The Science of Discworld Read online

  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 elements?

  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 explosions — 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, stable universe of Discworld.

  Silicon might also be able to do this, but nowhere near as readily; if you want other exotic lifeforms you have to start thinking in terms of organized vortices in the upper reaches of a sun, weird quantum assemblages in interstellar plasma, or completely implausible creatures based on non-material concepts such as information, thought, or narrativium. DNA is a different matter entirely: you could surely base lifeforms on other carbon-rich molecules. We can do it now, in laboratories, with minor variants of DNA. See Evolving the Alien by Jack Cohen and Ian Stewart.

  Ask Mummy or Daddy, if you have no idea what we’re talking about.

  There also ought to be 'Population III' stars, older than Population II and consisting entirely of hydrogen and helium. These would explain the occurrence of some heavy elements in Population II. However, nobody has ever confirmed finding a Population III star, though a whole group of them may have been sighted in 2001, in two tiny red patches in the galaxy cluster Abell 2218. These patches are highly magnified images of the same region of space: the two images, and the magnification, result from gravitational lensing, without which the stars would not have been visible at all. A recent, competing theory removes the need for Population III stars altogether. Instead, very soon after the Big Bang there were heavy elements around, even before any stars formed. So when the first stars condensed, they already were Population II. This contradicts what we say in the main text — lies-to-children, of course.

  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 universe 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 dreadful 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 expanding 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 argument 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 multitudinous 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 surprisingly 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 usually 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 Rince
wind and Twoflower do in The Colour of Magic, and watch stuff disappearing over it in Rimfall: 'The roaring 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 Circumfence, 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 indubitably 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 difference. 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 distance 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 scholars worked backwards from the answer.

  It is here that we encounter another feature of scientific reasoning. 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 distance 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 subjecting 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 surprisingly 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 circles whose centres rotated round other circles whose centres rotated round ...

  Isaac Newton replaced this theory, and its more accurate successors, 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 fullness 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 predicted. 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 relative', 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 forwards, 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-breaking paper on diffusion. A lot of other people — among them the Dutch physicist Hendrik Lorentz and the French mathematician Henri Poincaré — were working on the same idea, becau
se 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 predicted) is only the tiniest fraction of a second.