Archimedes made a brilliant discovery, but he didn't test his ideas like a scientist would now, and he didn't investigate the problem in a genuinely scientific way. His work was an important step along the path to science, but one step is not a path. And one thought is not a way of thinking.
What about the Archimedean screw? Was that science? This wonderful device is a helix that fits tightly inside a cylinder. You place the cylinder at a slant, with the bottom end in water; turn the helix, and after a while water comes out at the top. It is generally believed that the famous Hanging Gardens of Babylon were watered using massive Archimedean screws. How it works is more subtle than Ridcully imagines: in particular, the screw ceases to work if it is held at too steep an angle. Rincewind is right: an Archimedean screw is like a series of travelling buckets, separate compartments with water in them. Because they are separate, there is no continuous channel for the water to flow away along. As the screw turns, the compartments move up the cylinder, and the water has to go with them. If you hold the cylinder at too steep a slope, all the
'buckets' merge, and the water no longer climbs.
The Archimedean screw surely counts as an example of ancient Greek technology, and it illustrates their possession of engineering. We tend to think of the Greeks as 'pure thinkers', but that's the result of selective reporting. Yes, the Greeks were renowned for their (pure)
mathematics, art, sculpture, poetry, drama and philosophy. But their abilities did not stop there.
They also had quite a lot of technology. A fine example is the Antikythera mechanism, which is a lump of corroded metal that some fishermen found at the bottom of the Mediterranean Sea in
1900 near the island of Antikythera[58]. Nobody took much notice until 1972, when Derek de Solla Price had the lump X-rayed. It turned out to be an orrery: a calculating device for the movements of the planets, built from 32 remarkably precise cogwheels. There was even a differential gear.
Before this gadget was discovered, we simply didn't know that the Greeks had possessed that kind of technological ability.
We still don't understand the context in which the Greeks developed this device; we have no idea where these technologies came from. They were probably passed down from craftsman to craftsman by word of mouth -a common vehicle for technological extelligence, where ideas need to be kept secret and passed on to successors. This is how secret craft societies, the best known being the freemasons, arose.
The Antikythera mechanism was Greek engineering, no question. But it wasn't science, for two reasons. One is trivial: technology isn't science. The two are closely associated: technology helps to advance science, and science helps to advance technology. Technology is about making things work without understanding them, while science is about understanding things without making them work.
Science is a general method for solving problems. You're only doing science if you know that the method you're using has much wider application. From those written works of Archimedes that still survive, it looks as if his main method for inventing technology was mathematical. He would lay down some general principles, such as the law of the lever, and then he would think a bit like a modern engineer about how to exploit those principles, but his derivation of the principles was based on logic rather than experiment. Genuine science arose only when people began to realise that theory and experiment go hand in hand, and that the combination is an effective way to solve lots of problems and find interesting new ones.
Newton was definitely a scientist, by any reasonable meaning of the word. But not all the time.
The mystical passage that we've quoted, complete with alchemical symbols[59] and obscure terminology, is one that he wrote in the 1690s after more than twenty years of alchemical experimentation. He was then aged about 50. His best work, on mechanics, optics, gravity, and calculus, was done between the ages of 23 and 25, though much of it was not published for decades.
Many elderly scientists go through what is sometimes called a 'philosopause'. They stop doing science and take up not very good philosophy instead. Newton really did investigate alchemy, with some thoroughness. He didn't get anywhere because, frankly, there was nowhere to go. We can't help thinking, though, that if there had been somewhere, he would have found the way.
We often think of Newton as the first of the great rational thinkers, but that's just one aspect of his remarkable mind. He straddled the boundary between old mysticism and new rationality. His writings on alchemy are littered with cabbalistic diagrams, often copied from early, mystical sources. He was, as John Maynard Keynes said in 1942, 'the last of the Magicians ... the last wonder-child to whom the Magi could do sincere and appropriate homage'. What confuses the wizards is an accident of timing -well, we must confess that it is actually a case of narrative imperative. Having homed in on Newton as the epitome of scientific thinking, the wizards happen to catch him in post-philosopausal mode. Hex is having a bad day, or perhaps is trying to tell them something.
If Archimedes wasn't a scientist and Newton was only one sometimes, just what is science?
Philosophers of science have isolated and defined something called the 'scientific method', which is a formal summary of what the scientific pioneers often did intuitively. Newton followed the scientific method in his early work, but his alchemy was bad science even by the standards of his day, when chemists had already moved on. Archimedes doesn't seem to have followed the scientific method, possibly because he was clever enough not to need it. The textbook scientific method combines two types of activity. One is experiment (or observation - you can't experiment on the Big Bang but you can hope to observe traces that it left). These provide the reality-check that is needed to stop human beings believing something because they want it to be true, or because some overriding authority tells them that it's true. However, there is no point in having a reality-check if it's bound to work, so it can't just be the same observations that you started from.
Instead, you need some kind of story in your mind.
That story is usually dignified by the word 'hypothesis', but less formally it is the theory that you are trying to test. And you need a way to test it without cheating. The most effective protection against cheating is to say in advance what results you expect to get when you do a new experiment or make a new observation. This is 'prediction', but it may be about something that has already happened but not yet been observed. 'If you look at red giant stars in this new way then you will find that a billion years ago they used to ...' is a prediction in this sense.
The most naive description of the scientific method is that you start with a theory and test it by experiment. This presents the method as a single-step process, but nothing could be further from the truth. The real scientific method is a recursive interaction between theory and experiment, a complicity in which each modifies the other many times, depending on what the reality-checks indicate along the way.
A scientific investigation probably starts with some chance observation. The scientist thinks about this and asks herself 'why did that happen?' Or it may be a nagging feeling that the conventional wisdom has holes in it. Either way, she then formulates a theory. Then she (or more likely, a specialist colleague) tests that theory by finding some other circumstance in which it might apply, and working out what behaviour it predicts. In other words, the scientist designs an experiment to test the theory.
You might imagine that what she should be trying to do here is to design an experiment that will prove her theory is correct[60]. However, that's not good science. Good science consists of designing an experiment that will demonstrate that a theory is wrong -if it is. So a large part of the scientist's job is not 'establishing truths', it is trying to shoot down the scientist's own ideas.
And those of other scientists. This is what we meant when we said that science tries to protect us against believing what we want to be true, or what authority tells us is true. It doesn't always succeed, but that at least is the aim.
This is the ma
in feature that distinguishes science from ideologies, religions and other belief systems. Religious people often get upset when scientists criticise some aspect of their beliefs.
What they fail to appreciate is that scientists are equally critical about their own ideas and those of other scientists. Religions, in contrast, nearly always criticise everything except themselves.
Buddhism is a notable exception: it emphasises the need to question everything. But that may be going too far to be helpful.
Of course, no real scientist actually follows the textbook scientific method unerringly. Scientists are human beings, and their actions are driven to some extent by their own prejudices. The scientific method is the best one that humanity has yet devised for attempting to overcome those prejudices. That doesn't mean that it always succeeds. People, after all, are people.
The closest that Hex manages to come to genuine science is Phocian the Touched's lengthy and meticulous investigation of Antigonus's theory of the trotting horse. We hope that you have heard of neither of these gentlemen, since, to the best of our knowledge, they never existed. But then, neither did the Crab Civilisation -which didn't stop the crabs making their Great Leap Sideways. Our story here is modelled on real events, but we've simplified various otherwise distracting issues. With which we shall now distract you.
The prototype for Antigonus is the Greek philosopher Aristotle, a very great man who was 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 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 a
rrive 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.
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