The Science of Discworld II

information. I advise departure from this place at a convenient opportunity and in any case before this gentleman awakes.’
    â€˜Hex?’ said Ponder.
    â€˜Yes. Let me repeat my advice. Lack of absence from this place will undoubtedly result in metal entering the body.’
    â€˜But you’re talking via a crystal ball! Magic doesn’t work here!’
    â€˜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.
    â€˜You’ve brought us out through a one-way door, haven’t you …’ he said.
    â€˜Oook!’
    â€˜Well, how long will it take to find the way in?’
    The Librarian shrugged and returned his attention to the shelves.
    â€˜Leave now,’ said the crystal Hex. ‘Return later. The owner of this 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.’
    â€˜ Oook ?’
    1 Others found by research wizards include Objects In The Rear View Mirror Are Closer Than They Appear, No User Serviceable Parts Inside and, of course, May Contain Nuts.

FOUR
THE ADJACENT POSSIBLE
    T HE 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 bi-directional 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 1 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 Poincaré about a hundred years ago to open up the possibility of applying geometrical reasoning to dynamics. Poincaré’s metaphor has now invaded the whole of science, if not beyond, and we willmake good use of it in our discussion of the role of narrativium in the evolution of the mind.
    Poincaré was the archetypal absent-minded academic – no, come to think of it he was ‘present-minded 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.
    Poincaré 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