The Science of Discworld IV Judgement Da - By Terry Pratchett, Ian Stewart Page 0,121

universes that can sustain living creatures are extraordinarily unlikely. This coincidence violates, in the most dramatic manner possible, the Copernican principle that humans aren’t special.

Before Nicholas Copernicus published On the Revolutions of the Celestial Spheres in 1543, with a few honourable exceptions, almost everyone viewed humanity as the centre of the universe. This was so obviously true that it seemed ridiculous to deny it. Look around you. Everything else trails off into the distance, and you are smack bang in the middle. Your own senses prove that the stars and other celestial bodies revolve around the Earth. The natural shape for their orbits must surely be a circle, a perfect geometric figure; its perfection provides yet more evidence that everything was created for us, and that we are located at the heart of creation.

However, ancient astronomers were excellent observers, and when they looked at what the universe was actually doing, they realised that circles don’t fit. But they could save the ‘perfect form’ theory, because combinations of circles agree very closely with observations. In the second century AD, Claudius Ptolemaeus (Ptolemy) wrote the Almagest (‘the greatest’), which represented the movements of the Sun and planets around a stationary Earth. To match the complex trajectories observed, he employed several geometric constructions, involving spheres rotating on axes that are supported by other spheres. In a simplified form, the most important features of the Ptolemaic system were epicycles: circular orbits whose centres themselves revolved in circular orbits. If necessary, those centres might also revolve in circular orbits, and so on. In total, Ptolemy needed more than eighty spheres, but the resulting system was very accurate. Especially at a time when Earth was not recognised as a planet. That term referred to wandering stars, and the Earth was neither a star, nor a wanderer. It was fixed.

We are special.

Copernicus was clearly a contrarian, and he realised that everything makes a lot more sense if we’re not special, and the Earth is not at the centre. This is an instance of the mediocrity principle: as a working heuristic, it is best to avoid assuming that any given phenomenon has unusual, special features, or violates the laws of nature. One feature of Ptolemy’s system that may have led Copernicus to this view was a suspicious coincidence. The numbers associated with most of the epicycles – size, speed of rotation – were rather haphazard, with no clear patterns. But Copernicus noticed that identical copies of one particular set of epicycle data occurred many times over: in the motion of the Sun and of all the planets. He could cut the number of epicycles down from Ptolemy’s eighty to a mere thirty-four by transferring this one to the Earth. The Sun then became stationary, and everything else (bar the Moon) revolved around it – Earth included. By adopting an Earth-centred frame of reference, Ptolemy had been obliged to transfer the Earth’s motion round the Sun to every other body, by adding a single extra epicycle to all of them. Remove this common epicycle, and the description would be much simpler. But then you are faced with a radical change to the theory: among the many celestial bodies, only the Moon revolves around the Earth. Everything else revolves around the Sun.

That statement is open to challenge, on grounds discussed for flat Earths in chapter 8. You can represent the universe in any frame of reference you wish. There is nothing to stop you choosing a coordinate system in which the Earth is stationary, and you can even decide – depending on your assessment of your own importance in the scheme of things – that you are at the origin. It is entirely straightforward, for those who play this kind of game, to rewrite all of the laws of nature within that you-centred frame of reference. So there is a sense in which what’s in the middle and what goes round what is entirely arbitrary.

However, another philosophical principle, Occam’s razor, suggests that this freedom to choose is not terribly meaningful. William of Occam (or Ockham) is credited with the philosophical principle ‘entities should not be multiplied beyond necessity’.fn1 This tends to be interpreted as ‘simple explanations are better than complex ones’, but that goes beyond what William actually said. His point was that it is silly to include features that can be removed without making any significant difference. Complex explanations are often better than simple ones, but only when simpler ones won’t do the job. Interpreting Occam’s razor either way,