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

Falsifiability — where it appears

Whether a reading of a picture has enough independent statements in it to disagree with anything. A model with as many free numbers as the picture has marks is fitted exactly whatever the marks are, so its agreement is a fact about the count rather than about the picture.

Named by 6 essays across 3 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 one height, four columnsfloor: turned 0°, meets at column 345footstool: turned 28°, meets at column -137table: turned -17°, meets at column 622book: turned 41°, meets at column -443columns 1065 px apartheights 3e-12 px apart

One camera means one horizon, not one point

The test this field has been using asks whether a picture's surfaces share a meeting point. One camera photographing four parallel surfaces turned by different angles in their own planes gives them meeting points 1,065 px apart in column and identical in height to 3 × 10⁻¹² px — so the shared-point test charges 28.7 px to a picture one camera really took, and the charge grows with the turn. What one camera imposes is a shared vanishing line. The earlier verdicts survive intact, and for a narrower reason than they looked to have.

choices · Divergence 78.510.51421421051050∞78.510.51421421051050∞where the horizontal slit sits (m)where the vertical slit sits (m)8 with a centre, 17 with a measurenone with both

The exclusion is two conditions, not ten rows

Ten systems have been measured and none has both a centre and a true measure. Ten is not a proof. Swept across the whole two-slit family — eighty-one members, both parameters run out to infinity — a centre appears at exactly the eight members whose slits sit at one finite distance, a measure at exactly the seventeen with a slit at infinity, and at none of them both. The case the two conditions appear to leave open is closed by the rays themselves: one divide is a slit, and eight page points use 6.02 m of it.

choices · Exclusion 2 transversalsnoneunfalsifiable3 transversalsnoneunfalsifiable4 transversals15 transversals26 transversals38 transversals510 transversals713 transversals1017 transversals14independent statements a pavement makesthree unknowns, one equation per mark

Four marks before anything is said

A reader fitting a correct perspective to a row of transversals has three numbers to choose, so three transversals fit whatever they are and the fourth is the first that can disagree. Below that count a pavement is unfalsifiable, and a great many painted pavements are below it.

construction · Attribution wrong hzcorrectno shapefrom a zerosteppeda rulethe distance pointAlberti's sectionthe measuring pointa photographthe constant ratio60144157203036060read with the panel's own horizon60 drawings each

What a panel says about its maker

The reading assembled over this row, run against every procedure sixty times and scored — with the failures reported as carefully as the successes, because three of the five rows are refusals. A drawing names the class of error in it, not the recipe that produced it, and one procedure it never names at all.

construction · Attribution 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.

HorizonProjective invariantAttributionResidualToleranceTransversalConstant ratioCross-ratioIdentifiabilityViewing distanceAxis scaleCamera tilt

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