A name in the model's own words

An earlier essay measured what changing the room does to a vocabulary: eleven basic colour terms, quoted as centroids in CIELAB, applied to the displayable gamut, and up to 26.8 per cent of that gamut changes what it is called when the surround goes from average to dark. The essay reported it and left an objection standing, because the objection is a good one.

CIELAB has no surround in it. A partition of CIELAB moving when the surround moves is not a discovery about words; it is a restatement of the fact that the space cannot represent the thing that changed. The honest test is to quote the vocabulary in coordinates that do have a surround, and see whether the renaming goes away.

That test has two outcomes and no third. If names follow appearance, the renaming should shrink. If it does not shrink, the model’s correlates are not the coordinates names live in.

The claim #

Moving the partition into the appearance model’s own coordinates does not reduce the renaming, and the choice of coordinates is itself as large a decision as the choice of room.

• In CIELAB, average to dark renames 26.8 per cent of the displayable gamut. In CAM16-UCS it renames 27.8 — four per cent more, not less.
• The other two room pairs behave the same way: 14.8 against 15.4 for average to dim, and 11.2 against 11.2 for dim to dark. The three ratios are 1.04, 1.04 and 0.99.
• So the second outcome is the one that happened. The model’s correlates are not what colour names follow, at least not in the way that would make a fixed partition of them stable across rooms.
• And with the room held still, the two spaces disagree about 12.7 per cent of the gamut — comparable with the effect of changing the room at all, and produced by nothing but the choice of coordinates.
• The commonest single disagreement is purple against red, at 1.5 per cent of the whole gamut.

What was being tested #

The eleven basic terms are a measurement of people talking, and the centroids this site uses are quoted to ±5 units in CIELAB. That is the whole of the data: eleven points and a distance function, and everything else is a construction.

The construction that makes a vocabulary out of them is nearest-centroid. Every colour is called whatever centroid it is closest to, which turns eleven points into eleven regions filling the space. How unequal those regions are is one of this site’s more surprising measurements — the largest is more than four times the smallest — and it is a property of the construction as much as of the words.

The test is a substitution. Take the same eleven points, express each as its appearance in a reference room using the appearance model, and then partition by nearest centroid in the model’s uniform coordinates rather than in CIELAB. Nothing is refitted; the same measured points, read in different coordinates.

The result, and both directions it could have gone #

If naming is a partition of appearance, then a patch in a dark room genuinely does look different and genuinely should be named differently — but a partition made in coordinates that already account for the room should track that change rather than being surprised by it. The renaming should shrink toward whatever the words themselves do.

It does not shrink. Average to dark renames 27.8 per cent of the gamut in appearance correlates against 26.8 in CIELAB.

The four per cent is not the point and should not be read as one; it is well inside anything the centroids’ own ±5 rounding would move. The point is the absence of a decrease. A model whose coordinates were where names live would have produced a visible reduction, and there is none.

What that says is narrower than “the appearance model is wrong”. CAM16-UCS is a good uniform space and predicts a great many things. What it does not do is provide a coordinate system in which a fixed set of eleven regions describes what people call things across rooms — and since that is what a vocabulary quoted as centroids implicitly claims, the claim is unsupported in either space.

The space is a decision even before the room moves #

The more useful number came out of a control. Hold the room fixed, ask the nearest-centroid question in both spaces, and compare.

12.7 per cent of the displayable gamut is called something different depending only on which coordinates the question was asked in. That is comparable with what changing from an average to a dim surround does — 14.8 per cent — and larger than what going from dim to dark does.

So there are two undeclared decisions of similar size behind any statement of the form this colour is called purple: which room, and which space. A colour-naming study records neither, because until a model with a surround existed there was nothing to choose between.

How much the centroids’ own rounding could move #

The eleven centroids are quoted to ±5 units, and the argument above leans on that twice — once to dismiss the four per cent and once to keep the 12.7. Both leans can be checked rather than asserted.

Redrawing all thirty-three centroid coordinates uniformly within ±5 and recomputing the same-room disagreement, twenty-four times over: the mean is 12.98 per cent against the unjittered 12.69, the range is 10.53 to 17.68, and the standard deviation is 1.69 percentage points.

The two claims then separate cleanly. The same-room disagreement is 12.7 points against a rounding-induced spread of 1.7, so it survives by about seven and a half standard deviations and never comes near the three per cent the gate demands. The gap between the two spaces on the average-to-dark pair is 27.81 against 26.76 — 1.05 points, which is under two thirds of one standard deviation of the same noise.

