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Colour is the subject where a person's own eyes feel like sufficient evidence, so most of what is said about it is a slogan that quotes a real mechanism and forgets its stop. Blue and yellow make green is the standing example — true of paint, false of light, and the difference between them is not a detail but two different arithmetics. A claim of that shape survives because it sounds like a measurement.
There are 125 of them below. Each carries the verdict, what was found instead, and — the part that matters — the quantity that settles it, computed while this page is built from the same libraries the figures are drawn from. None of these numbers is typed in. If one of them stopped agreeing with the essay it points at, the build would stop rather than serve the page.
The verdicts are not all wrong, and the interesting ones are not. Almost nothing in this subject is simply false; the common failure is a true mechanism quoted past its own domain, which is why most rows below say right about one quantity, wrong about another. Distinguishing the two is most of the work, and it is the reason this site computes rather than cites.
Wrong
38 claims
A hex code identifies a colour.
It identifies three numbers, and a triple means nothing until a space, a transfer function, a white point and a display are named. The same three numbers sent to an sRGB display and to a Display P3 one are two different colours, and the gap is far larger than any tolerance a paint supplier would accept. This is the reason no figure on this site contains a hex code: a colour here begins as a spectrum and is integrated against a named observer before it is written down.
What settles it: one triple, two displays, ΔE00 = 3.72 — where 1.0 is about the threshold of noticing. Argued in A hex code is not a colour.
Two samples that match under one light match under any light.
Matching is an identity between three integrals, not between two spectra, so two quite different reflectances can produce the same three numbers under one illuminant and separate under another. This is not a curiosity at the edge of the subject: it is the ordinary failure mode of a paint touch-up, a garment sleeve against its body, and a dental crown against a tooth, and it is the reason a tolerance names its illuminant.
What settles it: ΔE00 = 0.000 under D65 and 10.22 under illuminant A — the same two reflectances, nothing changed but the lamp. Argued in Two spectra, one colour.
A metameric match survives as long as nobody changes the light.
It is broken by a corner, with no change of illuminant, observer or pigment. A bounce is elementwise multiplication, so a surface in an enclosure receives light carrying its own reflectance a second time; a metameric match is linear in reflectance and the square of a metameric black is not. Since ρ² differs by 2ρb + b², and the second term is non-negative everywhere, it cannot integrate to zero against any non-negative matching function. A metameric black is invisible and its square cannot be. The gap this leaves is in a document that exists: a colour tolerance names an illuminant, an observer and a limit, and has no field for the geometry.
What settles it: ΔE00 = 5.4e-14 on a flat wall, 5.07 at an enclosure of 0.5 and 19.55 in a nearly closed cavity — a smooth function of one geometric number, exactly zero only when the wall is flat. Argued in A corner is not a wall.
Every colour corresponds to a wavelength.
A large wedge of colour directions has no dominant wavelength at all. The purples are the clear case — they are not in the spectrum, and the line closing the horseshoe is a mixture line rather than a locus — but the ambiguity is wider than the purples themselves, and the answer moves when the white point moves, because a dominant wavelength is defined by a ray from a chosen white and not by the colour alone.
What settles it: 106.3° of the 360 around equal-energy white — 29.5% of all colour directions — reach the closing line rather than the spectral locus, and have no dominant wavelength. Argued in Not every colour has a wavelength.
A hundred per cent black ink prints black.
One film of black ink reaches L* 16, which is a dark charcoal, and it looks black on a page only because there is nothing blacker beside it. The last factor of six in a printed black comes from the three chromatic inks laid underneath, which have nothing to do with being black and everything to do with optical density adding when films are stacked. What limits the result is not the pigment but how much ink a sheet will take before it stops drying.
What settles it: L* 15.9 for one black film, 6.0 for a rich black at 240% ink, and 2.47 with all four solid. Argued in A black that is not black.
A light can be brown.
