.

Ridcully stopped outside the largest shack, from which the sound appeared to be issuing.

'Rincewind?' he said, beckoning. 'One for you, I think.'

'Yes, yes, all right,' said Rincewind, and entered with extreme caution.

It was dark inside, but he could see workbenches and a few tools, with a forgotten look about them. The shack must have been thrown up quickly. There wasn't even a floor; it had been built directly on the sand.

The singing was coming from a large horn attached to a device on a bench. Rincewind wasn't very good at technical things, but there was a large wheel projecting over the edge of the bench and it was turning slowly, probably because of the small weight, attached to it by string, which was gently descending towards the sand.

'Is everything okay?' said Ridcully, from outside.

'I've found a kind of voice mill,' said Rincewind.

'That's amazing,' said a voice from the shadows. 'That's exactly what my master called it.'

His name, he said, was Niklias the Cretan, and he was very old. And very pleased to see the wizards.

'I come up here sometimes,' he said. 'I listen to the voice mill and remember the old days. No one else comes here. They say it's the abode of madness. And they are right.'

The wizards were sitting around a fire of driftwood, that burned blue with the salt. They were tending to huddle, although they'd never admit it. They wouldn't have been wizards if they couldn't sense the strangeness in the place. It had the same depressing effect on the senses as an old battlefield. It had ghosts.

'Tell us,' said Ridcully.

'My master was Phocian the Touched,' said Niklias, and he said it the way of a man telling a story he'd told many times before. 'He was a pupil of the great philosopher Antigonus, who one day declared that a trotting horse must at all times have at least one foot on the ground, lest it fall over.

'There was much debate about this and my master, being very rich and also being a keen pupil, decided to prove that the philosopher was correct. Oh, dreadful day! For it was then the troubles began!

The old slave pointed to some derelict woodwork at the far end of the beach.

'That was our test track,' he said. 'The first of four. I helped him build it with my own hands. There was a lot of interest at that time, and many people came to watch the tests. We had hundreds, hun­dreds of slaves lying in rows, peering through little slits at just one tiny area of the track each. It didn't work. They argued about what they had seen.'

Niklias sighed. 'Time, said my master, was important. So I told him about work gangs, and how songs helped us keep time. He was very excited about that, and after some thought we built the voice mill which you have heard. Do not be afraid. There is no magic in it. Sound makes things shake, does it not? Sound in the big parchment horn, which I stiffened with shellac, writes the pattern of the sounds it hears on a warm wax cylinder. We used the weighted wheel to spin the cylinder, and it worked quite well after we devised the rocking-trap mechanism. After that, we used it to inscribe the perfect song, and every dawn before we began work we would sing it with the machine. Hundreds of slaves, all singing in perfect time on this beach. The effect was amazing.'

'I bet it was,' said Ridcully.

'But still it did not work, no matter what we devised. A trotting horse travels too fast. My master told me that we must be able to count in tiny parts of time, and after much thinking we built the toc-toc machine. Would you care to see it?'

It was like the voice mill, but had a much bigger wheel. And a pen­dulum. And a big pointer. As the big wheel turned very slowly, smaller wheels inside the mechanism spun in a blur, and caused a long pointer to revolve against a white-painted wooden wall, along an arc covered in tiny markers. The whole device was mounted on wheels, and had probably taken four men to move.

'I come and grease it occasionally,' said Niklias, patting the wheel. 'For old time's sake.'

The wizards looked at one another with a tame surmise, which is a wild surmise that had been thought about for a while.

'It's a clock,' said the Dean.

'Pardon?' said Niklias.

'We have something like them,' said Ponder. 'We use them for telling the time.'

The slave looked puzzled. 'For telling the time what?' he said.

'He means, so that we know what time it is,' said Ridcully.

'What ... time ... it ... is ... ' muttered the slave, as if trying a square thought in a round mind.

'What hour of the day it is,' said Rincewind, who had run into minds like this before.

'But we can see the sun,' said the slave. 'The toc-toc mechanism does not know where the sun is.'

'Oh, I know ... supposing a baker needed to know how long he should bake his loaves,' said Rincewind. 'Well, with a clock he-'

'How could he be a baker if he did not know how long it takes to bake a loaf?' said Niklias, smiling nervously. 'No, this is a special thing, sirs. It is not for uncursed men.'

'But, but ... you've got a device for recording sound, too!' Ponder burst out. 'You could record the speeches of great thinkers! Why, even after they were dead you could still hear-'

'Listen to the voice of people who aren't there?' said Niklias. His face clouded. 'Listen to the voices of dead men?

There was silence.

'Do tell us more about the fascinating project to find out if a trot­ting horse is ever entirely airborne,' said Rincewind, loudly and brightly.

The sun drifted down the sky or, rather, the horizon gradually rose. The wizards hated to think about that. You could lose your balance if you thought about it too much.

'... finally my master came up with a new idea,' said Niklias.

'Another one?' said the Dean. 'Was it better than his idea about dropping a horse from, a sling to see if it fell over?'

'Dean!' snapped Ridcully.

'Yes, it was,' said the old slave, who didn't seem to notice the sar­casm. 'We still used the sling, but this time we put it in a very large cart. The bottom of the cart was open, so that the horse's hooves just touched the ground. Are you following me? And then - and this is the clever part, I felt - my master arranged that the cart was pulled by four trotting horses'

He sat back, giving them a pleased look, as if expecting praise.

The Dean's expression slowly changed.

'Eureka!' he said.

'I've got a towel in my-' Rincewind began.

'No, don't you see? If the cart is being pulled forward then what­ever the horse does, the ground is disappearing backwards. So if you've got a trained horse and you can get it to trot while it's in the harness ... you designed the cart so that the pulling horses were off­set, so that the supported horse was trotting over unmarked sand?'

'Yes!' beamed Niklias.

'And you raked the sand so that the prints showed up?'

'Yes!'

Then whenever the horse touched the ground and the hoof was stationary relative to the ground, the ground would in fact be moving, and you'd get a smeared print, and if you carefully measured the total length of the ground covered during the trot, and added up the total of all the smears, and found that they were less than the total length of the track, then-'

'You'd be doing it wrong,' said Ponder.

'Yes!' said Niklias, delightedly. 'That's what we found!'

'No, of course it's right,' said the Dean. 'Listen: when the hoof is sta­tionary-'

'It's moving backwards relative to the horse at the same speed that the horse is moving forward,' said Ponder. 'Sorry.'

'No, listen,' the Dean protested. 'It must work, because when the ground isn 't moving-'

Rincewind groaned. Any minute now all the wizards would express an opinion, and none of them would listen to anyone else. And here it came ...

'Are you telling us parts of the horse are actually going backwards?'

'Perhaps if we pulled the cart in the opposite direction-'

'The hoof would definitely be stationary, look, because if the ground was moving forward-'

'It's no different than it would be if the horse was trotting all by itself! Look, supposing the cart and all the other horses were invisi­ble-'

'You're all wrong, you're all wrong! If the horse was ... no, wait a moment-'

Rincewind nodded to himself. The wizards were entering the spe­cial fugue state known as Hubbub, where no-one was going to be allowed to finish a sentence because someone else would drown them out. It was how the wizards decided things. In all likelihood, in this case it would result in them deciding that the horse should, log­ically, end up at one end of the beach, while all its feet were up at the other end.

'My master Phocian said we should try it, and the hooves just left hoofprints,' said Niklias the Cretan, when the argument had died away through lack of breath. 'Then we tried moving the beach under the horse ...'

'How?' said Ponder.

'We built a long flat barge, filled it full of sand and tried it in the lagoon,' said the slave. 'We suspended the horse from a gantry. Phocian felt we were getting somewhere when we moved the barge forward at twice the speed of the horse, but the beast kept trying to keep up ... and then there was the night of the big storm and the barge was sunk. Oh, those were a few busy months. We lost four horses and Nosios the Carpenter was kicked in the head.' The smile faded. And then ... and then ...'

'Yes?'

'... something terrible happened.'

The wizards leaned forward.

'... Phocian designed the fourth test. It's over there. Not much to see now, of course. People stole all the heavy cloth of the Endless Road and a lot of the woodwork, too.' The slave sighed. 'It was Hades to build and took many months to get right but, in short, it worked like this. We used a huge roll of heavy white cloth, which we rolled off one huge spindle and on to the other. Believe me, sirs, even that took some doing, and the work of forty slaves. At the place where the horse was to be suspended, we stretched the cloth tight over a shal­low trough of powdered charcoal, so that a little weight on the cloth would press it down on to the stuff…'

'Aha,' said the Dean. 'I think I can see this one ...'

Niklias nodded. 'My master commanded many changes before the device functioned to his satisfaction ... many gears and rollers and cranks, much rebuilding of strange mechanisms, much profanity which, I have no doubt, the gods noted. But finally we suspended the well-trained horse in its sling and the rider urged it into a trot as the cloth rolled beneath. And, yes, afterwards, oh sad that day, we measured the length of the cloth where the horse had trotted and the length of the smears of charcoal where a hoof had pressed on the cloth and ... I hardly dare say it, even now, the total length of the second was to the length of the first was as four is to five.'

'So for a fifth of the time all hooves were in the air!' said the Dean. Well done! I love a puzzle!'

'No, it was not well done!' shouted the slave. 'My master ranted! We did it again and again! And it was always the same!'

'I don't quite see the problem-' Ridcully began.

'He tore at his hair and raved at us, and most of the men fled! And then he went and sat in the waves on the shore, and after a long while I dared to go and speak to him, and he turned hollow eyes on me and said, "Great Antigonus is wrong. I proved him wrong! Not by thought­ful dispute, but by gross mechanical contrivances! I am ashamed! He is the greatest of philosophers! He had told us that the sun goes around the world, he had told us how the planets move! And if he is wrong, what is right? What have I done? I have squandered the wealth of my family. What fame is there for me now? What cursed work shall I do next? Should I steal the colours from a flower? Shall I say to everyone, 'What you think is right, is not right'? Shall I weigh the stars? Shall I plumb the utter depths of the sea? Shall I ask the poet to measure the width of love and the direction of pleasure? What have I made of myself ..." and he wept.'

There was silence. None of the wizards moved.

Niklias settled down a little. 'And then he bade me go back and he told me to take the little money that was left. In the morning he was gone. Some say he fled to Egypt, some say to Italy. But for myself. I think he did indeed plumb, at the last, the depth of the sea. For I do not know what he was, or what he had become. And presently peo­ple came and tore down most of the engines.'

He shifted his weight and looked at the remains of the strange devices, skeletal against the livid sunset. There was something wistful in his expression.

'No one comes now,' he said. 'Hardly anyone at all. This is where the Fates struck and the gods laughed at men. But I remember how he wept. And so I remain, to tell the story.'

TWENTY-TWO

THE NEW NARRATIVIUM

The wizards have been trying to find some 'psyence' in Roundworld, but it is proving even more elusive than the correct spelling. They are having problems because they are tackling a difficult question. There isn't a simple definition of 'science' that really captures what it is. And it's not the sort of thing that comes into existence at a single place and time. The development of science was a process in which non-science slowly became science. The two ends of the process are easily distinguished, but there's no special place in between where science suddenly came into being.

These difficulties are more common than you might expect. It is almost impossible to define a concept precisely - think of 'chair', for example. Is a large beanbag a chair? It is if the designer says it's a chair and someone uses it to sit on; it's not if a bunch of kids are throwing it at each other. The meaning of 'chair' does not just depend on the thing to which it is being applied: it also depends on the associated context. And as for processes in which something gradually changes into something else ... well, we're never comfortable with those. At what stage in its life does a developing embryo become a human being, for instance? Where do you draw the line?

You don't. If the end of a process is qualitatively different from the start, then something changes in between. But it need not be at a spe­cific place in between, and if the change is gradual, there isn't a line. Nobody thinks that when an artist is painting something, there is one special stroke of the brush at which it turns into a picture. And nobody asks 'Whereabouts in that particular brushstroke does the change take place?' At first there is a blank canvas, later there's a picture, but there isn't a well-defined moment at which one ceases and the other begins. Instead, there is a long period of neither.

We accept this about a painting, but when it comes to more emotive processes like embryos becoming human beings, a lot of us still feel the need to draw a line. And the law encourages us to think like that, in black and white, with no intervening shades of grey. But that's not how the universe works. And it certainly didn't work like that for science.

To complicate things even further, important words have changed their meaning. An old text from 1340 states that 'God of sciens is lord', but there the word 'sciens' means 'knowledge', and the phrase is say­ing that God is lord of knowledge. For a long time science was known as 'natural philosophy', but by 1725 the word 'science' is being used in essentially its modern form. The word 'scientist', however, seems to have been invented by William Whewell in his 1840 The Philosophy of the Inductive Sciences to describe a practitioner of science. But there were scientists before Whewell invented a word for them, otherwise he wouldn't have needed a word, and there was no science when God was lord of knowledge. So we can't just go by the words people use, as if words never change their meanings, or as if things can't exist before we have a word for them.

But surely science goes back a long, long way? Archimedes was a sci­entist, wasn't he? Well, it depends. It certainly looks to us, now, as if Archimedes was doing science; indeed we have reached back into his­tory, picked out some of his work (especially his buoyancy principle) and called it science. But he wasn't doing science then, because the context wasn't suitable, and his mind-set was not 'scientific'. We see him with hindsight; we turn him into something we recognise, but he wouldn't.

Archimedes made a brilliant discovery, but he didn't test his ideas like a scientist would now, and he didn't investigate the problem in a genuinely scientific way. His work was an important step along the path to science, but one step is not a path. And one thought is not a way of thinking.

What about the Archimedean screw? Was that science? This won­derful device is a helix that fits tightly inside a cylinder. You place the cylinder at a slant, with the bottom end in water; turn the helix, and after a while water comes out at the top. It is generally believed that the famous Hanging Gardens of Babylon were watered using mas­sive Archimedean screws. How it works is more subtle than Ridcully imagines: in particular, the screw ceases to work if it is held at too steep an angle. Rincewind is right: an Archimedean screw is like a series of travelling buckets, separate compartments with water in them. Because they are separate, there is no continuous channel for the water to flow away along. As the screw turns, the compartments move up the cylinder, and the water has to go with them. If you hold the cylinder at too steep a slope, all the 'buckets' merge, and the water no longer climbs.

The Archimedean screw surely counts as an example of ancient Greek technology, and it illustrates their possession of engineering. We tend to think of the Greeks as 'pure thinkers', but that's the result of selective reporting. Yes, the Greeks were renowned for their (pure) mathematics, art, sculpture, poetry, drama and philosophy. But their abilities did not stop there. They also had quite a lot of technology. A fine example is the Antikythera mechanism, which is a lump of cor­roded metal that some fishermen found at the bottom of the Mediterranean Sea in 1900 near the island of Antikythera. Nobody took much notice until 1972, when Derek de Solla Price had the lump X-rayed. It turned out to be an orrery: a calculating device for the movements of the planets, built from 32 remarkably precise cogwheels. There was even a differential gear. Before this gadget was discovered, we simply didn't know that the Greeks had possessed that kind of technological ability.

We still don't understand the context in which the Greeks developed this device; we have no idea where these technologies came from. They were probably passed down from craftsman to craftsman by word of mouth - a common vehicle for technological extelligence, where ideas need to be kept secret and passed on to successors. This is how secret craft societies, the best known being the freemasons, arose.

The Antikythera mechanism was Greek engineering, no question. But it wasn't science, for two reasons. One is trivial: technology isn't science. The two are closely associated: technology helps to advance science, and science helps to advance technology. Technology is about making things work without understanding them, while science is about understanding things without making them work.

Science is a general method for solving problems. You're only doing science if you know that the method you're using has much wider application. From those written works of Archimedes that still survive, it looks as if his main method for inventing technology was mathe­matical. He would lay down some general principles, such as the law of the lever, and then he would think a bit like a modern engineer about how to exploit those principles, but his derivation of the prin­ciples was based on logic rather than experiment. Genuine science arose only when people began to realise that theory and experiment go hand in hand, and that the combination is an effective way to solve lots of problems and find interesting new ones.

Newton was definitely a scientist, by any reasonable meaning of the word. But not all the time. The mystical passage that we've quoted, complete with alchemical symbols and obscure terminology, is one that he wrote in the 1690s after more than twenty years of alchemical experimentation. He was then aged about 50. His best work, on mechanics, optics, gravity, and calculus, was done between the ages of 23 and 25, though much of it was not published for decades.

Many elderly scientists go through what is sometimes called a 'philosopause'. They stop doing science and take up not very good philosophy instead. Newton really did investigate alchemy, with some thoroughness. He didn't get anywhere because, frankly, there was nowhere to go. We can't help thinking, though, that if there had been somewhere, he would have found the way.

We often think of Newton as the first of the great rational thinkers, but that's just one aspect of his remarkable mind. He straddled the boundary between old mysticism and new rationality. His writings on alchemy are littered with cabbalistic diagrams, often copied from early, mystical sources. He was, as John Maynard Keynes said in 1942, 'the last of the Magicians ... the last wonder-child to whom the Magi could do sincere and appropriate homage'. What confuses the wizards is an accident of timing - well, we must confess that it is actually a case of narrative imperative. Having homed in on Newton as the epitome of scientific thinking, the wizards happen to catch him in post-philosopausal mode. Hex is having a bad day, or perhaps is trying to tell them something.

If Archimedes wasn't a scientist and Newton was only one some­times, just what is science? Philosophers of science have isolated and defined something called the 'scientific method', which is a formal summary of what the scientific pioneers often did intuitively. Newton followed the scientific method in his early work, but his alchemy was bad science even by the standards of his day, when chemists had already moved on. Archimedes doesn't seem to have followed the sci­entific method, possibly because he was clever enough not to need it. The textbook scientific method combines two types of activity. One is experiment (or observation - you can't experiment on the Big Bang but you can hope to observe traces that it left). These provide the real­ity-check that is needed to stop human beings believing something because they want it to be true, or because some overriding authority tells them that it's true. However, there is no point in having a reality-check if it's bound to work, so it can't just be the same observations that you started from. Instead, you need some kind of story in your mind.

That story is usually dignified by the word 'hypothesis', but less formally it is the theory that you are trying to test. And you need a way to test it without cheating. The most effective protection against cheating is to say in advance what results you expect to get when you do a new experiment or make a new observation. This is 'pre­diction', but it may be about something that has already happened but not yet been observed. 'If you look at red giant stars in this new way then you will find that a billion years ago they used to ...' is a prediction in this sense.

The most naive description of the scientific method is that you start with a theory and test it by experiment. This presents the method as a single-step process, but nothing could be further from the truth. The real scientific method is a recursive interaction between theory and experiment, a complicity in which each modifies the other many times, depending on what the reality-checks indicate along the way.

A scientific investigation probably starts with some chance obser­vation. The scientist thinks about this and asks herself 'why did that happen?' Or it may be a nagging feeling that the conventional wisdom has holes in it. Either way, she then formulates a theory. Then she (or more likely, a specialist colleague) tests that theory by finding some other circumstance in which it might apply, and working out what behaviour it predicts. In other words, the scientist designs an experi­ment to test the theory.

You might imagine that what she should be trying to do here is to design an experiment that will prove her theory is correct. However, that's not good science. Good science consists of designing an exper­iment that will demonstrate that a theory is wrong - if it is. So a large part of the scientist's job is not 'establishing truths', it is trying to shoot down the scientist's own ideas. And those of other scientists. This is what we meant when we said that science tries to protect us against believing what we want to be true, or what authority tells us is true. It doesn't always succeed, but that at least is the aim.

This is the main feature that distinguishes science from ideologies, religions and other belief systems. Religious people often get upset when scientists criticise some aspect of their beliefs. What they fail to appreciate is that scientists are equally critical about their own ideas and those of other scientists. Religions, in contrast, nearly always crit­icise everything except themselves. Buddhism is a notable exception: it emphasises the need to question everything. But that may be going too far to be helpful.

