The Magic of Reality Read online

  I find this a rather disappointing myth, because it already assumes that there will be a winter and summer, and explains only how many months each will last. The Greek myth of Persephone is better in this respect at least.

  Persephone was the daughter of the chief god Zeus. Her mother was Demeter, fertility goddess of the Earth and the harvest. Persephone was greatly loved by Demeter, whom she helped in looking after the crops. But Hades, god of the underworld, home of the dead, loved Persephone too. One day, when she was playing in a flowery meadow, a great chasm opened up and Hades appeared from below in his chariot; seizing Persephone, he carried her down and made her the queen of his dark, underground kingdom. Demeter was so grief-stricken at the loss of her beloved daughter that she stopped the plants growing, and people began to starve. Eventually Zeus sent Hermes, the gods’ messenger, down to the underworld to fetch Persephone back up to the land of the living and the light. Unfortunately, it turned out that Persephone had eaten six pomegranate seeds while in the underworld, and this meant (by the kind of logic we have become used to where myths are concerned) that she had to go back to the underworld for six months (one for each pomegranate seed) in every year. So Persephone lives above ground for part of the year, beginning in the spring and continuing through summer. During this time, plants flourish and all is merry. But during the winter, when she has to return to Hades because she ate those pesky pomegranate seeds, the ground is cold and barren and nothing grows.

  What really changes day to night, winter to summer?

  Whenever things change rhythmically with great precision, scientists suspect that either something is swinging like a pendulum or something is rotating: going round and round. In the case of our daily and seasonal rhythms, it’s the second. The seasonal rhythm is explained by the yearly orbiting of the Earth around the sun, at a distance of about 93 million miles. And the daily rhythm is explained by the Earth’s spinning round and round like a top.

  The illusion that the sun moves across the sky is just that – an illusion. It’s the illusion of relative movement. You will have met the same kind of illusion often enough. You are in a train, standing at a station next to another train. Suddenly you seem to start ‘moving’. But then you realize that you aren’t actually moving at all. It is the second train that is moving, in the opposite direction. I remember being intrigued by the illusion the first time I travelled in a train. (I must have been very young, because I also remember another thing I got wrong on that first train journey. While we were waiting on the platform, my parents kept saying things like ‘Our train will be coming soon’ and ‘Here comes our train’, and then ‘This is our train now’. I was thrilled to get on it because this was our train. I walked up and down the corridor, marvelling at everything, and very proud because I thought we owned every bit of it.)

  The illusion of relative movement works the other way, too. You think the other train has moved, only to discover that it is your own train that is moving. It can be hard to tell the difference between apparent movement and real movement. It’s easy if your train starts with a jolt, of course, but not if your train moves very smoothly. When your train overtakes a slightly slower train, you can sometimes fool yourself into thinking your train is still and the other train is moving slowly backwards.

  It’s the same with the sun and the Earth. The sun is not really moving across our sky from east to west. What is really happening is that the Earth, like almost everything in the universe (including the sun itself, by the way, but we can ignore that), is spinning round and round. Technically we say the Earth is spinning on its ‘axis’: you can think of the axis as a bit like an axle running right through the globe from North Pole to South Pole. The sun stays almost still relative to the Earth (not relative to other things in the universe, but I am just going to write about how it seems to us here, on Earth). We spin too smoothly to feel the movement, and the air we breathe spins with us. If it didn’t, we would feel it as a mighty rushing wind, because we spin at a thousand miles an hour. At least, that is the spin speed at the equator; obviously we spin more slowly as we approach the North or South Pole because the ground we’re standing on has less far to go to complete a circuit round the axis. Since we can’t feel the spinning of the planet, and the air spins with us, it’s like the case of the two trains. The only way we can tell we are moving is to look at objects that are not spinning with us: objects like the stars and the sun. What we see is the relative movement, and – just as with the trains – it looks as though we are standing still and the stars and the sun are moving across our sky.

