The Science of Discworld II

dynamical system whose phase space has a huge number of dimensions, one or more per entity. This is correct, but the word ‘just’ is misleadingly dismissive. Dynamical systems with big phase spaces can do remarkable things, far more remarkable than what the solar system can do.
    The new ingredient in complex systems is that the rules are ‘local’, stated on the level of the entities. In contrast, the interesting features of the system itself are global, stated on the level of the entire system. Even if we know the local rules for entities, it may not be possible – either in practice, or in principle – to deduce the dynamical rules of the system as a whole. The problem here is that the calculations involved may be intractable, either in the weak sense that they would take far too long to do, or in the strong sense that you can’t actually do them at all.
    Suppose, for example, that you wanted to use the laws of quantum mechanics to predict the behaviour of a cat. If you take the problem seriously, the way to do this is to write down the ‘quantum wave-function’ of every single subatomic particle in the cat. Having done this, you apply a mathematical rule known as Schrödinger’s equation, which physicists tell us will predict the future state of the cat. 2
    However, no sensible physicist would attempt any such thing, because the wavefunction is far too complicated. The number of subatomic particles in a cat is enormous; even if you could measure their states precisely – which of course you can’t do anyway – the universe does not contain a sheet of paper big enough to list all the numbers. So the calculation can’t even get started, because in practical terms the present state of the cat is indescribable in the language of quantum wavefunctions. As for plugging the wavefunction into Schrödinger’s equation, well, forget it.
    Agreed, this is not a sensible way to model the behaviour of a cat. But it does make it clear that the usual physicists’ rhetoric about quantum mechanics being ‘fundamental’ is at best true in a philosophical sense. It’s not fundamental to our understanding of the cat, although it might be fundamental to the cat.
    Despite these difficulties, cats generally manage to behave like cats, and in particular they discover their own futures by living them. Down on the philosophical level, again, this may be because the universe is a lot better at solving Schrödinger’s equation than we are, and because it doesn’t need a description of the quantum wavefunction of the cat: it’s already got the cat, which is its own quantum wavefunction fromthis point of view.
    Let’s accept that, even though it’s rather likely that the universe doesn’t propagate a cat into its future by applying anything that corresponds to Schrödinger’s equation. The equation is a human model, not the reality. But even if Schrödinger’s equation is what the universe ‘really’ does – and more so if it’s not – there’s no way that we limited humans can follow the ‘calculation’ step by step. There are too many steps. What interests us about cats occurs on the system level: things like purring, catching mice, drinking milk, getting stuck in the catflap. Schrödinger’s equation doesn’t help us understand those phenomena.
    When the logical chain that leads from an entity-level description of a complex system to system-level behaviour is far too complicated for any human being to follow it, that behaviour is said to be an emergent property of the complex system, or just to be ‘emergent’. A cat drinking milk is an emergent property of Schrödinger’s equation applied to the subatomic particles that make up the cat. And the milk, and the saucer … and the kitchen floor, and …
    One way to predict the future is to cheat. This method has many advantages. It works. You can test it, so that makes it scientific . Lots of people will believe the evidence of their own eyes, unaware that eyes tell lies and you’ll never catch a competent charlatan in the act of cheating.
    The wizards got Shakespeare right, aside – at a late stage – from the minor matter of sex. When it comes to a baby’s sex, the Grand Master of Foretelling the Future was ‘Prince Monolulu’. He was a West African who wore very impressive tribal gear and