You spotted snakes with double tongue,

Thorny hedgehogs, be not seen;

Newts and blind-worms, do no wrong,

Come not near our fairy Queen.

I have had a most rare vision. I have had a dream, past the wit of man to say what dream it was. Man is but an ass if he go about to expound this dream. Methought I was - there is no man can tell what. Methought I was, and methought I had, but man is but a patched fool, if he will offer to say what methought I had. The eye of man hath not heard, the ear of man hath not seen, man's hand is not able to taste, his tongue to conceive, nor his heart to report, what my dream was.

This is the silliest stuff that ever I heard.

WILLIAM SHAKESPEARE A MIDSUMMER NIGHTS DREAM

I'm nae listenin' to them! They've got warts!

ARTHUR J. NIGHTINGALE THE SHORT COMEDY OF MACBETH

Apology: this book is a true account of events in the life of William Shakespeare, but only for a given value of 'true'.

Warning: May Contain Nuts

ONE

MESSAGE IN A BOTTLE

In the airy, crowded silence of the forest, magic was hunting magic on silent feet.

A wizard may be safely defined as a large ego which comes to a point at the top. That is why wizards do not blend well. That would mean looking like other people, and wizards do not wish to look like other people. Wizards aren't other people.

And therefore, in these thick woods, full of dappled shade, new growth and birdsong, the wizards who were in theory blending in, in fact blended out. They'd understood the theory of camouflage - at least they'd nodded when it was being explained - but had then got it wrong.

For example, take this tree. It was short, and it had big gnarly roots. There were interesting holes in it. The leaves were a brilliant green. Moss hung from its branches. One hairy loop of grey-green moss, in particular, looked rather like a beard. Which was odd, because a lump in the wood above it looked rather like a nose. And then there was a blemish in the wood that could have been eyes ...

But overall this was definitely a tree. In fact, it was a lot more like a tree than a tree normally is. Practically no other tree in the forest looked so tree-like as this tree. It projected a sensation of extreme barkness, it exuded leafidity. Pigeons and squirrels were queuing up to settle in the branches. There was even an owl. Other trees were just sticks with greenery on compared to the sylvanic verdanity of this tree ...

... which raised a branch, and shot another tree. A spinning orange ball spun through the air and went splat! on a small oak.

Something happened to the oak. Bits of twig and shadows and bark which had clearly made up an image of a gnarled old tree now equally clearly became the face of Archchancellor Mustrum Ridcully, Master of Unseen University (for the extremely magical) and running with orange paint.

'Gotcha!' shouted the Dean, causing the owl to leap from his hat. This was lucky for the owl, because a travelling glob of blue paint removed the hat a moment later.

'Ahah! Take that, Dean!' shouted an ancient beech tree behind him as, changing without actually changing, it became the figure of the Lecturer in Recent Runes.

The Dean spun around, and a blob of orange paint hit him in the chest.

'Eat permitted colourings!' yelled an excited wizard.

The Dean glared across the clearing to a crabapple tree which was, now, the Chair of Indefinite Studies.

'What? I'm on your side, you damn fool!' he said.

'You can't be! You made such a good target!'

The Dean raised his staff. Instantly, half a dozen orange and blue blobs exploded all over him as other hidden wizards let loose.

Archchancellor Ridcully wiped paint out of his eyes.

'All right, you fellows,' he sighed. 'Enough's enough for today. Time for tea, eh?'

It was so hard, he reflected, to get wizards to understand the concept of 'team spirit'. It simply wasn't part of wizardly thinking. A wizard could grasp the idea of, say, wizards versus some other group, but they lost their grip when it came to the idea of wizards against wizards. Wizard against wizards, yes, they had no trouble with that.

They'd start out as two teams, but as soon as there was any engage­ment they'd get all excited and twitchy and shoot other wizards indiscriminately. If you were a wizard then, deep down, you knew that every other wizard was your enemy. If their wands had been left unfettered, rather than having been locked to produce only paint spells - Ridcully had been very careful about that - then this forest would have been on fire by now.

Still, the fresh air was doing them good. The University was far too stuffy, Ridcully had always thought. Out here there was sun, and bird-song, and a nice warm breeze-

-a cold breeze. The temperature was plunging.

Ridcully looked down at his staff. Ice crystals were forming on it.

'Turned a bit nippy all of a sudden, hasn't it?' he said, his breath tin­gling in the frigid air.

And then the world changed.

Rincewind, Egregious Professor of Cruel and Unusual Geography, was cataloguing his rock collection. This was, these days, the ground state of his being. When he had nothing else to do, he sorted rocks. His predecessors in the post had spent many years bringing back small examples of cruel or unusual geography and had never had time to catalogue them, so he saw this as his duty. Besides, it was wonderfully dull. He felt that there was not enough dullness in the world.

Rincewind was the least senior member of the faculty. Indeed, the Archchancellor had made it clear that in seniority terms he ranked somewhat lower than the things that went 'click' in the woodwork. He got no salary and had complete insecurity of tenure. On the other hand, he got his laundry done free, a place at mealtimes and a bucket of coal a day. He also had his own office, no one ever visited him and he was strictly forbidden from attempting to teach anything to anyone. In academic terms, therefore, he considered himself pretty lucky.

An additional reason for this was that he was in fact getting seven buckets of coal a day and so much clean laundry that even his socks were starched. This was because no one else had realised that Blunk, the coal porter, who was far too surly to read, delivered the buckets strictly according to the titles on the study doors.

The Dean, therefore, got one bucket. So did the Bursar.

Rincewind got seven because the Archchancellor had found him a useful recipient of all the titles, chairs and.posts which (because of ancient bequests, covenants and, in one case at least, a curse) the University was obliged to keep filled. In most instances no one knew what the hell they were for or wanted anything to do with them, in case some clause somewhere involved students, so they were given to Rincewind.

Every morning, therefore, Blunk stoically delivered seven buckets to the joint door of the Professor of Cruel and Unusual Geography, the Chair of Experimental Serendipity, the Reader in Slood Dynamics, the Fretwork Teacher, the Chair for the Public Misunderstanding of Magic, the Professor of Virtual Anthropology and the Lecturer in Approximate Accuracy ... who usually opened the door in his under­pants - that is to say, opened the door in the wall whilst wearing his underpants - and took the coal happily, even if it was a sweltering day. At Unseen University you had budgets, and if you didn't use up everything you'd been given you wouldn't get as much next time. If this meant you roasted all summer in order to be moderately warm during the winter, then that was a small price to pay for proper fiscal procedures.

On this day, Rincewind carried the buckets inside and tipped the coal on the heap in the corner.

Something behind him went 'gloink'.

It was a small, subtle and yet curiously intrusive sound, and it accompanied the appearance, on a shelf above Rincewind's desk, of a beer bottle where no beer bottle had hitherto been.

He took it down and stared at it. It had recently contained a pint of Winkle's Old Peculiar. There was absolutely nothing ethereal about it, except that it was blue. The label was the wrong colour and full of spelling mistakes but it was mostly there, right down to the warning in tiny, tiny print: May Contain Nuts.

Now it contained a note.

He removed this with some care, and unrolled it, and read it.

Then he stared at the thing beside the beer bottle. It was a glass globe, about a foot across, and contained, floating within it, a smaller blue-and-fluffy-white globe.

The smaller globe was a world, and the space inside the globe was infinitely large. The world and indeed the whole universe of which it was part had been created by the wizards of Unseen University more or less by accident, and the fact that it had ended up on a shelf in Rincewind's tiny study was an accurate indication of how interested they were in it once the initial excitement had worn off.

Rincewind watched the world, sometimes, through an omniscope. It mostly had ice ages, and was less engrossing than an ant farm. Sometimes he shook it up to see if it would make it interesting, but this never seemed to have much of an effect.

Now he looked back at the note.

It was extremely puzzling. And the university had someone to deal with things like that.

Ponder Stibbons, like Rincewind, also had a number of jobs. However, instead of aspiring to seven, he perspired at three. He had long been the Reader in Invisible Writings, had drifted into the new post as Head of Inadvisably Applied Magic and had walked in all innocence into the office of Praelector, which is a university title meaning 'person who gets given the nuisance jobs'.

That meant that he was in charge in the absence of the senior members of the faculty. And, currently, this being the spring break, they were absent. And so were the students. The University was, there­fore, running at near peak efficiency.

Ponder smoothed out the beer-smelling paper and read:

TELL STIBBONS GET HERE AT ONCE. BRING LIBRARIAN. WAS IN FOREST, AM IN ROUND WORLD. FOOD GOOD, BEER AWFUL. WIZARDS USELESS. ELVES HERE TOO. DIRTY DEEDS AFOOT.

RIDCULLY

He looked up at the humming, clicking, busy bulk of Hex, the University's magical thinking engine, then, with great care, he placed the message on a tray that was part of the machine's rambling struc­ture.

A mechanical eyeball about a foot across lowered itself carefully from the ceiling. Ponder didn't know how it worked, except that it contained vast amounts of incredibly finely drawn tubing. Hex had drawn up the plans one night and Ponder had taken them along to the gnome jewellers; he'd long ago lost track of what Hex was doing. The machine changed almost on a daily basis.

The write-out began to clatter and produced the message:

+++ Elves have entered Roundworld. This is to be expected. +++

'Expected?' said Ponder.

+++ Their world is a parasite universe. It needs a host +++

Ponder turned to Rincewind. 'Do you understand any of this?' he said.

'No,' said Rincewind. 'But I've run into elves.'

'And?'

'And then I've run away from them. You don't hang around elves. They're not my field, unless they're doing fretwork. Anyway, there's nothing on Roundworld at the moment.'

'I thought you did a report on the various species that kept turning up there?'

'You read that?'

'I read all the papers that get circulated,' said Ponder.

'You do?'

'You said that every so often some kind of intelligent life turns up, hangs around for a few million years, and then dies out because the air freezes or the continents explode or a giant rock smacks into the sea.'

'That's right,' said Rincewind. 'Currently the globe is a snowball again.'

'So what is the faculty doing there now?'

'Drinking beer, apparently.'

'When the whole world is frozen?'

'Perhaps it's lager.'

'But they are supposed to be running around in the woods, pulling together, solving problems and firing paint spells at one another,' said Ponder.

'What for?'

'Didn't you read the memo he sent out?'

Rincewind shuddered. 'Oh, I never read those,' he said.

'He took everyone off into the woods to build a dynamic team ethos,' said Ponder. 'It's one of the Archchancellor's Big Ideas. He says that if the faculty gets to know one another better, they'll be a hap­pier, more efficient team.'

'But they do know one another! They've known one another for ages! That's why they don't like one another very much! They won't stand for being turned into a happy and efficient team!'

'Especially on a ball of ice,' said Ponder. 'They're supposed to be in woods fifty miles away, not in a glass globe in your study! There is no way to get into Roundworld without using a considerable amount of magic, and the Archchancellor has banned me from running the thaumic reactor at anything like full power.'

Rincewind looked again at the message from the bottle.

'How did the bottle get out?' he said.

Hex printed:

+++ I did that. I still maintain a watch on Roundworld. And I have been developing interesting procedures. It is now quite easy for me to reproduce an artefact in the real world +++

'Why didn't you tell us the Archchancellor needed help?' sighed Ponder.

+++ They were having such fun trying to send the bottle +++

'Can't you just bring them out, then?'

+++ Yes +++

'In that case-'

'Hold on,' said Rincewind, remembering the blue beerbottle and the spelling mistakes. 'Can you bring them out alive?

Hex seemed affronted.

+++ Certainly. With a probability of 94.37 per cent +++

'Not great odds,' said Ponder, 'But perhaps-'

'Hold on again,' said Rincewind, still thinking about that bottle. ' 'Humans aren't bottles. How about alive, with fully functioning brains and all organs and limbs in the right place?'

Unusually, Hex paused before replying.

+++ There will be unavoidable minor changes +++

'How minor, exactly.'

+++ I cannot guarantee reacquiring more than one of every 1 organ+++

There was a long, chilly silence from the wizards.

+++ Is this a problem? +++

'Maybe there's another way?' said Rincewind.

'What makes you think that?'

'The note asks for the Librarian.'

In the heat of the night, magic moved on silent feet.

One horizon was red with the setting sun. This world went around a central star. The elves did not know this and, if they had done, it would not have bothered them. They never bothered with detail of that kind. The universe had given rise to life in many strange places, but the elves were not interested in that, either.

This world had created lots of life. Up until now, none of it had ever had what the elves considered to be potential. But this time, there was definite promise.

Of course, it had iron, too. The elves hated iron. But this time, the rewards were worth the risk. This time ...

One of them signalled. The prey was close at hand. And now they saw it, clustered in the trees around a clearing, dark blobs against the sunset.

The elves assembled. And then, at a pitch so strange that it entered the brain without the need to use the ears, they began to sing.

TWO

THE UMPTY-UMPTH ELEMENT

Discworld runs on magic, Roundworld runs on rules, and even though magic needs rules and some people think rules are magical, they are quite different things. At least, in the absence of wizardly interference. This was the main scientific message of our last book, The Science of Discworld. There we charted the history of the universe from the Big Bang through to the creation of the Earth and the evolution of a not especially promising species of ape. The story ended with a final fast-forward to the collapse of the space elevator by which a mysteri­ous race (which could not possibly have been those apes, who were only interested in sex and mucking about) had escaped from the planet. They had left the Earth because a planet is altogether too dan­gerous a place to live, and had headed out into the galaxy in search of safety and a long-term chance of a decent pint.

The Discworld wizards never found out who the builders of the space elevator on Roundworld were. We know that they were us, the descendants of those apes, who'd brought sex and mucking about to high levels of sophistication. The wizards missed that bit, although, to be fair, the Earth had been in existence for over four billion years, and apes and humans were present only for a tiny percentage of that time. If the entire history of the universe were compressed to one day, we would have been present for the final 20 seconds.

Quite a lot of interesting things happened on Roundworld while the wizards were skipping ahead, and now, in this present book, the wiz­ards are going to find out what those things were. And of course they're going to interfere, and inadvertently create the world we live in today, just as their interference in the Roundworld Project inadver­tently created our entire universe. It has to work like that, doesn't it? That's how the story goes.

Seen from outside, as it sits in Rincewind's office, the entire human universe is a small sphere. Large quantities of magic went into its man­ufacture and, paradoxically, into maintaining its most interesting feature. Which is this: Roundworld is the only place on Discworld where magic does not work. A strong magical field protects it from the thaumic energies that surge around it. Inside Roundworld, things don't happen because people want them to or because they make a good narrative: they happen because the rules of the universe, the so-called 'laws of nature', make them happen.

At least, that was a reasonable way to describe things ... until human beings evolved. At that point, something very strange happened to Roundworld. It began, in various ways, to resemble Discworld. The apes acquired minds, and their minds started to interfere with the nor­mal running of the universe. Things started to happen because human minds wanted them to. Suddenly the laws of nature, which up to that point had been blind, mindless rules, were infused with purpose and intention. Things started to happen for a reason, and among these things that happened was reasoning itself. Yet this dramatic change took place without the slightest violation of the same rules that had, up to that point, made the universe a place without purpose. Which, on the level of the rules, it still is.

This seems like a paradox. The main content of our scientific com­mentary, interleaved between successive episodes of a Discworld story, will be to resolve that paradox: how did Mind (capital 'M' for 'meta­physical') come into being on this planet? How did a Mindless universe make up its own Mind? How can we reconcile human free will (or its semblance) with the inevitability of natural law? What is the rela­tion between the 'inner world' of the mind and the allegedly objective 'outer world' of physical reality?

The philosopher Rene Descartes argued that the mind must be built from some special kind of material - mind-stuff that was different from ordinary matter, indeed undetectable using ordinary matter. Mind was an invisible spiritual essence that animated otherwise unthinking matter. It was a nice idea, because it explained at a stroke why Mind is so strange, and for a long time it was the conventional view. Nevertheless, today this concept of 'Cartesian duality' has fallen out of favour. Nowadays only cosmologists and particle physicists are allowed to invent new kinds of matter when they want to explain why their theories totally fail to match observed reality. When cosmologists find that galaxies are rotating at the wrong speeds in the wrong places, they don't throw away their theories of gravitation. They invent 'cold dark matter' to fill in the missing 90 per cent of the mass of the uni­verse. If any other scientists did that kind of thing, people would throw up their hands in horror and condemn it as 'theory saving'. But cos­mologists seem to get away with it.

One reason is that this idea has many advantages. Cold dark mat­ter is cold, dark and material. Cold means that you can't detect it by the heat radiation that it throws off, because it doesn't. Dark means that you can't detect it by the light that it emits, because it doesn't. Matter means that it's a perfectly ordinary material thing (not some silly invention like Descartes' immaterial mind-stuff). Having said that, of course, cold dark matter is totally invisible, and it's definitely not the same as conventional matter, which isn't cold and isn't dark ...

To their credit, the cosmologists are trying very hard to find a way to detect cold dark matter. So far, they've discovered that it does bend light, so you can 'see' lumps of cold dark matter by the effect they have on images of more distant galaxies. Cold dark matter creates mirage-like distortions in the light from distant galaxies, smearing them out into thin arcs, centred on the lump of missing mass. From those distortions, astronomers can re-create the distribution of that otherwise invisible cold dark matter. The first results are coming in now, and within a few years it will be possible to survey the universe and find out whether the missing 90 per cent of matter really is there, cold and dark as expected, or whether the whole idea is nonsense.

Descartes' similarly invisible, undetectable mind-stuff has had a very different history. At first, its existence seemed obvious: minds simply do not behave like the rest of the material world. Then, its existence seemed obvious nonsense, because you can chop a brain into pieces, preferably after ensuring that its owner has previously departed this world, and look for its material constituents. And when you do, there's nothing unusual there. There's lots of complicated proteins, arranged in very elaborate ways, but you won't find a single atom of mind-stuff. We can't yet dissect a galaxy, so for now cosmologists can get away with their absurd invention of a face-saving new material. Neuroscientists, trying to explain the mind, have no such luxury. Brains are much easier to pull apart than galaxies.

Despite the change in current conventional wisdom, there remain a few diehard dualists who still believe in special mind-stuff. But today, nearly all neuroscientists believe that the secret of Mind lies in the structure of the brain, and even more importantly, in the processes that the brain carries out. As you read these words, you experience a strong sense of Self. There is a You that is doing the reading, and think­ing about the words and the ideas they express. No scientist has ever dissected out the bit of the brain that contains this impression of You. Most suspect that no such bit exists: instead, you feel like You because of the overall activity of your entire brain, plus the nerve fibres that are connected to it, bringing it sensations of the outside world and allowing it to control the movement of your arms, legs and fingers. You feel like you, in fact, because you are busily being You.

Mind is a process carried out within a brain made of perfectly ordi­nary matter, in accordance with the rules of physics. It is, however, a very strange process. There is a kind of duality, but it is a duality of interpretation rather than of physical material. When you think a thought - about, let us say, the Fifth Elephant that slipped off the back of Great A'Tuin, orbited in an arc of a circle and crashed on to the surface of the Discworld - the same physical act of thinking that thought has two distinct meanings.

One of them is straightforward physics. In your brain, various elec­trons are surging to and fro in various nerve fibres. Chemical molecules are combining together, or breaking up, to make new ones. Modern sensing apparatus, such as the PET scanner, can reconstruct a three-dimensional image of your brain, showing which regions are active when you are thinking about that elephant. Materially, your brain is buzzing in some complicated way. Science can see how it is buzzing, but it can't (yet) extract the elephant.

That's the second interpretation. From inside, so to speak, you have no sensation of those buzzing electrons and reacting chemicals. Instead, you have a very vivid impression of a large grey creature with flappy ears and a trunk, sailing improbably through space and crashing disastrously to the ground. Mind is what it feels like to be a brain. The same physical events acquire a totally different meaning when viewed from the inside. One task of science is to try to bridge the gap between those two interpretations. The first step is to figure out which bits of the brain do what when you think a particular thought. To reconstruct, in fact, the elephant from the electrons. That's not yet possible, but every day brings it a step closer. Even when sci­ence gets there, it will probably not be able to explain why your impression of that elephant is so vivid, or why it takes exactly the form that it does.

In the study of consciousness there is a technical term for what a perception 'feels like'. It is called a quale (pronounced 'kwah-lay', not 'quail'), a figment that our minds paint on to their model of the uni­verse in the way that an artist adds pigment to a portrait. Such qualia (plural) paint the world in vivid colours so that we can respond more quickly to it, and, in particular, respond to signs of danger, food, pos­sible sexual partners ... Science has no explanation of why qualia feel like they do, and it's not likely to get one. So science can explain how a mind works, but not what it is like to be one. No shame in that: after all, physicists can explain how an electron works, but not what it is like to be one. Some questions are beyond science. And, we suspect, beyond anything else: it is easy enough to claim an explanation of these metaphysical problems, but just as impossible to prove you're right. Science admits it can't handle these things, so at least it's honest.

At any rate, the science of the mind (small 'M' now because we're not talking metaphysics) addresses how the mind works, and how it evolved, but not what it's like to be one. Even with this limitation, the science of the brain is not the whole story. There is another important dimension to the question of Mind. Not how the brain works and what it does, but how it came to be like that.

How, on Roundworld, did Mind evolve from mindless creatures?

Much of the answer lies not inside the brain, but in its interactions with the rest of the universe. Especially other brains. Human beings are social animals, and they communicate with each other. The trick of communication made a huge, qualitative change to the evolution of the brain and its ability to house a mind. It accelerated the evolu­tionary process, because the transfer of ideas happens much faster than the transfer of genes.

How do we communicate? We tell stories. And that, we shall argue, is the real secret of Mind. Which brings us back to Discworld, because on Discworld things really do work the way human minds think they do on Roundworld. Especially when it comes to stories.

Discworld runs on magic, and magic is indissolubly linked to Narrative Causality, the power of story. A spell is a story about what a person wants to happen, and magic is what turns stories into reality. On Discworld, things happen because people expect them to. The sun comes up every day because that's its job: it was set up to provide light for the people to see by, and it comes up during the day when people need it. That's what suns do; that's what they're for. And it's a proper, sensible sun, too: a smallish fire not very far away, which goes over and under the Disc, incidentally but entirely logically causing one of the elephants to lift a leg to let it pass. It's not the ridiculous, pathetic kind of sun that we have - absolutely gigantic, infernally hot, and nearly a hundred million miles away because it's too dangerous to be near. And we go round it instead of it going round us, which is crazy, especially since what every human being on the planet sees, other than the visually impaired, is the latter. It's a terrible waste of mater­ial just to make daylight ...

On Discworld, the eighth son of an eighth son must become a wiz­ard. There's no escaping the power of story: the outcome is inevitable. Even if, as in Equal Rites, the eighth son of an eighth son is a girl. Great A'Tuin the turtle must swim though space with four elephants on its back and the entire Discworld on top of them, because that's what a world-bearing turtle has to do. The narrative structure demands it. Moreover, on Discworld everything that there is exists as a thing. To use the philosophers' language, concepts are reified: made real. Death is not just a process of cessation and decay: he is also a person, a skeleton with a cloak and a scythe, and he TALKS LIKE THIS. On Discworld, the narrative imperative is reified into a substance, narrativium. Narrativium is an element, like sulphur or hydrogen or uranium. Its symbol ought to be something like Na, but thanks to a bunch of ancient Italians that's already reserved for sodium (so much for So). So it's probably Nv, or maybe Zq given what they've done to sodium. Be that as it may, narrativium is an element on Discworld, so it lives somewhere in the Disc's analogue of Dmitri Mendeleev's periodic table. Where? The Bursar of Unseen University, the only wizard insane enough to understand imaginary numbers, would doubtless tell us that there is no question: it is the umpty-umpth element.

Discworld narrativium is a substance. It takes care of narrative imper­atives, and ensures they are obeyed. On Roundworld, our world, humans act as if narrativium exists here, too. We expect it not to rain tomorrow because the village fair is on, and it would be unfair (in both senses) if rain spoiled the occasion.

Or, more often, given the pessimistic ways of our country folk, we expect it to rain tomorrow because the village fair is on. Most people expect the universe to be mildly malevolent but hope it will be kindly disposed, whereas scientists expect it to be indifferent. Drought-struck farmers pray for rain, in the express hope that the universe or owner thereof will hear their words and suspend the laws of meteorology for their benefit. Some, of course, actually believe just that, and for all any­one can prove, they could be right. This is a tricky question, and a delicate one; let us just say that no reputable scientific observer has yet caught God breaking the laws of physics (although of course He might be too clever for them) and leave it at that for the moment.

And this is where Mind takes centre stage.

The curious thing about the human belief in narrativium is that once humans evolved on the planet, their beliefs started to be true. We have, in a way, created our own narrativium. It exists in our minds, and there it is a process, not a thing. On the level of the material universe, it's just one more pattern of buzzing electrons. But on the level of what it feels like to be a mind, it operates just like narrativium. Not only that: it operates on the material world, not just the mental one: its effects are just like those of narrativium. Generally our minds control our bodies - sometimes they don't, and indeed sometimes it's the other way round, especially during adolescence - and our bodies make things happen out there in the material world. Within each person there is a 'strange loop', which confuses the mental and material levels of existence.

This strange loop has a curious effect on causality. We get up in the morning and leave the house at 7.15 because we have to get to work by 9 o'clock. Scientifically, this is a very bizarre form of causality: the future is affecting the past. That doesn't normally occur in physics (except in very esoteric Quantum things, but let's not get distracted). In this case, science has an explanation. What causes you to get up at 7.15 is not actually your future arrival at work. If in fact you fall under a bus and never make it to work, you still got up at 7.15. Instead of backwards causality, you have a mental model, in your brain, which is your best attempt to predict the day ahead. In that model, realised as buzzing electrons, you think that you ought to be at work by nine. That model, and its expectation of the future, exists now, or more accu­rately, a short time in the past. It is that expectation that causes you to get up instead of lying in and having a well-deserved snooze. And the causality is entirely normal: from past to future by way of actions taking place in the present.

So that's all right then. Except that when you think of it, the causal­ity is still very strange. A few electrons, buzzing in ways that are meaningless from the outside of the brain in which they reside, lead to a coherent action by a 70-kilogram lump of protein. Well, at that time in the morning it's not a very coherent lump of protein, but you understand what we mean. That's why we call this very creative piece of confusion a strange loop.

Those mental models are stories, simplified narratives that corre­spond in a rough-hewn way to aspects of the world that we consider to be important. Note that 'we': all mental models are infected with human biases. Our minds tell us stories about the world, and we base a great many of our actions on what those stories say. Here, the story is 'the person who arrived at work late and was fired from their job'. That story alone will lever us out of bed at an unearthly hour, even if we get on well with the boss and fondly imagine that the story doesn't apply to us. In other words, we make up our world according to the stories that we tell ourselves, and each other, about it.

We build minds in our children that way, too. The Western child is brought up on stories like the time Winnie the Pooh went to Rabbit's house, ate too much honey and got stuck in the entrance hole on the way out. The story tells us not to be too greedy; that terrible things will happen to us if we are. Even the child knows that Winnie the Pooh is fiction, but they understand what the story is about. It does­n't lead them to avoid pigging out on honey, and it doesn't make them worry about getting stuck in the doorway when they try to leave the room after having eaten too much dinner. The story isn't about literal interpretations. It's a metaphor, and the mind is a metaphor machine.

The power of narrativium in Roundworld is immense. Things happen because of it that you would never expect from the laws of nature. For example, the laws of nature pretty much forbid an Earthbound object suddenly leaping up into space and landing on the Moon. They don't say it's impossible, but they do imply that you could wait a very long time indeed before it happened. Despite this, there is a machine on the Moon. Several. They all used to be down here. They are there because, centuries ago, people told each other romantic tales about the Moon. She was a goddess, who looked down on us. When full, she caused werewolves to change from humans into animals. Even then, humans were quite good at doublethink; the Moon was clearly a big silver disc, but, at the same time, she was a goddess.

Slowly those tales changed. Now the Moon was another world, and by harnessing the power of swans we could fly there in a chariot. Then (Jules Verne suggested) we could get there in a hollowed-out cylinder fired by a giant gun, located in Florida. Finally, in the 1960s, we found the right kind of swan (liquid oxygen and hydrogen) and the right kind of chariot (several million tons of metal) and we flew to the Moon. In a hollowed-out cylinder, launched from Florida. It wasn't exactly a gun. Well, actually it was in a basic physical sense; the rocket was the gun and it went along for the ride, firing burnt fuel in place of a bullet.

If we'd not told ourselves stories about the Moon, there would have been no point in going there at all. An interesting view, maybe ... but we 'knew' about the view only because we had told ourselves scien­tific stories about images sent back by space probes. Why did we go? Because we'd been telling ourselves that we would, one day, for sev­eral hundred years. Because we'd made it inevitable and introduced it into the 'future story' of a great many people. Because it satisfied our curiosity, and because the Moon was waiting. The Moon was a story waiting to be finished ('First human lands on the Moon!'), and we went there because the story demanded it.

When Mind evolved on Earth, a kind of narrativium evolved along­side it. Unlike the Discworld variety of narrativium, which on the Disc is just as real as iron or copper or praseodymium, our variety is purely mental. It is an imperative, but the imperative has not been reified into a thing. However, we have the sort of mind that respond to impera­tives, and to many other non-things. And so it feels to us as if our universe runs on narrativium.

There is a curious resonance here, and 'resonance' is definitely the word. Physicists tell a story about how carbon forms in the universe. In certain stars there is a particular nuclear reaction, a 'resonance' between nearby energy levels, which gives nature a stepping-stone from lighter elements to carbon. Without that resonance, so the story goes, carbon could not have formed. Now, the laws of physics as we currently understand them involve several 'fundamental constants', such as the speed of light, Planck's constant in quantum theory, and the charge on an electron. These numbers determine the quantitative implications of the physical laws, but any choice of constants sets up a potential universe. The way that a universe behaves depends on the actual numbers that are used in its laws. As it happens, carbon is an essential constituent of all known life. All of which leads up to a clever little story called the Anthropic Principle: that it's silly for us to ask why we live in a universe whose physical constants make that nuclear resonance possible - because if we didn't, there'd be no carbon, hence no us to ask about it.

