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 darkness. 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.
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, 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 ...