The Science of Discworld I

8. WE ARE STARDUST

(or at least we went to Woodstock)

IRON'S IRON.' BUT IS IT? Or is iron made from other things?

According to Empedocles, an ancient Greek, everything in the universe was a combination of four ingredients: earth, air, fire, and water. Set light to a stick and it burns (showing that it contains fire), gives off smoke (showing that it contains air), exudes bubbly liquids (show­ing that it contains water), and leaves a dirty heap of ash behind (showing that it contains earth). As a theory, it was a bit too simple-minded to survive for long, a couple of thousand years at best. Things moved more slowly in those days, and Europe, at least, was more interested in making sure that the peasants didn't get above their station and copying out bits of the Bible by hand in as labori­ous and colourful a manner as possible.

The main technological invention to come out of the Middle Ages was a better horse collar.

Empedocles's theory was a distinct advance on its predecessors. Thales, Heraclitus, and Anaximenes all agreed that everything was made from just one basic 'principle', or element, but they dis­agreed completely about what it was. Thales reckoned it was water, Heraclitus preferred fire, and Anaximenes was willing to bet the farm on air. Empedocles was a wishy-washy synthesist who thought everyone had a valid point of view: if alive today he would definitely wear a bad tie.

The one good idea that emerged from all this was that 'elemen­tary' constituents of matter should be characterized by having simple, reliable properties. Earth was dirty, air was invisible, fire burned, and water was wet.

Aside from the superior horse collar, the medieval period did act as a breeding ground for what eventually turned into chemistry. For centuries the nascent science known as alchemy had flourished; people had discovered that some strange things happen when you mix substances together and heat them, or pour acid over them, or dissolve them in water and wait. You could get funny smells, bangs, bubbles, and liquids that changed colour. Whatever the universe was made of, you could clearly convert some of it into something else if you knew the right trick. Maybe a better word is 'spell', for alchemy was akin to magic, lots of special recipes and rituals, many of which actually worked, but no theory about how it all fitted together. The big goals of alchemy were spells, recipes, for things like the Elixir of Life, which would make you live forever, and How to Turn Lead Into Gold, which would give you lots of money to finance your immortal lifestyle. Towards the end of the Middle Ages, alchemists had been messing about for so long that they got quite good at it, and they started to notice things that didn't fit the Greeks' theory of four elements. So they introduced extra ones, like salt and sulphur, because these substances also had simple, reliable properties, different from being dirty, invisible, burning, or wet. Sulphur, for example, was combustible (though not actually hot, you understand) and salt was incombustible.

By 1661 Robert Boyle had sorted out two important distinc­tions, putting them into his book The Sceptical Chymist. The first distinction was between a chemical compound and a mixture. A mixture is just different things, well, mixed up. A compound is all the same stuff, but whatever that stuff is, it can be persuaded to come apart into components that are other kinds of stuff- provided you heat it, pour acid on it, or find some other effective treatment. What you can't do is sort through it and find a different bit; for a mixture you can, although you might need very good eyesight and tiny fingers. The second distinction was between compounds and elements. An element really is one kind of stuff: you can't separate it into different components.

Sulphur is an element. Salt, we now know, is a compound made by combining (not just mixing) the two elements sodium (a soft, inflammable metal) and chlorine (a toxic gas). Water is a compound, made from hydrogen and oxygen (both gases). Air is a mixture, containing various gases such as oxygen (an element), nitrogen (also an element), and carbon dioxide (a combination of carbon and oxy­gen). Earth is a very complicated mixture and the mix varies from place to place. Fire isn't a substance at all, but a process involving hot gases.

It took a while to sort all this out, but by 1789 Antoine Lavoisier had come up with a list of 33 elements that were a reasonable selec­tion of the ones we use today. He made a few understandable mistakes, and he included both light and heat as elements, but his approach was systematic and careful. Today we know of 112 distinct elements. A few of these are artificially produced, and several of those have existed on Earth only for the tiniest fraction of a second, but most elements on the list can be dug up, extracted from the sea or separated from the air around us. And apart from a few more artificially produced elements that it might just be possible to make in future, today's list is almost certainly complete.

