Science of Discworld III

by Terry Pratchett

  3 Yes, traditionally ‘Indigo’ goes here, but that’s silly – Indigo is just another shade of blue. You could equally well insert ‘Turquoise’ between Green and Blue. Indigo was just included because seven is more mystical than six. Rewriting history, we find that we have left a place for Octarine, the Discworld’s eighth colour. Well, seventh, actually. Septarine, anyone?

  4 This is why, even today when the lustre of ‘the new mathematics’ has all but worn to dust, small children in mathematics classes spend hours drawing squiggly lines between circles containing pictures of cats to circles containing pictures of flowers, busily ‘matching’ the two sets. Neither the children nor their teachers have the foggiest idea why they are doing this. In fact they’re doing it because, decades ago, a bunch of demented educators couldn’t understand that just because something is logically prior to another, it may not be sensible to teach them in that order. Real mathematicians, who knew that you always put the roof on the house before you dug the foundation trench, looked on in bemused horror.

  5 Briefly: since the bit before the decimal point is a whole number, taking that into account multiplies the answer by aleph-zero. Now aleph-zero X aleph-zeroplex is less than or equal to aleph-zeroplex X aleph-zeroplex, which is (2 X aleph-zero)plex, which is aleph-zeroplex. OK?

  6 The proof isn’t hard, but it’s sophisticated. If you want to see it, consult a textbook on the foundations of mathematics.

  7 Curiously, it could expand to infinity in a finite time if it accelerated sufficiently rapidly. Expand by one light-year after one minute, by another light-year after half a minute, by another after a quarter of a minute … do a Zeno, and after two minutes, you have an infinite universe. But it’s not expanding that fast, and no one thinks it did so in the past, either.

  8 Actually a more sophisticated gadget called the Poincaré dodecahedral space, a slightly weird shape invented more than a century ago to show that topology is not as simple as we’d like it to be. But people understand ‘football’.

  9 Derived from a pun: m-brane for ‘membrane’. Opening up jokes about no-branes and p-branes. Oh well.

  FIFTEEN

  AUDITORS OF REALITY

  IT WAS ONE HOUR LATER. Wizards were ranged in rows across the width of the Great Hall in a variety of costumes, but mostly in what might be called Early Trouser; despite Rincewind’s view on nudity, a grubby shirt and pants would pass without comment in many ages and countries and lead to fewer arrests.

  ‘Right, then,’ said Ridcully, striding along the ranks ‘We’ve kept all this very simple so that even professors can understand! Ponder Stibbons has given all of you your tasks!’ He stopped in front of a middle-aged wizard. ‘You, sir, who are you?’

  ‘Don’t you know, sir?’ said the wizard, taken aback.

  ‘Slipped m’ mind, man!’ said Ridcully. ‘Big university, can’t be expected to recognise everyone!’

  ‘It’s Pennysmart, sir. Professor of Extreme Horticulture.’

  ‘Any good at it?’

  ‘Yes, sir!’

  ‘Any students?’

  ‘No, sir!’ said Pennysmart, looking offended.

  ‘That’s what I like to hear! And what will you be doin’ today?’

  ‘First, it appears, I shall be dropped waist-deep in a lagoon in the, the –’ he stopped, and fumbled a piece of paper out of his pocket ‘– Keeling Islands, where I shall attack the sand bottom round me with this rake,’ he held up the implement, ‘and then return here as soon as I see any humans.’

  ‘And how will you do that?’

  ‘Say aloud, “Return Me, Hex”,’ said Pennysmart, smartly.

  ‘Well done, good man,’ said the Archchancellor. He raised his voice. ‘Remember that, everyone! Exactly those words! Write them down if you can’t remember them. Hex will bring you back on the lawn outside the building. There will be hundreds of you and many of you have several tasks, so we don’t want any collisions! Now, if—’

  ‘Excuse me,’ said Pennysmart, raising a hand.

  ‘Yes?’

  ‘Why will I be standing in a lagoon flailing around with a rake, please?’

