Chapter Two
The Pool
Thursday, 06:00
The first thing you should know about swimming training at six in the morning is that the water is always described as warm by people who are not in it.
“Twenty-four degrees,” said Mr Wilding, the swimming coach, from the poolside, in a fleece, a woolly hat and a coat over the fleece, holding a mug of something that steamed. “Practically a bath. In.”
The Stanbury pool is twenty-five metres long, six lanes wide, and lives in a building that was once, according to the plaque by the door, a riding school, which explains the high roof and the smell. The smell is not horses any more. It is what everyone calls the chlorine smell, and here is the first thing Ada ever told me about swimming that I didn’t know: it isn’t chlorine. Clean, properly chlorinated water hardly smells at all. That sharp swimming-pool smell comes from chloramines, which are what you get when the chlorine reacts with things people bring into the water with them: sweat, skin, and, as Ada put it, “the other thing, which I’m not going to name before breakfast”. A pool that smells very strongly of chlorine is a pool with a lot of chloramines in it, which means it’s a pool with a lot of the other thing in it.
I have never been able to un-know that. I’m sorry that now you can’t either.
It was my fourth week at Stanbury and my third session with the squad. There are four squads, and I was in the bottom one, which trains in lanes one and two, and Ada was in the top one, which trains in lanes five and six and does not talk to anyone before seven o’clock. I lowered myself in. It was not like a bath. It was like being slowly swallowed by something very large and very cold, and I made the noise you make.
“Four hundred warm-up,” said Mr Wilding. “Choice. Go.”
I want to explain how I swam at the start of that term, because it matters for later, and because I suspect it is how most people swim.
I fought it. That’s the only way I can describe it. I swam as if the water were an enemy that had to be beaten, by force, every stroke, and I came to the end of every length breathing like a dog in a car and about a body’s length behind the girl next to me, who looked as if she was hardly trying.
At the end of the main set Mr Wilding sent the bottom squad to kick with boards and went to shout at lane six. And Ada, who had finished her set and was hanging off the lane rope between five and six with her goggles pushed up on her forehead, watched me kick one whole length. Then she ducked under two lane ropes, which you are not allowed to do, and came up next to me at the wall. Behind her, Mr Wilding was walking along lane six with his stopwatch, shouting times.
“You’re fighting it,” she said.
“I know,” I said. “Everybody says. How do I stop?”
Before she could answer, a girl from my squad came up behind us with her kickboard, and we had to flatten ourselves against the lane rope to let her through. Ada watched her go, kicking with her head up and her legs dragging along underneath her, with the expression of a scientist looking at a specimen.
“Like that,” she said. “That’s you. Exactly that.”
“You stop,” said Ada, “by understanding what you’re fighting.” She pushed her goggles further up. “Water’s heavy. About 800 times denser than air: a litre of water weighs as much as four bathfuls of air. Every time you move through it, you have to shove it out of the way, which means getting it moving, and getting something moving takes a push. That’s drag.”
“Why does heavy make it harder?”
“Because what you’re shoving is molecules. There are about 3 × 10²⁵ of them in a litre of water, and every one you shove needs a push to get it moving, and how big a push depends on how heavy it is. So it isn’t really how many there are. It’s how many, times how heavy each one is, and that total is what mass means. And air isn’t even one thing. It’s a mix of gases: mostly nitrogen, about a fifth oxygen, a pinch of argon and a trace of carbon dioxide, every one its own kind of molecule, flying about with far more empty space between them than molecules. One for one, those molecules are actually a bit heavier than a molecule of water. There are more than a thousand times fewer of them in every litre, so you hardly feel them, until you stick your hand out of a car window.”A litre of water is 1,000 g, and a water molecule weighs 18 atomic mass units, so it holds 1,000 ÷ 18 × 6.0 × 10²³ ≈ 3.3 × 10²⁵ molecules. Air is a mixture, not one substance: about 78% nitrogen (molecules of 28 units), 21% oxygen (32 units) and 1% argon (40 units), so its molecules average 0.78 × 28 + 0.21 × 32 + 0.01 × 40 ≈ 29 units. A litre of air weighs about 1.2 g, so it holds 1.2 ÷ 29 × 6.0 × 10²³ ≈ 2.5 × 10²² molecules: about 1,300 times fewer.
“So honey would be worse.”
“Much worse, but for a different reason. Honey’s sticky: its molecules cling to each other, and that’s a different kind of drag, the rubbing kind. You couldn’t swim through a pool of honey at all. But here’s a strange one. In 2004 two chemical engineers at the University of Minnesota, Brian Gettelfinger and Edward Cussler, filled a pool with water thickened with guar gum, a powder they put in ice cream, until it was twice as sticky as water, and raced swimmers through it. They swam just as fast. For something as big and as fast as a person, the stickiness hardly matters next to the weight of the water you have to shove. They got a prize for it: the Ig Nobel, for science that makes people laugh and then think.”
