A name moves with the reader

A colour has a name built the naming model used here: eleven basic terms as points in CIELAB, and a colour named by which point it is nearest. Three essays have since moved the answer. The choice of distance function renames a fifth of the displayable gamut. A name moves with the room renamed more than a quarter of it by changing the light. A name in the model’s own words renamed an eighth by changing the space.

All three held the observer fixed, and the coordinates a naming model reads are computed through one set of colour-matching functions. A reader has their own.

Nobody names the whole gamut the way the standard observer does #

Handed the same light, a population disagrees with the standard observer about several per cent of a display’s colours each, and about a quarter of the gamut somebody disagrees.

• Each observer renames between 3.5 and 13.1 per cent of the gamut, with a median of 8.1 per cent over 823 colours an OLED panel can make.
• 199 of those 823 colours — 24 per cent — have at least one observer in twenty giving a different name.
• The disagreement is not spread evenly over the terms: yellow is agreed by 84 per cent of observers, brown 85 and orange 87, while green is agreed by 97 and purple by 96.
• A narrower display is worse: the median observer renames 7.4 per cent of a wide-gamut LCD’s gamut, 8.1 of an OLED’s and 10.6 of a laser projector’s.

The light is the same; the coordinates are not #

The construction is the one the collection’s observer work uses, pointed at a naming question.

Each colour of the naming model’s own lattice — the displayable gamut in CIELAB, which is where the other naming measurements were taken — is turned into a light: the three primaries of a display, solved so that the mixture matches that colour exactly for the standard observer. 823 of the lattice’s colours can be made that way on an OLED panel with non-negative drive; the rest are outside its gamut and are dropped rather than approximated.

Every member of a population of sixty then reads that same light through their own cone fundamentals, adapts to their own view of the white, and is handed the result by the naming model. So the stimulus is identical for everybody and the coordinates are not, which is observer metamerism arriving at a word rather than at a colour difference.

That is the whole of the construction, and it is worth being clear about what it does not include. The population varies in the eye’s filters and pigments, not in vocabulary: every observer here uses the same eleven terms with the same centroids, and the naming rule is identical. Any disagreement is a disagreement about coordinates, not about language. Real people differ in both, and this essay measures the smaller half.

Which terms come apart #

Yellow is the least stable at 84 per cent, then brown at 85 and orange at 87. Green is the most stable at 97 and purple at 96. The pattern is not about how much of the gamut a term owns — purple covers 174 lattice colours and green 107, while brown covers 44 and orange 57, so the stable and unstable terms appear at both sizes.

What the unstable terms share is where their boundaries run. Yellow, brown and orange are packed into a narrow band of hue with short distances between their centroids, so a small shift in an observer’s coordinates crosses a boundary; green and purple own wide territories whose interiors are far from any rival. A name is not a threshold measured that geometry directly — two colours must move about ten just-noticeable differences apart before people stop calling them the same thing, and how far varies threefold across the space. The threefold variation is what shows up here as a spread in stability.

The individual cases are stranger than the averages suggest, and they say something the averages hide. On the most disputed colour of all — a pale yellow-green at lightness 70 — all sixty observers say green and the standard observer says yellow. On the next, a dark brown, fifty-nine say black. These are not colours the population is split about; they are colours where the whole population is on one side of a boundary and the standard observer is on the other.

That is what a boundary does to a vote. Away from a boundary everybody agrees, because a few units of coordinate shift changes nothing. At a boundary a few units changes the word, and since the population’s shifts are mostly in the same direction — they are dominated by the lens and macular filters, which yellow everybody’s view of the short wavelengths — the population moves together. The standard observer is not the centre of the population’s naming; it is one more observer, and near a boundary it is frequently outvoted.

Which words go where #

The renamings are not scattered across the vocabulary. Over the whole census — 4,229 disagreements out of 49,380 namings — ten transitions account for more than half of them, and the largest four are yellow to green (10 per cent of all renamings), yellow to white (9), purple to blue (6) and grey to green (5).

Those have a direction in common. An observer with a denser lens or more macular pigment absorbs more short-wavelength light, so their coordinates for the same stimulus move — and the words that move are the ones whose boundaries lie across that shift. Yellow losing to green and to white, purple losing to blue: these are the standard observer’s terms being outvoted on their short-wavelength sides.

It is worth noticing what is not in the list. Nobody renames red as green, or blue as yellow: the renamings are all between neighbours, and a neighbour in this model means a nearby centroid rather than a nearby word. The population’s disagreement is a boundary phenomenon throughout, and a boundary between two terms is exactly where a naming model is least entitled to be believed in the first place.

A wider gamut is named less consistently #

The median observer renames 7.4 per cent of the LCD’s gamut, 8.1 per cent of the OLED’s and 10.6 per cent of the laser projector’s; the share of colours with a dissenter in twenty runs 19, 24 and 30 per cent. The worst-named term changes too — yellow on the two panels, orange on the projector.

This is a narrow primary buys a disagreement arriving in the naming model. A display’s light is three narrow bands, a reader’s cones sit a few nanometres from the standard’s, and the narrower the bands the more those few nanometres matter. Everything that collection has measured about narrow primaries — the observer spread on a white, the soft proof’s reader stage, the gamut boundary becoming a band — reappears here as a word changing.

So a wide-gamut display buys reach in colours and spends it in agreement about what they are called. That is not an argument against wide gamuts; it is a term nobody prices, in a place nobody looks.

Beside the other three movers #

Four things now move a name in this collection, and they can be put in one order.

The room renames more than a quarter of the gamut, which is the largest of the four and the one a specification can most easily control: state the light. The metric renames a fifth — the choice between one distance function and another, which nobody records. The space renames an eighth, quoting the terms in an appearance model’s coordinates rather than CIELAB. And the reader renames about a twelfth, which is this essay.

