Chapter 13
Land Under Wave

The Queen walked over the turf towards Tiffany. Where she’d trodden, frost gleamed for a moment. The little part of Tiffany that was still thinking thought: That grass will be dead in the morning. She’s killing my turf.
The whole of life is but a dream, when you come to think of it,’ said the Queen in the same infuriat-ingly calm, pleasant voice. She sat down on the fallen stones. ‘You humans are such dreamers. You dream that you’re clever. You dream that you’re important. You dream that you’re special. You know, you’re almost better than dromes. You’re certainly more imaginative. I have to thank you.’
‘What for?’ said Tiffany, looking at her boots. Terror clamped her body in red-hot wires. There wasn’t anywhere to run to.
‘I never realized how wonderful your world is,’ said the Queen. ‘I mean, the dromes . . . well, they’re not much more than a kind of walking sponge, really. Their world is ancient. It’s nearly dead. They’re not really creative any more. With a little help from me, your people could be a lot better. Because, you see, you dream all the time. You, especially, dream all the time. Your picture of the world is a landscape with you in the middle of it, isn’t it? Wonderful. Look at you, in that rather horrible dress and those clumpy boots. You dreamed you could invade my world with a frying pan. You had this dream about Brave Girl Rescuing Little Brother. You thought you were the heroine of a story. And then you left him behind. You know, I think being hit by a billion tons of sea water must be like having a mountain of iron drop on your head, don’t you?’
Tiffany couldn’t think. Her head was full of hot, pink fog. It hadn’t worked.
Her Third Thoughts were somewhere in the fog, trying to make themselves heard.
‘Got Roland out,’ she muttered, still staring at her boots.
‘But he’s not yours,’ said the Queen. ‘He is, let us face it, a rather stupid boy with a big red face and brains made of pork, just like his father. You left your little brother behind with a bunch of little thieves and you rescued a spoiled little fool.’
There was no time! shrieked the Third Thoughts. You wouldn’t have got to him and got back to the lighthouse! You nearly didn’t get away as it was! You got Roland out! It was the logical thing to do! You don’t have to be guilty about it! What’s better, to try to save your brother and be brave, courageous, stupid and dead, or save the boy and be brave, courageous, sensible and alive?
But something kept saying that stupid and dead would have been more . . . right.
Something kept saying: Would you say to Mum that you could see there wasn’t time to rescue your brother so you rescued someone else instead? Would she be pleased that you’d worked that out? Being right doesn’t always work.
It’s the Queen! yelled the Third Thoughts. It’s her voice! It’s like hypnotism! You’ve got to stop listening!
‘I expect it’s not your fault you’re so cold and heartless,’ said the Queen. ‘It’s probably all to do with your parents. They probably never gave you enough time. And having Wentworth was a very cruel thing to do, they really should have been more careful. And they let you read too many words. It can’t be good for a young brain, knowing words like paradigm and eschatological. It leads to behaviour such as using your own brother as monster bait.’ The Queen sighed. ‘Sadly, that kind of thing happens all the time. I think you should be proud of not being worse than just deeply introverted and socially maladjusted.’
She walked around Tiffany.
‘It’s so sad,’ she continued. ‘You dream that you are strong, sensible, logical . . . the kind of person who always has a bit of string. But that’s just your excuse for not being really, properly human. You’re just a brain, no heart at all. You didn’t even cry when Granny Aching died. You think too much, and now your precious thinking has let you down. Well, I think it’s best if I just kill you, don’t you?’
Find a stone! the Third Thoughts screamed. Hit her!
Tiffany was aware of other figures in the gloom. There were some of the people from the summer pictures, but there were also dromes and the headless horseman and the Bumble-Bee women.
Around her, frost crept over the ground.
‘I think we’ll like it here,’ said the Queen.
Tiffany felt the cold creeping up her legs. Her Third Thoughts, hoarse with effort, shouted: Do something!
She should have been better organized, she thought dully. She shouldn’t have relied on dreams. Or . . . perhaps I should have been a real human being. More . .. . feeling. But I couldn’t help not crying! It just . . . wouldn’t come! And how can I stop thinking? And thinking about thinking? And even thinking about thinking about thinking?
She saw the smile in the Queen’s eyes, and thought: Which one of all those people doing all that thinking is me?
Is there really any me at all?
Clouds poured across the sky like a stain. They covered the stars. They were the inky clouds from the frozen world, the clouds of nightmare. It began to rain, rain with ice in it. It hit the turf like bullets, turning it into chalky mud. The wind howled like a pack of grimhounds.
Tiffany managed to take a step forward. The mud sucked at her boots.
‘A bit of spirit at last?’ said the Queen, stepping back.
Tiffany tried another step, but things were not working any more. She was too cold and too tired. She could feel her self disappearing, getting lost. . .
‘So sad, to end like this,’ said the Queen.
Tiffany fell forward, into the freezing mud.
The rain grew harder, stinging like needles, hammering on her head and running like icy tears down her cheeks. It struck so hard it left her breathless.
She felt the cold drawing all the heat out of her. And that was the only sensation left, apart from a musical note.
It sounded like the smell of snow, or the sparkle of frost. It was high and thin and drawn out.
She couldn’t feel the ground under her and there was nothing to see, not even the stars. The clouds had covered everything.
She was so cold she couldn’t feel the cold any more, or her fingers. A thought managed to trickle through her freezing mind. Is there any me at all? Or do my thoughts just dream of me?
The blackness grew deeper. Night was never as black as this, and winter never as cold. It was colder than the deep winters when the snow came down and Granny Aching would plod from snowdrift to snowdrift, looking for warm bodies. The sheep could survive the snow if the shepherd had some wits, Granny used to say. The snow kept the cold away, the sheep surviving in warm hollows under roofs of snow while a bitter wind blew harmlessly over them.
But this was as cold as those days when even the snow couldn’t fall, and the wind was pure cold itself, blowing ice crystals across the turf. Those were the killer days in early spring, when the lambing had begun and winter came howling down one more time . . .
There was darkness everywhere, bitter and starless.
There was a speck of light, a long way off.
One star. Low down. Moving . . .
It got bigger in the stormy night.
It zigzagged as it came.
Silence covered Tiffany, and drew her into itself.
The silence smelled of sheep, and turpentine, and tobaccco.
And then . . . came movement, as if she was falling through the ground, very fast.
And gentle warmth, and, just for a moment, the sound of waves.
And her own voice, inside her head.
This land is in my bones.
Land under wave.
Whiteness.
It tumbled through the warm, heavy darkness around her, something like snow but as fine as dust. It piled up somewhere below her, because she could see a faint whiteness.
A creature like an ice-cream cone with lots of tentacles shot past her and jetted away.
I’m underwater, thought Tiffany.
I remember. . .
This is the million-year rain under the sea, this is the new land being born underneath an ocean. It’s not a dream. It’s . . . a memory. The land under wave. Millions and millions of tiny shells . . .
This land was alive.
All the time there was the warm, comforting smell of the shepherding hut, and the feeling of being held in invisible hands.
The whiteness below her rose up and over her head, but it didn’t seem uncomfortable. It was like being in a mist.
Now I’m inside the chalk, like a flint, like a calkin . . .
She wasn’t sure how long she spent in the warm deep water, or if indeed any time really had passed, or if the millions of years went past in a second, but she felt movement again, and a sense of rising.
More memories poured into her mind.
There’s always been someone watching the borders. They didn’t decide to. It was decided for them. Someone has to care. Sometimes, they have to fight. Someone has to speak for that which has no voice . . ..
She opened her eyes. She was still lying in the mud, and the Queen was laughing at her and, overhead, the storm still raged.
But she felt warm. In fact, she felt hot, red-hot with anger . . . anger at the bruised turf, anger at her own stupidity, anger at this beautiful creature whose only talent was control.
This . . . creature was trying to take her world.
All witches are selfish, the Queen had said. But Tiffany’s Third Thoughts said: Then turn selfishness into a weapon! Make all things yours! Make other lives and dreams and hopes yours! Protect them! Save them! Bring them into the sheepfold! Walk the gale for them! Keep away the wolf! My dreams! My brother! My family! My land! My world! How dare you try to take these things, because they are mine!
I have a duty!
The anger overflowed. She stood up clenched her fists and screamed at the storm, putting into the scream all the rage that was inside her.
Lightning struck the ground on either side of her. li did so twice.
And it stayed there, crackling, and two dogs formed.
Steam rose from their coats, and blue light sparked from their ears as they shook themselves. They looked attentively at Tiffany.
The Queen gasped, and vanished.
‘Come by, Lightning!’ shouted Tiffany. ‘Away to me, Thunder!’ And she remembered the time when she’d run across the downs, falling over, shouting all the wrong things, while the two dogs had done exactly what needed to be done . . .
Two streaks of black and white sped away across the turf and up towards the clouds.
They herded the storm.
Clouds panicked and scattered, but always there was a comet streaking across the sky and they were turned. Monstrous shapes writhed and screamed in the boiling sky, but Thunder and Lightning had worked many flocks; there was an occasional snap of lightning-sparked teeth, and a wail. Tiffany stared upwards, rain pouring off her face, and shouted commands that no dog could possibly have heard.
Jostling and rumbling and screaming, the storm rolled off the hills and away towards the mountains, where there were deep canyons that could pen it.
Out of breath, glowing with triumph, Tiffany watched until the dogs came back and settled, once again, on the turf. And then she remembered something else: it didn’t matter what orders she gave those dogs. They were not her dogs. They were working dogs.
Thunder and Lightning didn’t take orders from a little girl.
And the dogs weren’t looking at her.
They were looking just behind her.
She’d have turned if someone had told her a horrible monster was behind her. She’d have turned if they’d said it had a thousand teeth. She didn’t want to turn round now. Forcing herself was the hardest thing she’d ever done.
She was not afraid of what she might see. She was terribly, mortally frightened, afraid to the centre of her bones of what she might not see. She shut her eyes while her cowardly boots shuffled her round and then, after a deep breath, she opened them again.
There was a gust of Jolly Sailor tobacco, and sheep, and turpentine.
Sparkling in the dark, light glittering off the white shepherdess dress and every blue ribbon and silver buckle of it, was Granny Aching, smiling hugely, glowing with pride. In one hand she held the huge ornamental crook, hung with blue bows.
She pirouetted slowly, and Tiffany saw that while she was a brilliant, glowing shepherdess from hat to hem, she still had her huge old boots on.
Granny Aching took her pipe out of her mouth, and gave Tiffany the little nod that was, from her, a round of applause. And then - she wasn’t.
Real starlit darkness covered the turf, and the night-time sounds filled the air. Tiffany didn’t know if what had just happened was a dream or had happened somewhere that wasn’t quite here or had only happened in her head. It didn’t matter. It had happened. And now—
‘But I’m still here,’ said the Queen, stepping in front of her. ‘Perhaps it was all a dream. Perhaps you have gone a little mad, because you are after all a very strange child. Perhaps you had help. How good are you? Do you really think that you can face me alone? I can make you think whatever I please—’
‘Crivens!’
‘Oh no, not them,’ said the Queen, throwing up her hands.
It wasn’t just the Nac Mac Feegles, but also Wentworth, a strong smell of seaweed, a lot of water and a dead shark. They appeared in mid-air and landed in a heap between Tiffany and the Queen. But a pictsie was always ready for a fight, and they bounced, rolled and came up drawing their swords and shaking sea water out of their hair.
‘Oh, ‘tis you, izzut?’ said Rob Anybody, glaring up at the Queen. ‘Face to face wi’ ye at last, ye bloustie ol’ callyack that ye are! Ye canna’ come here, unnerstand? Be off wi’ ye! Are ye goin’ to go quietly?’
The Queen stamped heavily on him. When she took her foot away, only the top of his head was visible above the turf.
‘Well, are ye?’ he said, pulling himself out as if nothing had happened. ‘I don’t wantae havtae lose my temper wi’ ye! An’ it’s no good sendin’ your pets against us, ‘cos you ken we can take ‘em tae the cleaners!’ He turned to Tiffany, who hadn’t moved. ‘You just leave this tae us, Kelda. Us an’ the Quin, we go way back!’
The Queen snapped her fingers. ‘Always leaping into things you don’t understand,’ she hissed. ‘Well, can you face these?’
Every Nac Mac Feegle sword suddenly glowed blue.
Back in the crowd of eerily lit pictsies a voice that sounded very much like that of Daft Wullie said:
‘Ach, we’re in real trouble noo . . .’
Three figures had appeared in the air, a little way away. The middle one, Tiffany saw, had a long red gown, a strange long wig and black tights with buckles on his shoes. The others were just ordinary men, it seemed, in ordinary grey suits.
‘Oh, ye are a harrrrrd wumman, Quin,’ said William the gonnagle, ‘to set the lawyers ontae us . . .’
‘See the one on the left there,’ whimpered a pictsie. ‘See, he’s got a briefcase! It’s a briefcasel Oh, waily, waily, a briefcase, waily . . .’
Reluctantly, a step at a time, pressing together in terror, the Nac Mac Feegles began to back away.
‘Oh, waily waily, he’s snappin’ the clasps,’ groaned Daft Wullie. ‘Oh, waily waily waily, ‘tis the sound o’ Doom when a lawyer does that!’
‘Mister Rob Anybody Feegle and sundry others?’ said one of the figures in a voice of dread.
‘There’s naebody here o’ that name!’ shouted Rob Anybody. ‘We dinnae know anythin’!’
‘We have heard a list of criminal and civil charges totalling nineteen thousand, seven hundred and sixty-three separate offences—’
‘We wasnae there!’ yelled Rob Anybody desperately. ‘Isn’t that right, lads?’
‘- including more than two thousand cases of Making an Affray, Causing a Public Nuisance, Being Found Drunk, Being Found Very Drunk, Using Offensive Language (taking into account ninety-seven counts of Using Language That Was Probably Offensive If Anyone Else Could Understand It), Committing a Breach of the Peace, Malicious Lingering—’
‘It’s mistaken identity!’ shouted Rob Anybody. ‘It’s no’ oour fault! We wuz only standing there an’ someone else did it and ran awa’!’
‘- Grand Theft, Petty Theft, Burglary, Housebreaking, Loitering With Intent To Commit a Felony—’
‘We wuz misunderstood when we was wee bairns!’ yelled Rob Anybody. ‘Ye’re only pickin’ on us cuz we’re blue! We always get blamed for every thin’! The polis hate us! We wasnae even in the country!’
But, to groans from the cowering pictsies, one of the lawyers produced a big roll of paper from his briefcase. He cleared his throat and read out: ‘Angus, Big; Angus, No’-As-Big-As-Big-Angus; Angus, Wee; Archie, Big; Archie, One-Eyed; Archie, Wee Mad—’
‘They’ve got oour names!’ sobbed Daft Wullie. They’ve got oour names\ It’s the pris’n hoose for us!’
‘Objection! I move for a writ of Habeas Corpus,’ said a small voice. ‘And enter a plea of Vis-nefaciem capite repletam, without prejudice.’
There was absolute silence for a moment. Rob Anybody turned to look at the frightened Nac Mac Feegles and said: ‘OK, OK, which of youse said that?’
The toad crawled out of the crowd, and sighed. ‘It suddenly all came back to me,’ it said. ‘I remember what I was now. The legal language brought it all back. I’m a toad now but. . .’ it swallowed, ‘once I was a lawyer. And this, people, is illegal. These charges are a complete tissue of lies based on hearsay evidence.’
It raised yellow eyes towards the Queen’s lawyers. ‘I further move that the case is adjourned sine die on the basis of Potest-ne mater tua suere, amice.’
The  lawyers  had  pulled  large  books   out  of nowhere and were thumbing through them hastily. ‘We’re not familiar with counsel’s terminology,’ said one of them.
‘Hey, they’re sweatin’,’ said Rob Anybody. ‘You mean we can have lawyers on oour side as well?’
‘Yes, of course,’ said the toad. ‘You can have defence lawyers.’
‘Defence?’ said Rob Anybody. ‘Are you tellin’ me we could get awa’ wi’ it ‘cos of a tishoo o’ lies?’
‘Certainly,’ said the toad. ‘And with all the treasure you’ve stolen you can pay enough to be very innocent indeed. My fee will be—’
It gulped as a dozen glowing swords were swung towards him.
‘I’ve just remembered why that fairy godmother turned me into a toad,’ it said. ‘So, in the circumstances, I’ll take this case pro bono publico.’
The swords didn’t move.
‘That means for free,’ it added.
‘Oh, right, we like the sound o’ that,’ said Rob Anybody, to the sound of swords being sheathed. ‘How come ye’re a lawyer an’ a toad?’
‘Oh, well, it was just bit of an argument,’ said the toad. ‘A fairy godmother gave my client three wishes - the usual health, wealth and happiness package -and when my client woke up one wet morning and didn’t feel particularly happy she got me to bring an action for breach of contract. It was a definite first in the history of fairy godmothering. Unfortunately, as it turned out, so was turning the client into a small hand mirror and her lawyer, as you see before you, into a toad. I think the worst part was when the judge applauded. That was hurtful, in my opinion.’
‘But ye can still remember all that legal stuff? Quid,’ said Rob Anybody. He glared at the other lawyers. ‘Hey, youse scunners, we got a cheap lawyer and we no’ afraid tae use him wi’ prejudice!’
The other lawyers were pulling more and more paperwork out of the air now. They looked worried, and a little frightened. Rob Anybody’s eyes gleamed as he watched them.
‘What does all that Viznee-facey-em stuff mean, my learned friend?’ he said.
‘Vis-ne faciem capite repletam,’ said the toad. ‘It was the best I could do in a hurry, but it means, approximately,’ he gave a little cough, ‘ “would you like a face which is full of head?”‘
‘And tae think we didnae know legal talkin’ was that simple,’ said Rob Anybody. ‘We could all be lawyers, lads, if we knew the fancy words! Let’s get them!’
The Nac Mac Feegle could change mood in a moment, especially at the sound of a battle cry. They raised their swords in the air.
‘Twelve hundred angry men!’ they shouted.
‘Nae more courtroom drama!’
‘We ha’ the law on oour side!’
‘The law’s made to tak’ care o’ raskills!’
‘No,’ said the Queen, and waved her hand.
Lawyers and pictsies faded away. There was just her and Tiffany, facing one another on the turf at dawn, the wind hissing around the stones.
‘What have you done with them?’ Tiffany shouted.
‘Oh, they’re around . . . somewhere,’ said the Queen airily. ‘It’s all dreams, anyway. And dreams within dreams. You can’t rely on anything, little girl. Nothing is real. Nothing lasts. Everything goes. All you can do is learn to dream. And it’s too late for that. And I. . . I have had longer to learn.’
Tiffany wasn’t sure which of her thoughts was operating now. She was tired. She felt as though she was watching herself from above and a little behind. She saw herself set her boots firmly on the turf, and then .. . .
. . . and then . . .
. . . and then, like someone rising from the clouds of a sleep, she felt the deep, deep Time below her. She sensed the breath of the downs and the distant roar of ancient, ancient seas trapped in millions of tiny shells. She thought of Granny Aching, under the turf, becoming part of the chalk again, part of the land under wave. She felt as if huge wheels, of time and stars, were turning slowly around her.
She opened her eyes and then, somewhere inside, opened her eyes again.
She heard the grass growing, and the sound of worms below the turf. She could feel the thousands of little lives around her, smell all the scents on the breeze, and see all the shades of the night. . .
The wheels of stars and years, of space and time, locked into place. She knew exactly where she was, and who she was, and what she was.
She swung a hand. The Queen tried to stop her, but she might as well have tried to stop a wheel of years. Tiffany’s hand caught her face and knocked her off her feet.
‘I never cried for Granny because there was no need to,’ she said. ‘She has never left me!’
She leaned down, and centuries bent with her.
‘The secret is not to dream,’ she whispered. ‘The secret is to wake up. Waking up is harder. I have woken up and I am real. I know where I come from and I know where I’m going. You cannot fool me any more. Or touch me. Or anything that is mine.’
I’ll never be like this again, she thought, as she saw the terror in the Queen’s face. I’ll never again feel as tall as the sky and as old as the hills and as strong as the sea. I’ve been given something for a while, and the price of it is that I have to give it back.
And the reward is giving it back, too. No human could live like this. You could spend a day looking at a flower to see how wonderful it is, and that wouldn’t get the milking done. No wonder we dream our way through our lives. To be awake, and see it all as it really is .. . . no one could stand that for long.
She took a deep breath, and picked the Queen up. She was aware of things happening, of dreams roaring around her, but they didn’t affect her. She was real and she was awake, more awake than she’d ever been. She had to concentrate even to think against the storm of sensations pouring into her mind.
The Queen was as light as a baby and changed shape madly in Tiffany’s arms - into monsters and mixed-up beasts, things with claws and tentacles. But, at last, she was small and grey, like a monkey, with a large head and big eyes and a little downy chest that went up and down as she panted.
She reached the stones. The arch still stood. It was never down, Tiffany thought. She had no strength, no magic, just one trick. The worst one.
‘Stay away from here,’ said Tiffany, stepping though the stone doorway. ‘Never come back. Never touch what is mine.’ And then, because the thing was so weak and baby-like, she added: ‘But I hope there’s someone who’ll cry for you. I hope the King comes back.’
‘You pity me?’ growled the thing that had been the Queen.
‘Yes. A bit,’ said Tiffany. Like Miss Robinson, she thought.
She put the creature down. It scampered across the snow, turned, and became the beautiful Queen again.
‘You won’t win,’ the Queen said. ‘There’s always a way in. People dream.’
‘Sometimes we waken,’ said Tiffany. ‘Don’t come back . . . or there will be a reckoning . . ..’
She concentrated, and now the stones framed nothing more - or less - than the country beyond.
I shall have to find a way of sealing that, said her Third Thoughts. Or her twentieth thoughts, perhaps. Her head was full of thoughts.
She managed to walk a little way and then sat down, hugging her knees. Imagine getting stuck like this, she thought. You’d have to wear earplugs and noseplugs and a big black hood over your head, and still you’d see and hear too much . . .
She closed her eyes, and closed her eyes again.
She felt it all draining away. It was like falling asleep, sliding from that strange wide-awakeness into just normal, everyday .. . . well, being awake. It felt as if everything was blurred and muffled.
This is how we always feel, she thought. We sleepwalk through our lives, because how could we live if we were always that awake—
Someone tapped her on the boot.
 

