The Science of Discworld IV Judgement Da - By Terry Pratchett, Ian Stewart Page 0,47

experiments, often using high voltage electricity, and in 1869 he gave himself a severe electric shock. He claimed that while he was unconscious a spirit had contacted him, telling him he was the Messiah. He changed his name to Koresh, Hebrew for Cyrus, and set out to save the soul of humanity. Teed’s reformulation of our planet’s shape stemmed from this experience. It went much further than merely proposing a hollow interior. According to his Cellular Cosmogony, we are inside the Earth, a hollow ball with the Sun at its centre. Gravity does not exist; instead, we are pinned to the planet’s surface by centrifugal force. The Sun is operated by batteries, and the stars are distorted images of it.

Koreshanity attracted adherents, and Teed preached celibacy,fn5 reincarnation and communism, as well as weird science. A foray into politics led to an assault by his opponents, and the injuries led to his death in 1908. With its leader gone, the cult faded away.

Now, there is a rather trivial sense in which Teed is right. A solid Earth surrounded by the rest of the universe can be transformed into a hollow Earth, surrounded by an infinite expanse of rock, whose interior contains the rest of the universe. All laws of nature, equations of mathematical physics and so on, can be transferred into the transformed coordinates. They will (usually) look different, but the two realisations match perfectly, are logically equivalent, and are physically indistinguishable. As far as mathematicians are concerned, they are ‘the same’.

To obtain a hollow Earth, use a geometric transformation invented by Ludwig Magnus in 1831: inversion. Choose a point in space as the origin; then transform a point distance d along a radius to the point that is distance 1/d along the same radius. This transformation leaves the sphere of unit radius unchanged, because 1/1 = 1, but it swaps the inside and outside of the sphere, because if d is bigger than 1 then 1/d is less than 1. The centre of the sphere goes to infinity; infinity goes to the centre of the sphere. Do this with the origin at the centre of the Earth and you get a hollow planet with the rest of the universe inside it, surrounded by an infinite expanse of rock.

You can play this game with any description of nature. You can use it to argue that the United Nations logo is the true shape of the Earth. You can rewrite astronomy in an Earth-centred frame of reference. If you transform every law of nature to match, no one can contradict you. There is a sensible way to play the game: some transformations take precedence because they lead to simpler equations. But Hollow Earth theories that use inversion as justification apply meaningless transformations that tell us nothing new about reality.

Some kind of world existing inside our planet, that is, underground, is a common element of many religions. We’ve already encountered the ancient Egyptian belief in the underworld. The Judaeo-Christian vision of Hell, until a few centuries ago, had elements in common. The Hindu Puranas tell of an underground city called Shamballa, and the same story occurs in Tibetan Buddhism. However, none of these myths suggests that the Earth is a hollow ball.

In 1692, the astronomer Edmond Halley, a leading scientist of the period, famous for a comet, was trying to explain why compasses don’t always point towards magnetic north. He suggested that the variations in direction could be explained if the Earth were a series of concentric spherical shells: a surface shell 800 kilometres thick, two smaller shells within it, and a solid ball in the middle. He thought that they were separated by atmospheres, rotated at different speeds, and had their own magnetic poles. Escaping gas at the poles glowed to create the auroras. It was a kind of magnetic version of Ptolemy’s crystal spheres, and like that theory, it explained a great deal and was completely wrong.

Pseudoscience got in on the act in a big way in 1818, when John Symmes advanced a similar model, in which the outer shell was 1300 kilometres thick with huge circular openings at both poles. Inside were four more shells, also with polar apertures. You have to remember that this was seventy-seven years before the Norwegian explorers Fridtjof Nansen and Hjalmar Johansen reached latitude 86˚ north in 1895, and ninety-one years before Robert Peary reached the North Pole in 1909 – or, as now seems plausible, got very close but maybe didn’t quite make it.