It took another while for us to get that far. The art of alchemy slowly gave way to the science of chemistry. Gradually the list of accepted elements grew; occasionally it shrunk when people real­ized that a previously supposed element was actually a compound, such as Lavoisier's lime, now known to be made from the elements calcium and oxygen. The one thing that didn't change was the only thing the Greeks had got right: each element was a unique individ­ual with its own characteristic properties. Density; whether it was solid, liquid, or gas at room temperature and normal atmospheric pressure; melting point if it was solid, for each element, these quantities had definite, unvarying values. It is the same on Discworld, with its to our eyes bizarre elements such as chelonium (for making world-bearing turtles), elephantigen (ditto elephants), and narrativium, a hugely important 'element' not just for Discworld, but for understanding our own world too. The charac­teristic feature of narrativium is that it makes stories hang together. The human mind loves a good dose of narrativium.

In this universe, we began to understand why elements were unique individuals, and what distinguished them from compounds. Again the glimmerings of the right idea go back to the Greeks, with Democritus' suggestion that all matter is made from tiny indivisible particles, which he called atoms (Greek for 'not divisible')- It is unclear whether anybody, even Democritus, actually believed this in Greek times, it may just have been a clever debating point. Boyle revived the idea, suggesting that each element corresponds to a single kind of atom, whereas compounds are combinations of dif­ferent kinds of atoms. So the element oxygen is made from oxygen atoms and nothing else, the element hydrogen is made from hydro­gen atoms and nothing else, but the compound water is not made from water atoms and nothing else, it is made from atoms of hydro­gen and atoms of oxygen.

By 1807, one of the most significant steps in the development of both chemistry and physics had taken place. The Englishman John Dalton had found a way to bring a degree of order to the different atoms that made up the elements, and to transfer some of that order to compounds too. His predecessors had noticed that when ele­ments combine together to form compounds, they do so in simple and characteristic proportions. So much oxygen plus so much hydrogen makes so much water, and the proportions by weight of oxygen and hydrogen are always the same. Moreover, those propor­tions all fit together nicely if you look at other compounds involving hydrogen and other compounds involving oxygen.

Dalton realized that all this would make perfect sense if each atom of hydrogen had a fixed weight, each atom of oxygen had a fixed weight, and the weight of an oxygen atom was 16 times that of hydrogen. The evidence for this theory had to be indirect, because an atom is far too tiny for anyone to be able to weigh one, but it was extensive and compelling. And so the theory of 'atomic weight' arrived on the scene, and it let chemists list the elements in order of atomic weight.

That list begins like this (modern values for atomic weights in brackets): Hydrogen (1.00794), Helium (4.00260), Lithium (6.941), Beryllium (9.01218), Boron (10.82), Carbon (12.011), Nitrogen (14.0067), Oxygen (15.9994), Fluorine (18.998403), Neon (20.179), Sodium (22.98977). A striking feature is that the atomic weight is nearly always close to a whole number, the first exception being chlorine at 35.453. All a bit puzzling, but it was an excellent start because now people could look for other patterns and relate them to atomic weights. However, looking for patterns proved easier than finding any. The list of elements was unstructured, almost random in its properties. Mercury, the only element known to be liquid at room temperature, was a metal. (Later just one further liquid was added to the list: bromine.) There were lots of other metals like iron, copper, silver, gold, zinc, tin, each a solid and each quite dif­ferent from the others; sulphur and carbon were solid but not metallic; quite a few elements were gases. So unstructured did the list of elements seem that when a few mavericks, Johann Dobereiner, Alexandre-Emile Beguyrer de Chancourtois, John Newlands, suggested there might be some kind of order dimly vis­ible amid the muddle and mess, they were howled down.

Credit for coming up with a scheme that was basically right goes to Dimitri Mendeleev, who finished the first of a lengthy series of 'periodic charts' in 1869. His chart included 63 known elements placed in order of atomic weight. It left gaps where undiscovered elements allegedly remained to be inserted. It was 'periodic' in the sense that the properties of the elements started to repeat after a certain number of steps, the commonest being eight.

According to Mendeleev, the elements fall into families, whose members are separated by the aforementioned periods, and in each family there are systematic resemblances of physical and chemical properties. Indeed those properties vary so systematically as you run through the family that you can see clear, though not always exact, numerical patterns and progressions. The scheme works best, however, if you assume that a few elements are missing from the known list, hence the gaps. As a bonus, you can make use of those family resemblances to predict the properties of those missing elements before anybody finds them. If those predictions turn out to be correct when the missing elements are found, bingo. Mendeleev's scheme still gets modified slightly from time to time, but its main features survive: today we call it the Periodic Table of the Elements.

