Concept

Procedure — where it appears

The sequence of drawn steps a construction is actually executed by, as against the geometry it computes. Two procedures can compute the same thing and differ entirely in which single step a hand performs, which is what decides the shape of the error they leave behind.

Named by 8 essays across 2 fields — each of them below, with the objects they name alongside it.

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
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
0.4000.6000.80011.201.40braccia in the pavement (log₁₀)the worst departure of a mark, in pixels (log₁₀)steppedmeasured from the zerothe same hand, laid off two ways√n against n^0.21

Stepped, or measured from the zero

The same hand at the same precision, laying the same braccia off two ways — dividers walked from the last mark accumulate and grow as the square root of the count, while marks set from a common origin do not accumulate at all. The difference is not which method was used — it is where the zero is, and only the second is recorded in the drawing.

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
the picture plane, in planto the observer, 208 px further downcorrect from 12 cm, at 160 mm widestation 520 px

Two rules for one pavement

Vignola set out two rules for laying a tiled floor and asserted that they agree. Executed from the same ground line and the same free parameter they agree to 2e-13 px; executed from the numbers their own wordings invite they part by 24 px. The quantity that separates them is the distance the reader has to stand at, and neither rule names it.

construction · Tworules

Named alongside it

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

AttributionTransversalDistance pointrandom walkcostruzione legittimaError termIdentifiabilityMeasuring pointResidualRoughnessViewing distanceBias

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