Terry Pratchett - The Science of Discworld

by Terry Pratchett

  In fact, the Dean’s mis-designed sun might have done us some good after all ...

  The Moon affects life on Earth in at least two or three ways that we know of, probably dozens more that we haven’t yet appreciated.

  The most obvious effect of the Moon on the Earth is the tides -a fact that the wizards are stumbling towards. Like most of science, the story of the tides is not entirely straightforward, and only loosely connected to what common sense, left to its own devices, would lead us to expect. The common sense bit is that the Moon’s gravity pulls at the Earth, and it pulls more strongly on the bit that is closest to the Moon. When that bit is land, nothing much hap­pens, but when it’s water - and more than half our planet’s surface is ocean - it can pile up. This explanation is a lie-to-children, and it doesn’t agree with what actually happens. It leads us to expect that at any given place on Earth, high tide occurs when the Moon is overhead, or at least at its highest point in the sky. That would lead to one high tide every day - or, allowing for a little complexity in the Earth-Moon system, one high tide every 24 hours 50 minutes.

  Actually, high tides occur twice a day, 12 hours and 25 minutes apart. Exactly half the figure.

  Not only that: the pull of the Moon’s gravity at the surface of the Earth is only one ten millionth of the Earth’s surface gravity; the pull of the Sun is about half that. Even when combined together, these two forces are not strong enough to lift masses of water through heights of up to 70 feet (21m)- the biggest tidal move­ment on Earth, occurring in the Bay of Fundy between Nova Scotia and New Brunswick.

  An acceptable explanation of the tides eluded humanity until Isaac Newton worked out the law of gravity and did the necessary calculations. His ideas have since been refined and improved, but he had the basics.

  For simplicity, ignore everything except the Earth and the Moon, and assume that the Earth is completely made of water. The watery Earth spins on its axis, so it is subjected to centrifugal force and bulges slightly at the equator. Two other forces act on it: the Earth’s gravity and the Moon’s. The shape that the water takes up in response to these forces depends on the fact that water is a fluid. In normal circumstances, the surface of a standing body of water is horizontal, because if it wasn’t, then the fluid on the higher bits would slosh sideways into the lower bits. The same kind of thing happens when there are extra forces acting: the surface of the water settles at right angles to the net direction of the combined forces.

  When you work out the details for the three forces we’ve just mentioned, you find that the water forms an ellipsoid, a shape that is close to a sphere but very slightly elongated. The direction of elongation points towards the Moon. However, the centre of the ellipsoid coincides with the centre of the Earth, so the water ’piles up’ on the side furthest from the Moon as well as on the side near­est it. This change of shape is only partly caused by the Moon’s gravity ’lifting’ the water closest to it. Most of the motion, in fact, is sideways rather than upwards. The sideways forces push more water into some regions of the oceans, and take it away from others. The total effect is tiny - the surface of the sea rises and falls through a distance of 18 inches (half a metre).

  The coast, where land meets sea, is what creates the big tidal movements. Most of the water is moving sideways (not up) and its motion is affected by the shape of the coastline. In some places the water flows into a narrowing funnel, and then it piles up much more than it does elsewhere. This is what happens in the Bay of Fundy. This effect is made even bigger because coastal waters are shallow, so the energy of the moving water gets concentrated into a thinner layer, creating bigger and faster movements.

  Finally, let’s put the sun back. This has the same kind of effect as the Moon, but smaller. When Sun and Moon are aligned - either both on the same side of the Earth, in which case we see a new moon, or both on opposite sides (full moon) - their gravitational pulls reinforce each other, leading to so-called ’spring tides’ in which high tide is higher than normal and low tide is lower. These have nothing to do with the season Spring. When the Sun and Moon are at right angles as seen from Earth, at half moon, the Sun’s pull cancels out part of the Moon’s, leading to ’neap tides’ with less movement than normal (these presumably have nothing to do with the season Neap ...).

  By putting all these effects together, and keeping good records of past tides, it is possible to predict the times of high and low tide, and the amount of vertical movement, anywhere on Earth.

