Episode 01 - From Myth To Model

Tomlin Hawthorne

Here is a question to start with. You are standing in Egypt, about 2,200 years ago. You own a stick. You have never left North Africa, there are no ships that cross oceans, and nobody will see the planet from above for another twenty-two centuries.

Tomlin Hawthorne

How big is the Earth?

Tomlin Hawthorne

Take a guess at how you would even begin. I'll wait.

Tomlin Hawthorne

By the end of this episode you will know how a librarian did it, with the stick, and got within a few per cent of the right answer. And I want to suggest that the way he did it is the whole subject of this series in miniature.

Tomlin Hawthorne

Welcome. This is a series about physics for people who were told, at some point, that physics was not for them. Possibly by a teacher. Possibly by a quadratic equation.

Tomlin Hawthorne

I want to make a promise and a confession. The promise is that there will be no problem sets. You will not be asked to calculate the tension in a rope. I have never met anyone whose life was improved by knowing the tension in a rope, including people who work with ropes.

Tomlin Hawthorne

The confession is that this is still going to be hard, in the way that a good novel is hard. The ideas are strange. Some of them took the cleverest people who ever lived several decades to accept, and a few of those people died still refusing. So if something in this series strikes you as absurd, you are in excellent company. Hold on to that feeling. It usually means you have understood the claim correctly.

Tomlin Hawthorne

So. Fifty episodes, from the first people who tried this to the questions nobody can answer yet. Why time runs one way. What light is. Whether the Moon is there when nobody looks, which sounds like a joke and was, for about thirty years, Albert Einstein's actual complaint.

Tomlin Hawthorne

But today we start before any of that. Today's question is: what kind of explanation is a physical explanation? What are these people doing, exactly?

Tomlin Hawthorne

Let me read you two accounts of where the world came from. Well, describe them.

Tomlin Hawthorne

The first is by Hesiod, a Greek poet, around 700 BC. In his telling, first there is Chaos, a sort of yawning gap. Then Earth appears, broad-chested, and then Love. Earth gives birth to Sky, who is the same size as her, so that he can cover her completely. They have children. The children are a problem. There is a castration, with a sickle. It is quite a family.

Tomlin Hawthorne

Now, I am not mocking this. It is a magnificent poem, and it is an explanation. It answers the question "why is the world like this?" and the form of the answer is a story about persons. Things happen because somebody wanted something. The sky is up there because of a relationship.

Tomlin Hawthorne

Here is the second account. About a century later, in a port city called Miletus on what is now the Turkish coast, a man named Thales says: everything is water.

Tomlin Hawthorne

That's it. That's the theory.

Tomlin Hawthorne

And it is wrong. I want to be clear about that. Everything is not water. If you take away one fact from this episode, it should not be that one.

Tomlin Hawthorne

But look at what kind of wrong it is. Thales has looked at the world, at ice and steam and rivers and the damp inside living things, and he has said: perhaps under all this variety there is one stuff, and the variety is that stuff rearranged. There are no persons in his account. Nobody wants anything. The explanation for nature is more nature.

Tomlin Hawthorne

And because it is a claim about stuff, you can argue with it. You cannot really argue with the sickle. You can argue with water. Fire, for instance. Is fire water? That seems like a difficulty.

Tomlin Hawthorne

Which brings me to my favourite person in today's episode, and he is not Thales. He is Thales's student. His name is Anaximander.

Tomlin Hawthorne

Anaximander listens to his teacher, the most famous wise man in the Greek world, and says, in effect: thank you, that was fascinating, I think you are mistaken. And then he explains why, in public, and offers something better.

Tomlin Hawthorne

The physicist Carlo Rovelli wrote a whole book arguing that this moment is the real birth of science. Before it, the world had two models for what you do with a teacher. You could revere the master and preserve his words, or you could reject him and start a rival school. Anaximander invents a third thing. You take your teacher seriously enough to learn everything he knows, and then you take him seriously enough to find the mistake.

Tomlin Hawthorne

That is still the whole method. Everything else is equipment.

Tomlin Hawthorne

And Anaximander's own idea is worth a moment, because it is one of the great leaps of the human mind and almost nobody has heard of it.