“And here’s the thing nobody tells you,” Ada went on. “Drag doesn’t go up with speed. It goes up with speed squared.”
“Is this physics?” I said. “It’s six in the morning.”
“It’s all physics. Swimming’s physics with a timing system.” She held up two fingers, dripping. “Go twice as fast, and the water pushes back four times as hard: 2² = 4. And the power you need, the energy every second, goes up with speed cubed, because you’re pushing four times as hard and covering the distance twice as fast: 2³ = 8.Power is energy used every second, measured in watts. One watt is one joule every second, and one joule is about what it takes to lift an apple (100 g) up one metre. So one watt is lifting an apple a metre, every second. Lifting your arm from your side to above your head once a second is about 10 watts of work on the arm; your muscles burn about four times that to do it. Running up the stairs at school: a hundred watts or more. Lying still, your whole body uses about 80. Eight times the power to go twice as fast.”
At the far end, Mr Wilding stopped and turned round. “Down,” said Ada, and we both dropped under, and crouched on the bottom of the shallow end looking at each other through our goggles, with my cheeks full of air and bubbles going up past Ada’s ear, for two whole seconds, until his back was to us again. We came up together.
I did the sum in my head, which is a thing I am quick at, and which is not the same as being good at swimming. “So if I wanted to go ten per cent faster...”
“1.1³.”Ten per cent faster means the old speed plus a tenth of it: 1 + 0.1 = 1.1 times the speed. Power goes with speed cubed, so the power is multiplied by 1.1 × 1.1 × 1.1 = 1.331, which is the old power plus 0.331 of it: about a third more. Ada didn’t even pause. “That’s 1.33. A third more power, for a tenth more speed. That’s why you can’t just try harder. Trying harder is the most expensive way there is to go faster. You can’t out-muscle v squared.”
“So what’s the cheap way?”
She grinned. It was the grin she gets when you ask exactly the question she wanted you to ask. “Change the other bits of the sum. Drag also goes up with how much of you is pushing into the water: your frontal area, the shape of you that has to push through it. Your head is up. Your head up means your hips drop, and your hips dropping means your whole body’s at a slant, and a slanted body shoves more than twice as much water as a flat one. You’re swimming like a bin lid. Here’s what that costs. The fastest women in the world swim at about two metres a second. At that speed, lying flat as a board, the water pushes back on them about as hard as an eight-kilo bag of shopping hanging off a rope. Swim like a bin lid, with your legs at a slant, and it’s nearer twenty kilos. Same swimmer, same speed, two and a half times the shove. Nobody gets two and a half times stronger. Not in a year. Not ever.”
“Thanks.”
Two more girls from my squad came past, kicking. We let them through, and then a third, Riya, from Ada’s year, who said “Ada, Wilding’s looking” out of the side of her mouth as she went by, and we both went under again, and counted to two, and came up.
“You’re welcome. Look.” She let go of the wall and floated on her front, arms stretched past her ears, one hand on top of the other, face down, completely still. Her legs sank, slowly, until she was lying at an angle, like a plank with a weight at one end. She lifted her face.
“See that? Remember the beach. Your lungs are full of air, so the buoyant part of you, the part the water pushes up, is your chest. But the heavy part of you is lower down: bone and muscle, hips and legs. Muscle’s denser than water. Fat floats, a bit. So there’s an upward push at your chest and a downward pull nearer your hips, and two forces like that, not in line, turn you round. Legs go down, like a see-saw.” She put her face back in the water and pressed her chest down, as if leaning on it, and her hips came up, and her legs came up with them, until she was lying flat along the surface like something poured. She came up again. “Press your chest down, your hips come up. It feels like you’re swimming downhill. You’re not. You’re swimming flat, for the first time in your life.”
“But why does pushing your chest down bring your legs up? Wouldn’t I just go down at the front?”
“See-saw. Where does a see-saw turn?”
“In the middle. Where it’s held up.”
“Where it’s held up. So where’s the water holding you up?”
I thought about the beach. “My lungs.”
“Your lungs. That’s the pivot. Just lying there, all the heavy bits of you, hips and legs, are on one side of it, and there’s hardly anything on the other side, so you turn: legs down, chest up. And you keep turning until the heavy end hangs straight underneath the floaty end, because that’s the only way round where the push and the pull are in line and there’s nothing left to turn you. Lie still for long enough and you end up standing up in the water, bobbing, with your face just out. Which is exactly what you did all summer.”
“So how does pressing help?”