The story of the carbon resonance can be found in many science books, because it creates a powerful impression of hidden order in the universe, and it seems to explain so much. But if we look a little more closely at this story, we find that it is a beautiful illustration of the seductive power of a compelling but false narrative. When a story seems to hang together, even consciously self-critical scientists can fail to ask the question that makes it fall apart.

Here's how the story goes. Carbon is created in red giant stars by a rather delicate process of nuclear synthesis, called the triple-alpha process. This involves the fusion of three helium nuclei. A helium nucleus contains two protons and two neutrons. If you fuse three helium nuclei together, you get six protons and six neutrons. That, as it happens, is a carbon nucleus.

All very well, but the odds on such a triple collision occurring inside a star are very small. Collisions of two helium nuclei are much more common, though still relatively rare. It is extremely rare for a third helium nucleus to crash into two that are just colliding. It's like paint-balls and wizards. Every so often, a paintball will go splat! against a wizard. But you wouldn't bet a lot of money on a second paintball hit­ting him at the exact same moment. This means that the synthesis of carbon has to take place in a series of steps rather than all at once, and the obvious way is for two helium nuclei to fuse, and then for a third helium nucleus to fuse with the result.

The first step is easy, and the resulting nucleus has four protons and four neutrons: this is one form of the element beryllium. However, the lifetime of this particular form of beryllium is only 10^-6 seconds, which gives that third helium nucleus a very small target to aim at. The chance of hitting this target is incredibly small, and it turns out that the universe hasn't existed long enough for even a tiny fraction of its carbon to have been made in this way. So triple collisions are out, and carbon remains a puzzle.

Unless ... there is a loophole in the argument. And indeed there is. The fusion of beryllium with helium, leading to carbon, would occur much more rapidly, yielding a lot more carbon in a much shorter time, if the energy of carbon just happens to be close to the combined ener­gies of beryllium and helium. This kind of near-equality of energies is called a resonance. In the 1950s Fred Hoyle insisted that carbon has to come from somewhere, and predicted that there must therefore exist a resonant state of the carbon atom. It had to have a very specific energy, which he calculated must be about 7.6 MeV.

Within a decade, it was discovered that there is a state with energy 7.6549 MeV. Unfortunately, it turns out that the combined energies of beryllium and helium are about 4 per cent higher than this. In nuclear physics, that's a huge error.

Oops.

Ah, but, miraculously, that apparent discrepancy is just what we want. Why? Because the additional energy imparted by the tempera­tures found in a red giant star is exactly what's needed to change the combined energy of beryllium and helium nuclei by that missing 4 per cent.

Wow.

It's a wonderful story, and it rightly earned Hoyle huge numbers of scientific brownie-points. And it makes our existence look rather delicate. If the fundamental constants of the universe are changed, then so is that vital 7.6549. So it is tempting to conclude that our universe's constants are fine-tuned for carbon, making it very special indeed. An it is equally tempting to conclude that the reason for that fine-tuning is to ensure that complex life turns up. Hoyle didn't do that, but many other scientists have given into these temptations.

Sounds good: what's wrong? The physicist Victor Stenger calls this kind of argument 'cosmythology'. Another physicist, Craig Hogan has put his finger on one of the weak points. The argument treats the temperature of the red giant and that 4 per cent discrepancy in energy levels as if they were independent. That is, it assumes that you can change the fundamental constants of physics without changing the way a red giant works. However, that's obvious nonsense. Hogan points out that 'the structure of stars includes a built-in thermostat that automatically adjusts the temperature to just the value needed to make the reaction go at the correct rate'. It's rather like being amazed that the temperature in a fire is just right to burn wood, when in fact that temperature is caused by the chemical reaction that burns the wood. This kind of failure to examine the interconnectedness of nat­ural phenomena is a typical, and quite common, error in anthropic reasoning.

In the human world, what counts is not carbon, but narrativium. And in that context we wish to state a new kind of anthropic princi­ple. It so happens that we live in a universe whose physical constants are just right for carbon-based brains to evolve to the point at which they create narrativium, much as a star creates carbon. And the nar­rativium does crazy things, like putting machines on the Moon. Indeed, if carbon did not (yet) exist, then any narrativium-based lifeform could find some way to manufacture it, by telling itself a really gripping story about the need for carbon. So causality in this universe is irredeemably weird. Physicists like to put it all down to the fundamental constants, but it's more likely an example of Murphy's law.

But that's another story.

The more we think about narrative in human affairs, the more we see that our world revolves around the power of story. We build our minds by telling stories. Newspapers select news according to its value as a story, not according to how intrinsically important it is. 'England loses cricket match to Australia' is a story (though not a very surprising one) and it goes on the front page. 'Doctors think that they may have improved the diagnosis of liver disease by 1 per cent' is not a story, even though most science works like that (and in years to come, depending on the state of your liver, you might think it's a rather more important story than a cricket match).

'Scientist claims cure for cancer' is a story, though, even if the supposed cure is nonsense. So are 'spiritualist medium claims a cure for cancer', and 'Secret code predictions hidden in the Bible', more's the pity.

As we write, there is a furore over a small group of people who are proposing to clone a human being. It's a major story, but very few newspapers are reporting the most likely result of this attempt, which will be abject failure. It took 277 failures, many rather nasty, before Dolly the Sheep was cloned, and she has now been found to have serious genetic defects, poor lamb.

Trying to clone a human may indeed be unethical, but that's not the best reason for objecting to this misguided and foolish attempt. The best reason is that it won't work, because nobody yet knows how to overcome numerous technical obstacles; moreover, if by some stroke of (mis)fortune it did happen to work, any child produced would have serious defects. Producing such a child, now that is unethical.

Making 'carbon copies' of human beings, which is the usual basis of the newspapers' story about the ethics, is beside the point. That's not what cloning does, anyway. Dolly the Sheep was not genetically identical to her mother, though she came close. Even if she had been, she would still have been a different sheep, moulded by different expe­riences. For that matter, the same would be true even if she was genetically identical to her mother. For the same reason, cloning a dead child will not bring that child back to life. Much of the media discus­sion of the ethics of cloning, like much of the public understanding of science, is vaguely stirred through with science fiction. In this arena, as in so many, the power of the story outweighs any questions about the real factual basis.

Human beings do not just tell stories, or just listen to them. The are more like Granny Weatherwax, who is aware of the power of stories on Discworld, and refuses to be trapped by the story's narrativium. Instead, she uses the power of story to mould events according to her own wishes. Roundworld priests, politicians, scientists, teachers and journalists have learned to use the power of story to get their messages across to the public, and to manipulate or persuade people to behave in particular ways. The 'scientific method' is a defense mechanism against that kind of manipulation. It tells you not to believe things because you want them to be true. The proper scientific response to any new discovery or theory, especially your own, is to look for ways to disprove it. That is, to try to find a different story that explains the same things.

The anthropologists got it wrong when they named our species Homo sapiens ('wise man'). In any case it's an arrogant and bigheaded thing to say, wisdom being one of our least evident features. In reality, we are Pan narrans, the storytelling chimpanzee.

At this point, the structure of The Science of Discworld 2: The Globe becomes very self-referential. You will need to bear that in mind as we proceed. The book is itself a story - no - two intertwined stories One, the odd-numbered chapters, is a Discworld fantasy. The other - the even-numbered chapters, is a story of the science of the Mind (metaphysical again). The two are closely related, designed to fit together like foot and glove; the science story is presented as a series of Very Large Footnotes to the fantasy story.

So far, so good ... but it gets more complicated. When you read a Discworld story, you play a curious mental game. You react as if the story is true, as if Discworld actually exists, as if Rincewind and the Luggage are real, and Roundworld is but a fragment of a long-forgotten dream. (Please stop interrupting, Rincewind, we know it's different from your point of view. Yes, of course we're the ones that don't exist, we're bundles of rules whose consequences take place only inside a small globe on a dusty shelf in Unseen University. Yes, we do appreciate that, and will you please shut up?) Sorry about that.

People have become very good at playing this game, and we will exploit that by setting Earth and Discworld on the same narrative level, so that each illuminates the other. In the first book, The Science of Discworld, the Discworld defined what is real. That's why reality makes such good sense. Roundworld is a magical construct, designed to keep the magic out, and that's why it makes no sense at all (to wizards, at least). In this sequel Earth acquires inhabitants, the inhabitants acquire minds, and minds do strange things. They bring narrativium to a story-less universe.

A computer can do a billion sums in the blink of a keystroke and get them all right, but it couldn't pretend to be a cowardly wizard if one walked up to it and thumped it on the memory cache. In contrast, we can think ourselves inside the mind of a cowardly wizard with ease, or recognize someone else when they're acting the part of one, but we're completely lost when it comes to doing several million sim­ple sums a second. Even though, to someone not of this universe, that might appear to be a simpler task.

That's because we run on narrativium, and computers don't.

THREE

JOURNEY INTO L-SPACE

It was three hours later, in the cool of Unseen University. Not much had changed in the High Energy Magic building, except that a screen had been set up to show the output of Ponder's iconograph projector.

'I don't see why you need it,' said Rincewind. 'There's only the two of us.'

'Ook,' agreed the Librarian. He was annoyed at having been woken from a doze in his library. It had been a very gentle awakening, sine no one wakes up a 300 lb orangutan roughly (twice, at least) but he was still annoyed.

'The Archchancellor says that we've got to be more organized about these things,' said Ponder. 'He says it's no use just shouting out "Hey, I've got a great idea!" These things have got to be presented properly. Are you ready?'

The very small imp that ran the projector raised a tiny thumb.

'Very well,' said Ponder. 'First slide. This is the Roundworld as it cur­rently-'

'It's the wrong way up,' said Rincewind.

Ponder looked at the image.

'It's a ball,' he snarled. 'It's floating in space. How can it be the wrong way up?'

'That crinkly continent should be at the top.'

'Very well!' snapped Ponder. 'Imp, turn it around. Right? Satisfied?'

'It's the right way up but now it's the wrong way arou-' Rincewind began.

There was a thwack as Ponder's pointer stick smacked into the screen. 'This is the Roundworld!' he snapped. 'As it exists at present! A world covered in ice! But time on Roundworld is subordinate to time in the real world! All times in Roundworld are accessible to us, in the same way that all pages in a book, though consecutive, are accessible to us! I have ascertained that the Faculty are on Roundworld but not in what appears to be the present time! They are several hundred mil­lion years in the past! Which is, from our point of view, perfectly capable of also being the present! I don't know how they got there! It should not be physically possible! Hex has located them! We have to assume that they can't get back the way they came! However - next slide please!'

Click!

'It's the same one,' said Rincewind. 'But now it's sideways-'

'A globe has no sideways!' said Ponder. There was a tinkle of break­ing glass from the direction of the projector, and some very small cursing.

'I just thought you wanted to do it properly,' murmured Rincewind. 'Anyway, this is going to be about L-space, isn't it? I know it is. You know it is.'

'Yes, but I don't say that yet! I've got another dozen slides to come!' gasped Ponder. 'And a flow chart!'

'But it is, isn't it,' said Rincewind wearily. 'I mean, they say they've found other wizards. That means libraries. That means you can get there through L-space.'

'I was going to say that's how we can get there,' said Ponder.

Yes, I know,' said Rincewind. 'That's why I thought I'd take the opportunity of saying "you" at this early juncture.'

'How can there be wizards on Roundworld?' said Ponder. 'When we know magic doesn't work there?'

'Search me,' said Rincewind. 'Ridcully did say they're useless.'

'And why can't the faculty come back by themselves? They were able to send the bottle! That must have used magic, surely?'

'Why not just go and ask them?' said Rincewind.

'You mean by homing in on the distinctive biothaumic signature of a group of wizards?'

'Well, I was thinking of waiting until something dreadful happened and you going to have a look in the wreckage,' said Rincewind. 'But the other stuff would probably work.'

"The omniscope locates them in approximately the 40,002,730,907^th century,' said Ponder, staring at the globe. 'I can't get an image. But if we can find a way to the nearest library-'

'Ook!' said the Librarian. And then he ooked some more. He ooked at length, with an occasional eek. Once he thumped his fist on the table. He didn't need to thump the table a second time. There wasn't, at that point, much in the way of table left to thump.

'He says only very senior librarians can use L-space,' said Rincewind, as the Librarian folded his arms. 'He was quite emphatic. He says it's not to be treated like some kind of magic funfair ride.'

'But it's an order from the Archchancellor!' said Ponder. 'There isn't any other way to get there!'

The Librarian looked a little uncertain at that. Rincewind knew why. It was hard to be an orangutan in Unseen University, and the only way the Librarian had been able to deal with it was by acknowledging Mustrum Ridcully as the alpha male, even though the Archchancellor seldom climbed up to a high place on the rooftops and called mourn­fully over the city at dawn. This meant that, unlike the other wizards, he found it very hard to shrug off an archchancelloric command. It was a direct, fang-revealing, chest-beating challenge. Rincewind had an idea.

'If we put the globe in the Library,' he said to the ape, 'then that would mean that even though you are travelling in L-space you would not be taking Mr. Stibbons anywhere outside the Library. I mean, the globe would be inside the library, so even though you'd wind up in the globe, you really wouldn't have travelled very far at all. A few feet, maybe. The globe's only infinite on the inside, after all.'

'Well, Rincewind, I am impressed,' said Ponder, while the Librarian looked perplexed. 'I'd always thought of you as rather stupid, but that was a remarkable piece of verbal reasoning. If we put the globe down right on the Librarian's desk, say, then the whole journey would take place inside the library, right?'

'Exactly,' said Rincewind, who was prepared to overlook 'rather stupid' in view of this unexpected praise.

'And it's perfectly safe in the library, after all ...'

'Big thick walls. Very safe place,' Rincewind agreed.

'So, put like that, no harm will come to us,' said Ponder.

'There you go with the "us" again,' said Rincewind, backing away.

'We'll find them and bring them back!' said Ponder. 'How hard can it be?'

'It can be incredibly hard! There's elves there! You know elves! They are dangerous! Drop your guard for a moment and they can control your mind!'

'They chased me through some woods once,' said Ponder. 'They are very frightening. I remember writing that down in my diary.'

'You wrote down in your diary that you were scared?'

Yes. Why not? Don't you?'

'I haven't got a big enough diary. But it makes no sense! There's nothing on the Roundworld that elves would be interested in! They like to have ... slaves. And we've never seen anything evolve that's bright enough to be a slave.'

'You might have missed something,' said Ponder.

'No, I say you, you say we,' said Rincewind.

They both stared at the globe.

'Look, it's like having a pot plant,' said Ponder. 'If it has greenfly, you try to squash them.'

'I never do that,' said Rincewind. 'Greenfly may be small, but there's a lot of them ...'

'It was a metaphor, Rincewind,' said Ponder, wearily.

'... I mean, supposing they decide to gang up?'

'Rincewind, you are the only other person here who knows any­thing at all about Roundworld. You will come with us or ... or ... I'll tell the Archchancellor about the seven buckets.'

'How do you know about the seven buckets?'

'And I'll explain to him how all of your jobs could easily be done by a simple set of instructions for Hex, too. It'd take me about, oh, thirty seconds. Let's see ...

# Rincewind

SUB WAIT

WAIT

RETURN

Or possibly

RUN RINCEWIND'

'You wouldn't do that!' said Rincewind. 'Would you?'

'Certainly. Now, are you coming? Oh, and bring the Luggage.'

Knowledge = power = energy = matter = mass, and on that simple equation rests the whole of L-space. It is via L-space that all books are connected (quoting the ones before them, and influencing the ones that come after). But there is no time in L-space. Nor is there, strictly speaking, any space. Nevertheless, L-space is infinitely large and connects all libraries, everywhere and everywhen. It's never further than the other side of the bookshelf, yet only the most senior and respected librarians know the way in.

From inside, L-space looked to Rincewind like a library designed by someone who did not have to worry about time, budget, strength of materials or physics. There are some laws, though, that are coded into the very nature of the universe, and one is: There Is Never Enough Shelf Space.

He turned and looked back. They'd entered L-space by walking through what had looked like a solid wall of books. He knew it was a solid wall, he'd taken books off those shelves before now. You had to be a very senior Librarian indeed to know in what precise circumstances you could step straight through it.

He could still see the library through the gap, but it faded from view as he watched. What remained was books. Mountains of books. Hills and valleys of books. Perilous precipices of books. Even in what passed for the sky, which was a sort of blue grey, there was a distant suggestion of books. There is never enough shelf space, anywhere.

Ponder was carrying a considerable amount of magical equipment. Rincewind, being a more experienced traveller, was carrying as little weight as possible. Everything else was being carried by the Luggage, which looked like a sea chest but with a number of pink, human-like and fully operational feet.

'Under the rules of the Roundworld, magic can't work,' said Ponder, as they followed the Librarian. 'Won't the Luggage stop existing?'

'It's worth a try,' said Rincewind, who felt that owning a semi-sapient and occasionally homicidal box on legs reduced his opportu­nities to make live friends, 'but it doesn't usually worry about rules. They bend round it. Anyway, it's already been there before, for a very long time, without any damage. To the Luggage, anyway.'

The walls of books shifted as the wizards approached; in fact, each step radically changed the nature of the bookscape which was in any case, said Ponder, a mere metaphorical depiction created by their brains to allow them to deal with the unimaginable reality. The shift­ing perspective would have given most people a serious headache at least, but Unseen University had rooms where the gravity moved around during the course of a day, one corridor of infinite length and several windows that only existed on one side of their walls. Life at UU reduced your capacity for surprise by quite a lot.

Occasionally the Librarian would stop, and sniff at the books near­est to him. At last he said 'ook', quietly, and pointed to another stack of books. There were, drawn gently on the spine of an old leather-bound volume, some chalk marks.

'Librarian-sign,' said Rincewind. 'He's been here before. We're close to Roundworld book-space.'

'How could he-' Ponder began, and then said: 'Oh. I see. Er ... Roundworld exists in L-space even before we created it? I mean yes, obviously I know that's true, but even so-'

Rincewind took a book from a pile near him. The cover was brightly coloured and made of paper, suggesting an absence of cows on the originating world, and had the title: Sleep Well My Lovely Falcon. The words inside made even less sense.

'It might not have been worth our trouble,' he said.

The Librarian said 'ook', which Rincewind understood as 'I'm going to get into real trouble with the Secret Masters of the Library for this day's work'.

Then the ape appeared to triangulate on the bookscape around him and knuckled forward, and vanished.

Ponder looked at Rincewind. 'Did you see how he did that?' he said and then a hairy red arm appeared out of the air and jerked him off his feet. A moment later the same thing happened to Rincewind.

It wasn't much of a library, but Rincewind knew how this worked. Two books were a library - for a lot of people, two books were an enormous library. But even one book could be a library, if it was a book that made a big enough dimple in L-space. A book with a title like 100 Ways with Broccoli was unlikely to be one such, whereas A Relationship Between Capital and Labour might be, especially if it has an appendix on making explosives. The deeply magical and interminably ancient volumes in the Library of UU strained the fabric L-space like a baby elephant on a worn-out trampoline, leaving it so thin that the Library was a potent and easy portal.

Sometimes, though, even one book could do that. Even one line. Even one word, in the right place and the right time.

The room was large, panelled and sparsely furnished. Quite a lot of paperwork was strewn on a desk. Quill pens lay by an inkwell. A win­dow looked out on to broad gardens, where it was raining. A skull lent a homely touch.

Rincewind leaned down and tapped it.

'Hello?' he said. He looked up at the others.

'Well, the one in the Dean's office can sing comic songs,' he said defensively. He stared at the paperwork on the desk. It was covered in symbols which had a magical look, although he didn't recognise any of them. On the other side of the room, the Librarian was leafing through one of the books. Strangely, they weren't on shelves. Some were neatly piled, others locked in boxes, or at least in boxes that were locked until the Librarian tried to lift the lid.

Occasionally he pursed his lips and blew a disdainful raspberry.

'Ook,' he muttered.

'Alchemy?' said Rincewind. 'Oh dear. That stuff never works.' He lifted up what looked like a small leather hatbox, and removed the lid. 'This is more like it!' he said, and pulled out a ball of smoky quartz. 'Our man is definitely a wizard!'

'This is very bad,' said Ponder, staring at a device in his hand. "Very, very bad indeed.'

'What is?' said Rincewind, turning around quickly.

'I'm reading a very high glamour quotient,' said Ponder.

'There's elves here?'

'Here? The place is practically elvish!' said Ponder. 'The Archchancellor was right.'

All three explorers stood quietly. The Librarian's nostrils flared. Rincewind sniffed, very cautiously.

'Seems okay to me,' he said, at last.

Then a man in black entered the room. He came in quickly, open­ing the door no more than necessary, in a kind of aggressive sidle, and stopped in astonishment. Then his hand flew to his belt and he drew a thin, businesslike sword.

He saw the Librarian. He stopped. And then it was really all over, because the Librarian could unfold his arm very fast and, importantly, there was a fist like a sledgehammer on the end of it.

As the dark figure slid down the wall, the crystal sphere in Rincewind's hand said: 'I believe I now have enough information. I advise departure from this place at a convenient opportunity and in any case before this gentleman awakes.'

'Hex?' said Ponder.

'Yes. Let me repeat my advice. Lack of absence from this place will undoubtedly result in metal entering the body.'

'But you're talking via a crystal ball! Magic doesn't work here!'

'Don't argue with a voice saying "run away"!' said Rincewind. 'That's good advice! You don't question it! Let's get out of here!'

He looked at the Librarian, who was sniffing along the bookshelves with a puzzled expression.

Rincewind had a sense for the universe's tendency to go wrong. He didn't leap to conclusions, he plunged headlong towards them.

'You've brought us out through a one-way door, haven't you ...' he said.

'Oook!'

'Well, how long will it take to find the way in?'

The Librarian shrugged and returned his attention to the shelves.

'Leave now,' said the crystal Hex. 'Return later. The owner of the house will be useful. But leave before Sir Francis Walsingham wakes up, because otherwise he will kill you. Steal his purse from him first. You will need money. For one thing, you will need to pay someone to give the Librarian a shave.'

'Oook?'

FOUR

THE ADJACENT POSSIBLE

The concept of L-space, short for 'Library-space', occurs in several of the Discworld novels. An early example occurs in Lords and Ladies, a story that is mostly about elvish evil. We are told that Ponder Stibbons is Reader in Invisible Writings, and this phrase deserves (and gets) an explanation:

The study of invisible writings was a new discipline made available by the discovery of the bi-directional nature of Library-space. The thaumic mathematics are complex, but boil down to the fact that all books, everywhere, affect all other books. This is obvious: books inspire other books written in the future, and cite books written in the past. But the General Theory of L-space suggests that, in that case, the contents of books as yet unwritten can be deduced from books now in existence.

L-space is a typical example of the Discworld habit of taking a metaphorical concept and making it real. The concept here is known as 'phase space', and it was introduced by the French mathematician Henri Poincare about a hundred years ago to open up the possibility of applying geometrical reasoning to dynamics. Poincare's metaphor has now invaded the whole of science, if not beyond, and we will make good use of it in our discussion of the role of narrativium in evolution of the mind.

Poincare was the archetypal absent-minded academic - no, come to think of it he was 'present-minded somewhere else', namely in his mathematics, and it's easy to understand why. He was probably the most naturally gifted mathematician of the nineteenth century. If you had a mind like his, you'd spend most of your time somewhere else too, revelling in the beauty of the mathiverse.

Poincare ranged over almost all of mathematics, and he wrote several best-selling popular science books, too. In one piece of research which single-handedly created a new 'qualitative' way of thinking about dynamics, he pointed out that when you are studying some physical system that can exist in a variety of different states, then it may be a good idea to consider the states that it could be in, but isn’t, as well as the particular state in which it is. By doing that, you set up a context that lets you understand what the system is doing, and why. This context is the 'phase space' of the system. Each possible state can be thought of as a point in that phase space. As time passes, the state changes, so this representative point traces out a curve, the trajectory of the system. The rule that determines the successive steps in the trajectory is the dynamic of the system. In most areas of physics, the dynamic is completely determined, once and for all, but we can extend, this terminology to cases where the rule involves possible choices. A good example is a game. Now the phase space is the space of possi­ble positions, the dynamic is the rules of the game and a trajectory is a legal sequence of moves by the players.

The formal setting and terminology for phase spaces is not as impor­tant, for us, as the viewpoint that they encourage. For example, you might wonder why the surface of a pool of water, in the absence of' wind or other disturbances, is flat. It just sits there, flat; it isn't even doing anything. But you start to make progress immediately if you ask the question 'what would happen if it wasn't flat?' For instance, why can't the water be piled up into a hump in the middle of the pond? Well, imagine that it was. Imagine that you can control the position of every molecule of water, and that you pile it up in this way, miracu­lously keeping every molecule just where you've placed it. Then, you let go. What would happen? The heap of water would collapse, and waves would slosh across the pool until everything settled down to that nice, flat surface that we've learned to expect. Again, suppose you arranged the water so that there was a big dip in the middle. Then as soon as you let go, water would move in from the sides to fill the dip.

Mathematically, this idea can be formalised in terms of the space of all possible shapes for the water's surface. 'Possible' here doesn't mean physically possible: the only shape you'll ever see in the real world, barring disturbances, is a flat surface. 'Possible' means 'conceptually possible'. So we can set up this space of all possible shapes for the surface as a simple mathematical construct, and this is the phase space for the problem. Each 'point' - location - in phase space represents a conceivable shape for the surface. Just one of those points, one state, represents 'flat'.

Having defined the appropriate phase space, the next step is to understand the dynamic: the way that the natural flow of water under gravity affects the possible surfaces of the pool. In this case, there is a simple principle that solves the whole problem: the idea that water flows so as to make its total energy as small as possible. If you put the water into some particular state, like that piled-up hump, and then let go, the surface will follow the 'energy gradient' downhill, until it finds the lowest possible energy. Then (after some sloshing around which slowly subsides because of friction) it will remain at rest in this lowest-energy state.

The energy in this problem is 'potential energy', determined by grav­ity. The potential energy of a mass of water is equal to its height above some arbitrary reference level, multiplied by the mass concerned. Suppose that the water is not flat. Then some parts are higher up than others. So we can transfer some water from the high level to the lower one, by flattening a hump and filling a dip. When we do that, the water involved moves downwards, so the total energy decreases. Conclusion: if the surface is not flat, then the energy is not as small as possible. Or, to put it the other way round: the minimum energy configuration occurs when the surface is flat.

The shape of a soap bubble is another example. Why is it round? The way to answer that question is to compare the actual round shape with a hypothetical non-round shape. What's different? Yes, the alternative isn't round, but is there some less obvious difference? According to Greek legend, Dido was offered as much land (in northern Africa) as she could enclose with a bull's hide. She cut it into a very long thin strip and enclosed a circle. There she founded the city of Carthage. Why did she choose a circle? Because the circle is the shape with greatest area, for a given perimeter. In the same way, a sphere is the shape with greatest volume, for a given surface area; or, to put it another way, it is the shape with the smallest surface area that contains a given volume. A soap bubble contains a fixed volume of air and its surface area gives the energy of the soap film due to surface tension. In the space of all possible shapes for bubbles, the one with the least energy is a sphere. All other shapes have larger energy, and are therefore ruled out.

You may not feel that bubbles are important. But the same princi­ple explains why Roundworld (the planet not the universe, but maybe that, too) is round. When it was molten rock, it settled into a spheri­cal shape, because that had the least energy. For the same reason, the heavy materials like iron sank into the core, and the lighter ones, like continents and air, floated up to the top. Actually, Roundworld isn't exactly a sphere, because it rotates, so centrifugal forces cause it to bulge at the equator. But the amount of bulge is only one-third of one per cent. And that bulging shape is the minimum-energy configura­tion for a mass of liquid spinning at the same speed as the Earth's rotation when it was just starting to solidify.

The physics here isn't important for the message of this book. What is important is the 'Worlds of If' point of view involved in the application of phase spaces. When we discussed the shape of water in a pond, we pretty much ignored the flat surface, the thing we were trying to explain. The entire argument hinged upon non-flat surfaces, humps and dips, and hypothetical transfers of water from one to the other. Almost all of the explanation involved thinking about things that don't actually happen. Only at the end, having ruled out all non-flat surfaces, did we observe that the only possibility left was therefore what the water would actually do. The same goes for the bubble.

At first sight, this might seem to be a very oblique way of doing physics. It takes the stance that the way to understand the real world is to ignore it, and focus instead on all the possible alternative unreal worlds. Then we find some principle (in this case, minimum energy) to rule out nearly all of the unreal worlds, and see what's left. Wouldn't it be easier to start with the real world, and focus solely on that? No, it wouldn't. As we've just seen, the real world alone is too limited to offer a convincing explanation. What you get from the real world alone is 'the world is like it is, and there's nothing more to be said'. However, if you take the imaginative leap of considering unreal worlds, too, you can compare the real world with all of those unreal worlds, and maybe find a principle that picks out the real one from all the others. Then you have answered the question 'Why is the world the way it is, rather than something else?'

An excellent way to approach 'why' questions is to consider alter­natives and rule them out. 'Why did you park the car round the corner down a side-street?' 'Because if I'd parked outside the front door on the double yellow lines, a traffic warden would have given me a park­ing ticket.' This particular 'why' question is a story, a piece of fiction: a hypothetical discussion of the likely consequences of an action that never occurred. Humans invented their own brand of narrativium as an aid to the exploration of I-space, the space of 'insteads'. Narrative provides I-space with a geography: if I did this instead of that, then what would happen would be ...

On Discworld, phase spaces are real. The fictitious alternatives to the one actual state exist, too, and you can get inside the phase space and roam over its landscape - provided you know the right spells, secret entrances and other magical paraphernalia. L-space is a case in point. On Roundworld, we can pretend that phase space exists, and we can imagine exploring its geography. This pretence has turned out to be extraordinarily insightful.