Chapter 14
Small Like Oak Trees

‘Hey, where did you get to?’ shouted Rob Anybody, glaring up at her. ‘One minute we was just aboout to give them lawyers a good legal seein’-to, next minute you and the Quin wuz gone!’
Dreams within dreams, Tiffany thought, holding her head. But they were over, and you couldn’t look at the Nac Mac Feegle and not know what was real.
‘It’s over,’ she said.
‘Didja kill her?’
‘No.’
‘She’ll be back then,’ said Rob Anybody. ‘She’s awfu’ stupid, that one. Clever with the dreaming, I’ll grant ye, but not a brain in her heid.’
Tiffany nodded. The blurred feeling was going. The moment of wide-awakeness had faded like a dream. But I must remember that it wasn’t a dream.
‘How did you get away from the huge wave?’ she asked.
‘Ach, we’re fast movers,’ said Rob Anybody. ‘An’ it was a strong lighthoose. O’ course, the water came up pretty high.’
‘A few sharks were involved, that kind of thing,’ said Not-as-big-as-Medium-Sized-Jock-but-bigger-than-Wee-Jock-Jock.
‘Oh, aye, a few sharkies,’ said Rob Anybody, shrugging. ‘And one o’ them octopussies—’
‘It was a giant squid,’ said William the gonnagle.
‘Aye, well, it was a kebab pretty quickly,’ said Daft Wullie.
‘Ha’ a heidful o’ held, you wee weewee!’ shouted Wentworth, overcome with wit.
William coughed politely. ‘And the big wave threw up a lot of sunken vessels full o’ trrrreasure,’ he said. ‘We stopped off for a wee pillage . .. .’
The Nac Mac Feegles held up wonderful jewels and big gold coins.
‘But that’s just dream treasure, surely?’ said Tiffany. ‘Fairy gold! It’ll turn into rubbish in the morning!’
‘Aye?’ said Rob Anybody. He glanced at the horizon. ‘OK, ye heard the kelda, lads! We got mebbe half an hour to sell it to someone! Permission to go offski?’ he added to Tiffany.
‘Er . . . oh, yes. Fine. Thank you—’
They were gone, in a split-second blur of blue and red.
But William the gonnagle remained for a moment. He bowed to Tiffany.
‘Ye didnae do at all badly,’ he said. ‘We’re proud o’ ye. So would yer grrranny be. Remember that. Ye are not unloved.’
Then he vanished too.
There was a groan from Roland, lying on the turf. He began to move.
‘Weewee men all gone,’ said Wentworth, sadly, in the silence that followed. ‘Crivens all gone.’
‘What were they?’ muttered Roland, sitting up and holding his head.
‘It’s all a bit complicated,’ said Tiffany. ‘Er . . . do you remember much?’
‘It all seems like . . . a dream . . .’ said Roland. ‘I remember . . . the sea, and we were running, and I cracked a nut which was full of those little men, and I was hunting in this huge forest with shadows—’
‘Dreams can be very funny things,’ said Tiffany carefully. She went to stand up and thought: I must wait here a while. I don’t know why I know, I just know. Perhaps I knew and have forgotten. But I must wait for something . . .
‘Can you walk down to the village?’ she said.
‘Oh, yes. I think so. But what did—?’
‘Then will you take Wentworth with you, please? I’d like to .. . . rest for a while.’
‘Are you sure?’ said Roland, looking concerned.
‘Yes. I won’t be long. Please? You can drop him off at the farm. Tell my parents I’ll be down soon. Tell them I’m fine.’
‘Weewee men,’ said Wentworth. ‘Crivens! Want bed.’
Roland was still looking uncertain.
‘Off you go!’ Tiffany commanded, and waved him away.
When the two of them had disappeared below the brow of the hill, with several backward glances, she sat down between the four iron wheels and hugged her knees.
Far off, she could see the mound of the Nac Mac Feegle. Already, they were a slightly puzzling memory, and she’d seen them only a few minutes ago. But when they’d gone, they left the impression of never having been there.
She could go to the mound and see if she could find the big hole. But supposing it wasn’t there? Or supposing it was, but all there was down there were rabbits?
No, it’s all true, she said to herself. I must remember that, too.
A buzzard screamed in the dawn greyness. She looked up as it circled into sunlight, and a tiny dot detached itself from the bird.
That was far too high up even for a pictsie to stand the fall.
Tiffany scrambled to her feet as Hamish tumbled through the sky. And then - something ballooned above him and the fall became just a gentle floating, like thistledown.
The bulging shape above Hamish was Y-shaped. As it got bigger, the shape become more precise, more . . . familiar.
He landed, and a pair of Tiffany’s pants, the long-legged ones with the rosebud pattern, settled down on top of him.
‘That was great,’ he said, pushing his way through the folds of fabric. ‘Nae more landin’ on my heid for me!’
‘They’re my best pants,’ said Tiffany, wearily. ‘You stole them off our clothes line, didn’t you . . .. ?’
‘Oh aye. Nice and clean,’ said Hamish. ‘I had to cut the lace off ‘cuz it got in the way, but I put it by and ye could easily sew it on again.’ He gave Tiffany the big grin of someone who, for once, has not dived heavily into the ground.
She sighed. She’d liked the lace. She didn’t have many things that weren’t necessary. ‘I think you’d better keep them,’ she said.
‘Aye, I will, then,’ said Hamish. ‘Noo, what wuz it. . . ? Oh, yes. Ye have visitors comin’. I spotted them out over the valley. Look up there.’
There were two other things up there, bigger than a buzzard, so high that they were already in full sunlight. Tiffany watched as they circled lower.
They were broomsticks.
I knew I had to wait! Tiffany thought.
Her ears bubbled. She turned and saw Hamish running across the grass. As she looked, the buzzard picked him up and sped onwards. She wondered if he was frightened or, at least, didn’t want to meet . . . whoever was coming
The broomsticks descended.
The lowest one had two figures on it. As it landed, Tiffany saw that one of them was Miss Tick, clinging anxiously onto a smaller figure who’d been doing the steering. She half climbed off, half fell off, and tottered over to Tiffany.
‘You wouldn’t believe the time I’ve had,’ she said. ‘It was just a nightmare! We flew through the storm! Are you all right?’
‘Er . . . yes . . .’
‘What happened?’
Tiffany looked at her. How did you begin to answer something like that?
‘The Queen’s gone,’ she said. That seemed to cover it.
‘What? The Queen has gone? Oh .. .. . er . . . these ladies are Mrs Ogg—’
‘Mornin’,’ said the broomstick’s other occupant, who was pulling at her long black dress, from under the folds of which came the sounds of twanging elastic. The wind up there blows where it likes, I don’t mind telling you!’ She was a short fat lady with a cheerful face like an apple that has been stored too long; all the wrinkles moved into different positions when she smiled.
‘And this,’ said Miss Tick, ‘is Miss—’
‘Mistress,’snapped the other witch, dismounting.
‘I’m so sorry, Mistress Weatherwax,’ said Miss Tick. ‘Very, very good witches,’ she whispered to Tiffany. ‘I was very lucky to find them. They respect witches up in the mountains.’
Tiffany was impressed that anyone could make Miss Tick flustered, but the other witch seemed to do it just by standing there. She was tall - except, Tiffany realized, she wasn’t that tall, but she stood tall, which could easily fool you if you weren’t paying attention - and like the other witch wore a rather shabby black dress. She had an elderly, thin face that gave nothing away. Piercing blue eyes looked Tiffany up and down, from head to toe.
‘You’ve got good boots,’ said the witch.
‘Tell Mistress Weatherwax what happened—’ Miss Tick began. But the witch held up a hand and Miss Tick stopped talking immediately. Tiffany was even more impressed now.
Mistress Weatherwax gave Tiffany a look that went right through her head and about five miles out the other side. Then she walked over to the stones, and waved one hand. It was an odd movement, a kind of wriggle in the air, but for a moment it left a glowing line. There was a noise, a chord, as though all sorts of sounds were happening at the same time. It snapped into silence.
‘Jolly Sailor tobacco?’ said the witch.
‘Yes,’ said Tiffany.
The witch waved a hand again. There was another sharp, complicated noise. Mistress Weatherwax turned suddenly and stared at the distant pimple that was the pictsie mound.
‘Nac Mac Feegle? Kelda? she demanded.
‘Er, yes. Only temporary,’ said Tiffany.
‘Hmmph,’ said Mistress Weatherwax.
Wave. Sound.
‘Frying pan?
‘Yes. It’s got lost, though.’
‘Hmm.’
Wave. Sound. It was as if the woman was extracting her history from the air.
‘Filled buckets?
‘And they filled up the log box, too,’ said Tiffany.
Wave. Sound.
‘I see. Special Sheep Liniment?’
‘Yes, my father says it puts—’
Wave. Sound.
‘Ah. Land of snow.’ Wave. Sound. ‘A queen.’ Wave. Sound. ‘Fighting.’
Wave, sound. ‘On the sea?’ Wave, sound, wave, sound . . .
Mistress Weatherwax stared at the flashing air, looking at pictures only she could see. Mrs Ogg sat down beside Tiffany, her little legs going up in the air as she made herself comfortable.
‘I’ve tried Jolly Sailor,’ she said. ‘Smells like toe-nails, don’t it?’
‘Yes, it does!’ said Tiffany, gratefully.
‘To be a kelda of the Nac Mac Feegle, you have to marry one of ‘em, don’t you?’ said Mrs Ogg, innocently.
‘Ah, yes, but I found a way round that,’ said Tiffany. She told her. Mrs Ogg laughed. It was a sociable kind of laugh, the sort of laugh that makes you comfortable.
The noise and flashing stopped. Mistress Weatherwax stood staring at nothing for a moment, and then said: ‘You beat the Queen, at the end. But you had help, I think.’
‘Yes, I did,’ said Tiffany.
‘And that was—?’
‘I don’t ask you your business,’ said Tiffany, before she even realized she was going to say it. Miss Tick gasped. Mrs Ogg’s eyes twinkled, and she looked from Tiffany to Mistress Weatherwax like someone watching a tennis match.
“Tiffany, Mistress Weatherwax is the most famous witch in all—’ Miss Tick began severely, but the witch waved a hand at her again. I really must learn how to do that, Tiffany thought.
Then Mistress Weatherwax took off her pointed hat and bowed to Tiffany.
‘Well said,’ she said, straightening up and staring directly at Tiffany ‘I didn’t have no right to ask you. This is your country, we’re here by your leave. I show you respect as you in turn will respect me.’ The air seemed to freeze for a moment and the skies to darken. Then Mistress Weatherwax went on, as if the moment of thunder hadn’t happened: ‘But if one day you care to tell me more, I should be grateful to hear about it,’ she said, in a conversational voice. ‘And them creatures that look like they’re made of dough, I should like to know more about them, too. Never run across  them before.  And your grandmother sounds the kind of person I would have liked to meet.’ She straightened up. ‘In the meantime, we’d better see if there’s anything left you can still be taught.’
‘Is this where I learn about the witches’ school?’ said Tiffany. There was a moment of silence.
‘Witches’ school?’ said Mistress Weatherwax.
‘Um,’ said Miss Tick.
‘You were being metapahorrical, weren’t you?’ said Tiffany.
‘Metapahorrical?’ said Mrs Ogg, wrinkling her forehead.
‘She means metaphorical,’ mumbled Miss Tick.
‘It’s like stories,’ said Tiffany. ‘It’s all right. I worked it out. This is the school, isn’t it? The magic place? The world. Here. And you don’t realize it until you look. Do you know the pictsies think this world is heaven? We just don’t look. You can’t give lessons on witchcraft. Not properly. It’s all about how you are . . . you, I suppose.’
‘Nicely said,’ said Mistress Weatherwax. ‘You’re sharp. But there’s magic, too. You’ll pick that up. It don’t take much intelligence, otherwise wizards wouldn’t be able to do it.’
‘You’ll need a job, too,’ said Mrs Ogg. There’s no money in witchcraft. Can’t do magic for yourself, see? Cast-iron rule.’
‘I make good cheese,’ said Tiffany.
‘Cheese, eh?’ said Mistress Weatherwax. ‘Hmm. Yes. Cheese is good. But do you know anything about medicines? Midwifery? That’s a good portable skill.’
‘Well, I’ve helped deliver difficult lambs,’ said Tiffany. ‘And I saw my brother being born. They didn’t bother to turn me out. It didn’t look too difficult. But I think cheese is probably easier, and less noisy.’
‘Cheese is good,’ Mistress Weatherwax repeated, nodding. ‘Cheese is alive.’
‘And what do you really do?’ said Tiffany.
The thin witch hesitated for a moment, and then:
‘We look to . . . the edges,’ said Mistress Weatherwax. ‘There’re a lot of edges, more than people know. Between life and death, this world and the next, night and day, right and wrong .. . . an’ they need watchin’. We watch ‘em, we guard the sum of things. And we never ask for any reward. That’s important.’
‘People give us stuff, mind you. People can be very gen’rous to witches,’ said Mrs Ogg, happily. ‘On bakin’ days in our village, sometimes I can’t move for cake. There’s ways and ways of not askin’, if you get my meaning. People like to see a happy witch.’
‘But down here people think witches are bad!’ said Tiffany, and her Second Thoughts added: Remember how rarely Granny Aching ever had to buy her own tobacco?
‘It’s amazin’ what people can get used to,’ said Mrs Ogg. ‘You just have to start slow.’
‘And we have to hurry,’ said Mistress Weatherwax. There’s a man riding up here on a farm horse. Fair hair, red face—’
‘It sounds like my father!’
‘Well, he’s making the poor thing gallop,’ said Mistress Weatherwax. ‘Quick, now. You want to learn the skills? When can you leave home?’
‘Pardon?’ said Tiffany.
‘Don’t the girls here go off to work as maids and things?’ said Mrs Ogg.
‘Oh, yes. When they’re a bit older than me.’
‘Well, when you’re a bit older than you. Miss Tick here will come and find you,’ said Mistress Weatherwax. Miss Tick nodded. ‘There’re elderly witches up in the mountains who’ll pass on what they know in exchange for a bit of help around the cottage. This place will be watched over while you’re gone, you may depend on it. In the meantime you’ll get three meals a day, your own bed, use of broomstick . . . that’s the way we do it. All right?’
‘Yes,’ said Tiffany, grinning happily. The wonderful moment was passing too quickly for all the questions she wanted to ask. ‘Yes! But, er . . .’
‘Yes?’ said Mrs Ogg.
‘I don’t have to dance around with no clothes on or anything like that, do I? Only I heard rumours—’
Mistress Weatherwax rolled her eyes. Mrs Ogg grinned cheerfully. ‘Well, that procedure does have something to recommend it—’ she began.
‘No,   you   don’t   have   to!’   snapped   Mistress Weatherwax.   ‘No   cottage  made   of  sweets,   no cackling and no dancing!’
‘Unless you want to,’ said Mrs Ogg, standing up. ‘There’s no harm in an occasional cackle, if the mood takes you that way. I’d teach you a good one right now, but we really ought to be going.’
‘But . . . but how did you manage it?’ said Miss Tick to Tiffany. This is all chalk! You’ve become a witch on chalk? How?’
‘That’s all you know, Perspicacia Tick,’ said Mistress Weatherwax. The bones of the hills is flint. It’s hard and sharp and useful. King of stones.’ She picked up her broomstick, and turned back to Tiffany. ‘Will you get into trouble, do you think?’ she said.
‘I might do,’ said Tiffany.
‘Do you want any help?’
‘If it’s my trouble, I’ll get out of it,’ said Tiffany. She wanted to say: Yes, yes! I’m going to need help! I don’t know what’s going to happen when my father gets here! The Baron’s probably got really angry! But I don’t want them to think I can’t deal with my own problems! I ought to be able to cope!
‘That’s right,’ said Mistress Weatherwax. Tiffany wondered if the witch could read minds.
‘Minds? No,’ said Mistress Weatherwax, climbing onto her broomstick. ‘Faces, yes. Come here, young lady.’
Tiffany obeyed.
‘The thing about witchcraft,’ said Mistress Weatherwax, ‘is that it’s not like school at all. First you get the test, and then afterwards you spend years findin’ out how you passed it. It’s a bit like life in that respect.’ She reached out and gently raised Tiffany’s chin so that she could look into her face. ‘I see you opened your eyes,’ she said.
‘Yes.’
‘Good. Many people never do. Times ahead might be a little tricky, even so. You’ll need this.’
She stretched out a hand and made a circle in the air around Tiffany’s hair, then brought her hand up over the head while making little movements with her forefinger.
Tiffany raised her hands to her head. For a moment she thought there was nothing there, and then they touched . . . something. It was more like a sensation in the air; if you weren’t expecting it to be there, your fingers passed straight through.
‘Is it really there?’ she said.
‘Who knows?’ said the witch. ‘It’s virtually a pointy hat. No one else will know it’s there. It might be a comfort.’
‘You mean it just exists in my head?’ said Tiffany.
‘You’ve got lots of things in your head. That doesn’t mean they aren’t real. Best not to ask me too many questions.’
‘What happened to the toad?’ said Miss Tick, who did ask questions.
‘It’s gone to live with the Wee Free Men,’ said Tiffany. ‘It turned out it used to be a lawyer.’
‘You’ve given a clan of the Nac Mac Feegle their own lawyer?’ said Mrs Ogg. That’ll make the world tremble. Still, I always say the occasional tremble does you good.’
‘Come, sisters, we must away,’ said Miss Tick, who had climbed on the other broomstick behind Mrs Ogg.
‘There’s no need for that sort of talk,’ said Mrs Ogg. That’s theatre talk, that is. Cheerio, Tiff. We’ll see you again.’
Her stick rose gently in the air. From the stick of Mistress Weatherwax, though, there was merely a sad little noise, like the thwop of Miss Tick’s hat point. The broomstick went kshugagugah.
Mistress Weatherwax sighed. ‘It’s them dwarfs,’ she said. They say they’ve repaired it, oh yes, and it starts first time in their workshop—’
They heard the sound of distant hooves. With surprising speed, Mistress Weatherwax swung herself off the stick, grabbed it firmly in both hands, and ran away across the turf, skirts billowing behind her.
She was a speck in the distance when Tiffany’s father came over the brow of the hill on one of the farm horses. He hadn’t even stopped to put the leather shoes on it; great slices of earth flew up as hooves the size of large soup plates,* each one shod with iron, bit into the turf.

Probably about eleven inches across. Tiffany didn’t measure them this time.

Tiffany heard a faint kshugagugahvwwoooom behind her as he leaped off the horse.
She was surprised to see him laughing and crying at the same time.
It was all a bit of a dream.
Tiffany found that a very useful thing to say. It’s hard to remember, it was all a bit of a dream. It was all a bit of a dream, I can’t be certain.
The overjoyed Baron, however, was very certain. Obviously this - this Queen woman, whoever she was, had been stealing children but Roland had beaten her, oh yes, and helped these two young children to get back as well.
Her mother had insisted on Tiffany going to bed, even though it was broad daylight. Actually, she didn’t mind. She was tired, and lay under the covers in that nice pink world halfway between asleep and awake.
She heard the Baron and her father talking downstairs. She heard the story being woven between them as they tried to make sense of it all. Obviously the girl had been very brave (this was the Baron speaking) but, well, she was nine, wasn’t she? And didn’t even know how to use a sword! Whereas Roland had fencing lessons at his school. . .
And so it went on. There were other things she heard her parents discussing later, when the Baron had gone. There was the way Ratbag now lived on the roof, for example.
Tiffany lay in bed and smelled the ointment her mother had rubbed into her temples. Tiffany must have got hit on the head, she’d said, because of the way she kept on touching it.
So . . . Roland with the beefy face was the hero, was he? And she was just like the stupid princess who broke her ankle and fainted all the time? That was completely unfair!
She reached out to the little table beside her bed where she’d put the invisible hat. Her mother had put down a cup of broth right through it, but it was still there. Tiffany’s fingers felt, very faintly, the roughness of the brim.
We never ask for any reward, she thought. Besides, it was her secret, all of it. No one else knew about the Wee Free Men. Admittedly Wentworth had taken to running through the house with a tablecloth round his waist shouting, ‘Weewee mens! I’ll scone you in the boot!’ but Mrs Aching was still so glad to see him back, and so happy that he was talking about things other than sweets, that she wasn’t paying too much attention to what he was talking about.
No, she couldn’t tell anyone. They’d never believe her, and suppose that they did, and went up and poked around in the pictsies’ mound? She couldn’t let that happen.
What would Granny Aching have done?
Granny Aching would have said nothing. Granny Aching often said nothing. She just smiled to herself, and puffed on her pipe, and waited until the right time . . .
Tiffany smiled to herself.
She slept, and didn’t dream.
And a day went past.
And another day.
On the third day, it rained. Tiffany went into the kitchen when no one was about and took down the china shepherdess from the shelf. She put it in a sack, then slipped out of the house and ran up onto the downs.
The worst of the weather was going either side of the Chalk, which cut through the clouds like the prow of a ship. But when Tiffany reached the spot where an old stove and four iron wheels stood out of the grass, and cut a square of turf, and carefully chipped out a hole for the china shepherdess, and then put the turf back. . .. it was raining hard enough to soak it in and give it a chance of surviving. It seemed the right thing to do. And she was sure she caught a whiff of tobacco.
Then she went to the pictsies’ mound. She’d worried about that. She knew they were there, didn’t she? So, somehow, going to check that they were there would be . . .. sort of. . .. showing that she doubted if they would be, wouldn’t it? They were busy people. They had lots to do. They had the old kelda to mourn. They were probably very busy. That’s what she told herself. It wasn’t because she kept wondering if there really might be nothing down the hole but rabbits. It wasn’t that at all.
She was the kelda. She had a duty.
She heard music. She heard voices. And then sudden silence as she peered into the gloom.
She carefully took a bottle of Special Sheep Liniment out of her sack and let it slide into darkness.
Tiffany walked away, and heard the faint music start up again.
She did wave at a buzzard, circling lazily under the clouds, and she was sure a tiny dot waved back.
On the fourth day, Tiffany made butter, and did her chores. She did have help.
‘And now I want you to go and feed the chickens,’ she said to Wentworth. ‘What is it I want you to do?’
‘Fee’ the cluck-clucks,’ said Wentworth.
‘Chickens,’ said Tiffany, severely.
‘Chickens,’ said Wentworth obediently.
‘And wipe your nose not on your sleeve! I gave you a handkerchief. And on the way back see if you can carry a whole log, will you?’
‘Ach, cravens,’ muttered Wentworth.
‘And what is it we don’t say?’ said Tiffany. ‘We don’t say the—’
‘- the crivens word,’ Wentworth muttered.
‘And we don’t say it in front of—’
‘- in fron’ of Mummy,’ said Wentworth.
‘Good. And then when I’ve finished we’ll have time to go down to the river.’
Wentworth brightened up.
‘Weewee mens?’ he said.
Tiffany didn’t reply immediately.
Tiffany hadn’t seen a single Feegle since she’d been home.
‘There might be,’ she said. ‘But they’re probably very busy. They’ve got to find another kelda, and . .. . well, they’re very busy. I expect.’
‘Weewee men say hit you in the head, fishface!’ said Wentworth happily.
‘We’ll see,’ said Tiffany, feeling like a parent. ‘Now please go and feed the chickens and get the eggs.’
When he’d wandered away, carrying the egg basket in both hands, Tiffany turned out some butter onto the marble slab and picked up the paddles to pat it into, well, a pat of butter. Then she’d stamp it with one of the wooden stamps. People appreciated a little picture on their butter.
As she began to shape the butter she was aware of a shadow in the doorway, and turned.
It was Roland.
He looked at her, his face even redder than usual. He was twiddling his very expensive hat nervously, just like Rob Anybody did.
‘Yes?’ she said.
‘Look, about. . . well, about all that. .. . about Roland began.
‘Yes?’
‘Look, I didn’t— I mean, I didn’t lie to anyone or anything,’ he blurted out. ‘But my father just sort of assumed I’d been a hero and he just wouldn’t listen to anything I said even after I told him how . . . how . . .’
‘- helpful I’d been?’ said Tiffany.
‘Yes . . .. I mean, no! He said, he said, he said it was lucky for you I was there, he said—’
‘It doesn’t matter,’ said Tiffany, picking up the butter paddles again.
‘And he just kept telling everyone how brave I’d been and—’
‘I said it doesn’t matter,’ said Tiffany. The little paddles went patpatpat on the fresh butter.
Roland’s mouth opened and shut for a moment.
‘You mean you don’t mind?’ he said at last.
‘No. I don’t mind,’ said Tiffany.
‘But it’s not fair!’
‘We’re the only ones who know the truth,’ said Tiffany.
Patapatpat. Roland stared at the fat, rich butter as she calmly patted it into shape.
‘Oh,’ he said. ‘Er . . . you won’t tell anyone, will you? I mean, you’ve got every right to, but—’
Patapatapat. . ..
‘No one would believe me,’ said Tiffany.
‘I did try,’ said Roland. ‘Honestly. I really did.’
I expect you did, Tiffany thought. But you’re not very clever and the Baron certainly is a man without First Sight. He sees the world the way he wants to see it.
‘One day you’ll be Baron, won’t you?’ she said.
‘Well, yes. One day. But look, are you really a witch?’
‘When you’re Baron you’ll be good at it, I expect?’ said Tiffany, turning the butter around. ‘Fair and generous and decent? You’ll pay good wages and look after the old people? You wouldn’t let people turn an old lady out of her house?’
‘Well, I hope I—’
Tiffany turned to face him, a butter paddle in each hand.
‘Because I’ll be there, you see. You’ll look up and see my eye on you. I’ll be there on the edge of the crowd. All the time. I’ll be watching everything, because I come from a long line of Aching people and this is my land. But you can be the Baron for us and I hope you’re a good one. If you are not . . . there will be a reckoning.’
‘Look, I know you were . . . were . . .’ Roland began, going red in the face.
‘Very helpful?’ said Tiffany.
‘. . . but you can’t talk to me like that, you know!’
Tiffany was sure she heard, up in the roof and on the very edge of hearing, someone say: ‘Ach, crivens, what a wee snotter . . .’
She shut her eyes for a moment, and then, heart pounding, pointed a butter paddle at one of the empty buckets.
‘Bucket, fill yourself!’ she commanded.
It blurred, and then sloshed. Water dripped down the side.
Roland stared at it. Tiffany gave him one of her sweetest smiles, which could be quite scary.
‘You won’t tell anyone, will you?’ she said.
He turned to her, face pale. ‘No one would believe me . . .’ he stammered.
‘Aye,’ said Tiffany. ‘So we understand one another. Isn’t that nice? And now, if you don’t mind, I’ve got to finish this and make a start on some cheese.’
‘Cheese? But you . . . you could do anything you wanted!’ Roland burst out.
‘And right now I want to make cheese,’ said Tiffany calmly. ‘Go away.’
‘My father owns this farm!’ said Roland, and then realized he’d said that out loud.
There were two little but strangely loud clicks as Tiffany put down the butter paddles and turned round.
‘That was a very brave thing you just said,’ she said, ‘but I expect you’re sorry you said it, now that you’ve had a really good think?’
Roland, who had shut his eyes, nodded his head.
‘Good,’ said Tiffany. Today I’m making cheese. Tomorrow I may do something else. And in a while, maybe, I won’t be here and you’ll wonder: Where is she? But part of me will always be here, always. I’ll always be thinking about this place. I’ll have it in my eye. And I will be back. Now, go away!’
He turned and ran.
After his footsteps had died away Tiffany said: ‘All right, who’s there?’
‘It’s me, mistress. No’-as-big-as-Medium-Sized-Jock-but-bigger-than-Wee-Jock-Jock, mistress.’ The pictsie appeared from behind the bucket, and added: ‘Rob Anybody said we should come tae keep an eye on ye for a wee while, and tae thank ye for the offerin’.’
It’s still magic even if you know how it’s done, Tiffany thought.
‘Only watch me in the dairy, then,’ she said. ‘No spying!’
‘Ach, no, mistress,’ said Not-as-big-as-Medium-Sized-Jock-but-bigger-than-Wee-Jock-Jock nervously. Then he grinned. ‘Fion’s goin’ off to be the kelda for a clan over near Copperhead Mountain,’ he said, ‘an’ she’s asked me to go along as the gonnagle!’
‘Congratulations!’
‘Aye, and William says I should be fine if I just work on the mousepipes,’ said the pictsie. ‘And . . . er . . .’
‘Yes?’ said Tiffany.
‘Er . . . Hamish says there’s a girl in the Long Lake clan who’s looking to become a kelda . . .. er . . . it’s a fine clan she’s from . . . er . . ..’ The pictsie was going violet with embarrassment.
‘Good,’ said Tiffany. ‘If I was Rob Anybody, I’d invite her over right away.’
‘You dinnae mind?’ said Not-as-big-as-Medium-Sized-Jock-but-bigger-than-Wee-Jock-Jock hopefully.
‘Not at all,’ said Tiffany. She did a little bit, she had to admit to herself, but it was a bit she could put away on a shelf in her head somewhere.
‘That’s grand!’ said the pictsie. The lads were a bit worried, ye ken. I’ll run up an’ tell them.’ He lowered his voice. ‘An’ would ye like me to run after that big heap o’ jobbies that just left and see that he falls off his horse again?’
‘No!’ said Tiffany hurriedly. ‘No. Don’t. No.’ She picked up the butter paddles. ‘You leave him to me,’ she added, smiling. ‘You can leave everything to me.’
When she was alone again she finished the butter . . . patapatapat. . .
She paused, put the paddles down, and with the tip of a very clean finger, drew a curved line in the surface, with another curved line just touching it, so that together they looked like a wave. She traced a third, flat curve under it, which was the Chalk.
Land Under Wave.
She quickly smoothed the butter again and picked up the stamp she’d made yesterday; she’d carved it carefully out of a piece of apple wood that Mr Block the carpenter had given her.
She stamped it onto the butter, and took it off carefully.
There, glistening on the oily, rich yellow surface, was a gibbous moon and, sailing in front of the moon, a witch on a broomstick.
She smiled again, and it was Granny Aching’s smile. Things would be different one day.
But you had to start small, like oak trees.
Then she made cheese . . .
. . . in the dairy, on the farm, and the fields unrolling, and becoming the downlands sleeping under the hot midsummer sun, where the flocks of sheep, moving slowly, drift over the short turf like clouds on a green sky, and here and there sheepdogs speed over the grass like shooting stars. For ever and ever, wold without end.
 

