Gear b1 Has 223 Teeth. Forty-Seven Of Them Are Cut Wrong.

ATHENS, Greece — Two hundred and twenty-three teeth. Forty-seven of them are in the wrong place.

That is the finding, and it is not a claim about what the Antikythera mechanism was for. The mechanism is what everybody says it is: a geared calculator of astronomical position, made in the second or first century BC, with no known successor for a thousand years. Nothing here disputes any of that.

This is a claim about a workshop.

The file with the label taken off

The tomographic volumes of the fragments have been open data since 2006. Anyone may download them, and the people who do are archaeologists, historians of astronomy, and enthusiasts.

We gave them to a gear metrologist.

Dr. Marit Ojeda-Lindqvist inspects gearboxes for a living — wind turbines, marine reduction drives, the occasional lift. She measures tooth pitch to a hundredth of a degree and writes the reports that decide whether a gearbox comes out of a nacelle.

She had not heard of the Antikythera mechanism. We took the label off the file, left the scale bar on, and asked one question: is this drive component within tolerance, and if not, where is it out.

It took eleven weeks, because b1 — the large wheel carrying 223 teeth, the Saros count — has 137 teeth still on it and 86 gaps, and every surviving tooth had to be segmented by hand out of a scan made for somebody else's purpose.

Forty-seven

Of the 137 teeth she could measure, 47 deviate from ideal spacing by more than 0.4 degrees. The worst is out by 1.6.

On a modern gear that size, a 0.4-degree pitch error is a scrap decision. She said so before she was told what she was looking at, which is the whole reason we did it in that order.

The count on its own is not the interesting part. What she found next is.

The errors are not scattered. Plot deviation against tooth number and they sit in three arcs — roughly teeth 14 to 31, 88 to 104, and 171 to 186 — and inside each arc the error runs steadily one way and then jumps back.

"That is not wear," she said. "Wear is smooth and it is worst where the load is. This is three places where somebody stopped and started again."

What a divider does overnight

Ferdinand Achterberg-Nwosu cuts clock wheels by hand in a workshop in east London. He has cut something over four hundred.

Nothing in the report surprised him.

You mark the circle with a divider, he said. You step it round. You file. Then it is dark, or it is Thursday, or a customer comes in, and you put the work down. When you pick it up you re-index off the last tooth you cut — and the last tooth you cut already carries every error you made before it.

"Three restarts on a 223-tooth wheel is a fast job," he said. "I would have expected five."

Four years

The part that matters is downstream.

Ojeda-Lindqvist propagated the measured pitch errors through the train as published — she did it the way she would for a gearbox, with no interest in what the pointer pointed at — and the answer is that the Saros pointer accumulates a visible offset in about three years and ten months of continuous turning.

Visible means roughly a pointer's width against the engraved scale. Not a catastrophe. Not a broken machine. A machine that has quietly stopped agreeing with the sky.

That figure rests on published tooth counts for every wheel below b1, and two of those counts are reconstructions rather than observations. Change either by one tooth and the answer moves by months. It does not move by years.

The requirement nobody writes on the card

If the pointer walks off inside four years, the object cannot have been a thing you set once and then consulted.

It had to be reset. By hand. By somebody who independently knew where the moon was, and who did it again every few years, for as long as the mechanism was in service.

That is an operating requirement, and it is a requirement for a person, not a part. It says something about who owned this and what they were doing with it that no amount of admiring the gear train will say.

What this is not

It is not evidence of a lost precision we have failed to appreciate. It is not evidence of incompetence either.

It is a hand-cut object that drifted, made by people who could see it drifting and evidently did not mind, because the correction cost a minute and they were standing right there.

Professor Xanthe Alkiviadis-Wren, whose reply runs at the foot of this page, thinks we have dressed a fifty-year-old observation as a discovery, and that marking an ancient wheel against a modern inspection drawing is a category error that happens to produce a good headline.

She is right about the first. On the second this desk still disagrees, and her argument is printed at her length, not ours, so that a reader can decide without taking our word for either.