Associated with any physical system, then, is a phase space, a space of the possible. If you're studying the solar system, then the phase space comprises all possible ways to arrange one star, nine planets, a considerable number of moons and a gigantic number of asteroids in space. If you're studying a sand-pile, then the phase space comprises the number of possible ways to arrange several million grains of sand. If you're studying thermodynamics, then the phase space comprises all possible positions and velocities for a large number of gas mole­cules. Indeed, for each molecule there are three position coordinates and three velocity coordinates, because the molecule lives in three-dimensional space. So with N molecules there are 6 N coordinates altogether. If you're looking at games of chess, then the phase space consists of all possible positions of the pieces on the board. If you're thinking about all possible books, then the phase space is L-space. And if you're thinking about all possible universes, you're contem­plating U-space. Each 'point' of U-space is an entire universe (and you have to invent the multiverse to hold them all ... )

When cosmologists think about varying the natural constants, as we described in Chapter 2 in connection with the carbon resonance in stars, they are thinking about one tiny and rather obvious piece of U-space, the part that can be derived from our universe by chang­ing the fundamental constants but otherwise keeping the laws the same. There are infinitely many other ways to set up an alternative universe: they range from having 101 dimensions and totally different laws to being identical with our universe except for six atoms of dys­prosium in the core of the star Procyon that change into iodine on Thursdays.

As this example suggests, the first thing to appreciate about phase spaces is that they are generally rather big. What the universe actually does is a tiny proportion of all the things it could have done instead. For instance, suppose that a car park has one hundred parking slots, and that cars are either red, blue, green, white, or black. When the car park is full, how many different patterns of colour are there? Ignore the make of car, ignore how well or badly it is parked; focus solely on the pattern of colours.

Mathematicians call this kind of question 'combinatorics', and they have devised all sorts of clever ways to find answers. Roughly speaking, combinatorics is the art of counting things without actually counting them. Many years ago a mathematical acquaintance of ours came across a university administrator counting light bulbs in the roof of a lecture hall. The lights were arranged in a perfect rectangular grid, 10 by 20. The administrator was staring at the ceiling, going '49, 50, 51 -'

'Two hundred,' said the mathematician.

'How do you know that?'

'Well, it's a 10 by 20 grid, and 10 times 20 is 200.' 'No, no,' replied the administrator. 'I want the exact number.' Back to those cars. There are five colours, and each slot can be filled by just one of them. So there are five ways to fill the first slot, five ways to fill the second, and so on. Any way to fill the first slot can be combined with any way to fill the second, so those two slots can be filled in 5 X 5 = 25 ways. Each of those can be combined with any of the five ways to fill the third slot, so now we have 25 x 5 = 125 pos­sibilities. By the same reasoning, the total number of ways to fill the whole car park is 5 x 5 x 5 ... X 5, with a hundred fives. This is 5¹⁰⁰, which is rather big. To be precise, it is

78886090522101180541172856528278622 96732064351090230047702789306640625

(we've broken the number in two so that it fits the page width) which has 70 digits. It took a computer algebra system about five seconds to work that out, by the way, and about 4.999 of those seconds were taken up with giving it the instructions. And most of the rest was used up printing the result to the screen. Anyway, you now see why com­binatorics is the art of counting without actually counting; if you listed all the possibilities and counted them '1, 2, 3, 4 ...' you'd never finish. So it's a good job that the university administrator wasn't in charge of car parking.

How big is L-space? The Librarian said it is infinite, which is true if you used infinity to mean 'a much larger number than I can envisage' or if you don't place an upper limit on how big a book can be, or if you allow all possible alphabets, syllabaries, and pictograms. If stick to 'ordinary-sized' English books, we can reduce the estimate. A typical book is 100,000 words long, or about 600,000 characters (letters and spaces, we'll ignore punctuation marks). There are 26 letters in the English alphabet, plus a space, making 27 characters that can go into each of the 600,000 possible positions. The counting principle that we used to solve the car-parking problem now implies that the maximum number of books of this length is 27^600,000, which is roughly 10^860,000 (that is, an 860,000-digit number). Of course, most those 'books' make very little sense, because we've not yet insisted that the letters make sensible words. If we assume that the words are drawn from a list of 10,000 standard ones, and calculate the number of ways to arrange 100,000 words in order, then the figure changes. 10,000^100,000 is equal to 10^400,000, and this is quite a bit smaller ... but still enormous. Mind you, most of those books wouldn't make much sense either; they'd read something like 'Cabbage patronymic forgotten prohibit hostile quintessence' continuing at book length. So maybe we ought to work with sentences ... At any rate, even if we cut the numbers down in that manner, it turns out that the universe is not big enough to contain that many physical books. So it's a good job that L-space is available, and now we know why there's never enough shelf space. We like to think that our major libraries, such as the British Library or the Library of Congress, are pretty big. But, in fact, the space of those books that actually exist is a tiny, tiny fraction of L-space, all the books that could have existed. In particular, we're never going to run out of new books to write.

Poincare's phase space viewpoint has proved to be so useful that nowadays you'll find it in every area of science - and in areas that aren't science at all. A major consumer of phase spaces is economics. Suppose that a national economy involves a million different goods - cheese, bicycles, rats-on-a-stick, and so on. Associated with each good is a price, say £2.35 for a lump of cheese, £449.99 for a bicycle, £15.00 for a rat-on-a-stick. So the state of the economy is a list of one million numbers. The phase space consists of all possible lists of a million num­bers, including many lists that make no economic sense at all, such as lists that include the £0.02 bicycle or the £999,999,999.95 rat. The econ­omist's job is to discover the principles that select, from the space of all possible lists of numbers, the actual list that is observed.

The classic principle of this kind is the Law of Supply and Demand, which says that if goods are in short supply and you really, really want them, then the price goes up. It sometimes works, but it often doesn't. Finding such laws is something of a black art, and the results are not totally convincing, but that just tells us that economics is hard. Poor results notwithstanding, the economist's way of thinking is a phase space point of view.

Here's a little tale that shows just how far removed economic the­ory is from reality. The basis of conventional economics is the idea of a rational agent with perfect information, who maximises utility. According to these assumptions, a taxi-driver, for example, will arrange his activities to generate the most money for the least effort.

Now, the income of a taxi-driver depends on circumstances. On good days, with lots of passengers around, he will do well; on bad days, he won't. A rational taxi-driver will therefore work longer on good days and give up early on bad ones. However, a study of taxi-drivers in New York carried out by Colin Camerer and others shows the exact opposite. The taxi-drivers seem to set themselves a daily tar­get, and stop working once they reach it. So they work shorter hours on good days, and longer hours on bad ones. They could increase their earnings by 8 per cent just by working the same number of hours every day, for the same total working time. If they worked longer on good days and shorter on bad ones, they could increase their earn­ings by 15 per cent. But they don't have a good enough intuition for economic phase space to appreciate this. They are adopting a com­mon human trait of placing too much value on what they have today, and too little on what they may gain tomorrow.

Biology, too, has been invaded by phase spaces. The first of these to gain widespread currency was DNA-space. Associated with every living organism is its genome, a string of chemical molecules called UNA. The DNA molecule is a double helix, two spirals wrapped round a common core. Each spiral is made up of a string of 'bases' or 'nucleotides', which come in four varieties: cytosine, guanine, adenine, thymine, normally abbreviated to their initials C, G, A, T. The sequences on the two strings are 'complementary': wherever C appears on one string, you get G on the other, and similarly for A and T. the DNA contains two copies of the sequence, one positive and on negative, so to speak. In the abstract, then, the genome can be thought of as a single sequence of these four letters, something like AATG GCCTCAG ... going on for rather a long time. The human genome for example, goes on for about three billion letters.

The phase space for genomes, DNA-space, consists of all possible sequences of a given length. If we're thinking about human beings the relevant DNA-space comprises all possible sequences of three billion code letters C, G, A, T How big is that space? It's the same problem as the cars in the car park, mathematically speaking, so the answer is 4x4x4x...x4 with three billion 4s. That is 4^{3,000,000,000}. This number is a lot bigger than the 70-digit number we got for the car-parking problem. It's a lot bigger than L-space for normal-size books, too. In fact, it has about 1,800,000,000 digits. If you wrote it out with 3,000 digits per page, you'd need a 600,000-page book to hold it.

The image of DNA-space is very useful for geneticists who are con­sidering possible changes to DNA sequences, such as 'point mutations' where one code letter is changed, say as the result of a copying error. Or an incoming high-energy cosmic ray. Viruses, in particular, mutate so rapidly that it makes little sense to talk of a viral species as a fixed thing. Instead, biologists talk of quasi-species, and visualise these as clusters of related sequences in DNA-space. The clusters slosh around as time passes, but they stay together as one cluster, which allows the virus to retain its identity.

In the whole of human history, the total number of people has been no more than ten billion, a mere 11-digit number. This is an incredi­bly tiny fraction of all those possibilities. So actual human beings have explored the tiniest portion of DNA-space, just as actual books have explored the tiniest portion of L-space. Of course, the interesting questions are not as straightforward as that. Most sequences of letters do not make up a sensible book; most DNA sequences do not corre­spond to a viable organism, let alone a human being.

And now we come to the crunch for phase spaces. In physics, it is reasonable to assume that the sensible phase space can be 'pre-stated' before tackling questions about the corresponding system. We can imagine rearranging the bodies of the solar system into any config­uration in that imaginary phase space. We lack the engineering capacity to do that, but we have no difficulty imagining it done, and we see no physical reason to remove any particular configuration from consideration.

When it comes to DNA-space, however, the important questions are not about the whole of that vast space of all possible sequences. Nearly all of those sequences correspond to no organism whatsoever, not even a dead one. What we really need to consider is 'viable-DNA-space', the space of all DNA sequences that could be realised within some viable organism. This is some immensely complicated but very thin part of DNA-space, and we don't know what it is. We have no idea how to look at a hypothetical DNA sequence and decide whether it can occur in a viable organism.

The same problem arises in connection with L-space, but there's a twist. A literate human can look at a sequence of letters and spaces and decide whether it constitutes a story; they know how to 'read' the code and work out its meaning, if it's in a language they understand. They can even make a stab at deciding whether it's a good story or a bad one. However, we do not know how to transfer this ability to a computer. The rules that our minds use, to decide whether what we're reading is a story, are implicit in the networks of nerve cells in our brains. Nobody has yet been able to make those rules explicit. We don't know how to characterise the 'readable books' subset of L-space.

For DNA, the problem is compounded because there isn't some kind of fixed rule that 'translates' a DNA code into an organism. Biologists used to think there would be, and had high hopes of learning the 'lan­guage' involved. Then the DNA for a genuine (potential) organism would be a code sequence that told a coherent story of biological development, and all other DNA sequences would be gibberish. In effect, the biologists expected to be able to look at the DNA sequence of a tiger and see the bit that specified the stripes, the bit that specified the claws, and so on. This was a bit optimistic. The current state of the art is that we can see the bit of DNA that specifies the protein from which claws are made, or the bits that make the orange, black and white pigments on the fur that show up as stripes, but that's about as far as our understanding of DNA narrative goes. It is now becoming clear that many non-genetic factors go into the growth of an organism, too, so even in principle there may not be a 'language' that translates DNA into living creatures. For example, tiger DNA turns into a baby tiger only in the presence of an egg, supplied by a mother tiger. The same DNA in the presence of a mongoose egg, would not make a tiger at all. Now, it could be that this is just a technical problem: that for each DNA code there is a unique kind of mother-organism that turns it into a living creature, so that the form of that creature is still implicit in the code. But theoretically, at least, the same DNA code could make two totally different organisms. We give an example in The Collapse of Chaos where the developing organism first 'looks' to see what kind of mother it is in, and then develops in different ways depending on what it sees.

Complexity guru Stuart Kauffman has taken this difficulty a stage fur­ther. He points out that while in physics we can expect to pre-stage the phase space of a system, the same is never true in biology. Biological systems are more creative than physical ones: the organisation of matter within living creatures is of a different qualitative nature from the organisation we find in inorganic matter. In particular, organisms can evolve, and when they do that they often become more complicated. The fish-like ancestor of humans was less complicate than we are today, for example. (We've not specified a measure of complexity here, but that statement will be reasonable for most sensible measures of complexity, so let's not worry about definitions. Evolution does not necessarily increase complexity, but it's at its mo puzzling when it does.)

Kauffman contrasts two systems. One is the traditional thermodynamic model in physics, of N gas molecules (modelled as hard spheres) bouncing around inside their 6N-dimensional phase space. Here we know the phase space in advance, we can specify the dynamic precisely, and we can deduce general laws. Among them is the Second Law of Thermodynamics, which states that with over­whelming probability the system will become more disordered as time passes, and the molecules will distribute themselves uniformly through­out their container.

The second system is the 'biosphere', an evolving ecology. Here, it is not at all clear which phase space to use. Potential choices are either much too big, or much too limited. Suppose for a moment that the old biologists' dream of a DNA language for organisms was true. Then we might hope to employ DNA-space as our phase space.

However, as we've just seen, only a tiny, intricate subset of that space would really be of interest - but we can't work out which sub­set. When you add to that the probable non-existence of any such language, the whole approach falls apart. On the other hand, if the phase space is too small, entirely reasonable changes might take the organisms outside it altogether. For example, tiger-space might be defined in terms of the number of stripes on the big cat's body. But if one day a big cat evolves that has spots instead of stripes, there's no place for it in the tiger phase space. Sure, it's not a tiger ... but its mother was. We can't sensibly exclude this kind of innovation if we want to understand real biology.

As organisms evolve, they change. Sometimes evolution can be seen as the opening-up of a region of phase space that was sitting there waiting, but was not occupied by organisms. If the colours and pat­terns on an insect change a bit, all that we're seeing is the exploration of new regions of a fairly well-defined 'insect-space'. But when an entirely new trick, wings, appears, even the phase space seems to have changed.

It is very difficult to capture the phenomenon of innovation in a mathematical model. Mathematicians like to pre-state the space of pos­sibilities, but the whole point about innovation is that it opens up new possibilities that were previously not envisaged. So Kauffman suggests that a key feature of the biosphere is the inability to pre-state a phase space for it.

At risk of muddying the waters, it is worth observing that even in physics, pre-stating the phase space is not as straightforward as it might appear. What happens to the phase space of the solar system if we allow bodies to break up, or merge? Supposedly the Moon was splashed off the Earth when it collided with a body about the size of Mars. Before that event, there was no Moon-coordinate in the phase-space of the solar system; afterwards, there was. So the phase space expanded when the Moon came into being. The phase spaces of physics always assume a fixed context. In physics, you can usually get away with that assumption. In biology, you can't.

There's a second problem in physics, too. That 6N-dimension phase space of thermodynamics, for example, is too big. It includes non-physical states. By a quirk of mathematics, the laws of motion of elastic spheres do not prescribe what happens when three or more collide simultaneously. So we must excise from that nice, simple 6N-dimensional space all configurations that experience a triple collision somewhere in their past or future. We know four things about these configurations. They are very rare. They can occur. They form an extremely complicated cloud of points in phase space. And it is impossible, in any practical sense, to determine whether a given configuration should or should not be excised. If these unphysical states were a bit more common, then the thermodynamic phase space would be just as hard to pre-state as that for the biosphere. However, they are a vanishingly small proportion of the whole, so we can jus about get away with ignoring them.

Nonetheless, it is possible to go some way towards pre-stating a phase space for the biosphere. While we cannot pre-state a space of all possible organisms, we can look at any given organism and at least in principle say what the potential immediate changes are. That is, we can describe the space of the adjacent possible, the local phase space. Innovation then becomes the process of expanding into the adjacent possible. This is a reasonable and fairly conventional idea. But, more controversially, Kauffman suggests the exciting possibility that there may be general laws that govern this kind of expansion, laws that have exactly the opposite effect to the famous Second Law of Thermodynamics. The Second Law in effect states that thermody­namic systems become simpler as time passes; all of the interesting structure gets 'smeared out' and disappears. In contrast, Kauffman's suggestion is that the biosphere expands into the space of the adja­cent possible at the maximum rate that it can, subject to hanging together as a biological system. Innovation in biology happens as rapidly as possible.

More generally, Kauffman extends this idea to any system composed of 'autonomous agents'. An autonomous agent is a generalised life-form, defined by two properties: it can reproduce, and it can carry out at least one thermodynamic work cycle. A work cycle occurs when a system does work and returns to its original state, ready to do the same again. That is, the system takes energy from its environment and trans­forms it into work, and does so in such a manner that at the end of the cycle it returns to its initial state.

A human being is an autonomous agent, and so is a tiger. A flame is not: flames reproduce by spreading to inflammable material nearby, but they do not carry out a work cycle. They turn chemical energy into fire, but once something has been burnt, it can't be burnt a second time.

This theory of autonomous agents is explicitly set in the context of phase spaces. Without such a concept, it cannot even be described. And in this theory we see the first possibility of obtaining a general understanding of the principles whereby, and wherefore, organisms complicate themselves. We are starting to pin down just what it is about lifeforms that makes them behave so differently from the bor­ing prescription of the Second Law of Thermodynamics. We paint a picture of the universe as a source of ever-increasing complexity and organisation, instead of the exact opposite. We find out why we live in an interesting universe, instead of a dull one.

FIVE

REMARKABLY LIKE ANKH-MORPORK

'How can you communicate like this?' panted Ponder, as they jogged along beside a broad river.

'Since the physics of Roundworld are subordinate to the physics of the real world, I can use anything considered to be a communication device,' said the voice of Hex, slightly muffled in Rincewind's pocket. 'The owner of the device believes it to be one such. Also, I can deduce much information from this world's footprint in L-space. And the Archchancellor was right. There is much Elvish influence here.'

'You can extract information from Roundworld books?' said Ponder.

'Yes. The phase space of books that relate to this world contains ten to the power of 1,100 to the power of n volumes,' said Hex. 'That's enough books to fill the univ-'

'Hold on, what is n?'

'The number of all possible universes.'

'Then that's enough books to fill all possible universes! Well ... as close as makes no difference, anyway.'

'Correct. That is why there is never enough bookshelf space. However, because of the subordinate temporal matrix of this world, I can use virtual computing,' said Hex. 'Once you know what the answer is, the process of calculation can be seriously reduced. Once the correct answer is found, the fruitless channels of inquiry cease to exist. Besides, if you deduct all the books that are about golf, cats, slood and cookery the number is really quite manageable.'

'Oook,' said the Librarian.

'He says he's not going to have a shave,' said Rincewind.

'It is essential,' said Hex. 'We are getting strange glances from peo­ple in the fields. We do not wish to attract a mob. He must be shaved, and given a robe and hat.'

Rincewind was doubtful. 'I don't think that'll fool anyone,' he said.

'My readings tell me that it will if you say he's Spanish.'

'What's Spanish?'

'Spain is a country some five hundred miles from this one.'

'And people there look like him?'

'No. But people here would be quite prepared to believe so. This is a credulous age. The elves have done a lot of damage. The great­est minds spend half their time busying themselves with the study of magic, astrology, alchemy and communion with spirits.'

'Well? Sounds just like life at home,' said Rincewind.

'Yes,' said Hex. 'But there is no narrativium in this world. No magic. None of those things work.'

'Then why don't they just stop trying it?' said Ponder.

'My inference is that they believe it should work if only they get it right.'

'Poor devils,' said Rincewind.

'They believe in those, too.'

'There's more houses ahead,' said Ponder. 'We're coming to a city. Er ... and we've got the Luggage with us. Hex, we haven't just got an orangutan with us, we've got a box on legs!'

'Yes. We must leave it in some bushes while we find a voluminous dress and a wig,' said Hex calmly. 'Fortunately, this is the right period.'

'A dress won't work, believe me!'

'It will if the Librarian sits on the Luggage,' said Hex. "That will bring him up to the right height and the dress will provide adequate cover for the Luggage.'

'Now hang on a moment,' said Rincewind. You saying that people here will believe an ape in a dress and a wig is a woman?'

'They will if you say she's Spanish.'

Rincewind took another look at the Librarian.

'Those elves really must have done a lot of damage,' he said.

The city was remarkably like Ankh-Morpork, although smaller and, unbelievably, smellier. One reason for that was the large number of animals in the streets. It was as if the place had been designed as village and simply scaled up.

The wizards hadn't been hard to find. Hex located them easily, in any case the noise could be heard in the next street. There was a tavern, with a courtyard, and in the courtyard a crowd of alcohol which contained people was watching a man trying to beat Archchancellor Ridcully with a very long and heavy staff.

He wasn't succeeding. Ridcully, who was stripped to the waist, was fighting back very effectively, putting his wizarding staff to the unusual task of hitting someone. He was a lot better at it than his opponent. Most wizards would die rather than take exercise, and did, but Ridcully had the rude health of a bear and only marginally better interpersonal skills. Despite his quite considerable if erratic erudition, at heart he was a man who'd rather smack someone around the ear than develop a complicated argument.

As the rescue party arrived, he hit the man across the head and the swept his feet from under him on the back-swing. A cheer went up the man went down.

Ridcully helped his stunned adversary to his feet and propelled him to a bench, where the man's friends poured beer over him. Then he nodded to Rincewind and company.

'Got here, then,' he said. 'Bring the stuff, did you? Who's the Spanish lady?'

'That's the Librarian,' said Rincewind. There wasn't a great deal vis­ible between the ruff and the red wig except an impression of extreme annoyance.

'Is it?' said Ridcully. 'Oh, yes. Sorry. Been here too long. This place gets to you. Good thinking, puttin' him in disguise. Hex suggested that, I expect.'

'We came as quick as we could, sir,' said Ponder. 'How long have you been here?'

'Couple of weeks,' said Ridcully. 'Not a bad place. Come and meet everyone.'

The rest of the wizards were sitting around a table. They were dressed in their normal wizarding outfits which, Rincewind had noticed, fitted in pretty well with the costumes in this town. But each man had equipped himself with a ruff, just to be on the safe side.

They nodded cheerfully at the newcomers. A forest of empty mugs in front of them went some way to explaining the cheer.

'You've detected elves?' said Ridcully, forcing enough wizards apart to give them seats.

'The place is lousy with glamour, sir.' said Ponder, sitting down.

'You're telling me,' said Ridcully. He glanced along the table. 'Oh, yes. We've found a friend. Dee, this is Mister Stibbons. Remember we told you about him?'

It was then that Ponder realised there were a couple of non-wizards in the party. It was quite hard to spot one, though, since for all practical purposes he fitted in well. He even had the right kind of beard.

'Er ... the noddlepate?' said Dee.

'No, that's Rincewind,' said Ridcully. 'Ponder is the clever one. And this ...' he turned to the Librarian, and words failed even him, 'Is ... a ... friend of theirs.'

'From Spanish,' said Rincewind, who didn't know what noddlepate meant but had formed a pretty good idea.

'Dee here is a sort of local wizard,' said Ridcully, in the loud voice he thought was a confidential whisper. 'Sharp as a tack, mind like a razor, but spends all his spare time trying to do magic!'

'Which doesn't work here,' said Ponder.

'Right! But everyone believes it does, despite everything. Amazing! That's what elves can do to a place.' Ridcully leaned forward, conspiratorially. 'They came straight through our world and straight on into this one and we got caught up in the ... what's it you call it when it's all swirly and chilly as hell?'

'Trans-dimensional flux, sir,' said Ponder.

'Right. We'd have been totally lost if our friend Dee here hadn't been working a magic circle at the time.'

There was silence from Rincewind and Ponder. Then Rincewind said: 'You said magic doesn't work here.'

'As with this crystal sphere,' said a voice from Rincewind's pocket, 'this world is quite capable of maintaining a passive receptor. Rincewind removed the scrying stone from his pocket.

'But that is mine,' said Dee, staring at it.

'Sorry,' said Rincewind. 'We just sort of found it and sort of picked it sort of up.'

'But it speaks!' gasped Dee. 'An ethereal voice!'

'No, it's just from another world that is much bigger than this one and can't be seen,' said Ridcully. 'There's nothing mysterious about it at all.'

With trembling fingers, Dee took the sphere from Rincewind and held it in front of his eyes.

'Speak!' he commanded.

'Permission denied,' said the crystal. 'You do not have the rights to do this.'

'Where did you tell him you came from?' Rincewind whispered Ridcully, as Dee tried to polish the ball with the sleeve of his robe.

'I just said we'd dropped in from another sphere,' said Ridcully. 'After all, this universe is full of spheres. He seemed to be quite happy about that. I didn't mention the Discworld at all, in case it confused him.

Rincewind looked at Dee's shaking hands and the manic glint in his eye.

'I just want to be clear,' he said slowly. 'You appeared in a magic circle, you told him you're from another sphere, he'd just spoken to crystal ball, you've explained to him that magic doesn't work and you don't want to confuse him?'

'Make him any more confused than he is already, you mean,' said the Dean. 'Confusion is the natural state of mind here, believe us. Do you know they think numbers are magical? Doing sums can get you into real trouble in these parts.'

'Well, some numbers are magi-' Ponder began.

'Not here they're not,' said the Archchancellor. 'Here I am, out in the open air, no magical protection and I'm going to say the number that comes after seven. Here it comes: eight. There. Nothing happened. Eight! Eighteen! Two fat ladies in very tight corsetry, eighty-eight! Oh someone pull Rincewind out from under the table, will you?'

While the Professor of Cruel and Unusual Geography was having some of it brushed off his robes, Ridcully continued: 'It's a mad world. No narrativium. People makin' up history as they go along. Brilliant men spendin' their time wondering how many angels can dance on the head of a pin-'

'Sixteen,' said Ponder.

'Yes, we know that because we can go and look, but here it's just another silly question,' said Ridcully. 'It'd make you cry. The history of this place goes backwards half the time. It's a mess. A parody of a world.'

'We made it,' said the Lecturer in Recent Runes.

'We didn't make it this badly,' said the Dean. 'We've seen the his­tory books here. There were some great civilisations thousands of years ago. There was a place like Ephebe that was really beginning to find things out. The wrong things, mostly, but at least they were making an effort. Even had a decent pantheon of gods. All gone now. Our chum here and his friends think everything worth knowing has been discovered and forgotten and, frankly, they're not totally wrong.'

'What can we do about it?' said Ponder.

'You can talk to Hex on that thing?'

Yes, sir.'

'Then Hex can do the magic back at UU and we'll find out what the elves did,' said Ridcully.

'Er,' Rincewind began, 'do we have the right to interfere?' They all stared at him.

'I mean, we never did it before,' he went on. 'Remember all those other creatures that evolved here? The intelligent lizards? The intelli­gent crabs? Those dog things? They all got completely wiped out by ice ages and falling rocks and we never did anything to stop it.'

They went on staring.

'I mean, elves are just another problem, aren't they?' said Rincewind. Maybe ... maybe they're just another form of big rock? Maybe ... maybe they always turn up when intelligence gets going? And the species is either clever enough to survive them or it ends up buried in the bedrock like all the others? I mean, perhaps it's a kind of, of a test? I mean…'

It dawned on Rincewind that he was not carrying the meeting, wizards were glaring at him.

'Are you suggesting that someone somewhere is awarding marks, Rincewind?' said Ponder.

'Well, obviously there is no-'

'Good. Shut up,' said Ridcully. 'Now, lads, let's get back to Mort Lake and get started.'

'Mort Lake?' said Rincewind. 'But that's in Ankh-Morpork!'

'There's one here, too,' said the Lecturer in Recent Runes, beaming.

'Amazing, isn't it? We never guessed. This world is a cheap parody of our own. As Above, So Below and all that.'

'But without magic,' said Ridcully. 'And with no narrativium. It doesn't know where it's going.'

'But we do, sir,' said Ponder, who had been scribbling in notebook.

'Do we?'

'Yes, sir. Remember? In about a thousand years' time it's going to be hit by a really big rock. I keep looking at the numbers, sir, and that's what it means.'

'But I thought we found there'd been a race that built huge struc­tures to get off the place?'

'That's right, sir.'

'Can a new species turn up in a thousand years?'

'I don't think so, sir.'

'You mean these are the ones that leave?'

'It seems like it, sir,' said Ponder.

The wizards looked at the people in the courtyard. Of course, the presence of beer always greases the rungs of the evolutionary ladder, but even so ...

At a nearby table, one man threw up on another one. There was general applause.

'I think,' said Ridcully, summing up the general mood, 'that we are going to be here for some time.'

SIX

THE LENS-GRINDER'S PHILOSOPHY

John Dee, who lived from 1527 to 1608, was a court astrologer to Mary Tudor. At one point he was impris­oned for being a magician, but in 1555 they let him out again, presumably for not being one. Then he became an astrologer for Queen Elizabeth I. He devoted much of his life to the occult, both alchemy and astrology. On the other hand, he was also the author of the first English translation of Euclid's Elements, the renowned treatise on geometry. Actually, if you believe the printed word, the book is attributed to Sir Henry Billingsley, but it was common knowledge that Dee did all the work, and he even wrote a long and erudite preface. Which may be why it was common knowledge that Dee did all the work.

To the modern mind, Dee's interests seem contradictory: a mass of superstitious pseudoscience mixed up with some good, solid science and mathematics. But Dee didn't have a modern mind, and he saw no particular contradiction in the combination. In his day, many mathe­maticians made their living by casting horoscopes. They could do the sums that foretold in which of the twelve 'houses' - the regions of the sky determined by the constellations corresponding to the signs of the Zodiac - a planet would be.

Dee stands at the threshold of modern ways of thinking about causality in the world. We call his time The Renaissance, and the ref­erence is to the rebirth of the philosophy and politics of ancient Athens. But perhaps this view of his times is mistaken, both because Greek society was not then as 'scientific' or 'intellectual' as we've been led to believe, and because there were other cultural currents that attributed to the culture of his times. Our ideas of narrativium may derive from the melding of these ideas into later philosophies, such as of Baruch Spinoza.

Stories encouraged the growth of occultism and mysticism. But they also helped to ease the European world out of medieval superstition into a more rational view of the universe.

Belief in the occult - magic, astrology, divination, witchcraft, alchemy - is common to most human societies. The European tradition occultism, to which Dee belonged, is based on an ancient, secret philosophy; it derives from two main sources, ancient Greek alchemy magic, and Jewish mysticism. Among the Greek sources is the Emeri Tablet, a collection of writings associated with Hermes Trismegist ('thrice master'), which was particularly revered by later alchemists; the Jewish source is the Kabbala, a secret, mystical interpretation of a sacred book, the Torah.

Astrology, of course, is a form of divination based on the stars and the visible planets. It may, perhaps, have contributed to the development of science by supporting people who wanted to observe and understand the heavens. Johannes Kepler, who discovered that planetary orbits are ellipses, made his living as an astrologer. Astrology survives in watered-down form in the horoscope columns of tabloid newspapers. Ronald Reagan consulted an astrologer during his time as American President. That stuff certainly hangs around.