Author’s Note

The painting that Tiffany ‘enters’ in this book really exists. It’s called The Fairy Fellers’ Master-Stroke, by Richard Dadd, and is in the Tate Gallery in London. It is only about 21 inches by 15 inches. It took the artist nine years to complete, in the middle of the nineteenth century. I cannot think of a more famous ‘fairy’ painting. It is, indeed, very strange. Summer heat leaks out of it.
What people ‘know’ about Richard Dadd is that ‘he went mad, killed his father, was locked up in a lunatic asylum for the rest of his life and painted a weird picture’. Crudely, that’s all true, but it’s a dreadful summary of the life of a skilled and talented artist who developed a serious mental illness.
A Nac Mac Feegle does not appear anywhere in the painting, but I suppose it’s always possible that one was removed for making an obscene gesture. It’s the sort of thing they’d do.
Oh, and the tradition of burying a shepherd with a piece of raw wool in the coffin was true, too. Even gods understand that a shepherd can’t neglect the sheep. A god who didn’t understand would not be worth believing in.
There is no such word as ‘noonlight’, but it would be nice if there was.

Once  upon a time, there was Discworld. There still is an adequate supply.
Discworld is the flat world, carried through space on the back of a giant turtle, which has been the source of, so far, twenty-three novels, four maps, an encylopaedia, two animated series, t-shirts, scarves, models, badges, beer, embroidery, pens, posters, and prob¬ably, by the time this is published, talcum power and body splash (if not, it can only be a matter of time).
It has, in short, become immensely popular.
And Discworld runs on magic.
Roundworld, our home planet, and by extension the universe in which it sits, runs on rules. In fact, it simply runs. But we have watched the running, and those observations and the ensuing deductions are the very basis of science.
Magicians and scientists are, on the face of it, poles apart. Certainly, a group of people who often dress strangely, live in a world of their own, speak a specialized language and frequently make statements that appear to be in flagrant breach of common sense have nothing in common with a group of people who often dress strangely, speak a specialized language, live in ... er ...
Perhaps we should try this another way. Is there a connection between magic and science? Can the magic of Discworld, with its eccentric wizards, down-to-Earth witches, obstinate trolls, fire-breathing dragons, talking dogs, and personified DEATH, shed any useful light on hard, rational, solid, Earthly science?
We think so.
We'll explain why in a moment, but first, let's make it clear what The Science of Discworld is not. There are several media tie-in The Science of... books at the moment, such as The Science of the X-Files and The Physics of Star Trek. They will tell you about areas of today's science that may one day lead to the events or devices that the fiction depicts. Did aliens crash-land at Roswell? Could an anti¬matter warp drive ever be invented? Could we ever have the ultra long-life batteries that Scully and Mulder must be using in those torches of theirs?
We could have taken that approach. We could, for example, have pointed out that Darwin's theory of evolution explains how lower lifeforms can evolve into higher ones, which in turn makes it entirely reasonable that a human should evolve into an orangutan (while remaining a librarian, since there is no higher life form than a librarian). We could have speculated on which DNA sequence might reliably incorporate asbestos linings into the insides of drag¬ons. We might even have attempted to explain how you could get a turtle ten thousand miles long.
We decided not to do these things, for a good reason ... um, two reasons.
The first is that it would be ... er ... dumb.
And this because of the second reason. Discworld does not run on scientific lines. Why pretend that it might? Dragons don't breathe fire because they've got asbestos lungs, they breathe fire because everyone knows that's what dragons do.
What runs Discworld is deeper than mere magic and more pow¬erful than pallid science. It is narrative imperative, the power of story. It plays a role similar to that substance known as phlogiston, once believed to be that principle or substance within inflammable things that enabled them to burn. In the Discworld universe, then, there is narrativium. It is part of the spin of every atom, the drift of every cloud. It is what causes them to be what they are and continue to exist and take part in the ongoing story of the world.
On Roundworld, things happen because the things want to hap¬pen. What people want does not greatly figure in the scheme of things, and the universe isn't there to tell a story.
With magic, you can turn a frog into a prince. With science, you can turn a frog into a Ph.D and you still have the frog you started with.
That's the conventional view of Roundworld science. It misses a lot of what actually makes science tick. Science doesn't just exist in the abstract. You could grind the universe into its component par¬ticles without finding a single trace of Science. Science is a structure created and maintained by people. And people choose what interests them, and what they consider to be significant and, quite often, they have thought narratively.
Narrativium is powerful stuff. We have always had a drive to paint stories on to the Universe. When humans first looked at the stars, which are great flaming suns an unimaginable distance away, they saw in amongst them giant bulls, dragons, and local heroes.
This human trait doesn't affect what the rules say, not much, anyway, but it does determine which rules we are willing to con¬template in the first place. Moreover, the rules of the universe have to be able to produce everything that we humans observe, which introduces a kind of narrative imperative into science too. Humans think in stories. Classically, at least, science itself has been the dis¬covery of 'stories', think of all those books that had titles like The Story of Mankind, The Descent ofMan, and, if it comes to that, A Brief History of Time.
Over and above the stories of science, though, Discworld can play an even more important role: What if? We can use Discworld for thought experiments about what science might have looked like if the universe had been different, or if the history of science had followed a different route. We can look at science from the outside.
To a scientist, a thought experiment is an argument that you can run through in your head, after which you understand what's going on so well that there's no need to do a real experiment, which is of course a great saving in time and money and prevents you from get¬ting embarrassingly inconvenient results. Discworld takes a more practical view, there, a thought experiment is one that you can't do and which wouldn't work if you could. But the kind of thought experiment we have in mind is one that scientists carry out all the time, usually without realizing it; and you don't need to do it, because the whole point is that it wouldn't work. Many of the most important questions in science, and about our understanding of it, are not about how the universe actually is. They are about what would happen if the universe were different.
Someone asks 'why do zebras form herds?' You could answer this by an analysis of zebra sociology, psychology, and so on ... or you could ask a question of a very different kind: 'What would hap¬pen if they didn't?' One fairly obvious answer to that is 'They'd be much more likely to get eaten by lions.' This immediately suggests that zebras form herds for self-protection, and now we've got some insight into what zebras actually do by contemplating, for a moment, the possibility that they might have done something else.
Another, more serious example is the question 'Is the solar sys¬tem stable?', which means 'Could it change dramatically as a result of some tiny disturbance?' In 1887 King Oscar II of Sweden offered a prize of 2,500 crowns for the answer It took about a century for the world's mathematicians to come up with a definite answer: 'Maybe'. (It was a good answer, but they didn't get paid. The prize had already been awarded to someone who didn't get the answer and whose prizewinning article had a big mistake right at the most interesting part. But when he put it right, at his own expense, he invented Chaos Theory and paved the way for the 'maybe'. Sometimes, the best answer is a more interesting question.) The point here is that stability is not about what a system is actually doing: it is about how the system would change if you disturbed it. Stability, by definition, deals with 'what if?'.
Because a lot of science is really about this non-existent world of thought experiments, our understanding of science must concern itself with worlds of the imagination as well as with worlds of real¬ity. Imagination, rather than mere intelligence, is the truly human quality. And what better world of the imagination to start from than Discworld? Discworld is a consistent, well-developed universe with its own kinds of rules, and convincingly real people live on it despite the substantial differences between their universe's rules and ours. Many of them also have a thoroughgoing grounding in 'common sense', one of science's natural enemies.
Appearing regularly within the Discworld canon are the buildings and faculty of Unseen University, the Discworld's premier col¬lege of magic. The wizards are a lively bunch, always ready to open any door that has 'This door to be kept shut' written on it or pick up anything that has just started to fizz. It seemed to us that they could be useful ...
If we, or they, compare Discworld's magic to Roundworld sci¬ence, the more similarities and parallels we find. Clearly, as the wizards of Unseen University believe, this world is a parody of the Discworld one. And when we didn't discover those, we found that the differences were very revealing. Science takes on a new character when you stop asking questions like 'What does newt DNA look like?' and instead ask 'I wonder how the wizards would react to this way of thinking about newts?'
There is no science as such on Discworld. So we have put some there. By magical means, the wizards on Discworld must be led to create their own brand of science, some kind of pocket universe' in which magic no longer works, but rules do. Then, as the wizards learn to understand how the rules make interesting things happen -rocks, bacteria, civilizations, we watch them watching ... well, us. It's a sort of recursive thought experiment, or a Russian doll wherein the smaller dolls are opened up to find the largest doll inside.
And then we found that ... ah, but that is another story.
TP, IS, & JC, DECEMBER 1998

PS We have, we are afraid, mentioned in the ensuing pages Schrodinger's Cat, the Twins Paradox, and that bit about shining a torch ahead of a spaceship travelling at the speed of light. This is because, under the rules of the Guild of Science Writers, they have to be included. We have, however, tried to keep them short.
We've managed to be very, very brief about the Trousers of Time, as well.

ONE

SPLITTING THE THAUM

SOME QUESTIONS SHOULD NOT BE ASKED. However, someone always does.
'How does it work?' said Archchancellor Mustrum Ridcully, the Master of Unseen University.
This was the kind of question that Ponder Stibbons hated almost as much as 'How much will it cost?' They were two of the hardest questions a researcher ever had to face. As the university's de facto head of magical development, he especially tried to avoid questions of finance at all costs.
'In quite a complex way.' he ventured at last.
'Ah.'
'What I'd like to know,' said the Senior Wrangler, 'is when we're going to get the squash court back.'
'You never play, Senior Wrangler,' said Ridcully, looking up at the towering black construction that now occupied the centre of the old university court.
'I might want to one day. It'll be damn hard with that thing in the way, that's my point. We'll have to completely rewrite the rules.'
Outside, snow piled up against the high windows. This was turn¬ing out to be the longest winter in living memory, so long, in fact, that living memory itself was being shortened as some of the older citizens succumbed. The cold had penetrated even the thick and ancient walls of Unseen University itself, to the general concern and annoyance of the faculty. Wizards can put up with any amount of deprivation and discomfort, provided it is not happening to them.
And so, at long last, Ponder Stibbons's project had been author¬ized. He'd been waiting three years for it. His plea that splitting the thaum would push back the boundaries of human knowledge had fallen on deaf ears; the wizards considered that pushing back the boundaries of anything was akin to lifting up a very large, damp stone. His assertion that splitting the thaum might significantly increase the sum total of human happiness met with the rejoinder that everyone seemed pretty happy enough already.
Finally he'd ventured that splitting the thaum would produce vast amounts of raw magic that could very easily be converted into cheap heat. That worked. The Faculty were lukewarm on the sub¬ject of knowledge for knowledge's sake, but they were boiling hot on the subject of warm bedrooms.
Now the other senior wizards wandered around the suddenly-cramped court, prodding the new thing. Their Archchancellor took out his pipe and absent-mindedly knocked out the ashes on its matt black side.
'Um ... please don't do that, sir,' said Ponder.
'Why not?'
'There might be ... it might... there's a chance that...' Ponder stopped. 'It will make the place untidy, sir,' he said.
'Ah. Good point. So it's not that the whole thing might explode, then?'
'Er ... no, sir. Haha,' said Ponder miserably. 'It'd take a lot more than that, sir...’
There was a whack as a squash ball ricocheted off the wall, rebounded off the casing, and knocked the Archchancellor's pipe out of his mouth.
'That was you. Dean,' said Ridcully accusingly. 'Honestly, you fellows haven't taken any notice of this place in years and suddenly you all want to, Mr Stibbons? Mr Stibbons?'
He nudged the small mound that was the hunched figure of the University's chief research wizard. Ponder Stibbons uncurled slightly and peered between his fingers.
'I really think it might be a good idea if they stopped playing squash, sir,' he whispered.
'Me too. There's nothing worse than a sweaty wizard. Stop it, you fellows. And gather round. Mr Stibbons is going to do his pres¬entation.' The Archchancellor gave Ponder Stibbons a rather sharp look. 'It is going to be very informative and interesting, isn't it, Mister Stibbons. He's going to tell us what he spent AM$55,879.45p on.'
'And why he's ruined a perfectly good squash court,' said the Senior Wrangler, tapping the side of the thing with his squash racket.
'And if this is safe? said the Dean. 'I'magainst dabbling in physics,'
Ponder Stibbons winced.
'I assure you, Dean, that the chances of anyone being killed by the, er, reacting engine are even greater than the chance of being knocked down while crossing the street,' he said.
'Really? Oh, well ... all right then.'
Ponder reconsidered the impromptu sentence he'd just uttered and decided, in the circumstances, not to correct it. Talking to the senior wizards was like building a house of cards; if you got anything to stay upright, you just breathed out gently and moved on.
Ponder had invented a little system he'd called, in the privacy of his head, Lies-to-Wizards. It was for their own good, he told him¬self. There was no point in telling your bosses everything; they were busy men, they didn't want explanations. There was no point in bur¬dening them. What they wanted was little stories that they felt they could understand, and then they'd go away and stop worrying.
He'd got his students to set up a small display at the far end of the squash court. Beside it, with pipes looping away through the wall into the High Energy Magic building next door, was a termi¬nal to HEX, the University's thinking engine. And beside that was a plinth on which was a very large red lever, around which someone had tied a pink ribbon.
Ponder looked at his notes, and then surveyed the faculty.
'Ahem ...' he began.
'I've got a throat sweet somewhere,' said the Senior Wrangler, patting his pockets.
Ponder looked at his notes again, and a horrible sense of hope¬lessness overcame him. He realized that he could explain thaumic fission very well, provided that the person listening already knew all about it. With the senior wizards, though, he'd need to explain the meaning of every word. In some cases this would mean words like 'the' and 'and'.
He glanced down at the water jug on his lectern, and decided to extemporize.
Ponder held up a glass of water.
'Do you realize, gentlemen,' he said, 'that the thaumic potential in this water ... that is, I mean to say, the magical field generated by its narrativium content which tells it that it is water and lets it keep on being water instead of, haha, a pigeon or a frog ... would, if we could release it, be enough to move this whole university all the way to the moon?'
He beamed at them.
'Better leave it in there, then,' said the Chair of Indefinite Studies.
Ponder's smile froze.
'Obviously we cannot extract all of it,' he said, 'But we...’
'Enough to get a small part of the university to the moon?' said the Lecturer in Recent Runes.
'The Dean could do with a holiday,' said the Archchancellor.
'I resent that remark, Archchancellor'
'Just trying to lighten the mood, Dean.'
'But we can release just enough for all kinds of useful work,' said Ponder, already struggling.
'Like heating my study,' said the Lecturer in Recent Runes. 'My water jug was iced up again this morning.'
'Exactly!' said Ponder, striking out madly for a useful Lie-to-Wizards. 'We can use it to boil a great big kettle! That's all it is! It's perfectly harmless! Not dangerous in any way! That's why the University Council let me build it! You wouldn't have let me build it if it was dangerous, would you?'
He gulped down the water.
As one man, the assembled wizards took several steps back¬wards.
'Let us know what it's like up there,' said the Dean.
'Bring us back some rocks. Or something,' said the Lecturer in Recent Runes.
'Wave to us', said the Senior Wrangler. 'We've got quite a good telescope.'
Ponder stared at the empty glass, and readjusted his mental sights once more.
'Er, no,' he said. 'The fuel has to go inside the reacting engine, you see. And then ... and then ...'
He gave up.
'The magic goes round and round and it comes up under the boiler that we have plumbed in and the university will then be lovely and warm,' he said. 'Any questions?'
'Where does the coal go?' said the Dean, 'It's wicked what the dwarfs are charging these days.'
'No, sir. No coal. The heat is ... free,' said Ponder. A little bead of sweat ran down his face.
'Really?' said the Dean. 'That'll be a saving, then, eh, Bursar? Eh? Where's the Bursar?'
'Ah ... er ... the Bursar is assisting me today, sir,' said Ponder. He pointed to the high gallery over the court. The Bursar was standing there, smiling his distant smile, and holding an axe. A rope was tied around the handrail, looped over a beam, and held a long heavy rod suspended over the centre of the reaction engine.
'It is ... er ... just possible that the engine may produce too much magic,' said Ponder. 'The rod is lead, laminated with rowan wood. Together they naturally damp down any magical reaction, you see. So if things get too ... if we want to settle things down, you see, he just chops through the rope and it drops into the very centre of the reacting engine, you see.'
'What's that man standing next to him for?'
'That's Mr Turnipseed, my assistant. He's the backup fail-safe device.'
'What does he do, then?'
'His job is to shout "For gods' sakes cut the rope now!" sir.'
The wizard nodded at one another. By the standards of Ankh-Morpork, where the common thumb was used as a temperature measuring device, this was health and safety at work taken to extremes.
'Well, that all seems safe enough to me,' said the Senior Wrangler.
'Where did you get the idea for this, Mister Stibbons?' said Ridcully.
'Well, er, a lot of it is from my own research, but I got quite a few leads from a careful reading of the Scrolls of Loko in the Library, sir.' Ponder reckoned he was safe enough there. The wizards liked ancient wisdom, provided it was ancient enough. They felt wisdom was like wine, and got better the longer it was left alone. Something that hadn't been known for a few hundred years probably wasn't worth knowing.
'Loko ... Loko ... Loko,' mused Ridcully. 'That's up on Uberwald, isn't it?'
That's right, sir.'
'Tryin' to bring it to mind,' Ridcully went on, rubbing his beard. 'Isn't that where there's that big deep valley with the ring of moun¬tains round it? Very deep valley indeed, as I recall.'
'That's right, sir. According to the library catalogue the scrolls were found in a cave by the Crustley Expedition...’
'Lots of centaurs and fauns and other curiously shaped magical whatnots are there, I remember reading.'
'Is there, sir?'
'Wasn't Stanmer Crustley the one who died of planets?'
'I'm not familiar with...’
'Extremely rare magical disease, I believe.'
'Indeed, sir, but…’
'Now I come to think about it, everyone on that expedition con¬tracted something seriously magical within a few months of getting back,' Ridcully went on.
'Er, yes, sir. The suggestion was that there was some kind of curse on the place. Ridiculous notion, of course.'
'I somehow feel I need to ask, Mister Stibbons ... what chance is there of this just blowin' up and destroyin' the entire university?'
Ponder's heart sank. He mentally scanned the sentence, and took refuge in truth. 'None, sir.'
'Now try honesty, Mister Stibbons.' And that was the problem with the Archchancellor. He mostly strode around the place shout¬ing at people, but when he did bother to get all his brain cells lined up he could point them straight at the nearest weak spot.
'Well ... in the unlikely event of it going seriously wrong, it ... wouldn't just blow up the university, sir'
'What would it blow up, pray?'
'Er ... everything, sir.'
'Everything there is, you mean?'
'Within a radius of about fifty thousand miles out into space, sir, yes. According to HEX it'd happen instantaneously. We wouldn't even know about it.'
'And the odds of this are ... ?'
'About fifty to one, sir.'
The wizards relaxed.
'That's pretty safe. I wouldn't bet on a horse at those odds,' said the Senior Wrangler. There was half an inch of ice on the inside of his bedroom windows. Things like this give you a very personal view of risk.

TWO

SQUASH COURT SCIENCE

A SQUASH COURT CAN BE USED to make things go much faster than a small rubber ball ...
On 2 December 1942, in a squash court in the basement of Stagg Field at the University of Chicago, a new technological era came into being. It was a technology born of war, yet one of its consequences was to make war so terrible in prospect that, slowly and hesitantly, war on a global scale became less and less likely. At Stagg Field, the Roman-born physicist Enrico Fermi and his team of scientists achieved the world's first self-sustaining nuclear chain reaction. From it came the atomic bomb, and later, civilian nuclear power. But there was a far more significant consequence: the dawn of Big Science and a new style of technological change.
Nobody played squash in the basement of Stagg Field, not while the reactor was in place, but a lot of the people working in the squash court had the same attitudes as Ponder Stibbons ... mostly insatiable curiosity, coupled with periods of nagging doubt tinged with a flicker of terror. It was curiosity that started it all and terror that concluded it.
In 1934, following a lengthy series of discoveries in physics related to the phenomenon of radioactivity, Fermi discovered that interesting things happen when substances are bombarded with 'slow neutrons', subatomic particles emitted by radioactive beryl¬lium, and passed through paraffin to slow them down. Slow neutrons, Fermi discovered, were just what you needed to persuade other elements to emit their own radioactive particles. That looked interesting, so he squirted streams of slow neutrons at everything he could think of, and eventually he tried the then obscure element uranium, up until then mostly used as a source of yellow pigment. By something apparently like alchemy, the uranium turned into something new when the slow neutrons cannoned into it, but Fermi couldn't work out what.
Four years later three Germans, Otto Hahn, Lise Meitner, and Fritz Strassmann, repeated Fermi's experiments, and being better chemists, they worked out what had happened to the uranium. Mysteriously, it had turned into barium, krypton, and a small quan¬tity of other stuff. Meitner realized that this process of 'nuclear fission' produced energy, by a remarkable method. Everyone knew that chemistry could turn matter into other kinds of matter, but now some of the matter in uranium was being transformed into energy, something that nobody had seen before. It so happened that Albert Einstein had already predicted this possibility on theoretical grounds, with his famous formula, an equation which the orang¬utan Librarian of Unseen University would render as 'Ook'. Einstein's formula tells us that the amount of energy 'contained' in a given amount of matter is equal to the mass of that matter, multi¬plied by the speed of light and then multiplied by the speed of light again. As Einstein had immediately noticed, light is so fast it does¬n't even appear to move, so its speed is decidedly big ... and the speed multiplied by itself is huge. In other words: you can get an awful lot of energy from a tiny bit of matter, if only you can find a way to do it. Now Meitner had worked out the trick.
A single equation may or may not halve your book sales, but it can change the world completely.
Hahn, Meitner and Strassmann published their discovery in the British scientific journal Nature in January 1939. Nine months later Britain was at war, a war which would be ended by a military appli¬cation of their discovery. It is ironic that the greatest scientific secret of World War II was given away just before the war began, and it shows how unaware politicians then were of the potential -be it for good or bad, of Big Science. Fermi saw the implications of the Nature article immediately, and he called in another top-ranking physicist, Niels Bohr, who came up with a novel twist: the chain reaction. If a particular, rare form of uranium, called ura-nium-235, was bombarded with slow neutrons, then not only would it split into other elements and release energy, it would also release more neutrons. Which, in turn, would bombard more uranium-235 ... The reaction would become self-sustaining, and the potential release of energy would be gigantic.
Would it work? Could you get 'something for nothing' in this way? Finding out was never going to be easy, because uranium-235 is mixed up with ordinary uranium (uranium-238), and getting it out is like looking for a needle in a haystack when the needle is made of straw.
There were other worries too ... in particular, might the experi¬ment be too successful, setting off a chain reaction that not only spread through the experiment's supply of uranium-235, but through everything else on Earth as well? Might the atmosphere catch fire? Calculations suggested: probably not. Besides, the big worry was that if the Allies didn't get nuclear fission working soon then the Germans would beat them to it. Given the choice between our blowing up the world and the enemy blowing up the world, it was obvious what to do.
That is, on reflection, not a happy sentence.

Loko is remarkably similar to Oklo in southeastern Gabon, where there are deposits of uranium. In the 1970s, French scientists unearthed evidence that some of that uranium had either been undergoing unusually intense nuclear reactions or was much, much older than the rest of the pknet.
It could have been an archaeological relic of some ancient civilization whose technology had got as far as atomic power, but a duller if more plausible expanation is that Oklo was a 'natural reac¬tor'. For some accidental reason, that particular patch of uranium was richer than usual in uranium-235, and a spontaneous chain reaction ran for hundreds of thousands of years. Nature got there well ahead of Science, and without the squash court.
Unless, of course, it was an archaeological relic of some ancient civilization.
Until late in 1998, the natural reactor at Oklo was also the best evidence we could find to show that one of the biggest 'what if?' questions in science had an uninteresting answer. This question was 'What if the natural constants aren't?
Our scientific theories are underpinned by a variety of numbers, the 'fundamental constants'. Examples include the speed of light, Planck's constant (basic to quantum mechanics), the gravitational constant (basic to gravitational theory), the charge on an electron, and so on. AD of the accepted theories assume that these numbers have always been the same, right from the very first moment when the universe burst into being. Our calculations about that early uni¬verse rely on those numbers having been the same; if they used to be different, we don't know what numbers to put into the calcula¬tions. It's like trying to do your income tax when nobody will tell you the tax rates. From time to time maverick scientists advance the odd 'what if?' theory, in which they try out the possibility that one or more of the fundamental constants isn't. The physicist Lee Smolin has even come up with a theory of evolving universes, which bud off baby universes with different fundamental constants. According to this theory, our own universe is particularly good at producing such babies, and is also particularly suited to the devel¬opment of life. The conjunction of these two features, he argues, is not accidental (the wizards at UU, incidentally, would be quite at home with ideas like this, in fact, sufficiently advanced physics is indistinguishable from magic).
Oklo tells us that the fundamental constants have not changed during the last two billion years, about half the age of the Earth and ten per cent of that of the universe. The key to the argument is a particular combination of fundamental constants, known as the 'fine structure constant'. Its value is very close to 1/137 (and a lot of ink was devoted to explanations of that whole number 137, at least until more accurate measurements put its value at 137.036). The advantage of the fine structure constant is that its value does not depend on the chosen units of measurement, unlike say, the speed of light, which gives a different number if you express it in miles per second or kilometres per second. The Russian physicist Alexander Shlyakhter analysed the different chemicals in the Oklo reactor's 'nuclear waste', and worked out what the value of the fine structure constant must have been two billion years ago when the reactor was running. The result was the same as today's value to within a few parts in ten million.
In late 1998, though, a team of astronomers led by John Webb made a very accurate study of the light emitted by extremely distant, but very bright, bodies called quasars. They found subtle changes in certain features of that light, called spectral lines, which are related to the vibrations of various types of atom. In effect, what they seem to have discovered is that many billion years ago, much further back than the Oklo reactor, atoms didn't vibrate at quite the same rate as they do today. In very old gas clouds from the early universe, the fine structure constant differs from today's value by one part in 50,000. That's a huge amount by the standards of this particular area of physics. As far as anyone can tell, this unexpected result is not due to experimental error. A theory suggested in 1994 by Thibault Damour and Alexander Polyakov does indicate a possible variation in the fine structure constant, but only one-ten thousandth as large as that found by Webb's team. It's all a bit of a puzzle, and most theorists sensibly prefer to hedge their bets and wait for further research. But it could be a straw in the wind: perhaps we will soon have to accept that the laws of physics were subtly different in the distant reaches of time and space. Not turtle-shaped, perhaps, but... different.