Of course, no real scientist actually follows the textbook scientific method unerringly. Scientists are human beings, and their actions are driven to some extent by their own prejudices. The scientific method is the best one that humanity has yet devised for attempting to over­come those prejudices. That doesn't mean that it always succeeds. People, after all, are people.

The closest that Hex manages to come to genuine science is Phocian the Touched's lengthy and meticulous investigation of Antigonus's the­ory of the trotting horse. We hope that you have heard of neither of these gentlemen, since, to the best of our knowledge, they never existed. But then, neither did the Crab Civilisation - which didn't stop the crabs making their Great Leap Sideways. Our story here is mod­elled on real events, but we've simplified various otherwise distracting issues. With which we shall now distract you.

The prototype for Antigonus is the Greek philosopher Aristotle, a very great man who was even less of a scientist than Archimedes, whatever anyone has told you. In his De Incessu Animalium {On the Gait of Animals) Aristotle says that a horse cannot bound. The bound is a four-legged gait in which both front legs move together, then both back legs move together. He's right, horses don't bound. But that is the least interesting thing here. Aristotle explains why a horse can't bound:

If they moved the fore legs at the same time and first, their progres­sion would be interrupted or they would even stumble forward ... For this reason, then, animals do not move separately with their front and back legs.

Forget the horse: many quadrupeds do bound, so his reasoning, such as it is, must be wrong. And a gallop is very close to a bound, except that the left and right legs move at very slightly different times. If the bound were impossible, then by the same token so should the gallop be. But horses gallop.

Oops.

You can see that all this is a bit too messy to make a good story, so in the interests of narrativium we have replaced Aristotle by Antigonus, and credited him with a very similar theory about a long-standing his­torical conundrum: does a trotting horse always have at least one hoof on the ground? (In a trot, diagonally opposite legs move together, and the pairs hit the ground alternately.) This is the kind of question that must have been discussed in ale-houses and public baths since well before the time of Aristotle, because it's just out of reach of the unaided human eye. The first definitive answer came in 1874 when Eadweard Muybridge (born Edward Muggeridge) used high-speed photography to show that sometimes a trotting horse has all four feet off the ground at once. The proportion of times this occurs depends on the speed of the horse, and can be more than Phocian's 20 per cent. It can also be zero, in a slow trot, which further complicates the science. Allegedly, Muybridge's photographs won Leland Stanford Jr, a former Governor of California, the tidy sum of $25,000 in a bet with Frederick MacCrellish.

But what interest us here is not the science of horse locomotion, fascinating as that may be. It is how a scientific mind would go about investigating it. And Phocian shows that the Greeks could have made a lot more progress than they did, if they'd thought like a scientist. There were no technological barriers to solving such problems; just mental and (especially) cultural ones. The Greeks could have invented the phonograph, but if they did, it left no trace. They could have invented a clock, and the Antikythera mechanism shows they had the technique, but it seems that they didn't.

The slaves' use of songs to keep time has its roots in later history. In 1604 Galileo Galilei used music as a way to determine short inter­vals of time in some of his experiments on mechanics. A trained musician can mentally subdivide a bar into 64 or 128 equal parts, and even untrained people can distinguish an interval of a hundredth of a second in a piece of music. The Greeks could have used Galileo's method if they'd thought of it, and advanced science by 2,000 years. And they could have invented innumerable Heath-Robinson gadgets to study a moving horse, if it had occurred to them. Why didn't they? Possibly because, like Phocian, they were too tightly focussed on spe­cific issues.

Phocian's approach to the trotting horse looks pretty scientific. First he tries the direct method: he gets his slaves to observe the horse while it is trotting, and see whether it is ever completely off the ground. But the horse is moving too fast for human vision to provide a convincing answer. So then he goes for the indirect approach. He thinks about Antigonus's theory, and homes in on one particular step: if the horse is off the ground, then it ought to fall over. That step can be tested in its own right, though in a different situation: a horse slung from a rope. (This way of thinking is called 'experimental design'.) If the horse does not fall over, then the theory is wrong. But this experiment is inconclu­sive, and even if the theory is wrong the conclusions could still be right, so he refines the hypothesis and invents more elaborate apparatus.

We don't want to go too deeply into details of design here. We can think of ways to make the experiment workable, but the discussion would be a bit technical. For example, it seems necessary to make the roll of cloth, the Endless Road, move at a speed that is non-zero, but is also different from the natural speed with which the horse would move if its feet were actually hitting solid ground. You might care to think about that, and you might even decide that we're wrong. And you might even be right.

We also acknowledge that Phocian's final experiment is open to many objections. And because the hooves of a trotting horse hit the ground in pairs, it is actually necessary to halve the total length of the charcoal smears before comparing them with the length of the cloth.

No matter, these are mere elaborations of what would otherwise be an entirely transparent story: you understand what we're getting at.

Taking all this into account, was Phocian a scientist?

No. Hex has bungled again, for despite Phocian's years of visibly 'scientific' activity, he falls down in two respects. One, open to dis­pute, is not his fault: he has no peers, no colleagues. There are no other 'scientists' for him to work with, or to criticise him. He's on his own and ahead of his time. Just as there cannot be just one wizard, there cannot be just one scientist. Science has a social dimension. The second reason, though, is decisive. He is mortified when his work proves that Antigonus, the great authority, is wrong.

Any genuine scientist would give their right arm to prove that the great authority is wrong.

That's how you make your reputation, and it's also the most impor­tant way to contribute to the scientific endeavour. Science is at its best when it changes people's minds. Very little of it does that, in part because our minds have been built by a culture that is pervaded by science anyway. If a scientist manages to spend 1 per cent of the time discovering things that are not what they expected, they are doing amazingly well. But boy, does that 1 per cent count for a lot.

This, then, is science. Questioning authority. Complicity between theory and experiment. And being within a community of like-minded people to question your work. Preferably accompanied by a conscious awareness of all of the above, and gratitude to your friends and col­leagues for their criticisms. And what's the aim? To find timeless truths? No, that's asking too much. To stop frail humans from falling for plausible falsehoods? Yes - including those of people who at least look and sound just like you. And to protect people from their willingness to believe a good story, just because it sounds right and doesn't upset them. And to protect them from the firm smack of authority, too.

It took humanity a long time to arrive at the scientific method. No doubt the reason for the delay was that if you do science properly, you often find yourself overturning entrenched, well-established beliefs, including your own entrenched, well-established beliefs. Science is not a belief system, but many areas of human activity are, so it is not surprising to find that the early developers of science often found themselves in conflict with authority. Perhaps the best-known exam­ple of this is Galileo, who ran into trouble with the Inquisition because of his theories about the solar system. Sometimes science exposes you to the firm smack instead.

Science, then, is not just a body of teachable facts and techniques. It is a way of thinking. In science, established 'facts' are always open to question, but few scientists will listen to you unless you can offer some evidence that the old ideas are wrong. If the people who invented those ideas are dead, then alternatives can quickly gain acceptance, and the scientific method is working well. If the people who invented those ideas are still around, in influential positions, then they can put a lot of obstacles in the way of the new suggestion and the people who proposed it. Then science is working badly, because people are behaving like people. Even so, the new idea still can dis­place the accepted wisdom. It just takes longer and needs really solid evidence.

Let's contrast science with alternative ways of thinking about the universe. The Discworld worldview is that the universe is run by magic: things happen because people want them to happen. You still have to find the right spell, or the narrative imperative has to be so strong that those things will happen anyway even if people don't want them to, but the universe exists in order to be there for people.

On Discworld and Roundworld, the worldview of the priesthood is similar, but with one important difference. They believe that the uni­verse is run by gods (or a god): things happen because the gods want them to happen, don't care if they happen, or have some ineffable long-term aim in view. However, it is possible for people to ask the priests to intercede with the gods, on their behalf, in the hope of influ­encing the gods' decisions, at least in minor ways.

The philosophical worldview, exemplified by Antigonus, is that the nature of the world can be deduced by pure thought, on the basis of a few deep, general principles. Observation and experiment are sec­ondary to verbal reasoning and logic.

The scientific worldview is that what people want has very little to do with what actually happens, and that it is unnecessary to invoke gods at all. Thought is useful, but empirical observations are the main test of any hypothesis. The role of science is to help us find out how the universe works. Why it works, or what manner of Being ultimately controls it, if any, is not a question that science is interested in. It is not a question to which anyone can give a testable answer.

Oddly enough, this hands-off approach to the universe has given us far more control over it than magic, religion or philosophy have done. On Roundworld, magic doesn't work, so it offers no control at all. Some people believe that prayer can influence their god, and that in this way human beings can have some influence over the world in which they live, like a courtier at a king's ear. Other people have no such beliefs, and consider the role of prayer to be largely psycholog­ical. It can have an effect on people, but not on the universe itself. And philosophy has a tendency to follow rather than lead.

Science is a form of narrativium. In fact, all four approaches to the uni­verse - magic, religion, philosophy and science - involve the construction of stories about the world. Oddly enough, these differ­ent kinds of story often have many parallels. There is a distinct resemblance between many religious creation myths and the cosmologists' 'Big Bang' theory of the origin of the universe. And the monotheistic idea that there is only one God, who created everything and runs everything, is suspiciously close to the modern physicists' idea that there should be a single Theory of Everything, a single fun­damental physical principle that unites both relativity and quantum mechanics into a satisfying and elegant mathematical structure.

The act of telling stories about the universe may well have been more important to the early development of humanity, and for the ini­tial growth of science, than the actual content of the stories themselves. Accurate content was a later criterion. When we start telling stories about the universe, the possibility arises of comparing those stories with the universe itself, and refining how well the stories fit what we actually see. And that is already very close to the scientific method.

Humanity seems to have started from a rather Discworldly view, in which the world was inhabited by unicorns and werewolves and gods and monsters, and the stories were used not so much to explain how the world worked, but to form a crucial part of the cultural Make-a-Human kit. Unicorns, werewolves, elves, fairies, angels, and other supernatural were not real. But that didn't actually matter very much: there is no problem in using unreal things to programme human minds. Think of all those talking animals.

The models employed by science are very similar in many respects. They, too, do not correspond exactly to reality. Think of the old model of an atom as a kind of miniature solar system, in which tiny hard par­ticles called electrons whirl around a central nucleus consisting of other kinds of tiny hard particles: protons and neutrons. The atom is not really like that. But many scientists still use this picture today as the basis for their investigations. Whether this makes sense depends upon what problem they are working on, and when it doesn't make sense, they use something more sophisticated, like the description of an atom as a probable cloud of 'orbitals' which represent not electrons, but places where electrons could be. That model is more sophisticated, and it fits reality more closely than a mini solar system, but it still isn't 'true'.

Science's models are not true, and that's exactly what makes them useful. They tell simple stories that our minds can grasp. They are lies-to-children, simplified teaching stories, and none the worse for that. The progress of science consists of telling ever more convincing lies to ever more sophisticated children.

Whether our worldview is magical, religious, philosophical or sci­entific, we try to alter the universe so that we can convince ourselves that we're in charge of it. If our worldview is magical, we believe that the universe responds to what we want it to do. So control is just a matter of finding the right way to instruct the universe about what our wishes are: the right spell. If our worldview is religious, we know that the gods are really in charge, but we hold out the hope that we can influence their decisions and still get what we want (or influence ourselves to accept whatever happens ...). If our worldview is philo­sophical, we seldom tinker with the universe ourselves, but we hope to influence how others tinker. And if our worldview is scientific, we start with the idea that controlling the universe is not the main objec­tive. The main objective is to understand the universe.

The search for understanding leads us to construct stories that map out limited parts of the future. It turns out that this approach works best if the map does not foretell the future like a clairvoyant, predict­ing that certain things will happen on certain days or in certain years. Instead, it should predict that if we do certain things, and set up a par­ticular experiment in particular circumstances, then certain things should happen. Then we can do an experiment, and check the rea­soning. Paradoxically, we learn most when the experiment fails.

This process of questioning the conventional wisdom, and modify­ing it whenever it seems not to work, can't go on indefinitely. Or can it? And if it stops, when does it stop?

Scientists are used to constant change, but most changes are small: they refine our understanding without really challenging anything. We take a brick out of the wall of the scientific edifice, polish it a bit, and put it back. But every so often, it looks as if the edifice is actually fin­ished. Worthwhile new questions don't seem to exist, and all attempts to shoot down the accepted theory have failed. Then that area of science becomes established (though still not 'true'), and nobody wastes their time trying to change it any more. There are always other sexier and more exciting areas to work on.

Which is much like putting a big plug in a volcano. Eventually, as the pressure builds up, it will give way. And when it does, there will be a very big explosion. Ash rains down a hundred miles away, half the mountain slides into the sea, everything is altered ...

But this happens only after a long period of apparent stability, and only after a huge fight to preserve the conventional ways of thinking. What we then see is a paradigm shift, a huge change in thought pat­terns; examples include Darwin's theory of evolution and Einstein's theory of relativity.

Changes in scientific understanding force changes in our culture. Science affects how we think about the world, and it leads to new technologies that change how we live (and, when misunderstood, deliberately or otherwise, some nasty social theories, too).

Today we expect big changes during our lifetimes. If children are asked to forecast the future, they'll probably come up with science-fictional scenarios of some kind - flying cars, holidays on Mars, better and smaller technology. They are probably wrong, but that doesn't matter. What matters is that today's children do not say: 'Change? Oh, everything will probably be pretty much the same. I’ll be doing just the same things that my Mum and Dad do now, and their Mum and Dad did before them.' Whereas even fifty years ago, one grandfa­ther, that was generally the prevailing attitude. Ten or eleven grandfathers ago, a big change for most people meant using a dif­ferent sort of plough.

And yet ... Underneath these changes, people are still people. The basic human wants and needs are much as they were a hundred grandfathers ago, even if we ever do take holidays on Mars (all that beach ... ). The realisation of those needs may be different - a ham­burger instead of a rabbit brought down with an arrow you made yourself - but we still want food. And companionship and sex and love and security and lots of other familiar things.

The biggest significant change, one that really does alter what it is like to be human, may well be modern communication and transportation.

The old geographical barriers that kept separate cultures separate have become almost irrelevant. Cultures are merging and reforming into a global multiculture. It's hard to predict what it will look like, because this is an emergent process and it hasn't finished emerging yet. It may be something quite different from the giant US shopping mall that is generally envisaged. That's what makes today's world so fascinating - and so dangerous.

Ultimately, the idea that we are controlling our universe is an illu­sion. All we know is a relatively small number of tricks, plus one great generic trick for generating more small tricks. That generic trick is the scientific method. It pays off.

We have also the trick of telling stories that work. By this stage in our evolution, we are spending most of our lives in them. 'Real life' -that is, the real life for most of us, with its MOT tests and paper wealth and social systems - is a fantasy that we all buy into, and it works pre­cisely because we all buy into it.

Poor old Phocian tried hard, but found that the old stories weren't true when he hadn't quite got as far as constructing a new one. He performed a reality check, and found that there wasn't one - at least, not one he'd like to believe was real. He suddenly saw a universe with no map. We've got quite good at mapping, since then.

TWENTY-THREE

PARAGON OF ANIMALS

The wizards went back to Dee's House in sombre mood, and spent the rest of the week sitting around and get­ting on one another's nerves. In ways they couldn't quite articulate, they'd been upset by the story.

'Science is dangerous,' said Ridcully at last. 'We'll leave it alone.'

'I think it's like with wizards,' said the Dean, relieved to be having a conversation again. 'You need to have more than one of them, otherwise they get funny ideas.'

'True, old friend,' said Ridcully, probably for the first time in his life. 'So ... science is not for us. We'll rely on common sense to see us through.'

'That's right,' said the Lecturer in Recent Runes. 'Who cares about trotting horses anyway? If they fall over they've only got themselves to blame.'

'As a basis for our discussion,' said Ridcully, 'let us agree on what we have discovered so far, shall we?'

'Yes. It's that whatever we do, the elves always win,' said the Dean. 'Er ... I know this may sound stupid ...' Rincewind began. 'Yes. It probably will,' said the Dean. You haven't been doing very much since we got back, have you?'

'Well, not really,' said Rincewind. 'Just walking around, you know. Looking at things.'

'Exactly! You haven't read a single book, am I correct? What good is walking around?'

'Well, you get exercise,' said Rincewind. 'And you notice things. Yesterday the Librarian and I went to the theatre.

They'd got the cheapest ticket, but the Librarian paid for two bags of nuts.

They'd found, once they had settled into this period, that there was no point in trying to disguise the Librarian too heavily. With a jerkin, a big floppy hood and a false beard he looked, on the whole, an improvement on most of the people in the cheap seats, the cheap seats in this case being so cheap they consisted, in fact, of standing up. The cheap feets, in fact.

The play had been called The Hunchback King, by Arthur J. Nightingale. It hadn't been very good. In fact, Rincewind had never seen a worse-written play. The Librarian had amused himself through­out by surreptitiously bouncing nuts off the king's fake hump. But people had watched it in rapt fascination, especially the scene where the king was addressing his nobles and uttered the memorable line: 'Now is the December of our discontent - I want whichever bastard is doing that to stop right now!'

A bad play but a good audience, Rincewind mused after they had been thrown out. Oh, the play was a vast improvement on anything the Shell Midden Folk could have dreamed up, which would have to be called 'If We'd Invented Paint We Could Watch It Dry', but the lines sounded wrong and the whole thing was laboured and had no flow. Nevertheless, the faces of the watchers had been locked on the stage. On a thought, Rincewind had put a hand over one eye and, con­centrating fearfully, surveyed the theatre. The one available eye watered considerably but had revealed, up in the expensive seats, several elves. They liked plays, too. Obviously. They wanted people to be imag­inative. They'd given people so much imagination that it was constantly hungry. It would even consume the plays of Mr Nightingale.

Imagination created monsters. It made you afraid of the dark, but not of the dark's real dangers. It peopled the night with terrors of its own.

So, therefore ... Rincewind had an idea.

'] think we should stop trying to influence the philosophers and schol­ars,' he said. 'People with minds like that believe all sort of things all the time. You can't stop them. And science is just too weird. I keep thinking of that poor man-'

'Yes, yes, yes, we've been through all this,' said Ridcully wearily. 'Get to the point, Rincewind. What have you got to say that's new?' 'We could try teaching people art,' said Rincewind. 'Art?' said the Dean. 'Art's for slackers! That'd make things worse!' 'Painting and sculpture and theatre,' Rincewind went on. 'I don't think we should try to stop what the elves began. I think we ought to encourage it as much as possible. Help the people here to get really good at imagining things. They're not quite there yet.'

'But that's just what the elves want, man!' snapped Ridcully. 'Yes!' said Rincewind, almost drunk with the novelty of having an idea that didn't include running away. 'Let's help the elves! Let's help them to destroy themselves.'

The wizards sat in silence. Then Ridcully said: 'What are you talk­ing about?'

'At the theatre I saw lots of people who wanted to believe that the world is different from the reality they see around them,' said Rincewind. 'We could-' He sought a way into Ridcully's famously hard-to-open mind. 'Well, you know the Bursar?' he said.

'A gentlemen of whose existence I am aware on a daily basis,' said Ridcully gravely. 'And I'm only glad that this time we've left him with his aunt.'

'And you remember how we cured his insanity?' 'We didn't cure it,' said Ridcully. 'We just doctored his medicine so that he permanently hallucinates that he is sane.'

'Exactly! You use the disease as the cure, sir! We made him more insane, so now he's sane again. Mostly. Apart from the bouts of weight­lessness, and, er, that business with the-'

'Yes, yes, all right,' said Ridcully. 'But I'm still waiting for the point of this.'

'Are you talking about fighting like those monks up near the Hub?' said the Lecturer in Recent Runes. 'Skinny little chaps who can throw big men through the air?'

