Chapter 0 — In the Beginning
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1. In the beginning
In the beginning there was nothing.
No space, no time. Nothing to experience, no one to experience.
Then there was something. Not the moon or the stars, not a thought, not a word. Something from before. A feeling.
One cheek was softer than the other. One moment there was light, the other not. One sound was the high voice, the other not. Sometimes, just briefly, something that tickled.
No word yet for anything at all. Not even for ‘it’.
Difference was felt.
That was you. A few hours old. A day. A week. No words, no ‘you’ facing a ‘world’. Still, all sorts of things came in. And really, that’s not odd at all. You can only feel warm if, somewhere, it is also less warm. Soft only exists next to something less soft. Whatever came in first could only have been difference. What else could it have been?
Feeling difference. That is — if you ask me — the first thing a human being does. Before thinking, before wanting, before talking.
Researchers do essentially the same thing — to understand anything, you need to know what differs from what. Two things that are the same tell you nothing. Two things that differ start to tell you something. Researchers measure, count, compare. Not everyone in their sample is the same age. Not everyone responds the same way to a medicine. Not everyone scores the same on a questionnaire. They note down difference, and try to make some sense of it. Numbers are tools. What researchers do is record difference.
So I propose — with all due respect to the old philosophers — a different sentence from the one we’re used to:
I feel difference, therefore I am.
Descartes said “I think, therefore I am.” Fine sentence. But to think, you already need language, an idea of an I, a world to think about. Feeling difference comes earlier. It is what happens before you know anything about it.
One thing first, out in the open.
The word difference is not the same as the experience of it. A baby feels it without a word. We have the word, and as soon as we have it, we’re quick to think we’ve got the thing as well. We have language. A handy tool. But there is a whole world between the word and what a newborn feels on her cheek.
That is what this book is about. Not just difference — also how we learn to work with language and numbers without forgetting that they are tools, and not the thing itself.
2. Comparing is what we do
Feeling difference is one thing. Noting difference down is another.
Because as soon as we try to say in what way one thing differs from the other, we put two things side by side. We compare. One cheek beside the other. One age beside the other. One measurement beside the other.
Comparing is what we do. Endlessly, often without noticing. One participant scores higher than another — that’s two numbers, side by side, a difference between them. One group gets a medicine and another doesn’t — two outcomes, side by side, a difference between them.
This isn’t my discovery. Carry van Bruggen wrote it down back in 1925, and she called it a formula:
There is no being other than being otherwise.
All seeing, judging and understanding, she writes further on in the same book, is a comparing, a distinguishing. Something is only something because it differs from something else. What we do here is write that down.
This is where it gets interesting. Because for that very same act — two things side by side, a difference between them — we’ve opened up the whole vocabulary. We say:
Sex has an effect on height. There is a relationship between sex and height. Sex and height are correlated. Height is associated with sex.
Four sentences, four words, one thing. We have language for the subtleties — effect, relationship, correlated, associated — and as soon as we have four different terms for it, we’re quick to think they’re four different things as well. They aren’t. It is one act under four names: we put two things side by side, and we look at whether their differences go together.
Just say it plainly, the way you’d say it over dinner: men are, on the whole, taller than women. That’s all it says. People differ in sex, they differ in height, and those two differences go together part of the way. Not in every case — you’ll know a tall woman and a short man. On the whole. The picture below, figure 0.1, shows exactly that and nothing more: two heaps, two middles, a difference between them — and one tall woman and one short man who bear out the not in every case.
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Figure 0.1. Two heaps on the same line, from short to tall: the women as open circles, the men as filled ones. The two heaps overlap: that is “not in every case”. The two middles stand apart: that is “on the whole”. Not a number in sight, because none is needed here yet.
That is all.
The grandfather walked through the wood. Beside him walked Moos.
They were not getting very far. Nor was that the idea. Long ago the grandfather had learned how to get everywhere quickly, and he was now unlearning it; Moos was helping. Moos stopped at everything. At a root that came up out of the ground. At a hole where something lived, or had lived, or one day would.
“See that tree?” said the grandfather. “Six steps.”
Moos took eleven, and laughed. Small steps count double.
By the tree lay a feather. Grey, with a white edge, curled over a little at the tip. Moos picked it up the way he picked everything up: as if nobody had ever seen it before.
“Duck,” said Moos.
He held the feather against his cheek for a moment.
It was not a duck, the grandfather thought. But he did not say so. Everything with wings was duck, for now, and it was not such a big mistake: he himself did not know whose feather it was. Somewhere above them sat a bird with one feather fewer. They did not see it.
“That bird,” said the grandfather, “might be looking at us right now.”
Moos looked up.
“Maybe it’s counting our steps,” said the grandfather. “Maybe it’s wondering what we’re called. Maybe they have a whole wood of their own up there, and want to know everything about it. Where the water tastes best. Whether big things are heavy too. Who has gone, and who is still here.”
It was quiet for a moment among the trees. It was not an empty silence; there were all sorts of things in it.
Further on, on a post beside the path, sat a gull. She had been sitting there the whole time. She watched.
