The Science of Discworld Revised Edition, Page 3

  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’.4 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.

  In 2001 another team led by John Webb analysed the absorption of light from distant quasars by clouds of interstellar gas, and announced that the fine structure constant has increased by one hundred thousandth since the Big Bang. This result, if true, implies that the gravitational, weak nuclear, and strong nuclear forces have all changed over time. The work is being checked for possible systematic errors, which might produce the same observations.

  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.

  1 Or at least, less radioactive. We can but hope.

  2 He was the victim of a magical accident, which he rather enjoyed. But you know this.

  3 They say that every formula halves the sales of a popular science book. This is rubbish – if it was true, then The Emperor’s New Mind by Roger Penrose would have sold one-eighth of a copy, whereas its actual sales were in the hundreds of thousands. However, just in case there is some truth to the myth, we have adopted this way of describing the formula to double our potential sales. You all know which formula we mean. You can find it written out in symbols on page 118 of Stephen Hawking’s A Brief History of Time – so if the myth is right, he could have sold twice as many copies, which is a mindboggling thought.

  4 The fine structure constant is defined to be the square of the charge of an electron, divided by 2 times Planck’s constant times the speed of light times the permittivity of the vacuum (as a handy lie, the last term might be thought as ‘the way it reacts to an electric charge’). Thank you.

  THREE

  I KNOW MY WIZARDS

  IT DID NOT take long for the faculty to put its collective finger on the philosophical nub of the problem, vis-à-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 wizards’ 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 ceasing to exist from the present onwards. They would cease to have existed at all, because of the multidirectional collapse of the thaumic 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 brightened 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.1

  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 difficulty 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 possible. 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 observant, 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.

  1 As yet unmeasured, but believed to be faster than light owing to its ability to move so quickly out of light’s way.

  FOUR

  SCIENCE AND MAGIC

  IF WE WANTED to, we could comment on several features 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 ceremonies, in which A Royal Personage or The President pulls a big lever or pushes a big button to ‘start’ some vast monument to technology – which has been running for days behind the scenes. When Queen 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 forgotten 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 remarkable, 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 offspring by way of their genes, did better than the others. And so they prospered, and outcompeted the others, so that soon the only turtles 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.1 They were going to learn this later on. What they did know was that Up There was, in human timescales, calm, ordered, regular. And predictable, too – you could set your stone circle by it.

  All this gave rise to a general feeling that Up There was different 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 speculating 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 people who could have your tongue torn out or banish you into Lion Country for disagreeing with them, it rapidly became an enormously 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 365¼ days long. They even knew about the ‘precession 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.