'Something like that, sir,' said Rincewind.

Ridcully prodded Ponder Stibbons.

'Did I miss a bit of conversation there?' he said.

'I think Rincewind means that if we take the elves' work even fur­ther it'll somehow end up defeating them,' said Ponder.

'Could that work?'

'Archchancellor, I can't think of anything better,' said Ponder. 'Belief doesn't have the same power on this world as it does on ours, but it is still pretty strong. Even so, the elves are here. They are a fixture.'

'But we know they ... sort of feed on people,' said Rincewind. 'We want them to go away. Um ... and I've got a plan.'

'You have a plan,' said Ridcully, in a hollow voice. 'Does anyone else have a plan? Anyone? Anyone? Someone?'

There was no reply.

'The play I saw was awful,' said Rincewind. 'These people might be a lot more creative than the Shell Midden People, but they've still got a long way to go. My plan ... well, I want us to move this world into the path of history that contains someone called William Shakespeare. And absolutely does not contain Arthur J. Nightingale.'

'Who's Shakespeare?' said Ponder.

'The man,' said Rincewind, 'who wrote this.' He pushed a battered manuscript across the table. 'Read it out from where I've marked it, will you?'

Ponder adjusted his spectacles, and cleared his throat.

'What a piece of work is, er, this is awful handwriting ... '

'Let me,' said Ridcully, taking the pages. 'You don't have the voice for this sort of thing, Stibbons.' He glared at the paper, and then: 'What a piece of work is a man! How noble in reason ... how infinite in fac­ulty ... in form and moving, how express and admirable! In action, how like an angel! In apprehension, how like a god! The beauty of the world, the paragon of animals ...'

He stopped.

And this man lives here?' he said.

'Potentially,' said Rincewind.

'This man stood knee deep in muck in a city with heads on spikes and wrote this?'

Rincewind beamed. 'Yes! In his world, he is probably the most influ­ential playwright in the history of the species! Despite requiring a lot of tactful editing by most directors, because he had his bad days just like everyone else!'

'By "his world" you mean-?'

'Alternate worlds,' muttered Ponder, who was sulking. He'd once played the part of Third Goblin in a school play and felt that he had rather a good speaking voice.

'You mean he should be here but ain't?' Ridcully demanded.

'I think he should be here but can't be,' said Rincewind. 'Look, these aren't the Shell Midden people, it's true, but artistically they're pretty low down the scale. Their theatre is awful, they haven't got any decent artists, they can't carve a decent statue - this world isn't what it should be.'

'And?' said Ponder, still smarting.

Rincewind signalled to the Librarian, who ambled around the table handing out small, green, cloth-bound books.

'This is another play he will write ... is ... writing ... wrote ... will have written,' he said. 'I think you'll agree that it could be very impor­tant ...'

The wizards read it. They read it again. They had a huge argument, but there was nothing unusual about that.

'It's an astonishin' play, in the circumstances,' said Ridcully, even­tually. 'And some of it is a bit familiar!'

'Yes,' said Rincewind. And I think that's because he'll write it after listening to you. We need him to. This is a man who can tell the audi­ence, tell the audience that they're watching a bunch of actors on a tiny stage and then make them see a huge battle, right there in front of their eyes.'

'Did I miss that bit?' said the Lecturer in Recent Runes, leafing hur­riedly through the pages.

'That's in another play, Runes,' said Ridcully. 'Do try to keep up. Well, Rincewind? Let's assume, shall we, that we're going along with your plan? We have to make sure this man exists here and writes this play in this world, do we? Why?'

'Can I leave that to Stage Two, sir? It will become obvious, I hope, but you never know if there are elves listening.'

The wizards were automatically impressed by the idea that this was a two-stage plan, but Ridcully persisted: 'I put it to you, Rincewind, that this is exactly the kind of play elves would want him to write.'

'Yes, sir. That's because they're stupid. Not like you, sir.'

'We have Hex's computational power,' said Ponder. 'It should be possible to make sure he turns up in this world, I think.'

'Um ... yes,' said Rincewind. 'But first we have to make the world the kind he can turn up in. This may take a bit of work. Some travel­ling may be involved. Back in time ... for thousands of years…'

Firelight glowed off the cave walls. The wizards sat on one side of the fire, on the big rock ledge overlooking the scrubland. The Stinky Cave People sat on the other.

The cave people watched the wizards with something like awe, but only because they'd never seen people eat like that. It was Ridcully who'd suggested that people bearing huge amounts of food are wel­come practically anywhere, but the other wizards considered that this was just an excuse for him to make a crude but serviceable bow and go and happily slaughter quite a lot of wildlife.

The wildlife was mostly leftovers now. The wizards moaned about the lack of onions, salt, pepper, garlic and, in Rincewind's case, pota­toes, but there was certainly no lack of meat.

They'd spent two weeks doing this, in caves across the continent. They were getting used to it, although bowel movements were becom­ing a problem.

Rincewind, however, was sitting some way from the fire with Burnt Stick Man.

Being good at languages was, here, not such an important skill as simply making yourself understood. But Burnt Stick Man was a quick study, and Rincewind already had several weeks of practice. While the dialogue took place in inflections and emphasis based upon the syl­lable 'grunt' aided by gestures, the translation went like this:

'Okay, so you've mastered the idea of charcoal, but may I draw your attention to these pigments I have here? They're Whiiite, very simple, Redddd, like blood, and Yell-low, like, er, egg yolks. Cluck cluck aaargh cackle? And this fourth colour is some sickly brown ochre I found which we'll call for the moment "baby poo".'

'With you so far, Pointy Hat Man.' This was conveyed by an enthu­siastic nod.

'So here's the big tip. Not many people know this,' said Rincewind. 'You take your animals, right, which you've already been trying to draw, well done, but you what we call "colour" them. You have to work hard on this bit. A chewed piece of wood will be your friend here. See how by a careful mixture of tints I'm giving it a certain, oh, je ne sais quoi…'

'Hey, that looks like a real buffalo! Scary stuff!' 'It gets better. May I have the charcoal? Thank you. What's this?' Rincewind carefully drew another figure. 'Man with big [expressive gesture]?' said Burnt Stick Man. 'What? Oh. Sorry, I got that wrong ... I mean this ...' 'Man with spear! Hey, he's throwing it at the buffalo!' Rincewind smiled. There had been a few false starts over the last couple of weeks, but Burnt Stick Man had exactly the right sort of mind. He was impressively simple, and people with truly simple minds were very rare.

'I knew there was something intelligent about you the moment I saw you,' he lied. 'Maybe it was the way your brow ridge came around the corner only two seconds before the rest of you did.' Burnt Stick Man beamed. Rincewind went on: 'And the question you've got to ask yourself now is: how real is this picture, really? And where was the picture before I drew it? What is going to happen now it's on the wall?' The wizards watched from the circle of firelight. 'Why's the man poking at the picture?' said the Dean. 'I think he's learnin' about the power of symbols,' said Ridcully. 'Hey, if anyone doesn't want any more ribs I'll finish 'em.'

'No barbecue sauce,' moaned the Lecturer in Recent Runes. 'How long before there's an agricultural revolution?'

'Could be a hundred thousand years, sir,' said Ponder. 'Perhaps a lot more.' The Lecturer in Recent Runes groaned and put his head in his hands.

Rincewind came and sat down. The rest of Burnt Stick Man's clan, greasy to the eyebrows with free food, watched him cautiously.

'That seemed to go well,' he said. 'He's definitely working out the link between pictures in his head and real life. Any potatoes yet?'

'Not for thousands of years,' groaned the Lecturer in Recent Runes.

'Damn. I mean, here's meat. There should be potatoes. How hard is that for a world to understand? Vegetables are less complicated than meat!' He sighed, and then stared.

Burnt Stick Man, who had been staring motionless at the drawing for a while, ambled to another rock wall and picked up a spear. He squinted at the buffalo drawing, which did indeed seem to move as the firelight flickered, paused, and then hurled the spear at it and ducked behind a rock.

'Gentlemen, we've found our genius and we're on our way,' said Rincewind. 'Ponder, can Hex move some buffaloes to right outside this cave at dawn tomorrow?'

'That shouldn't be hard, yes.'

'Good.' Rincewind looked around. 'And there's quite a few tall trees here, too. Which is just as well.'

It was dawn, and the tree was full of wizards.

The ground below was full of buffalo. Hex had moved an entire herd, which was now more or less penned in amongst the rocks and trees.

And, on the rocky ledge in front of the bewildered, panicking crea­tures, Burnt Stick Man and the other hunters stared down in disbelief.

But only for a moment. They had spears, after all. They got two of the creatures before the rest thundered away. And, afterwards, people were certainly showing Burnt Stick Man a bit of respect.

'All right, I think I see what you're getting at,' said Ridcully, as the wizards very carefully climbed down.

'Well, I don't,' said the Dean. 'You're teaching them basic magic. And that doesn't work here!'

'They think it does,' said Rincewind.

'But that was only because we helped them! What're they going to do tomorrow when he does another painting and no buffaloes turn up?'

'They'll think it's experimental error,' said Rincewind. 'Because it's so sensible, isn't it? You draw a magic picture, and the real thing turns up! It's so sensible that they'll take a lot of convincing that it doesn't work. Besides ... '

'Besides what?' said Ponder.

'Oh, I was thinking that if Burnt Stick Man is really sensible he'll keep an eye on the movements of the local animals and make sure he paints his pictures at the right time.'

Some more weeks went by. There were lots of men like Burnt Stick Man.

And even Red Hands Man ...

'... so,' said Rincewind, as he sat by the river, squeezing the clay, 'it's quite easy to make other things out of it than snakes.'

'Snakes are easy,' said Red Hands Man, stained with ochre to the armpits.

'And there's lots of snakes around here, is there?' said Rincewind. It looked like prime snake country.

'Lots of them.'

'Ever wondered why? You play around rolling snakes out of clay, and snakes turn up?'

'I'm making the snakes?' said Red Hands Man. 'How can that be? I was only doing it because of the enjoyable tactile sensations!'

'It's an intriguing thought, isn't it?' said Rincewind. 'But it's okay, I won't tell anyone else.'

Red Hands Man stared at his hands as if examining two lethal instru­ments. He seemed a little less bright than Burnt Stick Man.

'Ever thought about making something else?' said Rincewind. Something more edible?'

'Fish are good to eat,' Red Hands Man conceded.

'Why not try making a clay fish?' said Rincewind, with a sincere smile.

Next morning, it rained trout.

In the afternoon a very happy Red Hands Man, now hailed as the saviour of the clan that lived among the reeds, made a model of a big fat woman out of clay.

The wizards discussed the moral implications of allowing Hex to rain enormous women over a wide area. The debate took a long time, with many pauses for inward reflection, but at last the Dean was voted down. It was agreed that if you gave a man a fat woman, he'd just have a fat woman for a day, but if you helped a man become a very important man because he had the secret of buffaloes or fish, he could get himself as many fat women as he wanted.

Next morning they went forward a thousand years in time. There was hardly an unadorned cave on the continent, and quite a lot of fat women.

They went further ...

In a forest clearing, a man was making a god out of wood. Either it wasn't a very good carving, or it was a good carving but an ugly god. The wizards watched.

And the Queen of the Elves appeared, with a couple of elves in attendance. They were male or, at least, appeared male. The queen was angry.

'What are you doing, wizards?' she snapped.

Ridcully gave her a nod of annoying friendliness. 'Oh, just a little ... what are we calling it, Stibbons?'

'A sociological experiment, Archchancellor,' said Ponder. 'But you've been teaching them art! And sculpture!' 'And music,' said Ridcully happily. 'The Lecturer in Recent Runes is rather good with a lute, it turns out.'

'Only in a very amateur way, I'm afraid,' said the Lecturer in Recent Runes, blushing.

'Dashed easy to make, a lute,' said Ridcully. 'You just need a tor­toise shell and some sinews and you're well away. I myself have been renewing my acquaintance with the penny whistle of my boyhood, although I fear that the Dean's expertise with the comb-and-paper leaves something to be desired.'

'And why are you doing all this?' the queen demanded. 'Are you angry? We thought you'd be pleased,' said Ridcully. 'We thought you wanted them this way. You know - imaginative.'

'He created music?' said the Queen, glaring at the Lecturer in Recent Runes, who gave her an embarrassed wave.

'Oh, no, I assure you,' he said. 'Er, they'd worked up to, you know, basic percussion, the conch shell and so on, but it was all rather dull. We just helped them along a bit.'

'Gave them a few tips,' said Ridcully, jovially.

The Queen's eyes narrowed. 'Then you are planning something!' she said.

'Aren't they doing well?' said Ridcully. 'Look at that chap over there. Visualisin' a god. One with woodworm and knotholes, but pretty good all the same. Quite complex mental processes, really. We thought that if you want people with wild imaginations, then we'd help them to be really good at it. They'll fill the world with dragons and gods and mon­sters for you. You want that.'

The Queen gave him another look, and it was the look of a person with no sense of humour who nevertheless suspects that there's some joke somewhere that is on them.

'Why should you help us?' she said. 'You told me to consume your underthings!'

'Well, it's not as though this world is important enough to fight over,' said Ridcully.

'One of you isn't here,' said the Queen. 'Where is the stupid one?'

'Rincewind?' said the Archchancellor, with an innocent air that would not have fooled any human for a moment. 'Oh, he's doing pretty much the same thing, you know. Helping people imagine things. Which, I think, is what you want.'

TWENTY-FOUR

THE EXTENDED PRESENT

Art? It looks superfluous. Few of the stories we tell about human evolution, the Homo sapiens bit, see music or art as being integral to the process. Oh, it often comes in as a kind of epiphenomenon, as evi­dence of how far we'd got: 'Just look at those wonderful cave paintings, statuettes, polished jewellery and ornaments! That shows that our brain was bigger/better/more loving/nearer to that of the Lecturer in Recent Runes ...' But art has not been portrayed as a necessary part of the evolution that made us what we are; nor has music.

So why are Burnt Stick Man and Red Hands Man dabbling in art, and why does Rincewind want to encourage them?

We've been told the story of The Naked Ape doing sex, we've had Gossiping Apes and Privileged Apes, various kinds of apes becoming intelligent on the seashore or running down gazelles on the savannah. We've had lots of development-of-intelligence stories culminating in Einstein; we have given you the privilege/puberty ritual/selection story that culminates in Eichmann and Obedience to Authority; but we have not presented a version of our evolution whose culmination is Fats Waller, Wolfgang Amadeus Mozart, or even Richard Feynman on the bongo drums.

Well, now we will.

Music is an important part of most people's lives, and this is continu­ally reinforced by film and television. Background music is constantly informing us of imminent screen events, of tension and release, of characters' thoughts and, particularly, of their emotional states. It is very difficult for anyone brought up in the muzak environment of the twentieth century to imagine what the 'primitive' state of human musi­cal sense can have been.

When we listen to the music of far peoples, of 'primitive' tribes, we have to appreciate that their music has had as long to develop as Beethoven, and much longer than jazz. Like the amoeba or the chim­panzee, their music is contemporary with us, not ancestral, though it sounds primitive, just as they look primitive. And we wonder whether we are listening for the right things in the right way. It is tempting to think that popular music, going for instant appeal, might illuminate whatever inner structure of our brains 'fits', and is satisfied by, a musi­cal theme. If we were orthodox geneticists, we might have said 'genes for music' there. But we didn't.

In recent years, neuroscientists have developed techniques that allow us to look at what brains do when we carry out various actions. In particular, they reveal which bits of brain are active when we enjoy music. At the moment, with the terribly poor spatial and temporal res­olution that we get from MRI and PET scans, all we can see is that music excites the right side of the brain. If we are familiar with the music, then the brain's memory-regions turn on, and if we analyse it or try to pick up the lyrics, then the verbal-analysis parts light up. And opera picks up both of them, which could be why Jack likes it: he enjoys having his brain put through a blender.

Our affinity with music starts early. In fact, there's a lot of evidence that if we hear music in the womb, then it can affect our later musical preferences. Psychologists play music to babies as soon as they start kicking, and have discovered that they can categorise it, like we adults do, and into the same categories. If we play them Mozart, they stop kicking for a bit, about fifteen minutes; then they start kicking again, perhaps with some relation to the rhythm. The evidence is claimed, but it isn't very persuasive. If we then continue with a different bit of Mozart, or Haydn or Beethoven, then the kicking pauses, but it resumes after a minute or so. The Beatles, Stravinsky, sacred chants, or New Orleans jazz, make them pause for much longer, ten minutes or so.

Playing the same pieces months later reveals that the baby has some memory of the style as well as of the instruments. Apparently, a quar­tet by Mozart triggers recognition of the 'Mozart' style just as effectively as a Mozart symphony. Our brains have sophisticated music-recogni­tion modules, and we can use them before we speak, indeed before we are born. Why?

We're looking for the essence of music - as if we knew what the essence of sex was for the Naked Ape, or the essence of obedience for Eichmann - or come to that, what it means to be the most intelligent/extelligent creature on Roundworld. What we want is a story that puts the arts, and music, into an explanation of How We Got Here, and why we waste all that money on the arts faculties of uni­versities. Why is Rincewind so keen to bring art and music to our ancestors?

It was very common in the early years of the twentieth century to copy the music of 'primitive' tribes. Examples include Stravinsky's Rite of Spring and Manuel de Falla's Fire Dance, where the musical style was thought to give a primitive authenticity. People thought that Bronislaw Malinowski's tales of the Trobriand Islanders, with their amazing lack of the civilised sexual repressions so publicised by Freud in Viennese society, showed that Natural Humans were happier and less corrupt, and that their music - for flutes and drums - conveyed their state of innocence more effectively than classical symphonies. Jazz, invented by supposedly 'primitive' black musicians down in New Orleans, had resonances that seemed natural, animal (and, for certain Christians, evil). It was almost as if music were a language, parallel to the words, developed in different societies with different emphases, and more revealing of the nature of the people than other aspects of their culture.

This is the way the media have played it, and like the Flintstones and Stone Age society, we have an overlay of this outlook that it's very difficult to get away from. Margaret Mead, who was taken for a ride by her native girl friend and told the resulting story in Coming of Age in Samoa: A Psychological Study of Primitive Youth for Western Civilization, romanticised their music and dances in exactly this way.

When Hollywood needs to show the primitive-but-spiritual nature of Indian braves, cannibal tribes in Borneo, or Hawaiian indigenes, it shows us the rain dance, the marriage music, and the hula girls. When we go to these places, the locals put on these dances for us because it brings in tourist money. The complicity between muzak, hula dances, opera and background music in Hollywood films has completely buried our abilities to sort out what constitutes 'natural' art or music.

However, that's not what we want anyway. 'Natural' is an illusion. Desmond Morris made a lot of money selling paintings done by apes. The apes clearly enjoyed the whole business, and so did Morris, and presumably so did the people who bought them and looked at them in art galleries. There is also an elephant that paints, and signs its paint­ings. Sort of. There's a segment of modern painting whose philosophy seems to relate to this quest for the genuinely primitive. One side is the tackiest, painting by children, which clearly demonstrates the step­wise effects of the culture - the extelligence - on their burgeoning intelligence. To our inexpert eyes, though, these paintings demonstrate only the enormous gratification achieved by some parents in response to minimal effort by their children.

Another aspect, more intellectual, is the move towards apparently real-world constraints, like cubism, or attempts to develop styles that force us to re-evaluate how we see, like Picasso's profile faces but with the two eyes on one side. There is a very common modern form that arranges rectangles of paper with different textures, or sprays sparse paint droplets according to some minimal rule, or scatters charcoal dust on a bold swirly bright oil-paint background and then combs it into the texture and pattern of the whole canvas. All of these can give pleasure to the eye. Why? How do they differ from natural objects, some of which also give considerable pleasure?

