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✦ Ideas & theories · 20 September 2026

No need to count the teeth

For anyone with no appetite for formulas, or for being told where they give out. There is only the movement here.

The bathroom at home had a window forty centimetres by fifty, and it faced the right way: in the evenings Saturn passed through it. I had fitted a microscope eyepiece into the telescope, with a tube of cardboard rolled to size, and the field of view had shrunk so far that the planet crossed it in a few seconds. You had to chase it. It was not contemplation, it was pursuit.

When I managed to hold it still for a moment, I saw three grainy circles. A bigger one in the middle, two smaller ones either side, squashed flat. Not the rings in the photographs: three lopsided smudges, blurred by home-made optics.

That evening I learned nothing about Saturn. I learned something else, and I have never lost it: that there was an order up there, that the order did not depend on me, and that with a cardboard tube you could see a piece of it.

The clock with its wheels on show

There are antique clocks that have had their backs taken off, so you can watch all the gears turning. One wheel turns slowly, another quickly, a third the other way round. Nobody looking at them starts counting the teeth. And yet everyone understands, in a second, that the movement is ordered: watch long enough and you already know where the hand will be in a minute’s time, even if you could not say why.

That is what this page is: the clock with its back off. I am not asking you to count the teeth. I am only asking you to watch how they move together.

Two things, not one

The way I look at the world starts from a distinction that sounds like hair-splitting and is not. When we talk about what there is in a place, we are mixing up two different questions: how much of it there is, and how far it can move there.

Think of a river, and think of its bed. The water is one thing. The bed is another: it says how far the water can run at that point. You can have a pipe that is completely full and completely blocked — it is full, and nothing gets through. They are two independent properties, and we usually confuse them because in everyday life they nearly always go together.

From that distinction comes the thing I care about most, and it is not an explanation: it is a prohibition. A dam does not stop water. It diverts it, makes it rise, seep, evaporate, brim over. You can hold it back for a year or for a century, but not for ever. A permanent block does not exist in nature.

If you asked me to bet on a single thing out of everything I have thought in these years, I would bet on this one, because it is the only one that forbids something instead of explaining everything.

And the places where it seems to stop

There are places in the universe from which nothing comes back. We call them black holes, and the name makes you think of a mouth. To me they do not look like a mouth.

In this story they are the point where the bed closes. There is no wall and there is no monster: there is simply nowhere left to flow. Like a note that ends not because it meets a wall, but because the air that carried it runs out.

I am not telling you that this is how it is. I am telling you that this is how I saw it, and that seeing it this way made me ask the right questions — which is not the same as being right, and is no small thing.

Then I tried counting the teeth

Years after that evening at the window, I did the thing that ruins visions, and I did it on purpose: I demanded that this way of looking should produce numbers.

It went the way it usually goes. Many of the things I believed I had understood turned out to be things I wished I had understood. I withdrew twenty claims out of ninety-one, and not one of them fell because an experiment said no: they all fell on rereading, or on reading in full texts I had been citing at second hand.

What is left is smaller, and I care about it more for exactly that reason.

Because the movement did not fall. It is still there. It is the same thing I saw on the evening when Saturn kept slipping out of the eyepiece and I kept chasing it: not a fact I had understood, but an order that was there, and that went on being there even while I was looking at it badly, through a cardboard tube, from a bathroom window.

The boy with the cardboard telescope did not need to know how many wheels there were. He needed to know that there was a movement, that the movement had a direction, and that he could see it too.

You do not need to count the teeth to feel that the clock is working. That comes later, if you want to tell other people which clock it is — and that is another trade, one I learned late and badly, and have written about somewhere else.


This page is a story, not a proof: none of the images above proves anything, and where they break is written out in full in the dated reckoning. Where the boy with the cardboard tube came from is told instead in the Dispatches.

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