evidence · which ratios survive an interval — kodata

The Line on the Wall

A fable. It contains no figures at all — the numbers have had their say already, and what is left of them here is only their shape.

There was a town at the foot of a hill where, one spring, the children began to look tired.

Not ill. Tired. They came down to breakfast slowly and went up to bed late and answered questions a beat after they were asked. It was the kind of thing that is obvious to everybody and provable by nobody, and so the town argued about it for a season without getting anywhere.

What the council wanted was a number. How many of our children are unwell? Because you cannot put they seem tired in a ledger, and you cannot ask the province for help with a feeling.

So they sent for a physician, and the physician came with a list of twenty-one questions.

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She asked every child all twenty-one, and wrote the answers down, and added them up, and each child came away with a tally. A small tally meant a child who answered the way children usually answer. A large one meant a child who did not.

Then the council asked her for the number, and she said she could not give them one yet, because she had tallies and they had asked for a count.

They did not follow, so she explained. There is no place inside a child where well becomes unwell. There is only the tally, which runs smoothly from the smallest to the largest with no gap anywhere along it. If you want a count, someone has to draw a line across the tally and say: above this, unwell. And that someone will be me, and I will be guessing.

Draw it, said the council.

So she went to the wall of the meeting hall, where the tallies had been chalked up from smallest to largest, and she drew a line across them, and above the line there were some children and below it there were many, and the council wrote down the number of the ones above and sent it to the province, and that was the count.

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By then the town had already decided what the cause was.

A peddler had come through two years before selling small glass panes that lit up, and now every child in the town had one, and every parent could tell you exactly how late their child had been holding it. The panes were new. The tiredness was new. The council spent four meetings on the panes.

Prove it, they told the physician. Show us the children with the panes are the ones above the line.

And she said: I can show you that, and I would like you to watch how I do it.

She went back to the wall. She rubbed out her line and drew a new one, lower, and said: here, nearly every child in the town is above the line, and the ones with the panes are only slightly more likely to be among them, and you would conclude that the panes hardly matter. Then she drew it higher, near the top, and said: here, very few children are above the line, but those few hold the panes far more often than the rest, and you would conclude that the panes are a catastrophe.

She kept moving it. Each time she moved it she read out a sentence, and each sentence was true, and no two sentences agreed about how much the panes mattered.

I can give you any answer you would like, she said, and I will not have lied to you once. Tell me which sentence you want and I will tell you where to put the line. What I cannot do is tell you where the line belongs, because it does not belong anywhere. It only has to be somewhere.

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One of the councillors — the youngest, who had been quiet — asked a better question. She asked: of your twenty-one questions, which one do the pane-holders answer worst?

The physician said she had hoped very much that there would be an answer to that.

Because one question would have been a mechanism. One question answered badly and the rest answered normally would have meant the panes were doing something in particular, and something in particular can be understood, and sometimes undone. She had gone through the twenty-one looking for it.

What she found instead was that the pane-holders answered every question a little worse. Not one of them badly. All of them faintly, and by almost exactly the same faint amount, as though the panes did not cause any particular unhappiness but only made a child slightly readier to say yes to a long list of questions late in the evening.

You could take away her worst question and ask the other twenty. The pattern held. You could take away ten. It held. There was nothing to remove, because there was nothing in any one place to begin with.

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It was late, and the meeting had gone on, and the physician said one more thing before she packed up her list.

She said: of everything I measured on your children, the panes moved the tally least. What moved it most, by a long way, was how they slept. And they are not sleeping. Some of that is the panes. A good deal of it is the new road, and the mill that runs at night, and the fact that half of them are up before it is light to work the terraces.

Nobody wrote that down. There was no line for it, and no peddler to blame for it, and the road had been very expensive.

The count went to the province, with the line where she had first drawn it, because a line has to be somewhere. The panes were forbidden by the following spring, and then permitted again the spring after, on the grounds that nothing much had changed.

The children went on looking tired. The mill went on running. And in all of it, from the first meeting to the last, nobody thought to ask them what time they had gone to bed.