Now we want to make a giant leap and bring Mozart, jazz, paper-texture and charcoal-swirl oil paintings into the same frame. We think that this frame naturally includes ancient cave-paintings, which we know to be early, so have more claim to being genuinely primitive, if we could only look at them with the eyes and minds of viewers con­temporary with the artist. The same problem occurs with Shakespeare, too: we no longer have the ears or minds - the extelligence - of the first Elizabethan age.

We have to be more than a bit scientific here. We have to consider how we perceive light, sound, touch - what our sense organs tell us. For a start, they don't, and this is the first lesson. In his book Consciousness Explained, Daniel Dennett is very critical of the Cartesian Theatre picture of consciousness. In this picture, we imagine ourselves sitting in a little theatre in our minds, where our eyes and ears pipe in pictures and sounds from the outside world. In school we all learned that the eye is like a camera, and that a picture of the world is imaged in the plane of the retina, as if that was the difficult bit. No, the diffi­cult bit starts there, with different elements of that picture taking different routes into different parts of the brain.

When you see a moving red bus, the features 'moving', 'red' and 'bus' are separated fairly early in the brain's analysis of the scene ... and they don't just get put together again to synthesise your mental picture. Instead, your picture is synthesised from lots of clues, lots of bits, and nearly all of what you 'see' as you look around the room is only 'there' in your brain. It's not at all like a TV picture. It is not picked up instantly and updated, but nearly all of that 'detailed' sur­round is invented as a kind of wallpaper around the little bit that has your attention. Most of the details are not present as such in your mind at all, but that's the illusion that your mind presents to you.

When we see a painting ... except, again, we don't. There are sev­eral ways to convince people that they invent what they 'see', that perception is not simply a copy of the eye's image on the retina. There is, for example, a blind spot on the retina where the optic nerve leaves it. This is big. It's as big as 150 full moons (that's not a misprint: a hun­dred and fifty). Not that the moon is as big, to our eyes, as we usually think - and certainly not as big as Hollywood repeatedly shows it. We 'see' the full moon as much bigger than it 'is' (sorry, we have to use some trick to separate what's in your mind from reality out there), especially when it's near the horizon. The best way to appreciate that is to demonstrate to yourself that the moon's image is the size of your little fingernail at arm's length. Hold out your arm, and the tip of your littlest finger more than covers the moon. So the blind spot is smaller than our description may have suggested, but it's still a big chunk of the retinal image. We don't notice any hole in the picture we get of the outside world, though, because the brain fills in its best estimate of what's missing.

How does the brain know what's missing from right in front? It doesn't, and it doesn't have to: that's the point. Although 'fills in' and 'missing' are traditional terms in this area of science, they are, again, misleading. The brain doesn't notice that anything is missing, so there isn't a gap to be filled in. The neurons of the visual cortex, the part of the brain that analyses that retinal image into a scene that we can recognise and label, are wired up in elaborate ways, which reinforce certain perceptual prejudices.

For example, experiments with dyes that respond to the brain's elec­trical signals show that the first layer of the visual cortex detects lines - edges, mostly. The neurons are arranged in local patches, 'hyper-columns', which are assemblies of cells that respond to edges aligned along about eight different directions. Within a hypercolumn, all con­nections are inhibitory, meaning that if one neuron thinks it has seen an edge pointing along the direction to which it is sensitive, then it tries to stop the other neurons from registering anything at all. The result is that the direction of the edge is determined by a majority yote. In addition, there are also long-range connections between hyper-columns. These are excitatory, and their effect is to bias neighbouring hypercolumns to perceive the natural continuation of that edge, even if the signal they receive is too weak or ambiguous for them to come to that conclusion unaided.

This bias can be overcome by a sufficiently strong indication that there is an edge pointing in a different direction; but if the line gets faint, or part of it is missing, the bias automatically makes the brain respond as if the line was continuous. So the brain doesn't 'fill in' the gaps: it is set up not to notice that there are gaps. That's just one layer of the visual cortex, and it uses a rather simple trick: extrapolation. We have little idea, as yet, of the inspired guesswork that goes on in deeper layers of the brain, but we can be sure that it's even more clever, because it produces such a vivid sensation of a complete image.

What about hearing? How does that relate to sound? The standard lie-to-children about vision is that the cornea and lens make a picture on the retina, and that allegedly explains vision. Similarly, the corre­sponding lie-to-children about hearing centres on a part of the ear called the cochlea, whose structure allegedly explains how you analyse sound into different notes. In cross-section, the cochlea looks like a sliced snail-shell, and according to the lie-to-children, there are hair-cells all the way down the spiral attached to a tuned membrane. So different parts of the cochlea vibrate at different frequencies, and the brain detects which frequency - which musical note - it is receiving, by being told which part of the membrane is vibrating. In support of this explanation, we are told a rather nice story about boiler-makers, whose hearing was often damaged by the noise in the factories where they worked. Supposedly, they could hear all frequencies except ones near the frequency that was most common in making boilers. So just one place on their cochlea was burnt out, and the rest worked OK. This proved, of course, that the 'place' theory of hearing was correct.

Actually, this story tells you only how the ear can discriminate notes, not how you hear the noise. To explain that, it is usual to invoke the auditory nerve, which connects the cochlea to the brain. However, there are as many connections, or more, that go in the other direction, from brain to cochlea. You have to tell your ear what to hear.

Now that we can actually look at what the cochlea does when it's hearing, we find not one place vibrating for each frequency, but more like twenty. And these places move as you flex your outer ear. The cochlea is phase-sensitive, it can discriminate the kind of difference that makes an 'ooh' sound different from an 'eeh' at the same fre­quency. This is the kind of change to the sound that you make when you change the shape of your mouth as you speak. And surprise, sur­prise, that's just the difference that the cochlea - after your outer ear and your own particular auditory canal, and your own particular eardrum and those three little bones - can best discriminate. A record­ing from someone else's eardrum, played back up against yours, makes little sense. You have learned your own ears. But you have taught them, too.

There are about seventy basic sounds, called phonemes, that Homo sapiens uses in speech. Up to about six months old, all human babies can discriminate all of these, and an electrode on the auditory nerve gives different patterns of electrical activity for each. At about six to nine months old, we start talking scribble, and it very soon becomes English scribble or Japanese scribble. By a year old the Japanese ear cannot distinguish 'l' from 'r', because both phonemes send the same message from cochlea to brain. English babies can't discriminate the different clicks of the !Kung San, nor the differences between the dis­tinct 'r's in French. So our sense organs do not show us the real world. They stimulate our brains to produce, to invent if you like, an inter­nal world made of the counters, the Lego™ set, that each of us has built up as we mature.

Such apparently straightforward abilities as vision and hearing are far more complicated than we usually imagine. Our brains are much more than just passive recipients. An awful lot is going on inside our heads, and we project some of it back into what we think is the out­side world. We are conscious only of a small part of its output. These hidden depths and strange associations in the brain may well be responsible for our musical sensibilities.

Music exercises the mind; it's a form of play. It seems probable that our liking for music is linked to other things than our ears. In partic­ular, the brain's motor activity may be involved, as well as its sensory activity. In primitive tribes and advanced societies, music and dance often go together. So it may be the combination of sound and move­ment that appeals to our brains, rather than one or the other. In fact, music may be an almost accidental by-product of how our brains put the two together.

Patterns of movement have been common in our world for millions of years, and their evolutionary advantage is clear. The pattern 'climb a tree' can protect a savannah ape from a predator, and the same goes for the pattern 'run very fast'. Our bodies surround us with linked pat­terns of movement and sound. Like music, they are patterns in time, rhythms. Breathing, the heartbeat, voices in synch with lips, loud bangs in synch with things hitting other things.

There are common rhythms in the firing of nerve cells and the movement of muscles. Different gaits - the human walk and run, the walk-trot-canter-gallop of the horse - can be characterised by the tim­ing with which different limbs move. These patterns relate to the mechanics of bone and muscle, and also to the electronics of the brain and the nervous system. So Nature has provided us with rhythm, one of the key elements of music, as a side-effect of animal physiology.

Another key element, pitch and harmony, is closely related to the physics and mathematics of sound. The ancient Pythagoreans discov­ered that when different notes sounded harmonious, there was a simple mathematical relationship between the lengths of the strings that produced them, which we now recognise as a relation between their frequencies. The octave, for example, corresponds to a doubling of frequency. Simple whole number ratios are harmonious, compli­cated relationships are not.

One explanation for this is purely physical. If notes with frequencies that are not related by simple whole numbers are sounded together, they interfere with each other to produce 'beats', a jarring low-frequency buzz. Sounds that make the sensory hairs in our ears vibrate in simple patterns are necessarily harmonious in the Pythagorean sense, and if they aren't, we hear the beats and they have an unpleasant effect. There are many mathematical patterns in musical scales, and they can be traced, to a great extent, to the physics of sound.

Overlaid on the physics, though, are cultural fashions and traditions. As a child's hearing develops, its brain fine-tunes its senses to respond to those sounds that have cultural value. This is why different cultures have different musical scales. Think of Indian or Chinese music com­pared to European; think of the changes in European music from Gregorian chants to Bach's Well-Tempered Clavier.

This is where the human mind is situated: on the one hand, subject to the laws of physics and the biological imperatives of evolution; on the other, as one small cog in the great machine of human society. Our liking for music has emerged from the interaction of these two influences. This is why music has clear elements of mathematical pat­tern, but is usually at its best when it throws the pattern book away and appeals to elements of human culture and emotion that are - for now, at least - beyond the understanding of science.

Let's come down to Earth and ask a simpler question. The wells of human creativity run deep, but if you take too much water from a well it runs dry. Once Beethoven had written the opening bars of his Symphony in C Minor - dah-dah-da DUM - that was one less tune for the rest of us. Given the amount of music that has been composed over the ages, maybe most of the best tunes have been found already. Will the composers of the future be unable to match those of the past because the world is running out of tunes?

There is, of course, far more to a piece of music than a mere tune. There is melody, rhythm, texture, harmony, development ... But even Beethoven knew you can't beat a good tune to get your composition off the ground. By 'tune' we mean a relatively short section of music - what the cognoscenti call a 'motif' or a 'phrase', between one and thirty notes in length, say. Tunes are important, because they are the building blocks for everything else, be it Beethoven or Boyzone. A composer in a world that has run out of tunes is like an architect in a world that has run out of bricks.

Mathematically, a tune is a sequence of notes, and the set of all pos­sible such sequences forms a phase space: a conceptual catalogue that contains not just all the tunes that have been written, but all the tunes that could ever be written. How big is T-space?

Naturally, the answer depends on just what we are willing to accept as a tune. It has been said that a monkey typing at random would eventually produce Hamlet, and that's true if you're willing to wait a lot longer than the total age of the universe. It's also true that along the way the monkey will have produced an incredible amount of air­port novels. In contrast, a monkey pounding the keys of a piano might actually hit on a reasonable tune every so often, so it looks as though the space of acceptably tuneful tunes is a reasonable-sized chunk of the space of all tunes. And at that point, the mathematician's reflexes can kick in, and we can do some combinatorics again.

To keep things simple, we'll consider only European-style music based on the usual twelve-note scale. We'll ignore the quality of the notes; whether played on a piano, violin, or tubular bells, all that mat­ters is their sequence. We'll ignore whether the note is played loudly or softly, and - more drastically - we'll ignore all issues of timing. Finally, we'll restrict the notes to two octaves, 25 notes altogether. Of course all these things are important in real music, but if we take them into account their effect is to increase the variety of possible tunes. Our answer will be an underestimate, and that's all to the good since it will still turn out to be huge. Really, really huge, right? No - bigger than that.

For our immediate purposes only, then, a tune is a sequence of 30 or fewer notes, each chosen from 25 possibilities. We can count how many tunes there are in the same way that we counted arrangements of cars and DNA bases. So the number of sequences of 30 notes is 25 x 25 x ... x 25, with 30 repetitions of that 25. Computer job, that: it says that the answer is

867361737988403547205962240695953369140625

which has 42 digits. Adding in the 29-note tunes, the 28-note ones, and so on we find that T-space contains roughly nine million billion billion billion billion tunes. Arthur C. Clarke once wrote a science fic­tion story about the 'Nine billion names of God'. T-space contains a million billion billion billion tunes for every one of God's names. Assume that a million composers write music for a thousand years, each producing a thousand tunes per year, more prolific even than The Beatles. Then the total number of tunes they will write is a mere trillion. This is such a tiny fraction of that 42-digit number that those composers will make no significant inroads into T-space at all. Nearly all of it will be unexplored territory.

Agreed, not all of the uncharted landscape of tune-space consists of good tunes. Among its landmarks are things like 29 repetitions of middle C followed by F sharp, and

BABABABABABABABABABABABABABABA,

which wouldn't win any prizes for musical composition. Nevertheless, there must be an awful lot of good new tunes still waiting to be invented. T-space is so vast that even if good-tune-space is only a small proportion of it, good-tune-space must also be vast. If all of human­ity had been writing tunes non-stop since the dawn of creation, and went on doing that until the universe ended, we still wouldn't run out of tunes.

It is said that Johannes Brahms was walking along a beach with a friend, who was complaining that all of the good music had already been written. 'Oh, look,' said Brahms, pointing out to sea. 'Here comes the last wave.'

Now we come to what may well be the chief function of art and music for us - but not for edge people or chimpanzees, and probably not for Neanderthals. This, if we are right, is what Rincewind has in mind. When we look at a scene we see only the middle five to ten degrees of arc. We invent the rest all around that bit, and we give ourselves the illusion that we're seeing about ninety degrees of arc. We perceive an extended version of the tiny region that our senses are detecting. Similarly, when we hear a noise, especially a verbal noise, we set it in a context. We rehearse what we've heard, we anticipate what's com­ing, and we 'make up' an extended present, as if we'd heard the whole sentence in one go. We can hold the entire sentence in our heads, as if we heard it as a sentence, and not one phoneme at a time.

This is why we can get the words of songs completely wrong and not realise it. The Guardian newspaper ran an amusing section on this habit, with examples such as 'kit-kat angel' for 'kick-ass angel' - bit of a generation gap there, which underlines how our perceptions are biased by our expectations. Ian recalls an Annie Lennox song that really went 'a garden overgrown with trees', but always sounded like 'I'm getting overgrown with fleas'.

Holding a whole sentence, or a musical phrase, in our minds is what we do with time when we watch a TV or a cinema-screen. We run the frames together into a series of scenes, as well as making up all the spatial stuff that we're not actually looking at. The brain has so many tricks that its owner is not conscious of: as you sit there in the cinema your eyes are flicking from place to place on the screen, as they are doing while you read these words. But you turn off your perception as your eyes move, and re-jig your invented image so that your next retinal image is consistent with the previous version. That's why you get seasick or car-sick: if the outside image jumps about and isn't where you expect it to be, then that upsets your sense of balance.

Now think about a piece of music. Isn't the construction of an extended present precisely the exercise that your brain 'wants' to do with a series of sounds, but without the complication of the meanings! As soon as you get used to the style of a particular kind of music, you can listen to it and grasp whole themes, tunes, developments, even though you're hearing only one note at a time. And the instrumental­ist who is making the noise is doing the same kind of thing. His brain has expectations of what the music should sound like, and he fulfils those. To some extent.

So it seems that our sense of music may be tied to a sense of an extended present. Some possible scientific evidence for this proposi­tion has recently been found by Isabelle Peretz. In 1977 she identified a condition called 'congenital amusia'. This is not tone-deafness, but tune-deafness, and it should give us some insight into how normal people recognise tunes, by showing how that goes wrong. People with this condition cannot recognise tunes, not even 'Happy Birthday To You', and they have little or no sense of the difference between har­mony and dissonance. There is nothing physically wrong with their hearing, however, and they were exposed to music as children. They are intelligent and have no history of mental illness. What seems to be wrong is that when it comes to music, they have no sense of an extended present. They cannot tap their feet in rhythm. They have no idea what a rhythm is. Their sense of timing is impaired. Mind you, so is their sense of pitch; they cannot distinguish sounds separated by an interval of two semitones - adjacent white keys on a piano. So the lack of an extended present is not the only problem. Congenital amu­sia is rare, and it affects males and females equally. Its sufferers have no difficulty with language, however, suggesting that the brain's music modules, or at least those affected by amusia, differ from its language modules.

The same kind of interpretational step takes place in the visual arts, too. When you look at a painting - a Turner, say - it evokes in you a variety of emotions, perhaps nostalgia for a nearly forgotten holiday on a farm. That may give you a little burst of endorphins, chemicals in the brain that create a sense of well-being, but presumably you'd get much the same from a photograph or even a verbal description or a bit of pastoral poetry. The Turner painting does more than that, per­haps because it can be more sentimental, more idealised than a photo, however idyllic. It evokes the memory on a more personal level.

What about other kinds of painting: the paper textures, the charcoal smear? Jack went to an art gallery, as an innocent in art appreciation, and tried the 'context' trick that any novice is always told to try. You're supposed to sit in front of the picture, and gaze at it, and kind of sink into it and feel how it relates to its surroundings. The result was instruc­tive. When he paid attention to a small part of the canvas, he found that he could match the context that his brain had invented with the one that the artist had actually provided. The charcoal smear was par­ticularly good for this: each part implied something of the pattern of the whole. However, there were intriguing differences from part to part. There were variations on the theme, as in music, superimposed on the brain's expectations. Jack's brain enjoyed comparing the picture that it was inventing with the progressively different one that the artist was forcing his brain to construct.

Art goes back a long, long way, the further back we look, the more controversial the evidence is. The 'Dame a la Capuche', a 1.5-inch (3.5-cm) high statuette of a woman, exquisitely carved from mammoth-tusk ivory, is 25,000 years old. Some of the most elegant cave paintings, with simple, sweeping lines that depict horses, bison and the like, are found in the Grotte Chauvet in France, and in 1995 they were dated at 32,000 years old. The oldest art that undoubtedly is art is about 38,000 years old: beads and pendants, found in Russia. And some beads made from ostrich egg shells in Kenya, which may be 40,000 years old.

Further back, it all gets less certain. Ochre is a common pigment in rock drawings, and ochre 'crayons' found in Australia are 60,000 years old. There is a lump of rock from the Golan Heights, whose natural crevices have been worn deeper, presumably by a human hand wield­ing another lump of rock. It bears a vague resemblance to a woman, and it is about 250,000 years old. But maybe it's just a lump of rock that a child idly scratched, and the shape is accidental.

Imagine yourself in the cave as the artist paints bison on the wall. He (or she?) is creating a picture for your brain that differs progres­sively from the one that your brain expects: 'Now let's put a female woolly rhinoceros under him ...' There have been several 'artists' on television, doing precisely that trick. Rolf Harris was surprisingly good at drawing animal sketches before your very eyes. And they were iconic animals, too: sly fox and wise owl.

There it all is, tied up in a bundle. Our perceptions are tied to our expectations, and we do not segregate sensations from each other, or from memories. They are all played off against each other in the seclu­sion of our minds. We absolutely do not program our brains with direct representations of the real world. From the beginning we're instruct­ing our brains what to make of what we see, hear, smell and touch. We put spin on everything, and we anticipate, compare and contrast, construct lengths of time from successive instants, construct areas of picture from focused observation. We've been doing this, layer upon layer, taking more subtle nuances from conversation, from flirting glances, to 'Will she come to look like her mother does now?' assess­ments of the real world, all the time.

That's what our brains do, and what edge people's brains don't.

We suspect that Neanderthals didn't do that kind of thing much, either, because there's an alternative, and it's consistent with their cul­tural torpor. The alternative is to live in a world that you've set up to ensure that nothing is unexpected. All the events follow your expec­tations from previous events, so habit engenders security. Such a world is very stable, and that means it doesn't go anywhere much. Why try to leave the Garden of Eden? Gorillas don't.