THREE

I KNOW MY WIZARDS

IT DID NOT TAKE LONG for the faculty to put its col¬lective finger on the philosophical nub of the problem, vis-a-vis the complete destruction of everything.
'If no one will know if it happens, then in a very real sense it wouldn't have happened,' said the Lecturer in Recent Runes. His bedroom was on one of the colder sides of the university.
'Certainly we wouldn't get the blame,' said the Dean, 'even if it did.'
'As a matter of fact,' Ponder went on, emboldened by the wiz¬ards' relaxed approach, 'there is some theoretical evidence to suggest that it could not possibly happen, due to the non-temporal nature of the thaumic component.'
'Say again?' said Ridcully.
'A malfunction would not result in an explosion exactly, sir,' said Ponder. 'Nor, as far as I can work out, would it result in things ceas¬ing to exist from the present onwards. They would cease to have existed at all, because of the multidirectional collapse of the thau¬mic field. But since we are here, sir, we must be living in a universe where things did not go wrong.'
'Ah, I know this one,' said Ridcully. 'This is because of quantum, isn't it? And there's some usses in some universe next door where it did go wrong, and the poor devils got blown up?'
'Yes, sir Or, rather, no. They didn't get blown up because the device the other Ponder Stibbons would have built would have gone wrong, and so ... he didn't exist not to build it. That's the theory, anyway.'
'I'm glad that's sorted out, then,' said the Senior Wrangler briskly. 'We're here because we're here. And since we're here, we might as well be warm.'
'Then we seem to be in agreement,' said Ridcully. 'Mr Stibbons, you may start this infernal engine.' He nodded towards the red lever on the plinth.
'I was rather assuming you would do the honours, Archchancellor,' said Ponder, bowing. 'All you need to do is pull the lever. That will, ahem, release the interlock, allowing the flux to enter the exchanger, where a simple octiron reaction will turn the magic into heat and warm up the water in the boiler.'
'So it really is just a big kettle?' said the Dean.
'In a manner of speaking, yes,' said Ponder, trying to keep his face straight.
Ridcully grasped the lever.
'Perhaps you would care to say a few words, sir?' said Ponder.
'Yes.' Ridcully looked thoughtful for a moment, and then bright¬ened up. 'Let's get this over quickly, and have lunch.'
There was a smattering of applause. He pulled the lever. The hand on a dial on the wall moved off zero.
'Well, we're not blown up after all,' said the Senior Wrangler. 'What are the numbers on the wall for, Stibbons?'
'Oh, er ... they're ... they're to tell you what number it's got to,' said Ponder.
'Oh. I see.' The Senior Wrangler grasped the lapels of his robe. 'Duck with green peas today, gentlemen, I believe,' he said, in a far more interested tone of voice. 'Well done, Mr Stibbons.'
The wizards ambled off in the apparently slow yet deceptively fast way of wizards heading towards food.
Ponder breathed a sigh of relief, which turned into a gulp when he realized that the Archchancellor had not, in fact, left but was inspecting the engine quite closely.
'Er ... is there anything else I can tell you, sir?' he said, hurriedly.
'When did you really start it, Mister Stibbons?'
'Sir?'
'Every single word in the sentence was quite short and easy to understand. Was there something wrong about the way I assembled them?'
'I ... we ... it was started just after breakfast, sir,' said Ponder meekly. 'The needle on the dial was just turned by Mr Turnipseed by means of a string, sir'
'Did it blow up at all when you started it up?'
'No sir! You'd ... well, you'd have known, sir!'
'I thought you said back there that we wouldn't have known, Stibbons.'
'Well, no, I mean...’
'I know you, Stibbons,' said Ridcully. 'And you would never test something out publicly before trying it to see if it worked. No one wants egg all over their face, do they?'
Ponder reflected that egg on the face is only of minor concern when the face is part of a cloud of particles expanding outwards at an appreciable fraction of the speed of dark.
Ridcully slammed his hand against the black panels of the engine, causing Ponder visibly to leave the ground.
'Warm already,' he said. 'You all right up there, Bursar?'
The Bursar nodded happily.
'Good man. Well done, Mister Stibbons. Let's have lunch.'
After a while, when the footsteps had died away, it dawned on the Bursar that he was, as it were, holding the short end of the string.
The Bursar was not, as many thought, insane. On the contrary, he was a man with both feet firmly on the ground, the only diffi¬culty being that the ground in question was on some other planet, the one with the fluffy pink clouds and the happy little bunnies. He did not mind because he much preferred it to the real one, where people shouted too much, and he spent as little time there as possi¬ble. Unfortunately this had to include mealtimes. The meal service on Planet Nice was unreliable.
Smiling his faint little smile, he put down his axe and ambled off. After all, he reasoned, the point was that the wretched thing stayed out of the ... whatever it was, and it could certainly do a simple job like that without his watching it.
Unfortunately Mr Stibbons was too worried to be very obser¬vant, and none of the other wizards bothered much about the fact that everything which stood between them and thaumic devastation was blowing bubbles into his glass of milk.

FOUR

SCIENCE AND MAGIC

IF WE WANTED TO, we could comment on several fea¬tures of Ponder Stibbons's experiment, describing the associated science. For example, there is a hint of the 'many worlds' interpretation of quantum mechanics, in which billions of universes branch off from ours every time a decision might go more than one way. And there is the unofficial standard procedure of public opening cere-monies, in which A Royal Personage or The President pulls a big lever or pushes a big button to 'start' some vast monument to tech¬nology, which has been running for days behind the scenes. When Queeh Elizabeth II opened Calder Hall, the first British nuclear power station, this is just what went on, big meter and all.
However, it's a bit early for Quantum, and most of us have for¬gotten Calder Hall completely. In any case there's a more urgent matter to dispose of. This is the relation between science and magic. Let's start with science.

Human interest in the nature of the universe, and our place within it, goes back a long, long way. Early humanoids living on the African savannahs, for instance, can hardly have failed to notice that at night the sky was full of bright spots of light. At what stage in their evolution they first began to wonder what those lights were is a mystery, but by the time they had evolved enough intelligence to poke sticks into edible animals and to use fire, it is unlikely that they could stare at the night sky without wondering what the devil it was for (and, given humanity's traditional obsessions, whether it involved sex in some way). The Moon was certainly impressive, it was big, bright, and changed shape.
Creatures lower on the evolutionary ladder were certainly aware of the Moon. Take the turtle, for instance, about as Discwordly a beast as you can get. When today's turtles crawl up the beach to lay their eggs and bury them in the sand, they somehow choose their timing so that when the eggs hatch, the baby turtles can scramble towards the sea by aiming at the Moon. We know this because the lights of modern buildings confuse them. This behaviour is remark¬able, and it's not at all satisfactory to put it down to 'instinct' and pretend that's an answer. What is instinct? How does it work? How did it arise? A scientist wants plausible answers to such questions, not just an excuse to stop thinking about them. Presumably the baby turtles' moonseeking tendencies, and their mothers' uncanny sense of timing, evolved together. Turtles that just happened, by accident, to lay their eggs at just the right time for them to hatch when the Moon would be to seawards of their burial site, and whose babies just happened to head towards the bright lights, got more of the next generation back to sea than those that didn't. All that was needed to establish these tendencies as a universal feature of turtle-hood was some way to pass them on to the next generation, which is where genes come in. Those turtles that stumbled on a workable navigational strategy, and could pass that strategy on to their off¬spring by way of their genes, did better than the others. And so they prospered, and outcompeted the others, so that soon the only tur¬tles around were the ones that could navigate by the Moon.
Does Great A'Tuin, the turtle that holds up the elephants that hold up the Disc, swim through the depths of space in search of a distant light? Perhaps. According to The Light Fantastic, 'Philosophers have debated for years about where Great A'Tuin might be going, and have often said how worried they are that they might never find out. They're due to find out in about two months. And then they're really going to worry ...' For, like its earthbound counterpart, Great A'Tuin is in reproductive mode, in this case going to its own hatching ground to watch the emergence. That story ends with it swimming off into the cool depths of space, orbited by eight baby turtles (who appear to have gone off on their own, and perhaps even now support very small Discworlds) ...
The interesting thing about the terrestrial turtlish trickery is that at no stage is it necessary for the animals to be conscious that their timing is geared to the Moon's motion, or even that the Moon exists. However, the trick won't work unless the baby turtles notice the Moon, so we deduce that they did. But we can't deduce the existence of some turtle astronomer who wondered about the Moon's puzzling changes of shape.
When a particular bunch of social-climbing monkeys arrived on the scene, however, they began to ask such questions. The better the monkeys got at answering those questions, the more baffling the universe became; knowledge increases ignorance. The message they got was: Up There is very different from Down Here.
They didn't know that Down Here was a pretty good place for creatures like them to live. There was air to breathe, animals and plants to eat, water to drink, land to stand on, and caves to get out of the rain and the lions. They did know that it was changeable, chaotic, unpredictable ...
They didn't know that Up There, the rest of the universe, isn't like that. Most of it is empty space, a vacuum. You can't breathe vacuum. Most of what isn't vacuum is huge balls of overheated plasma. You can't stand on a ball of flame. And most of what isn't vacuum and isn't burning is lifeless rock. You can't eat rock. They were going to learn this later on. What they did know was that Up There was, in human timescales, calm, ordered, regular. And pre¬dictable, too, you could set your stone circle by it.
All this gave rise to a general feeling that Up There was differ¬ent from Down Here for a reason. Down Here was clearly designed for us. Equally clearly, Up There wasn't. Therefore it must be designed for somebody else. And the new humanity was already spec¬ulating about some suitable tenants, and had been ever since they'd hidden in the caves from the thunder. The gods! They were Up There, looking Down! And they were clearly in charge, because humanity certainly wasn't. As a bonus, that explained all of the things Down Here that were a lot more complicated than anything visible Up There, like thunderstorms and earthquakes and bees. Those were under the control of the gods.
It was a neat package. It made us feel important. It certainly made the priests important. And since priests were the sort of peo¬ple who could have your tongue torn out or banish you into Lion Country for disagreeing with them, it rapidly became an enor¬mously popular theory, if only because those who had other ones either couldn't speak or were up a tree somewhere.
And yet ... every so often some lunatic with no sense of self-preservation was born who found the whole story unsatisfying, and risked the wrath of the priesthood to say so. Such folk were already around by the time of the Babylonians, whose civilization flourished between and around the Tigris and Euphrates rivers from 4000 BC to 300 BC. The Babylonians, a term that covers a whole slew of semi-independent peoples living in separate cities such as Babylon, Ur, Nippur, Uruk, Lagash, and so on, certainly worshipped the gods like everyone else. One of their stories about gods is the basis of the Biblical tale of Noah and his ark, for instance. But they also took a keen interest in what those lights in the sky did. They knew that the Moon was round, a sphere rather than a flat disc. They probably knew that the Earth was round, too, because it cast a rounded shadow on the Moon during lunar eclipses. They knew that the year was about 365 1/4 days long. They even knew about the 'pre¬cession of the equinoxes', a cyclic variation that completes one cycle every 26,000 years. They made these discoveries by keeping careful records of how the Moon and the planets moved across the sky. Babylonian astronomical records from 500 BC survive to this day.
From such beginnings, an alternative explanation of the universe came into being. It didn't involve gods, at least directly, so it didn't find much favour with the priestly class. Some of their descendants are still trying to stamp it out, even today. The traditional priest¬hoods (who then and now often included some very intelligent people) eventually worked out an accommodation with this godless way of thinking, but it's still not popular with postmodernists, creationists, tabloid astrologers and others who prefer the answers you can make up for yourself at home.
The current name for what has variously been called 'heresy' and 'natural philosophy' is, of course, 'science'.
Science has developed a very strange view of the universe. It thinks that the universe runs on rules. Rules that never get broken. Rules that leave little room for the whims of gods.
This emphasis on rules presents science with a daunting task. It has to explain how a lot of flaming gas and rocks Up There, obeying simple rules like 'big things attract small things, and while small things also attract big things they don't do it strongly enough so as you'd notice', can have any chance whatsoever of giving rise to Down Here. Down Here, rigid obedience to rules seems notably absent. One day you go out hunting and catch a dozen gazelles; next day a lion catches you. Down Here the most evident rule seems to be 'There are no rules', apart perhaps from the one that could be expressed scientifically as 'Excreta Occurs'. As the Harvard Law of Animal Behaviour puts it: 'Experimental animals, under carefully controlled laboratory conditions, do what they damned well please.' Not only animals: every golfer knows that something as simple as a hard, bouncy sphere with a pattern of tiny dots on it never does what it's supposed to do. And as for the weather ...

Science has now divided into two big areas: the life sciences, which tell us about living creatures, and the physical sciences, which tell us about everything else. Historically, 'divides' is definitely the word, the scientific styles of these two big divisions have about as much in common as chalk and cheese. Indeed, chalk is a rock and so clearly belongs to the geological sciences, whereas cheese, formed by bacterial action on the bodily fluids of cows, belongs to the biological sciences. Both divisions are definitely science, with the same emphasis on the role of experiments in testing theories, but their habitual thought patterns run along different lines.
At least, until now.
As the third millennium approaches, more and more aspects of science are straddling the disciplines. Chalk, for instance, is more than just a rock: it is the remains of shells and skeletons of millions of tiny ocean-living creatures. And making cheese relies on chem¬istry and sensor technology as much as it does on the biology of grass and cows.
The original reason for this major bifurcation in science was a strong perception that life and non-life are extremely different. Non-life is simple and follows mathematical rules; life is complex and follows no rules whatsoever. As we said, Down Here looks very different from Up There.
However, the more we pursue the implications of mathematical rules, the more flexible a rule-based universe begins to seem. Conversely, the more we understand biology, the more important its physical aspects become, because life isn't a special kind of mat¬ter, so it too must obey the rules of physics. What looked like a vast, unbridgeable gulf between the life sciences and the physical sci¬ences is shrinking so fast that it's turning out to be little more than a thin line scratched in the sand of the scientific desert.
If we are to step across that line, though, we need to revise the way we think. It's all too easy to fall back on old, and inappropri¬ate, habits. To illustrate the point, and to set up a running theme for this book, let's see what the engineering problems of getting to the Moon tell us about how living creatures work.
The main obstacle to getting a human being on to the Moon is not distance, but gravity. You could waIk to the Moon in about thirty years, given a path, air, and the usual appurtenances of the experi¬enced traveller, were it not for the fact that it's uphill most of the way. It takes energy to lift a person from the surface of the planet to the neutral point where the Moon's pull cancels out the Earth's. Physics provides a definite lower limit for the energy you must expend, it's the difference between the 'potential energy' of a mass placed at the neutral point and the potential energy of the same mass placed on the ground. The Law of Conservation of Energy says that you can't do the job with less energy, however clever you are.
You can't beat physics.
This is what makes space exploration so expensive. It takes a lot of fuel to lift one person into space by rocket, and to make matters worse, you need more fuel to lift the rocket ... and more fuel to lift the fuel... and ... At any rate, it seems that we're stuck at the bottom of the Earth's gravity well, and the ticket out has to cost a fortune.
Are we, though?
At various times, similar calculations have been applied to living creatures, with bizarre results. It has been 'proved' that kangaroos can't jump, bees can't fly, and birds can't get enough energy from their food to power their search for the food in the first place. It has even been 'proved' that life is impossible because living systems become more and more ordered, whereas physics implies that all systems become more and more disordered. The main message that biologists have derived from these exercises has been a deep scepti¬cism about the relevance of physics to biology, and a comfortable feeling of superiority, because life is clearly much more interesting than physics.
The correct message is very different: be careful what tacit assumptions you make when you do that kind of calculation. Take that kangaroo, for instance. You can work out how much energy a kangaroo uses when it makes a jump, count how many jumps it makes in a day, and deduce a lower limit on its daily energy require¬ments. During a jump, the kangaroo leaves the ground, rises, and drops back down again, so the calculation is just like that for a space rocket. Do the sums, and you find that the kangaroo's daily energy requirement is about ten times as big as anything it can get from its food. Conclusion: kangaroos can't jump. Since they can't jump, they can't find food, so they're all dead.
Strangely, Australia is positively teeming with kangaroos, who fortunately cannot do physics.
What's the mistake? The calculation models a kangaroo as if it were a sack of potatoes. Instead of a thousand kangaroo leaps per day (say), it works out the energy required to lift a sack of potatoes off the ground and drop it back down, 1000 times. But if you look at a slow-motion film of a kangaroo bounding across the Australian outback, it doesn't look like a sack of potatoes. A kangaroo bounces, lolloping along like a huge rubber spring. As its legs go up, its head and tail go down, storing energy in its muscles. Then, as the feet hit the ground, that energy is released to trigger the next leap. Because most of the energy is borrowed and paid back, the energy cost per leap is tiny.
Here's an association test for you. 'Sack of potatoes' is to 'kan¬garoo' as 'rocket' is to, what? One possible answer is a space elevator. In the October 1945 issue of Wireless World the science-fic¬tion writer Arthur C. Clarke invented the concept of a geostationary orbit, now the basis of virtually all communications satellites. At a particular height, about 22,000 miles (35,000 km) above the ground, a satellite will go round the Earth exactly in synchrony with the Earth's rotation. So from the ground it will look as though the satellite isn't moving. This is useful for communica¬tions: you can point your satellite dish in a fixed direction and always get coherent, intelligent signals or, failing that, MTV.
Nearly thirty years later Clarke popularized a concept with far greater potential for technological change. Put up a satellite in geo¬stationary orbit and drop a long cable down to the ground. It has to be an amazingly strong cable: we don't yet have the technology but 'carbon nanotubes' now being created in the laboratory come close. If you get the engineering right, you can build an elevator 22,000 miles high. The cost would be enormous, but you could then haul stuff into space just by pulling on the cable from above.
Ah, but you can't beat physics. The energy required would be exactly the same as if you used a rocket.
Of course. Just as the energy required to lift a kangaroo is exactly the same as that required to lift a sack of potatoes.
The trick is to find a way to borrow energy and pay it back. The point is that once the space elevator is in place, after a while there's just as much stuff coming down it as there is going up. Indeed, if you're mining the Moon or the asteroids for metals, there will soon be more stuff coming down than goes up. The materials going down provide the lifting energy for those going up. Unlike a rocket, which gets used up every time you fire it, a space elevator is self-sustaining.
Life is like a space elevator. What life self-sustains is not energy, but organization. Once you have a system that is so highly organ¬ized that it can reliably make copies of itself, that degree of organization is no longer 'expensive'. The initial investment may have been huge, as for a space elevator, but once the investment has been made, everything else is free.
If you want to understand biology, it is the physics of space ele¬vators that you need, not the physics of rockets.
How can Discworld's magic illuminate Roundworld's science? Just as the gulf between the physical and biological sciences is turning out to be far narrower than we used to think, so the gulf between science and magic is also becoming smaller The more advanced our technologies become, the less possible it is for the everyday user to have any idea of how they work. As a result, they look more and more like magic. As Clarke realized, this tendency is inevitable; Gregory Benford went further and declared it desirable.
Technology works because whoever built it in the first place fig¬ured out enough of the rules of the universe to make the technology do what was required of it. You don't need to get the rules right to do this, just right enough, space rockets work fine even though their orbits are computed using Newton's stab at the rules of grav¬ity, which aren't as accurate as Einstein's. But what you can accomplish is severely constrained by what the universe will per¬mit. With magic, in contrast, things work because people want them to. You still have to find the right spell, but what drives the development is human wishes (and, of course, the knowledge, skill and experience of the practitioner). This is one reason why science often seems inhuman, because it looks at how the universe drives us, rather than the other way round.
Magic, however, is only one aspect of Discworld. There's a lot of science on Discworld, too, or at least rational engineering. Balls get thrown and caught, the biology of the river Ankh resembles that of a typical terrestrial swamp or sewage farm, and light goes in more or less straight lines. Very slowly, though. As we read in The Light Fantastic: 'Another Disc day dawned, but very gradually, and this is why. When light encounters a strong magical field it loses all sense of urgency. It slows right down. And on the Discworld the magic was embarrassingly strong, which meant that the soft yellow light of dawn flowed over the sleeping landscape like the caress of a gentle lover or, as some, would have it, like golden syrup.' The same quote tells us that as well as rational engineering there's a lot of magic in Discworld: overt magic which slows light down; magic that allows the sun to orbit the world provided that occasionally one of the elephants lifts its leg to let the sun pass. The sun is small, nearby, and travels faster than its own light. This appears to cause no major problems.
There is magic in our world, too, but of a different, less obvious kind. It happens around everybody all the time, in all those little causalities which we don't understand but just accept. When we turn the switch and the light comes on. When we get into the car and start the engine. When we do all those improbable and ridicu¬lous things that, thanks to biological causality, make babies. Certainly many people understand, often to quite a detailed degree, what is going on in particular areas, but sooner or later we all reach our Magical Event Horizon. Clarke's Law states that any sufficiently advanced technology looks like magic. 'Advanced' here is usually taken to mean 'shown to us by advanced aliens or people from the future', like television shown to Neanderthals. But we should real¬ize that television is magic to nearly everyone that uses it now, to those behind the camera as well as to those sitting on the couch in front of the moving picture in the funny box. At some point in the process, in the words of cartoonist S. Harris, 'a miracle occurs'.
Science takes on the aura of magic because the design of a civi¬lization proceeds by a type of narrative imperative, it makes a coherent story. In about 1970, Jack gave a lecture to a school audi¬ence on 'The Possibility of Life on Other Planets'. He talked about evolution, what planets were made of, all the things that you'd expect in such a lecture. The first question was from a girl of about 15, who asked 'You believe in evolution, don't you, sir?' The teacher went on about it not being a 'proper' question, but Jack answered it anyway, saying, rather pretentiously, 'No, I don't believe in evolu¬tion, like people believe in God ... Science and technology are not advanced by people who believe, but by people who don't know but are doing their best to find out ... steam engine ... spinning jenny ... television ...'At that, she was on her feet again: 'No, that ain't how television was invented!' The teacher tried to calm the discus¬sion by asking her to explain how she thought television was invented. 'My father works for Fisher Ludlow making pressed steel for car bodies. He gets paid and he gives some of the money to the government to give him things. So he tells the government he wants to watch television, and they pay someone to invent television, and they do!'
It's very easy to make this mistake, because technology pro¬gresses by pursuing goals. We get the feeling that if we pour in enough resources, we can achieve anything. Not so. Pour in enough resources, and we can achieve anything that is within reach of cur¬rent know-how, or possibly just a bit beyond if we're lucky. But nobody tells us about the inventions that fail. Nobody tries to raise funding for a project that they know can't possibly work. No fund¬ing body will pay for research projects in which we have no idea where to start. We could pour as much money as we liked into developing antigravity or faster-than-light travel, and we'd get nowhere.
When you can take a machine to bits and see how it works, you get a clear feeling for the constraints within which it has to operate. In such cases, you're not going to confuse science and magic. The first cars required an extremely hands-on starting system, you stuck a big handle into the engine and literally 'turned it over'. Whatever the engine did when it started, you knew it wasn't magic. However, as technology develops it usually doesn't remain trans¬parent to the user. As more people began to use cars, more and more of the obvious technology was replaced by symbols. You worked switches with labels to get things to happen. That's our version of the magic spell: you pull a knob called Cold Start and the engine does all the cold start things for itself. When Granny wants to drive she does not have to do much more than push the accelerator for 'Go'. Little imps do the rest, by magic.
This process is the core of the relation between science and magic in our own world. The universe into which we were born, and in which our species evolved, runs by rules, and science is our way of trying to work out what the rules are. But the universe that we are now constructing for ourselves is one that, to anyone other than a member of the design team and very possibly even to them, works by magic.

A special kind of magic is one of the many things that have made humans what they are. It's called education. It's how we pass on ideas from one generation to the next. If we were like computers, we'd be able to copy our minds into our children, so that they would grow up agreeing with every opinion that we hold dear. Well, actu¬ally they wouldn't, though they might start out that way. There is an aspect of education that we want to draw to your attention. We call it 'lies-to-children'. We're aware that some readers may object to the word 'lie', it got Ianand Jack into terrible trouble with some literally-minded Swedes at a scientific conference who took it all terribly seriously and spent several days protesting that 'It's not a for It is. It is for the best possible reasons, but it is still a lie. A lie-to-children is a statement that is false, but which nevertheless leads the child's mind towards a more accurate explanation, one that the child will only be able to appreciate if it has been primed with the lie.
The early stages of education have to include a lot of lies-to-chil¬dren, because early explanations have to be simple. However, we live in a complex world, and lies-to-children must eventually be replaced by more complex stories if they are not to become delayed-action genuine lies. Unfortunately, what most of us know about science consists of vaguely remembered lies-to-children. For exam¬ple, the rainbow. We all remember being told at school that glass and water split light into its constituent colours, there's even a nice experiment where you can see them, and we were told that this is how rainbows form, from light passing through raindrops. When we were children, it never occurred to us that while this explains the colours of the rainbow it doesn't explain its shape. Neither does it explain how the light from the many different raindrops in a thundershower somehow combines to create a bright arc. Why doesn't it all smudge out? This is not the place to tell you about the elegant geometry of the rainbow, but you can see why 'lie' is not such a strong word after all. The school explanation diverts our attention from the real marvel of the rainbow, the cooperative effects of all the raindrops, by trying to pretend that once you've explained the colours, that's it.
Other examples of lies-to-children are the idea that the Earth's magnetic field is like a huge bar magnet with N and S marked on it, the picture of an atom as a miniature solar system, the idea that a living amoeba is a billion-year-old 'primitive' organism, the image of DNA as the blueprint for a living creature, and the connection between relativity and Einstein's hairstyle (it's the sort of crazy idea that only people with hair like that can come up with). Quantum mechanics lacks a public 'icon' of this kind, it doesn't tell a simple story that a non-specialist can grab and hang on to, so we feel uncomfortable about it.
When you live in a complex world, you have to simplify it in order to understand it. Indeed, that's what 'understand' means. At different stages of education, different levels of simplification are appropriate. Liar-to-children is an honourable and vital profession, otherwise known as 'teacher'. But what teaching does not do -although many politicians think it does, which is one of the prob¬lems, is erect a timeless edifice of 'facts'. Every so often, you have to unlearn what you thought you already knew, and replace it by something more subtle. This process is what science is all about, and it never stops. It means that you shouldn't take everything we say as gospel, either, for we belong to another, equally honourable profes¬sion: Liar-to-readers.
On Discworld, one of Ponder Stibbons's lies-to-wizards is about to come seriously unstuck.

