The Science of Discworld IV Judgement Da - By Terry Pratchett, Ian Stewart Page 0,71

in 2011 showed that this effect could be accounted for by the way the craft were radiating heat, which created very small pressure effects.

Here, the underlying physical law, that of gravity, sets up the scenery: the backdrop against which the spaceship becomes a story. Pan narrans cannot help but see the spaceship as the most interesting item, because it doesn’t fit the story – it seems not to obey the law.

Our minds seem to have evolved to place extra weight on exceptions. The prolific science fiction and popular science author Isaac Asimov wrote: ‘The most exciting phrase to hear in science, the one that heralds new discoveries, is not “Eureka” but “That’s funny …”’ Law-abiding planets and comets are banal, unable to catch our attention. In the same way, we find the law-abiding mass of humanity essentially boring, so our stories are about witches and malefactors. Among Discworld’s characters, the witch Granny Weatherwax and the sweeper and history monk Lu-Tze catch our attention. It’s the exceptions to the law that make the law useful.

Are laws like that of gravity unique, special statements that are in some sense universally true? Would aliens come up with a theory like gravity, or is there something peculiarly human about falling apples, which leads our peculiar minds on to lunar orbits and solar systems? Is there perhaps a quite different way to describe solar systems?

Similarly, when Thomson started playing with cathode ray tubes, he had no idea that he was separating a beam of electrons, breaking up atoms. If we had started from some other particle than an electron, and we had gone on to find a zoo of others, would we have described the same zoo? Or would we have come up with a different zoo, which nevertheless describes the ‘real world’ as accurately as the one we’ve got?

Physicists, by and large, think not; they believe that there really are these particles out there, and that any scientific endeavour would find the same zoo. But the zoo you find depends on the theoretical model you use to direct the search. Ten years ago they had a different zoo, and in ten years’ time …

To expand on that point, consider the development of quantum mechanics. The relevant law here is the Schrödinger equation, which describes the state of a quantum system as a propagating wave. However, it seems to be impossible to detect this wave, as such, experimentally. Observations of a quantum system give specific results, and once you’ve made one observation, you’ve interfered with the hypothetical wave. So you can’t be sure that the next observation refers to the same wave. This apparently inherent indeterminacy has led to some extra interpretational features of the theory: that the quantum wave is a wave of probabilities, telling us what the state might be, and how likely any given choice is, but not what the state is; that measurements ‘collapse’ the wavefunction to a single state, and so on. By now this interpretation has become close to received gospel, and attempts to find alternatives are often dismissed out of hand. There is even a piece of mathematics, Bell’s theorem, which allegedly proves that quantum mechanics cannot be embedded within a broader deterministic local model, one that does not allow instant communication between widely separated entities.

All of the above notwithstanding, Pan narrans has problems with quantum indeterminacy. How does nature know what to do? This is the thinking behind Einstein’s famous remark about a (non-) dicing deity. Generations of physicists have become accustomed to the problem – the mathematics says ‘it’s just like that’, and there’s no need to worry about interpretations. But it’s not quite that simple, because working out the implications of the mathematics requires some extra bolt-on assumptions. ‘What it’s like’ could be a consequence of those assumptions, not of the mathematics itself.

It’s curious that we and Einstein use, as our icon for chance, the image of dice. A die (singular) is a cube, and when it is thrown, and bounces, it obeys the deterministic laws of mechanics. In principle, you ought to be able to predict the outcome as soon as the die leaves the hand. Of course there are modelling issues here, but that statement ought at least to be true of the idealised model. However, it’s not, and the reason is that the corners of the die amplify tiny errors of description. This is a form of chaos, related to the butterfly effect but technically different.

Mathematically, the probabilities of the die landing