Series

Stratification — the series

2 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. projectiveaffinemetricmidpointtwo equal sidesa right anglecross-ratioprojective———1.333333333affine0.500000——1.333333333metric0.5000001.00000090.000°1.333333333— means the stage does not determine it at allcross-ratio 1.333333 throughout

    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.

    part 4 · foundations
  2. 0204060204060how oblique the view of the plane is (°)what one pixel costs, against its cost at 20°a ratio of lengths — affinean angle — metric1 px on four corners, one homographya cross-ratio moves by 0e+0

    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.

    part 5 · foundations

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