Under the Pillow

There is a particular silence in a dormitory at twenty to seven on a Saturday. It is the silence of eleven girls who have been told they may sleep until eight and intend to use every minute.

I woke into it because something was pressing against my cheek. It was the corner of a notebook: a thick one, black, with an elastic band around it and a sheet of paper folded under the band. The notebook had been pushed under my pillow while I slept, which I would have found alarming if I hadn’t recognised the handwriting on the paper at once. Ada writes as if each letter has done something to annoy her.

I read it three times. Then I got out of bed, in my socks, and went to the window, as if I might see her from there, a small figure in a red coat crossing the playing fields. There was nothing out there but mist lying on the grass like milk in a saucer, and the rooks going up out of the trees behind the chapel, and the hill beyond, grey-green, with the sky just starting to go pale over it.

Gone to look for it. For the fireball. For the pieces. Of course she had. The only surprising thing was that I hadn’t woken at midnight to find her gone already.

I would like to tell you that I turned straight to the last page. It is what the girl in a proper adventure would do. I did not. Not then. I sat back down on my bed with the notebook in my lap and the elastic band around my wrist, and I did not open it at the back, because Ada had told me not to, and because she would know.

This is the most important fact about me, and you should have it before we go any further: I do what I am told, right up until the moment I don’t. It had never yet reached that moment. This was the day it did.

---

I knew the notebook. That was the strange thing. I had seen it dozens of times and never once been allowed to look inside it.

Ada had started it in January. I know because I was there: it was the last evening of the Christmas holidays, the night before Dad drove her back to Stanbury for the spring term, at the kitchen table at home. She had come back from the stationery shop with it that afternoon, and she sat down and wrote something on the first page and then tore the page out. Then she wrote something on the new first page and tore that out too. By the end of the evening there were four crumpled balls of paper on the table and one sentence in the book, and when I leaned over to read it she slammed it shut so fast she caught my fingers.

“What is it?”

“Nothing.”

“It’s not nothing, you’ve been writing it for three hours.”

“It’s for someone who’ll read it properly,” she said, “when it’s ready,” and she put the elastic band round it and took it upstairs.

After that, whenever Ada was home, the notebook was too. I was still at primary school then, so I only saw my sister at half-terms and holidays and on the odd weekend when Dad drove over to fetch her, and it came every single time. On the back seat of the car on the way home from Stanbury, balanced on her knees while she wrote over the bumps. On the arm of the sofa in the Easter holidays. On the bench at our old swimming club in the summer, the only six weeks of the year when we trained in the same pool, wrapped in a towel so the splashes couldn’t get at it. On the beach in August, in a freezer bag so the sand wouldn’t get in, with a biro clipped to the cover. She wrote in it the way other people check their phones. I had assumed it was a diary. I had assumed the someone who would read it properly was a boy, or a university, or God. It had never once occurred to me that it was me.

Now I held it and looked at it properly for the first time. It was fatter than a notebook ought to be, because things had been stuck into it: a folded map, a photograph of some kind of striped red rock, a printout of a graph, a pressed leaf. The corners were soft from being carried. There were coloured sticky tabs all down one edge, and on each one, in Ada’s furious capitals, a word: ATOMS. SAND. DICE. VENTS. COPIES. OXYGEN. GIRAFFES. The last tab, near the back, just said: THE END (NOT YET).

On the inside of the front cover she had drawn, very carefully in pencil, a tray with shallow dents in it and marbles sitting in them. I didn’t know what it meant. I would by breakfast.

And then I remembered something, sitting there while the dormitory breathed around me. I remembered being six, in the back of the car, on the long drive to Granny’s, with Ada nine and Dad driving and Mum asleep. And Ada asking Dad why the sky is blue. And Dad, who is an engineer and cannot resist a question like that, explaining about sunlight being all the colours mixed together, and the air scattering the blue part about more than the red. The more is the whole trick, he said. The red mostly goes straight through, but the blue gets bounced off the air in every direction, so wherever you stand and whichever way you look, some of it is coming at you from that bit of the sky. That’s all a blue sky is: bounced blue, arriving from everywhere. And nothing says a sky has to be blue. Ours is, because of what our air is made of and how much of it there is. On Mars, where robot rovers have taken photographs, the daytime sky is the colour of butterscotch, from fine red dust, and the sunsets are blue.seenHow we know NASA’s rover Spirit photographed a blue sunset over Gusev Crater on Mars in 2005, and Curiosity photographed another from Gale Crater in April 2015; the rovers’ daytime pictures show a tan, dusty sky. What “seen” means And our own sky changes colour every evening: when the Sun is low, its light comes through so much more air that most of the blue has been bounced away before it reaches you, and what’s left is orange and red.

