Visual Plane
every picture states the point it is correct from
Concept

Constant ratio — where it appears

The rule that spaces a pavement's transversals by a fixed fraction of the previous gap, taught for centuries and not a perspective of the room it claims to show. It is a fixed point, so a copyist who redraws from the method converges on it whatever the drawing in front of them showed.

Named by 4 essays across 2 fields — each of them below, with the objects they name alongside it.

the pavement implies a horizon 171 px off the topthe horizon the panel drewcorrect from 12 cm at 160 mm wide9.2 px from the truth, 0.17 px from a perspective

The rule that draws another room

The taught rule for spacing receding boards — each gap a fixed fraction of the last — is not a projection of anything, and it produces a pavement that is a correct perspective to within a fifth of a pixel. Of a room whose horizon is a hundred and seventy pixels from the one the panel drew. The error is not incoherence; it is a disagreement between two halves of one drawing.

wrong · Taughtratio 0.6000.7000.800010203040generations of copyingthe drawing's depth-spacing ratiocopying the methodcopying the marksone hand error, two kinds of copyist9 lineages

What survives being copied

A workshop copying a drawing from a drawing is a random walk — the spread across lineages grows as the square root of the generation, with a fitted exponent of 0.5001. A workshop copying the method is not, and its exponent is 0.012, which is no growth at all, and after forty generations two lineages started from different originals end up 5 × 10⁻¹⁵ apart. Copying the marks loses the picture; copying the recipe loses the original and keeps the recipe.

conventions · Transmission 0.6000.7000.8000255075100generations of copyingthe pavement's depth-spacing ratiothe workshop's taste7% of proposals rejectedband ±0.04

The workshop that throws drawings away

Adding a rule that discards a drawing which looks wrong turns the mark copyist's spread from a growing random walk into a stationary process — the fitted exponent falls from 0.542 to 0.022, indistinguishable from the method copyist's 0.033 — and the two mechanisms then separate only by where they settle, 0.7002 against 0.8000, seven and a half spreads apart.

conventions · Transmission 0.050.10.20.5125105101520braccia in the pavement, drawn to one page widthpixelsthe diagonal, by straightedgethe transversals, by fittingboth read on one pavement47× at eight braccia

The rule is exact for a floor that lengthens

The constant-ratio rule for spacing receding boards is an exact perspective — to the last digit, on the panel's own horizon — of a floor whose boards grow by the inverse of the ratio, 0.74 braccia deep at the front and 1.31 at the back on an eight-braccio pavement. The orthogonals agree with that floor. What says the tiles were meant to be square is a diagonal, which bends 8.1 pixels off straight where the reader's fitting test finds a sixth of one.

wrong · Taughtratio

Named alongside it

The objects these essays reach for when they reach for this one.

AttributionBiasDrifterror propagationFalsifiabilityHorizonModel errorProcedureProjective invariantrandom walkResidualTransversal

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