FIVE

THE ROUNDWORLD PROJECT

ARCHCHANCELLOR RIDCULLY AWOKE FROM AN AFTERNOON NAP in which he had been crawling through a baking desert under a flamethrower sky, and found that this was more or less true.
Superheated steam whistled from the joints of the radiator in the corner. Ridcully walked over through the stifling air and touched it gently.
'Ouch! Damnation!'
Sucking his right hand and using his left hand to unwrap the scarf from his neck, he strode out into the corridor and what looked like Hell with the heat turned up. Steam rolled along the corridors, and from somewhere overhead came the once-heard-never-forgot-ten thwack of a high-energy magical discharge. Violet light filled the windows for a moment.
'Will someone tell me what the heck is going on?' Ridcully demanded of the air in general.
Something like an iceberg loomed out of the steam. It was the Dean.
'I would like to make it absolutely clear, Archchancellor, that this is nothing to do with me!'
Ridcully wiped away the sweat that was beginning to trickle down his forehead.
'Why are you standin' there in just your drawers, Dean?'
'I…well, my room is absolutely boiling hot...’
'I demand you put something on, man, you look thoroughly unhygienic!'
There was another crack of discharged magic. Sparks flew off the end of Ridcully's fingers.
'I felt that one!' he said, running back into his room.
Beyond the window, on the other side of the gardens, the air wavered over the High Energy Magic building. As the Archchancellor watched, the two huge bronze globes on its roof became covered in crawling, zig-zagging purple lines.
He hit the floor rolling, as wizards are wont to do, just before the shock of the discharge blew the windows in.

Melted snow was pouring off the rooftops. Every icicle was a streaming finger of water.
A large door bumped and scraped its way across the steaming lawns.
Tor goodness' sake, Dean, handle your end, can't you?'
The door skidded a little further.
'It's no good, Ridcully, it's solid oak!'
'And I'm very glad of it!'
Behind Ridcully and the Dean, who were inching the door for¬ward largely by arguing with each other, the rest of the faculty crept forward.
The bronze globes were humming now, in the rapidly decreas¬ing intervals between discharges. They had been installed, to general scoffing, as a crude method of releasing the occasional erratic build-up of disorganized magic in the building. Now they were outlined in unhealthy-looking light.
'And we know what that means, don't we, Mister Stibbons?' said Ridcully, as they reached the entrance to the High Energy Magic building.
'The fabric of reality being unravelled and leaving us prey to creatures from the Dungeon Dimensions, sir?' mumbled Stibbons, who was trailing behind.
'That's right, Mister Stibbons! And we don't want that, do we, Stibbons?'
'No, sir.'
'No, sir! We don't, sir!' Ridcully roared. 'It'll be tentacles all over the place again. And none of us wants tentacles all over the place, do we?'
'No, sir.'
'No, sir! So switch the damned thing offt sir!'
'But it'd be certain death to go into...’ Ponder stopped, swallowed and restarted. 'In fact it would be uncertain death to go into the squash court at the moment, Archchancellor. There must be million of thaums of random magic in there! Anything could happen!'
Inside the HEM the ceiling was vibrating. The whole building seemed to be dancing.
'They certainly knew how to build, didn't they, when they built the old squash court,' said the Lecturer in Recent Runes, in an admiring tone of voice. 'Of course, it was built to contain large amounts of magic ...'
'Even if we could switch it off, I don't think that'd be such a good idea,' said Ponder.
'Sounds a lot better than what's happening now,' said the Dean.
'But is falling through the air better than hitting the ground?' said Ponder.
Ridcully sucked in his breath between his teeth.
'That's a point,' he said. 'Could be something of an implosion, I suppose. You can't just stop something like this. Something bad would happen.'
'The end of the world?' quavered the Senior Wrangler.
'Probably just this part of it,' said Ponder.
'Are we talking here about a sort of huge valley about twenty miles across with mountains all round it?' said Ridcully, staring at the ceiling. Cracks were zig-zagging across it.
'Yes, sir, I'm wondering if whoever tried this at Loko actually did manage to switch it off ...'
The walls groaned. There was a rattling noise behind Ponder. He recognized it, even above the din. It was the sound of HEX reset¬ting its writing device. Ponder always thought of it as a kind of mechanical throat-clearing.
The pen jerked in its complex network of threads and springs, and then wrote:
+++ This May Be Time For The Roundworld Project +++
'What are you talking about, man?' snapped Ridcully, who'd never quite understood what HEX was.
'Oh, that? That's been around for ages,' said the Dean. 'No one's ever taken it seriously. It's just a thought experiment. You couldn't do it. It's completely absurd. It needs far too much magic.'
'Well, we've got far too much magic,' said Ridcully. 'Right now we need to use it up.'
There was a moment's silence. That is, the wizards were silent. Overhead, magic flared into the sky with a sound like roaring gas.
'Can't let it build up here,' Ridcully went on. 'What's the Roundworld project then?'
'It was, er ... there was once some suggestion that it might be possible to create a ... an area where the laws of magic don't apply,' said Ponder. 'We could use it to learn more about magic.'
'Magic's everywhere? said Ridcully. 'It's part of what everywhere is'
'Yes, sir,' said Ponder, watching the Archchancellor carefully.
The ceiling creaked.
'What use would it be, anyway?' said Ridcully, still thinking aloud.
'Well, sir, you could ask what use is a new-born child ...'
'No, that's not the sort of question I ask,' said Ridcully. 'And it's a highly suspicious one, too.'
The wizards ducked as the latest discharge crackled overhead. It was followed by a louder explosion.
'I think the balls have just exploded, sir,' said Ponder.
'All right, then, how long would the project take to set up?' said Ridcully.
'Months,' said the Dean firmly.
'We've got about ten seconds to the next discharge, sir,' said Ponder. 'Only ... now the balls have gone it will simply earth itself...'
'Ah. Oh. Really? Well, then ...' Ridcully looked around at his fel¬low wizards as the wall began to shake again. 'It's been nice knowing you. Some of you. One or two of you, anyway ...'
The whine of increasing magic rose in pitch.
The Dean cleared his throat.
'I'd just like to say, Mustrum,' he began.
'Yes, old friend?'
'I'd just like to say ... I think I'd have made a much better Archchancellor than you.'
The whine stopped. The silence twanged. The wizards held their breath.
Something went 'ping'.
A globe about a foot across hung in the air between the faculty. It looked like glass, or the sheen of a pearl without the pearl itself.
From the squash court next door there was, instead of the wild roar of disorganized thaums, the steady thrum-thrum of purpose.
'What the heck is that ?' said Ridcully, as the wizards unfolded themselves.
HEX rattled. Ponder picked up the piece of paper.
'Well, according to this, it's the Roundworld Project,' he said. 'And it's absorbing all the energy from the thaumic pile.'
The Dean brushed some dust off his robe.
'Nonsense,' he said. 'Takes months. Anyway, how could that machine possibly know the spells?'
'Mr Turnipseed did copy in a lot of the grimoires last year,' said Ponder. 'It's vital that HEX knows basic spell structure, you see .,.'
The Senior Wrangler peered irritably at the sphere.
'Is this all it is?' he said. 'Doesn't seem much for all that effort.'
There was a frightening moment as the Dean walked up to the sphere and his nose, enormously magnified, appeared in it.
'Old Archchancellor Bewdley devised it,' he said. 'Everyone said it was impossible ...'
'Mr Stibbons?' said Ridcully.
'Yes, sir?'
'Are we in danger of blowing up at the moment?'
'I don't think so, sir. The ... project is sucking up everything.'
'Shouldn't it be glowing, then? Or something? What's in there?'
HEX wrote: +++ Nothing +++
'All that magic's going into empty space?'
+++ Empty Space Is Not Nothing, Archchancellor. There Is Not Even Empty Space Inside The Project. There Is No Time For It To Be Empty In +++
'What's it got in it, then?'
+++ I Am Checking +++, HEX wrote patiently.
'Look, I can stick my hand right in it,' said the Dean.
The wizards watched in horror. The Dean's fingers were visible, darkly, within the sphere, outlined in thousands of tiny sparkling lights.
'That was a really very foolish thing you just did,' said Ridcully. 'How did you know it wasn't dangerous?'
'I didn't,' said the Dean cheerfully, 'It feels ... cool. And rather chilly. Prickly, in a funny sort of way'
HEX rattled. Ponder walked back and looked down at the paper. 'It almost feels sticky when I move my fingers,' said the Dean.
'Er ... Dean?' said Ponder, stepping back carefully. 'I think it would be a really good idea if you pulled your hand out very, very carefully and really very soon.'
'That's odd, it's beginning to tingle...’
'Right now, Dean! Right now!'
For once, the urgency in Ponder's voice got through the Dean's cosmic self-confidence. He turned to argue with Ponder Stibbons just a moment before a white spark appeared in the centre of the sphere and began to expand rapidly.
The sphere flickered.
'Anyone know what caused that?' said the Senior Wrangler, his face bathed in the growing light of the Project.
'I think,' said Ponder slowly, holding up HEX's write-out, 'it was Time and Space starting to happen.'
In HEX's careful writing, the words said: +++ In The Absence Of Duration And Dimension, There Must Be Potentiality. +++
And the wizards looked upon the universe that was growing within the little sphere and spake amongst themselves, saying, 'It's rather a small one, don't you think? Is it dinner time yet?'
Later on, the wizards wondered if the new universe might have been different if the Dean had waggled his fingers in a different way. Perhaps, within it, matter might have naturally formed itself into, say, garden furniture, or one giant nine-dimensional flower a trillion miles across. But Archchancellor Ridcully pointed out that this was not very useful thinking, because of the ancient principle of WYGIWYGAINGW.

SIX

BEGINNINGS AND BECOMINGS

POTENTIALITY IS THE KEY.
Our immediate task is to start from a lot of vacuum and a few rules, and convince you that they have enormous potentiality. Given enough time, they can lead to people, turtles, weather, the Internet, hold it. Where did all that vacuum come from? Either the universe has been around forever, or once there wasn't a universe and then there was. The second statement fits neatly with the human predilection for creation myths. It also appeals to today's scientists, possibly for the same reason. Lies-to-children run deep. Isn't vacuum just . . . empty space? What was there before we had space? How do you make space? Out of vacuum? Isn't that a vicious circle? If in the past we didn't have space, how can there have been a 'there' for whatever it was to exist in? And if there was¬n't anywhere for it to exist, how did it manage to make space? Maybe space was there all along . . . but why? And what about time ? Space is easy compared to time. Space is just ... somewhere to put matter. Matter is just ... stuff. But time, time flows, time passes, time makes sense in the past and the future but not in the instanta¬neous, frozen present. What makes time flow? Could the flow of time be stopped? What would happen if it did?
There are little questions, there are medium-sized questions, and there are big questions. After which there are even bigger ques¬tions, huge questions, and questions so vast that it is hard to imagine what kind of response would count as an answer.
You can usually recognize the little questions: they look immensely complicated. Things like 'What is the molecular struc¬ture of the left-handed isomer of glucose?' As the questions get bigger, they become deceptively simpler: 'Why is the sky blue?' The really big questions are so simple that it seems astonishing that science has absolutely no idea how to answer them: 'Why doesn't the universe run backwards instead?' or 'Why does red look like that?’
All this goes to show that it's a lot easier to ask a question than it is to answer it, and the more specialized your question is, the longer are the words that you must invent to state it. Moreover, the bigger a question is, the more people are interested in it. Hardly anybody cares about left-handed glucose, but nearly all of us wonder why red looks the way it does, and we vaguely wonder whether it looks the same to everybody else.
Out on the fringes of scientific thought are questions that are big enough to interest almost everybody, but small enough for there to be a chance of answering them reasonably accurately. They are ques¬tions like 'How did the universe begin?' and 'How will it end?' ('What happens in between?' is quite a different matter.) Let us acknowledge, right up front, that the current answers to such questions depend upon various questionable assumptions. Previous generations have been absolutely convinced that their scientific theories were well-nigh perfect, only for it to turn out that they had missed the point entirely. Why should it be any different for our generation? Beware of scientific fundamentalists who try to tell you everything is pretty much worked out, and only a few routine details are left to do. It is just when the majority of scientists believe such things that the next revolution in our world-view creeps into being, its feeble birth-squeaks all but drowned by the earsplitting roar of orthodoxy.
Let's take a look at the current view of how the universe began. One of the points we are going to make is that human beings have trouble with the concept of 'beginning'. And even more trouble, let it be said, with 'becoming'. Our minds evolved to carry out rather spe¬cific tasks like choosing a mate, killing bears with a sharp stick, and getting dinner without becoming it. We've been surprisingly good at adapting those modules to tasks for which they were never 'intended', that is, tasks for which they were not used during their evolution, there being no conscious 'intention', such as planning a route up the Matterhorn, carving images of sea-lions on polar bears' teeth, and calculating the combustion point of a complex hydrocarbon mole¬cule. Because of the way our mental modules evolved, we think of beginnings as being analogous to how a day begins, or how a hike across the desert begins; and we think of becomings in the same way that a polar bear's tooth becomes a carved amulet, or a live spider becomes dead when you squash it.
That is: beginnings start from somewhere (which is where what¬ever it is begins), and becomings turn Thing One into Thing Two by pushing it across a clearly defined boundary (the tooth was not carved, but now it is; the spider was not dead, but now it is). Unfortunately the universe doesn't work in such a simple-minded manner, so we have serious trouble thinking about how a universe can begin, or how an ovum and a sperm can become a living child.
Let us leave becomings for a moment, and think about begin¬nings. Thanks to our evolutionary prejudices, we tend to think of the beginning of the universe as being some special time, before which the universe did not exist and after which it did. Moreover, when the universe changed from not being there to being there, something must have caused that change, something that was around before the universe began, otherwise it wouldn't have been able to cause the universe to come into being. When you bear in mind that the beginning of the universe is also the beginning of space and the beginning of time, however, this point of view is dis¬tinctly problematic. How can there be a 'before' if time has not yet started? How can there be a cause for the universe starting up, with¬out space for that cause to happen in, and time for it to happen?
Maybe there was something else in existence already ... but now we have to decide how that got started, and the same difficulties arise. All right, let's go the whole hog: something, perhaps the uni¬verse itself, perhaps some precursor, was around forever. It didn't have a beginning, it just was, always.
Satisfied? Things that exist forever don't have to be explained, because they don't need a cause? Then what caused them to have been around forever?
It now becomes impossible not to mention the turtle joke. According to Hindu legend, the Earth rides on the back of four elephants, which ride on a turtle. But what supports the turtle? In Discworld, Great A'Tuin needs no support, swimming through the universe unperturbed by any thought about what holds it up. That's magic in action: world-carrying turtles are like that. But according to the old lady who espoused the Hindu cosmology, and was asked the same question by a learned astronomer, there is a different answer: 'It's turtles all the way down!' The image of an infinite pile of turtles is instantly ludicrous, and very few people find it a satis¬fying explanation. Indeed very few people find it a satisfying kind of explanation, if only because it doesn't explain what supports the infinite pile of turtles. However, most of us are quite content to explain the origins of time as 'it's always been there'. Seldom do we examine this statement closely enough to realize that what it really says is 'It's time all the way back.' Now replace 'time' by 'turtle' and 'back' by 'down' ... Each instant of time is 'supported', that is, a causal consequence of, the previous instant of time. Fine, but that doesn't explain why time exists. What caused that infinite expanse of time? What holds up the whole pile?
All of which puts us in a serious quandary. We have problems thinking of time as beginning without a precursor, because it's hard to see how the causality goes. But we have equally nasty problems thinking of time as beginning with a precursor, because then we hit the turtle-pile problem. We have similar problems with space: either it goes on forever, in which case it's 'space all the way out' and we need somewhere even bigger to put the whole thing, or it stops, in which case we wonder what's outside it.
The real point is that neither of these options is satisfactory, and the origins of space and time fit neither model. The universe is not like a village, which ends at a fence or an imaginary line on the ground, neither is it like the distant desert which seems to vanish into eternity but actually just gets too far away for us to see it clearly. Time is not like a human lifespan, which starts at birth and ends at death, nor is it like the extended lifespan found in many religions, where the human soul continues to live indefinitely after death, and the much rarer belief (held, for example, by Mormons) that some aspect of each person was somehow already alive in the indefinite past.
So how did the universe begin? 'Begin' is the wrong word. Nonetheless, there is good evidence that the age of the universe is about 15 billion years, so nothing, not space, not time, existed before some instant of time roughly 15 billion years ago. See how our narrativium-powered semantics confuses us. This does not mean that if you went back 15 billion and one years, you would find nothing. It means that you cannot go back 15 billion and one years. That description makes no sense. It refers to a time before time began, which is logically incoherent, let alone physically so.
What cosmologists are pretty sure happened is this. The uni¬verse came into being as a tiny speck of space and time. The amount of space inside this tiny speck grew rapidly, and time began to elapse so that 'rapidly' actually had a meaning. Everything that there is, today, right out into the furthest depths of space, stems from that astonishing 'beginning'. Colloquially, the event is known as the Big Bang. The name reflects several features of the event -for example, that tiny speck of space/time was enormously hot, and grew in size exceedingly rapidly. It was like a huge explosion, but there was no stick of cosmic dynamite, sitting there in no-space with its non-material fuse burning away as some kind of pre-time pseudo-clock counted down the seconds to detonation. What exploded was, nothing. Space, time, and matter are the products of that explosion: they played no part in its cause. Indeed, in a very real sense, it had no cause.
The evidence in favour of the Big Bang is twofold. The first item is the discovery that the universe is expanding. The second is that 'echoes' from the Big Bang can still be detected today. The possi¬bility that the universe might be getting bigger first appeared in mathematical solutions to equations formulated by Albert Einstein. Einstein viewed spacetime as being 'curved'. A body moving through curved spacetime deviates from its normal straight line path, much as a marble rolling on a curved surface does. This devi¬ation can be interpreted as a 'force', something that pulls the body away from that ideal straight line. Actually there is no pull: just a bend in spacetime, causing a bend in the body's path. But it looks as if there's a pull. Indeed this apparent pull is what Newton called 'gravity', back in the days when people thought it really did pull bodies together. Anyway, Einstein wrote down some equations for how such a bendy universe ought to behave. They were very diffi¬cult equations to solve, but after making some extremely strong assumptions, basically that at any instant of time space is a sphere, mathematical physicists worked out few answers. And this tiny, very special list of solutions, the only ones their feeble methods could find, told them three things that the universe could do. It could stay the same size forever; it could collapse down to a single point; or it could start from a single point and grow in size without limit.
We now know that there are many other solutions to Einstein's equations, leading to all sorts of bizarre behaviour, but back in the days when today's paradigm was being set, these solutions were the only ones anybody knew. So they assumed that the universe must behave according to one or other of those three solutions. Science was subliminally prepared either for continuous creation (the uni¬verse is always the same) or for the Big Bang. The Big Crunch, in which the universe shrinks to an infinitely dense, infinitely hot point, lacked psychological appeal.
Enter Edwin Hubble, an American astronomer. Hubble was observing distant stars, and he made a curious discovery. The fur¬ther away the stars were, the faster they were moving. He knew this for distinctly indirect, but scientifically impeccable, reasons. Stars emit light, and light has many different colours, including 'colours' that the human eye is unable to see, colours like infra-red, ultra-vio¬let, radio, x-ray ... Light is an electromagnetic wave, and there is one 'colour' for each possible wavelength of light, the distance from one electromagnetic peak to the next. For red light, this distance is 2.8 hundred thousandths of an inch (0.7 millionths of a metre).
Hubble noticed that something funny was happening to the light emitted by stars: the colours were shifting in the red direction. The further away a star was, the bigger the shift. He interpreted this 'red shift' as a sign that the stars are moving away from us, because there is a similar shift for sound, known as the 'Doppler effect', and it's caused by the source of the sound moving. So the further away the stars are, the faster they're travelling. This means that the stars aren't just moving away from us, they're moving away from each other, like a flock of birds dispersing in all directions.
The universe, said Hubble, is expanding.
Not expanding into anything, of course. It's just that the space inside the universe is growing. That made the physicists' ears prick up, because it fitted exactly one of their three scenarios for changes in the size of the universe: stay the same, grow, collapse. They 'knew' it had to be one of the three, but which? Now they knew that, too. If we accept that the universe is growing we can work out where it came from by running time backwards, and this time-reversed universe collapses back to a single point. Putting time the right way round again, it must all have grown from a single point -the Big Bang. By estimating the rate of expansion of the universe we can work out that the Big Bang happened about 15 billion years ago.
There is further evidence in the Big Bang's favour: it left 'echoes'. The Big Bang produces vast amounts of radiation, which spreads through the universe. Because the universe is spherical, the radiation eventually comes back on itself like a round-the-world traveller. Over billions of years, the remnants of the Big Bang's radi¬ation smeared out into the 'cosmic background', a kind of low-level simmering of radiant energy across the sky, the light analogue of a reverberating echo of sound. It is as if God shouted 'Hello!' at the instant of creation and we can still hear a faint 'elloelloelloelloeiio ...' from the distant mountains. On Discworld this is exactly the case, and the Listening Monks in their remote temples spend their whole lives straining to pick out from the sounds of the universe the faint echoes of the Words that set it in motion.
According to the details of the Big Bang, the cosmic background radiation should have a 'temperature' (the analogue of loudness) of about 3° Kelvin (0° Kelvin is the coldest anything can get, equiv¬alent to about -273° Celsius). Astronomers can measure the temperature of the cosmic background radiation, and they do indeed get 3° Kelvin. The Big Bang isn't just a wild speculation. Not so long ago, most scientists didn't want to believe it, and they only changed their minds because of Hubble's evidence for the expansion of the universe, and that impressively accurate figure of 3° Kelvin for the temperature of the cosmic background radiation.
It was, indeed, a very loud, and hot, bang.

We are ambivalent, then, about beginnings, their 'creation myth' aspect appeals to our sense of narrative imperative, but we some¬times find the 'first it wasn't, then it was' lie-to-children unpalatable. We have even more trouble with becomings. Our minds attach labels to things in the surrounding world, and we interpret those labels as discontinuities. If things have different labels, then we expect there to be a clear line of demarcation between them. The universe, however, runs on processes rather than things, and a process starts as one thing and becomes another without ever crossing a clear boundary. Worse, if there is some apparent boundary, we are likely to point to it and shout 'that's it!' just because we can't see anything else worth getting agitated about. How many times have you been in a discussion in which some¬body says 'We have to decide where to draw the line'? For instance, most people seem to accept that in general terms women should be permitted abortions during the earliest stages of pregnancy but not during the very late stages. 'Where you draw the line', though, is hotly debated, and of course some people wish to draw it at one extreme or the other. There are similar debates about exactly when a developing embryo becomes a person, with legal and moral rights. Is it at conception? When the brain first forms? At birth? Or was it always a potential person, even when it 'existed' as one egg and one sperm?
The 'draw a line' philosophy offers a substantial political advan¬tage to people with hidden agendas. The method for getting what you want is first to draw the line somewhere that nobody would object to, and then gradually move it to where you really want it, arguing continuity all the way. For example, having agreed that killing a child is murder, the line labelled 'murder' is then slid back to the instant of conception; having agreed that people should be allowed to read whichever newspaper they like, you end up sup¬porting the right to put the recipe for nerve gas on the Internet.
If we were less obsessed with labels and discontinuity, it would be much easier to recognize that the problem here is not where to draw the line: it is that the image of drawing a line is inappropriate. There is no sharp line, only shades of grey that merge unnoticed into one another, despite which, one end is manifestly white and the other is equally clearly black. An embryo is not a person, but as it develops it gradually becomes one. There is no magic moment at which it switches from non-person to person, instead, it merges continuously from one into the other. Unfortunately our legal sys¬tem operates in rigid black-and-white terms, legal or illegal, no shades of grey, and this causes a mismatch, reinforced by our use of words as labels. A kind of triage might be better: this end of the spectrum is legal, that end of the spectrum is illegal, and in between is a grey area which we do our best to avoid if we possibly can. If we can't avoid it, we can at least adjust the degree of criminality and the appropriate penalty according to whereabouts in the spectrum the activity seems to lie.
Even such obviously black-and-white distinctions as alive/dead or male/female turn out, on close examination, to be more like a continuous merging than a sharp discontinuity. Pork sausages from the butcher's contain many live pig cells. With today's techniques you might even clone an adult pig from one. A person's brain can have ceased to function but their body, with medical assistance, can keep going. There are at least a dozen different combinations of sex chromosomes in humans, of which only XX represents the tradi¬tional female and XY the traditional male.
Although the Big Bang is a scientific story about a beginning, it also raises important questions about becomings. The Big Bang theory is a beautiful bit of science, very nearly consistent with the picture we now have of the atomic and the subatomic world, with its diverse kinds of atom, their protons and neutrons, their clouds of electrons, and the more exotic particles that we see when cosmic rays hit our atmosphere or when we insult the more familiar parti¬cles by slamming them together very hard. Now that physicists have 'found', or perhaps invented, the allegedly 'ultimate' constituents of these familiar particles (more exotic things known as quarks, glu-ons ... at least the names are familiar) they're starting to wonder whether there are more layers further down, more 'ultimate' still.
Turtles all the way down?
Does physics go all the way down, or does it stop at some level? If it stops, is that the Ultimate Secret, or just a point beyond which the physicists' way of thinking fails?
The conceptual problem here is difficult because the universe is a becoming, a process, and we want to think of it as a thing. We don't only find it puzzling that the universe was so different back then, that particles behaved differently, that the universe then became the universe now, and will perhaps eventually cease expand¬ing and collapse back to a point in a Big Crunch. We are familiar with babies becoming children becoming adults, but these processes always surprise us, we like things to keep the same char¬acter, so 'becoming' is difficult for our minds to handle.

There is another element of the first moments of our universe that is even more difficult to think about. Where did the Laws come from? Why are there such things as protons and electrons, quarks and gluons? We usually separate processes into two conceptually distinct causal chunks: the initial conditions, and the rules by which they are transformed as time passes. For the solar system, for instance, the initial conditions are the positions and speeds of the planets at some chosen instant of time; the rules are the laws of gravitation and motion, which tell us how those positions and speeds will change thereafter. But for the beginning of the universe, the initial conditions seem not to be there at all. Even there isn't there! So it seems that it's all done by rules. Where did the rules come from? Did they have to be invented? Or were they just sitting in some unimaginable timeless pseudo-existence, waiting to be called up? Or did they uncurl in the early moments of the universe, as Something appeared, so that the universe invented its own rules along with space and time?
During the becoming of its first moments, our universe kept changing its state, changing the rules it accessed. In this respect it was rather like a flame, which changes its composition according to its own dynamics and the things that it is burning. Flames are all more or less the same shape, but they don't inherit that shape from a 'parent'. When you set light to a piece of paper, the flame builds itself from scratch using the rules of the outside universe.
In the opening instants of the universe, it wasn't just substances, temperatures and sizes that changed. The rules by which they changed also changed. We don't like to think this way: we want immutable laws, the same always. So we look for 'deeper' laws to govern how the rules changed. Possibly the universe is 'really' gov¬erned by these deeper laws. But perhaps it just makes up its own rules as it goes along.

