The Science of Discworld Revised Edition

trapped in the Circumfence, a ten thousand mile long net set just below the Edge, one tiny bit of which is patrolled by Tethis the sea troll. And they can peer over the edge: ‘… the scene beneath him flipped into a whole, new, terrifying perspective. Because down there was the head of an elephant as big as a reasonably-sized continent … Below the elephant there was nothing but the distant, painful disc of the sun. And, sweeping slowly past it, was something that for all its city -sized scales, its crater-pocks, its lunar cragginess, was indubitably a flipper.’
    It is widely imagined that ancient people thought the Earth was flat, for all those obvious commonsense reasons. Actually, most ancient civilizations that left records seem to have worked out that the Earth has to be round. Ships came back from invisible lands over the horizon and, in the sky, a round sun and a round moon were a definite clue … 1
    That’s where science and common sense overlap. Science is common sense
applied to evidence
. Using common sense in that manner, you often come to conclusions that are very different from the obvious common sense
assumptions
that because the universe
appears
to behave in some manner, then it really does. Of course it also helps to realize that if you live on a very
big
sphere, it’s going to look pretty flat for quite a long way off. And if gravity always points towards the middle of the sphere, then things don’t actually roll around or fall off. But those are refinements.
    Around 250 BC a Greek called Eratosthenes tested the theory that the Earth is a sphere, and he even worked out just how big that sphere is. He knew that in the city of Syene – present-day Aswan in Egypt – the midday sun could be seen reflected in the bottom of a well. (This would not work in Ankh-Morpork, where the well-water is often more solid than the well that surrounds it.) Eratosthenes threw in a few other simple facts and got back a lot more than he’d bargained for.
    It’s a matter of geometry. The well was dug straight down. So the Sun at Syene had to be straight
up
– dead overhead. But in Eratosthenes’ home city of Alexandria, in the Nile delta, that didn’t happen. At midday, when the sun was at its highest, Eratosthenes cast a definite shadow. In fact, he estimated that at noon the angle between the Sun and the vertical was just over 7° – near enough 1/50 of 360°. Then came the leap of deduction. The Sun is in the same place wherever you observe it from. On other grounds, it was known that the Sun had to be a long way away from the Earth, and that meant that the Sun’s rays that hit the ground in Alexandria were very nearly parallel to those that went down the well in Syene. Eratosthenes reasoned that a round Earth would explain the difference. He deduced that the distance from Syene to Alexandria must be 1/50 of the circumference of the Earth. But how far was that?
    On such occasions it pays to be familiar with the camel-herders. Not just because the greatest mathematician in the world is the camel called You Bastard, as it is on Discworld (see
Pyramids)
, but because the camel trains from Alexandria to Syene took 50 days to make the trip, at an average speed of 100 stadia per day. So the distance from Alexandria to Syene was 5,000 stadia, and the circumference of the Earth was 250,000 stadia. The stadium was a Greek measure of distance, and nobody knows how long it was. Scholars
think
it was 515 feet (157 m), and if they’re right, Eratosthenes’ value was 24,662 miles (39,690 km). The true value is about 24,881 miles (40,042 km), so Eratosthenes got amazingly close. Unless – sorry, but we’re incorrigibly suspicious – the scholars worked backwards from the answer.
    It is here that we encounter another feature of scientific reasoning. In order to make comparisons between theory and experiment, you have to
interpret
the experiment in terms of your theory. To clarify this point, we recount the story of Ratonasticthenes, an early relative of Cut-me-own-throat Dibbler, who proved that the Discworld was round (and even estimated its circumference). Ratonasticthenes noticed that at midday in the Ramtops the Sun was overhead, whereas in Lancre, some 1000 miles away, it was at 84° to the vertical. Since 84° is roughly a quarter of 360°, Ratonasticthenes reasoned that the Discworld is round, and the distance from the Ramtops to Ankh-Morpork is one-quarter of the circumference. That puts the