Tomlin Hawthorne

Everyone at the time knew that things fall down. So the Earth must be sitting on something, or it would fall. Thales said it floats on water. Other traditions said a turtle, or pillars, or an elephant on a turtle, and at that point you have what we might call a supply-chain problem. What is the turtle standing on?

Tomlin Hawthorne

Anaximander says: the Earth isn't sitting on anything. It is floating in the middle of space, with sky all the way round, including underneath. And it does not fall, because there is no particular direction for it to fall in.

Tomlin Hawthorne

Think about how hard that is. He has understood that "down" is not a direction in the universe. Down is a direction toward the Earth. He worked that out in the sixth century BC, from an armchair, and he was right.

Tomlin Hawthorne

Now I owe you a stick.

Tomlin Hawthorne

Jump forward three hundred years, to Alexandria, around 240 BC. The head of the great library is a man called Eratosthenes. His colleagues nicknamed him Beta, because he was the second best in the world at everything. Which I think is meant to be an insult, and I would take it.

Tomlin Hawthorne

Eratosthenes has heard a report from a town in the far south of Egypt called Syene, where Aswan is today. The report says that at noon on the longest day of the year, the Sun shines straight down a deep well and lights the water at the bottom. Straight down. Vertical objects cast no shadow at all.

Tomlin Hawthorne

And he knows that in Alexandria, at the same moment on the same day, a vertical stick does cast a shadow. A short one. The Sun is a little off overhead, by about seven degrees.

Tomlin Hawthorne

Most people would file that under "huh." Eratosthenes sees what it means.

Tomlin Hawthorne

Picture it with me. If the Earth were flat, and the Sun very far away, then the Sun's rays would arrive parallel, and every stick everywhere would have the same shadow. They don't. So the ground at Alexandria must be tilted compared with the ground at Syene. The surface is curved. And the difference in the shadows tells you how much it curves between those two towns: seven degrees.

Tomlin Hawthorne

Seven degrees is about one-fiftieth of a full circle.

Tomlin Hawthorne

So the distance from Syene to Alexandria is one-fiftieth of the way round the world. He knows that distance, roughly, because people walked it and caravans timed it. So he multiplies by fifty.

Tomlin Hawthorne

His answer comes out somewhere near 40,000 kilometres. The modern figure is 40,000 kilometres. There is some argument about exactly how long his unit of length was, so he may have been off by ten or fifteen per cent, but come on. He measured a planet with a stick and a rumour about a well.

Tomlin Hawthorne

I love this for two reasons.

Tomlin Hawthorne

The first is that nothing about it needed special equipment. Anybody could have done it for thousands of years. What was missing was not technology. It was a way of looking: the idea that a small, dull fact, the length of a shadow, could be evidence about something enormous.

Tomlin Hawthorne

The second reason is more uncomfortable, and it's the important one. Eratosthenes had to assume something. He assumed the Sun is very far away, so that its rays arrive parallel.

Tomlin Hawthorne

Suppose he's wrong about that. Suppose the Earth is flat and the Sun is small and close, hovering a few thousand kilometres up. Then you get exactly the same shadows. A nearby lamp over a flat table gives different shadow angles at different places too.

Tomlin Hawthorne

So the measurement on its own does not settle it. What settles it is the measurement plus everything else you know: that ships disappear hull-first over the horizon, that the Earth's shadow on the Moon during an eclipse is always round, that travellers going south see new stars. Evidence comes in a web. No single strand holds the weight.

Tomlin Hawthorne

I am telling you this in episode one because people often picture science as a series of knockout proofs, and it almost never works like that. It works like a good legal case, or a good historical argument. And you already know how those work.

Tomlin Hawthorne

What Eratosthenes was using is called a model. That word is going to follow us around for fifty episodes, so let's get it straight.

Tomlin Hawthorne

A model is a deliberately simplified picture of something, built to answer particular questions. The best everyday example I know is the map of the London Underground, or any metro map. It is a terrible picture of London. The distances are wrong. The river is a blue suggestion. Stations that are a three-minute walk apart look like a journey.

Tomlin Hawthorne

And it is brilliant, because it is right about the one thing you need: what connects to what. It lies about almost everything in order to tell the truth about one thing.