Ada was quiet for a long time, the way she still goes quiet, and then she said, “But how do you know?”

Dad took his eyes off the road, which Mum would not have liked, and looked at her in the mirror. “Ada,” he said, “that is the best question there is, and most people go their whole lives without asking it.” He looked back at the road. “Strictly, you don’t. Not the way you know your own name. Somebody looks, and sees something. Once is just a story, so they look again, and other people look, somewhere else, with different equipment. Then somebody comes up with an explanation, and uses it to predict something nobody has looked at yet, and they go and look. If the prediction’s wrong, the explanation’s wrong, however much everybody likes it. If it’s right, the explanation survives. Not proved. Survives, until the next test.” He tapped the steering wheel. “The ones that survive thousands of tests are the ones you bet your life on. These brakes, for a start. And the bridge over the Tamar, in about three hours.”

And then, because he is Dad, he pointed at the satnav on the dashboard, the little screen with our car as an arrow crawling along a road. “You want to know how we know things? That thing shows where we are because a man called Einstein was right and a man called Newton was very slightly wrong.” And for the next forty miles he told us about it, and I understood about one word in five, and Ada understood all of them, and asked for more. (I got the other four words in five on the Saturday this story is about, in a minibus, from a physics teacher, and you’ll get them there too: chapter 12.)

I asked too, in the end. Not that day: that day I was six, and mostly wanted to know if we were nearly there. But the next time we drove to Granny’s I was the one who asked why the Moon kept following the car. A year after that I wanted to know why the bath water always went down the plughole the same way round, and whether it did that everywhere. I asked Mum, and Mum didn’t know, and Mum never guesses: we found out together, which with Mum means a library book, two websites that disagree and most of an evening, and the answer was better than the question. The Earth spins, and that gives a very gentle push to anything moving across it: water flowing towards a plughole gets turned a tiny bit, one way in the top half of the world and the other way in the bottom half. On something as big as a storm the push adds up, and it’s why hurricanes turn one way north of the equator and the other way south of it. But in a bath it’s so tiny that it loses to everything else, and the water goes whichever way it was already swirling when you pulled the plug. The Earth’s spin only wins if you fill a tank and leave it perfectly still for a whole day first, and an engineering professor in America once did exactly that, just to find out. His went anticlockwise. When some people in Australia did the same, theirs went clockwise.seenHow we know Ascher Shapiro, at the Massachusetts Institute of Technology, filled a tank about two metres across, left it to settle for a day, and saw it drain anticlockwise every time; he reported it in the journal Nature in 1962. A team in Sydney repeated it in 1965 and saw it go clockwise. What “seen” means That was when I learned that “let’s find out” is a real answer, and sometimes the best one.

So Ada wasn’t the one who asked and me the one who didn’t. We both asked. The difference was that Ada wrote her answers down.

I don’t think she ever stopped asking. I think, if I’m honest, the notebook is her answer, and she wrote it for the one person she was sure would keep on asking after her.

Someone’s alarm went off at the far end of the dormitory and was smacked quiet. Elsie turned over and said something about pancakes in her sleep. I pulled the duvet up over my head like a tent, clicked on the little torch on my keyring, slid off the elastic band, and opened the notebook at page one.

The first thing in it wasn’t science at all.

I read that twice. It’s for Stella. In January. Eight months before I’d come to Stanbury, before I’d even known for certain I was coming. I sat very still under the duvet in my torchlit tent, with the feeling you get at the top of a very high slide.

Then I turned the page.

Notebook 1

Rare Things Happen Often

How atoms, chance and a very long time made us and everything around us. By Ada, for Stella, who will read it properly.

Stella. If you’re reading this, either I’ve finished it and given it to you, or something’s happened and I haven’t, and you’ve got it anyway. Either way: hello. This is how you and I and everything alive got to be here, starting from nothing but atoms. It’s the most amazing story I know, and nobody ever told it to me properly, so I’m telling it to you. There’s no villain in it. There isn’t really anybody in it until the very end. But it has the biggest numbers you’ve ever seen, a lot of people who worked things out, and some things nobody has worked out yet, which might be the best part.

First, three rules.

Rule one. Nothing in this notebook wants anything.

Atoms want nothing. Molecules try nothing. Cells decide nothing. Evolution isn’t a person, and designs nothing. In here, nothing wants, tries, chooses or intends anything until about four billion years in, when something with a brain turns up, and even then only the thing with the brain does it. When something happens in here, it’s because of how often it happens, how much energy was around, and what happened to be next to what. That turns out to be enough. That’s the whole point.