Tribal life could be like that for Homo sapiens, except that reality always intrudes, for instance those barbarians up on the hill. But Neanderthals, maybe, weren't afflicted by barbarians. Certainly, noth­ing seems to have provoked big changes in their lifestyles, even over tens of thousands of years. Art does provoke changes. It makes us look at the world in new ways. The elves like that, it gives new ways for them to terrify people. But Rincewind has seen further than the elves are capable of seeing, and he's worked out where art takes us. Where? You'll soon find out.

TWENTY-FIVE

PARAGON OF VEGETABLES

The wine-dark sea lapped the distant shore. Nice coun­try, Rincewind thought. A bit like Ephebe. Grapes, olives, honey and fish and sunshine.

He turned back to his group of proto-actors. They were having difficulty grasping the idea.

'Like the priests do in the temples?' said a man. 'Is that what you mean?'

'Yes, but you can ... expand the idea,' said Rincewind. 'You can pre­tend to be the gods. Or anything else.'

'Wouldn't we get into trouble?'

'Not if you did it respectfully,' said Rincewind. 'And people would ... sort of see the gods. Seeing is believing, eh? Besides, children pre­tend to be other people all the time.'

'But that is childish play,' said the man.

'People might pay to see you,' said Rincewind. There was an imme­diate increase in interest. Human-shaped creatures were the same everywhere, Rincewind thought; if you got money for doing it, it had to be worth doing.

'Just gods?' said a man.

'Oh, no. Anything at all,' said Rincewind. 'Gods, demons, nymphs, shepherds-'

'No, I couldn't do a shepherd,' said the possible thespian. 'I'm a car­penter. I don't know shepherding.'

'But you know godding?'

'Well, yeah, that's just ... thundering and shouting and that kind of thing. Being a decent shepherd takes years of work.'

'You can't expect us to act like people,' said another man. 'That wouldn't be right.'

'It's not respectful,' said a third man.

Yes, we mustn't change things, thought Rincewind. The elves like that thinking. We mustn't change things, in case they end up different. Poor old Phocian ...

'Well, can you do trees?' he said. He was vaguely aware that actors warmed up by pretending to be trees, amongst other things, and this presumably prevented wooden performances.

'Trees are all right,' said a man. They're quite magical. But it would­n't be respectful to our friend over there to ask us to be carpenters.' 'All right, then, trees. That's a start. Now, stretch out your-' There was a roll of thunder and a goddess appeared. Her hair was in golden ringlets, her white robe flapped in the breeze, and there was an owl on her shoulder. The men ran away.

'Well, my little trickster,' said the goddess, 'and what are you teach­ing them?'

Rincewind clapped a hand over one eye for a moment. 'That owl's stuffed,' he said. 'You can't fool me! No animals stay around elves without going mad!'

The image of the goddess wavered as the Queen tried to maintain control, but glamour is susceptible to disbelief.

'Oh, so brave?' she said, defaulting to her usual appearance. She turned at a creaking noise behind her. The Luggage had tiptoed up and opened its lid.

'That doesn't frighten me,' she said.

'Really? It frightens me,' said Rincewind. 'Anyway, I'm simply brush­ing up their acting skills. Absolutely no problem there, is there? You should love these people. There's dryads, nymphs, satyrs, centaurs, harpies and big giants with one eye, unless that's a joke about sex I haven't fully understood yet. They believe in all of them and none of them exist! Except possibly the one-eyed giant, that one's a bit of a puzzler.'

'We have seen their performances,' said the Queen. 'They are not respectful of their gods.'

'But seeing is believing, isn't it? And you must admit, they've got a lot of gods. Dozens.'

He gave her a friendly smile, while hoping that she was keeping away from the local cities. They had a lot of temples in them, and shrines all over the place, but they also had a number of men who, while taking care to invoke the gods on every occasion, then appeared to expound ideas that didn't seem to have any place for gods in them, except as observers or decoration. But the actors liked playing gods ...

'You're up to something,' said the Queen. 'Everywhere we look, you wizards are teaching people art. Why?'

'Well, it's a rather drab planet,' said Rincewind.

'Everywhere we go, they're telling stories,' said the Queen, still slowly circling. 'They're filling the sky with pictures, too.'

'Oh, the constellations?' said Rincewind. 'They don't change, you know. Not like at home. Amazing. I tried getting one tribe to name that big one - you know, with what looks like a belt - I thought if they ended up calling it the Bursar, and that group of little stars off to the right became The Dried Frog Pills, it'd be a nice souvenir of our visit-'

'You're frightened of me, aren't you,' said the Queen. 'All you wiz­ards are frightened of women.'

'Not me!' said Rincewind. 'Women are less likely to be armed!'

'Yes you are,' the Queen insisted, moving closer. 'I wonder what your deepest desire is?'

Not to be here right now would be favourite, Rincewind thought.

'I wonder what I could give you,' said the Queen, caressing Rincewind's cheek.

'Everyone knows that anything you get from the elves is gone by morning,' said Rincewind, trembling.

'Yet many things are transient but pleasurable,' said the Queen, mov­ing rather too close. 'What is it you want, Rincewind?'

Rincewind shuddered. There was no way he could lie.

'Potatoes,' he said.

'Tuberous vegetables?' said the Queen, her brows knitting in puzzlement.

'Well, yes. They've got them on one of the other continents, but they're not what I'd call spuds, and Ponder Stibbons says that if we left things as they were then by the time they've been brought over to this continent and bred up a bit it'd be the end of the world. So we thought we ought to ginger up the creativity level a bit.'

'And that's it? That's why all you wizards are doing all this? Just to accelerate the breeding of a vegetable?

'The vegetable, thank you,' said Rincewind. 'And you did ask. The potato, in my opinion, is the crown of the vegetable kingdom. There's roast potatoes, jacket potatoes, boiled potatoes, fried potatoes, curried potatoes-'

'Just for a stupid tuber?'

'- potato soup, potato salad, potato pancakes -'

'All this for something that doesn't even see daylight!'

'-mashed potato, chipped potato, stuffed potato-'

The Queen slapped Rincewind's face. The Luggage bumped into the back of her legs. It wasn't entirely sure what was happening here. There were some things humans did that could be misinterpreted.

'Do you not think I could give you something better than a potato?' she demanded.

Rincewind looked puzzled.

'Are we talking about a sour cream topping with chives?' he said.

Something fell out of Rincewind's robe as he shifted uneasily. The Queen grabbed it.

'What's this?' she said. 'There's writing all over it!'

'It's just a script,' said Rincewind, still thinking about potatoes. 'A sort of story of a play,' he added. 'Nothing important at all. People going mad and getting killed, that sort of thing. And a glowworm.'

'I recognise this script! It's from the future of this world. Why would you carry it around? What is so special? Hah, are there potatoes in it?'

She leafed through the pages, as if she could read.

'This must be important!' she snapped. And vanished.

One solitary page slid down to the ground.

Rincewind bent down and picked it up. Then he shouted hotly at the empty air: 'I suppose a packet of crisps is out of the question?'

TWENTY-SIX

LIES TO CHIMPANZEES

A central feature of human extelligence is the ability to infer what is going on in another person's mind, to guess what the world looks like from their point of view. Which is what Rincewind is trying to stop the Queen of the Elves from doing. We can't make such inferences with perfect accuracy; that would be telepathy, which is almost certainly impossible, because each brain is wired up differently and therefore represents the universe in its own special way. But we've evolved to be pretty good at guessing.

This ability to get inside other people's heads has many beneficial consequences. One is that we recognise other people as people, not just automata. We recognise that they have a mind, that to them the universe seems just as real and vivid as it does to us, but that the vivid things they perceive may not be the same as those that we perceive. If intelligent beings are going to get along together without too much friction, it's important to realise that other members of your species have an internal mental universe, which controls their actions in the same way that your own mind controls yours.

When you can put yourself inside another person's mind, stories gain a new dimension. You can identify with a central character, and vicariously experience a different world. This is the appeal of fiction: you can captain a submarine, or spy on the enemy, from the safety and comfort of an armchair.

Drama has the same appeal, too, but now there are real people to identify with; people who play a fictional role. Actors, actresses. And they rely even more on getting inside other people's minds, espe­cially the minds of fictional characters. Macbeth. The Second Witch. Oberon. Titania. Bottom.

How did this ability arise? As usual, it seems to have come about because of a complicity between the internal signal-processing abilities of the brain and the external pressures of culture. It arose through an evolutionary arms race, and the main weapon in that race was the lie.

The story starts with the development of language. As the brains of proto-humans evolved, getting larger, there was room in them for more kinds of processing tasks to be carried out. Primitive grunts and ges­tures began to be organised into a relatively systematic code, able to represent aspects of the outside world that were important to the crea­tures concerned. A complicated concept like 'dog' became associated with a particular sound. Thanks to an agreed cultural convention, any­one who heard that sound responded to it with the mental image of a dog; it wasn't just a funny noise. If you try to listen to someone speaking a language that you know, focusing just on the noises that they are making and trying not to pick up the meaning of their words, you'll find that it's almost impossible. If they speak a language far removed from any that you know, however, their speech comes over as a meaningless gabble. It conveys less to you than a cat's miaow.

In the brain are circuits of nerve cells that have learned to decode gabble into meaning. We've seen that as a child grows, it begins by babbling a random assortment of phonemes, the 'units' of sound that a human mouth and larynx can produce. Gradually the child's brain prunes the list down to those sounds that it hears from its parents and other adults. While it is doing that, the brain is destroying connections between nerve cells that seem to be obsolete. Quite a lot of the early mental development of an infant consists of chopping down a ran­domly connected, all-purpose brain, and pruning it into a brain that can detect the things that are considered important in the child's cul­ture. If the child is not exposed to much linguistic stimulus in early childhood - such as a 'feral' child brought up by animals - then they can't learn a language properly in later life. After about the age of ten, the brain's ability to learn language fades away.

Much the same happens with other senses, in particular the sense of smell. Different people smell the same thing differently. To some, a particular odour may be offensive, to others innocuous, and to yet others, nonexistent. As with language, there are cultural biases to cer­tain smells.

The primary function of language - by which we mean 'the main evolutionary trick that made it advantageous, leading to its preserva­tion and enhancement by natural selection' - is to convey meaningful messages to other members of the same species. We do this in several ways: 'body language' and even bodily odours convey vivid messages, largely without our being conscious of them. But spoken language is far more versatile and adaptable than the other kinds, and we are very conscious of what others are saying. Especially when it is about us.

One of the commonest generic evolutionary tricks is to cheat. As soon as a bunch of organisms has evolved some specific ability or behaviour, a new possibility arises: subverting that behaviour. Predictable behaviour patterns provide a natural springboard from which organisms can leap out into the space of the adjacent possible. Bees evolved the abilities to collect nectar and pollen, to feed them­selves. Later, we subverted that activity by providing them with better homes than they would find in nature. We get to steal their honey, by providing them with hives as the up-market adjacent-possible homes.

Many evolutionary trends have arisen from subversion. So, as the ability to put specific thoughts into the minds of others became estab­lished, it was natural for evolution to experiment with methods for subverting that process. You didn't have to put your own genuine thoughts into the minds of others: you could try to put different thoughts there. Perhaps you could gain an advantage by misleading the creatures you were 'communicating' with. The result was the evolution of lying.

Many animals tell lies. Monkeys have been observed making the troupe's 'danger' call-sign. Then, as the rest of the troupe heads off for cover, the liar grabs the food that they have temporarily abandoned. On a more primitive but just as effective level, mimicry in the animal kingdom is a form of lying. A harmless hover-fly displays the black-and-yellow warning bands of a wasp, telling the lie 'I am dangerous, I can sting'.

As humanity evolved, those monkey lies turned into more sophis­ticated ape lies, then hominid lies, then human lies. As we became more intelligent, our capacity for telling lies co-evolved alongside another important ability: the ability to tell when someone was lying to you. A monkey troupe can evolve several defences against a mem­ber who abuses the danger-signal for his own ends. One is to recognise that this individual can't be trusted, and ignore their calls. The nursery tale of the little boy who cried 'wolf' exposes the dangers inherent in this area, both for the troupe and for the individual. Another is to punish the individual for telling the lie. A third is to evolve the ability to tell the difference between a lying danger-signal and a true one. Is the monkey crying 'danger' staring at someone else's food with a greedy glint in their eye?

Just as there are sound evolutionary reasons for telling lies, so there are sound evolutionary reasons for being able to detect them. If oth­ers are trying to manipulate you to their advantage, then it is very probably to your disadvantage. So it is in your best interests to realise that, and avoid being manipulated. The result is an inevitable arms race, in which the ability to tell lies is played off against the ability to detect them. It is no doubt still going on, but already the result is some very sophisticated lying, and some very sophisticated detection. Sometimes the look on a person's face tells us they're telling an untruth; sometimes the tone of voice.

One effective way to recognise a lie is to put yourself inside the other person's mind, and ask yourself whether what they are saying is consistent with what you have convinced yourself they are thinking. For instance, they are saying what a sweet little child you have, but you remember from previous encounters that usually they can't stand kids. Maybe your child is different, of course, but then you notice that worried look in their eyes, as if they'd rather be somewhere else ...

Empathy is not just a nice way to understand someone else's point of view. It's a weapon that you can use to your own advantage. Having understood their point of view, you can compare it with what they're saying, and work out whether to believe them. In this manner, the existence of lies in language's phase space of the adjacent possi­ble encouraged the development of human empathy, and with it, individual intelligence and collective social cohesion. Learning to tell lies was a major step forward for humanity.

We can put ourselves inside the minds of other people with some degree of credibility, because we are people ourselves. We do at least know what it's like to be a person. But even then, we are probably deluding ourselves if we think that we really know exactly what's going on inside someone else's mind, let alone what that feels like to them. Each human mind is wired differently, and is the product of its owner's own experiences. It is even more problematic whether we can imagine what it is like to be an animal. On Discworld, an accom­plished witch can put herself inside an animal's mind, as we see, for instance, in this passage from Lords and Ladies:

She Borrowed. You had to be careful. It was like a drug. You could ride the minds of animals and birds, but never bees, steering them gently, seeing through their eyes. Granny Weatherwax had many times flicked through the channels of consciousness around her. It was, to her, part of the heart of witchcraft. To see through other eyes ...

... through the eyes of gnats, seeing the slow patterns of time in the fast pattern of one day, their minds travelling rapidly as lightning ...

... to listen with the body of a beetle, so that the world is a three-dimensional pattern of vibrations ...

... to see with the nose of a dog, all smells now colours ...

It's a poetic image. Does a dog 'see' smells? There is a folk belief that smell is far more important to a dog than sight, but this could well be an exaggeration based on the more credible observation that smell is more important to dogs than it is to humans. But even here we must add 'consciously, at least', because we react subconsciously to pheromones and other emotionally loaded chemicals. Some years ago David Berliner was working on the chemicals in human skin, and he left an open beaker containing some skin extracts on the laboratory bench. Then he noticed that his lab assistants were becoming distinctly more animated than usual, with a lot of camaraderie and mild flirta­tion. He froze the extract and put it away in the laboratory refrigerator for safekeeping. Thirty years later, he analysed the substances in the beaker and found a chemical called androstenone, which is rather like a sex hormone. A series of experiments showed that this chemical was responsible for the animated behaviour. However, androstenone has no smell. What was going on?

Some animals possess a 'vomeronasal' organ (often called the 'sec­ond nose'). This is a small region of tissue in the nose, which detects certain chemicals but is separate from the standard olfactory (smelling) system. The conventional wisdom had long been that humans do not possess a vomeronasal organ, but the curious behaviour of his assis­tants made the scientist wonder. Berliner discovered that the conventional wisdom was wrong: some humans, at least, do have a vomeronasal organ, and it responds to pheromones. Those are spe­cial chemicals that trigger strong responses in animals, such as fear or sexual arousal. The vomeronasal organ's owners are not consciously aware that they are sensing anything, but boy, do they respond.

This story shows how easily we can get sensations wrong. In this case, you know what it vomeronasally smells like to be a human: you don't feel anything at all, not consciously. But you certainly respond! So your reactions, and what they 'feel like', are very different. The sounds we hear, the sensations of heat and cold on our skin, the smells that assail our nostrils, the unmistakable taste of salt ... all these are qualia, vivid 'feelings' stuck on to our perceptions by our minds to help us recognise them more readily. They have a basis in reality, yes, but they are not real features of the outside world. They must be real features of brain architecture and function, real things happening in real nerve cells, but that level of reality is very different from the level that we perceive.

So we should be suspicious of the belief that we can know what it feels like to be a dog. In 1974 the philosopher Thomas Nagel pub­lished a famous essay 'What is it like to be a bat?' in the Philosophical Review, in which he made the same point. We can imagine what it is like to be a human who is behaving - superficially at least - like a bat, but we have no idea what it feels like to the bat, and it is question­able whether human knowledge can ever extend in such a direction. We probably get bats wrong anyway. We know that bats use echo-location to sense their surroundings, much as a submarine uses sonar. The bat or submarine emits sharp pulses of sound, and hears the returning echoes. From those, it can 'compute' what the sound must be bouncing off. We naturally assume that the bat responds to echoes in the same kind of way that we would: it hears them. We naturally expect the qualia of bat echo-location to be similar to the human qualia evoked by sound-patterns, of which the richest example is music. So we imagine the bat flying along to the accompaniment of incredibly rapid rhythms played on bongo drums.

However, this could be a false analogy. Echo-location is the main sense of a bat, so the 'correct' corresponding sense of a human is its main sense, which is sight, not hearing. The August 1993 edition of Nature has a picture of a bat on the cover, with the words 'How bats' ears see'. This refers to a technical article, by Steven Dear, James Simmons and Jonathan Fritz, who discovered that the neurons in the part of the bat's brain that processes returning echoes are connected together in a very similar way to those in the human visual cortex. In terms of neural architecture, it looks very much as if the bat's brain uses the echoes to build up an image of its surroundings. Analogously, today's submarines use computers to turn a series of echoes into a three-dimensional map of the surrounding water. Figments of Reality developed this point to give a partial answer to Nagel's question:

[In effect] bats see with their ears, and their sonar qualia might well be like our visual ones. Intensity of sound might come over to the bat as a kind of 'brightness', and so on. Possibly the bat's sonar qualia 'see' the world in black and white and shades of grey, but they could also pick up and render vivid various more subtle features of sound reflec­tions. The closest analogy in humans is texture, which we sense by touch, but the bat could sense by sound. Soft objects reflect sound less well than hard ones, for instance. So bats may well 'see' textured sound. If so - and here our analogy is intended only as a very rough way to convey the idea - the sonar quale for a soft surface might 'look' green to the bat's mind, that for hard ones might look red, that for liquid ones like a colour only bees can see, and so on ...

On Roundworld, such statements are no more than guesswork, sup­ported by analogies of neural architecture. On Discworld, witches know what it feels like to be a bat, or a dog, or a beetle. And Angua the werewolf smells in colours, which is very close to our suggestion that bats hear in images and 'see' textures. But even on Discworld, the witches do not actually feel what it is like to be a bat. They feel what it is like to be a human who has 'borrowed' the sensory organs and neural processing equipment of a bat. It may feel quite different to be a bat when a witch is not hitching a free ride on its mind.

Even though we can't be certain what it feels like to be an animal, or another person, the attempt has several uses. As we said, the ability involved here is empathy: being able to understand what another per­son feels like. We've already seen that this is an important social skill, and that the same ability, deployed in a different way for a different purpose, gives us a chance to detect that someone else is lying to us. If we put ourselves inside their heads and realise that what they are saying is different from what we believe they are thinking, then we suspect them of lying.

