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 a second 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.61

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 roll of cloth, the Endless Road, move at a speed that is non-zero, but is also different from the natural speed with which the horse would move if its feet were actually hitting solid ground.62 You might care to think about that, and you might even decide that we're wrong. And you might even be right.

We also acknowledge that Phocian's final experiment is open to many objections. And because the hooves of a trotting horse hit the ground in pairs, it is actually necessary to halve the total length of the charcoal smears before comparing them with the length of the cloth.

No matter, these are mere elaborations of what would otherwise be an entirely transparent story: you understand what we're getting at.

Taking all this into account, was Phocian a scientist?

No. Hex has bungled again, for despite Phocian's years of visibly 'scientific' activity, he falls down in two respects. One, open to dispute, is not his fault: he has no peers, no colleagues. There are no other 'scientists' for him to work with, or to criticise him. He's on his own and ahead of his time.63 Just as there cannot be just one wizard, there cannot be just one scientist. Science has a social dimension.64 The second reason, though, is decisive. He is mortified when his work proves that Antigonus, the great authority, is wrong.

Any genuine scientist would give their right arm to prove that the great authority is wrong.

That's how you make your reputation, and it's also the most important way to contribute to the scientific endeavour. Science is at its best when it changes people's minds. Very little of it does that, in part because our minds have been built by a culture that is pervaded by science anyway.

If a scientist manages to spend 1 per cent of the time discovering things that are not what they expected, they are doing amazingly well. But boy, does that 1 per cent count for a lot.

This, then, is science. Questioning authority. Complicity between theory and experiment. And being within a community of like-minded people to question your work. Preferably accompanied by a conscious awareness of all of the above, and gratitude to your friends and colleagues for their criticisms. And what's the aim? To find timeless truths? No, that's asking too much. To stop frail humans from falling for plausible falsehoods? Yes -including those of people who at least look and sound just like you. And to protect people from their willingness to believe a good story, just because it sounds right and doesn't upset them. And to protect them from the firm smack of authority, too.

It took humanity a long time to arrive at the scientific method. No doubt the reason for the delay was that if you do science properly, you often find yourself overturning entrenched, well- established beliefs, including your own entrenched, well-established beliefs. Science is not a belief system, but many areas of human activity are, so it is not surprising to find that the early developers of science often found themselves in conflict with authority. Perhaps the best-known example of this is Galileo, who ran into trouble with the Inquisition because of his theories about the solar system. Sometimes science exposes you to the firm smack instead.

Science, then, is not just a body of teachable facts and techniques. It is a way of thinking. In science, established 'facts' are always open to question,65 but few scientists will listen to you unless you can offer some evidence that the old ideas are wrong. If the people who invented those ideas are dead, then alternatives can quickly gain acceptance, and the scientific method is working well. If the people who invented those ideas are still around, in influential positions, then they can put a lot of obstacles in the way of the new suggestion and the people who proposed it. Then science is working badly, because people are behaving like people. Even so, the new idea still can displace the accepted wisdom. It just takes longer and needs really solid evidence.

Let's contrast science with alternative ways of thinking about the universe. The Discworld worldview is that the universe is run by magic: things happen because people want them to happen. You still have to find the right spell, or the narrative imperative has to be so strong that those things will happen anyway even if people don't want them to, but the universe exists in order to be there for people.

On Discworld and Roundworld, the worldview of the priesthood is similar, but with one important difference. They believe that the universe is run by gods (or a god): things happen because the gods want them to happen, don't care if they happen, or have some ineffable long- term aim in view. However, it is possible for people to ask the priests to intercede with the gods, on their behalf, in the hope of influencing the gods' decisions, at least in minor ways.

The philosophical worldview, exemplified by Antigonus, is that the nature of the world can be deduced by pure thought, on the basis of a few deep, general principles. Observation and experiment are secondary to verbal reasoning and logic.

The scientific worldview is that what people want has very little to do with what actually happens, and that it is unnecessary to invoke gods at all. Thought is useful, but empirical observations are the main test of any hypothesis. The role of science is to help us find out how the universe works. Why it works, or what manner of Being ultimately controls it, if any, is not a question that science is interested in. It is not a question to which anyone can give a testable answer.