  There are similar tidal effects (large) on the Earth’s atmosphere, and (small) on the planet’s land masses. Tidal effects occur on other bodies in the solar system, and beyond. It is thought that Jupiter’s moon lo, whose surface is mostly sulphur and which has numerous active volcanoes, is heated by being ’squeezed’ repeatedly by tidal effects from Jupiter.

  Another effect of the Moon on the Earth, discovered in the mid-’90s by Jaques Laskar, is to stabilize the Earth’s axis. The Earth spins like a top, and at any given moment there is a line running through the centre of the Earth around which everything else rotates. This is its axis. The Earth’s axis is tilted relative to the plane in which the Earth orbits the Sun, and this tilt is what causes the seasons. Sometimes the north pole is closer to the sun than the south pole is, and six months later it’s the other way round. When the northern end of the axis is tilted towards the Sun, more sunlight falls on the northern half of the planet than on the southern half, so the north gets summer and the south gets winter. Six months later, when the axis points the other way relative to the sun, the reverse applies.

  Over longer periods of time, the axis changes direction. Just as a top wobbles when it spins, so does the Earth, and over 26,000 years its axis completes one full circle of wobble. At every stage, however, the axis is tilted at the same angle (23°) away from the perpendicu­lar to the orbital plane. This motion is called precession, and it has a small effect on the timing of the seasons - they slowly shift by a total of one year in 26,000. Harmless, basically. However, the axes of most other planets do something far more drastic: they change their angle to the orbital plane. Mars, for example, probably changes this angle by 90° over a period of 10-20 million years. This has a dramatic effect on climate.

  Suppose that a planet’s axis is at right angles to the orbital plane. Then there are no seasonal variations at all, but everywhere except the poles there is a day/night cycle, with equal amounts of day and night. Now tilt the axis a little: seasonal variations appear, and the days are longer in summer and shorter in winter. Suppose that the axis tilts 90°, so that at some instant the north pole, say, points directly at the sun. Half a year later, the south pole points at the Sun. At either pole, there is a ’day’ of half a year followed by a ’night’ of half a year. The seasons coincide with the day/night cycle. Regions of the planet bake in high heat for half a year, then freeze for the other half. Although life can survive in such circum­stances, it may be harder for it to get going in the first place, and it may be more vulnerable to extremes of climate, vulcanism, or meterorite impacts.

  The Earth’s axis can change its angle of tilt over very long peri­ods of time, much longer than the 26,000 year cycle of precession, but even over hundreds of millions of years the angle doesn’t change much. Why? Because, as Laskar discovered when he did the calculations, the Moon helps keep the Earth’s axis steady. So it is at least conceivable that life on Earth owes quite a lot to the calming influence of its sister world, however much it may madden us indi­vidually.

  A third influence of the Moon was discovered in 1998: a clear association between tides and the rate of growth of trees. Ernst Ziircher and Maria-Giulia Cantiani measured the diameters of young spruce trees grown in containers in the dark. Over periods of several days the diameters changed in step with the tides. The sci­entists interpret this as an effect of the Moon’s gravity on the transport of water within the tree. It can’t be variations in moon­light, which would perhaps affect photosynthesis, because the trees were grown in dar
kness. But the effect may be similar to one that occurs with creatures that live on the seashore. Because they evolved to live there, they have to respond to the tides, and evolu­tion sometimes achieves this by creating an internal dynamic that runs in step with the tides. If you remove the creatures to the labo­ratory, this internal dynamic makes them continue to ’follow’ the tides.

  The Moon has been important in another way. The Babylonians and Greeks knew that the Moon is a sphere; the phases are obvious, and there is also a slight wobble which means that, over time, humans see rather more than one half of the Moon’s surface. There it was, hanging in the sky - a big ball, not a disc like the sun, and a hint that perhaps ’big balls in space’ is a much better way of think­ing about the Earth and its neighbours than ’lights in the sky’.

  All this is a long way from lance-constable Angua ­even a long way from the female menstrual cycle. But it shows how much we are creatures of the universe. Things Up There really do affect us Down Here, every day of our lives.