  ‘Because if you don’t do that, Darwin will tread on the dorsal spine of an extremely poisonous fish,’ said Ponder Stibbons. ‘Now—’

  ‘Excuse me again, please,’ Pennysmart said.

  ‘Yes?’

  ‘Why won’t I tread on this fish?’

  ‘Because you will be lookin’ where you are treadin’, Mr Pennysmart,’ roared Ridcully.

  But a forest of other hands had gone up. About the only wizard without a hand aloft was Rincewind, who was staring gloomily at his feet.

  ‘What’s all this about?’ said the Archchancellor, irritably.

  ‘Why have I got to move a chair six inches?’

  ‘Why have I got to fill up a hole in the middle of a prairie?’

  ‘Why have I got to hide a pair of trousers?’

  ‘Why have I got to stuff a letter box full of starved snails?’

  Ponder waved his clipboard wildly to silence the clamour.

  ‘Because otherwise Darwin would have fallen off a chair or been thrown from a horse or would have been struck by a stone hurled by a rioter or an unwise letter would have reached its destination,’ he said. ‘But there are more than two thousand tasks, so I can’t explain every one. Some of them are the start of a quite astonishing causal chain.’

  ‘We are supposed to develop questioning minds, you know,’ someone muttered.

  ‘Yes, but not regarding university policy!’ said Ridcully. ‘You all have very simple jobs to do! Gentlemen, Mr Stibbons will call out your names, and you will step smartly into the circle! Over to you, Mr Stibbons!’

  Ponder Stibbons picked up a different clipboard. He was beginning to collect clipboards. They proclaimed order in an increasingly hard-to-understand world. That’s all I’ve ever really wanted, he thought. I just want to feel that things are being ticked off properly.

  ‘Now, chaps,’ he said. ‘This should not be hard, as the Archchancellor has said. If at all possible don’t talk to anyone and don’t touch anything. In and out, that’s the ticket. I want this done fast. I have a … theory about that. So don’t waste time, wherever you go. Are we all ready? Very well … Aardvarker, Professor A …’

  One by one, with confidence or trepidation or a mixture of both, wizards stepped into Hex’s circle of light and vanished. As they did so, little pointy-hatted wizard symbols appeared at points in the tangle of lights above.

  Rincewind watched gloomily, and didn’t join in the ragged cheer as, one by one, red circles began to wink out.

  Ponder had taken him aside earlier and had explained that, since Rincewind was so experienced at this sort of thing, he was going to be given four of the most, er, interesting tasks. That was how he had put it: ‘er, interesting’. Rincewind knew all about ‘er, interesting’. There was a giant squid out there with his name on it, that’s what it meant.

  A movement at the end on the hall made him look around. It was a chest, a metal-bound box of the kind favoured by people who bury treasure, and it walked on hundreds of little pink legs. He groaned. He’d left it asleep on the wardrobe in his bedroom, with its feet in the air.

  ‘Hmm?’ he said.

  ‘Rincewind! Off you go, best of luck!’ Ponder repeated. ‘Hurry up!’

  There was nothing for it. Rincewind walked into the circle, and fell over as the ship moved gently under him.

  It was dawn, and a clammy sea mist was drifting across the deck. Rigging creaked, the water lapped far below. There was no other sound. The air smelled warm and exotic.

  There was a small cannon only a few feet away. Rincewind knew about them. He was the only wizard to have seen one, over in the Agatean Empire, where they were known as ‘Barking Dogs’. He was sure that one of the rules associated with them was ‘do not stand in front’.

  Slowly, he reached inside his shirt and pulled out his pointy hat. It was red, or rather, it was the col
our that red becomes after being washed, eaten, retrieved, scorched, buried, crushed, engulfed, washed again and wrung out far, far too often.

  No wearing of pointy hats? Were they mad? He pulled at it a bit to get it back to its comfortable shapeless shape, and put it on. That felt much better. A pointy hat meant you weren’t just anyone.

  He unrolled his instructions.

