Terry Pratchett - The Science of Discworld II - The Globe

Sometimes, though, even one book could do that. Even one line. Even one word, in the right place and the right time.

The room was large, panelled and sparsely furnished. Quite a lot of paperwork was strewn on a desk. Quill pens lay by an inkwell. A window looked out on to broad gardens, where it was raining. A skull lent a homely touch.

Rincewind leaned down and tapped it.

'Hello?' he said. He looked up at the others.

'Well, the one in the Dean's office can sing comic songs,' he said defensively. He stared at the paperwork on the desk. It was covered in symbols which had a magical look, although he didn't recognise any of them. On the other side of the room, the Librarian was leafing through one of the books. Strangely, they weren't on shelves. Some were neatly piled, others locked in boxes, or at least in boxes that were locked until the Librarian tried to lift the lid.

Occasionally he pursed his lips and blew a disdainful raspberry.

'Ook,' he muttered.

'Alchemy?' said Rincewind. 'Oh dear. That stuff never works.' He lifted up what looked like a small leather hatbox, and removed the lid. 'This is more like it!' he said, and pulled out a ball of smoky quartz. 'Our man is definitely a wizard!'

'This is very bad,' said Ponder, staring at a device in his hand. "Very, very bad indeed.'

'What is?' said Rincewind, turning around quickly.

'I'm reading a very high glamour quotient,' said Ponder.

'There's elves here?'

'Here? The place is practically elvish!' said Ponder. 'The Archchancellor was right.'

All three explorers stood quietly. The Librarian's nostrils flared. Rincewind sniffed, very cautiously.

'Seems okay to me,' he said, at last.

Then a man in black entered the room. He came in quickly, opening the door no more than necessary, in a kind of aggressive sidle, and stopped in astonishment. Then his hand flew to his belt and he drew a thin, businesslike sword.

He saw the Librarian. He stopped. And then it was really all over, because the Librarian could unfold his arm very fast and, importantly, there was a fist like a sledgehammer on the end of it.

As the dark figure slid down the wall, the crystal sphere in Rincewind's hand said: 'I believe I now have enough information. I advise departure from this place at a convenient opportunity and in any case before this gentleman awakes.' Hex?' said Ponder.

'Yes. Let me repeat my advice. Lack of absence from this place will undoubtedly result in metal entering the body.'

But you're talking via a crystal ball! Magic doesn't work here!'

'Don't argue with a voice saying "run away"!' said Rincewind. 'That's good advice! You don't question it! Let's get out of here!'

He looked at the Librarian, who was sniffing along the bookshelves with a puzzled expression.

Rincewind had a sense for the universe's tendency to go wrong. He didn't leap to conclusions, he plunged headlong towards them.

'You've brought us out through a one-way door, haven't you ...' he said.

'Oook!'

'Well, how long will it take to find the way in?'

The Librarian shrugged and returned his attention to the shelves.

'Leave now,' said the crystal Hex. 'Return later. The owner of the house will be useful. But leave before Sir Francis Walsingham wakes up, because otherwise he will kill you. Steal his purse from him first. You will need money. For one thing, you will need to pay someone to give the Librarian a shave.'

'Oook?'

The concept of L-space, short for 'Library-space', occurs in several of the Discworld novels. An early example occurs in Lords and Ladies, a story that is mostly about elvish evil. We are told that Ponder Stibbons is Reader in Invisible Writings, and this phrase deserves (and gets) an explanation: The study of invisible writings was a new discipline made available by the discovery of the bidirectional nature of Library-space. The thaumic mathematics are complex, but boil down to the fact that all books, everywhere, affect all other books. This is obvious: books inspire other books written in the future, and cite books written in the past. But the General Theory [12] There's a Special Theory as well, but no one bothers with it much because it's self-evidently a load of marsh-gas. [This footnote is a footnote in the original quotation. So this is a metafootnote.] of L-space suggests that, in that case, the contents of books as yet unwritten can be deduced from books now in existence.

L-space is a typical example of the Discworld habit of taking a metaphorical concept and making it real. The concept here is known as 'phase space', and it was introduced by the French mathematician Henri Poincare about a hundred years ago to open up the possibility of applying geometrical reasoning to dynamics. Poincare's metaphor has now invaded the whole of science, if not beyond, and we will make good use of it in our discussion of the role of narrativium in evolution of the mind.

Poincare was the archetypal absent-minded academic -no, come to think of it he was 'presentminded somewhere else', namely in his mathematics, and it's easy to understand why. He was probably the most naturally gifted mathematician of the nineteenth century. If you had a mind like his, you'd spend most of your time somewhere else too, revelling in the beauty of the mathiverse.

Poincare ranged over almost all of mathematics, and he wrote several best-selling popular science books, too. In one piece of research which single-handedly created a new 'qualitative'

way of thinking about dynamics, he pointed out that when you are studying some physical system that can exist in a variety of different states, then it may be a good idea to consider the states that it could be in, but isn’t as well as the particular state in which it is. By doing that, you set up a context that lets you understand what the system is doing, and why. This context is the

'phase space' of the system. Each possible state can be thought of as a point in that phase space.

As time passes, the state changes, so this representative point traces out a curve, the trajectory of the system. The rule that determines the successive steps in the trajectory is the dynamic of the system. In most areas of physics, the dynamic is completely determined, once and for all, but we can extend, this terminology to cases where the rule involves possible choices. A good example is a game. Now the phase space is the space of possible positions, the dynamic is the rules of the game and a trajectory is a legal sequence of moves by the players.

The formal setting and terminology for phase spaces is not as important, for us, as the viewpoint that they encourage. For example, you might wonder why the surface of a pool of water, in the absence of' wind or other disturbances, is flat. It just sits there, flat; it isn't even doing anything.

But you start to make progress immediately if you ask the question 'what would happen if it wasn't flat?' For instance, why can't the water be piled up into a hump in the middle of the pond?

Well, imagine that it was. Imagine that you can control the position of every molecule of water, and that you pile it up in this way, miraculously keeping every molecule just where you've placed it. Then, you let go. What would happen? The heap of water would collapse, and waves would slosh across the pool until everything settled down to that nice, flat surface that we've learned to expect. Again, suppose you arranged the water so that there was a big dip in the middle. Then as soon as you let go, water would move in from the sides to fill the dip.

Mathematically, this idea can be formalised in terms of the space of all possible shapes for the water's surface. 'Possible' here doesn't mean physically possible: the only shape you'll ever see in the real world, barring disturbances, is a flat surface. 'Possible' means 'conceptually possible'. So we can set up this space of all possible shapes for the surface as a simple mathematical construct, and this is the phase space for the problem. Each 'point' -location -in phase space represents a conceivable shape for the surface. Just one of those points, one state, represents 'flat'.