Gauge — the series
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Seven numbers no picture can name
Shift a whole reconstruction by a metre and a half, turn it half a radian, scale it by 2.7, and every photograph of it stays where it was to a hundredth of a billionth of a pixel. Move one point by fifty millimetres and they move by two thirds of a pixel.
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An uncertainty is quoted from something
One adjustment, one set of marks read to a pixel, and its uncertainty written four ways. Held at the first camera, the last camera is 105 mm from certain; held at nothing, every camera is within 4 to 6 mm. A ratio of two distances carries 0.1465 per cent in all four, to two parts in a billion.
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The eighth held number bends the scene
Four surveyed points, each 10 mm out in a different direction. Hold seven of their coordinates during an adjustment and the courtyard's shape moves by a trillionth of a millimetre; hold eight and it moves by 0.59 mm, because seven numbers choose a frame and the eighth makes a claim the pictures disagree with.
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A survey is trusted at its own accuracy, unless its error has a shape
Entered into an adjustment with a stated accuracy, a survey whose errors are random gives the smallest shape error when the stated accuracy is the true one — at 1, 5 and 20 mm alike. Stated twenty times too tight it can cost thirteen times the error; twenty times too loose, almost nothing. But twelve surveys all 10 mm out in fixed directions are best trusted anywhere from 0.3 mm to 10 mm, and the size of their error cannot say which.