Counting — where it appears
Named by 4 essays across 3 fields — each of them below, with the objects they name alongside it.
Counting is a measurement
A tiled floor gives its area with no reference length at all — count the tiles and multiply. The count is an integer, so it is exact wherever it can be made, which is a completely different error law from the rectifier's smooth decay. And the distance at which it fails is set by the tile's depth edge, which foreshortens as one over the depth squared, so 18.7 m for a 62 cm tile, where the across edge alone would have allowed 217.
A grid stops a copy drifting
A figure copied by hand from the last copy drifts as a random walk, by the square root of the copies. Copied on a ruled grid, with each landmark brought back to a line, it does not drift at all, because rounding throws the error away. That is how a correcting code works. It holds only below a sharp threshold on the hand, and the grid's size is the trade between how much it corrects and how much it can say.
A grid on the wall is a scale without a projection
An Egyptian canon rules a wall into squares and counts a figure's height against the ruling — no horizon, no centre, and a length recovered to 1.4e-14% of error where the same reading taken off a pinhole misses by 58%. Applied instead to a pinhole picture, the furthest of six equal figures reads at 19% of its true height.
A flight that has ends
A real staircase has three families of faces and the rule proposed last round predicted three pictures. It supports four, because a picture is fixed by a direction and the flight's two sides point opposite ways — one kind of face that no single direction reaches both of. The rule counts words and the object counts orientations.
Named alongside it
The objects these essays reach for when they reach for this one.
Canon of proportioncentre of projectionDrawing conventionDrawing systeminstrument limitParallel projectionTrue scaleAnamorphosisArea scaleCoverageDesign planeDiscrete not continuous