Alchemy is more interesting. It is often said to be an early forerunner of chemistry, although the principles underlying chemistry largely derive from other sources. The alchemists played around with apparatus that led to useful chemists' gadgets like retorts and flasks and they discovered that interesting things happen when you heat certain substances or combine them together. The alchemists' big discoveries were salt ammoniac (ammonium chloride), which can be made to react with metals, and the mineral acids - nitric, sulphuric and hydrochloric.

The big goal of alchemy would have been much bigger if they ever achieved it: the Elixir of Life, the source of immortality. The Chinese alchemists described this long-sought substance as 'liquid gold'. The narrative thread here is clear: gold is the noble metal, incor­ruptible, ageless. So anyone who could somehow incorporate gold into his body would also become incorruptible and ageless. The nobil­ity shows up differently: the noble metal is reserved for the 'noble' humans: emperors, royalty, the people on top of the heap. Much good did this do them. According to the Chinese scholar Joseph Needham, several Chinese emperors probably died of elixir poisoning. Since arsenic and mercury were common constituents of supposed elixirs, this is hardly a surprise. And it is all too plausible that a mystic quest for immortality would shorten life, not prolong it.

In Europe, from about 1300 onwards, alchemy had three main objec­tives. The Elixir of Life was still one, and a second was finding cures for various diseases. The alchemical search for medicines eventually led somewhere useful. The key figure here is Phillipus Aureolus Theophrastus Bombastus von Hohenheim, mercifully known as 'Paracelsus', who lived from 1493 to 1541.

Paracelsus was a Swiss physician whose interest in alchemy led him to invent chemotherapy. He placed great store in the occult. As a stu­dent aged 14 he wandered from one European university to another, in search of great teachers, but we can deduce from what he wrote about the experience, somewhat later, that he was disappointed. He wondered why 'the high colleges managed to produce so many high asses', and clearly wasn't the kind of student to endear himself to his teachers. 'The universities,' he wrote, 'do not teach all things. So a doc­tor must seek out old wives, gypsies, sorcerers, wandering tribes, old robbers, and such outlaws and take lessons from them.' He would have had a high old time on Discworld, but would have learned a lot.

After ten years' wandering, he returned home in 1524 and became lecturer in medicine at the university of Basel. In 1527 he publicly burned the classic books of earlier physicians, the Arab Avicenna and the Greek Galen. Paracelsus cared not a whit for authority. Indeed his assumed name, 'para-Celsus', means 'above Celsus', and Celsus was a leading Roman doctor of the first century.

He was arrogant and mystical. His saving grace was that he was also very bright. He placed great importance on using nature's own powers of healing. For example, letting wounds drain instead of padding them with moss or dried dung. He discovered that mercury was an effective treatment for syphilis, and his clinical description of that sexually transmitted disease was the best available.

The main objective for most alchemists was far more selfish, sights were set on just one thing: transmuting base metals like lead into gold. Again, their belief that this was possible rested on a story. They knew from their experiments that sal ammoniac and other substances could change the colour of metals, so the story 'Metals can be transmuted' gained ground. Why, then, should it not be possible to start with lead, add the right substance, and end up with gold? The story seemed compelling; all that they lacked was the right substance. They called it the Philosopher's Stone.

The search for the Philosopher's Stone, or rumours that it had been found, got several alchemists into trouble. Noble gold was the prerogative of the nobility. While the various kings and princes wouldn't have minded getting their hands on an inexhaustible supply of gold, they didn't want their rivals to beat them to it. Even searching for the Philosopher's Stone could be considered subversive, just as searching for a cheap source of renewable energy now is apparently considered subversive by oil corporations and nuclear energy companies. In 1595 Dee’s companion Edward Kelley was imprisoned by Rudolf II and died trying to escape, and in 1603 Christian II of Saxony imprisoned and tortured the Scottish alchemist Alexander Seton. A dangerous thing, a clever man.

The story of the Philosopher's Stone never reached its climax, alchemists never did turn lead into gold. But the story took a long time to die. Even around 1700, Isaac Newton still thought it was worth having a go, and the idea of turning lead into gold by chemical means was finally killed off only in the nineteenth century. Nuclear reactions, mind you, are another matter: the transmutation can be done, but is wildly uneconomic. And unless you're very careful, the gold is radioactive (although, of course, this will keep the money circulating quickly, and we might see a sudden upsurge of philanthropy). How did we get from alchemy to radioactivity? The pivotal period of Western history was the Renaissance, roughly spanning the fifteenth and sixteenth centuries, when ideas imported from the Arab world col­lided with Greek philosophy and mathematics, and Roman artisanship and engineering, leading to a sudden flowering of the arts and the birth of what we now call science. During the Renaissance, we learned to tell new stories about ourselves and the world. And those stories changed both.

In order to understand how this happened, we must come to grips with the real Renaissance mentality, not the popular view of a 'Renaissance man'. By that phrase, we mean a person with expertise in many areas - like Roundworld's Leonardo da Vinci, who bears a suspicious resemblance to the Disc's Leonard of Quirm. We use this phrase because we contrast such people with what we call a 'well-educated' person today.

In medieval Europe, and indeed long after that, the aristocracy con­sidered 'education' to mean classical knowledge - the culture of the Greeks - plus a lot of religion, and not much else. The king was expected to be well informed about poetry, drama and philosophy, but he wasn't expected to know about plumbing or brickwork. Some kings did in fact get rather interested in astronomy and science, either out of intellectual interest or the realisation that technology is power, but that wasn't part of the normal royal curriculum.

This view of education implied that the classics were all the vali­dated knowledge that an 'educated' person needed, a view not far from that of many English 'public' schools until quite recently, and of the politicians they have produced. This view of what was needed by the rulers contrasted with what was needed by the children of the peasantry (artisan skills and, lately, the 'three Rs').

Neither the classics nor the three Rs formed the basis for the gen­uine Renaissance man, who sought a fusion of those two worlds. Pointing to the artisan as a source of worldly experience, of knowledge of the material world and its tools such as an alchemist might use, led to a new rapprochement between the classical and the empirical, between intellect and experience. The actions of such men as Dee, even those of the occultist Paracelsus in his medical prescriptions emphasised this distinction, and started the fusion of reason and empiricism that so impresses us today.

As we've said, the word 'Renaissance' refers not just to rebirth, but to a specific rebirth, that of ancient Greek culture. This, however, is a modern view, based on a mistaken view of the Greeks, and of the Renaissance itself. In 'classical' education, no attention is paid to engineering. Of course not. Greek culture ran on pure intellect, poetry an philosophy. They didn't have engineers.

Oh, but they did. Archimedes constructed great cranes that could lift enemy ships out of the water, and we still don't know exactly how he did it. Hero of Alexandria (roughly contemporary with Jesus) wrote many texts about engines and machines of various kinds of the previous three hundred years, many of which show that prototypes may have been made. His coin-operated machines were not too different from those that could be found on any city street in 1930s London or New York, and would probably have been more reliable when it came to disgorging the chocolate, if the Greeks had known about chocolate. The Greeks had elevators, too.

The problem here is that information about the technical aspects of Greek society has been transmitted to us through a bunch of theologians. They liked Hero's steam engine, and indeed many of them have a little glass one on their desk, a sort of Theologians' Toy that they could spin with a candle flame. But the mechanical ideas behind such toys just passed them by. And, just as Greek engineering has not been transmitted to us by theologians, the spiritual attitude of the Renaissance has not come down to us through our 'rational' school teachers. Much of the attempted spirituality within the alchemical position was basically a religious stance, marvelling at the Works of the Lord as they were exposed by the marvels of changes of state an form, when materials were subjected to heat, to 'percussion', and to solution and crystallisation.

This stance has been taken over by today's innocents of rigorous thinking, the New Agers, who find spiritual inspiration in crystals and anodised metals, spherical spark-machines and Newton's pendulums, but do not ask the deeper questions that lie behind these toys. We find the very real awe inspired by science's quest for understanding to be considerably more spiritual than New Age attitudes.

Today there are mystic massage-therapists, aromatherapists, iridologists, people who believe that you can 'holistically' tell what's wrong with someone by examining their irises or the balls of their feet - only - and who root their beliefs in the writings of Renaissance eccentrics like Paracelsus and Dee. But those men would have been horrified to be cited as authorities, especially by such closed-minded descendants.

Prominent among those who refer back to Paracelsus for authority are homeopathists. A basic belief of homeopathy is that medicines become more powerful the more they are diluted. This stance lets them promote their medicine as being totally harmless (it's just water) but also extraordinarily effective (as water isn't). They notice no contra­diction here. And homeopathic headache tablets say 'Take one if mild, three if painful'. Shouldn't it be the other way round?

Such people see no need to think about what they are doing, because they base their beliefs on authority. If a question is not raised by that authority, then it's not a question they want to ask. So, in sup­port of their theories, homeopaths quote Paracelsus: 'That which makes disease is also the cure.' But Paracelsus built his entire career on not respecting authority. Moreover, he never said that a disease is always its own cure.

Contrast this modern spectrum of silliness with the robust, critical attitude of most Renaissance scholars to the idea that arcane practices can lay bare the bones of the world. People such as Dee, indeed Isaac Newton, took that critical position very seriously. To a great extent, so did Paracelsus: for example he repudiated the idea that the stars and planets control various parts of the human body. The Renaissance view was that God's creation has mysterious elements, but those elements are hidden, implicit in the nature of the universe, rather than arcane.

This view is very close to Antonie van Leeuwenhoek's marvelling at the animalcules in dirty water, or semen: the astonishing discovery that the Wonders of Creation extended down into the microscopic realm. Nature, God's Creation, was much more subtle. It provided hidden wonders to marvel at as well as the overt artistic vision. Newton was taken with the implicit mathematics of the planets in just this way: there was more to God's invention than was apparent to the unaided eye, and that resonated with his Hermetic beliefs (a philosophy derived from the ideas of Hermes Trismegistos). The crisis of atomism at time was the crisis of pre-formation: if Eve had within her all daughters, each having within her her daughters like a set of Russian dolls, then matter must be infinitely divisible. Or, if not, we could work out the future date of Judgement Day by discovering how many generations there were until we got to the last, empty daughter.

A characteristic of Renaissance thinking, then, was a degree of humility. It was critical about its own explanations. This attitude contrasts favourably with such modern religions as homeopathy, Scientology, creeds that arrogantly claim to offer a 'complete' explanation of the Universe in human terms.

Some scientists are equally arrogant, but good scientists are always aware that science has limitations, and are willing to explain what they are. 'I don't know' is one of the great, though admittedly under-utilised scientific principles. Admitting ignorance clears away so much pointless nonsense. It lets us cope with stage magicians performing the beautiful, and very convincing, illusions - convincing, that is, while we keep our brains out of gear. We know they have to be tricks, and admitting ignorance lets us avoid the trap of believing the illusion to be real merely because we don't know how the trick works. Why should we? We're not members of the Magic Circle. Admitting ignorance similarly protects us against mystic credulity when we encounter natural events that have not yet caught the eye of a competent scientist (and his grant-awarding body), and that still seem to be ... magic. We say 'The magic of nature' ... more the Wonder of Nature, or the Miracle of Life.

This is a stance that nearly all of us share, but it's important to understand the historical tradition it is grounded in. It isn't simply a case of admiring the complexity of God's works. It implies the attitudes of Newton, van Leeuwenhoek and earlier; indeed, right back to Dee. And, doubtless, to some Greek, or several. It involves the Renaissance belief that if we investigate the wonder, the marvel, the miracle, then we'll find even more wonders, marvels and miracles: gravity, say, or spermatozoa.

So what do we, and what did they, mean by 'magic? Dee spoke of the arcane arts, and Newton was committed to many explanations that were 'magickal', especially his commitment to action at a distance, 'gravity', which derived from the mystical attraction/repulsion basics of his Hermetic philosophy.

So 'magic' means three things, all apparently quite different. Meaning one is: 'something to be wondered at', and this ranges from card tricks to amoebas to the rings of Saturn. Meaning two is turning a verbal instruction, a spell, into material action, by occult or arcane means ... turning a person into a frog, or vice versa, or a djinn building a cas­tle for his master. The third meaning is the one we use: the technical magic of turning a light switch on, and getting light, without even having to say 'fiat lux'.

Granny Weatherwax's recalcitrant broomstick is type two magic, but her 'headology' is largely a very, very good grasp of psychology (type three magic carefully disguised as type two). It brings to mind Arthur C. Clarke's phrase 'Any sufficiently advanced technology is indistin­guishable from magic', which we quoted and discussed in The Science of Discworld. Discworld exemplifies magic by spells, and indeed is maintained as an unlikely creation by being immersed in a strong mag­ical field (type two). Adults of Earthly cultures, like Roundworld, pretend to have lost intellectual belief in magic of the Discworld kind, while their culture is turning more and more of their technology into magic (third kind). And the development of Hex throughout the books is turning Sir Arthur on his head: Discworld's sufficiently advanced magic is now practically indistinguishable from technology.

We can see, as (fairly) rational adults, where the first kind of magic comes from. We see something wonderful and feel tremendously happy that the universe is a place that can include ammonites, say, or kingfishers. But where did we get our belief in the second, irrational kind of magic? How does it come about that all cultures have children that begin their intellectual lives by believing in magic, instead of the real causality that surrounds them?

A plausible explanation is that human beings are initially programmed through fairy stories and nursery tales. All human cultures tell stories to their children; part of the development of our specific humanity is the interaction that we get with early language.

All cultures use animal icons for this nursery tuition, so we in the West have sly foxes, wise owls and frightened chickens. They seem to come out of a human dreamtime, where all animals seem to be types of human being in a different skin, and talk as a matter of course. We learn what the subtle adjectives mean from the actions - and words - of the creatures in the stories. Inuit children don't have a 'sly' fox icon; their fox is 'brave' and 'fast', while the Norwegian iconic fox is secretive and wise, full of good advice for respectful children. The causality in these stories is always verbal: 'So the fox said ... and they did it!' or 'I'll huff and I'll puff and I'll blow your house down.' The earliest communicated causality that the child meets is verbal instructions that cause material events. That is, spells.

Similarly, parents and carers are always transmuting the child's expressed desires into actions and objects, from food appearing on the table when the child is hungry to toys and other birthday and Christmas gifts. We surround these simple verbal requests with 'magical' ritual. We require the spell to begin with 'please', and its execution to be recognised by 'thank you'. It is indeed not surprising that our children come to believe that the way to acquire or access bits of the real world is simply to ask - indeed, simply asking or commanding is the classic spell. Remember 'open, sesame'?

To a child, the world does work like magic. Later in life, we wish that we could go on like that, with our 'wishes coming true'. So we design our shops, our webpages, our cars to fit this truly 'childish' view of the world.

Coming home in the car and clicking the garage open, clicking the infrared remote to open or lock the car, changing TV channels - even switching on the light by the wall switch - are just that kind of magic. Unlike our Victorian forebears, we like to hide the machinery and pre­tend it's not there. So Clarke's dictum is not at all surprising. What it means is that this ape keeps trying, with incredible ingenuity, to get back into the nursery, when everything was done for it. Maybe other intelligent/extelligent species will have a similar helpless early life, which they will attempt to compensate for or relive through their tech­nology? If so, they will 'believe in magic', too, and we will be able to diagnose this by their possession of 'please' and 'thank you' rituals.

We can see this philosophy surviving into adulthood in different human cultures. In 'adult' stories like the Arabian Nights, an assort­ment of djinni and other marvels grant the heroes' wishes by magical means, just like those child-wishes coming true. Many 'romantic' adult stories have the same kind of setting, as do many fantasy tales. Fairness demands we add that, contrary to popular opinion, modern fantasy stories don't; it's hard to get much tension in a plot when anything is possible at the snap of a wand and so the practice of 'magic' therein tends to be difficult, dangerous and to be avoided wherever possible. Discworld is a magical world - we can hear the thoughts of a thun­derstorm, for example, or the conversation of dogs - but magic in the pointy hat sense is very seldom used. The wizards and witches treat it rather like nuclear weaponry: it does no harm for people to know you've got it, but everyone will be in trouble if it gets used. This is magic for grown-ups; it has to be hard, because we know there's no such thing as a free goblin.

Unfortunately, adult beliefs about causality are usually contaminated by the less sophisticated wish-fulfilment philosophy that we carry with us from the tinkly magic of our infancies. For example, scientists will object to alternative theories on the grounds that 'if that was true, we wouldn't be able to do the sums'. Why do they think that nature cares whether humans can do the sums? Because their own desire to do the sums, which lets them write papers for learned journals, contaminates their otherwise rational view. There's a feeling of feet being stamped; the Almighty should change Her laws so that we can do the sums.

There are other ways to set up beliefs about causality, but they are difficult for creatures immersed in their own cultural assumptions: nearly everything that an adult human being is required to do is either made magical by technology, or it is to do with another human being, serving or being served.

These management, leadership and aristocracy issues have been handled very differently in different societies. Feudal societies have baronial class, who are in many respects allowed to remain in the nursery personas by being surrounded by servants and slaves and other parent-surrogates. Rich people in more complex societies, a high-status people in general (knights, kings, queens, princesses, Mafia bosses, operatic divas, pop idols, sports stars) seem to have set societies around them that pander to their needs in a very child-pampering way. As our society has become more technical, more and more of us, right down to the lowest status levels of society, have come to benefit from the accumulating magic of technology. Supermarkets have democratised and validated the provision of all we could want to each of our child-natures. The child-magic has been appropriated by more and more adults, through technology, and the legitimate kind, the 'wonder of nature' magic, has lost out.

In the mid-seventeenth century there was a philosopher, Baruch Spinoza, who derived from the synthetic Renaissance position, and from his criticism of Descartes' publications, a wholly new view of causality. He was one of several figures who bridged the Renaissance and helped engender the Enlightenment. He developed his critical view of his own Jewish cultural authorities into a new rational view of universal causality. He rejected Moses' hearing God's voice, and angels, and lots more 'occult' thinking, particularly early cabbalism; he took the naive magic out of his own religion. He was a lens-grinder, an occupation that requires the persistent checking of performance against reality. So he put in the artisan's view of causality, and he took out the magic of God's word. The Jewish community in Amsterdam excommunicated him. They'd learned about that from the Catholics, but it didn't translate very well into Jewish practice, even of those times.

Spinoza was a pantheist. That is, he believed there is a little bit of God in everything. His main reason for believing this was that if God were separate from the material universe, then there would be an entity greater than God, namely, the entire universe plus God. It fol­lows that Spinoza's God is not a being, not a person in whose image humanity can be made. For this reason, Spinoza was often considered to be an atheist, and many orthodox Jews still view him that way. Despite this, his Ethics makes a beautiful, logically argued case for a particular type of pantheism. In fact, Spinoza's viewpoint is almost indistinguishable from that of most philosophically inclined scientists, from Newton to Kauffman.

Before Spinoza, even his supposed predecessors like Descartes and Leibniz had God moving things in the World by the power of his Voice: magic, child-thinking. Spinoza introduced the idea that an over­arching God could run the universe without being anthropomorphic. Many modern Spinozans see the set of rules, devised, described or attributed by science to the physical world, as the embodiment of that kind of God. That is to say, what happens in the material world hap­pens that way because God, or the Nature of the Physical World, constrains it to do so. And out of that come ideas resembling narrativium instead of magic and wish-fulfilment.

A Spinozan view of child development sees the opposite of wish-fulfilment. There are rules, constraints, that limit what we can do. The child learns, as she grows, to modify her plans as she perceives more of the rules. Initially, she might attempt to cross the room assuming that the chair is not an obstacle; when it doesn't move out of her way, she will feel frustration, a 'passion'. And throws a paddy. Later, as she constructs her path to avoid the chair, more of her plans will peace­ably, and successfully, come to fruition. As she grows and learns more of the rules - God's Will or the warp and woof of universal causation - this progressive success will produce a calm acceptance of con­straints: peace rather than passion.

Kauffman's At Home in the Universe is a very Spinozan book because Spinoza saw that we do indeed make our home, with the reward of peace and the discipline of passion and its control, each of us in their own universe. We fit the universe as a whole, we evolved in it and of it, and a successful life is based on appreciating how it constrains our plans and rewards our understanding. 'Please' and 'thank you' have no place in Spinozan prayer. That view melds the artisan with the philosopher, the tribal respect for tradition with the barbarian virtues of love and honour.

And it gives us a wholly new kind of story with a civilising message. Instead of the barbarian 'And then he rubbed the lamp again ... a again the genie appeared', we have the first king's son taking on a task, to win the hand of the fair princess ... and he fails. Amazing! No barbarian protagonist ever fails. Indeed, nobody ever ultimately fails except evil giants, sorcerers and Grand Viziers, in tribal or barbarian magical tales. However, the new story tells of the second king's s learning from this failure, and shows the listener - the learner - ho difficult the task is. Nevertheless, again he fails, because learning not easy. But the third son - or the third billygoat Gruff or the third pig, with his house of brick - shows how to succeed in a Spinoza enlightened world of observation and experience. Stories in which people learn from the failures of others are a hallmark of a civilised society.

Narrativium has entered our Make-a-Human kit. It makes a different kind of mind from the tribal one, which is all 'do this because we've always done it that way and it works' and 'don't do that because it's taboo, evil and we'll kill you if you do'. And it also differs from the barbarian mind: 'That way lies honour, booty, much wealth and many children (if I can only get a djinn, or a dgun); I would no demean myself, dishonour these hands, with menial work.' In contrast, the civilised child learns to repeat the task, to work with the grain of the universe.

The reader of tales that have been moulded and informed by narrativium is prepared to do whatever an understanding of the task requires. Perhaps, in the universe of the story, qualifying for princesses' hands in marriage isn't the preoccupation of the average middle-class but the attitude of the third prince will serve him well down the mine, in the Stock Exchange, in the Wild West (according to Hollywood, a great purveyor of narrativium), or as father and baron. We say 'he' because 'she' has a more difficult time: narrativium has not been mined and modelled for girls, and the way the feminist myths are shaping it does not seem to address the same questions as the old boy-oriented models. But we can put that right if we realise that narrativium trains by constraint.

Discworld, although technically a world run on fairy tale rules, derives much of its power and success from the fact that they are con­sistently challenged and subverted, most directly by the witch Granny Weatherwax, who cynically uses them or defies them as she sees fit. She roundly objects to girls being forced by the all-devouring 'story' to marry a handsome prince solely on the basis of their shoe size; she believes that stories are there to be challenged. But she herself is part of a larger story, and they follow Riles, too. In a sense, she's always trying to saw off the branch she's sitting on. And her stories derive their power from the fact that we have been programmed from an early age to believe in the monsters that she is battling.

SEVEN

CARGO CULT MAGIC

The phrase that kept occurring to Rincewind was cargo-cult. He'd run across it - he encountered most things by running across them - on isolated islands out on the big oceans.

Say that, once, a lost ship arrived, and while taking on food an water it handed out a few goodies to the helpful locals, like steel knives, arrowheads and fish-hooks. And then it sailed away, and after a while the steel wore out and the arrowheads got lost.

What was needed was another ship. But not many ships came to these lonely islands. What was needed was a ship attractor. Some sort of decoy. And it didn't much matter if it was made out of bamboo and palm leaves, so long as it looked like a ship. Ships would be bound to be attracted to another ship, or else how did you get small boats?

As with many human activities, it made perfect sense, for certain-values of 'sense'.

Discworld magic was all about controlling the vast oceans of magic that poured though the world. All the Roundworld magicians could do was to build something like bamboo decoys on the shores of the big, cold, spinning universe, which pleaded: please let the magic come.

'It's terrible,' he said to Ponder, who was drawing a big circle on the floor, to Dee's fascination. 'They believe they live in our world. With the turtle and everything!'

'Yes, and that's strange because the rules here are quite easy to spot,' said Ponder. 'Things tend to become balls, and balls tend to move in circles. Once you work that out, everything else falls into place. In a curved movement, of course.'

He went back to chalking the circle.

The wizards had been staying in Dee's house. He seemed quite happy about this, in a mildly bemused way, like a peasant who had suddenly been visited by a family of unexpected relatives from the big city who were doing incomprehensible things but were rich and interesting.

The trouble was, Rincewind thought, that the wizards were explain­ing to Dee that magic didn't work while, at the same time, doing magic. A crystal ball was giving instructions. An ape was knuckling in and out of, for want of a better word, fresh air, and wandering around Dee's library making excited 'ook' noises and assembling the books to make a proper entrance in L-space. And the wizards them­selves, as was their wont, prodded at things and argued at cross-purposes.

And Hex had tracked down the elves. It made no sense, but their descent on Roundworld had plunged through time and come to rest millions of years in the past.

Now the wizards had to get there. As Ponder explained, sometimes resorting to hand gestures for the hard of comprehension, this wasn't difficult. Time and space in the round universe were entirely subor­dinate. The wizards, being made of higher-order stuff, could quite easily be moved around within it by magic from the real world. There were additional, complex reasons, mostly quite hard to spell.

The wizards didn't understand almost all this, but they did like the idea of being high-order stuff.

'But there was nothing back there,' said the Dean, watching Ponder Work on the circle. 'There wasn't even anyone you could call people, Hex says.'

'There were monkeys,' said Rincewind. 'Things like monkeys, any­way.' He had his own thoughts on this score, although the accepted wisdom on Discworld was that monkeys were the descendants of people who had given up trying.

'Oh, the monkeys,' snapped Ridcully. 'I remember them. Completely useless. If you couldn't eat it or have sex with it, they just didn't want to know. They just mucked about.'

'I think this was even before that,' said Ponder. He stood up and brushed chalk dust off his robe. 'Hex thinks that the elves did something to ... something. Something that became humans.'

'Interfered with them?' said the Dean.

'Yes, sir. We know they can affect people's minds when they sing-'

'You said became humans? said Ridcully.

'Yes, sir. Sorry, sir. I really don't want to have that argument all over again, sir. On Roundworld, things become other things. At least, some of some things become other things. I'm not saying that happens on Discworld, sir, but Hex is quite certain that it happens here. Can we just pretend for a moment, sir, that this is true?'

'For the sake of argument?'

'Well, for the sake of not having an argument, sir, really,' said Ponder. Mustrum Ridcully on the subject of evolution could go on for far too long.

'All right, then,' said the Archchancellor with some reluctance.

'And we know, sir, that elves can really affect the minds of lesser creatures ...'

Rincewind let the words go over his head. He didn't need to be told this. He'd spent far more time in the field - and the ditch, the forest, hiding in the reeds, staggering across deserts - and had run into and away from elves a couple of times. They didn't like all the things that Rincewind thought made life worthwhile, like cities and cookery and not being hit over the head with rocks on a regular basis. He'd never been certain if they actually ate anything, other than for amusement; they acted as if what they really consumed was other creatures' fear.

They must have loved humanity when they found it. Humanity was very creative, when it came to being frightened. It was good at filling the future full of dread.

And then it had gone and spoiled everything by using that won­derful, fear-generating mind for thinking up things to take the fear away - like calendars, locks, candles and stories. Stories in particular. Stories were where the monsters died.

While the wizards argued, Rincewind went to see what the Librarian was doing. The ape, shorn of his dress but still wearing his ruff to con­form to local clothing standards, was as happy as, well, as happy as a librarian among books. Dee was quite a collector. Most of the books were about magic or numbers or magic and numbers. They weren't very magical, though. The pages didn't even turn by themselves.

The crystal sphere had been placed on a shelf, so that Hex could watch.

'The Archchancellor wants us all to go back and stop the elves,' said Rincewind, sitting down on a stack of titles. 'He thinks we can ambush them before they do anything. Me, I don't think it's going to work.'

Ook?' said the Librarian, sniffing a bestiary and laying it aside.

'Because things generally don't, that's why. Best laid plans, and all that. And these aren't best laid plans, anyway. "Let's get back there and beat the devils to death with big iron bars" is not, in my opinion, a best laid plan. What's funny?'

The Librarian's shoulders were shaking. He passed a book across to Rincewind, who read the passage that had been pointed out by a black fingernail.

He stopped reading, and stared at the Librarian.

It was uplifting. Oh, it was uplifting. Rincewind hadn't read any­thing like it. But ...

He'd spent the day in this city. There were dog fights and bear pits and that wasn't the worst of it. He'd seen the heads on spikes over the gates. Of course, Ankh-Morpork had been bad, but Ankh-Morpork had thousands of years of experience of being a big city and had become, well, sophisticated in its sins. This place was half farmyard.

The man who wrote this woke up every morning in a city that burned people alive and had still written this.

'-what a piece of work is a man ... how noble in reason ... how infinite in faculty ... in form, in moving, how express and admirable ...'

The Librarian was almost sobbing with laughter.

'Nothing to laugh at, it's a perfectly valid point of view," said Rincewind. He shuffled the pages.

'Who wrote this?' he said.

'According to the flows of L-space, he is widely regarded as one of the greatest playwrights who ever lived,' said Hex, from the shelf.

'What was his name?'

'His own spelling is inconsistent,' said Hex, 'but the consensus is that his name was William Shakespeare.'

'Does he exist on this world?'

'Yes. In one of the many alternate histories.'

'So not actually here, then?'

'No. The leading playwright in this city is Arthur J. Nightingale.'

'Is he any good?'

'He is the best they have. Objectively, he is dreadful. His play King Rufus III is widely considered the worst play ever written.'

'Oh.'

'Rincewind!' bellowed the Archchancellor.

The wizards were gathering in the circle. They had tied horseshoes and bits of iron to their staffs and had the look of high-order men prepared to kick low-order ass. Rincewind tucked the pages in his robe, picked up Hex and hurried over.

'I'll just-' he began.

'You're coming, too. No arguing. And the Luggage,' snapped Ridcully.

'But-'

'Otherwise we might have a talk about seven buckets of coal,' the Archchancellor went on.

He knew about the buckets. Rincewind swallowed.

'Leave Hex behind with the Librarian, will you?' said Ponder. 'He can keep an eye on Dr Dee.'

'Isn't Hex coming?' said Rincewind, alarmed at the prospect of losing the only entity at UU that seemed to have a grasp on things.

'There will be no suitable avatars,' said Hex.

'He means no magic mirrors, no crystal balls,' said Ponder. 'Nothing that people expect to be magical. No people at all, where we're going. Put Hex down. We'll be back instantly, in any case. Ready, Hex?'