SEVEN

BEYOND THE FIFTH ELEMENT

IN THE QUIET OF THE NIGHT, HEX COMPUTED. Along its myriad glass tubes, the ants scurried. Crude magic sparkled along cobwebs of fine bronze wire, changing colour as it changed logic states. In the special room next door the beehives, long-term storage, buzzed. The thing that went 'parp' did so occasionally. Huge wheels turned, stopped, turned back. And still it wasn't enough.
The light of the Project fell across HEX's keyboard. Things were happening in there, and HEX did not understand them. And that was taxing, because there was something there to understand.
HEX was largely self-designed, which was why it worked better than most things in the University. It generally tried to develop a responsive way of coming to grips with any new task; the bees had been a particularly good idea, because although the memory retrieval was slow, the total memory increased with time and good apiary practice.
Now it reasoned thus:
One day it would find a way of increasing its conceptual capac¬ity to understand what was happening in the Project;
If this could ever happen, then, according to Stryme's Directionless Law, there was already a shape in happening-space, where time did not exist, caused by the fact of that happening; all that was required was a virtual collapse of the wave form;
... and, although this was in a very strict sense garbage, it was not complete garbage. Any answer that would exist somewhere in the future must, inevitably, be available in potentia now.
The ants went faster. Magic flashed. HEX could be said to be concentrating.
Then silvery, shimmering lines appeared in the air around it, outlining towers of unimaginable cogitation.
Ah. That was acceptable.
Once-and-future computing was now in operation. Of course, it always had been.
HEX wondered how much he should tell the wizards. He felt it would not be a good idea to burden them with too much input.
HEX always thought of his reports as Lies-to-People.
It was the second day ...
The Project was nudged gently under a glass dome to prevent any more interference. A variety of spells had been installed around it.
'So that's a universe, is it?' said the Archchancellor.
'Yes, sir. HEX says that ...' Ponder hesitated. You had to think hard before trying to explain things to Mustrum Ridcully.'... HEX seems to suggest that complete and utter nothing is automatically a universe waiting to happen.'
'You mean nothing becomes everything?'
'Why, yes, sir. Er ... in a way, it has to, sir.'
'And the Dean here swirled it all around and that started it off?'
'It could have been anything at all, sir. Even a stray thought. Absolute nothing is very unstable. It's so desperate to be something?’
'I thought you had to have creators and gods,' mumbled the Senior Wrangler.
'I should jolly well think so,' said Ridcully, who was examining the Project with a thaumic omniscope. 'It's been here since last night and there's nothing to be seen except elements, if you could call them that. Bloody stupid elements, too. Half of them fall to bits as soon as you look at them.'
'Well, what do you expect?' said the Lecturer in Recent Runes. 'They're made out of nothing, right? Even a really bad creator would at least have started with Earth, Air, Fire, Water and Surprise.'
'Proper worlds are out of the question here, too,' said Ridcully, peering into the omniscope again. 'There's no sign of chelonium and elephantigen. What kind of worlds can you build without them?'
Ridcully turned to Ponder.
'Not much of a universe, then,' he said. 'It must have gone wrong, Mister Stibbons. It's a dud. By now the first human should be looking for his trousers.'
'Perhaps we could give him a hand,' said the Senior Wrangler.
'What are you suggesting?'
'Well, it's our universe, isn't it?'
Ponder was shocked. 'We can't own a universe, Senior Wrangler!'
'It's a very small one.'
'Only on the outside, sir. HEX says it's a lot bigger on the inside.'
'And the Dean stirred it up,' the Senior Wrangler went on.
'That's right!' said the Dean. 'That means I'm a sort of god.'
'Waggling your fingers around and saying "oo, it prickles" is not godliness,' said Ridcully severely.
'Well, I'm the next best thing,' said the Dean, reluctant to let go of anything that placed him socially higher than the Archchancellor.
'My grandmother always said that cleanliness was next to godli¬ness,' mused the Lecturer in Recent Runes.
'Ah, that's more like it,' said Ridcully cheerfully. 'You're more like a janitor, Dean.'
'I was really just suggesting that we give the thing a few shoves in the right direction,' said the Senior Wrangler. 'We are, after all, learned men. And we know what a proper universe ought to be like, don't we?'
'I imagine we have a better idea than the average god with a dog's head and nineteen arms, certainly,' said Ridcully. 'But this is pretty second-rate material. It just wants to spin all the time. What do you expect us to do, bang on the side and shout "Come on, you lot, stop messing about with stupid gases, they'll never amount to any¬thing"?'
They compromised, and selected a small area for experimentation. They were, after all, wizards. That meant that if they saw something, they prodded it. If it wobbled, they prodded it some more. If you built a guillotine, and then put a sign on it saying 'Do Not Put Your Neck On This Block', many wizards would never have to buy a hat again.
Moving the matter was simple. As Ponder said, it almost moved under the pressure of thought.
And spinning it into a disc was easy. The new matter liked to spin. But it was also far too sociable.
'You see?' said Ridcully, around mid-morning. 'It seems to get the idea, and then you just end up with a ball of rubbish.'
'Which gets hot in the middle, have you noticed?' said Ponder.
'Embarrassment, probably,' said the Archchancellor. 'We've lost half the elements since elevenses. There's no more cohenium, explodium went ten minutes ago, and I'm beginning to suspect that the detonium is falling to bits. Temporarium didn't last for any time at all.'
'Any Runium?' said the Lecturer in Recent Runes.
HEX wrote: +++ Runium May Or May Not Still Exist. It Was Down To One Atom Ten Minutes Ago, Which I Do Not Seem to Be Able To Find Any More +++
'How's Wranglium doing?' said the Senior Wrangler hopefully.
'Exploded after breakfast, according to HEX. Sorry,' said Ridcully. 'You can't build a world out of smoke and mirrors. Damn ... there goes Bursarium, too. I mean, I know iron rusts, but these elements collapse for a pastime.'
'My hypothesis, for what it's worth,' said the Lecturer in Recent Runes, 'is that since it was all started off by the Dean, a certain Dean-like tendency may have imparted itself to the ensuing ... er ... developments.'
'What? You mean we've got a huge windy universe with a ten¬dency to sulk?'
'Thank you, Archchancellor,' said the Dean.
'I was referring to the predilection of matter to ... er ... accrete into ... er ... spherical shapes.'
'Like the Dean, you mean,' said Archchancellor.
'I can see I'm among friends here,' said the Dean.
There was a soft chime from the apparatus that had been accu¬mulated around the Project.
'That'll be etherium vanishing,' said Ridcully gloomily. 'I knew that'd be the next to go.'
'Actually ... no,' said Ponder Stibbons, peering into the Project. 'Er ... something has caught fire.'
Points of light were appearing.
'I knew something like that would happen,' said the Archchancellor. 'All those discs are heating up, just like damn com¬post heaps.'
'Or suns,' said Ponder.
'Don't be silly, Stibbons, they're far too large for that. I'd hate to see one of those floating over the clouds,' said the Lecturer in Recent Runes.
'I said there was far too much gas,' the Archchancellor went on. 'That wraps it up, then.'
'I wonder,' said the Senior Wrangler.
'What?' said the Dean.
'Well, at least we've got some heat in there ... and there nothing like a good furnace for improving matters.'
'Good point,' said Ridcully. 'Look at bronze, you can make that out of just about anything. And we could burn off some of the rub¬bish. All right, you fellows, help me dump more of the stuff in it...'
Around about teatime, the first of the furnaces exploded, just as happened every day down at the Alchemists' Guild.
'Ye gods,' said Ridcully, watching the shapes in the omniscope.
'Yo?' said the Dean.
'We've made new elements!'
'Keep it down, keep it down!' hissed the Senior Wrangler.
'There's iron ... silicon ... we've got rocks, even ...'
'We're going to be in serious trouble if the alchemists' guild finds out,' said the Lecturer in Recent Runes. 'You know we're not supposed to do that stuff.'
'This is a different universe,' said Ridcully. He sighed. 'You have to blow things up to get anything useful.'
'I see politicium is still there in large quantities, then,' said the Senior Wrangler.
'I meant that this is a godless reality, gentlemen.'
'Excuse me, the Dean began.
'I shouldn't look so smug if I was you, Dean,' said Ridcully. 'Look at the place. Everything wants to spin, and sooner or later you have balls.'
'And we're getting the same sort of stuff that we get here, isn't that strange?' said the Senior Wrangler, as Mrs Whitlow the house¬keeper came in with the tea trolley.
'I don't see why,' said the Dean. 'Iron's iron.'
'Well, it's a whole new universe, so you'd expect new things, wouldn't you? Metals like Noggo, perhaps, or Plinc.'
'What's your point, Senior Wrangler?'
'I mean, take a look at the thing now ... all those burning explod¬ing balls do look a bit like the stars, don't they? I mean they're vaguely familiar. Why isn't it a universe full of tapioca, say, or very large chairs? I mean, if nothing wants to be something, why can't it be anything?’
The wizards stirred their tea and thought about this.
'Because,' said the Archchancellor, after a while.
'That's a good answer, sir,' said Ponder, as diplomatically as he could, 'But it does rather close the door on further questions.'
'Best kind of answer there is, then.'
The Senior Wrangler watched Mrs Whitlow produce a duster and polish the top of the Project.
'"As Above, So Below",' said Ridcully, slowly.
'Pardon?' said the Senior Wrangler.
'We're forgetting our kindergarten magic, aren't we? It's not even magic, it's a ... a basic rule of everything. The project can't help being affected by this world. Piles of sand try to look like moun¬tains. Men try to act like gods. Little things so often appear to look like big things made smaller. Our new universe, gentlemen, will do its crippled best to look like ours. We should not be surprised to see things that look hauntingly familiar. But not as good, obviously.'
The inner eye of HEX gazed at a vast cloud of mind. HEX couldn't think of a better word. It didn't technically exist yet, but HEX could sense the shape. It had hints of many things, of tradition, of libraries, of rumour ...
There had to be a better word. HEX tried again.
On Discworld, words had real power. They had to be dealt with carefully.
What lay ahead had the shape of intelligence, but only in the same way that a sun had the shape of something living out its brief life in a puddle of ditchwater.
Ah ... eJrtelligence would do for now.
HEX decided to devote part of its time to investigating this inter¬esting thing. It wanted to find out how it had developed, what kept it going ... and why, particularly, a small but annoying part of it seemed to believe that if everyone sent five dollars to the six names at the top of the list, everyone would become immensely rich.

EIGHT

WE ARE STARDUST
(or at least we went to Woodstock)

IRON'S IRON.' BUT IS IT? Or is iron made from other things?
According to Empedocles, an ancient Greek, everything in the universe was a combination of four ingredients: earth, air, fire, and water. Set light to a stick and it burns (showing that it contains fire), gives off smoke (showing that it contains air), exudes bubbly liquids (show¬ing that it contains water), and leaves a dirty heap of ash behind (showing that it contains earth). As a theory, it was a bit too simple-minded to survive for long, a couple of thousand years at best. Things moved more slowly in those days, and Europe, at least, was more interested in making sure that the peasants didn't get above their station and copying out bits of the Bible by hand in as labori¬ous and colourful a manner as possible.
The main technological invention to come out of the Middle Ages was a better horse collar.
Empedocles's theory was a distinct advance on its predecessors. Thales, Heraclitus, and Anaximenes all agreed that everything was made from just one basic 'principle', or element, but they dis¬agreed completely about what it was. Thales reckoned it was water, Heraclitus preferred fire, and Anaximenes was willing to bet the farm on air. Empedocles was a wishy-washy synthesist who thought everyone had a valid point of view: if alive today he would definitely wear a bad tie.
The one good idea that emerged from all this was that 'elemen¬tary' constituents of matter should be characterized by having simple, reliable properties. Earth was dirty, air was invisible, fire burned, and water was wet.
Aside from the superior horse collar, the medieval period did act as a breeding ground for what eventually turned into chemistry. For centuries the nascent science known as alchemy had flourished; people had discovered that some strange things happen when you mix substances together and heat them, or pour acid over them, or dissolve them in water and wait. You could get funny smells, bangs, bubbles, and liquids that changed colour. Whatever the universe was made of, you could clearly convert some of it into something else if you knew the right trick. Maybe a better word is 'spell', for alchemy was akin to magic, lots of special recipes and rituals, many of which actually worked, but no theory about how it all fitted together. The big goals of alchemy were spells, recipes, for things like the Elixir of Life, which would make you live forever, and How to Turn Lead Into Gold, which would give you lots of money to finance your immortal lifestyle. Towards the end of the Middle Ages, alchemists had been messing about for so long that they got quite good at it, and they started to notice things that didn't fit the Greeks' theory of four elements. So they introduced extra ones, like salt and sulphur, because these substances also had simple, reliable properties, different from being dirty, invisible, burning, or wet. Sulphur, for example, was combustible (though not actually hot, you understand) and salt was incombustible.
By 1661 Robert Boyle had sorted out two important distinc¬tions, putting them into his book The Sceptical Chymist. The first distinction was between a chemical compound and a mixture. A mixture is just different things, well, mixed up. A compound is all the same stuff, but whatever that stuff is, it can be persuaded to come apart into components that are other kinds of stuff- provided you heat it, pour acid on it, or find some other effective treatment. What you can't do is sort through it and find a different bit; for a mixture you can, although you might need very good eyesight and tiny fingers. The second distinction was between compounds and elements. An element really is one kind of stuff: you can't separate it into different components.
Sulphur is an element. Salt, we now know, is a compound made by combining (not just mixing) the two elements sodium (a soft, inflammable metal) and chlorine (a toxic gas). Water is a compound, made from hydrogen and oxygen (both gases). Air is a mixture, containing various gases such as oxygen (an element), nitrogen (also an element), and carbon dioxide (a combination of carbon and oxy¬gen). Earth is a very complicated mixture and the mix varies from place to place. Fire isn't a substance at all, but a process involving hot gases.
It took a while to sort all this out, but by 1789 Antoine Lavoisier had come up with a list of 33 elements that were a reasonable selec¬tion of the ones we use today. He made a few understandable mistakes, and he included both light and heat as elements, but his approach was systematic and careful. Today we know of 112 distinct elements. A few of these are artificially produced, and several of those have existed on Earth only for the tiniest fraction of a second, but most elements on the list can be dug up, extracted from the sea or separated from the air around us. And apart from a few more artificially produced elements that it might just be possible to make in future, today's list is almost certainly complete.
It took another while for us to get that far. The art of alchemy slowly gave way to the science of chemistry. Gradually the list of accepted elements grew; occasionally it shrunk when people real¬ized that a previously supposed element was actually a compound, such as Lavoisier's lime, now known to be made from the elements calcium and oxygen. The one thing that didn't change was the only thing the Greeks had got right: each element was a unique individ¬ual with its own characteristic properties. Density; whether it was solid, liquid, or gas at room temperature and normal atmospheric pressure; melting point if it was solid, for each element, these quantities had definite, unvarying values. It is the same on Discworld, with its to our eyes bizarre elements such as chelonium (for making world-bearing turtles), elephantigen (ditto elephants), and narrativium, a hugely important 'element' not just for Discworld, but for understanding our own world too. The charac¬teristic feature of narrativium is that it makes stories hang together. The human mind loves a good dose of narrativium.
In this universe, we began to understand why elements were unique individuals, and what distinguished them from compounds. Again the glimmerings of the right idea go back to the Greeks, with Democritus' suggestion that all matter is made from tiny indivisible particles, which he called atoms (Greek for 'not divisible')- It is unclear whether anybody, even Democritus, actually believed this in Greek times, it may just have been a clever debating point. Boyle revived the idea, suggesting that each element corresponds to a single kind of atom, whereas compounds are combinations of dif¬ferent kinds of atoms. So the element oxygen is made from oxygen atoms and nothing else, the element hydrogen is made from hydro¬gen atoms and nothing else, but the compound water is not made from water atoms and nothing else, it is made from atoms of hydro¬gen and atoms of oxygen.

By 1807, one of the most significant steps in the development of both chemistry and physics had taken place. The Englishman John Dalton had found a way to bring a degree of order to the different atoms that made up the elements, and to transfer some of that order to compounds too. His predecessors had noticed that when ele¬ments combine together to form compounds, they do so in simple and characteristic proportions. So much oxygen plus so much hydrogen makes so much water, and the proportions by weight of oxygen and hydrogen are always the same. Moreover, those propor¬tions all fit together nicely if you look at other compounds involving hydrogen and other compounds involving oxygen.
Dalton realized that all this would make perfect sense if each atom of hydrogen had a fixed weight, each atom of oxygen had a fixed weight, and the weight of an oxygen atom was 16 times that of hydrogen. The evidence for this theory had to be indirect, because an atom is far too tiny for anyone to be able to weigh one, but it was extensive and compelling. And so the theory of 'atomic weight' arrived on the scene, and it let chemists list the elements in order of atomic weight.
That list begins like this (modern values for atomic weights in brackets): Hydrogen (1.00794), Helium (4.00260), Lithium (6.941), Beryllium (9.01218), Boron (10.82), Carbon (12.011), Nitrogen (14.0067), Oxygen (15.9994), Fluorine (18.998403), Neon (20.179), Sodium (22.98977). A striking feature is that the atomic weight is nearly always close to a whole number, the first exception being chlorine at 35.453. All a bit puzzling, but it was an excellent start because now people could look for other patterns and relate them to atomic weights. However, looking for patterns proved easier than finding any. The list of elements was unstructured, almost random in its properties. Mercury, the only element known to be liquid at room temperature, was a metal. (Later just one further liquid was added to the list: bromine.) There were lots of other metals like iron, copper, silver, gold, zinc, tin, each a solid and each quite dif¬ferent from the others; sulphur and carbon were solid but not metallic; quite a few elements were gases. So unstructured did the list of elements seem that when a few mavericks, Johann Dobereiner, Alexandre-Emile Beguyrer de Chancourtois, John Newlands, suggested there might be some kind of order dimly vis¬ible amid the muddle and mess, they were howled down.
Credit for coming up with a scheme that was basically right goes to Dimitri Mendeleev, who finished the first of a lengthy series of 'periodic charts' in 1869. His chart included 63 known elements placed in order of atomic weight. It left gaps where undiscovered elements allegedly remained to be inserted. It was 'periodic' in the sense that the properties of the elements started to repeat after a certain number of steps, the commonest being eight.
According to Mendeleev, the elements fall into families, whose members are separated by the aforementioned periods, and in each family there are systematic resemblances of physical and chemical properties. Indeed those properties vary so systematically as you run through the family that you can see clear, though not always exact, numerical patterns and progressions. The scheme works best, however, if you assume that a few elements are missing from the known list, hence the gaps. As a bonus, you can make use of those family resemblances to predict the properties of those missing elements before anybody finds them. If those predictions turn out to be correct when the missing elements are found, bingo. Mendeleev's scheme still gets modified slightly from time to time, but its main features survive: today we call it the Periodic Table of the Elements.
We now know that there is a good reason for the periodic structure that Mendeleev uncovered. It stems from the fact that atoms are not as indivisible as Democritus and Boyle thought. True, they can't be divided chemically, you can't separate an atom into component pieces by doing chemistry in a test tube, but you can 'split the atom' with apparatus that is based on physics rather than chemistry. The 'nuclear reactions' involved require much higher energy levels, per atom, than you need for chemical reactions, which is why the old-time alchemists never managed to turn lead into gold. Today, this could be done, but the cost of equipment would be enormous, and the amount of gold produced would be extremely small, so the scientists would be very much like Discworld's own alchemists, who have only found ways of turning gold into less gold.
Thanks to the efforts of the physicists, we now know that atoms are made from other, smaller particles. For a while it was thought that there were just three such particles: the neutron, the proton, and the electron. The neutron and proton have almost equal masses, while the electron is tiny in comparison; the neutron has no electrical charge, the proton has a positive charge, and the electron has a negative charge exactly opposite to that of the proton. Atoms have no overall charge, so the numbers of protons and electrons are equal. There is no such restriction on the number of neutrons. To a good approximation, you get an element's atomic weight by adding up the numbers of protons and neutrons, for example oxygen has eight of each, and 8 + 8 = 16, the atomic weight.
Atoms are incredibly small by human standards, about a hun¬dred millionth of an inch (250 millionths of a centimetre) across for an atom of lead. Their constituent particles, however, are consider¬ably smaller. By bouncing atoms off each other, physicists found that they behave as if the protons and neutrons occupy a tiny region in the middle, the nucleus, but the electrons are spread outside the nucleus over what, comparatively speaking, is a far bigger region. For a while, the atom was pictured as being rather like a tiny solar system, with the nucleus playing the role of the sun and the electrons orbiting it like planets. However, this model didn't work very well, for example, an electron is a moving charge, and according to classical physics a moving charge emits radiation, so the model predicted that within a split second every electron in an atom would radiate away all of its energy and spiral into the nucleus. With the kind of physics that developed from Isaac Newton's epic discoveries, atoms built like solar systems just don't work. Nevertheless, this is the public myth, the lie-to-children that auto¬matically springs to mind. It is endowed with so much narrativium that we can't eradicate it.
After a lot of argument, the physicists who worked with matter on very small scales decided to hang on to the solar system model and throw away Newtonian physics, replacing it with quantum the¬ory. Ironically, the solar system model of the atom still didn't work terribly well, but it survived for long enough to help get quantum theory off the ground. According to quantum theory the protons, neutrons, and electrons that make an atom don't have precise loca¬tions at all, they're kind of smeared out. But you can say how much they are smeared out, and the protons and neutrons are smeared out over a tiny region near the middle of the atom, whereas the elec¬trons are smeared out all over it.
Whatever the physical model, everyone agreed all along that the chemical properties of an atom depend mainly on its electrons, because the electrons are on the outside, so atoms can stick together by sharing electrons. When they stick together they form molecules, and that's chemistry. Since an atom is electrically neutral overall, the number of electrons must equal the number of protons, and it is this 'atomic number', not the atomic weight, that organizes the periodic¬ities found by Mendeleev However, the atomic weight is usually about twice the atomic number, because the number of neutrons in an atom is pretty close to the number of protons for quantum rea¬sons, so you get much the same ordering whichever quantity you use. Nevertheless, it is the atomic number that makes more sense of the chemistry and explains the periodicity. It turns out that period eight is indeed important, because the electrons live in a series of 'shells', like Russian dolls, one inside the other, and until you get some way up the list of elements a complete shell contains eight electrons.
Further along, the shells get bigger, so the period gets bigger too. At least, that's what Joseph (J. J.) Thompson said in 1904. The modern theory is quantum and more complicated, with far more than three 'fundamental' particles, and the calculations are much harder, but they have much the same implications. Like most sci¬ence, an initially simple story became more complicated as it was developed and headed rapidly towards the Magical Event Horizon for most people.
But even the simplified story explains a lot of otherwise baffling things. For instance, if the atomic weight is the number of protons plus neutrons, how come atomic weight isn't always a whole num¬ber? What about chlorine, for instance, with atomic weight 35.453? It turns out there are two different kinds of chlorine. One kind has 17 protons and 18 neutrons (and 17 electrons, naturally, the same as protons), with atomic weight 35. The other kind has 17 protons and 20 neutrons (and 17 electrons, again), an extra two neutrons, which raises the atomic weight to 37. Naturally occurring chlorine is a mixture of these two 'isotopes', as they are called, in roughly the proportions 3 to 1. The two isotopes are (almost) indistinguish¬able chemically, because they have the same number and arrangement of electrons, and that's what makes chemistry work; but they have different atomic physics.
It is easy for a non-physicist to see why the wizards of UU con¬sidered this universe to be made in too much of a hurry out of obviously inferior components ...

Where did all those 112 elements come from? Were they always around, or did they get put together as the universe developed?
In our Universe, there seem to be five different ways to make elements:

• Start up a universe with a Big Bang, obtaining a highly energetic ('hot') sea of fundamental particles. Wait for it to cool (or possibly use one you made earlier ...). Along with ordinary matter, you'll proba¬bly get a lot of exotic objects like tiny black holes, and magnetic monopoles but these will disappear pretty quickly and only conven¬tional matter will remain, mostly. In a very hot universe, electromagnetic forces are too weak to resist disruption, but once the universe is cool enough, fundamental particles can stick together as a result of electromagnetic attraction. The only element that arises directly in this manner is hydrogen, one electron joined with one proton. However, you get an awful lot of it: in our universe it is by far the commonest element, and nearly all of it arose from the Big Bang. Protons and electrons can also associate to form deuterium (one electron, one proton, one neutron) or tritium (one electron, one proton, two neutrons), but tritium is radioactive, meaning that it spits out neutrons and decays into hydrogen again. A far more sta¬ble product is helium (two electrons, two protons, two neutrons), and helium is the second most abundant element in the universe.

• Let gravity get in on the act. Now hydrogen and helium collect together to form stars, the wizards' 'furnaces'. At the centre of stars, the pressure is extremely high. This brings new nuclear reac¬tions into play, and you get nuclear fusion, in which atoms become so squashed together that they merge into a new, bigger atom. In this manner, many other familiar elements were formed, from carbon, nitrogen, oxygen, to the less familiar lithium, beryllium and so on up to iron. Many of these elements occur in living creatures, the most important being carbon. For reasons to do with its unique electron structure, carbon is the only atom that can combine with itself to form huge, complex molecules, without which our kind of life would be impossible. Anyway, the point is that most of the atoms from which you are made must have come into being inside a star. As Joni Mitchell sang at Woodstock:: 'We are stardust.’ Scientists like quot¬ing this line, because it sounds as though they were young once.

• Wait for some of the stars to explode. There are (comparatively) small explosions called novas, meaning 'new (star)', and more vio¬lent ones, supernovas. (What's 'new' is that usually we can't see the star until it explodes, and then we can.) It's not just that the nuclear fuel gets used up: the hydrogen and helium that fuel the star fuse into heavier elements, which in effect become impurities that dis¬turb the nuclear reaction. Pollution is a problem even at the heart of a star. The physics of these early suns changes, and some of the larger ones explode, generating higher elements like iodine, tho¬rium, lead, uranium, and radium. These stars are called 'Population II' by astrophysicists, they are old stars, low in heavy elements, but not lacking them entirely.