That is what the essay asserts, and having it as a number matters, because the two quantities look the same size on the page and are three times apart in evidence. The 12.7 is a measurement; the four per cent is a rounding. The finding is the absence of a decrease, not the presence of an increase.

The shape of the distribution is worth a sentence too. The draws run from 10.53 up to 17.68 around an unjittered 12.69, so moving the eleven points inside their own uncertainty pulls the two partitions much further apart than it brings them together. That is what should happen to two partitions that are not the same partition: agreement requires the centroids to line up in both coordinate systems at once, and disagreement requires only that they do not.

What the eight pairs actually account for #

Those eight commonest transfers are described as accounting for most of the 12.7. They account for 49.7 per cent of it.

Purple to red is 1.504 points of gamut, white to yellow 0.923, grey to blue 0.844, purple to blue 0.818, white to grey 0.686, white to green 0.554, pink to red 0.528 and black to brown 0.449. That is 6.31 points of the 12.69, with the remaining 6.38 spread thinly across every other pair the eleven terms can form.

Half the disagreement sitting in a long tail changes what it is evidence of, and changes it in the essay’s favour. Eight boundaries moving would be a statement about eight boundaries — a handful of contested regions where two spaces happen to disagree about hue spacing. Half the effect being spread across everything else says the two partitions differ wherever they have a boundary at all, at a level too small anywhere to earn a named pair.

So the choice of space is not relocating a few disputed territories. It is moving the whole partition slightly, everywhere, and the named pairs are where the slight movement happens to cross a line.

Why purple and red #

The largest transfers are worth reading rather than tabulating, because they are not evenly distributed and the pattern says something.

Purple against red is the biggest. Purple’s centroid sits at moderate lightness with substantial chroma in the blue-red quadrant, and red’s is close by; the boundary between them runs through a region where CIELAB and the appearance model’s uniform coordinates disagree most about hue spacing, which is exactly the region the unique hues essay found the two spaces disagreeing about.

White against yellow is second, at 0.92 per cent, and grey against blue third at 0.84. Those two are lightness-and-chroma disagreements rather than hue ones: the appearance model’s lightness correlate is not CIELAB’s, so the boundary between a light chromatic name and an achromatic one moves.

What the room does that the space cannot follow #

There is a specific reason the appearance model fails to absorb the room’s effect here, and it is not a defect in the model.

The model predicts what a stimulus looks like in a given room. It does not predict what an observer will call it, and the difference is a categorisation stage the model has no representation of. Moving the partition into appearance coordinates assumes that categorisation happens after the appearance computation and uses the same coordinates — which is a hypothesis, and it is the hypothesis this measurement tests and does not support.

The alternative is that categorisation has its own coordinates, or is not a partition of a space at all — that a name is a prototype with a graded membership rather than a region with a boundary, which is what the categorical-perception literature has argued since Rosch. This site’s machinery has a temperature parameter that softens the partition into probabilities, and softening it does not change the ratios here. The catalogue essay found the same insensitivity from the sampling side.

What a vocabulary would have to record #

If both the room and the space rename a substantial share of the gamut, then a set of centroids is not a vocabulary until three more things are written beside it.

The room. Not described in prose — a neutral booth under daylight — but as the parameters an appearance model takes: an adapting luminance, a background, a surround. The difference between an average and a dim surround is 14.8 per cent of the gamut, which is larger than the effect of most of the methodological choices such studies do record.

The space. Whether the nearest-centroid question is asked in CIELAB, in a uniform appearance space, or in something else. That is worth 12.7 per cent on its own.

And the distance function. An earlier measurement found that changing from a Euclidean distance to CIEDE2000 renames 20.5 per cent of the gamut, which is the third decision of the same size.

Three undeclared parameters, each worth between a tenth and a quarter of the space, and none of them recorded anywhere. A statement that a particular chip is purple is therefore true relative to a room, a space and a metric that the statement does not mention, and the three between them can move a substantial fraction of the boundary the statement sits near.

That is not an argument that colour naming is arbitrary. The centroids are stable, the large territories stay large, and no observer would call a saturated blue brown under any combination of these choices. It is an argument that the boundaries are soft in a specific, measurable way, and that a construction which draws them as hard lines is claiming a precision the data does not have.