“It puts weight on the other side of the pivot. Your head’s heavy: about a twelfth of all of you, so three or four kilos, and your two arms together are a bit more than that.Biomechanics tables, made by weighing the parts of bodies, give the head and neck as about 8% of a person’s whole mass, and each whole arm as about 5%. For someone of 40 kg, that’s a head of about 0.08 × 40 ≈ 3.2 kg and two arms of about 2 × 0.05 × 40 = 4 kg. Lift your head to look where you’re going, and the only way to do it is to arch your back, which tips your hips down: that’s the bin lid. Put your head down between your arms, stretch your arms out in front, and lean on your chest, and now all of that is out in front of the pivot, pulling the front end down. Push one end of a see-saw down and the other end comes up. And it’s not only how heavy, it’s how far: weight right out at the end of a see-saw turns it far more than the same weight near the middle, which is why stretching your arms all the way out helps so much.” She stretched one arm forward along the water to show me. “So press down, towards the bottom of the pool, and reach forward. Not up, and not back.”
“Wouldn’t I just go down at the front?”
“That’s the beach again. The deeper you push your chest, the more of it’s under the water, the more water it shoves aside, and the harder the water shoves back up. So the pivot stays about where it is, and the back end of you has nowhere to go but up.” She held up a finger. “But only if you’re stiff. You’re a stiff plank, more or less, and that’s the bit nobody tells you: you have to make yourself one. Squeeze your tummy and your bum, as if somebody’s about to poke you in the stomach. Go floppy in the middle, and pressing your chest just folds you at the waist: your front goes down, your legs stay exactly where they were, and you’re a V instead of a plank. And being stiff costs you. It’s muscles working the whole length, and you’ll feel it tomorrow. It’s just a lot cheaper than dragging your legs.”
“Go on, then. One length.” Ada looked over her shoulder. Mr Wilding had got to the shallow end of lane six and was turning round. “I’ll be in five.” And she was gone, under the rope, before I could say anything.
I pushed off. Face down, arms out, head between them, chest pressed, tummy squeezed as if somebody were about to poke it. I tried it. It felt like swimming downhill. It also lasted about four kicks: the moment I lifted my head to breathe, my legs sank, and I had to find the press all over again, and by halfway I could feel the muscles round my middle, which I hadn’t known I had. In lane five, all the way up, a black cap swam breaststroke level with me, slower than I had ever seen Ada swim anything, with its goggles turned towards me under the water.
At the far wall she was already there, hanging on the rope between two and three as if she’d been there all along. Mr Wilding was at the other end, shouting at someone else.
“Better,” said Ada. “Now: streamline. Off every wall, arms squeezed behind your head, hands stacked, head between your arms, not in front. Push off, and don’t do anything. Just glide. You’re going the fastest you’ll go all length right after you push off, and every bit of you sticking out throws that away. One hand out of line, or a bent elbow, is about a sixth more of you facing the water. At world-record speed that’s another twelve newtons, a bag of sugar’s worth of shove, every second you’re gliding, for nothing.”
“And then?”
“And then, when you actually swim, don’t spin your arms like a washing machine. Catch the water and push a big lot of it backwards, slowly, instead of a little bit of it quickly.” She saw my face. “There’s a reason. It’s to do with momentum and energy, and I’ll explain it some day when your lips aren’t blue.” (She did, in the end: on a bench at the County Championships, an hour before my first race.)
They were blue. I could feel my teeth starting to go, that fast, uncontrollable chatter, like a sewing machine. Ada, who had been in the same water for exactly as long as I had, was not shivering at all.
“How are you not cold?”
“I am cold. I’m just less cold than you.” She looked at me the way she looks at a problem. “You’re small. You leak heat. I’ll explain that too, some day.” (She did that too, in notebook 10, with shrews.)
“Why not now?”
“Because Wilding’s coming back, and I’m in the wrong lane, and he’s going to kill me.” She pulled her goggles down. “Oh, and Stella? Everything I just told you? It’s all the same thing. Physics is the rules for everything. Chemistry is physics about what atoms’ electrons do. Biology’s chemistry that got complicated. You’re just a very small, very cold bit of physics trying to get to the other end of a pool.”
“I thought you said nothing tries,” I said. She’d been saying it all summer, to anyone who’d listen, and some who wouldn’t.
Ada stopped, half under the lane rope, and looked back at me, and for a moment she was the most pleased I had ever seen her. “Things with brains try,” she said. “You’ve got a brain. So try. Just try the cheap way.”
Then she ducked under the ropes, and Mr Wilding roared “GRAHAM!”, which is our surname, and it was obvious from the way he said it that he meant her and not me.
