Episode 18 - The spectrum, colour, and Goethe's quarrel with Newton

Tomlin Hawthorne

If you're looking at a screen, or you've got one near you, find something yellow on it. A lemon, a taxi, a smiley face.

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Here's the question. How much yellow light is coming out of that screen?

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None. None at all. There isn't a single source of yellow light anywhere in your phone. If you could look closely enough, and by the end of this episode you will, you'd see that the lemon is made of tiny red lights and tiny green lights, side by side, and nothing else.

Tomlin Hawthorne

The yellow is being made somewhere, though. You can see it. Today's question is where. What is colour, and where does it live?

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Last time I asked you to melt a bar of chocolate in a microwave with the turntable out. If you did, you found soft spots about six centimetres apart. Double that, multiply by the two thousand four hundred and fifty million on the back of the oven, and you get very close to three hundred thousand kilometres a second. You measured the speed of light with confectionery. I hope it tasted of achievement.

Tomlin Hawthorne

And we learned what light is. A wave in electric and magnetic fields. So colour ought to be simple now. And in one way it is, and in another way it's one of the most slippery things in the series. To show you both, I need to stage a fight.

Tomlin Hawthorne

In the red corner, Isaac Newton, whom you know.

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In the other, Johann Wolfgang von Goethe. The author of Faust. The greatest writer in the German language, a statesman, a man who was a celebrity across Europe at twenty-five and remained one for sixty years.

Tomlin Hawthorne

Goethe published a great many things. And late in life he told his secretary which of them he was proudest of. Not Faust. Not the poems. He said that as a poet he didn't think much of himself; there had been better ones. But in the difficult science of colours, he was the only person in his century who knew the truth.

Tomlin Hawthorne

He meant his Theory of Colours. It runs to well over a thousand pages, it took him twenty years, and a large part of it is an attack on Newton so ferocious that his friends were embarrassed. He calls Newton's theory an old castle, riddled with rats and owls, that ought to be pulled down.

Tomlin Hawthorne

As physics, Goethe's book is wrong. I should say that plainly. But he was on to something that Newton had left out, and by the end of the episode I hope you'll think, as I do, that it was a draw.

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So. Newton first.

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It's 1666. He's twenty-three, at home on the farm during the plague, the same eighteen months in which he's thinking about the apple. He has bought a glass prism at a country fair. People knew that prisms made colours. The usual explanation was that the glass stained the light somehow, added colour to it, the way a dye stains water.

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Newton darkens his room. He makes a small hole in the window shutter, so a single beam of sunlight comes in. He puts the prism in the beam. And on the far wall, twenty feet away, he gets a band of colour. Red at one end, then orange, yellow, green, blue, violet.

Tomlin Hawthorne

Everybody had seen that much. But Newton notices something about its shape. The beam came in round. The patch on the wall is a long strip, five times longer than it is wide. The prism has stretched the light out, and stretched it according to colour. The red has been bent least, the violet most.

Tomlin Hawthorne

Then he does the experiment he called the crucial one. He puts a board in the way with a slit in it, so that only one colour gets through. Just the green, say. And he sends that green light through a second prism.

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If the glass were adding colour, the second prism should change the green into something else. It doesn't. The green goes in and green comes out. It bends, by the same amount as before, and that's all. It can't be split any further.

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And then the final step. He uses a lens to bring the whole coloured strip back together to a point. And where the colours overlap again, the spot is white.

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So here's Newton's conclusion, and it overturned two thousand years of thinking. White light isn't pure. Everyone since Aristotle had assumed white was the simple, original thing, and colours were white light that had been dimmed or tainted. It's the other way round. White is the mixture. The colours are the ingredients. The prism doesn't add anything. It sorts.

Tomlin Hawthorne

A small confession on Newton's behalf. He said there were seven colours in the spectrum. There aren't seven of anything. It's a smooth blend. But Newton had a mystical streak, and he believed colours should match the seven notes of the musical scale. So he put in orange and, especially, indigo, to make the number come out. Indigo has been confusing schoolchildren for three and a half centuries because Isaac Newton wanted light to be in tune.