For a moment the circle glowed, and the wizards vanished.

Dr Dee turned to the Librarian.

'It works!' he said. 'The Great Seal works! Now I can-'

He vanished. And the floor vanished. And the house vanished. And the city vanished. And the Librarian landed in the swamp.

EIGHT

PLANET OP THE APES

'What a piece of work is a man! How noble in reason! How infinite in faculty! In form, in moving, how express and admirable! In action how like an angel! In apprehension how like a god!'

But you wouldn't want to watch him eat, close up ...

William Shakespeare was another key figure in the transition from medieval mysticism to post-Renaissance rationalism. We were going to mention him, but we had to wait for him to turn up in Roundworld.

Shakespeare's plays are a cornerstone of our present Western civil­isation. They led us from a confrontation between aristocratism, barbarism and tradition-bound tribalism into real civilisation as we know it. And yet ... he seems to be a contradiction: uplifting sentiments in a barbarous age. That's because he was standing at a pivot point in history. The elves have been seeking something that will become human, and will interfere with Roundworld to make sure they get it. Humans are superstitious. But the human condition can also create a Shakespeare. Though not in this version of history.

The elves aren't the only Discworld inhabitants that have interfered with Roundworld: the wizards have tried some 'uplift' of their own, in the sense of David Brin, and using the techniques of Arthur C. Clark near the end of The Science of Discworld, the apes of Roundworld are sitting in their cave, watching a manifestation from another dimension, an enigmatic black rectangular slab ... The Dean of Unseen University taps on it with his pointer, to attract attention, and chalks the letters R-O-C-K. 'Rock. Can anyone tell me what you do with it?' But all the apes are interested in is S-E-X.

The next time the wizards look at Roundworld, the space elevator is collapsing. The planet's inhabitants are heading out into the uni­verse on vast ships made from the cores of comets.

Something very dramatic has happened between the apes and the space elevator. What was it? The wizards have no idea. They doubt very much it could have had much to do with those apes, who were very much The Wrong Stuff.

In the first volume of The Science of Discworld, we explored no fur­ther. We left a gap. It was a tiny part of the historical record on the geological timescales that governed everything up to the ape, but rather a big gap in terms of changes to the planet. But now even the wizards are aware that the apes, unpromising material as they may have been, did in fact evolve into the creatures that built the space elevator and fled from a very dangerous planet in search of, as Rincewind would put it, a place where you are not hit on the head with rocks on a regular basis. And, apparently, a key step in their evo­lution was elvish interference.

How did it actually happen on Roundworld? Here, the whole process took a mere five million years. One hundred thousand Grandfathers ago, we and the chimpanzees shared a distant ancestor. The chimpanzeelike ancestor of Man was also the Manlike ancestor of the chimpanzee. To us, it would have looked astonishingly like a chim­panzee - but to a chimpanzee, it would have looked astonishingly like a human.

DNA analysis shows, beyond any shadow of reasonable doubt, that our closest living relatives are chimpanzees: the ordinary ('robust') chimpanzee Pan troglodytes and the more slender ('gracile') bonobo Pan paniscus, often politically incorrectly called the pygmy chim­panzee. Our genomes have 98 per cent in common with both, leading Jared Diamond to refer to humans as 'the third chimpanzee' in a book of the same title.

The same DNA evidence indicates that we and today's chim­panzees parted company, specieswise, those five million yean (100,000 Grandfathers) ago. That figure is debatable, but it can't be very far wrong. The gorillas split off a little earlier. The earliest fos­sils of our 'hominid' ancestors are found in Africa, but there are numerous later fossilised hominids from other parts of the world such as China and Java. The oldest known are two species of Australopithecus, each about 4-4.5 million years old. The Australopithecines had a good run: they hung around until about 1-1.5 million years ago, at which point they gave way to genus Homo: Homo rudolfensis, Homo habilis, Homo erectus, Homo ergaster, Hot heidelbergensis, Homo neanderthalensis, and finally us, Homo sapiens. And somehow another Australopithecine inserted itself into the middle of those Homos. In fact the more hominid fossils we find, the more complicated our conjectured ancestry becomes, and it now looks as if many different hominid species coexisted on the plains of Africa for most of the past five million years.

Today's chimpanzees are quite bright, probably a lot brighter than the apes that the Dean tried to teach spelling to. Some remarkable experiments have shown that chimps can understand a simple version of language, presented to them as symbolic shapes. They can even form simple concepts and make abstract associations, all within a linguistic frame. They can't build a space elevator, and they never will unless they evolve considerably and avoid being killed for 'bush meat'.

We can't build one either, but it might take no more than a couple of hundred years before the things are sprouting all along the equator. All you need is a material with enough tensile strength, perhaps some composite involving carbon nanotubes. Then you dangle cable from geostationary satellites, hang elevator compartments from them, equip them with suitable space elevator music ... after which, leaving the planet becomes entirely straightforward. The energy cost, hence the marginal financial cost, is near enough zero, because for every­thing that needs to go up, something else needs to come down. It could be moon rock, or platinum mined in the asteroid belt, or the astronaut that the person going up is due to replace on duty. The cap­ital cost of such a project is enormous, though, which is why we're not in any great hurry right now.

The big scientific problem in this connection is: how can evolution get so quickly from an ape that can't compete mentally with a chim­panzee to a godlike being that can write poetry as good as Shakespeare's, and has advanced so rapidly from that point that it will surely soon erect (drop) a space elevator? 100,000 Grandfathers hardly seems long enough, given that it took about 50 million Grandfathers to get from a bacterium to the first chimpanzee.

Something that dramatic needed a new trick. That trick was the invention of culture. Culture allowed any individual ape to make use of the ideas and discoveries of thousands of other apes. It let the ape collective acquire knowledge cumulatively, so that it didn't all get lost when its owner died. In Figments of Reality we coined the term 'extelligence' for this suite of tricks, and the word is beginning to become common currency. Extelligence is like our own personal intelligence, but it lives outside us. Intelligence has limits; extelligence is infinitely expandable. Extelligence lets us pull ourselves upwards, as a group, by our own mental bootstraps.

The contradiction between Shakespeare's noble sentiments and the heads-on-spikes culture in which he lived is a consequence of his posi­tion as a very intelligent intelligence in a not-very-extelligent extelligence. Many individuals possessed the nobility to qualify for Shakespeare's praise, but their as yet rudimentary extelligence had not yet transmitted that nobility into the general culture. The culture was, or claimed to be, noble in principle - kings taking their authority from God Himself - but it was a barbarian style of nobility. And it was welded to a barbarian cruelty, the kings' means of self-preservation.

There may be many ways to make intelligent creatures, and many more ways to knit them together into an extelligent culture. The crab civilisation in The Science of Discworld was doing fine until its Great Leap Sideways was clobbered by an inbound comet. We made that one up, but who knows what might have happened a hundred mil­lion years ago? All we know for sure - or for a given value of 'sure', since even now a lot of our knowledge is guesswork - is that some things like apes turned into us. It takes a special kind of arrogance and blindness to extrapolate that story to the rest of the universe with­out wondering about alternatives.

An important ingredient in our story was brains. Weight for weight, humans have far bigger brains than any other animal on the planet. The average human brain has a volume of about 1,350 cubic centimetres, which is roughly three times as great as the brain of apes with the same size body as ours. Whale brains are bigger than ours, but whales are even bigger, so the amount of whale per brain cell is greater than the amount of human per brain cell. When it comes to the brains, quantity is less important than quality, of course. But a brain capable of really complicated things like carbon nanotube engineering and fixing dishwashers has to be fairly large, because the abilities of small brains are limited by lack of room to do anything interesting. We'll see shortly that brains alone are not enough. Nonetheless, without out brains, or adequate substitutes, you don't get very far.

There are two main theories of human origins. One is rather dull and probably correct; the other is exciting and most likely wrong. Nevertheless, the second one has quite a lot going for it and is a better story, so let's take a look at them both.

The dull, conventional theory is that we evolved on the savannahs. Roving groups of early apes trailed through the long grass, picking up whatever food - seeds, lizards, insects - they could find, much like today's baboons. And as they did so, lions and leopards prowled through the long grass looking for monkeys. Those monkeys or apes that were better at spotting the telltale flicker of a big cat's tail, and finding a tree rather quickly, survived to have babies; those that per­formed poorly at such tasks did not. The babies inherited those survival skills, and passed them on to their babies.

What these tasks need is computational power. Spotting a tail and finding a tree are pattern-recognition problems. Your brain needs to pick out the tail-shape from a background of similarly buff-coloured rocks and mud; it has to choose a tree that is tall enough, and climbable enough, without being too climbable, and it has to be able to do it fast. A capacious brain with a big memory (of past occasions when something hairy poked out from behind a rock, and of locations for climbable trees) can pick up the visual traces of a lion much more effectively than a small brain can. A brain whose nerve cells transmit signals to each other more quickly can analyse incoming sensory data and conclude 'lion' a lot faster than a slower brain can. So there was evolutionary pressure on the early apes and monkeys to develop big­ger and faster brains. There was also evolutionary pressure on the lions to conceal themselves more effectively, so that those bigger and faster ape and monkey brains still didn't notice anything suspicious. So a predator-prey 'arms race' developed, a positive feedback loop that made both lions and apes far more effective in their ecological roles.

That is the conventional story of human evolution. But there is another story, less orthodox, with two main sources.

Human beings are very weird apes, indeed very weird animals alto­gether. They have extremely short fur, mostly just a downy covering. They walk upright on two legs. They have a layer of fat, all the year round. They mate face-to-face (often). They have exceptionally good breath-control; good enough to be able to speak. They weep and they sweat. They adore water, and can swim long distances. A newborn baby, dropped in a pool, can keep itself afloat: the ability to swim is instinctive. All these peculiarities led Elaine Morgan to write The Aquatic Ape in 1982. There she suggested a radical theory: that humans evolved not on the savannahs, surrounded by fierce predators, but on the beach. That explains the swimming, the upright stance (it's easier to evolve a two-legged gait if you are buoyed up by seawater), and the lack of hair (which causes problems when you swim, providing an evolutionary reason for it to disappear). In fact it can be argued that it explains all of the peculiarities of humans that we've just listed. The original scientific underpinnings of this theory were developed by Alister Hardy.

In their 1991 The Driving Force Michael Crawford and David Marsh took the story one stage further, by added one extra ingredient. Literally. The most important thing that the beach provides is seafood. And the most important thing that seafood provides is 'essential fatty acids', which are a crucial ingredient in brains. In fact, nearly two-thirds of the human brain is made from them. Fatty acids are good for making membranes, and brains use electrical signals in membranes to compute. Myelin, in a membrane sheath surrounding nerve cells, speeds up the transmission of signals in the human nervous system by a factor of five or so. It takes a lot of essential fatty acids, then, to make a big, fast human brain, so it must have taken almost as much to make the brain of our distant ape ancestor. Oddly, though, our bod­ies cannot make those special fatty acids from simpler chemicals, like we make most complicated biochemicals that we need. We have to get the fatty acids, ready-made, from our food; that's why the word 'essential' is used to describe them. Even more oddly, there are few essential fatty acids out on the savannahs. They would exist only in living creatures, of course, but even there, they are fairly rare. The rich­est source of essential fatty acids is seafood.

Perhaps all this explains why we want to spend so much time on the beach. But whatever the explanation, the ability to make big brain was one key step in our evolution away from our hairy, quadrupedal 100,000-fold great grandfather.

Big brains, however, are not enough. What really matters is what you do with them. And what we managed to do was to play off one brain against another, so that over the millennia they got better and better at competing and communicating.

Ape brains competing with lion brains leads to an arms race that improves both, but the arms race is fairly slow, because both brains are being used for very limited purposes as far as the competition goes. Ape brains competing with other ape brains gives the whole brain a workout, all the time, so the rate of evolution is likely to be much higher.

For every species, the main competition comes from other creatures of the same species. This is reasonable; they're the ones that want exactly the same resources that you do. This opens the door to elvish interference, in our Discworld metaphor. The nasty side of human nature, which in extremes leads to evil, is inescapably bound up with the nice side. One very direct way to compete with your neighbour is to bash him on the head, hard.

However, there are more subtle ways to gain evolutionary advance­ment, as we will see later. The elvish approach is crude, and ultimately self-defeating, for a sufficiently extelligent species.

The possession of brains opens up new non-genetic ways to pass characteristics on to your children. You can give them a good start in life by moulding how their brains react to the outside world. The generic term for this kind of non-genetic transfer between the gener­ations is privilege. There are numerous instances of privilege in the animal kingdom. When a mother blackbird provides yolk in her egg for the baby blackbird to feed from, that's privilege. When a cow pro­vides milk for her calf, that's even more privilege. When a mother tarantula wasp provides a paralysed, living spider for her grubs to grow in, that's privilege.

Humans have taken privilege to a qualitatively new level. Human parents invest an astonishing amount of time and effort in their chil­dren, and spend decades - entire lifetimes, in many ways - looking after them. In conjunction with big brains, slowly getting bigger as each generation passes, privilege leads to two new tricks, learning and teaching. Those tricks feed off each other, and both require the best brain you can acquire.

Genes are involved in building brains, and genes can perhaps pre­dispose individuals to be unusually good at learning or teaching. However, both of these educational processes involve far more than mere genes: they take place within a culture. The child does not just learn from its parents. It learns from its grandparents, from its siblings, from its aunts and uncles, from the whole troupe or tribe. It learns, as all parents discover, to their dismay, from undesirable sources as well as authorised ones. Teaching is the attempt to transmit ideas from the adult brain to that of the child; learning is the child's attempt to insert those ideas into its brain. The system is imperfect, with a lot of garbled messages along the way, but despite its faults it is much faster than genetic evolution. That's because brains, networks of nerve cells, can adapt much more rapidly than genes can.

The faults, oddly enough, probably accelerate the process, because they are a source of creativity and innovation. An accidental misunderstanding may sometimes lead to an improvement. In this respect, cultural evolution is just like genetic evolution: it is only because the DNA copying system makes mistakes that organisms can change.

Culture didn't arise in a vacuum: it had many precursors. One crucial step towards the development of culture was the invention of the nest. Before nests came into being, any experimentation by the young either worked, or led to a quick death. Within the protection of the nest, however, young animals can try things out, make mistakes and profit from them; for example, by learning not to do the same thing again. Outside the nest, they never get a chance to try a second time. In this manner nests led to another development, the role of play in educating the young animal. Mother cats bring half-dead mice for their kittens to practise hunting on. Mother birds of prey do the same for their offspring. Polar bear cubs slide down snow-slopes and look cute. Play is good fun, and the kids enjoy it; at the same time, it equips them for their adult roles.

Social animals, ones that gather in groups and operate as groups, are a fertile breeding-ground for privilege and for education. And with appropriate communication, groups of animals can achieve things that no individual can manage. A good example is dogs, which evolve the ability to hunt in packs. When such tricks are being played, it is important to have some recognition signal that lets the pack distinguish its own members from outsiders, otherwise the pack can do the work and then an outsider can steal the food. Each dog pack h its own call-sign, a special howl that only insiders know. The more elaborate your brain, the more elaborate the communication from brain to brain can be, and the more effectively education works.

Communication helps with the organisation of group behaviour, and it opens up survival techniques that are more subtle than bashing oth­ers on the head. Within the group, cooperation becomes a far more viable option. Today's great apes generally work as small groups, and it seems likely that their ancestors did the same. When humans split off from the chimpanzee lineage, those groups became what we now call tribes.

Competition between tribes was intense, and even today some jun­gle tribes in South America and New Guinea think nothing of killing anyone they meet who comes from a different tribe. This is a rever­sion to the 'bash on the head' option, but now one group cooperates to bash the other group's members on the head. Or, usually, one such member at a time. Less than a century ago, most such tribes did the same (one of the stories we've told ourselves throughout our tribal history is that we are The People, The True Human Beings - which means that everyone else isn't).

Chimpanzees have been observed killing other chimpanzees, and they regularly hunt smaller monkeys for meat. That isn't cannibalism. The food is a different species. Most humans cheerfully consume other mammals, even quite intelligent ones like pigs.

Just as dog-packs need an agreed recognition signal to identify their members, so each tribe needs to establish a distinct identity. The pos­session of big brains makes it possible to do this by means of elaborate, shared rituals.

Ritual is by no means confined to humans: many species of birds, for instance, have special mating dances, or engage in strange devices to attract the female's attention, like the decorative collections of berries and pebbles assembled by the male bower-bird. But humans, with their highly developed brains, have turned ritual into a way of life. Every tribe, and nowadays every culture, has developed a Make-a-Human kit whose object is to bring up the next generation to adopt the tribal or cultural norms and pass them on to their own children.

It doesn't always work, especially nowadays when the world has shrunk and cultures clash across non-geographical boundaries - Iranian teenagers accessing the Internet, for example - but it still works surprisingly well. Corporations have taken up the same idea, with 'corporate bonding' sessions. This is what the wizards were up to with their paintballs. Studies have shown that sessions of this kind have no useful effect, but businesses still waste billions on them every year. The second most probable reason is that such sessions are fun anyway. The first most probable is that everyone likes an opportunity to shoot Mr Davis in Human Resources. And one important reason is that it sounds as though it ought to work; our culture is full of stories where such things do.

An important part of the Make-a-Human kit is the Story. We tell our children stories, and through those stories they learn what it is like to be a member of our tribe or our culture. They learn from the story of Winnie the Pooh getting stuck in Rabbit's hole that greed can lead to constraints on food. From the Three Little Pigs (a civilising story, not a tribal one) they learn that if you watch your enemy for repetitive patterns, you can outwit him. We use stories to build our brains, and then we use the brains to tell ourselves, and each other, stories.

As time passes, those tribal stories acquire their own status, and peo­ple cease to question them because they are traditional tribal stories. They acquire a veneer of - well, the elves would call it 'glamour'. They seem wonderful, despite numerous obvious faults, and most people do not question them. On Discworld, precisely this process occurred with stories and folk-memories about elves, as we can illustrate with three quotations from Lords and Ladies. In the first, the god of all small furry prey, Herne the Hunted, has just come to the terrified realisation that 'They're all coming back!' Jason Ogg, who is a blacksmith, the eldest son of the witch Nanny Ogg, and not very bright, asks her who They are:

'The Lords and Ladies,' she said.

'Who're they?'

Nanny looked around. But, after all, this was a forge ... It wasn't just a place of iron, it was a place where iron died and was reborn. If you couldn't speak the words here, you couldn't speak 'em anywhere.

Even so, she'd rather not.

'You know,' she said. 'The Fair Folk. The Gentry. The Shining Ones. The Star People. You know.'

'What?'

Nanny put her hand on the anvil, just in case, and said the word.

Jason's frown very gently cleared, at about the same speed as a sunrise.

'Them?' he said. 'But aren't they nice and-'

'See?' said Nanny. 'I told you you'd get it wrong!'

You said: The Shining Ones. You said: The Fair Folk. And you spat, and touched iron. But generations later, you forgot about the spitting and the iron, and you forgot why you used those names for them, and you remembered only that they were beautiful ... We're stupid, and the memory plays tricks, and we remember the elves for their beauty and the way they move, and we forget what they were. We're like mice saying, 'Say what you like, cats have got real style.'

Elves are wonderful. They provoke wonder.

Elves are marvellous. They cause marvels.

Elves are fantastic. They create fantasies.

Elves are glamorous. They project glamour.

Elves are enchanting. They weave enchantment.

Elves are terrific. They beget terror.

The thing about words is that meanings can twist just like a snake, and if you want to find snakes look for them behind words that have changed their meaning.

No-one ever said elves are nice.

Elves are bad.

For most purposes (though, admittedly, not when dealing with elves) it doesn't greatly matter if the traditional tales make no real sense. Father Christmas and the Tooth Fairy make no immediate sense (on Roundworld, but see Hogfather for their Discworld significance). Mind you, it's clear why children are happy to believe in such generosity. The most important role of the tribal Make-a-Human kit is to provide the tribe with its own collective identity, making it possible for it to act as a unit. Tradition is good for such purposes; sense is optional. All religions are strong on tradition, but many are weak on sense, at least if you take their stories literally. Nevertheless, religion is absolutely central to most cultures' Make-a-Human kit.

The growth of human civilisation is a story of the assembly of ever-larger units, knitted together by some version of that Make-a-Human kit. At first, children were taught what they must do to be accepted as members of the family group. Then they were taught what they must do to be accepted as members of the tribe. (Believing apparently ridiculous things was a very effective test: the naive outsider would all too readily betray a lack of belief, or would simply have no idea what the appropriate belief was. Is it permitted to pluck a chicken before dark on Wednesday? The tribe knew, the outsider did not, and sine any reasonable person would guess 'yes' the tribal priesthood could go a long way by making the accepted answer 'no'.) After that, the same kind of thing happened for the local baron's serfs, for the village, the town, the city and the nation. We spread the net of True Human Beings.

Once units of any size have acquired their own identity, they can function as units, and in particular they can combine forces to make a bigger unit. The resulting structure is hierarchical: the chains of com­mand reflect the breakdown into sub-units and sub-sub-units. Individual people, or individual sub-units, can be expelled from the hierarchy, or otherwise punished, if they stray outside accepted (or enforced) cultural norms. This is a very effective way for a small group of people (barbarian) to maintain control over a much larger group (tribal). It works, and because of that we still labour under its restrictions, many of which are undesirable. We have invented technique like democracy to try to mitigate the undesirable effects, but these techniques bring new problems. A dictatorship can generally take action more rapidly than a democracy, for example. It's harder to argue.

The path from ape to human is not just one of evolutionary pres­sures producing more and more effective brains; not just a tale of the evolution of intelligence. Without intelligence, we could never have got started on that path, but intelligence alone was not enough. We had to find a way to share our intelligence with others, and to store useful ideas and tricks for the benefit of the whole group, or at least, those in a position to make use of it. That's where extelligence comes into play. Extelligence is what really gave those apes the springboard that would launch them into sentience, civilisation, technology, and all the other things that make humans unique on this planet. Extelligence amplifies the individual's ability to do good - or evil. It even creates new forms of good and evil, such as, respectively, coop­eration and war.

Extelligence operates by putting ever more sophisticated stories into the Make-a-Human-Being kit. It pulled us up by our own bootstraps: we could climb from tribal to barbarian to civilised.

Shakespeare shows us doing it. His period was not a rebirth of Hellenistic Greece or Imperial Rome. Instead, it was the culmination of the barbarian ideas of conquest, honour and aristocracy, codified in the principles of chivalry, meeting its match in the written princi­ples of a tribal peasantry, and disseminated by printing. This kind of sociological confrontation produced many events in which the two cultures meet head on.

This was exemplified by the Warwickshire enclosure uprisings. In Warwickshire, the aristocracy carved up land into small parcels, and the peasantry got very upset because the aristocracy didn't give any heed to what kind of land was in each parcel. All the aristocrats knew about peasant farming was a simplistic calculation: this much land will suffice for that many peasants. The peasants knew what was actually involved in growing food, so that the only thing you could do with a small piece of woodland, for instance, was to chop down all the trees to make room to grow some food.

Today's bean-counting managerial style in many businesses, and all British public services, is exactly the same. This kind of confrontation between the barbarian attitudes of the nobility and the tribal ones of the peasantry is precisely portrayed in many of Shakespeare's plays, as an illustration of low-life, with its folk wisdom as comic relief and pathos, set against the lofty ideals of the ruling classes - leading so often to tragedy.

But also to high comedy. Think of Theseus, Duke of Athens, on the one hand, and Bottom on the other, in A Midsummer Night's Dream.

NINE

THE ELVISH QUEEN

In the heat of the night, magic moved on silent feet.

One horizon was red with the setting sun. This world went around a central star. The elves did not know this. If they had done, it would not have bothered them. They never bothered with detail of that kind. The universe had given rise to life in many strange places, but the elves were not interested in that, either.

This world had created lots of life, too. None of it had ever had what the elves considered to be potential. But this time ...

It had iron, too. The elves hated iron. But this time, the rewards were worth the risk. This time ...

One of them signalled. The prey was close at hand. And now they saw it, clustered in the trees around a clearing, dark blobs against the sunset.

The elves assembled. And then, at a pitch so strange that it entered the brain without the need to use the ears, they began to sing.

'Charge!' cried Archchancellor Ridcully.

The wizards, all bar Rincewind, charged. He peered around from behind a tree.

The elf song, a creative dissonance of tones that went straight into the back of the brain, ceased abruptly.

Thin figures spun around. Almond eyes glowed in triangular faces.

People who knew the wizards only as the world's most avid diners would have been quite surprised at their turn of speed. Besides, while it may take a little while for a wizard to reach maximum acceleration, he's then very hard to stop. And he carries such a cargo of aggression; the stratagems of the Uncommon Room at UU are guaranteed to give any wizard a maximum load of virulence just itching for a target.

The Dean hit first, striking an elf a blow with his staff. A horseshoe had been wired to the end. The elf screamed and twisted back, clutch­ing at its shoulder.

There were many elves but they hadn't been expecting an attack. And iron was so powerful. A handful of flung nails had the effect of buckshot. Some tried to fight back, but the dread of iron was too strong.

The prudent and the survivors took to their skinny heels, while the dead evaporated.

The attack took less than thirty seconds. Rincewind watched it from behind his tree. He was not being cowardly, he reasoned. This was a job for specialists, and could safely be left to the senior wizards. If, later on, there was a problem involving slood dynamics or fretwork, or someone needed to misunderstand some magic, he would be happy to step forward.

There was a rustling behind him.

Something was there. What it was changed as he turned and stared. The first talent of the elves was their singing. It could turn other creatures into potential slaves. The second talent was their ability to change not their shape but how their shape was perceived. For a moment Rincewind caught sight of a slim, spare figure glaring at him and then, in one blurred moment, it became a woman. A queen, in a red dress and a rage.

'Wizards?' she said. 'Here? Why? How? Tell me!' A gold crown glittered in her dark hair and murder gleamed in her eyes as she advanced on Rincewind, who backed up against his tree. 'This is not your world!' the elf queen hissed. 'You'd be amazed,' said Rincewind. 'Now!' The queen's brow wrinkled. 'Now?' she repeated. 'Yes, I said now,' Rincewind said, grinning desperately. 'Now was the word I said, in fact. Now!'

For a moment the queen looked puzzled. And then she somer­saulted backwards in a high arc, just as the Luggage's lid snapped shut where she had been. She landed behind it, hissed at Rincewind, and vanished into the night.

Rincewind glared at the box. 'Why did you wait? Did I tell you to wait?' he demanded. 'You just like to stand right behind people and wait for them to find out, right?'

He looked around. There was no sign of any more elves. In the mid­dle distance the Dean, having run out of enemies, was attacking a tree.

Then Rincewind looked up. Along the branches, clinging to one another and staring down at him in wide-eyed amazement, were dozens of what looked, in the moonlight, like rather small and wor­ried monkeys.

'Good evening!' he said. 'Don't worry about us, we're just passing through ...'

'Now this is where it all gets complicated,' said a voice behind him. It was a familiar one, being his own. 'I've only got a few seconds before the loop closes, so here's what you have to do. When you go back to Dee's time ... hold your breath.'

Are you me?' said Rincewind, peering into the gloom.

'Yes. And I'm telling you to hold your breath. Would I lie to me?'

There was an inrush of air as the other Rincewind disappeared and, down in the clearing, Ridcully bellowed Rincewind's name.

Rincewind stopped looking around and hurried down to the other wizards, who were looking immensely pleased with themselves.

Ah, Rincewind, I thought you wouldn't want to be left behind,' said the Archchancellor, grinning nastily. 'Got any, did you?'

'The queen, in fact,' said Rincewind. 'Really? I'm impressed!'

'But she - it got away.'

'They've all gone,' said Ponder. 'I saw a blue flash on that hill up there. They've gone back to their world.'

'D'you think they'll come back?' said Ridcully.

'It doesn't matter if they do, sir. Hex will spot them and we can always get there in time.'

Ridcully cracked his knuckles. 'Good. Capital exercise. Much better than magicking paint at one another. Builds grit and team interdependency. Someone go and stop the Dean attacking that rock, will you? He does rather get carried away.'

A faint white ring appeared on the grass, wide enough to hold the wizards.

'Ah, the ride back,' said the Archchancellor, as the excited Dean was hustled towards the rest of the group. 'Time to-'

The wizards were suddenly in empty air. They fell. All but one of them were not holding their breath before they hit the river.

Wizards do, however, have good floating capabilities and a tendency to bob up and down. And the river was in any case rather like a slowly moving swamp. Floating logs and mud banks choked it. Here and there, mud banks had become sufficiently established to sprout a crop of trees. By degrees, and with much arguing about where dry land actually began - it was not very obvious - they splashed their way to the shore. The sun was hot overhead, and clouds of mosquitoes shim­mered among the trees.

'Hex has brought us back to the wrong time,' said Ridcully, wring­ing out his robe.

'I don't think he'd do that, Archchancellor,' said Ponder, meekly. 'The wrong place, then. This is not a city, in case you hadn't noticed.'

Ponder looked around in bewilderment. The landscape around them was not exactly land and not exactly river. Ducks were quacking, somewhere. There were blue hills in the distance.

'On the upside,' said Rincewind, extracting frogs from a pocket, 'everything smells better.'

'This is a swamp, Rincewind.'

'So?'

'And I can see smoke,' said Ridcully.

There was a thin grey column in the middle distance.

Reaching it took a lot longer than the mere distance suggested. Land and water were contesting every step of the way. But, eventually, and with only one sprain and a number of bites, the wizards reached some thick bushes and peered into the clearing beyond.

There were some houses, but that was stretching the term. They were little more than piles of branches with reed roofs.

'They could be savages,' said the Lecturer in Recent Runes.

'Or perhaps someone sent them all out into the country to forge a dynamic team spirit,' said the Dean, who had been badly bitten.

'Savages would be too much to hope for,' said Rincewind, watch­ing the huts carefully.

'You want to find savages?' said Ridcully.

Rincewind sighed. 'I am the Professor of Cruel and Unusual Geography, sir. In an unknown situation, always hope for savages. They tend to be quite polite and hospitable provided you don't make any sudden moves or eat the wrong sort of animal.'