  1. Remove ball from ‘cannon’

  There was no one around. There was a stack of metal balls by the cannon. Rincewind pulled the barrel around with some effort, felt down the hole, and grunted as his fingers touched the top of another ball at the far end.

  How could he get it out? The way to get a ball out of a Barking Dog was to set a match to its tail, but Ponder had said this wasn’t an option. He cast around, and saw a bundle of tools by the stack; one was a rod with an end like a super-corkscrew.

  Carefully, he pushed it down the cannon, wincing at every clink. Twice he felt the curved springy bits engage with the ball, and twice it came away and rolled back with a thud.

  At the third attempt he was able to get the tapped ball almost out of the mouth of the barrel, and slid his fingers under it.

  Well, that wasn’t too hard, was it? He dropped it over the side, where the sea swallowed it with a ‘plomp!’

  This caused no stir anywhere. Job done, and nothing horrible had happened at all! He pulled a scrap of paper out of his pocket. It was important to get the words right.

  ‘Return—’ he began, and stopped. With a little metallic grinding noise, another ball rolled gently off the pile, across the deck, and leapt into the cannon’s mouth.

  ‘O-kay,’ said Rincewind slowly. Of course. Obviously. Why had he thought otherwise for even one second?

  Sighing, he picked up the ball grasper, rammed it down the barrel, caught the ball, and jerked it out so hard that it would have made a giveaway noise hitting the deck. Fortunately, it landed on Rincewind’s foot.

  A little metallic sound disturbed him while he was lying across the barrel making the traditional ‘gheeee’ noise of those who are screaming through clenched teeth.

  It was the noise of another cannon ball rolling across the deck. He jumped on it, picked it up, and felt a slight resistance trying to tug it out of his hands. He wrenched against the invisible force, spun around and the ball flew out of his hands and over the rail.

  This time the ‘plomp!’ caused an interrogatory mumble from below decks.

  The last remaining ball started to roll towards the cannon.

  ‘Oh no you don’t!’ snarled Rincewind, and grabbed it. Again the force tried to pull the ball away from him, but he clung on tightly.

  There was the sound of footsteps climbing stairs. Somewhere close, in the fog, someone sounded angry.

  Then in the billows in front of Rincewind there was … something. He couldn’t make out the shape, but it disturbed the fog, making an outline of sorts. It looked like—

  It let go as someone hurried closer. Rincewind growled in triumph, staggered backwards, tipped over the rail and, still clutching the cannon ball, went ‘plomp!’

  ‘Look at the red circles, sir!’ shouted Ponder.

  Erratically, in the drifting tangle of lights, the red circles were winking out. The yellow line was extending.

  ‘That’s the style, Mr Stibbons!’ the Archchancellor roared. ‘Keep pounding away!’

  Wizards were scuttling through the hall, getting fresh instructions, catching their breath and disappearing in the circle again.

  Ridcully nodded at the stretcher containing the screaming Pennysmart, as it was hurried away to the Infirmary.

  ‘Never seen that shade of purple on a leg,’ he said. ‘I told him to look where he was going. You heard me, didn’t you?’

  ‘He says he was dropped right on top of the fish,’ said Ponder. ‘I’m afraid Hex is running at the very limit of his power, sir. We’re bending an entire timeline. You’ve got to expect some accidents. A few of the returning wizards are reappearing in the fountain. We just have to accept that it’s better than them reappearing inside walls.’

  Ridcully surveyed the throng, and said: ‘Here comes one from the fountain, by the look of it …’

  Rincewind limped in, his face like thunder, water still streaming off him, with something grasped in his hands. Halfway across the hall a fish fell out of his robe, in obedience to the unbreakable laws of humour.

  He reached Ponder, and dropped the cannon ball on the floor.

  ‘Do you know how hard it is to shout underwater?’ he demanded.

  ‘But I see you were successful, Rincewind,’ said Ridcully.

  Rincewind looked up. All over the streaming lines, little pointy wizard symbols were appearing and disappearing.

