The Science of Discworld

by Terry Pratchett

  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 presentation.' 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'm against 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 himself. There was no point in telling your bosses everything; they were busy men, they didn't want explanations. There was no point in burdening 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 terminal 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 hopelessness 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 backwards.

  '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 mountains 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 contracted 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 shouting 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.

  Wizard or 'Real' Squash bears very little relationship to the high speed sweat bath played elsewhere. Wizards see no point in moving fast. The ball is lobbed lazily. Certain magical inconsistencies are built into the floor and walls, however, so that the wall a ball hits is not necessarily the wall it rebounds from. This was one of the factors which, Ponder Stibbons realized some time afterwords, he really ought to have taken into consideration. Nothing excites a magical particle like meeting itself coming the other way.

  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 beryllium, 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 quantity 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 orangutan 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, multiplied by the speed of light and then multiplied by the speed of light again. As Einstein had immediately noticed, light is so fast it doesn'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 application 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 uranium-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 experiment 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 planet.

  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 reactor'. 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 universe rely on those numbers having been the same; if they used to be different, we don't know what numbers to put into the calculations. 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 development 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.