The word 'lie' has negative overtones, deservedly so, but what we're talking about here can be constructive as well as destructive, and often is. For the purposes of the present discussion, a lie is anything con­trary to the truth, but it's not at all clear what 'the truth' is, or even whether there is only one of it, as the word 'the' would seem to indi­cate. When two people have a row, it is generally impossible for either of them, or anyone else, to figure out exactly what really happened. Our thoughts are tainted by perceptions. This is unavoidable, because what we think of as being 'real' is what our minds make of what comes from the sense organs: fudged, tuned, and mangled by a suc­cession of interpretations by different bits of brain, plus some wallpaper additions. We never know what is really out there around us. All we know is what our minds construct from what our eyes, ears and fin­gers report.

Not to put too fine a point on it, those perceptions are lies. The vivid universe of colour that our brain derives from the light that falls on our retinas does not really exist. The redness of a rose is derived from its physical features, but 'being red' is not a physical feature as such. 'Emitting light of a certain wavelength' gets closer to being a physical feature. However, the vivid redness that we 'see' does not correspond to a specific wavelength. Our brains correct the colours of visual images for shadows, light reflected on to parts of the image by other parts of a different colour, and so on. Our sensation of redness is a decoration added to the perception by our brain: a quale. So what we 'see' is not an accurate perception of what is there, but a mental trans­form of a sensory perception of what is there.

To a bee, that same uniformly red rose may look very different, with obvious markings. The bee 'sees' in ultraviolet, a wavelength outside our range of perceptions. The rose emits a whole distribution of wave­lengths of light; we see a small part of that, and call it reality. The bee sees a different part and responds to it in its own beelike way, using the markings to land on the flower and collect nectar, or to dismiss it from consideration and fly on to the next possibility. Neither the bee's perception, nor ours, is the reality.

In Chapter 24 we explained that our minds select what they per­ceive in more ways than just passively ignoring signals that our senses can't pick up. We fine-tune our senses to see what we want them to see, hear what we want them to hear. There are more nerve connec­tions going from the brain to the ear than there are from the ear to the brain. Those connections adapt the ear's ability to perceive certain sounds, maybe by making it more sensitive to sounds that could rep­resent danger and less sensitive to sounds that don't really matter much. People who are not exposed to certain sounds as children, when their ears and brains are being tuned to pick up language, can­not distinguish them as adults. To the Japanese, the two phonemes 'l' and 'r' sound identical.

The lies that our senses tell us are not malicious. They are partial truths rather than untruths, and the universe is so complicated, and our minds are so simple in comparison, that the best we can ever hope for is half-truths. Even the most esoteric 'fundamental' physics is at best a half-truth. Indeed, the more 'fundamental' it becomes, the less true it gets. It is therefore no surprise that the most effective method we have yet devised for passing extelligence on to our children is a systematic series of lies. It is called 'education'.

We can hear the hackles rising even as we write, as quantum sig­nals echo back down the timelines from future readers in the teaching profession turning to this page. But before hurling the book across the room or sending an offended e-mail to the publisher, ask yourself just how much of what you tell children is true. Not worthy, not defensi­ble: true. At once you'll find yourself on the defensive: 'Ah, yes, but of course children can't understand all of the complexities of the real world. The teacher's job is to simplify everything as an aid to under­standing ...' Quite so.

Those simplifications are lies, within the meaning we are currently attaching to that word. But they are helpful lies, constructive lies, lies that even when they are really very wrong still open the door to a bet­ter understanding next time round. Consider, for example, the sentence 'A hospital is a place where people are sent so that the doctors can make them better'. Well, no sensitive adult would wish to tell a child that sometimes people go into hospital alive and come out dead. Or that often it's not possible to make them better. For a start, the child may have to go into hospital at some stage, and too big a dose of truth early on might make it difficult for the parents to persuade them to do so without making a fuss. Nonetheless, no adult would consider that sentence to be an accurate statement of what hospitals are really about. It is, at best, an ideal to which hospitals aspire. And when we justify our description on the grounds that the truth would upset the child, we are admitting that the sentence is a lie, and asserting that social conventions and human comfort are more important than giving an accurate description of what the world is about.

They often are, of course. A lot depends on context and intention. In Chapter 4 of The Science of Discworld we called these helpful untruths and half-truths 'lies-to-children'. They must be distinguished from the much less benevolent 'lies-to-adults', another word for which is 'politics'. Lies-to-adults are constructed with the express purpose of concealing intentions; their aim is to mislead. Some newspapers tell lies-to-adults; others do their best to tell truths-to-adults, although they always end up by telling adult versions of lies-to-children.

In the twenty-fifth Discworld novel The Truth, journalism comes to the Disc, in the form of William de Worde. His career begins with a monthly newsletter sent to various Discworld notables, usually for five dollars each month, but in the case of one foreigner for half a cartload of figs twice per year. He writes one letter, and pays Mr Cripslock the engraver in the Street of Cunning Artificers to turn it into a woodcut, from which he prints five copies. From these small beginnings emerges Ankh-Morpork's first newspaper, when de Worde's ability to sniff out a story is allied to the dwarves' discovery of movable type. It is rumoured that the dwarves have found a way to turn lead into gold -and since the type is made of lead, in a way they have.

The main journalistic content of the novel is a circulation battle between de Worde's Ankh-Morpork Times, with its banner 'THE TRUTH SHALL MAKE YOU FREE', and the Ankh-Morpork Inquirer (THE NEWS YOU ONLY HEAR ABOUT). The Times is an upmarket broadsheet, running stories with headlines like 'Patrician Attacks Clerk With Knife (He had the knife, not the clerk)', and checking its facts before pub­lishing them. The Inquirer is a tabloid, whose headlines are more of the 'ELVES STOLE MY HUSBAND' kind, and it saves money by mak­ing all the stories up. As a result, it can undercut its upmarket competitor when it comes to price, and the stories are much more interesting. Truth eventually prevails over cheap nonsense, however, and de Worde learns from his editor Sacharissa a fundamental princi­ple of journalism:

'Look at it like this,' said Sacharissa, starting a fresh page. 'Some peo­ple are heroes. And some people jot down notes.'

'Yes, but that's not very-'

Sacharissa glanced up and flashed him a smile. 'Sometimes they're the same person,' she said.

This time it was William who looked down, modestly.

'You think that's really true?' he said.

She shrugged. 'Really true? Who knows? This is a newspaper, isn't it? It just has to be true until tomorrow.'

Lies-to-children, even the broadsheet newspaper sort, are mostly benign and helpful, and even when they are not, they are intended to be that way. They are constructed with the aim of opening a path­way that will eventually lead to more sophisticated lies-to-children, reflecting more of the complexities of reality. We teach science and art and history and economics by a series of carefully constructed lies. Stories, if you wish ... but then, we've already characterised a story as a lie.

The science teacher explains the colours of the rainbow in terms of refraction, but slides over the shape of the rainbow and the way those colours are arranged. Which, when you come to think of it, are more puzzling, and more what we want to know about when we ask why rainbows look like they do. There's a lot more to the physics than a raindrop acting as a prism. Later, we may develop the next level of lie by showing the child the elegant geometry of light rays as they pass through a spherical raindrop, refracting, reflecting, and refracting back out again, with each colour of light focused along a slightly different angle. Later still, we explain that light does not consist of rays at all, but electromagnetic waves. By university, we are telling undergradu­ates that those waves aren't really waves at all, but tiny quantum wave-packets, photons. Except that the 'wave-packets' in the textbooks don't actually do the job ... And so on. All of our understanding of nature is like this; none of it is Ultimate Reality.

TWENTY-SEVEN

LACK OF WILL

The wizards were never quite certain where they were. It wasn't their history. History gets named afterwards: The Age of Enlightenment, the Depression. Which is not to say that people sometimes aren't depressed with all the enlightenment around them, or strangely ele­vated during otherwise grey times. Or periods are named after kings, as if the country was defined by whichever stony-faced cut-throat had schemed and knifed his way to the top, and as if people would say, 'Hooray, the reign of the House of Chichester - a time of deep divi­sion along religious lines and continuing conflict with Belgium - is now at an end and we can look forward to the time of the House of Luton, a period of expansion and the growth of learning! The plough­ing of the big field is going to be a lot more interesting from now on!'

The wizards had settled for calling the time they'd arrived 'D' and, now, they were back there, in some cases quite suntanned.

They had commandeered Dee's library again.

'Stage One seemed to have worked quite well, gentlemen,' said Ponder Stibbons. 'The world is certainly a lot more colourful. We do seem to have, er, assisted the elves in the evolution of what I might venture to call Homo narrans, or "Storytelling Man".'

'There's still religious wars,' said the Dean. 'And still the heads on spikes.'

'Yes, but for more interesting reasons,' said Ponder. 'That's humans for you, sir. Imagination is imagination. It gets used for everything. Wonderful art and really dreadful instruments of torture. What was that country where the Lecturer in Recent Runes got food poisoning?'

'Italy, I think,' said Rincewind. 'The rest of us had the pasta.'

'Well, it's full of churches and wars and horrors and some of the most amazing art. Better than we've got at home. We can be proud of that, gentlemen.'

'But when we showed them the book the Librarian found in L-space, of Great Works of Art with the full colour pictures ...' mumbled the Chair of Indefinite Studies, as if he had something on his mind but wasn't certain how to phrase it.

'Yes?' said Ridcully.

'... well, it wasn't actually cheating, was it?'

'Of course not,' said Ridcully. 'They must have painted them some­where. Some other dimension. Something quantum. A parallel eventuality or something with that sort of a name. But that doesn't matter. It all goes round and round and it comes out here.'

'But I think we said too much to that big chap with the bald head,' said the Dean. 'The artist, remember? Could've been the double of Leonard of Quirm? Beard, good singing voice? You shouldn't have told him about the flying machine that Leonard built.'

'Oh, he was scribbling so much stuff no one'll take any notice,' said Ridcully. Anyway, who'll remember an artist who can't get a simple smile right? The point is, gentlemen, that the fantastic imagination and the, er, practical imagination go hand in hand. One leads to the other. Can't separate them with a big lever. Before you can make something, you have to picture it in your head.'

'But the elves are still here,' said the Lecture in Recent Runes. 'All we've done is do their work even better! I don't see the point!'

Ah, that's Stage Two,' said Ponder. 'Rincewind?'

'What?'

'You're going to talk about Stage Two. Remember? You told us you wanted to get the world to the right stage?'

'I didn't know I had to make a presentation!'

'You mean you don't have any slides? No paperwork at all?'

'Paperwork slows me down,' said Rincewind. 'But it's obvious, isn't it? We say Seeing is Believing ... and I thought about that, and it's not really true. We don't believe in chairs. Chairs are just things that exist.'

'So?' said Ridcully.

'We don't believe in things we can see. We believe in things that we can't see.'

'And?'

'And I've been checking this world against L-space and I think we've made it the one where humans survive,' said Rincewind. 'Because now they can picture gods and monsters. And when you can picture them, you don't need to believe in them any more.'

After a long silence the Chair of Indefinite Studies said, 'Is it just me, or has anyone else noticed how many huge cathedrals they've been building on this continent? Big, big buildings full of wonderful crafts­manship? And those painters we talked to have been very keen on religious paintings ...'

'And your point is ... ?' said Ridcully.

'It's just that this has been happening at the same time as people have been really taking an interest in how the world works. They're asking more questions. How? and Why? and questions like that,' said the Chair of Indefinite Studies. 'They're acting like Phocian but with­out going mad. Rincewind seems to be suggesting that we're killing off the gods of this place.'

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-a-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 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 time 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, towards 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. 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-pie, 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 particle 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 Schrodinger's equation, which physicists tell us will predict the future state of the cat.

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 Schrodinger's equation, well, forget it.

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 Schrodinger'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 Schrodinger's equation. The equation is a human model, not the reality. But even if Schrodinger'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. Schrodinger'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 Schrodinger'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.

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, while 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 Yossarians 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 'alternate 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 Yilane, 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 Paradox 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 imperative 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.

There are practical problems in making such a gadget, the main one(!) being that the wormhole will collapse too quickly for an object to pass through it, unless it is held open by threading 'exotic matter' with negative energy through it. Nonetheless, none of this is forbid­den by the current laws of physics. So what of the paradoxes? It turns out that the laws of physics forbid genuine paradoxes, although they permit many apparent paradoxes. A useful technique for understand­ing the difference is known as a Feynman diagram, which is a picture of the motion of an object (usually a particle) in space and time.

For example, here is an apparent time travel paradox. A man is imprisoned in a concrete cell, locked from the outside, with no food, no water and no possibility of escape. As he sits in a corner in despair, waiting for death, the door opens. The person who has opened it is ... himself. He has returned in a time machine from the future. But how (the paradox) did he get to the future in the first place? Well, a kind person opened the door and set him free ...

There seems to be something very odd about the causality in the story, but the corresponding Feynman diagram shows that it violates none of the laws of physics. First, the man follows a space-time path that puts him inside the cell and then removes him from it through opened door. This time-line continues into his future until he encoun­ters a time machine. Then the time-line reverses direction, heading into the past, until he encounters a locked cell. He opens it, and his time-line reverses again, propelling him into his own future. So the man follows a single zig-zag path through time, and at every step the laws of physics hold good. Provided his time machine violates no physical law, of course.

If you try to 'explain' the grandfather paradox by this method, it doesn't work. The time-line leading from grandfather to killer is sev­ered when the killer returns; there is no consistent scenario, even in a Feynman diagram. So some stories of time travel are consistent with the laws of physics, and have their own kind of causal logic, albeit twisted; but other equally plausible stories are inconsistent with the laws of physics. You can rescue the Grandfather Paradox by assum­ing that changing the past in a logically inconsistent way switches you into a different alternate universe - say a quantum-mechanical paral­lel world. But then it wasn't your grandfather that you killed, but the grandfather of an alternate you. So this 'resolution' of the Grandfather Paradox is a cheat.

Faced with all this, the way that the wizards handle the complica­tions of time travel seems quite reasonable!

TWENTY-NINE

ALL THE GLOBE'S A THEATRE

The elves did not spend a lot of time in serious thought. They could control people who could do the thinking for them. They didn't play music, they did not paint, they never carved stone or wood. Control was the tal­ent, and it was the only one they had ever needed.

Nevertheless, there were ones who had survived for many thou­sands of years, and while they had no great intelligence they had accumulated that mass of observations, experience, cynicism and mem­ory that can pass for wisdom among people who don't know any better. One of the wisest things they did was not read.

They had found some clerks to read the play.

They listened.

Then, when it was over, the Queen said: 'And the wizards have been showing great interest in this man?'

'Yes, your majesty,' said one of the old ones.

The Queen frowned. 'This ... play is ... good. It treats us ... kindly. We are firm but fair with mortals. We offer rewards to those who deal well with us. Our beauty is satisfactorily referred to. Our ... issues with our husband are treated more romantically than I would like, but, nev­ertheless ... it is positive, it enhances us, it places us yet more firmly in the human world. One of the wizards was actually carrying this.'

One of the senior elves cleared its throat. 'Our grip is loosening, your majesty. Humanity is becoming more, shall we say, questioning?'

The Queen shot it a glance. But it was older than many Queens, and did not step back.

'You think it will do us harm? Is it a plot against us?'

The senior elves looked at one another. The main reason that they thought it was a plot was that they were predisposed to see plots. In the court of Faerie, an inability to see it coming meant that it took you by the throat.

'We think it may be,' one said at last.

'How? In what way?'

'We know the wizards have been seen in the company of the author,' said the elf.

'Then perhaps they are endeavouring to stop him writing the play, have you thought of that?' snapped the Queen. 'Can you see any way in which those words harm us?'

'We are agreed that we cannot ... nevertheless, we have a sense that in some way-'

'It is so simple! At last we are done some real honour and the wiz­ards will try to stop it! Are you so stupid that you cannot see that?'

Her long dress swirled as she turned on her heel. 'It will happen,' she said. 'I will see to it!'

The senior elves filed out, not looking at her face. They knew those moods.

On the stairs one said to the others: 'Purely out of interest ... can any of us put a girdle around the Earth in three minutes?'

"That would be a very big girdle,' said an elf.

'And would you wish to be called Peaseblossom?'

The eyes of the old elf were grey, flecked with silver. They had seen horrible things under many suns, and in most cases had enjoyed them. Humans were a valuable crop, the elf conceded. There had never been a species like it for depth of awe, terror and superstition. No other species could create such monsters in its heads. But sometimes, it con­sidered, they were not worth the effort.

'I think not,' it said.

'Well, now, Will - do you mind if I call you Will? Oh, Dean, fetch Will another pint of this really unpleasant ale, will you? Now ... where was I ... oh yes, I really enjoyed that play of yours. Magnificent, I thought!' Ridcully beamed. Around him, the inn hummed with life.

Will tried to focus. 'Which one was that, good sir?' he said.

Ridcully's smile remained fixed, but began to unravel around the edges. He was never one for unnecessary reading.

'The one with the king in it,' he said, aiming for safety.

On the other side of the table Rincewind did some desperate pan­tomime.

'The rabbit,' said Ridcully. 'The rat. The ferret. Sounds like ... hat. Rat. Rodent. Thing with teeth.'

Rincewind gave up, leaned across and whispered.

'Something about the shrew,' said Ridcully. Rincewind whispered a little harder.

'The one about the tame shrew. The man married a shrew. A shrewish woman. Not a real shrew, obviously, haha. No one would marry a real shrew. It would be a completely foolish idea.'

Will blinked. He was not, as an actor and a writer, averse to alco­hol bought by other people, and these people were being very good hosts. It was just that they seemed to be completely deranged.

'Er ... I thank you,' he said. He was aware of being stared at, and also of a strange but not unpleasant animal smell. He turned on the bench and was rewarded with a grin. It occupied all the space between a deep hood and a jerkin. There were a couple of brown eyes, too, but it was the grin his gaze kept coming back to.

The Librarian raised his tankard and gave Will a friendly nod. This caused the grin to get bigger.

'Now I'm sure you hear this all the time,' said Ridcully, slapping Will so hard on the back that his drink slopped, 'but we've got an idea for you. Dean, more ale all round, eh? It really is very weak stuff. Yes, an idea.' He poked Will in the chest. 'Too many kings, that's the trouble. What the public wants now, what puts bums on seats-'

'Feet,' said Rincewind.

'What?'

'Bums on feet, Archchancellor. It's mostly standing room in the theatre.'

'Feet, then. Bums, anyway. Thank you, Dean. Cheers.' Ridcully wiped his mouth delicately and turned his attention again to Will, who tried to avoid the prodding finger.

'Bums on, haha, feets,' he said, and blinked. 'Funny thing, funny thing, something similar happened to us, 'smatterofact, few years ago, Midsummer's Eve, these chaps were going to put on a play thingy for the king, next thing, elves all over the place, haha. Why, yes, Runes, I'll have another if you're paying, it's far too sweet to be a serious drink. Where was I? Ah. Elves. What you've got to do, what you've gotta do ... is ... why aren't you writing this down?'

In the morning Rincewind opened his eyes at the fourth attempt and with the assistance of both hands. There was a moment of brain lag, where the little wheels spun happily with no work to do, and then big horrible machinery cut in.

'Whg d'hl der ...' he said, and then got control of his mouth as well.

Bits of last night crept out of hiding to do their treacherous dance before his eyes. He groaned.

'We couldn't have done that, could we?' he muttered.

And memory said: that was only the start ...

Rincewind sat up and waited until the world stopped moving.

He'd been on the floor in the library. The other wizards lay scat­tered around the room or sprawled across piles of books. The air smelled of beer.

A veil will be drawn over the following half an hour, and lifted to find the wizards sitting around the table.

'It must've been the pork scratchings,' said the Dean.

'I don't remember any pork scratchings,' muttered Ponder.

'Something crunchy, anyway. They may have been moving about.'

'There's no doubt in my mind that it was caused by all this travel­ling we've been doing,' said Ridcully. 'That sort of thing must take a terrible toll on the system. We've been concentrating so hard, d'yer see, that the moment we relaxed the strain we just unwound, like a big spring.'

