Concept

random walk — where it appears

A quantity built by adding an independent step to the last value, so that each term carries every error before it. Its departure grows as the square root of the number of steps rather than staying flat, and its residual wanders where an independent one scatters.

Named by 6 essays across 3 fields — each of them below, with the objects they name alongside it.

0.30.50.7125×10⁻⁴0.0010.0020.0050.010.02how finely each point is read (px, log scale)worst camera-centre error, as a fraction of the track's mean radius (log)chained pairsadjusted togetheradjustment is 4.0–9.2× better6 views · identical observations

A chain and an adjustment

Composing pairwise poses along a sequence is supposed to drift. Measured over five links it wanders instead — one chain ends closer to the truth than its own worst link — and the real cost of chaining turns out to be something else entirely.

manyviews · Drift
-200204060050100150link along the streetscale error relative to the first link (%)average 28.6 %16 streets · ties by mean of ratios · marks read to 1 pxspread after 199 links ±7.3 %

A scale chain leans rather than wanders

A camera driven 200 m along a street, each pair's scale handed to the next through the points they share. Across sixteen streets the scale does not spread the way a random walk would — 7.3 per cent after 199 links, where independent ties would give 108 — and its average leans by an amount the choice of average decides, from +28.6 per cent to −12.2.

manyviews · Drift
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 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

Named alongside it

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

DriftProcedureAttributionBiasConstant ratioerror propagationError termMeasuring pointModel errorRelative poseResidualRoughness

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