Concept

Attribution — where it appears

Deciding which procedure or instrument produced a finished picture, from the picture alone. It is a question about what a drawing records rather than about what it depicts, and the useful part of the answer is usually the list of things it cannot record.

Named by 9 essays across 4 fields — each of them below, with the objects they name alongside it.

00.50011.5000.5001the lens's radial coefficient, −k₁the worst transversal's distance from a correct perspective, in pxa reader's ruler, 0.2 pxk₁ = −0.40a photographed pavement, against its lens5.7 px of bow at the threshold

The lens a pavement can hide

A photographed pavement reads as a correct drawing up to a radial coefficient of about four tenths — a lens strong enough to bow a straight edge across the page by nearly six pixels and to print as twenty per cent distortion at the frame's corner. The reason is that a pavement sits near the principal point, which is the one part of the frame a radial map barely touches.

lens · Taughtratio
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
the distance pointAlberti's sectionthe measuring pointcorrect from 12 cm at 160 mm widethree routes, 0e+0 px apart

Three procedures, one panel

Alberti's lateral section, the distance-point construction and a pinhole camera put every transversal at the same pixel — and every reading of the finished drawing therefore returns the same number for all three. The methods are distinguishable on the desk and indistinguishable on the panel, which is the fact any attribution has to start from.

construction · Attribution
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
10121416-1000100how far the distance point was misplaced, in pixelsthe distance the finished drawing is correct from, in cmas intendedevery point passes the reader's own test4/3 to 8e-15

The slip that leaves no trace

A distance point put twenty-four pixels wrong moves the pavement by two and a half and leaves the reader's projective test reading exactly four thirds. The same slip on Alberti's section moves the drawing by the same amount and is caught, so the difference is not the size of the error — it is that one of them lands back on the set of correct drawings.

construction · Attribution
the distance pointone mark on the horizonleaves another exact drawingAlberti's sectionone mark per braccio, each from the panelleaves errors each its ownthe measuring pointdividers walked along the measuring lineleaves errors that accumulatea photographnoneleaves a smooth curvethe constant ratioone ratio, applied throughoutleaves a smooth curveone hand step eachand four kinds of trace

One hand step each

Every classical perspective construction has exactly one step a person performs by hand, and the four constructions perform four different steps. That single difference decides everything a finished drawing can say about its maker, because the answers are identical and only the mistakes are not.

construction · Handerror
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

Named alongside it

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

ProcedureTransversalCross-ratioProjective invariantResidualToleranceConstant ratioDistance pointFalsifiabilityHorizonIdentifiabilityModel error

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