  TWENTY-ONE

  THE LIGHT YOU SEE THE DARK BY

  THERE WAS NO DARK. This came as such a shock to Ponder Stibbons that he made HEX look again. There had to be Dark, surely? Otherwise, what was there for the light to show up against?

  Eventually, he reported this lack to the other wizards.

  ’There should be lots of Dark and there isn’t,’ he said flatly. There’s just Light and ... no light. And it’s a pretty strange light, too.’

  ’In what way?’ said the Archchancellor.

  ’Well, sir, as you know,[25] there’s ordinary light, which travels at about the same speed as sound . . . ’

  ’That’s right. You’ve only got to watch shadows across a land­scape to realize that.’

  ’Quite, sir ... and then there’s meta-light, which doesn’t really travel at all because it is already everywhere.’

  ’Otherwise we wouldn’t even be able to see darkness,’ said the Senior Wrangler.

  ’Exactly. But the Project universe has just got the one sort of light. HEX thinks it moves at hundreds of thousands of miles a sec­ond.’

  ’What use is that?’

  ’Er . . . in this universe, that’s as fast as you can go.’

  ’That’s nonsense, because -’ Ridcully began, but Ponder held up a hand. He had not been looking forward to this one.

  ’Please, Archchancellor. It’s doing the best it can. Just trust me on this one. Please? Yes, I can see all the reasons why it’s impossi­ble. But, in there, it seems to work. HEX has written pages of stuff about it, if anyone’s interested. Just don’t ask me about any of it. Please, gentlemen? It’s all supposed to be logical but you’ll find your brain squeaking around until the ends point out of your ears.’

  He placed his hands together and tried to look wise.

  ’It really is almost as if the Project is aping the real universe -’ ’Ook.’

  ’I beg your pardon,’ said Ponder. ’A figure of speech.’

  The Librarian nodded at him and knuckled his way across the floor. The wizards watched him carefully.

  ’You really believe that that thing,’ said the Dean, pointing, ’with its moon-hating water and worlds that go around suns -’

  ’As far as I can see from this,’ interrupted the Senior Wrangler, who’d been reading HEX’s write-out on the more complex physics of the Project, ’if you were travelling in a cart at the speed of light, and threw a ball ahead of you ...’ he turned over the page, read on silently for a moment, creased his brows, turned the page over to see if any enlightenment was to be found on the other side, and went on ’... your twin brother would ... be fifty years older than you when you got home ... I think.’

  ’Twins are the same age,’ said the Dean, coldly. ’That’s why they are twins.’

  ’Look at the world we’re working on, sir,’ said Ponder. ’It could be thought of as two turtle shells tied together. It’s got no top and bottom but if you think of it as two worlds, bent around, with one sun and moon doing the work of two ... it’s similar.’

  He fried in their gaze.

  ’In a way, anyway,’ he said.

  Unnoticed by the others, the Bursar picked up the write-out on the physics of the Roundworld universe. After making himself a paper hat out of the title page, he began to read ...

  TWENTY-TWO

  THINGS THAT AREN’T

  LIGHT HAS A SPEED - SO WHY NOT DARK?

  It’s a reasonable question. Let’s see where it leads. In the 1960s a biological supply company advertised a device for scientists who used micro­scopes. In order to see things under a microscope, it’s often a good idea to make a very thin slice of whatever it is you’re going to look at. Then you put the slice on a glass slide, stick it under the microscope lens, and peer in at the other end to see what it looks like. How do you make the slice? Not like slicing bread. The thing you want to cut - let’s assume it’s a piece of liver for the sake of argument - is too floppy to be sliced on its own.

  Come to think of it, so is a lot of bread.

  You have to hold the liver firmly while you’re cutting it, so you embed it in a block of wax. Then you use a gadget called a micro­tome, something like a miniature bacon-slicer, to cut off a series of very thin slices. You drop them on the surface of warm water, stick some on to a microscope slide, dissolve away the wax, and prepare the slide for viewing. Simple . . .