On the way back the feather got lost. Moos did not notice; finding had been the work, keeping did not matter. The grandfather did notice, and said nothing. Something of every walk stays behind in the wood, he thought. Perhaps that was fair. Then they would know something about us, too.
And Moos would forget this morning. The grandfather knew that too. That is how the first years go: they are felt and not kept. That was why he walked so slowly. He was remembering the morning for two.
3. Reality is too big
So far we’ve been talking about difference, and about comparing. Two things side by side, a difference between them. Clear.
But here comes something annoying. Because reality is not always clear. In fact, usually not at all. Reality gets in its own way.
Imagine: you’re standing in a bakery. You ask for a loaf. The baker looks at you, thinks for a moment, and says:
“Well, look — if we’re talking about a loaf, then we’d better just agree what we mean by that. A white loaf counts, obviously, but my sister-in-law always says a proper loaf is really a sourdough. These days they put all sorts in — pumpkin seeds, linseed — and I don’t know where you stand on that. A supermarket loaf off the shelf is technically a loaf too, but morally I’m not so sure.”
And you go home with paperwork. With a recipe.
That is what reality does to us all day long. Not a loaf, but a recipe. Not an answer, but a detour. Not a closed case, but a chain of agreements, every one of which we have yet to make.
Science is not all-knowing. Science is making agreements so that we can deal with that too-big, too-complicated reality. We agree what we call a child, and what counts as heart surgery, and when someone has died from the operation. We agree that a metre is this long, that a degree Celsius is this much warmer than the one before, that a 7 on one questionnaire is not the same as a 7 on another. We even agree on how we write it down: a club of psychologists — the American Psychological Association, APA for short — has laid down what a number in an article ought to look like, down to the last digit. None of it fell from the sky. It is all imposed, agreed, provisional, debatable. Rather annoying, really.
This is a good moment to say something personal. Otherwise you’ll soon start wondering why I get so excited about a word like ‘clarity’.
My father is a lovely man — I’ll say that up front, because I’m about to tease him a little. He has one trait that sets him apart from most men: ask him whether it’s raining, and you get something like:
“Well, you have to look at it like this — I was actually meant to go on a rambling-club walk this morning, and then the choir had another rehearsal, where they still can’t agree about that new conductor, but that’s another story — and when I’d stepped outside for a moment after that conversation with your aunt, who’s still having trouble with her hip, I thought: hello, something’s dripping, and that makes me think of the summer of ’72, because back then…”
By the time I knew whether it was raining, I’d been through six topics, and it had already stopped raining.
That is where my love of clarity comes from. Not out of anger at him — we get on well — but simply because the sun can shine through one small cloud without anyone first dragging in six other topics.
Clarity out of gratitude. That is what I’m trying to do here. And as it happens, it’s what science is trying to do too: being clear where reality isn’t. Making agreements where there were none yet.
Making a baker commit to a loaf.
4. What we do see, what we don’t
Being clear where reality isn’t. Nicely put, if I say so myself. But there’s a catch.
Because every agreement we make — what we call a child, what a loaf is, how long a metre is — also leaves something outside the agreement. We choose what we count, and in doing so we choose what we don’t count.
That’s not a shortcoming. That’s what an agreement is.
There’s something I’d like you to take with you through this whole book. A question — an attitude, really:
What do we see? And what do we not see?
It’s what a scientist asks themselves after every measurement. And what a reader ought to ask of every statistic that comes along.
Not everything we don’t see is absent. In fact, most of what we don’t see is simply there. Waiting.
We measure a height, and the other heights — on other days, other people, other planets — simply go on existing. We measure an effect of a medicine on blood pressure, and the people we didn’t measure are walking around somewhere with their own version of the effect. It isn’t gone because we don’t see it. It just isn’t in our measurement.
That is what uncertainty is. Not failure. Not ‘we haven’t worked everything out yet’. Uncertainty is contact. It is the fact that reality is bigger than our measurement — and that we want to keep being honest about that.
In this book you’ll often come across numbers that look very certain. An average of 150. A difference of 5.4. A probability of .03 — and that missing zero before the decimal point isn’t sloppiness: for something that can never be bigger than 1 anyway, statisticians leave it out. The number is an agreement. The reality underneath it is bigger, skewed, varied. The number held on to something, and let a great deal go.
In every measurement there is something fixed, and something that stays free. What’s fixed: the agreements. What stays free: everything reality does outside them.
So this book is not about what we know for sure. It’s about how we deal honestly with what we do know and what we don’t.
5. What comes next
Right.
We have difference. We have comparing. We have the reality that is too big, and agreements that give us something to hold on to all the same. We have the question — What do we see? And what do we not see?
That’s enough to be going on with.
What comes next is a language for difference. Ways to count it, to summarise it, and — above all — to see how differences go together. Because that’s where it gets interesting: not just that things differ, but that their differences have something to do with each other. Height with age. Blood pressure with medicine. Weight with species.
In the beginning there was nothing. Then something. A difference.
The rest of this book is about how we make something of it.