'Wrong sort of animal?' said Ridcully.

'Taboo, sir. They tend to be related. Or something.'

'That sounds rather ... sophisticated,' said Ponder suspiciously.

'Savages often are,' said Rincewind. 'It's the civilised people that give you trouble. They always want to drag you off somewhere and ask you unsophisticated questions. Edged weapons are often involved. Trust me on this. But these aren't savages, sir.'

'How can you tell?'

'Savages build better huts,' said Rincewind firmly. 'These are edge people.'

'I've never heard of edge people!' said Ridcully.

'I made it up,' said Rincewind. 'I run into them occasionally. People that live right on the edge, sir. Out on rocks. In the worst kind of desert. No tribe or clan. That takes too much effort. Of course, so does beating up strangers, so they're the best kind of people to meet.'

Ridcully looked around at the swamp. 'But there's waterfowl every­where,' he said. 'Birds. Eggs. Lots of fish, I'll be bound. Beavers. Animals that come down to drink. I could eat myself greasy to the eye­brows here. This is good country.'

'Hold on, one of them's coming out.' said the Lecturer in Recent Runes.

A stooping figure had emerged from a hut. It straightened up, and stared around. Huge nostrils flared.

'Oh my, look what just fell out of the ugly tree,' said the Dean. 'Is it a troll?'

'He's certainly a bit rugged,' said Ridcully. 'And why is he wearing boards?'

'I think he's just not very good at tanning hides,' said Rincewind.

The enormous shaggy head turned towards the wizards. The nos­trils flared again.

'He smelled us,' said Rincewind, and started to turn. A hand grabbed the back of his robe.

'This is not a good time to run away, Professor,' said Ridcully, lift­ing him off the ground in one hand. 'We know you're good at languages. You get on with people. You have been chosen to be our ambassador. Do not scream.'

'Besides, the thing looks like cruel and unusual geography,' said the Dean, as Rincewind was thrust out of the bushes.

The big man watched him, but made no attempt to attack.

'Go on!' hissed the bushes. 'We need to find out when we are!'

'Oh, right,' said Rincewind, eyeing the giant cautiously. 'And he's going to tell me, is he? He's got a calendar, has he?'

He advanced carefully, hands up to show that he didn't have a weapon. Rincewind was a great believer in not being armed. It made you a target.

The man had obviously seen him. But he didn't seem very excited about it. He watched Rincewind as someone might watch a passing cloud.

'Er ... hello,' said Rincewind, stopping just out of range. 'Me big fella Professor of Cruel and Unusual Geography belong Unseen University, you ... oh dear, you haven't even discovered washing, have you? Either that or it's the clothes belong you. Still, no obvious weapons. Er ...'

The man took a few steps forward and tugged the hat off Rincewind's head in one quick movement.

'Hey-!'

What was visible of the big face broke into a grin. The man turned the hat this way and that. Sunlight sparkled off the word 'Wizzard' in cheap sequins.

'Oh, I see,' said Rincewind. 'Pretty glitter. Well, that's a start ...'

TEN

BLIND MAN WITH LANTERN

The wizards are now beginning to understand that, while you can eliminate evil by eliminating extelligence, the result can be about as interesting as watching daytime television. Their plan to stop the elves inter­fering with human evolution has worked, but they don't like the result. It is bland and unintelligent. It has no spark of creativity.

How did human creativity arise? By now you won't be surprised to learn that it came from stories. Let's take a closer look at the current scientific view of human evolution, and fill in that gap between R-O-C-K and the space elevator.

An elf, observing Earth's landmasses 25 million years ago, would have seen vast areas of forest. From the hills of northern India to Tibet and China, and down into Africa, these forests held a great variety of small apes, ranging from about half the size of chimpanzees to the size of gorillas. The apes were at home on the ground and in the lower branches of the forest, and they were so common that today we have many fossils of them. In addition, the Old World monkeys were starting to diversify in the upper levels of the forest. Earth was a Monkey Planet.

But also a Snake Planet, a Big Cat Planet, a Nematode Planet, an Alga Planet and a Grass Planet. Not to mention Plankton Planet, Bacterium Planet and Virus Planet. The elf might not have noticed that the African apes had produced several ground-dwelling kinds, not very different from the monkey-derived baboons. And it might also have failed to spot the presence of gibbons in the high branches, alongside the monkeys. These creatures were not particularly remarkable against a background of spectacular large mammals like rhinoceroses, a variety of forest elephants, bears. But we humans are interested in them, because they were our ancestors.

We call them 'woods-apes', dryopithecines. Some, known as Ramapithecus, were of lighter build - the jargon is 'gracile'. Others, such as Sivapithecus, were big and strong - 'robust'. The lineage of Sivapithecus was the one that led to orangutans. These early apes would have been shy, morose creatures like today's wild apes, occa­sionally playful, but the adults would have been very belligerent and conscious of status within the group.

The forests inhabited by the woods-apes slowly dwindled as the cli­mate cooled and dried, and grasslands - savannah country - took over. There were ice ages, but in the region of the tropics these did not reduce temperatures severely. However, they did change the patterns of rainfall. The monkeys thrived, producing many ground-living kinds like baboons and vervets, and the ape populations got smaller.

By ten million years ago, there were few apes left. There are almost no fossil apes from that period. It seems plausible that, as now and as previously, those apes that did still exist were forest creatures. Some, like today's chimpanzees, gorillas and orangutans, were probably com­mon in a few locations in the forests, but you'd have needed a lot of luck to find them. The observing elf might, even then, have put all of these apes on its Endangered List of Earth Mammals. Like very nearly all animal groups that had evolved, the forest apes were soon to be history rather than ecology. The common ancestor of humans and chimpanzees was, then, a not very remarkable ape that probably lived much as the different chimpanzees do now: some in flooded forest like today's bonobos, some in rain-forest, and some in fairly open woodland grading into grasslands. The gorilla lineage separated from the other apes around this time.

At first, the elf would probably not have been very interested as - according to one of the two popular theories of human origins - a new kind of ape began to evolve a more upright stance than those of its relatives, lost its hair, and moved out on to the savannah. Many other mammals did the same; there was a new kind of living to be made on the great grass plains. Giant hyenas, massive wild dogs, lions and cheetahs made a good living from the vast herds of herbivores that lived on the productive savannah grasses; the giant pythons were probably originally savannah animals, too.

The story has been told many times, in many versions. And that's just the point: we understand our ancestry through story. We would­n't be able to work out our ancestry from the fossils that we have discovered unless we'd learned just what clues to look for, especially since few fossil sites have enough evidence left.

The new ancestral plains ape saw the world differently. Judging from the behaviour of today's chimpanzees, especially bonobos, it was a highly intelligent animal. We call their fossils southern apes, australopithecines, and there are hundreds of books that tell stories about them. They may have sojourned by the sea, doing clever things on beaches. Some certainly lived on lake margins. Today's chimpanzees use stones to smash hard nuts open, and sticks to extract ants from nests; the australopithecines also used stones and sticks as tools, rather more so than their cousins the chimpanzees now do. They may have killed small game, as chimpanzees do. They probably used sexual behaviour to hang much of their pleasure on, like today's bonobos, but most likely they were more gender-conscious and male-dominant. Like previous apes, they diverged into gracile and robust lines. The robust ones, called Anthropithecus boisi, or even a different genus Zinjanthropus ('nutcracker man') and other defamatory names, were vegetarians like today's gorillas, and probably left no descendants in modern times.

This kind of split into gracile and robust forms, by the way, seems to be one of the standard patterns of evolution. Mathematical models sug­gest that it probably happens when a mixed population of big and small creatures can exploit the environment more effectively than a single population of medium-sized ones, but this idea has to be con­sidered highly speculative until more evidence comes in. The zoological world was recently given a reminder of how common such a split is, and of how little we really know about the creatures of our own planet.

The animal involved could not have been better known, nor more appropriate to Discworld: the elephant. As every child learns at an early age, there are two kinds of elephant, two distinct species: the African elephant and the Indian elephant.

Not so. There are three species. Zoologists have been arguing for at least a century about what they thought was at most a subspecies of 'the' African elephant Loxodonta africana. The typical big, burly African elephant lives on the savannah. The elephants that live in the forest are shy, and difficult to spot: there is just one of them in the Paris zoo, for example. Biologists had assumed that because the for­est elephants and the savannah elephants can interbreed at the edges of the forest, they could not be separate species. After all, the stan­dard definition of a species, promoted by the evolutionary biologist Ernst Mayr, is 'able to interbreed'. So they either insisted that there was just one species, or that 'African elephant' had a distinguished subspecies, the forest elephant Loxodonta africana cyclotis. On the other hand, zoologists who have had the good fortune to see forest elephants are in no doubt that they look very different from the savannah ones: they are smaller, with straighter, longer tusks, and round ears, not pointed ones. Nicholas Georgiadis, a biologist at the Mpala Research Centre in Kenya, has said: 'If you see a forest ele­phant for the first time, you think, "Wow, what is that?'" But because biologists knew, on theoretical grounds, that the animals had to be all the same species, the observational evidence was rejected as inconclusive.

However, in August 2001 a team of four biologists - Georgiadis, Alfred Roca, Jill Pecon-Slattery and Stephen O'Brien - reported in the journal Science their 'Genetic evidence for two species of elephant in Africa'. Their DNA analysis makes it absolutely clear that the African elephant really does come in two distinct forms: the usual robust form, and a separate gracile form. Moreover, the gracile African elephants really are a different species from the robust ones. As different, in fact, as either African species is from the Indian one. So now we have the robust African plains elephant Loxodonta africana and the gracile African forest elephant Loxodonta cyclotis.

What of the belief that there could be only one species because of the potential for interbreeding? This particular definition of species is taking a hammering at the moment, and deservedly so. The main rea­son is a growing realisation that even when animals can interbreed, they may decide not to.

The story of the Third Elephant is not new: only the names have been changed. Before 1929 every zoologist 'knew' there was only one species of chimpanzee; after 1929, when the bonobos of the inacces­sible swamps of Zaire were recognised as a second species, it became obvious to many zoos that they had possessed two distinct chimpanzee species for years, but not realised it. Exactly the same story is now being played out with elephants.

As we've mentioned, Discworld recently revived interest in its fifth elephant, a story told, you will be surprised to hear, in The Fifth Elephant. According to legend, there were originally five elephants standing on Great A'Tuin and supporting the Disc, but one slipped, fell off the turtle, and crashed into a remote region of Discworld:

They say that the fifth elephant came screaming and trumpeting through the atmosphere in the young world all those years ago and landed hard enough to split continents and raise mountains.

No one actually saw it land, which raised the interesting philo­sophical question: when millions of tons of angry elephant come spinning through the sky, and there is no one to hear it, does it - philosophically speaking - make a noise?

And if there was no one to see it hit, did it actually hit?

There is evidence, in the form of vast deposits of fat and gold (the great elephants that support the world do not have ordinary bones), deep underground in the Schmaltzberg mines. However, there is a more down-to-Disc theory: some catastrophe killed off millions of mammoths, bison and giant shrews, and then covered them over. On Roundworld, there would be a good scientific test to distinguish the two theories: are the deposits of fat shaped like a crash-landed ele­phant? But there's no point even in looking, on Discworld, because narrative imperative will ensure that they are, even if they were formed by millions of mammoths, bison and giant shrews. Reality has to fol­low the legend.

Roundworld has so far reached only its third elephant, although Jack hopes that some careful selective breeding might yet bring back a fourth: the pygmy elephant, which lived in Malta and was about the size of a Shetland pony. It would make a marvellous pet - except that, like many diminutive creatures, it would probably be rather bad-tempered. And the very devil to discourage from getting on the settee.

We are a gracile ape (not that you'd notice in some parts of the world, where many of us more closely resemble a robust hippopotamus). About four million years ago one gracile lineage of apes started to get bigger brains and better tools. Against all the rules of taxonomy we call this lineage, our lineage, Homo: it really should be Pan, because we are the third chimpanzee. We use this name because it is certainly our own lineage, and we prefer to think of ourselves as being enor­mously different from the apes. In this we could be right: we may indeed share 98 per cent of our genes with chimpanzees, but then, we share 47 per cent with cabbages. Our big difference from the apes is cultural, not genetic. Anyway, within the Homo lineage we again find gracile and robust stocks. Homo habilis was our gracile tool-making ancestor, but Homo ergaster and others went the vegetarian, robust way. If there actually is a yeti or a bigfoot, the best bet is a robust Homo. From Homo habilis's success, a larger-brained Homo spread out over Africa, into Asia (as Peking Man) and Eastern Europe about 700 million years ago.

We have labelled one variety of these fossils Homo erectus. The vis­iting elf would certainly have noticed this fellow. He had several kinds of tools, and he used fire. He may even have possessed language, of a kind. What we have every reason to suspect that he did, that his ancestors and cousins only occasionally achieved, was to 'understand' his world and change it. Chimpanzees engage in quite a lot of 'if ... then' activities, including lying: 'if I pretend not to have seen that banana, I can come back and get it later when that big male won't steal it from me'.

The young of this early hominid grew up in family groups where things were happening that were unlike anything anywhere else on the planet. Sure, there were lots of other mammal nests, packs and troupes, where the young were playing at being adult or just fooling around; nests were safe, and trial-and-error was rarely lethal, so the young could learn safely. But in the human lineage, father was mak­ing stone tools, grunting at his women about the children, about the cave, about putting more wood on the fire. There would be favourite gourds for banging, perhaps for fetching water, spears for hunting, lots of stones for tools.

Meanwhile, in Africa, another new lineage had arisen about 120,000 years ago, and spread; we call it ancient Homo sapiens, and it led to us. Its brain was even bigger, and in caves on the coast of South Africa it - we - had begun to make better tools, and to make primitive paint­ings on rocks and cave walls. Our population exploded, and we migrated. We reached Australia just over 60,000 years ago, and Europe about 50,000 years ago.

In Europe there had been a moderately robust Homo, the Neanderthal Homo sapiens neanderthalensis, a subspecies. Some anthropologists consider us to be a sister subspecies, Homo sapiens sapiens or, loosely speaking, 'Seriously wise man'. Wow. The Neanderthals' stone tools were well developed for various functions, but these particular hominids seem not to have been progressive. Their culture hardly changed over tens of thousands of years. But they seem to have had some kind of spiritual impulse, for they buried their dead with ceremony - or, at least, with flowers.

Our more gracile ancestors, the Cro-Magnon people, lived at the same time as the last of the Neanderthals, and there are many theo­ries about what happened when the two subspecies interacted. Basically, we survived and the Neanderthals didn't ...

Why? Was it because we bashed them on the head more effectively than they bashed us? Did we outbreed them? Inbreed them? Squeeze them out into the 'edge country'? Crush them with superior extelligence? We'll put our own theory forward later in the book.

We don't subscribe to the 'rational' story of human evolution and devel­opment, the story that has named us so pretentiously Homo sapiens sapiens. Briefly, that story focuses on the nerve cells in our brains, and says that our brains got bigger and bigger until finally we evolved Albert Einstein. They did, and we did, and Albert was indeed pretty bright, but nonetheless the thrust of that story is nonsense, because it doesn't discuss why, or even how, our brains got bigger. It's like describing a cathedral by saying 'You start with a low wall of stones and as time passes you add more stones so that it gets higher and higher'. There's a lot more to a cathedral than that, as its builders would attest.

What actually happened is much more interesting, and you can see it going on all around you today. Let's look at it from the elf's view­point. We don't programme our children rationally, as we might set up a computer. Instead, we pour into their minds loads of irrational junk about sly foxes, wise owls, heroes and princes, magicians and genies, gods and demons, and bears that get stuck in rabbit-holes; we frighten them half to death with tales of terror, and they come to enjoy the fear. We beat them (not very much in the last few decades, but for thousands of years before that, for sure). We embed the teaching messages in long sagas, in priestly injunctions, and invented histories full of dramatic lessons; in children's stories that teach them by indi­rection. Stand near a children's playground, and watch (these days, check with the local police station first, and in any case be sure to wear protective clothing). Peter and Iona Opie did just that, many years ago, and collected children's songs and games, some of them thou­sands of years old.

Culture passes through the whirlpool that is the child community without needing adults for its transmission: you will all remember Eeny-Meeny-Miny-Mo, or some other counting-out ritual. There is a children's subculture that propagates itself without adult intervention, censorship, or indeed knowledge.

The Opies later collected, and began to explain to adults, the orig­inal nursery stories like Cinderella and Rumpelstiltskin. In late medieval times, Cinderella's slipper had been a fur one, not glass. And that was a euphemism, because (at least in the German version) the girls gave the prince their 'fur slipper' to try on ... The story came to us through the French, and in that language 'verre' can either be 'glass' or 'fur'. The Grimm brothers went for the hygienic alternative, saving parents the danger of embarrassing explanations.

Rumpelstiltskin was an interestingly sexual parable, too, a tale to pro­gramme the idea that female masturbation leads to sterility. Remember the tale? The miller's daughter, put in the barn to 'spin straw into gold', virginally sits on a little stick that becomes a little man ... The denoue­ment has the little man, when his name is finally identified, jumping in to 'plug' the lady very intimately, and the assembled soldiers can't pull him out. In the modern bowdlerised version, this survives vestigially as the little man pushing his foot through the floor and not being able to pull it out, a total non sequitur. So none of those concerned, king, miller or queen, can procreate (the stolen first child has been killed by the soldiers), and it all ends in tears. If you doubt this interpretation, enjoy the indirection: 'What is his name? What is his name?' recurs in the story. What is his name? What is a stilt with a rumpled skin? Whoops. The name has an equivalent derivation in many languages, too. (In Discworld, Nanny Ogg claimed to have written a children's story called 'the Little Man Who Grew Too Big', but, then, Mrs Ogg always believed that a double entendre can mean only one thing.)

Why do we like stories? Why are their messages embedded so deeply in the human psyche?

Our brains have evolved to understand the world through patterns. These may be visual patterns, such as the tiger's stripes, or aural ones, like the howl of the coyote. Or smells. Or tastes. Or narratives. Stories are little mental models of the world, sequences of ideas strung like beads on a necklace. Each bead leads inexorably to the next bead; we know that the second little pig is going to get the chop: the world would not be working properly if it didn't.

We deal not just in patterns, but also in meta-patterns. Patterns of patterns. We watch archer-fish shooting down insects with jets of water, we enjoy the elephant using its nose to acquire doughnuts from zoo visitors (less these days, alas); we delight in the flight of house-martins (there are fewer swallows to enjoy now) and the songs of garden-birds. We admire the weaver birds' nests, the silk moths' cocoons, the cheetahs' speed. All these things are characteristic of the creatures concerned. And what is characteristic of us? Stories. So, by the same token, we enjoy the stories of people. We are the storytelling chimpanzee, and we appreciate the meta-pattern involved in that.

When we became more social, collecting into groups of a hundred or more, probably with agriculture, more stories appeared in our extelligence, to guide us. We had to have rules for behaviour, ways to deal with the infirm and the handicapped, ways to divert violence. In early and present-day tribal societies, everything that is not forbidden is mandatory. Stories point to difficult situations, like the Good Samaritan story in the New Testament; the Prodigal Son, too, is instructive by indirection, like Rumpelstiltskin. To drive that home, here is a tale from the Nigerian Hausa tribe, Blind Man's Lantern.

A young man is coming home late from seeing his girlfriend in the next village; it is very dark under a starry sky and the path back to his own village is not easy to follow. He sees a lantern bobbing towards him, but when it gets closer he sees that it is carried by the Blind Man of his own village.

'Hey, Blind Man,' he says. 'You whose darkness is no darker than your noonday! What do you carry a lantern for?'

'It is not for my need I carry this lantern,' says the Blind Man. 'It is to keep off you fools with eyes!'

We, as a species, don't only specialise in storytelling. Just as with the other specialities above, our species has a few more oddities. Probably the most odd characteristic that our elvish observer would note is our obsessive regard for children. We not only care for our own children, which is entirely to be expected biologically, but for other people's children, too; indeed for other humankind's children (we often find foreign-looking children more attractive than our own); indeed for the children of all land vertebrate species. We coo over lambs, fawns, newly hatched turtles, even tadpoles!

Our sibling species, chimpanzees, are far more realistic. They too prefer baby animals. They prefer them for food, being more tender. (Humans also have a liking for lamb, calf, piglet, duckling ... We can coo over them and eat them.) After the kind of warfare now well doc­umented between chimpanzee groups, the victors will kill and eat the young of the vanquished. Male lions will kill the young of prides they take over, and eating the corpses is not unusual. Many mammalian females will eat their young if both are starving, and will frequently 're-process' the first litter in this manner anyway.

No, it's very clear that we are the odd men out. Odd Men indeed. We do have mental circuits to delight in, and protect, our own babies, so that the later Mickey Mouse converged on the outline of a three-year-old toddler, as did E.T. It is no wonder that so many people paid his phone bill. But we also go daft about cuddly juveniles of far too many other kinds. Biologically, this is very odd.

A by-product of our finding other species' babies so attractive has clearly been the domestication of dogs, cats, goats, horses, elephants, hawks, chickens, cattle ... These symbioses have given immense plea­sure to billions of people, and to their animals, and have contributed greatly to our nutrition. Those who feel that we have exploited the animals unfairly should consider the alternatives for the animals, in the wild, where nearly all of them are eaten alive as babies, without even the benefit of a quick death.

Agriculture can perhaps be attributed to our other propensity, storytelling: the seed becoming the plant has served as an image for so many new words and thoughts, metaphors, new understandings of nature. And the wealth generated by agriculture permitted people to afford princes and philosophers, peasants and popes. The cultural capital has grown as we have passed our knowledge on to succeed­ing generations. But it's more comfortable to enjoy that culture if there are a couple of warehouses full of barley for beer, wheat in the fields and cows in the meadows.

We have very recently made the whole business of symbiosis with plants and animals much more technical - those controversial 'genet­ically modified organisms' - and we have lost a lot by taking our animal helpers out of the system, especially dogs and horses, and replacing them with machinery.

We could not have predicted what the animal and plant symbioses did for us, for our extelligence, and we don't know what losing them will do. Events like that explode on us as the bicycle ride that is extel­ligence careers down this long technical hill, and can have totally unexpected effects.

Yes, the Ford Model T made motoring affordable to many more peo­ple - but a socially much more important change was that it gave privacy in comfort for the first time, so that a large proportion of the next generation was sired on the upholstery of the car's back seat. Similarly, the dog coming in as a symbiont meant that we could hunt more successfully. Then, as a guard dog, it meant that private farms could be protected, and there was help with rounding up the animals and keeping away predators, including human ones. Lapdogs proba­bly affected our sexual courtesies, particularly in eighteenth-century France, and dog and cat shows have stirred our upper-middle classes with, in modern England, the lower aristocracy.

Think for a moment about what we've done to dogs and cats. More than horses and cows, they grow up in our families. We play with them, like we play with our own children, and the play often involves our own children. As with our own children, this interaction begets minds in our pets. Even human children don't do much good on the mind front if they don't play. And Jack found, and showed Ian, that even invertebrates, bright invertebrates like mantis shrimps, can acquire minds if they're involved in play activities. We described in Figments of Reality how this happens. Let's just note here that we have uplifted our symbionts into the world of mind. Dogs worry about things, much more than wolves do. So dogs have at least some sense of themselves as a creature that lives in time, with some kind of awareness that it has a future as well as a present. Mind is catching.

Usually we think of the domestication of the dog as a selection process driven by human intentions. The process may have started accidentally, perhaps with a tribe bringing up a wolf pup that the kids had brought into the cave, but at a relatively early stage it became a deliberate training programme. Proto-dogs were selected for obedience to their master and for useful skills such as hunting. As time passed, obedience evolved into devotion, and the modern dog arrived on the scene.

However, there is an attractive alternative theory: the dogs selected us. It was the dogs that trained the humans. In this scenario, humans that were willing to allow wolf pups into the cave, and had the abil­ity to train them, were rewarded by the dogs, for example by a willingness to assist in the hunt. Those humans that performed best at these tasks found it easier to acquire new pups and train new generations. The selection on the human side would have been cultural rather than genetic, because there hasn't been enough time for genetic influences to make a lot of difference directly. However, there may well have been selection on the genetic level for having enough intelligence to appreciate how useful a trained wolf could be, or having the generalised teaching skills, such as persistence, to carry out successful training. At any rate, the tribe as a whole bene­fited from those few individuals who could train proto-dogs, so that the selective pressure in favour of generalised dog-training genes must have been slight.

This isn't one of those either-or choices: we are not obliged to accept one theory to the exclusion of the other. And this is a point we should make very firmly, for this and many other theories: things hap­pen, all over the place and apparently in some confusion, and afterwards mankind goes and chops it all up into 'stories'. We need to do it like that that, but occasionally we should stand back and realise what it is we are doing.

In the case of the dogs, there is in all likelihood a fair amount of truth in both theories, and what happened was a complicit co-evolu­tion of dogs and people. As dogs became more obedient and easier to train, people became more willing to train them; as people became more willing to consider possessing a dog, the dogs became more adept at playing along and making themselves useful.

The situation is, perhaps, more clear-cut with cats. Here it was very much a case of the cats being in the driving-seat. Rudyard Kipling's Just-So Story of 'The Cat That Walks By Itself' is too naive an accep­tance of the impression that cats set out to give - that they do things their own way and merely tolerate those people who play along - but in most cases you can't train a cat. Very few cats are willing to per­form tricks, whereas many dogs visibly enjoy performing for human pleasure. To the ancient Egyptians, cats were tiny gods on Earth, per­sonified in the cat-goddess Bastet. Bastet was originally worshipped around Bubastis, in the Nile delta, and she had a lion's head; later, this transmuted (transmogrified?) into a cat's head. Bastet-worship then spread to Memphis, where she became conflated with Sakhmet, a local lion-headed goddess. Bastet was a generalised goddess of things that were especially important to women, such as fertility and safe child­birth. Cats were also worshipped, as godling avatars of Bastet - and they were often mummified because of their religious significance. There was a sort of dog-god, the jackal-headed Anubis, but the difference was that he had a substantial 'hands-on' job: he was the god of embalming, and his role was to assist (or impede) the passage of the dead through the underworld. Anubis judged whether the dead were worthy of the afterlife. The only duties that the cat-godlings had were to allow humans to worship them.

Nothing new there, then.

Even today, cats assiduously give the impression of being inde­pendent; they seldom come when called, and are liable to depart at a moment's notice for reasons that are never very clear. All cat-owners know, however, that this impression is superficial: their cats need atten­tion, and know it. But this need shows up indirectly. For example. Ian's cat 'Ms Garfield' usually comes out to the front of the house to greet the arrival of the family car, but her pleasure at the car's appear­ance is heavily disguised as a strident harangue: 'Where the bloody hell have you lot been?' After absences on holiday or overseas, fam­ily members find that whenever they are in the garden, the cat coincidentally is in the same part of the garden - but either asleep or apparently just passing through. It looks as though house-cats are slowly losing the domestication battle, but putting up a strong fight. Feral cats are another matter, and real working cats like farm cats are often genuinely independent. These days, though, many farm cats are treated much like house-cats. At any rate, there are some good research projects still to be carried out on the co-evolution of ancient humans and their livestock and pets.

In another instance of this co-evolution, the horse made chivalry a possible culture (hence the name, of course: compare the French cheval') and enabled the Mongols to achieve one of the largest, best-controlled empires in human history. Under the Khans it was said that a virgin could walk unmolested from Seville to Hang Chou. Only in the twentieth century was that again achievable, with luck and possibly a harder search for the virgin. The Spanish took horses to America, where humans had killed off several equine species some 13,000 years before, and changed the lives of all the North American Indian tribes - and the cowboys, of course. And, a little later, Hollywood.

The horse did wonders for the genetics of humans, too. Just as they say that the invention of the bicycle saved East Anglia from an incest implosion, so the people that had come out of Africa were only a tiny part of early Homo sapiens's genetic diversity. All recent studies of the DNA genetics of human populations agree that the genetic diversity outside Africa is only a tiny fraction of the diversity that is still found on that continent. Those who left, to go as far as Australia or China, to Western Europe or via the high Arctic to America, are less diverse in total than many small indigenous African peoples. With the arrival of the horse, it became possible for traders to carry goods - and gene alleles - for very long distances, very effec­tively. So the out-of-Africa humans have inherited a relatively small part of the African gene-pool: they are genetically impoverished, but well stirred.

At the end of the twentieth century there was, for some years, a belief that Homo sapiens was a polyphyletic species. This word means that different groups of Homo sapiens evolved from different groups of Homo erectus in different places. This, it was thought, might account for the racial differences, especially differences in skin pigmentation, that seemed to fit geography pretty well. From DNA studies, we now know this theory can't be true. On the contrary, there was a bottle­neck in our population as we came out of Africa - humanity was reduced to rather small numbers - and all of us living today, all of the out-of-Africa 'races', were extracted from that small population. All the Homo erectus died out. The evidence so far looks as if there was only one exodus, of a minimum of some 100,000 people. We were all there in potentia in that tiny population, Japanese and Eskimos and Norsemen and Sioux and Beaker people and Mandarin Chinese; Indians and Jews and Irishmen. In the same way, all the current kinds of dog were 'present' in the original domesticated wolf (assuming it was indeed a wolf) - that is, they were in the wolfs space of the adja­cent possible - and we've pulled out Saint Bernards and chihuahuas and labradors and King Charles spaniels and poodles from that local region of organism-space.

There was, about thirty years ago, a brief fashion for the concept of 'mitochondrial Eve', and many media reports seem to have picked up the idea that there was just one woman, a veritable Eve, in that ancestral bottleneck. This is nonsense, but the media reports were writ­ten up to encourage the belief. The real story, as always, was a little more complicated, and it goes like this. There are mitochondria in the cells of people, indeed of most animals and plants. These are the billions-of-generations, descendants of symbiotic bacteria, and they still have some of their ancient DNA heredity, called mitochondrial DNA. Mitochondria from the mother go into the embryo's cells, but those from father do not: they die, or go only into the placenta. In any event, mitochondrial inheritance is very nearly all maternal. The mitochon­drial DNA accumulates mutations over time, with important genes changing less (presumably because the resulting babies, if any, were defective) and some DNA sequences changing quite quickly. That enables us to judge how far back it is to the common ancestor of any pair of women, from the accumulated differences in several DNA sequences. Surprisingly, nearly all such pairs from very different women converge on to a single consensus sequence, about 70,000 years ago.