The wizards brightened up. Rascally drunkenness was too much of an embarrassment to men who could sit through an entire meal at the UU high table, but time sickness ... yes, that had a certain cachet. They could live with time sickness although, at the moment, they were wish­ing they didn't have to.

'That's right!' said the Lecturer in Recent Runes. 'It wasn't the fight!'

'And it couldn't possibly have been the carousing, which was really quite moderate by our standards,' said the Dean.

'In fact we didn't get drunk at all!' said the Chair of Indefinite Studies, brightly.

Unfortunately, Rincewind's memory was literally treacherous. It worked perfectly.

'So, then,' he said, wishing that he didn't have to, 'we didn't tell Will all that stuff?'

'What stuff?' said Ridcully.

'All about our magical library, for one thing. And you kept saying "Here's a good one, I bet you can use this" and you told him about those witches up in Lancre and how they got the new king on the throne, and that time the elves broke through, and how the Selachii and the Venturi families are always fighting-'

'We did?' said Ridcully.

'Yes. And about the countries we've visited. Lots of things.'

'Why didn't someone stop me?'

'The Dean did try. That's when you hit him with the Chair of Indefinite Studies, I think.'

The wizards sat in ale-smelling gloom.

'Should we have another try?' said the Lecturer in Recent Runes.

'What, and tell him to forget it all?' said Ridcully. 'Talk sense, man.'

'Perhaps we could go back in time and stop ourselves telling-'

'Don't say that! No more of that!' snapped the Archchancellor.

Rincewind pulled a copy of the play towards him. The wizards froze.

'Go on,' said Ridcully. 'Tell us the worst. What did he write?'

Rincewind opened the book and read a couple of lines at random:

'You spotted snakes, with double tongue; Thorny hedgehogs, be not-'

'No, no, no,' muttered the Dean, his head in his hands. 'Please tell me no one sang him the Hedgehog Song!'

Rincewind's lips moved as he read on. He turned over a few pages.

He flicked back to the beginning.

'It's all here,' he said. 'Same rather bad jokes, same unbelievable confusions, everything! Just as it was before! But it's going to happen here!'

The wizards looked at one another and dared to share a smug expression.

'Ah well, there we are then,' said Ridcully, sitting back. 'Job done.'

Rincewind turned some more pages. His recollections of the night were not coherent, but even a genius couldn't have made sense out of a bunch of drunken wizards all talking at once.

'Hex?' he said.

The crystal ball said: 'Yes?'

'Will this play be performed in this world?'

'That is the intention,' said the voice of Hex.

'And then what will happen?'

Hex told them, and added: 'That is one outcome.'

'Just a moment,' said Ponder Stibbons. 'There's more than one outcome?'

'Certainly. The play may not take place. Phase space contains a broadsheet account of a disruption of the first performance, followed by a fire in which a number of people died. Subsequently the theatres were closed and the playwright died during a riot. He was struck by a pike.'

'You mean a halberd, of course,' said Ridcully.

'A pike,' Hex repeated. 'A fishmonger was involved.'

'What happened to civilisation?'

Hex was silent for a moment, and then said: 'Humanity failed by three years to leave the planet.'

THIRTY

LIES TO HUMANS

Please tell me no one sang him the Hedgehog Song ...

The Hedgehog Song, a Discworld ditty in the gen­eral tradition of Eskimo Nell, first made its appearance in Wyrd Sisters with its haunting refrain 'The hedgehog can never be buggered at all'. The wizards have wielded the power of story with a vengeance. They have used it to prime their secret weapon, Shakespeare, and are convinced that he will prove more effective than a MIRVed ICBM. But before he's launched, they've very properly started to worry about collateral dam­age: possible cultural contamination by the Hedgehog Song.

It is a consequence only marginally less dire than eternal elf-infestation, but on the whole, preferable.

In the real Roundworld, the power of story is just as great as it is in the fictional counterpart. Stories have power because we have minds, and we have minds because stories have power. It's a complicity, and all that remains is to unwrap it.

As we do so, bear in mind that Discworld and Roundworld are not so much different as complementary. Each, in its own estimation at least, gave birth to the other. On Roundworld, the Disc is seen as fan­tasy, the invention of an agile mind; Discworld is a series of stories (amazingly successful) along with ceramic models, computer games and cassette tapes. Discworld runs on magic, and on narrative imper­ative. Things happen on Discworld because people assume they will, and because some things have to happen to complete the story. From the standpoint of Roundworld, Discworld is a Roundworld invention.

The Discworld view is similar, but inverted. The wizards of Unseen University know that Roundworld is merely a Discworld creation, an unanticipated spin-off from an all-too-successful attempt to split the thaum and create the first self-sustaining magical chain reaction. They know this because they were there when it happened. Roundworld was deliberately created to keep magic out. Surprisingly, the magic-free vacuum acquired its own regulatory principle. Rules. Things happen on Roundworld because they are consequences of the rules. However, it is astonishingly difficult to look at the rules and under­stand what their consequences will be. Those consequences are emergent. The wizards discovered this to their cost, as every attempt to do something straightforward in Roundworld - like creating life or jump-starting extelligence - went seriously awry.

These two worldviews are not mutually contradictory, for they are worldviews of two different worlds. Yet, thanks to the interconnectedness of L-space, each world illuminates the other.

The strange duality between Roundworld and Discworld parallels another: the duality between Mind and Matter. When Mind came to Roundworld, a very remarkable change occurred. Narrative imperative appeared in Roundworld. Magic came into existence. And elves, and vampires, and myth, and gods. Characteristically, all of these things came into being in an indirect and offbeat way, like the relationship between rules and consequences. Things didn't exactly happen because of the power of story. Instead, the power of story made minds try to make the things in the story happen. The attempts were not always suc­cessful, but even when they failed, Roundworld was usually changed.

Narrative imperative arrived on Roundworld like a small god, and grew in stature according to human belief. When a million human beings all believe the same story, and all try to make it come true, their combined weight can compensate for their individual ineffectiveness.

There is no science in Discworld, only magic and narrativium. So the wizards put science into Discworld in the form of the Roundworld Project, as detailed in The Science of Discworld. With elegant symme­try, there was no magic or narrativium in Roundworld, so humans put them there, in the form of story.

Before narrative imperative can exist, there has to be narrative, and that's where Mind proved decisive. The imperative followed hard on the heels of the narrative, and the two complicitly co-evolved, for as soon as there was a story, there was someone who wanted to make it come true. Nonetheless, the story beat the compulsion by a nose.

What makes humans different from all other creatures on the planet is not language, or mathematics, or science. It is not religion, or art, or politics, either. All of those things are mere side effects of the inven­tion of story. Now it might seem that without language there can be no stories, but that is an illusion, brought about by our current obses­sion with recording stories as words on paper. Before there was a word for 'elephant' it was possible to point at an elephant and make evoca­tive gestures, to draw an elephant on the cave wall and add spears flying towards it, or to mould a model of an elephant from clay and act out a hunting scene. The story was as clear as day, and an elephant-hunt would follow hard on its heels.

We are not Homo sapiens, Wise Man. We are the third chimpanzee. What distinguishes us from the ordinary chimpanzee Pan troglodytes, and the bonobo chimpanzee Pan paniscus, is something far more sub­tle than our enormous brain, three times as large as theirs in proportion to body weight. It is what that brain makes possible. And the most sig­nificant contribution that our large brain made to our approach to the universe was to endow us with the power of story. We are Pan narrans, the storytelling ape.

Even today, five million years since we and the other two species of chimpanzee went our separate evolutionary ways, we still use stories to run our lives. Every morning we buy a newspaper to find out, so we tell ourselves, what is happening in the world. But most things that are happening in the world, even rather important ones, never make it into the papers. Why not? Because newspapers are written by jour­nalists, and every journalist learned at their mother's knee that what grabs newspaper readers is a story. Events with zero significance for the planet, such as a movie star's broken marriage, are stories. Events that matter a great deal, such as the use of chlorofluorocarbons (CFCs) as propellants in aerosol cans of shaving-cream, are not stories. Yes, they can become stories, and in this case do when we discover that those selfsame CFCs are destroying the ozone layer; we even have a title for the story, The Ozone Hole. But nobody knew or recognised there was a story when shops first started selling aerosol cans, even though that was the decisive event.

Religions have always recognised the power of a good story. Miracles run better at the box-office than mundane good actions. Helping an old lady across the road isn't much of a story, but raising the dead most certainly is. Science is riddled with stories. In fact, if you can't tell a convincing story about your research, nobody will let you publish it. And even if they did, nobody else would understand it. Newton's laws of motion are simple little stories about what hap­pens to lumps of matter when they are given a push - stories only a little more precise than 'if you keep pushing, it will go faster and faster'. And 'Everything moves in circles', as Ponder would insist.

Why are we so wedded to stories? Our minds are too limited to grasp the universe for what it is. We're very small creatures in a very big world, and there is no way that we could possibly represent that world in full, intricate detail inside our own heads. Instead, we oper­ate with simplified representations of limited parts of the universe. We find simple models that correspond closely to reality extremely attrac­tive. Their simplicity makes them easy to comprehend, but that's not much use unless they also work. When we reduce a complex universe to a simple principle, be it The Will of God or Schrodinger's Equation, we feel that we've really accomplished something. Our models are sto­ries, and conversely, stories are models of a more complex reality. Our brains fill in the complexity automatically. The story says 'dog' and we immediately have a mental picture of the beast: a big, bumbling Labrador with a tail like a steam-hammer, tongue lolling, ears flop­ping. Just as our visual system fills in the blind spot.

We learn to appreciate stories as children. The child's mind is quick and powerful, but uncontrolled and unsophisticated. Stories appeal to it, and adults rapidly discovered that a story can put an idea into a child's head like nothing else can. Stories are easy to remember, both for teller and listener. As that child grows to adulthood, the love of stories remains. An adult has to be able to tell stories to the next gen­eration of children, or the culture does not propagate. And an adult needs to be able to tell stories to other adults, such as their boss or their mate, because stories have a clarity of structure that does not exist in the messiness of the real world. Stories always make sense: that's why Discworld is so much more convincing than Roundworld.

Our minds make stories, and stories make our minds. Each culture's Make-a-Human kit is built from stories, and maintained by stories. A story can be a rule for living according to one's culture, a useful sur­vival trick, a clue to the grandeur of the universe, or a mental hypothesis about what might happen if we pursue a particular course. Stories map out the phase space of existence.

Some stories are just entertainment, but even those usually have a hidden message on a deeper, possibly more earthy, level - as with Rumpelstiltskin. Some stories are Worlds of If, a way for minds to try out hypothetical choices and imagine their consequences. Word-play in the Nest of the Mind. And some of those stories have such a compelling logic that narrative imperative takes over, and they transmute into plans. A plan is a story together with the intention of making it come true.

Inside Roundworld, as it sits in its glass globe within the con­fining walls of the library of Unseen University, our story is coming to its climax. Will Shakespeare has written a play (it is, of course, A Midsummer Night's Dream), a play that the elves believe will consol­idate their power over human minds. The narrative of this play has collided with Rincewind's mental model of what he wants to do, and the flying sparks have ignited a plot. How will it all end? That is one of the compulsive aspects of a story. You'll just have to wait and see.

We have seen how history unfolds an emergent dynamic, so that even though everything is following rigid rules, even history itself has to wait and see how it all turned out. Yes, everything is following the rules, but there is no short cut that will take you to the destination before the rules themselves get there. History is not a story that exists in a book, the fatalistic 'it is written'. It is a story that makes itself up as it goes along, like a story that someone is reading and you are lis­tening to. It is being written ...

Philosophically, there ought to be a big difference between a story that is already written, and one that is being created word by word as you read it. The one is a story whose every sentence is predetermined; not only can there be only one possible outcome, but the outcome is already 'known'. The other is a story whose next sentence does not yet exist, whose ending in unknown even to the storyteller. You are reading the first kind of story, but while we were writing it, it was the second kind of story. In fact, it started out as a totally different story, but we never wrote that one at all. The philosophers realised long ago that it is no easy matter to determine which kind of story fits our world. If we had the ability to run the world again, we might discover that it does different things on the second occasion, and if so, the history of the universe would be a story that unfolds as it goes, not one already committed to paper.

But this doesn't look like a feasible experiment.

Our fascination with stories lays us open to a variety of errors in our relationship with the outside world. The rapid spread of rumours, for instance, is a tribute to how our love of a juicy story overcomes our critical faculties. The mechanism is precisely the one that the scientific method tries very hard to protect us against: believing something because you want it to be true. Or, for some rumours, because you fear it could be true. A rumour is one example of a more general con­cept, introduced in 1976 by Dawkins in The Selfish Gene. He came up with this notion in order to be able to discuss an evolutionary system that was different from the Darwinian evolution of organisms. It is the meme. The associated subject of 'memetics' is science's attempt to com­prehend the power of story.

The word 'meme' was coined by deliberate analogy with 'gene', and 'memetics' with 'genetics'. Genes are passed from one generation of organisms to the next; memes are passed from one human mind to another human mind. A meme is an idea that is so attractive to human minds that they want to pass it on to others. The song 'Happy Birthday to You' is a highly successful meme; so, for a long time, was Communism, though that was a complicated system of ideas, a memeplex. Ideas exist as some cryptic pattern of activity in brains, so brains, and their associated minds, provide an environment in which memes can exist and propagate. Indeed, replicate, for when you teach a child to sing 'Happy Birthday to You', you don't forget the song yourself. The Hedgehog Song is an equally successful Discworld meme.

As the home computer spread across the globe, and became inex­tricably wired into the Internet's extelligence, an environment was created that gave birth to an insidious silicon-based form of meme: the computer virus. All viruses so far seem to have been written deliber­ately by humans, although at least one turned out to be a far more successful replicator than its designer had intended, thanks to a pro­gramming error. 'Artificial life' simulations using evolving computer programs are often run inside a 'shell' that isolates them from the out­side world, because of the unlikely but possible evolution of a really nasty computer virus. The world's computer network is certainly com­plex enough to evolve its own viruses, given enough time.

Memes are mind-viruses.

In The Meme Machine, Susan Blackmore says that 'Memes spread themselves around indiscriminately without regard to whether they are useful, neutral, or positively harmful to us.' The song 'Happy Birthday to You' is mostly harmless, although it is just about possible to see it as an insidious piece of propaganda for global commerce if you're that way inclined. Advertising is a conscious attempt to unleash memes; a successful advertising campaign starts to build its own momentum as it spreads by word of mouth as well as overt TV or newspaper ads. Some advertising is beneficial (Oxfam, say) and some is manifestly harmful (tobacco). In fact, many memes are harmful, but still propa­gate very effectively: among them are the chain-letter and its financial analogue, pyramid selling. Just as DNA propagates without having any conscious intentions of its own, so memes replicate without having conscious objectives. The people who set the memes loose may have had overt intentions, but the memes themselves don't. Those that per­form well, leading human minds to pass them on in quantity, thrive; those that do not, die out, or at best live on as small, isolated pockets of infection. The spread of a meme is much like the spread of a dis­ease. And just as you can protect yourself against some diseases, by taking the right precautions, you can also protect yourself against becoming infected with a meme. The ability to think critically, and to question statements that rest on authority instead of evidence, are quite effective defences.

This is our message to you. You need not be a victim of the power of story, like Vorbis the Quisitor, smitten by an earthbound tortoise, the Wrath of Om. You can be a Granny Weatherwax, sailing through story-space like a master navigator, attuned to every breath of narra­tive wind (and a lot of it is, mark you), tacking against the gale like a maverick, avoiding the Shoals of Dogma and the Scylla and Charybdis of Indecision ...

Sorry, we got carried away. What we mean is: if you understand the power of story, and learn to detect abuses of it, you might actually deserve the appellation Homo sapiens.

Blackmore's book argues that many aspects of human nature are explained much better by memetics, the mechanisms whereby memes exist and propagate, than by any existing rival theory. In our termi­nology, memetics illuminates the complicity between intelligence and extelligence, between the individual mind and the culture of which it is but one tiny part. Some critics counter that the memeticists can't even say what the basic unit of a meme is. For example, are the first four notes of Beethoven's Fifth Symphony (dah-dah-da DUM) a meme, or is the meme really the whole symphony? Both replicate success­fully: the second in the minds of music-lovers, the first in a weird variety of minds.

However, this kind of criticism never carries much weight when a new theory is being developed. Not that this stops the critics, of course. By the time a scientific theory can 'define' its concepts with complete precision, it's dead. Very few concepts can actually be defined com­pletely: not even something like 'alive'. What, precisely, does 'tall' mean? 'Rich'? 'Wet'? 'Convincing'? Let alone 'slood'. If it comes to the crunch, the basic unit of genetics has not been defined in any con­vincing way, either. Is it a DNA base? A DNA sequence that codes for proteins, a 'gene' in the most limited sense? A DNA sequence with a known function - a 'gene' in its broadest sense? A chromosome? An entire genome? Does it have to exist inside an organism? Most DNA in the world contributes nothing genetic to the future: there's DNA in dead skin flakes, falling leaves, rotting logs ...

Dawkins's famous phrase 'It is raining DNA outside', applied to downy seeds of the willow tree at the start of chapter 5 of The Blind Watchmaker, is poetic. But very little of that DNA leads anywhere; it's just another molecule to be broken down as the falling seeds rot. A few seeds survive to germinate; fewer still produce plants; and most of those die or are eaten before they grow into a willow tree and pro­duce the next rainfall of seeds. DNA has to be in the right place (in sexual species, eggs or sperm) at the right time (fertilisation) before it propagates itself in any genetic sense. None of this stops genetics being a real science, and a very exciting and important one. So the fuzziness of definitions is not a good stick with which to beat the memetic dog, or indeed any dog that has anything going for it.

In his original discussion, almost as an aside, Dawkins suggested that religion is a meme, which goes something like 'If you wish to avoid the everlasting fires, you must believe this, and pass it on to your children'. The popularity of religion is no doubt more complicated than that; nevertheless, there is the germ of an idea here, because that sentence does correspond rather closely to the central message of many - not all - religions. The theologian John Bowker was sufficiently disturbed by this suggestion that he wrote Is God a Virus? to shoot it down. The fact that he bothered shows that he saw it as an important (and from his viewpoint dangerous) question.

Blackmore recognises that a religion, or any ideology, is too com­plex to be propagated by a single meme, just as an organism is too complex to be propagated by a single gene. Dawkins recognised this, too, and came up with a concept that he called 'coadapted meme com­plexes'. These are systems of memes that replicate collectively. The meme 'If you wish to avoid the everlasting fires, you must believe this, and pass it on to your children' is too simple to get very far, but if it is allied to other memes like 'The way to avoid the everlasting fires can be found in the Holy Book' and 'You must read the Holy Book or face eternal damnation', then the whole collection of memes forms a network that replicates far more effectively.

A complexity theorist would call such a collection of memes an 'autocatalytic set': each meme is catalysed, its replication is assisted, by some or all of the others. In 1995 Hans-Cees Speel coined the term 'memeplex'. Blackmore has a whole chapter on 'Religions as memeplexes'. If this line of argument bothers you, hang on a minute. Are you saying that religion is not a collection of beliefs and instructions that can be passed very successfully from one person to another? That's what 'memeplex' means. Anyway, replace 'religion' by 'politi­cal party' if you want to - not the one you support, naturally. Those other idiots who advocate/despise (delete whichever is inapplicable) free market economics, state pensions, public ownership of industry, private ownership of public services ... And bear in mind that while the secret of the spread of your own religion may be that it is The Truth, that can't possibly be the secret of the spread of all those other false religions in the world. Why the devil do sensible people believe that kind of rubbish?

Because it is a successful memeplex.

