Stratification — the series
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What one picture of a plane determines
A photograph of a tiled floor fixes that floor's geometry up to a projectivity, and no further. Supplying the horizon buys back the midpoint — exactly, and nothing else. Supplying the image of one circle buys the right angle and the ratio of two lengths at right angles. Three stages, three prices, and a quantity a stage does not determine has no value rather than a wrong one.
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The ladder of assumptions is a ladder of conditioning
Push the four corners of a board by one pixel and read three quantities through the one recovered map. A cross-ratio does not move at all — it is read in the picture and never went through the map. A ratio of parallel lengths moves by a tenth of a per cent at twenty degrees of obliquity and by 1.6 per cent at seventy-eight. An angle moves by sixteen thousandths of a degree and by nine tenths. The stratification ladder is usually taught as a hierarchy of what is assumed; it is also a hierarchy of what a pixel costs.