  ‘No one told me it would fight back! It fought back! The cannon tried to load itself!’

  ‘Aha!’ said Ridcully. ‘The enemy is revealed! We’re nearly there! If they are breaking the—’

  ‘It was an Auditor,’ said Rincewind, flatly. ‘It was trying to be invisible but I saw it outlined in the fog.’

  Ridcully sagged a little. A certain exuberance faded from his face. He said, ‘Oh, darn,’ because an amusing misunderstanding in his youth had led him to believe that this was the worst possible word you could say.

  ‘We’ve found no evidence of them,’ said Ponder Stibbons.

  ‘Here? Did we look? We wouldn’t find any anyway, would we?’ said Ridcully. ‘They’d show up as natural forces.’

  ‘But how could they exist here? All those things work by themselves here!’

  ‘Same way we did?’ said Rincewind. ‘And they’ll meddle with anything. You know them. And they really, really hate people …’

  Auditors: personifications of things that have no personality that can be imagined. Wind and rain are animate, and thus have gods. But the personification of gravity, for example, is an Auditor or, rather Auditors. In universes that run on narrativium rather than automatic, they are the means by which the most basic things happen.

  Auditors are not only unimaginative, they find it impossible to imagine what imagination is.

  They are never found in groups of less than three, at least for long. In ones and twos they quickly develop personality traits that make them different, which to them is fatal. For an Auditor to have an opinion that differs from that of its colleagues is certain … cessation. But while individual Auditors cannot hold an opinion (because that would make them individual), Auditors as a whole certainly can, and with grim certainty they hold that the multiverse would be a lot better off with no life in it. Life gets in the way, tends to be messy, acts unpredictably and reverses entropy.

  Life, they believe, is an unwanted by-product. The multiverse would be more reliable if there wasn’t any. Unfortunately, there are rules. Gravity is not allowed to increase a millionfold and laminate all local life forms to the bedrock, highly desirable though that would appear to be. Simply mugging life forms merely walking, flying, swimming or oozing past would attract attention from higher authority, which Auditors dread.

  They are weak, not very clever and always afraid. But they can be subtle. And the wonderful thing about intelligent life, they have discovered, is that with some care it can be persuaded to destroy itself.

  SIXTEEN

  MANIFEST DESTINY

  THE WIZARDS ARE DISCOVERING THAT changing history is not so easy, even when you’ve got a time machine. The Auditors aren’t helping, but history has its own metaphorical Auditor, often called ‘historical inertia’. Inertia is the innate tendency of moving objects to continue moving along much the same track, even if you try to divert them; it is a consequence of Newton’s laws of motion. Historical inertia has a similar effect but a different cause: changing a single historical event, however important it may appear, may have no significant effect on the social context that directs the path of history.

  Imagine we’ve got a time machine, and go back to the past. Not too far, just to the assassination of Abraham
Lincoln. In our history, the President lived till the following morning, so a tiny deflection of the assassin’s bullet could make all the difference. So we arrange a small deflection, and he is hit but recovers, with no noticeable brain damage. He cuts a couple of appointments while he recuperates, and then he goes on to do … what?

  We don’t know anything about that new version of history.

  Or do we? Of course we do. He doesn’t turn into a hippopotamus, for a start, or a Ford Model T. Or disappear. He goes on being President Abraham Lincoln, hedged in by all the political expediencies and impossibilities that existed in our version of history and still exist in his.

  The counterfactual1 scenario of a live Lincoln raises many questions. How much do you think being the American President is like driving a car, going where you want to? Or sitting in a train, observing the terrain that others drive you through?

  Somewhere in between, no doubt.

  Ordinarily, we don’t have to think much about counterfactuals, precisely because they are contrary to fact. But mathematicians think about them all the time – ‘if what I think happens is wrong, what can I deduce that might prove it wrong?’ Any consideration of phase spaces automatically gets tangled up in worlds of if. You don’t really understand history unless you can take a stab at what might have happened if some major historical event had not occurred. That’s a good way to appreciate the significance of that event, for a start.