The Science of Discworld II

outcome.
    Black paint? You may know this superstitious practice, but if not: painting the kitchen ceiling black is supposed to guarantee a boy. 1 The wizards will try anything. To begin with. And if it doesn’t work, they’ll try something else, until eventually they get somewhere.
    Why is it unreasonable to expect them to succeed in one go, but reasonable to expect them to achieve their objective by repeated refinements?
    History is like that.
    There is a dynamic to history, but we find out what that dynamic is only as the events concerned unfold. That’s why we can put a name to historical periods only after they’ve happened. That’s why the history monks on Discworld have to wander the Disc making sure that historical events that ought to happen do happen. They are theguardians of narrativium and they spread it around dispassionately to ensure that the whole world obeys its storyline. The history monks come into their own in Thief of Time . Using great spinning cylinders called Procrastinators, they borrow time from where it is not needed and repay it where it is:
    According to the Second Scroll of Wen the Eternally Surprised , Wen the Eternally Surprised sawed the first procrastinator from a trunk of a wamwam tree, carved certain symbols on it, fitted it with a bronze spindle, and summoned the apprentice, Clodpool.
    â€˜Ah, very nice, master,’ said Clodpool. ‘A prayer wheel, yes?’
    â€˜No, this is nothing like as complex,’ said Wen. ‘It merely stores and moves time.’
    â€˜That simple, eh?’
    â€˜And now I shall test it,’ said Wen. He gave it a half-turn with his hand.
    â€˜Ah, very nice, master,’ said Clodpool. ‘A prayer wheel, yes?’
    â€˜No, this is nothing like as complex,’ said Wen. ‘It merely stores and moves time.’
    â€˜That simple, eh?’
    â€˜And now I shall test it,’ said Wen. He moved it a little less this time.
    â€˜That simple, eh?’
    â€˜And now I shall test it,’ said Wen. This time he twisted it gently to and fro.
    â€˜That si-si-si That simple-ple, eh eheh simple, eh?’ said Clodpool.
    â€˜And I have tested it,’ said Wen.
    On Roundworld we don’t have history monks – or, at least, we’ve never caught anyone playing that role, but could we ever do so? – but we do have a kind of historical narrativium. We have a saying that ‘history repeats itself’ – the first time as comedy, the second time as tragedy, because the one thing we learn from history is that we never learn from history.
    Roundworld history is like biological evolution: it obeys rules, but even so, it seems to make itself up as it goes along. In fact, it seems to make up its rules as it goes along. At first sight, that seemsincompatible with the existence of a dynamic, because a dynamic is a rule that takes the system from its present state to the next one, a tiny instant into the future. Nonetheless, there must be a dynamic, otherwise historians would not be able to make sense of history, even after the event. Ditto evolutionary biology.
    The solution to this conundrum lies in the strange nature of the historical dynamic. It is emergent. Emergence is one of the most important, but also the most puzzling, features of complex systems. And it is important for this book, because it is the existence of emergent dynamics that leads humans to tell stories. Briefly: if the dynamic wasn’t emergent, then we wouldn’t need to tell stories about the system, because we’d all be able to understand the system on its own terms. But when the dynamic is emergent, a simplified but evocative story is the best description that we can hope to find …
    But now we’re getting ahead of our own story, so let’s back up a little and explain what we’re talking about.

    A conventional dynamical system has an explicit, pre-stated phase space. That is, there exists a simple, precise description of everything that the system can possibly do, and in some sense this description is known in advance. In addition, there is a fixed rule, or rules, that takes the current state of the system and transforms it into the next state. For example, if we are trying to understand the solar system, from a classical point of view, then the phase space comprises all possible positions and velocities for the planets, moons, and other bodies, and the rules are a combination of