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After Maxwell, we can say what the ingredients are.

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Light is an electromagnetic wave. And the colours are different wavelengths. Red light has a wavelength of about seven hundred billionths of a metre. Violet is about four hundred. The other colours are in between. The prism bends short waves more than long ones, and that's the sorting.

Tomlin Hawthorne

Now here's the part I find wonderful. Maxwell's equations don't stop at red and violet. Why would they?

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In 1800 the astronomer William Herschel, the man who discovered Uranus, was curious which colour of sunlight carried the most heat. So he spread out a spectrum with a prism and put thermometers in the different colours. And for a comparison, he put one more thermometer just past the red end, in the dark, where there was no light at all.

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That one got hottest.

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There was something there. Invisible, beyond the red, and carrying heat. We call it infrared. It's what you feel on your skin from a fire across the room.

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A year later a young German, Johann Ritter, reasoned that if there's something beyond the red, there might be something beyond the violet. He used a chemical that darkens in light, and found that it darkened fastest in the empty space just past the violet. Ultraviolet. It's what gives you sunburn.

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And it goes on in both directions. Longer than infrared: microwaves, and then radio waves, which can be the length of a football pitch. Shorter than ultraviolet: X-rays, and then gamma rays, which are smaller than an atom.

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All of it is the same thing. All of it is light. The radio signal carrying this podcast, the heat from your radiator, the X-ray at the dentist. Same wave, same speed, different length.

Tomlin Hawthorne

And the part we can see is tiny. If you laid the whole range out as a piano keyboard, with each octave a doubling of frequency, the keyboard would have dozens of octaves. The eye sees less than one. One octave out of all that. We've been looking at the universe through a letterbox.

Tomlin Hawthorne

Why that octave? Two reasons, and they're the same reason. It's where the Sun gives out most of its light. And it's a range that passes cleanly through air and through water. Eyes evolved, in the sea, to use the light that was there. If we'd grown up round a cooler star, we'd see what we now call infrared, and have some other word for it.

Tomlin Hawthorne

So that's Newton's side. Colour is wavelength. Red is seven hundred, violet is four hundred. Done.

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And now Goethe gets his say. Because that account, clear as it is, leaves out something that should bother you.

Tomlin Hawthorne

Your phone screen.

Tomlin Hawthorne

There's no wavelength for yellow coming out of it. Yellow light, real yellow, the kind from a sodium street lamp, has a wavelength of about five hundred and eighty. Your screen doesn't make that. It makes red, around six hundred and thirty, and green, around five hundred and thirty, and it shines both at you from dots too small to tell apart. And you see yellow. The same yellow. You can't tell the difference between the two.

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So two completely different things in the world, a single wave of five-eighty, and a mixture of six-thirty and five-thirty, produce one experience.

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Here's why. At the back of your eye there are three kinds of colour sensor. They're called cones. Roughly, one kind responds best to long waves, one to medium, one to short. Every colour you've ever seen is your brain's interpretation of just three numbers: how strongly each kind of cone is firing.

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Pure yellow light tickles the long and the medium cones about equally. Red plus green light also tickles the long and the medium cones about equally. Your brain gets the same report. It says yellow.

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It goes further. Think of magenta, that vivid pinkish purple. Find it in the rainbow. You can't. It isn't there. There's no wavelength of magenta. It's what your brain reports when the long cones and the short cones fire together and the middle ones don't, which no single wave can do. Magenta is a colour the brain invents.

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So colour, the thing you experience, isn't wavelength. It's something eyes and brains build, using wavelength as raw material. A dog, with two kinds of cone, lives in a different coloured world. A bee sees ultraviolet patterns on flowers that are invisible to us. Neither is seeing things wrong.

Tomlin Hawthorne

And this was Goethe's ground. He'd started, it must be said, with a mistake. He borrowed some prisms, and when the owner asked for them back he hastily looked through one at a white wall, expecting to see it burst into colours. It stayed white. And he exclaimed that Newton was wrong. He'd misunderstood the experiment: you need a narrow beam.

