The Science of Discworld IV

attractor, because the attractor may not undergo any radical change – it need not encounter a tipping point. It can get a bit bigger, a bit smaller, or move around a little. We can’t observe attractors directly, but we can reconstruct them mathematically from observations, processed in the right way. The simplest way to detect change in the attractor is to observe data such as long-term averages of temperature, size and frequency of hurricanes, likelihood of flooding etc. Many objections to ‘climate change’ confuse climate with weather.
    We wrote a long piece in
The Science of Discworld III
about causality, and don’t want to repeat that here. Enough to say that there is not any single cause of any event; it is almost always truer to declare that all of the preceding events contribute, than to point to one cause. However, stories do have a linear structure: A causes B causes C … The law courts are full of that kind of story, as are most novels, and pretty well all detective stories and science fiction. Even Discworld stories rely on that fictional causality for their coherence. But this is because we are the storytelling ape. A story is a linear sequence of words. It is interesting to speculate whether an advanced alien culture would of necessity concoct such false-to-fact linearly causal stories. Could one always attribute events to three or four, or ten or twenty or a thousand, causes? Or is that the storytelling ape’s way of seeing causality?
    If we truly live in a deterministic universe, whatever that means, each successive state is the inevitable result of the immediately preceding state, including such minor causes as the gravitational influences of far stars, even the gravitational influences of the beasts on the planets around far stars. This picture is consistent with certain portrayals of the universe, where for some elements (spaceships approaching the speed of light are favourite candidates) what is in the future for some is on the left for others, while to the right are events-past. So every event is already ‘there’, in some frame of reference. This portrays the whole universe as a vast crystalline structure, with the future just as determinate as the past.
    We find this representation as unsatisfactory as the perpetually-dividing Trousers of Time image. Historically, some of it derives from a misreading of Einstein’s concept of a world-line in relativity, a fixed curve running across spacetime and describing the entire history of a particle. One curve, calculated using Einstein’s equations, so one history, right? It’s a valid image in a world with only one particle, whose state can be measured exactly, to infinitely many decimal points. It’s not sensible for the vast, complex universe. If you start drawing a curve in spacetime, and allow it to develop as it grows, at any given stage you may have no idea where it will go next, no way to predict its future path. Einstein’s equations don’t help, because you can’t measure the current state of the universe exactly. That’s not a deterministic universe in any meaningful sense, but after infinite time you’ve got just one curve, one world-line – just as before.
    Faced with a choice between two extremes, a world that is random or one that is completely predetermined, most of us dislike both. Neither matches our experiences. That doesn’t prove either of them is wrong, but it makes a key point: any theoretical model must explain our daily experiences. It may well demonstrate that deep down, things are not as we assume; however, it does have to explain how what we assume emerges from the model, even if it’s a misinterpretation of what is ‘really’ happening in the model. For example, the standardclaim that science has proved atoms to be mostly empty space does
not
prove that the apparent solidity of a table is an illusion. You also have to explain why it seems solid to us; then you discover that empty space isn’t empty at all, but filled with quantum fields and forces. Which is what ‘solid’ means at that level of description.
    So we would like to find some leeway, some
choosable
indeterminacy in what happens, if only to foster our illusion of having free will. We would like to think that on an appropriate level of description, what we decide to do is not simply what we
have
to do.
    Worryingly, the great (though sometimes misguided) philosopher René Descartes would have had sympathy with this approach, but that’s