A single woman, the ancestor of us all.

Eve?

Well, that was the story that the media latched on to, and you can see why. However, it doesn't hang together. The occurrence of just one mitochondrial DNA sequence doesn't mean that there was just one woman with that sequence, or that she was the ancestress of all the other women whose DNA was sequenced. Evidence based on the current diversity of various genes shows that there were at least 50,000 women in the human population 70,000 years ago, and many of them will have had that particular DNA sequence, or one that cannot be distinguished from it with the evidence remaining today. The lineages of the women who did not have that sequence contin­ued for some time, but eventually died out: their 'branch' of the human family tree doesn't reach all the way to the present day. We can't be certain why those lineages died out, but in mathematical models such effects are commonplace. Perhaps the women carrying sequences like today's sole survivor were more 'fit', or they simply came to outnumber the others by chance. It is even possible that the choice of the contemporary women to test was in some way biased, and that more than one mitochondrial DNA sequence is actually present in today's women.

How do we know that there were at least 100,000 humans 70,000 years ago, and not, as in the stories, just two 6,000 years ago? Many (about 30 per cent) of the genes in the cell nucleus have several ver­sions in today's human population. Like most 'wild' populations (not bred in the laboratory or for dog shows), each individual human has two versions of about 10 per cent of his or her genes, different ver­sions received from father and mother in sperm and egg. Humans have roughly 30,000 genes, of which about 3,000 will be represented by two versions in the average person. For some genes, notably those of the immune system that give each of us a very specific lock-and-key individuality, making us susceptible to some ailments but resistant to others, there are hundreds of versions of each gene (of four important ones, anyway). The (common) chimpanzee has a set of these immune variants that is very like the human: in one list of 65 variants of one immune gene, only two were not exactly the same. We don't know about the DNA of enough bonobos yet to see if the story is the same for them, but the smart money says that it will be, possibly even more so. The gorilla set seems to be a little different again (but only about thirty gorillas have been tested).

At any rate, all of these immune gene variants had to come out of Africa in that 'bottleneck' population that produced all the ex-African human populations. It is unreasonable to suppose that each individ­ual inherited different versions of each variable gene from their parents: some will have carried only one version, the same from both parents, and no one can have carried more than two. The humans that came out of Africa have about 500 immune variants, at least, in common with chimpanzees, out of about 750 possibilities. The humans who stayed in Africa have more: they weren't subject to the bottleneck. There are many other genes where several ancient versions (ancient because they're common to us, chimpanzees, perhaps gorillas, maybe other species) have come through; 100,000 people is a reasonable min­imum to carry all those. If you want to be critical and get that number down a bit, you could argue that a few variants from African popula­tions may have been mixed in later, for example via slavery to the US, or to Mediterranean peoples and then via Phoenician sailors to the rest of us. Still, the evidence does not point to an Adam and an Eve, unless they came with a lot of servants, slaves or concubines. The Biblical stories don't mention those.

ELEVEN

THE SHELLFISH SCENE

The wizards watched carefully.

'There's five of them sitting there with him now.' said Ponder. 'And some children. He seems to be get­ting on well enough.'

'They're very interested in his hat,' said the Dean. 'A pointy hat always commands respect in any culture,' said Ridcully. 'Then why have several of them tried to eat it?' said the Lecturer in Indefinite Studies.

'At least they don't appear to be warlike,' said Ponder. 'Let's go and introduce ourselves, shall we?'

And, again, when the wizards arrived at the little group around the fire there was the strange sensation of ... nothing. No surprise, no shock. The heavy people treated them as if they'd just returned from the bar; their curiosity level extended perhaps to the flavour of crisps they'd brought back, but no further.

'Friendly souls, ain't they?' said Ridcully. 'Which one's the boss?' Rincewind looked up, and then turned and snatched his hat from a big fist.

None of them,' he snapped. 'Stop pinching the sequins!'

'Have you mastered their language?'

'I can't! They don't have one! It's all point and kick! That's my hat, thank you so very very!'

'We watched you walking around,' said Ponder. 'Surely you've learned something?'

'Oh, yes,' said Rincewind. 'Follow me, and I'll show you - give me my hat'

Holding his sequin-stripped hat firmly on his head with both hands, he led the wizards to a big lagoon on the other side of the village. An arm of the river flowed through it; the water was crystal clear.

'See the shells?' said Rincewind, pointing to a large heap a little way from the beach.

'Freshwater mussels,' said Ridcully. 'Very nutritious. Well?'

'It's a big heap, right?'

'And?' said Ridcully. 'I'm quite fond of mussels myself.'

'You see that hill further along the bank? The one covered in grass? And the one behind that, with all the shrubs and trees? And the - well, see how the whole area is a lot higher than rest of the land around here? If you want to know why, just kick the soil away. It's mussel shells all the way down! These people have been here for thousands and thousands of years!'

The tiny clan had followed them and were watching with the uncomprehending interest that was their ground-state expression. Several of them waded in after mussels.

'That's a lot of shellfish,' said the Dean. 'Obviously not a taboo animal.'

'Yes, and that's surprising because frankly these people seem related to them,' said Rincewind wearily. 'Their stone tools are frankly rub­bish and they can't build huts and they can't even make fire.'

'But we saw a-'

'Yes. They've got fire. They wait for lightning to strike a tree or set fire to grass,' said Rincewind. 'Then they just keep it going for years and years. Believe me, it took a lot of grunting and pointing to work that one out. And they have no idea about art. I mean, you know, pic­tures? I drew a picture of a cow in the dirt and they seemed puzzled. 1 really think they were just seeing ... well, lines. Just lines.'

'Perhaps you're not very good at cow pictures?' said Ridcully.

'Look around,' said Rincewind. 'No beads, no face paint, no deco­ration. You don't have to be very advanced to knock out a bear claw necklace. Even people who live in caves know how to draw. Ever seen those caves up in Ubergigle? Buffaloes and mammoths as far as the eye can see.'

'I must say you've seemed to strike up a rapport with them very quickly, Rincewind,' said Ponder.

'Well, I've always been good at understanding other people enough to get an inkling of when to start running,' said Rincewind.

'You don't always have to run, do you?'

'Yes. Of course. The important thing is to know when it's the appropriate moment, though. Ah, this one's Ug,' said Rincewind, as a white-haired man prodded him with a thick finger. 'So are all the others.'

The current Ug pointed towards the Shell Midden foothills.

'He appears to want us to go with him,' said Ponder.

'He might,' said Rincewind. 'Or he might be pointing out where he last had a really satisfying bowel movement. See them all watching us?'

'Yes.'

'See that strange expression they have?'

'Yes.'

'You wonder what they're thinking?'

'Yes.'

'Nothing. Believe me. That expression means that they're waiting for the next thought to turn up.'

Beyond the Shell Midden Mountains was a thicket of willows, and in the centre of the thicket was a much older tree, or what remained of one. It had been split in two, was now dead, and at some point had been burned.

The clan hung back, but the white-haired Ug followed them into it a little way.

Something crackled under Rincewind's foot. He looked down, saw a yellowing bone, and nearly experienced an appropriate moment. Then he spotted the faint hummocks around the clearing, many of them overgrown.

'And here's the tree that fire came from,' said Ridcully, who had noticed them as well. 'Sacred ground, gentlemen. And they bury their dead.'

'Not exactly buried,' said Rincewind. 'More just left, I think you'll find. I think they just want to show me where they got fire.'

Ridcully reached for his pipe.

'These people really don't make it?' he said.

'They didn't understand the question,' said Rincewind. 'Well, I say question ... they didn't understand what I hope was the question. We're not talking progressive thinkers here. It must have been a big step when they invented the idea of taking the skins off animals before wearing them. I've never met any people quite so ... well, dull. I can't work them out. They're not exactly stupid, but their idea of repartee is an answer within ten minutes.'

'Well, this'll buck their ideas up,' said Ridcully, and lit his pipe. 'I expect they'll be impressed!'

The Ugs looked at one another. They watched the Archchancellor blowing smoke. And then they attacked.

On the Discworld the only tribe known to have absolutely no imag­inations whatsoever are the N'tuiftif, although they are gifted with great powers of observation and deduction. They just never invent anything. They were the first tribe ever to borrow fire. Being surrounded by other tribes who were as imaginative as anything, they are also very good at hiding; when you are surrounded by tribes to whom a stick means club, prod, lever, world domination, you are at a natural disadvan­tages when, to you, a stick means 'stick'.

To someone else a stick currently meant 'pole'.

A figure vaulted across the clearing and landed in front of the Ugs.

Orangutans do not enter the boxing ring, being too intelligent. If they did, however, the fact that they could knock out the opponent without getting up off their stool would quite make up for lack of finesse in the footwork.

Most of the tribe turned to run, and would have come face to face with the Luggage if it had a face. They rocked when it butted them, and tried to wonder what it was. And by then the Librarian was on top of them.

Those that worked out this was a good time to flee, fled. Those that didn't, stayed on the ground where they had been put.

The astonished Archchancellor was still holding the burning match when the Librarian advanced on him, screaming loudly.

'What say?' he said.

'There's a lot about him being in a library and the next minute being in the river over there,' Ponder supplied. 'That all? Sounded more.' 'The rest was swearing, sir.' 'Apes swear?' 'Yes, sir. All the time.'

There was another burst from the Librarian, accompanied by a pounding of knuckles on the ground. 'More swearing?' said Ridcully.

'Oh yes, sir. He's really quite upset. Hex has told him there are no longer any libraries whatsoever at any point in the planet's history.'

'Ow!'

'Quite, sir.'

'I burned my fingers!' Ridcully sucked his thumb. 'Where is Hex, anyway?'

'I was just wondering that, sir. After all, the crystal ball belonged in the city which isn't here any more ...'

They turned and looked at the tree.

It must have blazed furiously when the lightning struck. Probably it had been dead and dry anyway. There were only a few stumps of branches. The whole thing was black, and strangely ominous against the green of the willows.

Rincewind was sitting at the top.

'What the hell are you doing up there, man?' Ridcully bellowed.

'I can't run across water, sir,' Rincewind called down. 'And ... I think I've found Hex. This tree talks ..."

TWELVE

EDGE PEOPLE

Rincewind's 'edge people' are a caricature of early hominids, and quite close to what anthropologists used to think Neanderthals were like. We now think that Neanderthals had a bit more going for them, quite apart from burying their dead. At least, it suits the mood of the times to desire to think that they did have something happening behind that big brow-ridge. A bone with holes in it, which some archaeologists believe to be a 43,000-year-old Neanderthal bone flute, has been found in Slovenia. But others dis­pute that it is a musical instrument. Francesco d'Errico and Philip Chase have studied the bone carefully, and they are certain that the holes were gnawed in it by animals, not bored by a musically minded Neanderthal. We do not know if it's been handed to a musician ...

Whatever the status of the flute, it is clear that Neanderthal culture didn't change significantly over long periods of time. The culture that led to us did. It changed dramatically, and so far it's never stopped. What made us so different from the Neanderthals?

According to the Out of Africa theory, our ancestors, and everybody else's, came from an original population that evolved in Africa. They migrated through the Middle East; the ones bound for Australia prob­ably left from South Africa, but might have gone round through the Far East and Malaysia. If you've got boats, you can do either.

In principle the immune-gene story that we discussed in Chapter 10 could tell us more, but nobody's yet done the research: either the Australian 'aborigines' have the same gene spectrum as the rest of us post-bottleneck humans, or they have their own small and characteristic selection instead. Whichever is the case, it will tell us something interesting, but until someone gathers the genetic data, we have no idea which interesting thing it will tell us. A lot of science is like that, a win-win situation. But try explaining that to the bean-counters who control research funding.

When we speak of 'migrations' in this context, you shouldn't think of the exodus of the Hebrews from Egypt. It wasn't a case of one group of humans taking forty years or whatever and conquering other hominids along the way. It was more likely the successive formation of small settlements, slowly getting further and further away from the original homeland. The people themselves didn't even know that they were migrating. It was just 'Hey, Alan, why don't you and Marilyn set­tle down to hunter-gathering a couple of valleys over, by that nice Euphrates river?' Then, after a hundred years, there would be a few settlements on the far side of the river, too. This isn't pure speculation: archaeologists have found some of the settlements.

If humans formed new settlements a mile away every ten years, it would take only 50,000 years, a mere 1,000 grandfathers, for them to diffuse from Africa all the way to the frozen north. And they surely dif­fused faster than that. Hardly anybody actually went anywhere; it was just that the kids set up home a few hundred yards along the track, where there was a bit more room to bring up their kids.

As we diffused, we diversified. It is impressive how diverse we are, physically and culturally. But perhaps, from the elvish viewpoint, we're all much the same, from Chinese to Inuit to Maya to Welshman. Our similarities are far greater than our differences. We had diversified in Africa, too, from the tall willowy Masai and Zulus to the !Kung 'pygmies' and the stout Yoruba. These peoples are really, anciently, different: they differ from us, and from each other, almost as much as wolves differ from jackals. The post-bottleneck humans differentiated quite recently, just as the breeds of dogs differentiated from one kind of wolf (or perhaps it was a jackal).

This kind of rapid differentiation is a standard evolutionary story, called 'adaptive radiation'. 'Radiation' means 'spread', and 'adaptive' means that the organisms change as they spread, adapting to new envi­ronments - and, especially, to the changes brought about by their own adaptive radiation. It happened to 'Darwin's finches', where one small group of finches of a single species arrived in the Galapagos islands, and within a few million years had radiated into 13 separate species, plus a 14th on the Cocos Islands. (We wonder what the legend of The Fourteenth Finch might be.) Another well-known example is the vast array of cichlid fish that diversified in Lake Victoria over the last half a million years or so. There they produced variants for the catfish niche, for the planktonic filter-feeder, for the general-detritus feeder; they evolved into species with big crushing teeth for eating mollusc-shells, species that specialised in scraping scales or fins off other fish, and species that specialised in eating the eyes of other fish. Yes, really: when fish from that species were caught, all they had in their stom­achs was eyes. These cichlids ranged in size from a couple of centimetres to half a metre. The original river-dwelling species Haplochromis burtoni, whose descendants they all are, grows to a length of 10-12 centimetres.

Curiously, the range of genetics of these fishes was quite small, considering their morphological and behavioural ranges: about the same as out-of-Africa humans, but not as wide as in-Africa humans. At least, that's the case according to some reasonable ways to esti­mate genetic diversity.

The second part of this story nearly always involves extinction: just occasionally, one of the newly differentiated species has evolved a new and successful trick, and survives while all the others perish.

But the usual demise of these specialised, adaptively radiated fish happens when a professional specialist - a catfish perhaps, whose ancestors have been feeding on detritus for 20 million years - comes in and takes over from the amateur cichlid catfish. Unfortunately, in this case, it wasn't an inoffensive catfish, but the Nile perch, a spe­cialised carnivore from an ancient stock. The Nile perch has now cleaned out nearly all of the Lake Victoria cichlid explosion, which is why we wrote the previous passage in the past tense. The main remnants of that glorious radiation of the cichlids are now to be found in the homes of a few amateur hobbyists, who are keeping some of the odd cichlid species in aquaria, and the Geoffrye Museum in London, which by chance has one of the largest ranges of cichlids and is now sponsored by public bodies. We don't know yet if any of the cichlid variants in Lake Victoria has hit on a trick to survive even the Nile Perch.

It's difficult to know what Nile Perch is about to come in and prune Homo sapiens' current diversity. With luck, it will be our own propen­sity to miscegenation, aided and abetted by airlines, despite the contrary admonitions of our priests. Maybe we'll all be mixed up into one fairly diverse type. Or maybe it will be Independence Day aliens, out to conquer the galaxy. Or perhaps more competent ones, with ele­mentary virus protection software.

Were we the Nile Perch for the Neanderthals? What was special about us that they couldn't compete with? In an editorial in Astounding Science Fact and Fiction, John Campbell Jr proposed that we have been selecting ourselves - in very elvish ways - from earliest times. Campbell credited his idea to the nineteenth-century anthropologist Lewis Morgan, but in truth Campbell contributed most of the story.

It runs: we select ourselves, through puberty rituals and other tribal rites. To some extent these interact with our religious stories, but as a socialising technique the puberty ritual may have preceded all but the most basic of animistic beliefs. It certainly sits at the base of our Make-a-Homo-sapiens kit. But the Neanderthals may not have possessed such a cultural kit, at least not in the same effective form. If they didn't, they would probably have been much like Rincewind's edge people, indeed like all the other great apes: settled and (mostly) con­tented in their Garden of Eden, but not going anywhere.

What is so special about puberty rituals? What story makes them a necessary part of how we evolved ourselves into the storytelling ani­mal? Just this, said Campbell: puberty rituals select the breeders. This is the standard mechanism of 'unnatural selection' used to breed new varieties of dahlias or dogs, only here it bred new varieties of humans or stabilised existing varieties. The wizards have always known about unnatural selection, and it is reified on Discworld as the God of Evolution in The Last Continent. Unnatural selection is not just a mat­ter of genetics, either. If you don't get to breed, then you don't have the opportunity to pass on your cultural prejudices to your children. At best you can try to pass them on to other people's children.

Here's how it works. Over there, we see a group of half a dozen lads, perhaps aged 11 to 14. The older men have prepared an ordeal, and the kids must endure this to become accepted as full members of the tribe: that is, breeders. Perhaps they will be circumcised or other­wise wounded, and the wounds will be 'dressed' with painful herbs; perhaps they will be whipped with scorpions or biting insects; per­haps their faces will be seared with red-hot metal brands; perhaps (indeed, usually) the older men will violate them sexually. They will be starved, purged, beaten ... oh yes, we are a very inventive species in this regard.

Those who ran away were not accepted into the group, and so were not breeders. So, in particular, they were not our ancestors, because they weren't anyone's ancestors. In contrast, those who sub­mitted to the humiliation were rewarded by acceptance into the tribe. Campbell's insight was that these puberty rituals selected against the immediate animal avoidance-of-pain response, and selected for both imagination and heroism: 'If I bear this pain now I will be rewarded by getting the privileges these old men get, and I can imagine that they went through exactly this, and survived.'

Later on it was the priests who administered the pain. That is how they became the priests, and how successive generations came to 'respect' them and their teachings. By then, humiliation had become its own reward, at both ends of the instrument of torture (see Small Gods), and humans had been selected for obedience to authority.

Indeed, Stanley Milgram's book Obedience to Authority shows just how obedient we are, by using the authority of a white laboratory coat to force people to torture other people, remotely. The other people were actually actors, responding to 'mild', 'strong' and 'excruciating' pain - or so the experimental subject was led to believe - with the appropriate actions. Milgram's book shows how human beings invented authority and obedience, both very elvish sentiments. That ingredient in the story of our evolution explains Adolf Eichmann as well as Einstein: we won't go any deeper into that issue here, because we've already covered it in The Privileged Ape and Figments of Reality. A few people refused Milgram's instructions, though, and these mav­ericks have always been generated either by experience (some of the refusers had survived concentration camps, or had been otherwise tor­tured themselves) or by the Make-a-Human kit itself. Many of these kits generate a few mavericks, and we are optimistic about the Western one that uses Hollywood films to laud resistance to authority. But perhaps that comes only by working through the right genetics and the right home background.

Many of these ancient rituals have become empty now. Jews use circumcision to test the parents' commitment, rather than that of the baby, who has no choice. Jack was the Boston foreskin collector in the early 1960s; it was a very good source of the living human skin samples that he needed for his research on pigment cells in the skin. He saw a lot of parents, many of whom went very pale and a few of whom fainted: more men did that than women. The Jewish Bar Mitzvah is very daunting to the child, in prospect, though, as with cir­cumcision, nobody fails it - not any more. But people did fail in the past, with serious consequences. For example in the ghettos, where only a third of the population married, the mothers of the 'best' girls chose only the boys who performed their Bar Mitzvah best. This would account for the kind of verbal success that the Jewish faction of many Western populations has achieved. Another explanation, that Jews were permitted verbal abilities only because land- or property-owning was denied them, is a contextual constraint within which they had to live. Why they were good enough verbally to succeed despite that con­straint is the interesting question, and Bar Mitzvah competition and selection of breeders is a persuasive answer.

Gypsy populations provide a possible counterexample, though, with very little testing of young men before marriage, which frequently takes place at ages that other cultures consider to be pre-pubertal. The few gypsies who have been successful in Western cultures have not been primarily verbally successful. Music provides a good contrast, with gyp­sies excelling in dance while classical composers and instrumental soloists are often Jewish. Of course, gypsies also share our common selective ancestry, if we're right about puberty rites being ancestral and effectively universal.

The other great apes don't torture their children for ritual purposes, and the other hominids like Neanderthals probably didn't either. So they haven't produced a civilisation. Sorry, but that which does not kill us does appear to have made us strong.

There is another story that we now tell, about what happened to the young men around the time when people were inventing agriculture, which explains barbaric societies. Don't get us wrong here: we don't mean that torturing adolescents is barbaric. It's not, from the tribal point of view. It is an entirely proper way to get them accepted into the tribe. 'We've done it ever since god-on-high made the world, and to prove it, here's the holy circumcision-knife we've always used.' No, from the tribal point of view, the barbarians that we have in mind are awful; they don't have any rules or traditions ... Even the Manky tribe, over that way a couple of miles, is better than them; at least the Mankies have traditions, even if they are different from ours. And we've stolen some of their women, and they have the most amazing tricks ...

The problem is that lot up on the hillside, the young men who have been expelled from the tribe because they failed the rituals, or went of their own accord (and so failed the test anyway). 'Couple of my brothers up there with 'em, and Joel's boy, and of course the four kids that were left when Gertie died. Oh, they're all right on their own; it's when they're in that gang together, all doing their hair in that same funny way to be different, that you lock up the sheep and let the dogs loose. They've got these funny words like "honour" and "bravery" and "pillage" and "hero" and "our gang". When my broth­ers come down the valley to my farm - by themselves - I give 'em some food. But some gang of young men, I'm not saying it was that lot and I'm not saying it wasn't, set the Brown's farm alight, just for the hell of it ...'

In any cowboy film we find the message that barbarism is opposed to tribalism, that honour and tradition are not good bedfellows. And that, having selected himself or herself for imagination and the ability to endure pain for future pleasure, Homo sapiens is now prepared to die for his or her beliefs, for his or her gang, for honour, for hatred, or for love.

Civilisation, as we know it, seems to combine elements of both ways of human culture, tribal by tradition and barbaric for honour, for pride. Nations are internally tribal, but present a barbarian face to other nations. Our extelligence tells us stories, and we tell our children sto­ries, and the stories guide us about what to be or do in what circumstances. Shakespeare is the ultimate civiliser, in this view. His plays were composed against the barbarian background, in a city where you could see heads on spikes and ritually dismembered bod­ies; all of them were set on the tribal, traditional base that is most of human life, most of the time. He tells us very persuasively that evil fails in the end, that love conquers, and that laughter - the greatest gift that barbarism brought to tribalism - is one of the sharpest weapons, because it civilises.

Cohens are the hereditary High Priest lineage of the Jews. Jack was once asked, in Jerusalem, whether he was not proud to be a Cohen, in view of the noble Jewish history that the High Priests had promoted. Jack sees this nobility as based in about six inches of blood in the streets, nearly all of it other people's, so he is not proud. Instead, to the extent that any of us is responsible for what their ancestors did, he is ashamed. He loves Small Gods, in much the way he enjoys the Jewish Day of Atonement, Yom Kippur: it engenders a feeling of repentance, and he can always find plenty to repent. He is sure that this emotion - guilt - is a legacy of the Morgan/Campbell selection of his ancestors through tribal rituals.

Tribesmen aren't 'proud'; for them, everything that isn't mandatory is forbidden, so what is there to be proud about? You can praise your children for doing things right, or admonish or punish them for doing things wrong, but you can't take pride in what you - a fully fledged member of the tribe - do. That comes with the territory. However, you can be guilty about not having done the things that you should have done. Having said that, High Priests waging war on dissenters or neigh­bouring tribes, leading to atrocities like heads on spikes, is straight barbarism.

The distinction between tribalism and barbarism is illuminated by the story of Dinah in chapter 34 of Genesis. Dinah, an Israelite, was the daughter of Leah and Jacob, and 'when Schechem the son of Hamor the Hivite, prince of the country, saw her, he took her, and lay with her, and defiled her'. Then Schechem fell in love with her, and wanted to make her his wife. But the sons of Jacob felt that maybe Schechem had gone about things in the wrong order: "... the men were grieved, and they were very wroth, because he had wrought folly in Israel in lying with Jacob's daughter, which thing ought not to be done'. So when Hamor, the father of Schechem, asked for approval of the marriage, and for an intermingling of his tribe with the Israelites, the sons of Jacob came up with a cunning plan.

They told the Hivites that they would agree to the proposal, but only after the Hivites had circumcised themselves, so that they were just like the Israelites. The Hivites were willing to go along with this, because they told themselves that 'These men are peaceable with us, therefore let them dwell in the land, and trade therein; for the land, behold, it is large enough for them; let us take their daughters to us for wives, and let us give them our daughters'. The decision was made, and 'every male was circumcised, all that went out of the gate of the city'. And they stood around in pain for a couple of days. At that point, Dinah's brothers Simeon and Levi hauled Dinah out of Schechem's house, put all the Hivite men to the sword, destroyed their city and took all their domestic animals, their wealth, their children and their wives. This story of deceit and betrayal has not been given much cir­culation in recent years; it doesn't appeal to people's sense of humour any more, as it once did.

At any rate, in that story, the Hivite response to Schechem's crime is tribal, but the Israelites behave like barbarians. The Hivites, after their initial mistake, want to make amends and coexist peacefully, and they're prepared to offer dowries and other concessions to try to make up for what Schechem did. But all that matters to the Israelites is a twisted kind of 'honour', in which cruelty, murder and theft are justi­fied to protect Dinah's reputation. Or, more likely, their own sense of manhood.

A favourite Discworld character is Cohen the Barbarian, a satire on sword-and-sorcery heroes like Conan the Barbarian, all muscles and trolls' teeth necklaces and testosterone-propelled heroism. He first appears in the second Discworld novel The Light Fantastic:

'Hang on, hang on,' said Rincewind. 'Cohen's a great chap, neck like a bull, got chest muscles like a sack of footballs. I mean, he's the Disc's greatest warrior, a legend in his own lifetime. I remember my grandad telling me he saw him ... my grandad telling me he ... my grandad ...'

He faltered under the gimlet gaze.

'Oh,' he said. 'Oh. Of course. Sorry.'

'Yesh,' said Cohen, and sighed. 'Thatsh right, boy. I'm a lifetime in my own legend.'

Cohen, by then 87, is the sort of barbarian whose hordes ride into town, set the houses on fire and look wistfully at the women. But he's no softie: as he ages, he goes hard, like oak. In Interesting Times he explains to Rincewind why, in the area known as the Ramtops, there's no future in the Barbarian business any more:

'Fences and farms, fences and farms everywhere. You kill a dragon these days, people complain. You know what? You know what hap­pened?'

'No. What happened?'

'Man came up to me, said my teeth were offensive to trolls. What about that, eh?'

According to Jewish tradition, Cohens are the true Cohanim, the lin­eal descendants of Aaron. Recent research into the genetics of Cohens has turned up some interesting findings about the very prideful (bar­baric) issue of Cohen heredity. Professor Vivian Moses (yes, indeed ...) and a group of scientists in Israel decided to check whether the tradition has any factual basis. Just as the mitochondrial DNA sequence traces female heredity, so the Y-chromosome, possessed only by males, can be used to trace male heredity.

There has been an interesting division of the Jewish peoples, and that provides a scientific check on the story of the Cohanim. During the Diaspora, some Jews remained in North Africa, but one large population went into Spain. They are known as Sephardi, and the Rothschilds, Montefiores and other banking families are all Sephardic. Another, more diffuse population went into middle-Europe, especially Poland, and they are known as Ashkenazi. Moses and his colleagues looked at the Y-chromosomes of representative Sephardi and Ashkenazi Cohens and non-Cohens ('Israelites'). They found characteristic DNA sequences, specific to Cohanim, in about half of the Cohens that they tested, but with small and characteristic differ­ences in the three groups. From these differences it is reasonable to suppose that Ashkenazi and Sephardi Jews separated rather less than 2,000 years ago, and that all Cohens were a single group only 2,500 years ago.

This looks like a very nice story, with the DNA evidence support­ing the expected history. But science is the best guard against believing things because you want to. There is a factor that Moses and his colleagues didn't explicitly consider, and it needs to be explained away, because it makes those figures much too good.

Most human groups pretend to practise monogamy, but like swans and gibbons and other creatures that we thought were faithful for life, there are plenty of adulterous relationships and children 'whose legal and biological parentage differ'. In English society, about one child in seven is in that position, and the proportion doesn't differ much between the slums of Liverpool and the stockbroker belt of Maidenhead.

The most restrained people that we know, in this regard, are the Amish of Eastern Pennsylvania and other parts of the United States, for whom the figure is a mere one in twenty. So, to err on the safe side, let's assume that all of the Mrs Cohens, from the present day back 100 generations to the sons of Aaron, were as well behaved as the Amish. Then the proportion of Cohen males with Aaron's Y-chromo-some should be 0.95¹⁰⁰, which is considerably less than one in a hundred. So how can it be as high as one in two?

There is a possible explanation, consonant with what we know about human sexuality, or at least with what John Symons, an expert on human sexual practices, says in his books. According to many sur­veys of sexual behaviour, going right back to Alfred Kinsey around 1950, women practise adultery with men of both higher and lower sta­tus. The two situations frequently occur in different social contexts, with women 'doing favours for' higher status men (think Clinton), but going down-market for 'a bit of rough'. Overwhelmingly often, however, when a baby results the father is of higher status than the woman's husband or regular partner.

This implies that if Mrs Cohen, living in a ghetto or any other predominantly Jewish society, wants to go up-market, her only choices are other Cohens. So the maintenance of the Aaron Y-chromosome may have been assured by sexual snobbery rather than amazing fidelity, and that's a much more likely story.