Every time you catch me writing that an atom wants something, I owe you a pound. You know why.

I did know why. It was because of a giraffe.

It was the Easter holidays, and there was a nature programme on, and a deep, kind voice said that, over many generations, the giraffe had stretched its neck to reach the highest leaves. Ada threw a cushion at the television.

“It didn’t stretch anything,” she said. “Stretching your neck doesn’t give your children longer necks. If the ones that happened to be born with longer necks got more leaves, and so had more babies, then the next lot had longer necks, on average. Nobody’s neck got longer on purpose. Nothing wanted anything.”

“It’s a figure of speech,” said Mum.

“It’s a figure of speech that’s wrong.” Ada went and got the cushion back. “Every book does it. Atoms want full shells. Molecules try to join up. Cells decide to divide. Evolution designs an eye. It makes it sound as if there’s somebody in there wanting it all to happen, and the whole point is that there isn’t. It’s not a harmless shortcut. It smuggles in the exact thing that isn’t needed.”

Dad got the jar we keep for coins off the kitchen windowsill and put it on the coffee table. “Every time anybody in this house says something wants something,” he said, “a pound in the jar.”

“Including you,” said Mum, to Ada.

There were eleven pounds in it by the end of the holidays, and nine of them were Dad’s.

…

Rule two. I’ll be careful with the word “know”.

Remember the car, and the blue sky, and “how do you know”? Dad’s answer is rule two, and I’ve kept it. Science isn’t a pile of facts. It’s a way of finding things out. Once is just a story: look again, get other people to look, use the explanation to predict something nobody has seen yet, and go and see. An explanation that passes isn’t proved. It survives, until the next test.

So I’m going to mark the things in here that aren’t obvious, in the margin, three ways:

• seenHow we know An example of seen: how far away the Moon is. In 1969 the astronauts of Apollo 11 left a panel of small mirrors on the Moon, and later missions left more. Observatories on Earth fire pulses of laser light at them and time the faint echo: about two and a half seconds there and back. The speed of light is known, so that gives the distance, about 384,000 km, to within a few millimetres, and observatories in several countries have been doing it for more than fifty years. What “seen” means means someone has observed or measured it directly, and other people have repeated it.
• worked outHow we know An example of worked out: the centre of the Sun is about 15 million degrees. Nobody has been there, and no thermometer would survive it. It’s calculated from things that are measured, like the Sun’s weight, its size and how much light it gives out, using the physics of hot gas. And the calculation has been tested. It also predicts how many neutrinos, ghostly particles made only in the Sun’s core, should reach the Earth, and detectors in deep mines count them. For thirty years they found too few, and the puzzle turned out to be about the neutrinos, not the Sun: they change type on the way here. Counted properly, in 2001, they matched. What “worked out” means means it’s calculated or inferred from things that were measured, but nobody has watched it happen.
• best guessHow we know An example of best guess: dark matter. Galaxies spin as if they held far more mass than all the stars and gas we can see (across the whole universe, about five times more), and several completely different measurements agree that the extra mass is there. What it actually is, nobody knows. There are rival ideas, and experiments deep underground waiting to catch any of them. Until one works, it’s a best guess. What “best guess” means means it fits the evidence but hasn’t been properly tested yet, or there are rival explanations.

“Worked out” isn’t second best. Nobody has watched the Earth form, but radioactive clocks in the oldest rocks, in meteorites and in rocks from the Moon all give the same age, by different routes. Provisional doesn’t mean flimsy. It means honest.

Rule three. The numbers are the story. I’ll write very big and very small numbers the way scientists do: 10³ is a thousand, 10⁹ a billion, 10⁻³ a thousandth. Each step of one in the little raised number is ten times bigger, so 10²¹ isn’t “a bit more” than 10¹⁸: it’s a thousand times more. When you meet one, stop and feel how big it is. If you skip the numbers you’ll think I’m just telling you things.

I stopped there, because a head came round the curtain of my cubicle, and it was Elsie, with her hair sticking straight up.

“Wat r u doing,” she said, which is how Elsie talks before eight o’clock, as if she’s texting out loud.

“Reading.”

“Under your duvet. With a torch. At like, seven. On a Saturday.” She squinted at the page. “Is that homework?”

“It’s my sister’s,” I said. “It’s about how life started.”

Elsie considered this, and then said, “You’re so weird,” with great affection, and went back to bed.