• There are two kinds of supernova, and the other type creates heavy elements in abundance, leading to 'Population I' stars, which are much younger than Population II. Because many of these ele¬ments have unstable atoms, various other elements are made by their radioactive decay. These 'secondhand' elements include lead.

• Lastly, human beings have made some elements by special arrange¬ments in atomic reactors, the best known being plutonium, a by-product of conventional uranium reactors and a raw material for nuclear weapons. Some rather exotic ones, with very short lifetimes, have been made in experimental atombashers: so far we've got to element 112. Physicists always fight over who got what first and who therefore has the right to propose a name, so at any given time the heaviest elements are likely to have been assigned temporary (and ludicrous) names such as 'ununnilium' for element 110, dog-Latin for '1-1-0-ium'.
What's the point of making extremely short-lived elements like these? You can't use them for anything. Well, like mountains, they are there; moreover, it always helps to test your theories on extreme cases. But the best reason is that they may be steps towards some¬thing rather more interesting, assuming that it actually exists. Generally speaking, once you get past polonium at atomic number 84 everything is radioactive, it spits out particles of its own accord and 'decays' into something else, and the greater an element's atomic number, the more rapidly it decays. However, this tendency may not continue indefinitely. We can't model heavy atoms exactly, in fact we can't even model light atoms exactly, but the heavier they are the worse it gets.
Various empirical models (intelligent approximations based on intuition, guesswork, and fiddling adjustable constants) have led to a surprisingly accurate formula for how stable an element should be when it has a given number of protons and a given number of neu¬trons. For certain 'magic numbers', Roundworld terminology that suggests the physicists concerned have imbibed some of the spirit of Discworld and realized that the formula is closer to a spell than a theory, the corresponding atoms are unusually stable. The magic numbers for protons are 28, 50,82,114, and 164; those for neutrons are 28, 50, 82, 126, 184, 196, and 318. For example the most stable element of all is lead, with 82 protons and 126 neutrons.
Only two steps beyond the incredibly unstable element 112 lies element 114, tentatively named eka-lead. With 114 protons and 184 neutrons it is doubly magic and is therefore likely to be a lot more stable than most elements in its vicinity. The uncertainty arises from worries about the approximations in the stability formula, which may not work for such large numbers. Every wizard is aware that spells can often go wrong. Assuming that the spell works, though, we can play Mendeleev and predict the properties of eka-lead by extrapolating from those in the 'lead' series in the periodic table (carbon, silicon, germanium, tin, lead). As the name suggests, eka-lead turns out to resemble lead, it's expected to be a metal with a melting point of 70°C and a boiling point of 150°C at atmospheric pressure. Its density should be 25% greater than that of lead.
Even further out lies the doubly magic element 164, with 164 protons and 318 neutrons, and beyond that, the magic numbers may continue ... It is always dangerous to extrapolate, but even if the formula is wrong, there could well be certain special configura¬tions of protons and neutrons that are stable enough for the corresponding elements to hang around in the real universe. Perhaps this is where elephantigen and chelonium come from. Possibly Noggo and Plinc await our attention, somewhere. Maybe there are stable elements with vast atomic numbers, some might even be the size of a star. Consider, for instance, a neutron star, one made almost entirely of neutrons, which forms when a larger star collapses under its own gravitational attraction. Neutron stars are incredibly dense: about forty trillion pounds per square inch (100 billion kg/cc), twenty million elephants in a nutshell. They have a surface gravity seven billion times that of the Earth, and a magnetic field a trillion times that of the Earth. The particles in a neutron star are so closely packed that in effect it is one big atom.
Bizarre though they are, some of these superheavy elements may lurk in unusual corners of our universe. In 1968 it was suggested that elements 105-110 could sometimes be observed in cosmic rays, highly energetic particles coming from outer space, but these reports went unconfirmed. It is thought that cosmic rays originate in neutron stars, so maybe in the astonishing conditions found there superheavy elements are formed. What would happen if Population I stars changed by accumulating superheavy stable ele¬ments?
Because the stellar population numbers go III, II, I as time passes, a convention that astrophysicists may yet have cause to regret, we must name these hypothetical stars 'Population 0'. At any rate, the future universe could easily contain stellar objects quite different from anything we know about today, and as well as novas and supernovas, we might witness even more energetic explo¬sions, hypernovas. There might even be further stages -Population minus I and the like. As we've said, our universe often seems to make up its rules as it goes along, unlike the rational, sta¬ble universe of Discworld.

NINE

EAT HOT NAPHTHA, EVIL DOG!

THE ROCKS FELL GENTLY TOGETHER AGAIN, and to the annoyance of the Archchancellor they moved in curved lines while doing so.
'Well, I think we've proved that a giant turtle made of stone isn't going to work,' said the Senior Wrangler, sighing.
'For the tenth time,' sighed the Lecturer in Recent Runes.
'I told you we'd need chelonium,' said Archchancellor Ridcully.
Early attempts spun gently a little way away. Small balls, big balls ... Some of them even had a mantle of gases, pouring out of the clumsy aggregations of ice and rock. It was as if the new uni¬verse had some basic idea of what it ought to be, but it couldn't quite manage to get a grip.
After all, the Archchancellor pointed out, once people had something to stand on they'd need something to breathe, wouldn't they? Atmospheres seemed to turn up on cue. But they were dread¬ful things, full of stuff not even a troll would suck.
In the absence of gods, he declared, and a series of simple tests had found no trace of deitygen, it was up to men to get it right.
The High Energy Magic building was getting crowded now. Even the student wizards were taking an interest, and usually they weren't even seen during daylight. The Project promised to offer even greater attractions than staying up all night playing with HEX and eating herring and banana pizza.
More desks had been moved in. The Project was in an expand¬ing circle of instruments and devices, because it appeared that every wizard apart from, possibly, the Professor of Eldritch Lacemaking, had decided he was working on something that would benefit immensely from access to the Project. There was certainly room. While the Project was indeed about a foot wide, the space inside seemed to be getting bigger by the second. A universe offers lots of space, after all.
And while ignorant laymen objected to magical experiments that were by no means dangerous, there being less than one chance in five of making a serious breach in the fabric of reality, there was no one in there to object to anything.
There were, of course, accidents ...
'Will you two stop shouting!' yelled the Senior Wrangler. Two student wizards were arguing vehemently, or at least repeatedly stating their point of view in a loud voice, which suffices for argu¬ment most of the time.
'I'd spent ages putting together a small icy ball and he sent that wretched great rock smack into it, sir.'
'I wasn't trying to!' said the other student. The Senior Wrangler stared at him, trying to remember his name. As a general rule, he avoided getting to know the students, since he felt they were a tedious interruption to the proper running of college life.
'What were you trying to do, then ... boy?' he said.
'Er ... I was trying to hit the big ball of gas, sir. But it just sort of swung around it, sir.'
The Senior Wrangler looked around. The Dean was not present. Then he looked into the Project.
'Oh, I see. That one. Quite pretty. All those stripes. Who built that?'
A student raised his hand.
'Ah, yes ... you,' said the Senior Wrangler. 'Good stripes. Well done. What's it made of?'
'I just dragged a lot of ice together, sir. But it got hot.'
'Really? Ice gets hot in a ball?'
In a big ball, sir.'
'Have you told Mister Stibbons? He likes to know that sort of thing.'
'Yes, sir.'
The Senior Wrangler turned to the other student.
'And why were you throwing rocks at his big ball of gas?'
'Er ... because you score ten for hitting it, sir.'
The Senior Wrangler looked owlishly at the students. It all became clear. He'd wandered into the HEM one night when he couldn't sleep and a mob of students had been hunched over the keyboards of HEX and shouting things like 'I've got the battering ram! Hah, eat hot naphtha, evil dog!' Doing that sort of thing in a whole new universe seemed ... well, impolite.
On the other hand, the Senior Wrangler shared with some of his colleagues an unformed thought that pushing back the boundaries of knowledge was not quite ... well, polite. Boundaries were there for a reason.
'Are you meaning to tell me,' he said, 'that faced with the multi¬tudinous possibilies of the infinity that is the Project you are using it to play some sort of game?'
'Er ... yes, sir'
'Oh.' The Senior Wrangler looked closely at the big ball of gas. A number of small rocks were already spinning slowly around it. 'Well, then ... can I have a go?'

TEN

THE SHAPE OF THINGS

WHEN WIZARDS FIND A NEW THING, THEY PLAY WITH IT. So do scientists. They play with ideas so wild that often they seem to defy common sense, and then they insist that those ideas are right, and common sense isn't. They often make out a sur¬prisingly good case. Einstein once said something nasty about common sense being akin to nonsense, but he went too far. Science and common sense are related, but indirectly. Science is something like a third cousin of common sense twice removed. Common sense tells us what the universe seems like to creatures of our particular size, habits, and disposition. For instance, common sense tells us that the Earth is flat. It looks flat, leaving out the hills, valleys, and other bumps and dents ... If it wasn't flat, things ought to roll around or fall off. Despite this, the Earth isn't flat. On Discworld, in contrast, the relation between common sense and reality is usu¬ally very direct indeed. Common sense tells the wizards of Unseen University that Discworld is flat, and it is. To prove it, they can go to the Edge, as Rincewind and Twoflower do in The Colour of Magic, and watch stuff disappearing over it in Rimfall: 'The roar¬ing was louder now. A squid bigger than anything Ricewind had seen before broke the surface a few hundred yards away and thrashed madly with its tentacles before sinking away ... They were running out of world.' Then they can be trapped in the Grcumfence, a ten thousand mile long net set just below the Edge, one tiny bit of which is patrolled by Tethis the sea troll. And they can peer over the edge: '... the scene beneath him flipped into a whole, new, terrifying perspective. Because down there was the head of an elephant as big as a reasonably-sized continent... Below the elephant there was nothing but the distant, painful disc of the sun. And, sweeping slowly past it, was something that for all its city-sized scales, its crater-pocks, its lunar cragginess, was indu¬bitably a flipper.'
It is widely imagined that ancient people thought the Earth was flat, for all those obvious commonsense reasons. Actually, most ancient civilizations that left records seem to have worked out that the Earth has to be round. Ships came back from invisible lands over the horizon and, in the sky, a round sun and a round moon were a definite clue ...
That's where science and common sense overlap. Science is common sense applied to evidence. Using common sense in that manner, you often come to conclusions that are very different from the obvious common sense assumptions that because the universe appears to behave in some manner, then it really does. Of course it also helps to realize that if you live on a very big sphere, it's going to look pretty flat for quite a long way off. And if gravity always points towards the middle of the sphere, then things don't actually roll around or fall off. But those are refinements.

Around 250 BC a Greek called Eratosthenes tested the theory that the Earth is a sphere, and he even worked out just how big that sphere is. He knew that in the city of Syene, present-day Aswan in Egypt, the midday sun could be seen reflected in the bottom of a well. (This would not work in Ankh-Morpork, where the well-water is often more solid than the well that surrounds it.) Eratosthenes threw in a few other simple facts and got back a lot more than he'd bargained for.
It's a matter of geometry. The well was dug straight down. So the Sun at Syene had to be straight up, dead overhead. But in Eratosthenes' home city of Alexandria, in the Nile delta, that didn't happen. At midday, when the sun was at its highest, Eratosthenes cast a definite shadow. In fact, he estimated that at noon the angle between the Sun and the vertical was just over 7°, near enough 1/50 of 360°. Then came the leap of deduction. The Sun is in the same place wherever you observe it from. On other grounds, it was known that the Sun had to be a long way away from the Earth, and that meant that the Sun's rays that hit the ground in Alexandria were very nearly parallel to those that went down the well in Syene. Eratosthenes reasoned that a round Earth would explain the differ¬ence. He deduced that the distance from Syene to Alexandria must be 1/50 of the circumference of the Earth. But how far was that?
On such occasions it pays to be familiar with the camel-herders. Not just because the greatest mathematician in the world is the camel called You Bastard, as it is on Discworld (see Pyramids), but because the camel trains from Alexandria to Syene took 50 days to make the trip, at an average speed of 100 stadia per day. So the dis¬tance from Alexandria to Syene was 5,000 stadia, and the circumference of the Earth was 250,000 stadia. The stadium was a Greek measure of distance, and nobody knows how long it was. Scholars think it was 515 feet (157 m), and if they're right, Eratosthenes' value was 24,662 miles (39,690 km). The true value is about 24,881 miles (40,042 km), so Eratosthenes got amazingly close. Unless, sorry, but we're incorrigibly suspicious, the schol¬ars worked backwards from the answer.
It is here that we encounter another feature of scientific reason¬ing. In order to make comparisons between theory and experiment, you have to interpret the experiment in terms of your theory. To clarify this point, we recount the story of Ratonasticthenes, an early relative of Cut-me-own-throat Dibbler, who proved that the Discworld was round (and even estimated its circumference). Ratonasticthenes noticed that at midday in the Ramtops the Sun was overhead, whereas in Lancre, some 1000 miles away, it was at 84° to the vertical. Since 84° is roughly a quarter of 360°, Ratonasticthenes reasoned that the Discworld is round, and the dis¬tance from the Ramtops to Ankh-Morpork is one-quarter of the circumference. That puts the circumference of this spherical Discworld at 4,000 miles (6,400 km). Unfortunately for this theory, it was known on other grounds that Discworld is some 10,000 miles (16,000 km) from rim to rim. Still, you can't let an awkward fact get in the way of a good theory, and Ratonasticthenes went to his grave believing that it was a small world after all.
His error was to interpret perfectly good observational data in terms of a flawed theory. Scientists repeatedly return to established theories to test them in new ways, and tend towards testiness with those priests, religious or secular, who know the answers already -whatever the questions are. Science is not about building a body of known 'facts'. It is a method for asking awkward questions and sub¬jecting them to a reality-check, thus avoiding the human tendency to believe whatever makes us feel good.

* * *

From the earliest times, humans have been interested not just in the shape of the world, but in the shape of the universe. To begin with, they probably thought that these were the same question. Then they worked out, using roughly the same sort of geometry as Eratosthenes, that those lights in the sky were a very long way away. They came up with an amazing range of myths about the sun-god's fiery chariot and so on, but after the Babylonians got the idea of making accurate measurements, their theories started to lead to sur¬prisingly good predictions of things like eclipses and the motion of the planets. By the time of Ptolemy (Claudius Ptolemaeus, AD 100-160) the best model of planetary motion involved a series of 'epicycles', the planets moved as if they were rotating round cir¬cles whose centres rotated round other circles whose centres rotated round ...
Isaac Newton replaced this theory, and its more accurate succes¬sors, with a rule, the law of gravity; it describes how each body in the universe attracts every other body. It explained Johannes Kepler's discovery that planetary orbits are ellipses, and in the full¬ness of time it explained a lot of other things too.
After a few centuries of stunning success, Newton's theory ran into its first big failure: it made incorrect predictions about the orbit of Mercury. The place in its orbit at which Mercury came closest to the sun didn't move quite the way Newton's law pre¬dicted. Einstein came to the rescue with a theory based not on attractive forces, but on geometry, on the shape of spacetime. This was the celebrated Theory of Relativity. The theory came in two flavours: Special Relativity and General Relativity. Special Relativity is about the structure of space, time, and electromagnet-ism; General Relativity describes what happens when you throw in gravity too.
The main point to appreciate is that 'Relativity' is a silly name. The whole point of Special Relativity is not that 'everything is rel¬ative', but that one particular thing, the speed of light, is unexpectedly absolute. The thought experiment is well known. If you're travelling in a car at 50 mph (80 kph) and you fire a gun for¬wards, so that the bullet moves at 500 mph (800 kph) relative to the car, then it will hit a stationary target at a speed of 550 mph (880 kph), adding the two components. However, if instead of firing the gun you switch on a torch, which 'fires' light at a speed of 670,000,000 mph (186,000 mps or 300,000 kps), then that light will not hit the stationary target at a speed of 670,000,050 mph. It will hit it at 670,000,000 mph, exactly the same speed as if the car had been stationary.
There are practical problems in staging that experiment, but less graphic and dangerous ones have indicated what the result would be.
Einstein published Special Relativity in 1905, along with the first serious evidence for quantum mechanics and a ground-break¬ing paper on diffusion. A lot of other people, among them the Dutch physicist Hendrik Lorentz and the French mathematician Henri Poincare, were working on the same idea, because electro-magnetism didn't entirely agree with Newtonian mechanics. The conclusion was that the universe is a lot weirder than common sense tells us, although they probably didn't use that actual word. Objects shrink as they approach the speed of light, time slows down to a crawl, mass becomes infinite ... and nothing can go faster than light. Another key idea was that space and time are to some extent interchangeable. The traditional three dimensions of space plus a separate one for time are merged into a single unified spacetime with four dimensions. A point in space becomes an event in spacetime.
In ordinary space, there is a concept of distance. In Special Relativity, there is an analogous quantity, called the interval between events, which is related to the apparent rate of flow of time. The faster an object moves, the slower time flows for an observer sitting on that object. This effect is called time dilation.
If you could travel at the speed of light, time would be frozen.
One startling feature of relativity is the twin paradox, pointed out by Paul Langevin in 1911. Again, it is a classic illustration. Suppose that Rosencrantz and Guildenstern are born on Earth on the same day. Rosencrantz stays there all his life, while Guildenstern travels away at nearly lightspeed, and then turns round and comes home again. Because of time dilation, only one year (say) has passed for Guildenstern, whereas 40 years have gone by for Rosencrantz. So Guildenstern is now 39 years younger than his twin brother. Experiments carrying atomic clocks around the Earth on jumbo jets have verified this scenario, but aircraft are so slow compared to light that the time difference observed (and pre¬dicted) is only the tiniest fraction of a second.
So far so good, but there's no place yet for gravity. Einstein racked his brains for years until he found a way to put gravity in: let spacetime be curved. The resulting theory is called General Relativity, and it is a synthesis of Newtonian gravitation and Special Relativity. In Newton's view, gravity is a force that moves particles away from the perfect straight line paths that they would otherwise follow In General Relativity, gravity is not a force: it is a distortion of the structure of spacetime. The usual image is to say that space-time becomes 'curved', though this term is easily misinterpreted. In particular, it doesn't have to be curved round anything else. The cur¬vature is interpreted physically as the force of gravity, and it causes light rays to bend. One result is 'gravitational lensing', the bending of light by massive objects, which Einstein discovered in 1911 and published in 1915. The effect was first observed during an eclipse of the Sun. More recently it has been discovered that some distant quasars produce multiple images in telescopes because their light is lensed by an intervening galaxy.

Einstein's theory of gravity ousted Newton's because it fitted observations better, but Newton's remains accurate enough for many purposes, and is simpler, so it is by no means obsolete. Now it's beginning to look as if Einstein may in turn be ousted, possibly by a theory that he rejected as his greatest mistake.
In 1998 two different observations called Einstein's theory into question. One involved the structure of the universe on truly mas¬sive scales, the other happened in our own backyard. The first has survived everything so far thrown at it; the second can possibly be traced to something more prosaic. So let's start with the second curious discovery.
In 1972 and 1973 two space probes, Pioneer 10 and 11, were launched to study Jupiter and Saturn. By the end of the 1980s they were in deep space, heading out of the known solar system. There has long been a belief, a scientific legend waiting to happen, that beyond Pluto there may be an as yet undiscovered planet, Planet X. Such a planet would disturb the motions of the two Pioneers, so it was worth tracking the probes in the hope of finding unexpected deviations. John Andersen's team found deviations, all right, but they didn't fit Planet X, and they didn't fit General Relativity either. The Pioneers are coasting, with no active form of propul¬sion, so the gravity of the Sun (and the much weaker gravity of the other bodies of the known solar system) pulls on them and gradu¬ally slows them down. But the probes were slowing down a tiny bit more than they should have been. In 1994 Michael Martin sug¬gested that this effect had become sufficiently well established that it cast doubt on Einstein's theory, and in 1998 Anderson's team reported that what was observed could not be explained by such effects as instrument error, gas clouds, the push of sunlight, or the gravitational pull of outlying comets.
Three other scientists quickly responded by suggesting other things that might explain the anomalies. Two wondered about waste heat. The Pioneers are powered by onboard nuclear generators, and they radiate a small amount of surplus heat into space. The pressure of that radiation might slow the craft down by the observed amount. The other possible explanation is that the Pioneers may be venting tiny quantities of fuel into space. Anderson thought about these explanations and found problems with them both.
The strangest feature of the observed slowing down is that it is precisely what would be predicted by an unorthodox theory sug¬gested in 1983 by Mordehai Milgrom. This theory changes not the law of gravity, but Newton's law of motion: force equals mass times acceleration. Milgrom's modification applies when the acceleration is very small, and it was introduced in order to explain another gravitational puzzle, the fact that galaxies do not rotate at the speeds predicted by either Newton or Einstein. This discrepancy is usually put down to the existence of 'cold dark matter' which exerts a grav¬itational pull but can't be seen in telescopes. If galaxies have a halo of cold dark matter then they will rotate at a speed that is inconsis¬tent with the matter in the visible portions. A lot of theorists dislike cold dark matter (because you can't observe it directly, that's what 'cold dark' means) and Milgrom's theory has slowly gained in pop¬ularity. Further studies of the Pioneers may help decide.
The other discovery is about the expansion of the universe. The universe is getting bigger, but it now seems that the very distant universe is expanding faster than it ought to. This startling result -confirmed by later, more detailed studies, comes from the Supernova Cosmology project headed by Saul Perlmutter and its arch-rival High-Z Supernova Search Team headed by Brian Schmidt. It shows up as a slight bend in a graph of how a distant supernova's apparent brightness varies with its red shift. According to General Relativity, that graph ought to be straight, but it's not. It behaves as if there is some repulsive component to gravity which only shows up at extremely long distances, say half the radius of the universe. A form of antigravity, in fact.
Curiously, Einstein originally included a repulsive force of this kind in his relativistic equations for gravity: he called it the cosmo-logical constant. Later he changed his mind and threw the cosmological constant out, complaining that he'd been foolish to include it in the first place. He died thinking it was a blemish on his record, but maybe his original intuition was spot on after all.
There is also a possible link to the other deep physical theory, quantum mechanics. At first this looked unlikely. If there is an antigravity effect, then it should stem from Vacuum energy', a form of energy that, if it exists, is stored in empty space ... (As we write this, we can picture Ridcully's expression. We shall have to ignore it. This isn't something sensible, like magic. This is science. Empty space can be full of interest.)
However, quantum theory predicts that if vacuum energy exists in today's universe, then it would produce an antigravity effect 10119 (1 followed by 119 zeros) times as big as what's observed. Although astronomers are accustomed to larger experimental errors than you find in most other sciences, this is too much for even them to swal¬low. But late in 1998 Robert Matthews wondered whether the antigravity effect might come from a relic of the vacuum energy of an earlier phase of the universe. His idea is related to a sixty-year-old piece of speculation by Paul Dirac, one of the founders of quantum theory. Dirac noticed a strange coincidence. The electro¬magnetic force between a proton and an electron is 1040 (1 followed by 40 zeros) times as great as the gravitational force between them. The age of the universe is also 1040 times as great as the time it takes light to cross one atom. It's not hard to come up with numerologi-cal accidents of this kind, but Dirac had a hunch that this one might indicate some deep connection between the expansion of the uni¬verse and the microscopic quantum realm. Now Matthews has come up with a possible explanation of the coincidence, and it fits the antigravity effect.
According to the Big Bang theory, the early history of the uni¬verse involves a number of 'phase transitions', dramatic changes of state which result in big qualitative changes in how the universe works. The earliest one occurred when the strong nuclear force sep¬arated from the electromagnetic forces and the weak nuclear force. The last in this series of phase transitions was the quark-hadron transition, in which quarks grouped together to produce the more familiar protons and neutrons. If the universe has somehow retained the vacuum energy from this phase transition, then it will exhibit an antigravity effect of just the right size. So these curious observations may be telling us something rather curious about the early universe.

ELEVEN

NEVER TRUST A CURVED UNIVERSE

PONDER STIBBONS HAD SET UP A DESK a little separate from the others and surrounded it with a lot of equipment, primarily in order to hear himself think.
Everyone knew that stars were points of light. If they weren't, some would be visibly bigger than others. Some were fainter than others, of course, but that was probably due to clouds. In any case their purpose, according to established Discworld law, was to lend a little style to the night.
And everyone knew that the natural way for things to move was in a straight line. If you dropped something, it hit the ground. It didn't curve. The water fell over the edge of the world, drifting sideways just a tiny bit to make up for the spin, but that was com¬mon sense. But inside the Project, spin was everything. Everything was bent. Archchancellor Ridcully seemed to think this was some sort of large-scale character flaw, akin to shuffling your feet or not owning up to things. You couldn't trust a universe of curves. It was¬n't playing a straight bat.
At the moment Ponder was rolling damp paper into little balls. He'd had the gardener push in a large stone ball that had spent the last few hundred years on the university's rockery, relic of some ancient siege catapult. It was about three feet across.
He'd hung some paper balls of string near it. Now, glumly, he threw others over it and around it. One or two did stick, admittedly, but only because they were damp. He was in the grip of some thought, You had to start with what you were certain of. Things fell down. Little things fell down on to big things. That was common sense.
But what would happen if you had two big things all alone in the universe?
He set up two balls of ice and rock, in an unused corner of the Project, and watched them bang into each other. Then he tried with ball of different sizes. Small ones drifted towards big ones but, oddly enough, the big ones also drifted slightly towards the small ones.
So ... if you thought that one through ... that meant that if you dropped a tennis ball to the ground it would certainly go down, but in some tiny, immeasurable way the world would, very slightly, come up.
And that was insane.
He also spent some time watching clouds of gas swirl and heat in the more distant regions of the Project. It was all so ... well, god¬less.
Ponder Stibbons was an atheist. Most wizards were. This was because UU had some quite powerful standing spells against occult interference, and knowing that you're immune from lightning bolts does wonders for an independent mind. Because the gods, of course, existed. Ponder wouldn't even attempt to deny it. He just didn't believe in them. The god currently gaining popularity was Om, who never answered prayers or manifested himself. It was easy to respect an invisible god. It was the ones that turned up every¬where, often drunk, that put people off.
That's why, hundreds of years before, philosophers had decided that there was another set of beings, the creators, that existed inde¬pendently of human belief and who had actually built the universe. They certainly couldn't have been gods of the sort you got now, who by all accounts were largely incapable of making a cup of coffee.
The universe inside the Project was hurtling through its high¬speed time and there was still nothing in there that was even vaguely homely for humans. It was all too hot or too cold or too empty or too crushed. And, distressingly, there was no sign of nar-rativium.
Admittedly, it has never been isolated on Discworld either, but its existence had long ago been inferred, as the philosopher Lye Tin Wheedle had put it: 'in the same way that milk infers cows'. It might not even have a discrete existence. It might be a particular way in which every other element spun through history, something that they had but did not actually possess, like the gleam on the skin of a polished apple. It was the glue of the universe, the frame that held all the others, the thing that told the world what it was going to be, that gave it purpose and direction. You could detect narra-tivium, in fact, by simply thinking about the world.
Without it, apparently, everything all was just balls spinning in circles, without meaning.
He doodled on the pad in front of him:
There are no turtles anywhere.
'Eat hot plasma! Oh ... sorry, sir.'
Ponder peered over his defensive screen.
'When worlds collide, young man, someone is doing something wrong!'
That was the voice of the Senior Wrangler. It sounded more petulant than usual.
Ponder went to see what was going on.