Brown is a dark orange, dark means much darker than the white in the field, and a stimulus with nothing brighter beside it has no white to be dark against. Holding one stimulus fixed in XYZ and raising the surround takes its lightness from the top of the scale to the bottom while its brightness rises — the two attributes move in opposite directions, and only the relative one has a name attached. The same argument rules out olive, navy, maroon and grey lights, and rules in every category that is not defined by darkness.
What settles it: the same light reads J = 151.8 against a white below it and J = 16.1 against one 67× brighter — brown only in the second. Argued in There is no brown light.
Two lamps sold as the same colour temperature are the same colour.
A nominal temperature is not a chromaticity; it is a quadrangle, and two lamps out of one box can sit at opposite corners of it. The 4000 K bin spans 3,791 to 4,233 kelvin crossed with a green–pink range wide enough to be seen on its own, and its worst corner pair is further apart than any tolerance a paint supplier would accept. The reason nobody complains is chromatic adaptation: in a room lit by either, the same surfaces differ by about one unit.
What settles it: ΔE00 11.3 between two corners of one bin, against 1.04 on surfaces once the observer has adapted. Argued in White is a region.
A display's white is a good enough light to judge a print by.
Judged as an illuminant by the same index a lamp is judged by, a display's white scores worse than a fluorescent tube — and the wider the gamut, the worse it gets, because the narrow primaries that buy a large triangle are exactly the ones that leave holes in the spectrum. Every source compared here is at D65 to within thirty kelvin, so none of the difference is a white-point difference and no calibration touches it.
What settles it: a laser projector's white scores 67.6 against a triphosphor tube's 81.2, at one chromaticity. Argued in A screen is a poor lamp.
Two colour-difference formulae differ in scale, so a tolerance in one is a tolerance in the other.
A difference in scale is absorbed by renaming the tolerance. A difference in *order* is not: if one formula says batch A is worse and the other says batch B is, no rescaling of either makes them agree, and one of the two answers is going to be acted on. Over the whole space the two disagree about a seventh of comparisons; among pairs sitting near a tolerance of one unit — which is where every acceptance decision is made — they disagree about nearly half.
What settles it: 13.4% of comparisons inverted overall, 43.2% near ΔE 1, against 50% for a coin flip. Argued in Which of two is worse.
A screen delivers the most colour in a dark room.
A room does two opposite things to a display at once. Turning it down shrinks the appearance solid, because a dark surround compresses the lightness scale; turning it up shrinks it too, because light falls on the screen and raises the black. So there is a brightness at which the display delivers most, it is neither dark nor bright, and it scales with the panel — a room whose white is about a fifth of the display's. The dark room every calibration standard specifies costs about a tenth of the solid, which is a fair price for a different objective and is never stated as a price.
What settles it: best at 200 lux for a 300 cd/m² panel, with 87% of that volume delivered at 0.1 lux. Argued in A display in a room is a smaller display.
Dither works by reducing the error.
It raises the error, by about forty per cent, and moves it. A quantised gradient's error is a staircase whose power sits in a few frequency components; a dithered one's is noise of the same power spread over every component there is. Read as components — the form every contrast threshold underneath was measured in — the mask's largest visible component is twenty times smaller. Read at a point in space, which is what this site's own model did for a phase, it comes out worse.
What settles it: the error rises 1.42× while the most visible component falls 19.7×. Argued in Every threshold was measured with a grating.
Two lamps of the same colour temperature can be mixed without changing the light.
Mixing light is addition, and every quantity a lamp is specified by is a nonlinear function of the spectrum, so none of them mixes. Two Planckian radiators sit exactly on the locus by construction; their equal mixture lies on the chord between them, which is measurably off it — a pink cast that would fail a specification neither parent fails. The rendering index does not interpolate either: two sources with holes in different places fill each other's in, and the best mixture can beat both parents.
What settles it: two lamps at Duv 0.0000 mix to Duv -0.0064 at a correlated colour temperature of 3953 K. Argued in Two lamps do not average.
A halftone screen is visible across a printed page.