Tomlin Hawthorne

Every theory in physics is like that. The question to ask of a model is never "is this the whole truth?" It never is. The question is "which parts of this are carrying the weight, and how would I know if they failed?"

Tomlin Hawthorne

Which lets me say a word in defence of a man who usually plays the villain in these stories. Aristotle.

Tomlin Hawthorne

Aristotle's physics said: heavy things fall faster than light things. Things in motion come to a stop unless something keeps pushing them. Earthy stuff goes down, fiery stuff goes up.

Tomlin Hawthorne

You may have been told this was foolish. I'd like you to go and check. Drop a hammer and a feather. Slide a book across a table and take your hand away. Light a candle. Aristotle is describing the world you actually live in, a world with air and friction in it, and he is describing it well. His model held for two thousand years, and it lasted because it worked.

Tomlin Hawthorne

It took a genuinely odd person, whom we will meet in episode four, to suspect that the friction was hiding something. Being replaced by a better model is not the same as having been stupid. Almost everyone in this series was eventually replaced.

Tomlin Hawthorne

Theory.

Tomlin Hawthorne

In ordinary speech, a theory is a hunch. "I have a theory about why Marcus is never at the Monday meeting." It means a guess you haven't checked.

Tomlin Hawthorne

In physics the word means nearly the opposite. A theory is the big explanatory structure, the thing that has been tested from every direction anyone could think of and has survived. The hunch has a different name. It's called a hypothesis, or on a good day, a conjecture.

Tomlin Hawthorne

So when someone says that relativity is "only a theory," the right response is: yes, in the way that Hamlet is only a play. That is its category. It isn't a mark out of ten.

Tomlin Hawthorne

And what makes a guess graduate into a theory? Richard Feynman, who will be a regular guest in this series in spirit, gave the recipe in a lecture in 1964, and he got a laugh for how simple it was. First, you guess. Then you work out what would follow if your guess were right. Then you compare that with what nature actually does. If it disagrees with experiment, the guess is wrong.

Tomlin Hawthorne

And then he added the part that matters. It makes no difference how beautiful your guess is, he said, or how clever you are, or what your name is. If it disagrees with experiment, it's wrong.

Tomlin Hawthorne

That is Anaximander again. It doesn't matter that your teacher is Thales.

Tomlin Hawthorne

So, back to the question I opened with. What kind of explanation is a physical explanation?

Tomlin Hawthorne

Here is my best short answer. It explains nature by nature, with no one's wishes involved. It is built as a model, simplified on purpose. It sticks its neck out, by saying something that could turn out false. And it is held by people who have agreed, in advance, to be told they are wrong.

Tomlin Hawthorne

That last one is the hardest. It is much harder than the mathematics.

Tomlin Hawthorne

I'll leave you with a question I can't answer, and we will come back to it in the very last episode to see whether your view has moved.

Tomlin Hawthorne

We talk about the laws of nature. It's an odd phrase when you look at it. A law, in the usual sense, is something a legislature passes and people sometimes break. Nature has no legislature and, as far as we can tell, no offenders.

Tomlin Hawthorne

So is a law of nature discovered, like a continent? Was it sitting there before anyone looked? Or is it invented, like a grammar, a tidy system that we lay over a world that is just doing what it does?

Tomlin Hawthorne

Is it more like a statute, a rule of grammar, or a habit?

Tomlin Hawthorne

Physicists split on this, and they get surprisingly heated.

Tomlin Hawthorne

And your challenge for the week. It takes five minutes and a piece of paper.

Tomlin Hawthorne

Draw Eratosthenes. A circle for the Earth, two sticks standing on it a little way apart, and parallel lines coming in from the Sun. Convince yourself the shadows have to differ.

Tomlin Hawthorne

Then draw the other version. A flat line for the ground, the same two sticks, and a small Sun close overhead. Convince yourself you get shadows that differ in just the same way.

Tomlin Hawthorne

And then ask: if those were the only two drawings I had, what else would I go and look at to decide between them?

Tomlin Hawthorne

If you can answer that, you have done some physics, and you didn't need a single equation. You did need a stick.

Tomlin Hawthorne

Next time: how big is big? We are going to travel from the inside of a proton to the edge of the visible universe in about eighteen minutes, and find out why there are no ants the size of horses. There's a reason, and you'll be glad of it.