  A famous thinker called Wittgenstein once asked a friend and pupil called Elizabeth Anscombe,

  ‘Why do people say it was natural to think that the sun went round the Earth rather than that the Earth turned on its axis?’

  Miss Anscombe answered,

  ‘I suppose because it looked as if the sun went round the Earth.’

  ‘Well,’ Wittgenstein replied, ‘what would it have looked like if it had looked as if the Earth turned on its axis?’

  You try and answer that!

  If the Earth is spinning at a thousand miles an hour, why, when we jump straight up in the air, don’t we come down in a different place? Well, when you are on a train travelling at 100 mph, you can jump up in the air and you still land in the same place on the train. You can think of yourself as being hurled forwards by the train as you jump, but it doesn’t feel like that because everything else is moving forwards at the same rate. You can throw a ball straight up on a train and it comes straight down again. You can play a perfectly good game of ping-pong on a train, so long as it is travelling smoothly and not accelerating or decelerating or going fast around a corner. (But only in an enclosed carriage. If you tried to play ping-pong on an open truck the ball would blow away. This is because the air comes with you in an enclosed carriage, but not when you are standing on an open truck.) When you are travelling at a steady rate in an enclosed railway carriage, no matter how fast, you might as well be standing stock still as far as ping-pong, or anything else that happens on the train, is concerned. However, if the train is speeding up (or slowing down), and you jump up in the air, you will come down in a different place! And a game of ping-pong on an accelerating or decelerating or turning train would be a strange game, even though the air inside the carriage is dead still relative to the carriage. We’ll come back to this later, in connection with what it is like when you throw things about in an orbiting space station.

  Working round the clock – and the calendar

  Night gives way to day, and day gives way to night, as the part of the world we happen to be standing on spins to face the sun, or spins into the shade. But almost as dramatic, at least for those of us who live far from the equator, is the seasonal change from short nights and long, hot days in summer to long nights and short, cold days in winter.

  The difference between night and day is dramatic – so dramatic that most species of animal can thrive either in the day or in the night but not both. They usually sleep during their ‘off’ period. Humans and most birds sleep by night and work at the business of living during the day. Hedgehogs and jaguars and many other mammals work by night and sleep by day.

  In the same way, animals have different ways of coping with the change between winter and summer. Lots of mammals grow a thick, shaggy coat for the winter, then shed it in spring. Many birds, and mammals too, migrate, sometimes huge distances, to spend the winter closer to the equator, then migrate back to the high latitudes (the far north or far south) for the summer, where the long days and short nights provide bumper feeding. A seabird called the Arctic tern carries this to an extreme. Arctic terns spend the northern summer in the Arctic. Then, in the northern autumn, they migrate south – but they don’t stop in the tropics, they go all the way to the Antarctic. Books sometimes describe the Antarctic as the ‘wintering grounds’ of the Arctic tern, but of course that’s nonsense: by the time they get to the Antarctic it is the southern summer. The
Arctic tern migrates so far that it gets two summers: it has no ‘wintering grounds’ because it has no winter. I’m reminded of the joking remark of a friend of mine who lived in England during the summer, and went to tropical Africa to ‘tough out the winter’!

  Another way some animals avoid the winter is to sleep through it. It’s called ‘hibernation’, from hibernus, the Latin word for ‘wintry’. Bears and ground squirrels are among the many mammals, and quite a lot of other kinds of animals, that hibernate. Some animals sleep continuously through the whole winter; some sleep for most of the time, occasionally stirring into sluggish activity and then sleeping again. Usually their body temperature drops dramatically during hibernation and everything inside them slows down almost to a stop: their internal engines just barely tick over. There’s even a frog in Alaska which goes so far as to freeze solid in a block of ice, thawing out and coming to life again in the spring.

