Terry Pratchett - The Science of Discworld

by Terry Pratchett

  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) indistinguish­able 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 con­sidered 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 proba­bly get a lot of exotic objects like tiny black holes, and magnetic monopoles but these will disappear pretty quickly and only conven­tional 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 sta­ble 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 reac­tions 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.[16] 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::[17] ’We are stardust. Scientists like quot­ing 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 vio­lent 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 dis­turb 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, tho­rium, 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.[18] Because many of these ele­ments 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 arrange­ments 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 some­thing 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 neu­trons. 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 configura­tions 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 asurface 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 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.

  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 anddents ... 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 Rincewind 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 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 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 ...[19]

  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 refin
ements.

  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.