  But the device that the company was selling wasn’t a microtome: it was something to keep the wax block cool while the microtome was slicing it, so that the heat generated by the friction would not make the wax difficult to slice and damage delicate details of the specimen.

  Their solution to this problem was a large concave (dish-shaped) mirror. You were supposed to build a little pile of ice cubes and ’focus the cold’ on to your specimen.

  Perhaps you don’t see anything remarkable here. In that case you probably speak of the ’spread of ignorance’, and draw the curtains in the evening to ’keep the cold out’ - and the darkness.[26]

  In Discworld, such things make sense. Lots of things are real in Discworld while being mere abstractions in ours. Death, for exam­ple. And Dark. On Discworld you can worry about the speed of Dark, and how it can get out of the way of the light that is plough­ing into it at 600 mph.[27] In our world such a concept is called a ’privative’ - an absence of something. And in our world, privatives don’t have their own existence. Knowledge does exist, but igno­rance doesn’t; heat and light exist, but cold and darkness don’t. Not as things.

  We can see the Archchancellor looking puzzled, and we realize that here is something that runs quite deep in the human psyche. Yes, you can freeze to death, and ’cold’ is a good word for describ­ing the absence of heat. Without privatives, we would end up talking like the pod people from the Planet Zog. But we run into trouble, though, if we forget that we’re using them as an easy short­hand.

  In our world there are plenty of borderline cases. Is ’drunk’ or ’sober’ the privative? In Discworld you can get ’knurd’, which is as far on the other side of sober as drunk is on the inebriated side,[28] but on planet Earth there’s no such thing. By and large, we think we know which member of such a pairing has an existence, and which is merely an absence. (We vote for ’sober’ as the privative. It is the absence of drink, and - usually - the normal state of a person.[29] In fact that normal state is only called sobriety when the subject of drink is at hand. There’s nothing strange about this. ’Cold’ is the normal state of the universe, after all, even though as a thing it does not exist. Er ... we’re not going to get past you on this one, are we, Archchancellor?)

  Thinking is required if our language isn’t to fool us. However, as ’focusing the cold’ shows, we sometimes don’t stop to think.

  We’ve done it before. At the start of the book, we mentioned phlogiston, considered by early chemists to be the substance that made things burn. It must do: you could see the phlogiston coming out as flames, for goodness’ sake. Gradu
ally, however, clues that supported the opposite view accumulated. Things weigh more after they’ve burned than they did before, for instance, so phlogiston seemed to have negative weight. You may think this is wrong, inci­dentally; surely the ash left by a burnt log weighs a lot less than the log, otherwise nobody would bother having bonfires? But a lot of that log goes up in smoke, and the smoke weighs quite a bit; it rises not because it’s lighter than air but because it’s hot. And even if it were lighter than air, air has weight, too. And as well as the smoke, there’s steam, and all sorts of other junk. If you burn a lump of wood, and collect all the liquids, gases, and solids that result, the final total weighs more than the wood.

  Where does the extra weight come from? Well, if you take the trouble to weigh the air that surrounds the burning wood, you’ll find that it ends up lighter than it was. (It’s not so easy to do both of these weighings while keeping track of what came from where -think about it. But the chemists found ways to achieve this.) So it looks as if something gets taken out of the air, and once you’re real­ized that’s what’s going on, it’s not hard to find out what it is. Of course, it’s oxygen. Burnt wood gains oxygen, it doesn’t lose phlo­giston.

  This all makes far more sense, and it also explains why phlogis­ton wasn’t such a silly idea. Negative oxygen, oxygen that ought to be present but isn’t, behaves just as nicely as positive oxygen in all the balancing equations that chemists used to check the validity of their theories. So much phlogiston moving from A to B has exactly the same effect on observations as the same amount of oxygen mov­ing from B to A. So phlogiston behaved just like a real thing - with that embarrassing exception that when your measurements became accurate enough to detect the tiny amounts involved, phlogiston weighed less than nothing. Phlogiston was a privative.