  Even those animals, like us, that don’t hibernate or migrate to avoid the winter have to adapt to the changing seasons. Leaves sprout in spring and fall in autumn (which is why it’s called the ‘fall’ in America), so trees that are a lush green in summer become gaunt and bare in winter. Lambs are born in spring, so they get the benefit of warm temperatures and new grass as they are growing. We may not grow long, woolly coats in winter, but we often wear them.

  So we can’t ignore the changing seasons, but do we understand them? Many people don’t. There are even some people who don’t understand that the Earth takes a year to orbit the sun – indeed, that’s what a year is! According to a poll, 19 per cent of British people think it takes a month, and similar percentages have been found in other European countries.

  Even among those who understand what a year means, there are many who think the Earth is closer to the sun in summer, more distant in winter. Tell that to an Australian, barbecuing Christmas dinner in a bikini on a baking hot beach! The moment you remember that in the southern hemisphere December is midsummer and June is midwinter, you realize that the seasons can’t be caused by changes in how close the Earth is to the sun. There has to be another explanation.

  We can’t get very far with that explanation until we have looked at what makes heavenly bodies orbit other heavenly bodies in the first place. So that’s what we’ll do next.

  Into orbit

  Why do the planets stay in orbit around the sun? Why does anything stay in orbit around anything else? This was first understood in the seventeenth century by Sir Isaac Newton, one of the greatest scientists who ever lived. Newton showed that all orbits were controlled by gravity – the same force of gravity that pulls falling apples towards the ground, but on a larger scale. (Alas, the story that Newton got the idea when an apple bounced off his head is probably not really true.)

  Newton imagined a cannon on top of a very high mountain, with its barrel pointing horizontally out to sea (the mountain is on the coast). Each ball it fires seems to start off moving horizontally, but at the same time it is falling towards the sea. The combination of motion out over the sea and falling towards the sea results in a graceful downward curve, culminating in a splash. It is important to understand that the ball is falling all the time, even on the earlier, flatter part of the curve. It’s not that it travels flat horizontally for a while, then suddenly changes its mind like a cartoon character who realizes he ought to be falling and therefore starts doing so!

  The cannonball starts falling the moment it leaves the gun, but you don’t see the falling as downward motion because the ball is moving (nearly) horizontally as well, and quite fast.

  Now let’s make our cannon bigger and stronger, so that the cannonball travels many miles before it finally splashes into the sea. There is still a downward curve, but it’s a very gradual, very ‘flat’ curve. The direction of travel is pretty nearly horizontal for quite a lot of the way, but nevertheless it is still falling the whole time.

  Let’s carry on imagining a bigger and bigger cannon, more and more powerful: so powerful that the ball travels a really long way before it goes into the sea. Now the curvature of the Earth starts to make itself felt. The ball is still ‘falling’ the whole time, but because the planet’s surface is curved, ‘horizontal’ now starts to mean something a bit odd. The cannonball still follows a graceful curve, as before. But as it slowly curves towards the sea, the sea curves away from it because the planet is round. So it takes even longer for the cannonball finally to splash down into the sea. It is still falling all the time, but it is falling around the planet.

  You can see the way the argument is going. We now imagine a cannon so powerful that the ball keeps going all the way around the Earth till it arrives back where it started. It is still ‘falling’, but the curve of its fall is matched by the curvature of the Earth so that it goes right round the planet without getting any closer to the sea. It is now in orbit and it will keep on orbiting the Earth for an indefinite time, assuming that there is no air resistance to slow it down (which in reality there would be). It will still be ‘falling’, but the graceful curve of its prolonged fall will go all around the Earth, and around again and again. It will behave just like a miniature moon. In fact, that is what satellites are – artificial ‘moons’. They are all ‘falling’ but they never actually come down. The ones that are used for relaying long-distance telephone calls or television signals are in a special orbit called a geostationary orbit. This means that the rate at which they go around the Earth has been cunningly arranged so that it is exactly the same as the rate at which the Earth spins on its own axis: that is, they orbit the Earth once every 24 hours. This means, if you think about it, that they are always hovering above exactly the same spot on the Earth’s surface. That is why you can aim your satellite dish precisely at the particular satellite that is beaming down the television signal.