We now know that there is a good reason for the periodic structure that Mendeleev uncovered. It stems from the fact that atoms are not as indivisible as Democritus and Boyle thought. True, they can't be divided chemically, you can't separate an atom into component pieces by doing chemistry in a test tube, but you can 'split the atom' with apparatus that is based on physics rather than chemistry. The 'nuclear reactions' involved require much higher energy levels, per atom, than you need for chemical reactions, which is why the old-time alchemists never managed to turn lead into gold. Today, this could be done, but the cost of equipment would be enormous, and the amount of gold produced would be extremely small, so the scientists would be very much like Discworld's own alchemists, who have only found ways of turning gold into less gold.

Thanks to the efforts of the physicists, we now know that atoms are made from other, smaller particles. For a while it was thought that there were just three such particles: the neutron, the proton, and the electron. The neutron and proton have almost equal masses, while the electron is tiny in comparison; the neutron has no electrical charge, the proton has a positive charge, and the electron has a negative charge exactly opposite to that of the proton. Atoms have no overall charge, so the numbers of protons and electrons are equal. There is no such restriction on the number of neutrons. To a good approximation, you get an element's atomic weight by adding up the numbers of protons and neutrons, for example oxygen has eight of each, and 8 + 8 = 16, the atomic weight.

Atoms are incredibly small by human standards, about a hun­dred millionth of an inch (250 millionths of a centimetre) across for an atom of lead. Their constituent particles, however, are consider­ably smaller. By bouncing atoms off each other, physicists found that they behave as if the protons and neutrons occupy a tiny region in the middle, the nucleus, but the electrons are spread outside the nucleus over what, comparatively speaking, is a far bigger region. For a while, the atom was pictured as being rather like a tiny solar system, with the nucleus playing the role of the sun and the electrons orbiting it like planets. However, this model didn't work very well, for example, an electron is a moving charge, and according to classical physics a moving charge emits radiation, so the model predicted that within a split second every electron in an atom would radiate away all of its energy and spiral into the nucleus. With the kind of physics that developed from Isaac Newton's epic discoveries, atoms built like solar systems just don't work. Nevertheless, this is the public myth, the lie-to-children that auto­matically springs to mind. It is endowed with so much narrativium that we can't eradicate it.

After a lot of argument, the physicists who worked with matter on very small scales decided to hang on to the solar system model and throw away Newtonian physics, replacing it with quantum the­ory. Ironically, the solar system model of the atom still didn't work terribly well, but it survived for long enough to help get quantum theory off the ground. According to quantum theory the protons, neutrons, and electrons that make an atom don't have precise loca­tions at all, they're kind of smeared out. But you can say how much they are smeared out, and the protons and neutrons are smeared out over a tiny region near the middle of the atom, whereas the elec­trons are smeared out all over it.

Whatever the physical model, everyone agreed all along that the chemical properties of an atom depend mainly on its electrons, because the electrons are on the outside, so atoms can stick together by sharing electrons. When they stick together they form molecules, and that's chemistry. Since an atom is electrically neutral overall, the number of electrons must equal the number of protons, and it is this 'atomic number', not the atomic weight, that organizes the periodic­ities found by Mendeleev However, the atomic weight is usually about twice the atomic number, because the number of neutrons in an atom is pretty close to the number of protons for quantum rea­sons, so you get much the same ordering whichever quantity you use. Nevertheless, it is the atomic number that makes more sense of the chemistry and explains the periodicity. It turns out that period eight is indeed important, because the electrons live in a series of 'shells', like Russian dolls, one inside the other, and until you get some way up the list of elements a complete shell contains eight electrons.

Further along, the shells get bigger, so the period gets bigger too. At least, that's what Joseph (J. J.) Thompson said in 1904. The modern theory is quantum and more complicated, with far more than three 'fundamental' particles, and the calculations are much harder, but they have much the same implications. Like most sci­ence, an initially simple story became more complicated as it was developed and headed rapidly towards the Magical Event Horizon for most people.

But even the simplified story explains a lot of otherwise baffling things. For instance, if the atomic weight is the number of protons plus neutrons, how come atomic weight isn't always a whole num­ber? What about chlorine, for instance, with atomic weight 35.453? It turns out there are two different kinds of chlorine. One kind has 17 protons and 18 neutrons (and 17 electrons, naturally, the same as protons), with atomic weight 35. 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 a surface 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.