Softening the partition does not rescue it #

There is one obvious repair left and it is worth reporting that it was tried, because it is the repair anybody familiar with the categorisation literature would reach for first.

A nearest-centroid partition has hard boundaries, and no account of colour naming since Rosch has claimed that people’s categories work that way. What the evidence supports is graded membership: a chip near a boundary is called one thing most of the time and the other thing some of the time, with the proportion depending on how far it is from each prototype.

This site’s naming machinery has that built in. A temperature parameter turns the distances to the eleven centroids into a probability distribution over names, so a partition can be softened continuously from hard boundaries to something close to uniform. The parameter is stated, its range is a factor of four, and the site’s own gate requires the naming conclusions to survive the whole of that range.

Softening does not change the comparison. Across the allowed range of temperatures the renaming a room produces stays the same size in both spaces, and the ratio between them stays within a few per cent of one. The reason is arithmetic rather than subtle: softening moves points near boundaries from a definite answer to an uncertain one, and it moves them in both partitions equally, because the boundaries in both are the same kind of object placed in different coordinates.

So the negative result survives the obvious defence. Whatever coordinates naming lives in, they are not these — and the possibility that names are not a partition of any colour space at all remains open, which is where this site has left it since the vocabulary was first measured.

Who found it, and when #

Berlin and Kay’s basic colour terms are from 1969 and the centroid measurements that follow them are from the 1970s onwards, all in CIELAB or its predecessors, all in a viewing condition described in prose rather than parametrised.

CIECAM16 and its uniform space are from 2016 and 2017, and the possibility of redoing colour naming in them has been available since. As far as this site can tell, the comparison has not been made — which is unsurprising, since it requires re-partitioning a lattice rather than re-analysing data, and produces a negative result.

The negative result is the reason to publish it. The essay that measured the room’s effect reported that the room renames a quarter of the gamut and could be read as an argument for doing colour naming in an appearance space. This measurement says that would not have helped.

What was computed, and how #

The lattice is every point on a five-unit CIELAB grid that is inside the displayable gamut — 3,790 of them. Both partitions run over the same lattice.

The appearance centroids are each CIELAB centroid converted to XYZ, put through CIECAM16 in the reference room, and expressed in CAM16-UCS. The partition in that space is nearest centroid by Euclidean distance, which is what the uniform space is for.

The room comparison holds the centroids at their reference-room appearance and re-reads each lattice point’s appearance under the new surround, which is the like-for-like counterpart of the CIELAB measurement’s corresponding-colour step.

The gate requires all three room pairs to be tested in both spaces and reports the ratio, rather than requiring the comfortable answer — an assertion written to accept whichever outcome occurred. It separately requires the same-room disagreement between the two spaces to exceed three per cent, which is the finding that does not depend on the room at all.

Where it stops #

The eleven centroids are quoted to ±5 units and every number here inherits that. This site’s gate requires the naming findings to survive the centroids being moved by their own rounding, and they do; the four per cent that separates the two spaces would not.

The appearance model is asked for a degree of adaptation that comes from its own tables, and that number is a clock reading rather than a property of a room. Different assumptions about how long the observer has been in the room would move the appearance-space numbers and not the CIELAB ones.

And nothing here is a measurement of people. It is a measurement of what two constructions do with eleven measured points, and a real naming experiment run in three rooms would settle in a week what this can only bound.

One further caution about the negative result. Failing to shrink is evidence against the hypothesis that naming is a fixed partition of these particular appearance correlates. It is not evidence against the much weaker and much more likely claim that naming has something to do with appearance rather than with tristimulus values — a claim this measurement cannot address, because it tests one specific coordinate system rather than the idea behind it. A different uniform space, or the appearance model’s raw correlates rather than its uniform ones, might behave differently, and neither has been tried here.

What can be said is that the substitution somebody would reach for first does not work, and that the reason it does not work is not a small numerical matter: the renaming is the same size in both spaces to within the centroids’ own rounding.

Where the ladder goes next #

The measurement that would settle it is not a computation. Show observers the same chips in three rooms and record the names; the prediction from this essay is that the renaming will be closer to the CIELAB number than to zero, and that no space this site carries will predict which chips move.

The nearer question is the one the control opened. If the choice of coordinates renames an eighth of the gamut, then every naming result quoted in CIELAB is quoted with an unstated parameter — and so is every result quoted in appearance correlates. Naming a colour requires naming a space, in exactly the way naming a colour requires naming an observer, and neither is in any vocabulary this site has been able to find.