What one change of light costs, surface by surface — daylight to tungsten
Drawn at its defaults, in the set an average is taken over. It takes no options at all, so every essay calling it gets this exact drawing.
Called by 20 essays
the blast radius of changing it
A mean has a set under it
Every adaptation number this collection publishes is an average over a hundred and twenty-five surfaces that were written down once, in one file, with no argument for how many there should be or how saturated. The average runs from exactly zero to twice itself across them, and the set has never been varied.
Difference and uniformityA lattice is a quadrature rule
Walking a set of test surfaces more finely does not converge on a better answer, because refining a lattice under a constraint changes which corners of the region get sampled and not only how densely. The lattice used here turns out to be a two per cent biased estimate of the integral it stands for.
Difference and uniformityThe error on a gap is not the errors at its ends
Comparing two rows of a table by looking at whether their error bars overlap is the wrong comparison, and here it is wrong by a factor of up to 3.4. The same 125 surfaces score both rows, so the difference between them is quieter than either — and how much quieter is a measurement of how alike the two rows are.
What light isFour steps the test set cannot order
The adaptation census prints fourteen numbers to four figures and its ranking is asked to say which lamps adaptation handles worst. Nine of its thirteen steps are established beyond any doubt the test set can raise; the other four are not, and three of them are consecutive — a tungsten lamp, a halogen lamp and a white LED are simply not ordered.
Where the model breaksThe instrument named the pair that moved
A standard error over a test set flagged four steps of the adaptation census as unresolved. Rebuilding the set three different ways reversed exactly one pair, and it was one of the four. Rebuilding it to a different rule reversed a pair the error separated by nearly nine standard errors — which is not a failure of the instrument but a statement of what it is about.
What a scene doesA theorem about a family
A change of light acts on the test surfaces used here as an exact 3×3 matrix with no residual whatsoever, and the whole adaptation argument is built on that being exact. It is exact because the surfaces span exactly three dimensions, and they span exactly three dimensions because three basis functions were written down.
What light isA fourth dimension has a shape
How much a fourth reflectance dimension costs spans a factor of nine across four equally plausible shapes at one amplitude, and the expensive ones are not the shapes a variance figure would identify. The band that hurts is set by the illuminant rather than by the eye, which is why a triphosphor tube and a tungsten lamp disagree about it.
What light isThe row a fourth dimension improves
Giving the test surfaces one more degree of freedom makes almost every change of light harder for an adapted observer — but not all of them, and which one it helps depends entirely on what the extra dimension looks like. A triphosphor tube is improved by one shape and hurt more than anything else in the census by another.
Difference and uniformitySaturation is nearly everything
The set of test surfaces has three numbers describing it, and only one of them matters. How saturated the surfaces are carries an elasticity of about 0.7 on every result computed over them; how bright they are carries 0.10. A test chart's chroma range decides its answer and its lightness range does not.
Where the model breaksThe input nobody declared
An audit that swept every declared width in this collection found the largest elasticity anywhere to be about a half. The most elastic input turns out to be one that was never declared, never quoted with a range and never varied — and being undeclared is exactly why it escaped the audit that was looking for it.
What the eye doesThe surfaces that answer nothing
Five of the hundred and twenty-five test surfaces contribute exactly zero to every number the adaptation census reports — not approximately, exactly — and the reason is the one fact about von Kries adaptation that makes it worth having at all. Counting the set by how much it contributes gives about a hundred members rather than a hundred and twenty-five.
Where the model breaksA mean is not a worst case
Every adaptation number this collection publishes is an average over objects, and the reader asking whether adaptation will fail them is asking about the object it fails on. That object costs between 1.9 and 4.0 times the published figure, and how uneven a change of light is across objects turns out to be a property of the change rather than a constant.
Matching and measuringAn extremum is still not a sample
Two rounds ago three measurements turned up that took a maximum over a sample of a set and were short by up to a factor of two. The same error was live in a fourth place the whole time, on the set of surfaces every adaptation number is averaged over, and it is short by up to a third.
What a scene doesEvery worst surface sits on a declaration
Bounding the wall in a painted room produced a real worst case — the residual turns over at a band six nanometres wide because a narrower band returns too little light. Bounding the surfaces the residual is averaged over produces nothing of the kind, because all fourteen answers sit exactly on two numbers somebody typed and the one constraint that comes from the world never binds at all.
What a camera doesA chart decides what a camera scores
A camera profile's reported error changes by a factor of five when the test chart's saturation changes, with the camera and its matrix untouched. The elasticity is 0.67 — the same figure, to two per cent, that an entirely unrelated measurement over an entirely unrelated set of surfaces gives.
Where the model breaksWhat the audit still cannot reach
Two rounds have now swept every declared width in this collection and one of its structural choices. Three structural choices remain, none of them has a multiplier to sweep, and the reason each resists is different — which makes the list a description of where this kind of audit ends rather than a queue of work.
What light isThe census in six units
Recomputing every change of light in the adaptation census under six colour-difference formulae, with the scale factor divided out, leaves a table whose levels move by up to a factor of three point seven. The rows that move most are the mild ones, which is the opposite of what a reader would guess and is a property of where each formula was fitted.
Difference and uniformityA dial through a discrete menu
ΔE*94 is ΔE*ab with two weighting constants in it, and at zero those constants make every weight exactly one — so the two ends of the oldest disagreement in colour difference are joined by a line rather than separated by a choice. Walking it gives a derivative where a menu gives only a spread, and the derivative says the published weighting is on the far side of the interesting part.
Where the model breaksTwo instruments and one ranking
A sampling error over a hundred and twenty-five surfaces and a change of colour-difference formula share no arithmetic at all, and they were asked the same question of the same table. Every adjacency the whole menu reverses had already been flagged as unresolved. And one the test set settles at nine standard errors is reversed by four of the five formulae, which is what makes them two instruments rather than one.
Difference and uniformityThe disagreement is at the near end
Every colour-difference formula on the menu was fitted to threshold data, so the expectation is that they agree about pairs an observer can only just tell apart and diverge on large differences. They do the opposite. Proportionally the disagreement is largest at the near end, by a factor of six for the appearance unit, and the cause is an exponent of 0.63.