Tomlin Hawthorne

But then he did twenty years of careful looking. At coloured shadows: stand between a candle and the twilight and your shadow from the candle is blue. At after-images: stare at a red patch, look away at a white wall, and a green one floats there. At how a colour changes depending on what's next to it. None of that is in Newton. All of it is true. Painters took it up. Turner made a painting and named it after Goethe's theory. The science of how we perceive colour starts as much with him as with anyone.

Tomlin Hawthorne

Newton had told us what light is. Goethe was trying to tell us what colour is like. And he was right that the first doesn't settle the second.

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One more witness, and this one's for the classicists.

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In 1858 William Gladstone, between spells as Chancellor of the Exchequer, published a three-volume study of Homer. And tucked into it is a chapter on Homer's use of colour, in which Gladstone points out something very odd.

Tomlin Hawthorne

Homer's sea is wine-dark. Fine, poetic. But so are his oxen. His honey is green. His sheep are violet. Iron is violet too. And the sky, that brilliant Aegean sky, is never once called blue. There's no word for blue in the Iliad or the Odyssey at all.

Tomlin Hawthorne

Gladstone concluded that the Greeks must have been partly colour-blind. They weren't. Their eyes were the same as ours. But it turned out not to be only Homer. Scholars looked at ancient Hebrew, at the Vedas, at the Icelandic sagas. No blue. And across the world's languages, colour words turn up in a surprisingly regular order. Black and white first. Then red. Then green or yellow. Blue comes late, nearly always last.

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Guy Deutscher tells this story in a book called Through the Language Glass. And it leaves a real question. They saw the same wavelengths we do. Did they see the same sky?

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While we're on the sky. Why is it blue?

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Sunlight is white: all the colours. As it comes down through the air, it hits molecules, and they scatter a little of it sideways. And they scatter short waves far more than long ones. Blue light gets bounced around the sky about five times more than red. So when you look up, away from the Sun, what reaches your eye is the scattered light, and it's mostly blue. The sky is the blue that was taken out of the sunbeam.

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And at sunset, you're looking at the Sun through a great thickness of air, edge-on. Nearly all the blue has been scattered out of the beam along the way. What's left to reach you is the red and orange.

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A blue sky and a red sunset are the same fact, seen from two angles.

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The myth of the week: that colour is in things. That a tomato is red the way it's round.

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A tomato absorbs most of the light that falls on it and throws back the long waves. That's all it does. Red is what happens when those waves reach an eye like yours. In the dark, the tomato isn't red. Under a pure green light, it's black.

Tomlin Hawthorne

And the question to take away.

Tomlin Hawthorne

Newton says colour is wavelength and gives you a number. Goethe says colour is an experience and gives you a thousand pages. Are they disagreeing? Or are they answering two different questions that happen to use the same word?

Tomlin Hawthorne

And where else does this happen? Where else do the sciences and the humanities think they're arguing, when one is describing the mechanism and the other is describing what it's like? I can think of a few. Music. Pain. Time, perhaps, from two episodes back.

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Your challenge. Three things to see.

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One. Put a single drop of water on your phone screen, on a white area. It acts as a magnifying glass. Look closely. You'll see the red, green and blue dots. Slide the drop on to something yellow. No yellow dots.

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Two. Find an old CD or DVD. Tilt it under a lamp. The fine grooves spread the light into a spectrum, just as a prism does. That's Newton's experiment, on a coaster.

Tomlin Hawthorne

Three. A glass of water, a few drops of milk, and the torch on your phone, in a dark room. Shine the torch through the glass from one side. Look at the glass from the side: it's faintly blue. Now look straight down the beam, through the glass, at the torch. It's orange. You've made a sky and a sunset in a tumbler.

Tomlin Hawthorne

Next time. In 1835, a great French philosopher announced the one thing humanity would never, ever know. He picked the chemical composition of the stars. He'd have been safer with almost anything else.