  When an object, such as a space station, is in orbit, it is ‘falling’ the whole time, and all the objects in the space station, whether we think of them as light or heavy, are falling at the same rate. This is a good place to stop a moment and explain the difference between mass and weight, as I promised to do back in the previous chapter.

  All objects in an orbiting space station are weightless. But they are not massless. Their mass, as we saw in that chapter, depends on the number of protons and neutrons they contain. Weight is the pull of gravity on your mass. On Earth we can use weight to measure mass because the pull is (more or less) the same everywhere. But because more massive planets have stronger gravity, your weight changes depending which planet you are on, whereas your mass stays the same wherever you are – even if you are completely weightless in a space station in orbit. You’d be weightless on the space station because you and the weighing machine would both be ‘falling’ at the same rate (in what is called ‘free fall’); so your feet would exert no pressure on the weighing machine, which would therefore register you as weightless.

  But although you’d be weightless, you’d be far from massless. If you jumped vigorously away from the ‘floor’ of the space station, you’d shoot towards the ‘ceiling’ (it wouldn’t be obvious which was floor and which ceiling!) and, no matter how far away the ceiling was, you’d bang your head and it would hurt, just as if you had fallen on your head. And everything else in the space station would still have its own mass likewise. If you had a cannonball in the cabin with you, it would float about weightlessly, which might make you think it was light like a beach ball of the same size. But if you tried to throw it across the cabin, you’d soon know that it wasn’t light like a beach ball. It would be hard work to throw it, and you might find yourself shooting backwards in the opposite direction if you tried. The cannonball would feel heavy, even though it would show no special tendency to go ‘downwards’ towards the floor of the space station. If you succeeded in throwing the cannonball across the room, it would behave like any heavy object when it hit something in its path, and it would not be good if it hit one of your fellow astronauts on the head, either directly or after bouncing off t
he wall. If it hit another cannonball, the two would bounce off each other with a proper ‘heavy’ feel, unlike, say, a pair of ping-pong balls, which would also bounce off each other but lightly. I hope that gives you a feel for the difference between weight and mass. In the space station, a cannon ball has much more mass than a balloon, although both have the same weight – zero.

  Eggs, ellipses and escaping gravity

  Let’s go back to our cannon on the mountain-top, and make it more powerful still. What will happen? Well, now we need to acquaint ourselves with the discovery of the great German scientist Johannes Kepler, who lived just before Newton. Kepler showed that the graceful curve by which things orbit other things in space is not really a circle but something known to mathematicians since ancient Greek times as an ‘ellipse’. An ellipse is sort of egg-shaped (only ‘sort of’: eggs are not perfect ellipses). A circle is a special case of an ellipse; think of a very blunt egg, an egg so short and squat that it looks like a ping-pong ball.

  There’s an easy way to draw an ellipse, while at the same time convincing yourself that a circle is a special case of an ellipse. Take a piece of string and make it into a loop by tying the ends together, in as neat and small a knot as you can. Now stick a pin in a pad of paper, loop the string around the pin, stick a pencil through the other end of the loop, pull it tight and draw all around the pin with the string loop at full stretch. You’ll draw a circle, of course.

  Next, take a second pin and stick it in the pad, right next to the first pin so that they are touching. You’ll still draw a circle because the two pins are so close together that they count as a single pin. But now here’s the interesting part. Move the pins apart a few inches. Now when you draw with the string at full stretch, the shape you produce will not be a circle, it will be an ‘egg-shaped’ ellipse. The further apart you place the two pins, the narrower the ellipse will be. The closer you place the two pins to each other, the wider – the more circular – the ellipse will be until, when the two pins become one pin, the ellipse will be a circle – the special case.