TWELVE

WHERE DO RULES COME FROM?

SOMETHING IS MAKING ROUNDWORLD DO STRANGE THINGS . . .
It seems to be obeying rules. Or maybe it's just making them up as it goes along.
Isaac Newton taught us that our universe runs on rules, and they are mathematical. In his day they were called 'laws of nature', but 'law' is too strong a word, too final, too arrogant. But it does seem that there are more or less deep patterns in how the universe works. Human beings can formulate those patterns as mathematical rules, and use the resulting descriptions to work out some aspects of nature that would otherwise be totally mysterious, and even exploit them to make tools, vehicles, technology.
Thomas Malthus changed a lot of people's minds when he found a mathematical rule for social behaviour. He said that food grows arithmetically (1-2-3-4-5), but populations grow geometri¬cally (1-2-4-8-16). Whatever the growth rates, eventually population will outstrip food supply: there are limits to growth. Malthus's law shows that there are rules Down Here as well as Up There, and it tells us that poverty is not the result of evil or sin. Rules can have deep implications.
What are rules? Do they tell us how the universe 'really' works, or do our pattern-seeking brains invent or select them?
There are two main viewpoints here. One is fundamentalist at heart, as fundamentalist as the Taliban and Southern Baptists -indeed, as fundamentalist as the exquisitor Vorbis in Small Gods who states his position thus: ' . . . that which appears to our senses is not the fundamental truth. Things that are seen and heard and done by the flesh are mere shadows of a deeper reality.'
Scientific fundamentalism holds that there is one set of rules, the Theory of Everything, which doesn't just describe nature rather well, but is nature. For about three centuries science seems to have been converging on just such a system: the deeper our theories of nature become, the simpler they become too. The philosophy behind this view is known as reductionism, and it proceeds by tak¬ing things to bits, seeing what the bits are and how they fit together, and using the bits to explain the whole. It's a very effective research strategy, and it's served us well for a long time. We've now managed to reduce our deepest theories to just two: quantum mechanics and relativity.
Quantum mechanics set out to describe the universe on very small scales, subatomic scales, but then became involved in the largest scales of all, the origin of the universe in the Big Bang. Relativity set out to describe the universe on very large scales, supergalactic ones, but then became involved in the smallest scales of all, the quantum effects of gravity. Despite this, the two theories disagree in fundamental ways about the nature of the universe and what rules it obeys. The Theory of Everything, it is hoped, will sub¬tly modify both theories in such a way that they fit seamlessly together into a unified whole, while continuing to work well in their respective domains. With everything reduced to one Ultimate Rule, reductionism will have reached the end of its quest, and the uni¬verse will be completely explained.
The extreme version of the alternative view is that there are no ultimate rules, indeed that there are no totally accurate rules either. What we call laws of nature are human approximations to regulari¬ties that crop up in certain specialized regions of the universe -chemical molecules, galaxy dynamics, whatever. There is no reason why our formulations of regularities in molecules and regularities in galaxies should be part of some deeper set of regularities that explains both, any more than chess and soccer should somehow be aspects of the same greater game. The universe could perfectly well be patterned on all levels, without there being an ultimate pattern from which all the others must logically follow. In this view, each set of rules is accompanied by a statement of which areas it can safely be used to describe, 'use these rules for molecules with fewer than a hundred atoms' or 'this rule works for galaxies provided you don't ask about the stars that make them up'. Many such rules are con¬textual rather than reductionist: they explain why things work the way they do in terms of what is outside them.
" Evolution, especially before it was interpreted through the eyes of DNA, is one of the clearest examples of this style of reasoning. Animals evolve because of the environment in which they live, including other animals. A curious feature of this viewpoint is that to a great extent the system builds its own rules, as well as obeying them. It is rather like a game of chess played with tiles that can be used to build new bits of board, upon which new kinds of chess piece can move in new ways.
Could the entire universe sometimes build its own rules as it proceeds? We've suggested as much a couple of times: here's a sense in which it might happen. It's hard to see how rules for matter could meaningfully 'exist' when there is no matter, only radiation, as there was at an early stage of the Big Bang. Fundamentalists would maintain that the rules for matter were always implicit in the Theory of Everything, and became explicit when matter appeared. We wonder whether the same 'phase transition' that created matter might also have created its rules. Physics might not be like that, but biology surely is. Before organisms appeared, there couldn't have been any rules for evolution.
For a more homely example, think of a stone rolling down a bumpy hillside, skidding on a clump of grass, bouncing wildly off bigger rocks, splashing through muddy puddles, and eventually coming to rest against the trunk of a tree. If fundamentalist reduc-tionism is right, then every aspect of the stone's movement, right down to how the blades of grass get crushed, what pattern the mud makes when it splatters, and why the tree is growing where it is any¬way, are consequences of one set of rules, that Theory of Everything. The stone 'knows' how to roll, skid, bounce, splash, and stop because the Theory of Everything tells it what to do. More than that: because the Theory of Everything is true, the stone itself is tracking through the logical consequences of those rules as it skit¬ters down the hillside. In principle you could predict that the stone would hit that particular tree, just by working out necessary conse¬quences of the Theory of Everything.
The picture of causality that this viewpoint evokes is one in which the only reasons for things to happen are because the Theory of Everything says so. The alternative is that the universe is doing whatever the universe does, and the stone is in a sense exploring the consequences of what the universe does. It doesn't 'know' that it will skid on grass until it hits some grass and finds itself skidding. It doesn't 'know' how to splash mud all over the place, but when it hits the puddle, that's what happens. And so on. Then we humans come along and look at what the stone does, and start finding pat¬terns. 'Yes, the reason it skids is because friction works like this ...' 'And the laws of fluid dynamics tell us that the mud must scatter like that...'
We know that these human-level rules are approximate descrip¬tions, because that's why we invented them. Mud is lumpy, but the rules of fluid dynamics don't take account of lumps. Friction is something rather complicated involving molecules sticking together and pulling apart again, but we can capture a lot of what it does by thinking of it as a force that opposes moving bodies when in contact with surfaces. Because our human-level theories are approximations, we get very excited when some more general prin¬ciple leads to more accurate results. We then, unless we are careful, confuse 'the new theory gives results that are closer to reality than the old' with 'the new theory's rules are closer to the real rules of the universe than the old one's rules were'. But that doesn't follow: we might be getting a more accurate description even though our rules differ from whatever the universe 'really' does. What it really does may not involve following neat, tidy rules at all.

There is a big gap between writing down a Theory of Everything and understanding its consequences. There are mathematical sys¬tems that demonstrate this point, and one of the simplest is Langton's Ant, now the small star of a computer program. The Ant wanders around on an infinite square grid. Every time it comes to a square, the square changes colour from black to white or from white to black, and if it lands on a white square then it turns right, but if it lands on a black square then it turns left. So we know the Theory of Everything for the Ant's universe, the rule that governs its complete behaviour by fixing what can happen on the small scale - and everything that happens in that universe is 'explained' by that rule.
When you set the Ant in motion, what you actually see is three separate modes of behaviour. Everybody, mathematician or not -immediately spots them. Something in our minds makes us sensi¬tive to the difference, and it's got nothing to do with the rule. It's the same rule all the time, but we see three distinct phases:

• SIMPLICITY: During the first two or three hundred moves of the Ant, starting on a completely white grid, it creates tiny little pat¬terns which are very simple and often very symmetric. And you sit there thinking 'Of course, we've got a simple rule, so that will give simple patterns, and we ought to be able to describe everything that happens in a simple way.'

• CHAOS: Then, suddenly, you notice it's not like that any more. You've got a big irregular patch of black and white squares, and the Ant is wandering around in some sort of random walk, and you can't see any structure at all. For Langton's Ant this kind of pseudo¬random motion happens for about the next 10,000 steps. So if your computer is not very fast you can sit there for a long time saying 'Nothing interesting is going to happen, it's going to go on like this forever, it's just random.' No, it's obeying the same rule as before. It's just that to us it looks random.

• EMERGENT ORDER: Finally the Ant locks into a particular kind of repetitive behaviour, and it builds a 'highway'. It goes through a cycle of 104 steps, after which it has moved out two squares diago¬nally and the shape and the colours along the edge are the same as they were at the beginning of that cycle. So that cycle repeats for¬ever, and the Ant just builds a diagonal highway, for ever.

Those three modes of activity are all consequences of the same rule, but they are on different levels from the rule itself. There are no rules that talk about highways. The highway is clearly a simple thing, but a 104-step cycle isn't a terribly obvious consequence of the rule. In fact the only way mathematicians can prove that the Ant really does build its highway is to track through those 10,000 steps. At that point you could say 'Now we understand why Langton's Ant builds a highway.' But no sooner.
However, if we ask a slightly more general question, we realize that we don't understand Langton's Ant at all. Suppose that before the Ant starts we give it an environment, we paint a few squares black. Now let's ask a simple question: does the Ant always end up building a highway? Nobody knows. All of the experiments on com¬puters suggest that it does. On the other hand, nobody can prove that it does. There might be some very strange configuration of squares, and when you start it off on that it gets triggered into some totally different behaviour. Or it could just be a much bigger high¬way. Perhaps there is a cycle of 1,349,772,115,998 steps that builds a different kind of highway, if only you start from the right thing. We don't know. So for this very simple mathematical system, with one simple rule, and a very simple question, where we know the Theory of Everything ... it doesn't tell us the answer.

Langton's Ant will be our icon for a very important idea: emergence, Simple rules may lead to large, complex patterns. The issue here is not what the universe 'really does'. It is how we understand things and how we structure them in our minds. The simple Ant and its tiled universe are technically a 'complex system' (it consists of a large number of entities that interact with each other, even though most of those entities are simply squares that change colour when an Ant walks on them).
We can create a system, and give it simple rules which 'common sense' suggests should lead to a rather dull future, and we will often find that quite complex features will result. And they will be 'emer¬gent', that is, we have no practical way of working out what they are going to be apart from ... well, watching. The Ant must dance. There are no short cuts.
Emergent phenomena, which you can't predict ahead of time, are just as causal as the non-emergent ones: they are logical conse¬quences of the rules. And you have no idea what they are going to be. A computer will not help, all it will do is run the Ant very fast.
A 'geographical' image is useful here. The 'phase space' of a sys¬tem is the space of all possible states or behaviours, all of the things that the system could do, not just what it does do. The phase space of Langton's Ant consists of all possible ways to put black and white squares on a grid, not just the ones that the Ant puts there when it follows its rules. The phase space for evolution is all con¬ceivable organisms, not just the ones that have existed so far. Discworld is one 'point' in the phase space of consistent universes. Phase spaces deal with everything that might be, not what is.
In this imagery, the features of a system are structures in phase space that give it a well-defined 'geography'. The phase space of an emergent system is indescribably complicated: a generic term for such phase spaces is 'Ant Country', which you can think of as a computational form of infinite suburbia. To understand an emergent feature you would have to find it without traversing Ant Country step by step. The same problem arises when you try to start from a Theory of Everything and work out what it implies. You may have pinned down the micro-rules, but that doesn't mean that you understand their macro-consequences. A Theory of Everything would tell you what the problem is, in precise language, but that might not help you solve it.
Suppose, for instance, that we had very accurate rules for fun¬damental particles, rules that really do govern everything about them. Despite that, it's pretty clear that those rules would not greatly help our understanding of something like economics. We want to understand someone who goes into a supermarket, buys some bananas, and pays over some money. How do we approach that from the particle rules? We have to write down an equation for every particle in the customer's body, in the bananas, in the note that passes from customer to cashier. Our description of the trans¬action, money for bananas, and our explanation of it is in terms of an incredibly complicated equation about fundamental particles.
Solving that equation is even harder. And it might not even be the only fruit they buy.
We're not saying that the universe hasn't done it that way. We're saying that even if it has, that won't help us understand anything. So there's a big, emergent gap between the Theory of Everything and its consequences.
A lot of philosophers seem to have got the idea that in an emer¬gent phenomenon the chain of causality is broken. If our thoughts are emergent properties of our brain, then to many philosophers they are not physically caused by the nerve cells, the electrical cur¬rents, and the chemicals in the brain. We don't mean that. We think it's confused nonsense. We're perfectly happy that our thoughts are caused by those physical entities, but you can't describe someone's perceptions or memory in terms of electrical currents and chemi¬cals.
Human beings never understand things that way. They under¬stand things by keeping them simple, in Archchancellor Ridcully's case, the simpler the better. A little narrativium goes a long way: the simpler the story, the better you understand it. Storytelling is the opposite of reductionism; 26 letters and some rules of grammar are no story at all.

One set of modern physical rules poses more philosophical ques¬tions than all the others combined: Quantum Mechanics. Newton's rules explained the universe in terms of force, position, speed, and the like, things that make intuitive sense to human beings and let us tell good stories. A century or so ago, however, it became clear that the universe's hidden wiring has other, less intuitive layers. Concepts such as position and speed not only ceased to be funda¬mental, they ceased to have a well defined meaning at all.
This new layer of explanation, quantum theory, tells us that on small scales the rules are random. Instead of something happening or not, it may do a bit of both. Empty space is a seething mass of potentialities, and time is something you can borrow and pay back again if you do it quickly enough for the universe not to notice. And the Heisenberg Uncertainty Principle says that if you know where something is then you can't also know how fast it's going. Ponder Stibbons would consider himself lucky if he did not have to explain this to his Archchancellor.
A thorough discussion of the quantum world would need a book all to itself, but there's one topic that benefits from some Discworld insights. This is the notorious case of the cat in the box. Quantum objects obey Schrodinger's Equation, a rule named after Erwin Schrodinger which describes how 'wave functions', waves of quantum existence, propagate through space and time. Atoms and their sub-atomic components aren't really particles: they're quan¬tum wave functions.
The early pioneers of quantum mechanics had enough problems solving Schrodinger's equation: they didn't want to worry about what it meant. So they spatchcocked together a cop-out clause, the 'Copenhagen interpretation' of quantum observations. This says that whenever you try to observe a quantum wave function it imme¬diately 'collapses' to give a single particle-like answer. This seems to promote the human mind to a special status, it has even been sug¬gested that our purpose in the universe is to observe it, thereby ensuring its existence, an idea that the wizards of UU consider to be simple common sense.
Schrodinger, however, thought this was silly, and in support he introduced a thought experiment now called Schrodinger's Cat. Imagine a box, with a lid that can be sealed so tightly that nothing, not even the barest hint of a quantum wavelet, can leak out. The box contains a radioactive atom, which at some random moment will decay and emit a particle, and a particle detector that releases poi¬son gas when it detects the atom decaying. Put the cat in the box and close the lid. Wait a bit.
Is the cat alive or dead?
If the atom has decayed, then the cat's dead. If not, it's alive. However, the box is sealed, so you can't observe what's inside. Since unobserved quantum systems are waves, the quantum rules tell us that the atom must be in a 'mixed' state, half decayed and half not. Therefore the cat, which is a collection of atoms and so can be con¬sidered as a gigantic quantum system, is also in a mixed state: half alive, half dead. In 1935 Schrodinger pointed out that cats aren't like that. Cats are macroscopic systems with classical yes/no physics. His point was that the Copenhagen interpretation does not explain, or even address, the link from microscopic quantum physics to macroscopic classical physics. The Copenhagen interpre¬tation replaces a complex physical process (which we don't understand) by a piece of magic: the wave collapses as soon as you try to observe it.
Most of the time this problem is discussed, physicists manage to turn Schrodinger's point on its head. 'No, quantum waves really are like that!' And they've done lots of experiments to prove they're right. Except... those experiments have no box, no poison gas, no alive, no dead, and no cat. What they have is quantum-scale ana¬logues, an electron for a cat, positive spin for alive and negative for dead, and a box with Chinese walls, through which anything can be observed, but you take great care not to notice.
These discussions and experiments are lies-to-children: their aim is to convince the next generation of physicists that quantum-level systems do actually behave in the bizarre way that they do. Fine ... but it's got nothing to do with cats. The wizards of Unseen University, who know nothing about electrons but have an intimate familiarity with cats, wouldn't be fooled for an instant. Neither would the witch Gytha Ogg, whose cat Greebo is shut in a box in Lords and Ladies. Greebo is the sort of cat that would take on a fero¬cious wolf and eat it. In Witches Abroad he eats a vampire by accident, and the witches can't understand why the local villagers are so ecstatic.
Greebo has his own way of handling quantum paradoxes: 'Greebo had spent an irritating two minutes in that box. Technically, a cat locked in a box may be alive or it may be dead. You never know until you look. In fact, the mere act of opening the box will determine the state of the cat, although in this case there were three determinate states the cat could be in: these being Alive, Dead, and Bloody Furious.'
Schrodinger would have applauded. He wasn't talking about quantum states: he wanted to know how they led to ordinary, clas¬sical physics in the large, and he could see that the Copenhagen interpretation didn't have anything to say about that. So how do classical yes/no answers emerge from quantum Ant Country? The closest we have to an answer is something called 'decoherence', which has been studied by a number of physicists, among them Anthony Leggett, Roland Omnes, Serge Haroche and Luis Davidovich. If you have a big collection of quantum waves and you leave it to its own devices, then the component waves get out of step and fuzz out. This is what a classical object is 'really' like from the quantum standpoint, and it means that cats do, in fact, behave like cats. Experiments show that the same is true even when the role of the detector is played by a microscopic quantum object: a photon's wave function can collapse without any observers being aware, at the time, that it has done so. Even with a quantum cat, death occurs at the instant that the detector notices that the atom has decayed. It doesn't require a mind.
In short, Archchancellor, the universe always notices the cat. And a tree in a forest does make a sound when it falls, even if no one is around. The forest is always there.

THIRTEEN

NO, IT CAN'T DO THAT

ARCHCHANCELLOR RIDCULLY LOOKED AROUND at his colleagues. They'd chosen the long table in the Great Hall for the meeting, since the HEM was getting too crowded.
'All here? Good,' he said. 'Carry on, Mister Stibbons.'
Ponder sifted through his papers.
'I've, er, asked for this meeting,' he said, 'because I'm afraid we're doing things wrong.'
'How can that be?' said the Dean. 'It's our universe!'
'Yes, Dean. And, er, no. It's made up its own rules.'
'No, no, it can't do that,' said the Archchancellor. 'We're intelli¬gent creatures. We make the rules. Lumps of rock don't make rules,'
'Not exactly', sir,' said Ponder, employing the phrase in its tradi¬tional sense of 'absolutely wrong'. 'There are some rules in the Project.'
'How? Is someone else meddling with it?' the Dean demanded. 'Has a Creator turned up?'
'An interesting thought, sir. I'm not qualified to answer that one. The point I'm trying to make is that if we want to do anything con¬structive, we've got to obey the rules.'
The Lecturer in Recent Runes looked down at the table in front of him. It had been laid for lunch.
'I don't see why,' he said. 'This knife and fork don't tell me how to eat.'
'Er ... in fact, sir, they do. In a roundabout way.'
'Are you trying to tell us that the rules are built in?' said Ridcully.
'Yes, sir. Like: big rocks are heavier than small rocks.'
'That's not a rule, man, that's just common sense!'
'Yes, sir It's just that the more I look into the Project, the more I'm not sure any more what common sense is. Sir, if we're going to build a world it has to be a ball. A big ball'
'That's a lot of outmoded religious nonsense, Mister Stibbons.'
'Yes, sir. But in the Project universe, it's real. Some of the ba ... the spheres the students have made are huge.'
'Yes, I've seen them. Showy, to my mind,'
'I was thinking of something smaller, sir. And ... and I'm pretty sure things will stay on it. I've been experimenting.'
'Experimenting?' said the Dean. 'What good does that do?'
The doors were flung open. Turnipseed, Ponder's assistant, hur¬ried across to the table in a state of some agitation.
'Mister Stibbons! HEX has found something!'
The wizards turned to stare at him. He shrugged.
'It's gold,' he said.

'The Guild of Alchemists is not going to be happy about this,' said the Senior Wrangler, as the entire faculty clustered around the project. 'You know what they are for demarcation.'
'Fair enough,' said Ridcully, steering the omniscope. 'We'll just give them a few minutes to turn up, otherwise we'll go on as we are, all right?'
'How can we get it out?' said the Dean.
Ponder looked horrified. 'Sir! This is a universe! It is not a piggy-bank! You can't just turn it upside down, stick a knife in the slot and rattle it around!'
'I don't see why not,' said Ridcully, without looking up. 'It's what people do all the time.' He adjusted the focus. 'Personally I'm glad nothing can get out of the thing, though. Call me old fash¬ioned, but I don't intend to occupy the same room as a million miles of exploding gas. What happened?'
'HEX says one of the new stars exploded.'
'They're too big to be stars, Ponder, We've been into this.'
'Yes, sir,' Ponder disagreed.
'They've only been around for five minutes.'
'A few days, sir. But millions of years in Project time. People have been dumping rubbish into it, and I think some just drifted in and ... I don't think it was a very well-made st, furnace in the first place.'
The exploding star was shrinking now, but flinging out a great halo of brilliant gases that even lit up one side of the rocky lumps the wizards had been making. Things want to come together and get big, Ponder thought. But when they're big enough, they want to explode. Another law.
'There's lead and copper here, too,' said Ridcully. 'We're in the money now, gentlemen. Except that in this universe there's nothing to spend it on. Even so, it seems we're making progress. You're looking peaky, Mister Stibbons. You ought to get some sleep.'
Progress, thought Ponder. Was that what they were making? But without narrativium, how did anything know?

It was day four. Ponder had been awake all night. He wasn't sure, but he thought he'd probably been awake the previous night, too. He may have nodded off for a while, pillowing his head on the growing pile of screwed-up pieces of paper, with the Project wink¬ing and twinkling in front of him. If so, he'd dreamed of nothing.
But he'd decided that Progress was what you made it.
After breakfast, the wizards looked at the ball which currently occupied the centre of the omniscope.
'Um, I used iron to start with,' said Ponder. 'Well, mostly iron. There's quite a lot of it about. Some of the ices are really nasty things, and rock by itself just sits there. See this one here?'
A smaller ball of rock hung in space a little way away.
'Yes, very dull,' said the Senior Wrangler. 'Why's it got holes all over it?'
'I'm afraid that when I was dropping rocks on the ball of iron there were a few that went out of control.'
'Could happen to anyone, Stibbons,' said the Archchancellor generously. 'Did you add gold?'
'Oh yes, sir. And other metals,'
'Gold does give a crust some style, I think. Are these volcanoes?'
'Sort of, sir. They are the, er, acne of young worlds. Only unlike ours, where the rock is melted in the internal magical fields gener¬ated in the sub-strata, the magma is kept molten by the heat trapped inside the sphere.'
'Very smoky atmosphere. I can hardly see anything.'
'Yes, sir.'
'Well, I don't call it much of a world,' said the Dean, sniffing. 'Practically red hot, smoke belching out everywhere ...'
'The Dean does have a point, young man,' said Ridcully. He was extra kind, just to annoy the Dean. 'It's a brave attempt, but you just seem to have made another ball.'
Ponder coughed. 'I just put this one together for demonstration purposes, sir.' He fiddled with the controls of the omniscope. The scene flickered, and changed. 'Now this,' he said, and there was a twinge of pride in his voice, 'is one I made earlier.'
They stared into the lens.
'Well? Just more smoke,' said the Dean.
'Cloud, sir, in fact,' said Ponder.
'Well, we can all make clouds of gas...’
'Er ... it's water vapour, sir,' said Ponder.
He reached over and adjusted the omniscope.
The room was filled with the roar of the biggest rainstorm of all time.

By lunchtime it was a world of ice.
'And we were doing so well,' said Ridcully.
'I can't think what went wrong,' said Ponder, wringing his hands. 'We were getting seas!'
'Can't we just warm it up?' said the Senior Wrangler.
Ponder sat down on his chair and put his head in his hands.
'Bound to cool a world down, all that rain,' said the Lecturer in Recent Runes, slowly.
'Very good ... er, rocks,' said the Dean. He patted Ponder on the back.
'Poor chap looks a bit down,' hissed the Senior Wrangler to Ridcully. 'I don't think he's been eating properly.'
'You mean ... not chewing right?'
'No eating enough, Archchancellor.'
The Dean picked up a piece of paper from Ponder's crowded desk.
'I say, look at these,' he said.
On the paper was written, in Ponder's very neat handwriting:

THE RULES
1 Things fall apart, but centres hold.
2 Everything moves in curves.
3 You get balls.
4 Big balls tell space to bend.
5 There are no turtles anywhere.
6 ... It's so depressing.

'Always been a bit of a one for rules, our Ponder,' said the Senior Wrangler.
'Number Six doesn't sound incredibly well formulated,' said Ridcully.
'You don't think he's going a bit bursar, do you?' said the Lecturer in Recent Runes.
'He always thinks everything has to mean something,' said Ridcully, who generally took the view that trying to find any deep meaning to events was like trying to find reflections in a mirror: you always succeeded, but you didn't learn anything new.
'I suppose we could simply heat the thing up,' said the Senior Wrangler.
'A sun should be easy,' said Ridcully 'A big ball of fire should be no problem to a thinking wizard.' He cracked his knuckles. 'Get some of the students to put Mister Stibbons to bed. We'll soon have his little world all warm or my name's not Mustrum Ridcully.'