The evidence for memetic transmission of ideologies is extensive. For example, every one of the world's religions (barring ancient ones whose origins are lost in the mists of time) seems to have started with a very small group of believers and a charismatic leader. They are specific to particular cultural backgrounds; the meme needs a fertile substrate on which to grow. Many cherished beliefs of Christianity, for example, seem absurd to anyone not brought up in the Christian tradition. Virgin birth? (Well, that one was actually an inspired mistranslation of the Hebrew for 'young woman', but no matter.) Restored the dead to life? Communion wine becomes blood? Communion wafers are the body of Christ - and you eat them? Really? To believers, of course, all this makes perfect sense, but to outsiders, uninfected by the meme, it's laughable.

Blackmore points out that when it comes to a choice between doing good and spreading the meme, religious people tend to go for the meme. To most Catholics, and many other people, Mother Teresa was a saint (and she looks well set to become one in the fullness of time). Her work in the slums of Calcutta was selfless and altruistic. She did a lot of good, no question. But some Calcuttans feel that she diverted attention away from the real problems, and helped only those who accepted the teachings of her faith. For example, she was staunchly against birth control, the one practical thing that would have done the most good for the young women who needed her help. But the Catholic memeplex forbids birth control, and in a crunch, the meme wins. Blackmore sums up her analysis like this:

These religious memes did not set out with an intention to succeed. They were just behaviours, ideas and stories that were copied from one person to another ... They were successful because they hap­pened to come together into mutually supportive gangs that included all the right tricks to keep them safely stored in millions of brains, books and buildings, and repeatedly passed on to more.

In Shakespeare, memes become art. And now we move up another conceptual level. In drama, genes and memes cooperate to produce a temporary construct on a stage, for other extelligences to view. Shakespeare's plays give them pleasure, and change their minds. They, and works like them, redirect human culture by attacking our own mental elvishness.

The power of story. Don't leave home without it. And never, never, never underestimate it.

THIRTY-ONE

A WOMAN ON STAGE

It was the smell of the theatre Rincewind remembered. People talked about 'the smell of the greasepaint, the roar of the crowd' but, he assumed, the word 'roar' must have been taken to mean the same as 'stink'. He also wondered why this theatre was called The Globe. It was not even completely circular. But, he supposed, the new world might happen here ...

He'd made a big concession for the occasion. He'd unstitched the few remaining sequins from the word WIZZARD' on his hat. Given its general lack of shape, and his robe's raggedness, it now made him look far more like one of the crowd, albeit a one that knew the mean­ing of the word 'soap'.

He worked his way back through the throng to the wizards, who had managed to get real seats.

'How is it going?' said Ridcully. 'Remember, lad, the show must go on!'

'Things are fine, as far as I can see,' whispered Rincewind. 'No sign of any elves at all. We did spot a fishmonger in the crowd, so the Librarian slugged him and hid him behind the theatre, just in case.'

'You know,' said the Chair of Indefinite Studies, who was leafing through the script, 'this chap would write much better plays if he didn't have to have actors in them. They seem to get in the way all the time.'

'I read the Comedy of Errors last night,' said the Dean. 'And I could see the error right there. There wasn't any comedy. Thank gods for directors.'

The wizards looked at the crowd. It wasn't as well behaved even as the ones back home; people were picnicking, small parties were being held, and there was a general sense that the audience looked upon the actual play as pleasant background noise to their personal social occasions.

'How will we know when it starts?' said the Lecturer in Recent Runes.

'Oh, trumpets get blown,' said Rincewind, 'and then generally two actors come on and tell one another what they already know.'

'No sign of the elves anywhere,' said the Dean, looking around with a hand over one eye. 'I don't like it. It's too quiet.'

'No, sir, no, sir,' said Rincewind. 'That's not the time not to like it. The time not to like it is when it's suddenly as noisy as all hell, sir.'

'Well, you get backstage with Stibbons and the Librarian, will you?' said Ridcully. 'And try not to look conspicuous. We mustn't take any chances.'

Rincewind worked his away around behind the stage, trying not to look conspicuous. But it was a first night, and there was an informal­ity about the whole business that he'd never seen back home. People just seemed to wander around. Back home, there never seemed to be so much pretence; here, the actors played at being people and, down below, people played at being an audience. The overall effect was rather pleasing. The plays had a conspiratorial quality. Make it inter­esting enough, their audience was saying, and we'll believe anything. If you don't, we'll have a party with our friends right here and throw nuts at you.

Rincewind sat down on a pile of boxes offstage and watched as the play began. There were raised voices and the gentle, subtle sound of an expectant audience ready to tolerate quite a lot of plot exposition provided there was a joke or a murder at the end of it.

There was no sign of elves, no telltale shimmer in the air. The play wound on. Sometimes there was laughter, in which the deep boom of Ridcully was distinctly noticeable, especially, for some reason, when the clowns were on stage.

The stage elves met with approval, too. Peaseblossom, Cobweb, Moth and Mustardseed ... creatures of blossom and air. Only Puck seemed to Rincewind to be anything like the elves he knew, and even he seemed more of a prankster than anything else. Of course, the elves could be pranksters, too, especially if a footpath ran beside a really dangerous ravine. And the glamour they used ... well, here it was charming ...

... and there was the Queen, a few feet away. She didn't flash into existence, she emerged from the scenery. A group of lines and shad­ows that had always been there suddenly, without actually changing, became a figure.

She was wearing a black lace dress hung about with diamonds, so that she looked like walking night.

She turned to Rincewind, with a smile.

'Ah, potato man,' she said. 'We see your wizardly friends out there. But they won't be able to do anything. This show will go on, you know. Just as written.'

'... will go on ...' murmured Rincewind. He couldn't move. She'd hit him with her full force. In desperation, he tried to fill his mind with potatoes.

'We know you told him a garbled version,' said the Queen, walking around his quivering body. 'And a lot of nonsense it was. So I appeared to him in his room and put the whole thing in his mind. So simple.'

Roast potatoes, thought Rincewind. Sort of gold with brown edges, and maybe almost black here and there so they're nice and crunchy ...

'Can't you hear the applause?' said the Queen. 'They like us. They actually like us. We'll be in their paintings and stories from now on. You'll never get us out of there ...'

Chips, thought Rincewind, straight from the deep fryer, with little bubbles of fat still spitting and popping ... but he couldn't stop his treacherous head from nodding.

The Queen looked puzzled.

'Don't you think about anything but potatoes?' she said.

Butter, thought Rincewind, chopped chives, melted cheese, salt ...

But he couldn't stop the thought. It opened up inside his head, pushing away all potato-shaped fantasies. All we have to do is nothing, and we've won!

'What?' said the Queen.

Mash! Huge mounds of mash! Creamed mash!

'You're trying to hide something, wizard!' said the Queen, a few inches from his face. 'What is it?'

Potato cakes, fried potato skins, potato croquettes ...

... no, not potato croquettes, no one ever did them properly ... and it was too late, the Queen was reading him like a book.

'So ...' she said. 'You think only mysteries last? Knowledge in unbelief? Seeing is disbelieving?

There was a creaking above them.

'The play's not over, wizard,' said the Queen. 'But it's going to stop right now!'

At this point, the Librarian dropped on her head.

Winkin the glove stitcher and Coster the apple seller discussed the play on the way home.

'The bit with the queen and the man with the asses ears was good,' said Winkin.

'Aye, it was.'

'And the wall bit, too. When the man said "he is no crescent, and his horns are invisible within the circumference", I nearly widdled my breeches. I like a good joke, me.'

'Aye.'

'But I didn't understand why all those people in the fur and feathers and stuff were chased across the stage by the man in the hairy red costume, and why the fat men in the expensive seats all got up and on to the stage and why the idiot in the red dress was running around screaming about potatoes, whatever they are. While Puck was speak­ing at the end I definitely thought I could hear a fight going on.'

'Experimental theatre,' said Winkin.

'Good dialogue,' said Coster.

'And you've got to hand it to those actors, the way they kept going,' said Winkin.

Yeah, and I could have sworn there was another Quene up on stage,' said Coster, 'and she looked like a woman. You know, the one who was trying to strangle that man babbling about potatoes.'

'A woman on stage? Don't be daft,' said Winkin. 'Good play, though.'

'Yeah. I think they could cut out the chase sequence, though,' said Coster. 'And frankly I don't think you could get a girdle that big.'

'Yes, it would be dreadful if special effects took over,' said Winkin.

Wizards, like many large men, can be quite light on their feet. Rincewind was impressed. By the sound of it, they were right behind him as he sped along the path by the river.

'Best not to wait for a curtain call, I thought,' Ridcully panted.

'Did you see me ... wallop the Queen with a horseshoe?' wheezed the Dean.

'Yes ... pity it was an actor,' said Ridcully. 'The other one was the elf. Still, not a complete waste of a horseshoe.'

'But we certainly showed them, eh?' said the Dean.

'The history is completed,' said the voice of Hex, from Ponder's bouncing pocket. 'Elves will be viewed as fairies and such they will become. Over the course of several centuries belief in them will dwin­dle as they are moved into the realm of art and literature, which is where the remnant of them will subsequently exist. They will become a subject suitable for the amusement of children. Their influence will be severely curtailed but will never die away completely.'

'Never?' panted Ponder, who was getting winded.

'There will always be some influence. Minds on this world are extremely susceptible.'

'Yes, but we've pushed imagination to the next stage,' puffed Ponder. 'People can imagine that the things they imagine are imagi­nary. Elves are little fairies. Monsters get pushed off the map. You can't fear the unseen when you can see it.'

'There will be new kinds of monsters,' said Hex, from Ponder's pocket. 'Humans are very inventive in that respect.'

'Heads ... on ... spikes,' said Rincewind, who liked to save his breath for running.

'Many heads,' said Hex.

'There's always heads on spikes somewhere,' said Ridcully.

'The Shell Midden People didn't have heads on spikes,' said Rincewind.

'Yes, but they didn't even have spikes,' said Ridcully.

'You know,' wheezed Ponder, 'we could have just told Hex to move us directly to the opening into L-space ...

They landed on the wooden floor, still running.

'Can we teach him to do that on Discworld?' said Rincewind, after they'd picked themselves up from the heap by the wall.

'No! Otherwise what use would you be?' said Ridcully. 'Come on, let's go ...'

Ponder hesitated by the L-space portal. It was filled with dull, grey­ish light, and a distant view of mountains and plains of books.

'There's still elves here,' he said. 'They're persistent. They might find some way to-'

'Will you come on?' snapped Ridcully. 'We can't fight every battle.'

'Something could still go wrong, though.'

'Whose fault will that be now? No, come on.'

Ponder looked around, gave a little shrug, and stepped into the hole.

After a moment a hairy red arm came through and pulled more books through the hole, piling them up until it was a wall of books.

Brilliant light, so strong that it lanced out between the pages, flashed for a while somewhere in the heap.

Then it went dark. After a moment, a book slipped out of the pile, and it collapsed, the books tumbling to the floor, and there was nothing left but a bare wall.

And, of course, a banana.

THIRTY TWO

MAY CONTAIN NUTS

We are the storytelling ape, and we are incredibly good at it.

As soon as we are old enough to want to under­stand what is happening around us, we begin to live in a world of stories. We think in narrative. We do it so automatically that we don't think we do it. And we have told our­selves stories vast enough to live in.

In the sky above us, patterns older than our planet and unimagin­ably far away have been fashioned in gods and monsters. But there are bigger stories down below. We live in a network of stories that range from 'how we got here' to 'natural justice' to 'real life'.

Ah, yes ... 'real life'. Death, who acts as a kind of Greek chorus in the Discworld books, is impressed by some aspects of humanity. One is that we have evolved to tell ourselves interesting and useful little lies about monsters and gods and tooth fairies, as a kind of prelude to creating really big lies, like 'Truth' and Justice'.

There is no justice. As Death remarks in Hogfather, you could grind the universe into powder and not find one atom of justice. We cre­ated it, and while we acknowledge this fact, nevertheless there is a sense in which we feel it's 'out there', big and white and shining. It's another story.

Because we rely so much on them, we love stories. We require them on a daily basis. So a huge service industry has grown up over several thousand years.

The basic narrative forms of drama - the archetypal stories - can all be found in the works of the ancient Greek playwrights: Aeschylus, Aristophanes, Euripides, Sophocles ... Most of the dramatic tricks go back to ancient Greece, especially Athens. No doubt they are older than that, for no tradition starts in fully developed form. The 'chorus', a gaggle of bit-players who form a backdrop for the main action and in various ways reinforce it and comment on it, is of Greek or earlier origin. So is the main division of the form of a play, though not nec­essarily its substance, into comedy and tragedy. So, possibly, is the invention of the huge stuffed joke willy, always good for a laugh from the cheap seats.

The Greek concept of tragedy was an extreme form of narrative imperative: the nature of the impending disaster had to be evident to the audience and to virtually all of the players; but it also had to be evident that it was going to happen anyway, despite that. You were Doomed, as you should be - but we'll watch anyway, to see how interestingly you'll be Doomed. And if it sounds silly to watch a drama when you know the ending in advance, consider this: how likely is it, when you settle down to watch the next James Bond movie, that he won't defuse the bomb? In fact you'll be watching a narrative as rigid as any Greek drama, but you'll watch anyway to see how the trick is done this time.

In our story, Hex is the chorus. In form, our tale is comedy; in sub­stance, it is closer to tragedy. The elves are a Discworld reification of human cruelty and wickedness, they are evil incarnate because - tra­ditionally - they have no souls. Yet in their various aspects they fascinate us, as do vampires and monsters and werewolves. It'd be a terrible event if the last jungle yields up its tiger, and so it would be, too, when the last forest yields up its werewolf (yes, all right, techni­cally they don't exist, but we hope you know what we mean: it'd be a bad day for humanity when we stop telling stories).

We've piled on to elves and yetis and all the other supernatural aspects of ourselves; we're happier to say that monsters are out there in the deep dark forest than locked in here with us. Yet we need them, in a way we find hard to articulate; the witch Granny Weatherwax tried to summarise it in Carpe Jugulum, when she said 'We need vampires, if only to remind us what garlic is for'. G.K. Chesterton did rather better when, in an article defending fairy stories, he disputed the sug­gestion that stories tell children that there are monsters. Children already know there are monsters, he said. Fairy stories tell them that monsters can be killed.

We need our stories to understand the universe, and sometimes we forget that they're only stories. There is a proverb about the finger and the moon; when a wise man points at the Moon, the fool looks at the finger. We call ourselves Homo sapiens, possibly out of a hope that this may be true, but the storytelling ape has a tendency to confuse moons and fingers.

When your god is an ineffable essence that exists outside of space and time, with unimaginable knowledge and indescribable powers, a god of boundless sky and high places, belief slips easily into the mind.

But the ape isn't happy with that. The ape gets bored with things it can't see. The ape wants pictures. And it gets them, and then a god of endless space becomes an old man with a beard sitting in the clouds. Great art takes place in the god's honour, and every pious brush gen­tly kills what it paints. The wise man says 'But this is just a metaphor!', and the ape says 'Yeah, but those tiny wings couldn't lift a cherub that fat!' And then not so wise men fill the pantheon of heaven with hier­archies of angels and set the plagues of man on horseback and write down the dimensions of Heaven in which to imprison the lord of infinite space. The stories begin to choke the system ...

Seeing is not believing.

Rincewind knows this, which is why he encourages Shakespeare to make elves real. Because once you're called Mustardseed, it's down­hill all the way ...

The elves cannot understand Rincewind's ploy. Not until his thoughts give it away to the Queen of the Elves, and the salvation of the world rests upon 300 pounds of plummeting orangutan. Nevertheless, the plan worked very well. This is Oberon, near the end of the play:

Through the house give glimmering light,

By the dead and drowsy fire;

Every elf and fairy sprite

Hop as light as bird from brier;

And this ditty, after me,

Sing and dance it trippingly.

There's no hope for them. Next stop, nursery wallpaper. Whereas witches, now:

Scale of dragon, tooth of wolf,

Witch's mummy, maw and gulf

Of the ravin'd salt-sea shark,

Root of hemlock digg'd I'th' dark,

Liver of blaspheming Jew,

Gall of goat, and slips of yew

Silver'd in the moon's eclipse,

Nose of Turk, and Tartar's lips,

Finger of birth-strangled babe

Ditch-delivered by a drab-

Make the gruel thick and slab;

Add thereto a tiger's chaudron,

For th' ingredience of our cauldron.

No contest. What's a chaudron? Entrails. Definitely no contest. The witches appear on stage in Macbeth only three times, but they steal the show. They probably got fan mail. The fairies are present for a large part of A Midsummer Night's Dream, but it is Bottom that steals the show and only Puck has a glimmer of the old evil. They've been parcelled, stamped and sent on their way to Tinkly Wood.

To be sure, Shakespeare's Oberon is not all sweetness and light. He uses the juice of a herb, the flower known as Love-in-idleness, to enchant Titania, Queen of the Fairies, because she has gained possession of a changeling child, and he wants it. He makes her fall in love with Bottom, who at that point in the story is an ass. And he is appeased, and she is entirely happy with the turn of events, when she gives him the child. But that's low-level, sanitised nastiness, a fret­ful squabble, not a war.

The allure of the unknown fades into the tawdry reality of a spe­cific representation, once you see it dripping sequins. Abraham's God of Extelligence was far more compelling than a few golden (probably just gold leaf) idols. But when the Renaissance artists started to paint God as a bearded man in the clouds, they opened the way to doubt. The image just wasn't impressive enough. The pictures on radio are always so much better than those on TV.

For the last few hundred years, humanity has been killing its myths. Faith and superstition have been giving way, slowly and against con­siderable resistance, to the critical assessment of evidence. They may, perhaps, be enjoying a bit of a revival: many rational thinkers have bemoaned the slide into cults and the weird offshoots of New Ageism ... But those are all very subdued versions of the old myths, the old beliefs; their teeth have been drawn.

Science alone is not The Answer. Science too has its myths. We have shown you some of them, or at least what we believe to be some of them. The misuse of anthropic reasoning is a clear example, as in the case of the carbon resonance, but argued with no thought for the fudge-factor of the red giant.

The ideal of the scientific method is often not realised. Its usual state­ment is an oversimplification in any case, but the basic worldview captures the essence. Think critically about what you are told. Do not accept the word of authority unthinkingly. Science is not a belief sys­tem: no belief system instructs you to question the system itself. Science does. (There are many scientists, however, who treat it as a belief system. Be wary of them.)

The most dangerous myths and ideologies, today, are the ones that have not yet been destroyed by the rising ape. They still strut their stuff on the world's stage, causing grief and havoc - and the tragedy is that it's all to no purpose. Most of it doesn't matter. Issues like abortion do matter, to some extent; even 'pro-choice' adherents would prefer that the choice should not be necessary. Issues like short skirts or lengths of beards do not matter, and it's foolish and dangerous to make a big fuss about them on a planet that is bursting at the seams with an excess of people. To do so is to promote the memeplex above the good of humanity. It is the action of a barbarian mind, a mind sufficiently removed from reality that the consequences of its resident memeplex do not affect it directly. It is not the actions of the naive young men who carry the suicide bomb, or fly the airliner into a skyscraper, that are the root of the problem; it is the actions of the evil old men who lead them to behave like that, all for the sake of a few memes.

The key memes are not religious, in this case, we suspect, even though religion is often blamed: that's mostly a smokescreen. Those old men are motivated by political memes, and the religious meme­plex is merely another of their weapons. But they are also trapped in their own stories, and this is high tragedy. Granny Weatherwax would never make that mistake.

The elves are still with us, in our heads. Shakespeare's humanity, and the critical faculties encouraged by science, are two of our weapons against them. And fight them we must.

And to achieve that, we need to invent the right stories. The ones we've got have brought us a long way. Plenty of creatures are intelli­gent, but only one tells stories. That's us, Pan narrans.

And what about Homo sapiens? Yes, we think that would be a very good idea ...