I looked at the three marks in the margin. Seen. Worked out. Best guess. I thought about Dad in the car, taking his eyes off the road. And I wondered whether anyone had ever written anything for me that they’d torn out four first pages to get right. Then I turned the page.

…

A drop of the sea.

Put one drop of seawater on the tip of your finger. That’s about one twentieth of a millilitre.

Water is made of molecules, each one an oxygen atom with two hydrogen atoms attached. There are about 1.7 × 10²¹ of them in your drop worked outHow we know Nobody counts them. We weigh the drop, and divide by the weight of one water molecule. That weight was pinned down in 1908, at the Sorbonne in Paris, by the physicist Jean Perrin. He watched grains of gum, much smaller than a speck of dust but big enough for a microscope, being jiggled about in water by molecules far too small to see, and measured how far the grains wandered. Three years earlier Albert Einstein had worked out how far they should wander for any given number of molecules, so Perrin’s measurements gave the number. Completely different methods since give the same one: X-rays through crystals, the electric charge carried by atoms in a current, and, for the 2019 redefinition of the kilogram, counting the atoms in an almost perfect ball of silicon. What “worked out” means: seventeen hundred billion billion. If all eight billion people alive today counted one molecule each per second, without ever stopping to sleep, it would take them about six thousand seven hundred years to finish your drop.?1.7 × 10²¹ molecules shared among 8 × 10⁹ people is about 2.1 × 10¹¹ each, counted one a second. A year has about 3.16 × 10⁷ seconds, so that is 2.1 × 10¹¹ ÷ 3.16 × 10⁷ ≈ 6,700 years.

None of them is still. At room temperature a water molecule is moving, on average, at about 600 metres per second worked outHow we know Calculated from the temperature and the weight of a water molecule. The calculation has been checked where it can be watched directly, in gases: fire a beam of molecules at a row of spinning discs with slots in them, and only molecules of one particular speed get through every slot. Change how fast the discs spin, count what gets through, and you have the whole spread of speeds. The physicist Otto Stern did the first version in Frankfurt in 1920, and the measured speeds match the calculated ones. What “worked out” means, which is nearly twice the speed of sound in air. But in a liquid the molecules are packed shoulder to shoulder, so it gets almost nowhere. It travels a small fraction of its own width, strikes a neighbour, rebounds, strikes another, more than a trillion (10¹²) times a second worked outHow we know A molecule moving at about 600 metres per second, with its neighbours about 0.3 millionths of a millimetre away, reaches one about 600 ÷ 0.0000000003 = 2 × 10¹² times a second. The spacing comes from the drop’s weight and the number of molecules in it. There’s a check: flashes of laser light a millionth of a millionth of a second long can follow the links between neighbouring water molecules breaking and re-forming, and they change on that same timescale. What “worked out” means.

Now scale up. The oceans hold about 1.3 billion cubic kilometres of water worked outHow we know From the depth of the sea floor over the whole Earth. Ships map it by sending pulses of sound down and timing the echo: under a kilometre of water it comes back about 1.3 seconds later. Between the ships’ tracks, satellites measure tiny bumps in the height of the sea surface, raised by the pull of mountains underneath. Depth times area, added up: in 2010 the oceanographers Matthew Charette and Walter Smith got 1.33 billion cubic kilometres. What “worked out” means, which is something like 5 × 10⁴⁶ molecules. They’ve been here for most of the Earth’s 4.5 billion years: about 1.4 × 10¹⁷ seconds.

Multiply those by the collisions per second and you get a number of collisions with more than seventy digits. Almost all of them are water hitting water. But other things are dissolved in that water, and a very small fraction of a number like that is still a very big number.

Everything in this notebook is about what happens when something unlikely gets that many chances.

By the time I’d finished that page, the light through my duvet had gone from grey to white, and the dormitory was waking round me in the usual way: somebody’s hairdryer, somebody shouting about a missing sock, Maisie singing the same line of the same song over and over. I switched off my torch and lay under the covers for a minute, thinking about seventeen hundred billion billion molecules on the end of my finger, all jostling, and none of them knowing anything about it.

Then I put the end of my finger on the radiator under the window, which had just come on, and kept it there until it was too hot. Ada had written a line about this in the margin, small, beside the six hundred metres a second: That jostling is what heat IS. There’s no separate stuff called heat. Warmer just means faster, on average. So the molecules in the radiator were jostling harder than the ones in my finger, and every time they hit, they shoved mine a bit faster, and that was all “hot” meant. My finger didn’t know anything about it either. It just hurt.

Then the bell went for breakfast, and I had a decision to make about what I was going to say when somebody asked me where my sister was.