The Science of Discworld II

even less of a scientist than Archimedes, whatever anyone has told you. In his De Incessu Animalium ( On the Gait of Animals ) Aristotle says that a horse cannot bound. The bound is a four-legged gait in which both front legs move together, then both back legs move together. He’s right, horses don’t bound. But that is the least interesting thing here. Aristotle explains why a horse can’t bound:
    If they moved the fore legs at the same time and first, their progression would be interrupted or they would even stumble forward … For this reason, then, animals do not move separately with their front and back legs.
    Forget the horse: many quadrupeds do bound, so his reasoning, such as it is, must be wrong. And a gallop is very close to a bound, except that the left and right legs move at very slightly different times. If the bound were impossible, then by the same token so should the gallop be. But horses gallop.
    Oops.
    You can see that all this is a bit too messy to make a good story, so in the interests of narrativium we have replaced Aristotle by Antigonus, and credited him with a very similar theory about a long-standing historical conundrum: does a trotting horse always have at least one hoof on the ground? (In a trot, diagonally opposite legs move together, and the pairs hit the ground alternately.) This is the kind of question that must have been discussed in ale-houses and public baths since well before the time of Aristotle, because it’s just out of reach of the unaided human eye. The first definitive answer came in 1874 when Eadweard Muybridge (born Edward Muggeridge) used high-speed photography to show that sometimes a trotting horse has all four feet off the ground at once. The proportion of times this occurs depends on the speed of the horse, and can be more than Phocian’s 20 per cent. It can also be zero, in a slow trot, which further complicates the science. Allegedly, Muybridge’s photographs won Leland Stanford Jr, a former Governor of California, the tidy sum of $25,000 in a bet with Frederick MacCrellish.
    But what interest us here is not the science of horse locomotion, fascinating as that may be. It is how a scientific mind would go about investigating it. And Phocian shows that the Greeks could have made a lot more progress than they did, if they’d thought like a scientist. There were no technological barriers to solving such problems; just mental and (especially) cultural ones. The Greeks could have invented the phonograph, but if they did, it left no trace. They could have invented a clock, and the Antikythera mechanism shows they had the technique, but it seems that they didn’t.
    The slaves’ use of songs to keep time has its roots in later history. In 1604 Galileo Galilei used music as a way to determine short intervals of time in some of his experiments on mechanics. A trained musician can mentally subdivide a bar into 64 or 128 equal parts, and even untrained people can distinguish an interval of a hundredth of asecond in a piece of music. The Greeks could have used Galileo’s method if they’d thought of it, and advanced science by 2,000 years. And they could have invented innumerable Heath-Robinson gadgets to study a moving horse, if it had occurred to them. Why didn’t they? Possibly because, like Phocian, they were too tightly focussed on specific issues.
    Phocian’s approach to the trotting horse looks pretty scientific. First he tries the direct method: he gets his slaves to observe the horse while it is trotting, and see whether it is ever completely off the ground. But the horse is moving too fast for human vision to provide a convincing answer. So then he goes for the indirect approach. He thinks about Antigonus’s theory , and homes in on one particular step: if the horse is off the ground, then it ought to fall over. That step can be tested in its own right, though in a different situation: a horse slung from a rope. (This way of thinking is called ‘experimental design’.) If the horse does not fall over, then the theory is wrong. But this experiment is inconclusive, and even if the theory is wrong the conclusions could still be right, so he refines the hypothesis and invents more elaborate apparatus. 5
    We don’t want to go too deeply into details of design here. We can think of ways to make the experiment workable, but the discussion would be a bit technical. For example, it seems necessary to make the