THIRTEEN

STATUS QUO

The breeze shook the willows. And, in the centre of the willows, the lightning-struck tree spoke, in a very faint voice. The Ugs had seen lightning strike the same tree three times. It was the highest point in the area, thanks to the shell mounds.

Even for creatures so preternaturally against thinking any kind of new thoughts, this made an impression. In some way, they'd felt, the tree had importance. It was an important thing. The place of the tree was an important place, where the sky touched the ground.

It wasn't much of an opening, it was a story without a plot and it barely amounted to a belief, but Hex had to make do with what could be found.

Now the wizards were considering the future, or futures.

'Nothing changes?' said the Dean.

'No, sir,' said Ponder, for the fourth time. 'And, yes, this is indeed the same time as the city we were in. But things are different.'

'The city was almost modern!'

'Yes, it had heads on spikes,' said Rincewind.

'It was a bit backward, admittedly,' said Ridcully. 'And the beer was foul. But it had possibilities.'

'But I don't understand! We stopped the elves,' said the Dean.

'And now we've got thousands and thousands of years of this,' said Ponder. 'That's what Hex says. These people won't even have learned how to make fire before the big rock hits. Rincewind is right. They're not exactly stupid, they just don't ... progress. Remember the crab civilisation we found?'

'But they had wars and took prisoners and slaves!' said the Lecturer in Recent Runes.

'Yes. Progress,' said Ponder.

'Heads on spikes,' said Rincewind.

'Do stop going on about that, it was only two heads,' snapped Ponder.

'Perhaps we did something else that changed history,' said the Chair of Indefinite Studies. 'Maybe we trod on the wrong insect or some­thing? Only a thought,' he added, when they glared at him.

'We just saw off the elves, that's all we did,' said Ridcully. 'Elves cause exactly the sort of things we've seen here. Superstition and-'

'The Ugs aren't superstitious,' said Rincewind.

'They didn't like it when I struck that match!'

'They didn't start worshipping you, either. They just don't like things that happen too quickly. But I told you, they don't draw pictures, they don't use body paint, they don't make things ... I asked Ug about the sky and the moon, and as far as I can tell they don't think about them. They're just things in the sky.'

'Oh, come now,' said Ridcully, 'everyone tells stories about the moon.'

'They don't. They don't have any stories at all,' said Rincewind.

There was silence as this sank in.

'Oh dear,' said Ponder.

'No narrativium,' said the Dean. 'Remember? That's what this uni­verse lacks. We never found a trace of it. Nothing knows what it's supposed to be.'

'There must be something like it, surely?' said Ridcully. 'The place looks normal, after all. Seeds grow up into trees and grass, by the look of it. Clouds know they have to stay up in the sky.'

'If you remember, sir,' said Ponder, using the tone that meant I know you've forgotten, sir, 'we found that this universe has things that work instead of narrativium.'

'Then why are these people just sittin' about?'

'Because that's all they have to do!' said Rincewind. There doesn't seem to be much around that can hurt them, there's enough food, the sun is shining ... it's all gravy! They're like ... lions. Lions don't need stories. Eat when you're hungry, sleep when you're tired. That's all they need to know. What else do they need?'

'But it must get cold in the winter, surely?'

'So? It gets warmer in the spring! It's just like the moon and the stars! Things happen!'

'And they've been like this for hundreds of thousands of years,' said Ponder.

There was some more silence.

'Remember those stupid big lizards?' said the Dean. 'They lasted for more than a hundred million years, I remember. I suppose they were quite successful, in their way.'

'Successful?' said Ridcully.

'I mean they lasted a long time.'

'Really? And did they build a single university?'

'Well, no-'

'Did they draw a single picture? Invent writing? Offer even small classes of elementary tuition?'

'Not that I know-'

'And they all got killed off by a yet another big rock,' said Ridcully. 'They really did not know what hit them. Bein' around for millions of years is not an achievement. Even lumps of stone can manage that.'

The circle of wizards was sunk in gloom.

'And Dee's people were doin' quite well,' muttered Ridcully. 'Terrible beer, of course.'

'I suppose ...' Rincewind began.

'Yes?' said the Archchancellor.

'Well ... how about if we went back and stopped us from stopping the elves? And least we'd be back among people more interesting than cows.'

'Could we do that?' said Ridcully to Ponder.

'I suppose so,' said Ponder. 'Technically, if we stop ourselves, then nothing will change, I assume. All this won't have happened ... I think. That is to say, it will have happened, because we'll remember it, but then it won't have happened.'

'Fair enough,' said Ridcully. Wizards do not have a lot of patience with temporal paradoxes.

'Can we stop ourselves?' said the Dean. 'I mean, how do we do it?'

'We'll just explain the situation to us,' said Ridcully. 'We're reason­able men.'

'Hah!' said Ponder, and then looked up. 'Oh, sorry, Archchancellor. I must have been thinking about something else. Do go on.'

'Ahem. If I was just about to fight elves, and someone who looked very much like me came up and told me not to, I'd assume it was an elvish trick,' said the Lecturer in Recent Runes. 'They can make you think they look like someone else, you know.'

'I'd know me if I saw me!' said the Dean.

'Look, it's easy,' said Rincewind. 'Trust me. Just tell yourself some­thing about yourself that no one else could possibly know.'

A worried look crossed the Dean's face.

'Would that be wise?' he said. Like many people, wizards often have secrets they don't want themselves to know.

Ridcully stood up. 'We know it'll work,' he said, 'because it's already happened to us. Think about it. We must succeed in the end, because we know a species like this gets off the planet.'

'Yes,' said Ponder, slowly, 'and, then again, no.'

'What the hell does that mean?' Ridcully demanded.

'Well ... we've been to a future where it happens, certainly,' said Ponder, twiddling his pencil nervously. 'But there are other futures. The multiplex nature of the universe that allows it to absorb and cush­ion the effects of apparent paradoxes also means that nothing is certain, even if you know it is.' He tried to avoid Ridcully's stare. 'We went to a future. At the moment, it exists only in our memories. Then, it was real. Now, it may never be. Look, Rincewind was telling me about some play writer he's found, born around about Dee's time but not in this branch of the universe. Yet we know he has an existence, because L-space contains all possible books in all possible histories. Do you see what I mean? Nothing is certain.'

After a while, the Chair of Indefinite Studies said, 'You know, I think I prefer the kind of universal law that says the third son of a king always gets the princess. They make sense.'

'The universe is so big, sir, that it obeys all possible laws,' said Ponder. 'For a given value of "teapot".'

'Look, if we go back in time and talk to ourselves, why don't we remember it?' said the Lecturer in Recent Runes.

Ponder sighed. 'Because although it has already happened to us, it hasn't yet happened to us.'

'I, er, tried something like that,' said Rincewind. 'While you were having your mussel soup just now I got Hex to send me back in time to warn myself to hold my breath when we landed in the river. It worked.'

'Did you hold your breath?' 'Yes, because I've warned myself.'

'So ... was there any time anywhere where you didn't hold your breath, thus giving yourself a mouthful of river water and causing you to go back to make sure you did?'

'Probably there was, I think, but there isn't now.' 'Oh, I see,' said the Lecturer in Recent Runes. 'You know, it's a good job we're wizards, otherwise this time travel business could really be confusing ...'

'At least we know that Hex can still make contact with us,' said Ponder. 'I'll ask him to move us back again.' The Librarian watched them go. A moment later, the rest of everywhere went with them.

FOURTEEN

POOH AND THE PROPHETS

The Ugs have no real stories, hence no sense of their place in time. They have no conception of the future, and therefore no wish to change it.

We know that there are other futures ... As Ponder Stibbons remarks, we live in a multiplex universe. We look at the past and we see times and places where things could have been different, and we wonder whether we could have ended up in a different present. By analogy, we look at the pre­sent and imagine many different futures. And we wonder which of them will happen, and what we can do now to affect the choice.

We could be wrong. Maybe the fatalist view, 'it is written', is right. Maybe we are all automata, working out the deterministic future of a clockwork universe. Or maybe the Quantum philosophers are right, and all possible futures (and pasts) coexist. Or maybe everything that exists is just one point in a multiplex phase space of universes, a sin­gle card dealt from Fate's deck.

How did we acquire this sense of ourselves as beings who exist in time? Who remember their past, and use it to try (usually unsuccess­fully) to control their future?

It all goes back a long, long way.

Watch a proto-human watching a zebra watching a lioness. The three mammalian brains are doing very different things. The herbivore brain has seen the lioness, is barely conscious (we guess, watch some horses in a field) of the whole 360 degrees of his environment, and has marked some things, like that tuft of grass over there, that female over there who could just be in heat, that male who's giving her the right signals, the three bushes that could have a surprise behind them .. the lioness moves, she suddenly gets priority, but not totally because there are other considerations. Another lioness could well be behind those bushes, and I'd better move up on that nice grass before Nigella does ... Looking at that grass makes me think of the taste of that long grass ... THE LIONESS IS MOVING.

The lioness is thinking: that's a nice zebra stallion, won't go for him he's too strong (memory of a previous eye injury from a zebra kick) but if I get him running, Dora behind those bushes can probably jump on the young female over there who is trying to attract the male, then I can run after it with her ...

There is probably no more of a plan than that in the zebra's brain but it does foresee a little bit of the future and plug memories into present planning. If I stand up now ...

The human is looking at the lioness and the zebra. Even if it's a Homo erectus, we bet it had stories in its head: that lioness will run out, the zebra will startle, the other lioness will go for ... ah, that young female. Then I can run out there and get in front of the young male; I see myself running at him and hitting him with this stone. Homo sapi­ens may well have done better from the beginning; his brain was bigger and probably better. He may, from the beginning, have had room for several alternative, thought about 'or' scenarios and proba­bly the 'and' one which goes 'and I will be a big hunter and meet interesting women'. 'If' probably came along later, perhaps with cave paintings, but making predictions put our ancestors way ahead of their predators and their prey.

There has been a variety of suggestions about why our brains sud­denly grew to nearly double their previous size, from the need to keep the faces of our social group in mind while gossiping about them, to the need to compete with other hunter-gatherers, to the competitive nature of language and its structuring of the brain so that lying could be successful for the li-ar, but then the li-ee got better at detecting lies. Such escalations all have an attraction to them. They make good sto­ries, ones that we can easily imagine, filling in the background just as we do with hearing sentences or enjoying pictures. That doesn't make them true, of course, just as our attraction to the supposed seashore phase of our history doesn't make 'aquatic apes' true either. The sto­ries serve as placeholders for whatever the real pressures were: the meta-explanation of why our brain growth took off is that competitive advantage was to be won by All Of The Above routes, and many more.

Perhaps the human viewer of that wildlife scene is a cameraman for a natural history TV series. Even a mere 15 years ago, he would have had an Arriflex (or if he was paying for it himself, perhaps just a Bolex H16) 16mm film camera with a very precious 800 feet (260 metres) of film loaded, and perhaps another dozen film packs in his rucksack (800 feet gives about 40 minutes of filming: if you're very good, or very lucky, five minutes of useful stuff). Now he has a video camera that would have seemed miraculous then, which can reuse and reuse a length of tape until it's full of five-minute sequences, end to end. All the things he wished for, then, are in the apparatus in his hand now: it stays in focus, it compensates for a bit of wobble, it goes down to unbelievably low light levels (for those of us who grew up with photographic film) and it zooms over a range much wider than we ever had before.

It's magic, in fact.

And in his head are a dozen alternative scenarios for the lions and zebras, which he'll flick to instantly as the animals act to constrain their futures. He's actually thinking about other things altogether, letting the experienced professional part of his brain do the work while he day­dreams ('I'll get an award for this and meet interesting women'). It's like driving on a quiet motorway: a lot of the thinking has been taken out of it.

Our ancestors honed that ability, to consider alternative scenarios. And within any of those scenarios, the ability to make a story of what was happening was a very powerful way to remember it and to commu­nicate it. And, particularly, to employ it as a parable, to direct your future action or that of your children. Human beings need a very long time to get that brain up-and-running, at least twice as long as their brother and sister chimpanzees. That is why three-year-old chimps are nearly adult in chimp behaviour, and can do some of the mental tricks of six- or seven-year-old children.

But the young chimps don't hear stories. Our children have been hearing stories since they recognised any words at all, and by three years old they are making up their own stories about what is hap­pening around them. We are all impressed by their vocabulary skills, and by their acquisition of syntax and semantics; but we should also note how good they are at making narratives out of events. From about five years old, they get their parents to do things for them by placing those things in narrative context. And most of their games with peers have a context, within which stories are played out. The con­text they create is just like that of the animal and fairy stories we tell them. The parents don't instruct the child how to do this, nor do the children have to elicit the 'right' storytelling behaviours from their par­ents. This is an evolutionary complicity. It seems very natural - after all, we are Pan narrans - that we tell stories to children, and that chil­dren and parents enjoy the activity. We learn about 'narrativium' very early in our development, and we use it and promote it for the whole of our lives.

Human development is a complex, recursive behaviour. It is not simply reading out DNA 'blueprints' and making another working part (contrary to the new folk-biology of genes). To show you how truly remarkable our development is, despite seeming so simple and so nat­ural, let's have a look at some earlier parent-child behaviour.

Keep in mind a distinction that is being imported into more and more scientific thinking, that between 'complicated' and 'complex'. 'Complicated' means a whole set of simple things working together to produce some effect, like a clock or an automobile: each of the com­ponents - brakes, engine, body-shell, steering - contributes to what the car does by doing its own thing, pretty well. There are some inter­actions, to be sure. When the engine is turning fast, it has a gyroscopic effect that makes the steering behave differently, and the gearbox affects how fast the engine is going at a particular car speed. To see human development as a kind of car assembly process, with the suc­cessive genetic blueprints 'defining' each new bit as we add them, is to see us as only complicated.

A car being driven, however, is a complex system: each action it takes helps determine future actions and is dependent upon previous actions. It changes the rules for itself as it goes. So does a garden. As plants grow, they take nutrients from the soil, and this affects what else can grow there later. But they also rot down, adding nutrients, providing habitat for insects, grubs, hedgehogs ... A mature garden has a very different dynamic from that of a new plot on a housing estate.

Similarly, we change our own rules as we develop.

There are always several superficially different, non-overlapping descriptions of any complex system, and one way to deal with a com­plex system is to collect these descriptions and choose appropriate ones for different ways of influencing its behaviour. An amusingly simple example can be seen in many French and Swiss railway sta­tions and airports: a sign that says

LOST PROPERTY OBJETS TROUVES

The French means 'found objects'. But we don't think that this is a case of the English losing objects and the French finding them. It's two descriptions of the same situation.

Now look at a baby in a pram, throwing its rattle out on to the pavement for Mummy, or child-minder, or indeed passers-by, to retrieve. We probably think that the child is not coordinated enough yet to keep its rattle within reach: we think 'Lost Property'. Then we see Mummy give the rattle back to the child, to be rewarded with a smile, and we think 'No, it's more subtle: there is a baby teaching its mother to fetch, just as we adults do with dogs'. Now we think 'Objets Trouves'. The baby's smile is itself part of a complex, reciprocal sys­tem of rewards that was set up long ago in evolution. We watch babies copy' the smiles of parents - but no, it can't be copying, because even blind babies smile. Anyway, copying would be immensely difficult: from anywhere on the retina, the undeveloped brain must 'sort out' a face with a smile, then work out which of its own muscles to work to produce that effect, without a mirror. No, it's a pre-wired reflex. Babies reflexively react to cooing sounds and to pre-wired recognition of smiles; an upwardly-curved line on a piece of paper works just as well. The 'smile' icon rewards the adult, who then tries hard to keep the baby doing it. The complex interactions proceed, changing both partici­pants progressively.

They can be analysed more easily in unusual situations, such as sighted children with 'signing' parents, perhaps deaf or dumb, but occasionally as part of a psychological experiment. For example in 2001 a team of Canadian researchers headed by Laura Ann Petitto stud­ied three children, about six months old, all with perfect hearing but born to deaf parents. The parents 'cooed over' the babies in sign lan­guage, and the babies began to 'babble' sign language - that is, make a variety of random gestures with their hands - in return. The parents used an unusual and very rhythmic form of sign language, quite unlike anything they would use to adults. Similarly, adults speak to babies in a rhythmic sing-song voice, and between the ages of about six months and a year the babies' babble takes on properties of the parents' spe­cific language. They are rewiring and 'tuning' their sense organs, in this case the cochlea, to hear that language best.

Some scientists think that babbling sounds is just random opening and closing of the jaw, but others are convinced it is an essential stage in the learning of language. The use of special rhythms by parents, and the spontaneous 'babbling' with hand-movements when the par­ents are deaf, indicate that the second theory is closer to the mark. Petitto suggests that the use of rhythm is an ancient evolutionary trick, exploiting the natural sensitivities of the young child.

As the child grows, its complex interaction with surrounding humans comes to produce wholly unexpected results: what we call 'emergent' behaviour, meaning that it is not overtly present in the behaviour of the components. Where two or more systems interact like this, we call the process a complicity. The interaction of an actor with an audience can build up a wholly new and unexpected relationship. The evolu­tionary interaction of blood-sucking insects with vertebrates paved the way for protozoan blood parasites that cause diseases like malaria and sleeping-sickness. The car-and-driver behaves differently from either alone (and car-and-driver-and-alcohol is even less predictable). Similarly, human development is a progressive interaction between the child's intelligence and the culture's extelligence: a complicity. This complicity progresses from simple vocabulary-learning to the syntax of little sentences and the semantics of fulfilling the child's needs and wants and the parents' expectations. The beginning of storytelling then becomes an early threshold into worlds that our kin the chimpanzees know not of.

The stories that all human cultures use to mould the expectations and behaviour of the growing child use iconic figures: always some animals, and then status-figures of the culture (princesses, wizards, giants, mermaids). These stories sit in all our minds, contributing to our acting, our acting-out, our thinking, our predicting what will hap­pen next, as caveman or cameraman. We learn to expect outcomes of particular kinds, frequently expressed in ritual words ('And they all lived happily ever after' or 'So it all ended in tears'). The stories that have been used in England over the centuries have changed in com­plicity with the changing culture - making the culture change, and responding to those changes, like a river changing its path across a wide flood-plain that it has itself built. The Grimm Brothers and Hans Christian Andersen were but the last of a long series, with Charles Perrault accumulating the Mother Goose tales around 1690; there were many collections before that, especially some interesting Italian group­ings and retellings for adults.

The great advantage we all get from this programming is very clear. It trains us to do 'What if ...?' experiments in our minds, using the rules that we've picked up from the stories, just as we picked up syntax by hearing our parents talking. These stories-of-the-future enable us to set ourselves in an extended imagined present, just as our vision is an extended picture reaching much further out in all directions than the tiny central part to which we're paying attention. These abilities enable each of us to see ourselves as being set in a nexus of space and time; our 'here' and 'now' form only the starting place for our seeing our­selves in other places at other times. This ability has been called 'time-binding', and has been seen as miraculous, but it seems to us that it is the culmination (for now) of an entirely natural progression that starts from interpreting and enlarging vision or hearing, and from 'making sense' in general. The extelligence uses this faculty, and hones and improves it for each of us, so that we can use metaphor to navi­gate our thoughts. Pooh Bear getting stuck, and unable to exit with dignity because he ate too much honey, is precisely the kind of para­ble that we carry with us to guide our actions, as metaphor, from day to day. So are Biblical stories, with all their lessons for life.

Holy books like the Bible and the Koran take this ability one giant step further. The Biblical prophets do, wholesale, what each of us has been programmed to do retail for our own life and those of our own nearest and dearest. The prophets predicted what would happen to everybody in the tribe if they continued their current behaviour, and thereby changed that behaviour. This was a step on the way to those modern prophets who predict The End Of The World some time soon. They seem to feel that they have perceived a trend, a constraint in the universe, that the rest of us have not understood, and whose proper­ties are directing the universe along some undesirable or calamitous path. Though they don't usually mean 'universe', they mean 'my world and nearer ones'. So far they haven't been right. But we would not be here to write these words if they had been, which is another anthropic issue, but not a very important one because they have been wrong rather often. They predict what will happen If This Goes On; but, increasingly it seems, This doesn't Go On for very long because it's unexpectedly replaced by a new This.

We all think that we can become better prophets with practice. We all think we have a clever way to build 'the road not taken' into our experience. Then we invent time travel, at least in our imaginations. We all want to go back to the beginning of that argument with the boss, and do it right this time. We want to unravel the chain of causality that led to boring edge people. We want to avoid the bad effects of elves but retain the good ones. We want to play pick-and-mix with universes.

However, despite their emphasis on prophecy, monotheist faiths have real trouble with multiple futures. Having simplified their theol­ogy down to one God, they also tend to believe that there can be only one 'right way to heaven'. The priests tell the people what they must do, and at least while the religion is fresh the priests are fine exam­ples. This is what gets you to heaven, they say: no adultery, no murder, no failure to give a tithe to the Church, and no undercutting the other clergy for indulgences. Then the gateway to heaven becomes 'strait', narrower and narrower, until only the blessed and the saints can get in without spending time in some purgatory or other.

Other religions, notably extreme versions of Islam, promise heaven as the reward for a martyr's death. These ideas are more closely asso­ciated with barbarian views of the future than tribal ones: paradise, like Valhalla for the Norse heroes, will be full of the hero's rewards, from perpetually renewed women to ample food and drink and hero's games. But they are also associated, as they were not in the more purely barbarian Norse legends, with a belief in fate, in the will of a god that nothing can avoid or deny. This is the other way for author­ity to force obedience: the promise of ultimate reward is a very persuasive story.

Barbarians, for whom honour, glory, power, and love, dignity, brav­ely are the meaningful concepts, get plus points for denying authority and shaping events to their own desires. They have, among their gods and heroes, the mischievous unpredictable ones like Lemminkainen and Puck.

Barbarian nursery stories, like their sagas, laud the hero. They show how luck is associated with particular attitudes, especially a pure heart that does not seek immediate or ultimate reward. There is frequently a test of this purity, from helping a poor blind cripple, who turns out to be a god in disguise, to curing or feeding a desperate animal, who comes to your aid later.

The agents in many of these stories are supernatural - out of the order of things, magical and causeless - 'people', such as fairies (including fairy queens and fairy godmothers), avatars of the gods, demons, and djinni. People, especially heroes or aspiring heroes (such as Siegfried, but also Aladdin), attain control over these supernatural beings with the assistance of magic rings, named swords, spells, or merely by their own inner nobility. This changes their fortunes, and luck comes to be on their side; they win battles and bouts against long odds, they climb tall mountains, they kill immortal dragons and mon­sters. No tribal thinker would even dream of stories like these. For them, fortune favours the well-prepared.

Man is forever inventive, and we have stories that counter even the most heroic tales: the Sidh, the seven-foot-tall elves of Lords and ladies and old Irish folklore, the Devil who buys your soul and has you at his mercy even if you repent, the Grand Vizier, James Bond's opponents.

What is interesting in our discussion of stories here is the charac­ters of these anti-heroes. They don't have any. Elves are the High Folk, but they don't have lives of their own; they are simply portrayed as being antithetic to what people, especially heroes, want to do. We don't care about the human aspects of James Bond's iconic enemies: they are always portrayed as being mindlessly cruel, or avid for power without responsibility and without having to overcome obstacles. They are ciphers, they don't have creative personalities, and they don't learn. If they did, one of them would have shot James Bond dead with a simple gun many years ago, after learning what happens to those who put their trust in laser beams and circular saws. They'd remove his watch first, too.

Rincewind would characterise the elves as 'edge fairies'. They don't tell stories to themselves or, rather, they keep telling the same old story.

It is natural to think of stories as resting on language, but the causal­ity probably works the other way round. Gregory Bateson, in his book Mind and the Universe, devotes several chapters to human languages and how we use them to think. But his start on the subject is a beautiful mistake. He starts by looking at an 'outside' view of language, a kind of chemical analogy. Words, he says, are obviously the atoms of language, phrases and sentences the molecules, atoms in combi­nation. Verbs are reactive atoms, link nouns together, and so on. He discusses paragraphs, chapters, books ... and fiction, that he claims, very persuasively, is the ultimate triumph of human language.

Bateson shows us a scenario where an audience is watching a mur­der on stage, and nobody runs to phone the police. And then he goes into another mode, addressing his readers directly. He tells them that he felt that he'd done a really good job on the introduction to lan­guage, so he rewarded himself with a visit to the Washington Zoo. Almost the first cage inside the gate had two monkeys playing at fight­ing, and as he watched them, the whole beautiful edifice that he had written turned upside down in his mind. The monkeys had no verbs, no nouns, no paragraphs. But they understood fiction perfectly.

What does this tell us? Not just that we can rewrite that scene with the boss in our minds. Not even that we can go and see her, and dis­cuss what happened. Its most important implication is that the distinction between fiction and fact sits at the base of language, not at the pinnacle. Verbs and nouns are the most rarefied of abstractions, not the original raw material. We do not acquire stories through lan­guage: we acquire language through stories.

FIFTEEN

TROUSER LEG OF TIME

In the heat of the night, magic moved on silent feet.

One horizon was red with the setting sun. This world went around a central star. The elves did not know this. If they had done, it would not have bothered them. They never bothered with detail of that kind. The universe had given rise to life in many strange places, but the elves were not interested in that, either.

This world had created lots of life, too. None of it had ever had what the elves considered to be potential. But this time ...

It had iron, too. The elves hated iron. But this time, the rewards were worth the risk. This time ...

One of them signalled. The prey was close at hand. And now they saw it, clustered in the trees around a clearing, dark blobs against the sunset.

The elves assembled. And then, at a pitch so strange that it entered the brain without the need to use the ears, they began to sing.

'Chmmmmph!' said Archchancellor Ridcully, as a heavy body landed on his back and clamped a hand over his mouth, forcing him back down into the long, dewy grass.

'Listen very carefully!' hissed a voice in his ear. 'When you were small, you had a one-eared toy rabbit called Mr Big Pram! On your sixth birthday your brother hit you on the head with a model boat! And when you were twelve ... do the words "jolly lolly" ring a bell?'

'Mmph!'

'Very well. I'm you. There's been one of those temporal things Mister Stibbons is always goin' on about. I'm taking my hand away now and we'll both quietly crawl away without the elves seeing us. Understand?'

'Mmp.'

'Good man.'

Elsewhere in the bushes the Dean whispered into his own ear: 'Under a secret floorboard in your study-'

Ponder whispered to himself: 'I'm sure we both agree that this should not really be happening ...'

In fact the only wizard who did not bother with concealment was Rincewind, who tapped himself on the shoulder and evinced no sur­prise at seeing himself. In his life he had seen far more unusual things than his own doppelganger.

'Oh, you,' he said.

"fraid so,' he said glumly.

'Was it you that turned up just now to tell me I should hold my breath?'

'Er ... possibly, but I think I've been superseded by me.'

'Oh. Has Ponder Stibbons being talking about quantum again?'

'You got it in one.'

'Another mess up?'

'More or less. It turns out stopping the elves is a really bad idea.'

'Typical. Do we both survive? There's not much room in the office, what with all the coal-'

'Ponder Stibbons says we may end up remembering everything, because of residual quantum infraction, but we'll sort of be the same person.'

'Any big teeth or sharp edges involved?'

'Not so far.'

'Could be worse, then, all things considered.'

In pairs, the wizards assembled as quietly as they could. Apart from Ridcully, who seemed to quite enjoy his own company, they tried not to look at their doppelgangers; it's quite embarrassing being in the company of someone who knows everything about you, even if that person is yourself.

A few feet away, with the suddenness of lightning, a pale circle appeared on the grass.

'Our transport is here, gentlemen,' said Ponder. One of the Deans, who was standing well apart from the other Dean, raised his hand.

'What happens to the ones of us that stay behind?' he said. 'It won't matter,' said Ponder Stibbons. 'They'll vanish the moment we do, and the ones of us who end up in the, er, other trouser leg of time will have the memories of both of us. I think that's right, isn't it?' 'Yes,' said Ponder Stibbons. 'A pretty good summation for the lay­man. So, gentlemen, are we ready? One of everyone, into the circle now, please.'

Only the Rincewinds did not move. They knew what to expect. 'Depressing, isn't it,' said one of them, watching the fighting. Both Deans had managed to knock one another out of the circle on the very first charge.

'Especially the way one of the Stibbonses has just laid out the other one with a left hook,' said the other Rincewind. 'An unusual skill in a man of his education.'

'Doesn't give you a lot of confidence, I admit. Toss a coin?' 'Yes, why not ...' They did so.

'Fair enough,' said the winner. 'Nice to have met me.' He picked his way delicately across the groaning bodies and the last couple of strug­gling wizards, sat down in the centre of the circle of light, and pulled his hat as far down over his head as possible.

A moment later he became, very briefly, a six-dimensional knot and became untied again on a wooden floor in a library.

'Well, that was relatively painful,' he murmured, and looked around. The Librarian was sitting on his stool. The wizards were around Rincewind, looking amazed and, in some cases, slightly bruised. Dr Dee was watching them with concern.

'Oh dear, I see it did not work,' he said, and sighed. 'It never works for me, either. I will instruct the servants to fetch some food.' When he'd gone, the wizards looked at one another. 'Did we go?' said the Lecturer in Recent Runes. 'Yes, but we came back at the same time,' said Ponder. He rubbed his chin.

'I can remember everything,' said the Archchancellor. 'Amazin'! I was the one that got left behind and the one that-'

'Let's just not talk about it, shall we?' said the Dean, brushing his robe.

There was the sound of a muffled voice trying to make itself heard. The Librarian opened his paw.

'Attention please. Attention please,' said Hex.

Ponder took the sphere.

'We're listening.'

'Elves are approaching this property.'

'What, here? In broad daylight?' said Ridcully. 'On our damn world? While we're actually here? The nerve!'

Rincewind looked out of the window on to the drive below.

'Is it me,' said the Dean, 'or has it got colder?'

A carriage was rolling up, with a couple of footmen trotting along beside it. It was a fine one, by the standards of the city. There were plumes on the horse. And everything about it was either black or sil­ver.

'It's not just you,' said Rincewind, backing away from the window.

There were sounds at the front door. The wizards heard the distant voice of Dee, and then the creak of the stairs.

'Brethren,' he said, pushing open the door. 'There appears to be a visitor for you downstairs.' He gave them a worried smile. 'A lady.'