I swam the last four lengths of that session pressing my chest down and holding my streamline off the walls until I nearly ran out of breath, and I will not pretend it was a miracle. I was still a body’s length behind the girl next to me. But on the last length, for about two strokes, I felt it: the water stopped being a wall and turned into something I was going through, instead of something I was hitting.
In the changing room I wrote three new words in the list at the back of my planner, with my fingers still too cold to hold the pen properly. Drag. Streamline. Chloramines.
That evening, in prep, there was a sheet of paper in my pigeonhole, folded in four, with Ada’s capitals on the outside: THE SUMS BEHIND THE BIN LID. READ IT SLOWLY. I MEAN IT.
I didn’t read it slowly. I don’t read anything slowly. I’m the person who finishes the class reader on the first night and spends the rest of the term pretending not to know the ending. Grown-ups read about 240 words a minute How we know In 2019 Marc Brysbaert, a psychologist at Ghent University in Belgium, put together 190 studies of silent reading, with 18,573 readers between them, all timed reading passages and then checked to make sure they had understood them. Adults reading English managed about 238 words a minute for non-fiction and 260 for fiction, and most fell between about 175 and 320. What “seen” means, and I had timed myself once, on a Jacqueline Wilson, under the duvet, and I was faster than that, and I was proud of it.
The sheet had about forty words on it, and a line that went F = ½ × ρ × Cd × A × v². I got to the end of it and had no idea what I had just read. I read it again. Ten minutes later I was still on it, so I took it down to the Year 10 common room, which Year 7s are not allowed into, and stood in the doorway until Ada noticed me.
“It’s broken,” I said. “I can read a whole chapter in ten minutes. This is one line.”
“It isn’t one line.” She took the sheet. “When you read a story, most of the words tell you things you could nearly have guessed. She opened the door. She went in. Your eyes run ahead, your brain fills in the rest, and it’s right nearly every time. That’s why you’re fast. A formula doesn’t let you guess anything. Every letter in it is a sentence, and some of them are a whole page.” She put her finger on the little 2. “That’s go twice as fast and the water pushes back four times as hard, and behind it is every measurement anybody made to find that out. Write all of this out in words, with what each letter means and why it’s there, and it’s pages. You’re not reading slowly. You’re reading pages.” She handed it back. “There are formulas five letters long that people have written whole books about. E = mc² has several.”
“So how do I read it?”
Ada counted on her fingers, which she only does when she’s thought about something before.
“One. One letter at a time. Say what it stands for and what it’s measured in. If you can’t, find out before you go on. It’s always written somewhere underneath.
“Two. Ask what it does. Is it multiplied by something, or added to it? Squared? On the top, or the bottom? Double this one, and what happens to that one: twice as much, four times as much, or a bit more each time, like interest? That’s the important bit. The shape of it. Straight line, squared, cubed, exponential. The people who are good at physics read equations like that, as shapes, not as strings of letters How we know In 2001 Bruce Sherin, a researcher in how people learn physics, published a study in the journal Cognition and Instruction of university students he had filmed working through physics problems in pairs. The ones who did well read an equation as a small set of familiar patterns, such as “this one goes up as that one goes up”, “a starting amount plus a change”, or “two things balancing”, and used those patterns to build and check what they wrote. He called the patterns symbolic forms. What “seen” means.
“Three. Use it. Put your own numbers in, not a world record’s. Then put in silly ones. What if the speed’s nothing? What if it’s a hundred metres a second? If the answer’s silly, either you’ve misunderstood something or you’ve found something.
“Four. Explain it, a line at a time, in your own words. To me, to Maisie, to the wall. It sounds stupid. It works How we know In 1989, at the University of Pittsburgh, the psychologist Michelene Chi and her colleagues asked university students to think aloud while they studied worked examples of mechanics problems, and then tested them on new problems. The students who did best were the ones who had stopped at each line and explained to themselves why it was there. In 1994 the same group asked thirteen-year-olds to explain each sentence of a biology text to themselves as they read it once, and they understood it better than classmates who read it twice. It’s been tested many times since, and is called the self-explanation effect. What “seen” means.
“Five. Go away. Come back tomorrow and see what’s still there.”
“Do I have to learn it by heart?”
“No. Nobody remembers every half and every rho. If you need the half, you look it up. What you keep is what it says: the drag goes up with the square of the speed, the power with the cube, and your shape is multiplied in with the speed, so a better shape helps at every speed. That’s what you’ll still know when you’re forty.” She turned back to her homework. “Now go away. You’re not allowed in here.”
I went back to prep and read the sheet the way she’d said. It took me forty minutes, and I said “drag area” out loud to the wall twice, and the girl at the next desk moved. This is what was on it, so that you can take forty minutes too.
That was Thursday. On Friday night, the sky caught fire.