The ordering is useful because the four are not equally fixable. The room and the space are choices somebody makes and can write down. The metric is a convention that could be agreed. The reader is none of those: a naming model has no way to be right about a word for everybody, because the coordinates it reads differ between people looking at the same light. It is the irreducible member of the set, and at 8 per cent of the gamut it is the smallest — which is a more comfortable finding than the alternative would have been.

What this does and does not license #

The number to take away is the shape rather than the size. A naming model quoted as though it produced the name of a colour is quoting one observer’s answer, and the fraction of a gamut where a second observer would say otherwise is a few per cent for an ordinary display and a tenth for a wide one.

Where that matters is anywhere a name is used as a specification or an interface: a product listed as brown, an accessibility rule written in terms of red and green, a search that returns “yellow” things, a voice assistant asked for a purple light. In each of those, a few per cent of the space is a place where the system and the person disagree about the word for something they are both looking at — and neither of them is wrong.

Where it does not matter is in the model’s own business. The terms are centroids and the rule is nearest-neighbour; the observer is one more input, and this essay has measured it the way the others measured the room and the space. There is no word for that colour is the standing warning that the model’s failures are its own rather than the language’s, and that remains true: the disagreement here is between observers using one vocabulary, not between vocabularies.

The observer in a word #

The standard observer is not a description of anybody’s eye, and this essay is one more place where that shows.

An observer is a contract put the position plainly: six departures, all above a delivery tolerance, no reader matching the standard on any of them — and none of that is a demolition, because the standard is an agreement about what a number means rather than a claim about a person. A name inherits the agreement along with the number. When a naming model says a colour is yellow, the full statement is this colour is yellow to the observer the coordinates were computed through, and the population measured here is how much that qualification is worth: about a twelfth of the gamut, for an ordinary panel.

Whose eyes made the same point about matching and noted that the cost grows every time the primaries get narrower. Naming behaves the same way and for the same reason, which is a small piece of evidence that the effect measured here is the receptor variation rather than an artefact of the naming rule: if it were the rule, the three displays would not order themselves by primary width.

The closest relative in the collection is a gamut has a population, which found that whether a display can reproduce a paint is a fact about somebody’s cones, so a gamut boundary is a band rather than a curve. A naming boundary is a band in the same sense and for the same reason. The difference is that a gamut’s band can be reported as an uncertainty, and a word cannot: there is no way to say this is yellow ± 8 per cent of readers in a product listing, an accessibility rule or a voice command.

What was computed, and how #

The lattice is the naming model’s displayable gamut in CIELAB at a ten-unit step. For each of its colours, three Gaussian display primaries are solved so the mixture’s tristimulus values, for the standard observer, equal that colour’s; a colour needing a negative drive is dropped. That leaves 823 colours on the OLED panel, 802 on the LCD and 823 on the projector.

The population is sixty observers drawn with a fixed seed from the collection’s own template — lens age, macular pigment, cone optical density and pigment peak wavelengths varied as the literature reports. Each reads each light, adapts by CAT16 from their own view of D65, and the naming model takes it from there with the same eleven centroids and the same ΔE₀₀ nearest-neighbour rule for everybody.

The reported quantities are the share of colours each observer names differently from the standard observer, the share of observers agreeing colour by colour, and both aggregated by the standard observer’s own term.

Where the measurement stops #

The population is a model of eyes and not of people. Real observers differ in which terms they use, where they put the boundaries, and how consistently they answer at all — and the literature on basic colour terms is largely about those differences rather than about receptor variation. This essay holds language fixed to isolate the receptor part, which is the part colorimetry is responsible for.

The naming rule is also the collection’s own: eleven centroids, nearest in ΔE₀₀. Another rule — probabilities rather than a winner, or a different metric — would move which colours sit near a boundary and therefore how much the population disagrees. The site’s own measurement of that is the fifth of the gamut the metric renames, which is larger than the observer effect measured here.

The lattice is also a lattice. Colours are counted rather than weighted by area or by how often anybody looks at them, so “eight per cent of the gamut” is eight per cent of a regular sampling of CIELAB, not of what a reader encounters. A weighting by the colours that actually appear on screens would move the figure in a direction nobody can predict without the weights, and the honest version of the sentence is the one with the lattice named in it.

And the display is idealised: three Gaussian primaries, no viewing flare, no surround. A real panel adds a black level and a room, both of which move colours towards the neutral boundaries where the disagreement lives.

Still open: whether people’s boundaries move with their eyes #

The experiment this points at is a naming study run with the observers’ own colour-matching functions measured alongside their names. If a person whose lens is denser also puts their yellow-green boundary where their coordinates predict, then the receptor variation measured here is part of the spread that naming studies report, and could be removed from it.

If the boundaries do not move with the eyes — if people learn where the word goes from the world rather than from their receptors — then naming is more stable across a population than colorimetry is, and the disagreement measured here is a property of the model rather than of the readers. That would be the more interesting answer, and it would make the naming model’s coordinates the wrong input.

An input that is not on the form #

The habit is about the argument a calculation takes without being asked for it.

A naming model’s signature is a colour in, a word out. The colour is three numbers, and three numbers are the output of an observer — so the observer is an argument, unnamed, defaulted, and identical in every published naming study. The same is true of a gamut, a tolerance, an appearance prediction and an index: each carries an observer it does not mention, and each therefore reports one reader’s answer as the answer.

The move is to make the hidden argument explicit and sweep it. It usually costs nothing but a loop, because the means to vary it already exist for some other purpose — here, a population built to price observer metamerism, pointed at a question about words.

The failure mode is to read a model’s silence about an input as independence from it. A word that comes out of three numbers inherits everything those three numbers inherited.