It is visible where the reader is looking and nowhere else. Eccentricity does two things to a fine pattern — it raises the threshold and it lowers the cutoff frequency — and a screen sits high on the sensitivity function's falling edge where the second dominates completely. The previous phase guessed the two effects would multiply; at five degrees off axis that guess is fifty-three times too generous and by twenty degrees it is out by eight orders of magnitude.
What settles it: visible at 8.1× threshold at fixation and gone by 5°, against a product prediction still above threshold at 10°. Argued in A tint at the edge of a page.
Reading a filtered field at its worst point is the conservative choice.
It is a different question, not a safer answer. Every threshold under this site's spatial machinery was measured with a grating, so the model is a statement about components; read at a point it answers something it was never fitted to. Of seven claims on this site audited both ways, five disagree by more than half again and four reverse direction outright — and the disagreement is not confined to comparisons involving noise, which is where the previous phase's rule said it would stop.
What settles it: 5 of 7 claims disagree and 4 reverse, the worst by 111×. Argued in The list nobody made.
A viewing booth inside its uniformity tolerance lights its whole sample plane the same way.
Uniformity is specified on illuminance, which is one integral of the spectrum against one function. A phosphor-converted source emits a different spectrum at every angle, so two positions on a compliant sample plane are lit by two different lights — and the repair is geometric rather than colorimetric: a source whose converter is the same thickness in every direction has no angular colour at all, and passes the same uniformity figure.
What settles it: ΔE00 2.40 across the plane at 72.6% illuminance uniformity, against 0e+0 for a dome source that passes the same figure. Argued in The booth is a luminaire.
A change of light moves a surface, and how much an observer is left with depends on how big the change was.
It depends on the shape of the change and hardly at all on its size. The largest change in this site's census — a bounce off a green wall, ΔE00 23.6 — leaves seven per cent of itself after adaptation, and a triphosphor tube less than a third that size leaves nearly a third of itself. A change of light is exactly a matrix on tristimulus values and adaptation is a diagonal one, so what survives is the part that is off the diagonal, which is a property of the spectrum rather than of the distance travelled.
What settles it: 33% left of a change of ΔE00 7.1, against 11% left of one of 31.4. Argued in What no adaptation can remove.
Colour names move when the room does because CIELAB has no room in it, so an appearance space would fix it.
It does not fix it. Quoting the eleven basic terms in an appearance model's own uniform coordinates and re-partitioning the gamut in each of the standard's three rooms leaves the renaming where it was — four per cent larger, which is well inside the centroids' own rounding. And with the room held still, the two spaces disagree about an eighth of the gamut on their own, which is a decision of the same size as the room and is recorded nowhere.
What settles it: 26.8% renamed in CIELAB against 27.8% in appearance correlates, with 12.7% renamed by the space alone. Argued in A name in the model's own words.
A correction matrix converts a measurement made one way into a measurement made another.
Not between two measurement conditions on a brightened substrate. The term that differs is the light the paper emits, which arrives in proportion to how much substrate is showing through the ink rather than to what the patch reflects — largest on the bare sheet and essentially zero on a solid. A linear map applies a correction proportional to the patch's own values, which is the wrong shape, so the best possible fit improves the tints by damaging the solids.
What settles it: the best least-squares 3×3 over 17 patches leaves 22.9% of the disagreement and makes 4 patches worse. Argued in A tolerance cannot cross a condition.
Two lamps of the same colour temperature light a scene the same way.
Not if anything in the scene fluoresces. A xenon flash and a phosphor-converted white LED can be within a few thousandths of a chromaticity of each other and differ completely below 400 nanometres, where the LED emits nothing at all because its pump die is at 450. A white balance divides out the first difference and cannot touch the second, since it is a diagonal matrix and the difference is an addition.
What settles it: the whites are ΔE00 3.25 apart and the brightened sheet 11.84, after each is referred to its own lamp's white. Argued in A camera cannot record the excitation.
The L, M and S axes an appearance model adapts in are the cone responses.
They were fitted to corresponding-colour judgements — a person matching appearance across a change of light — by finding the basis in which a diagonal scaling works best. That optimises the predictive performance of a diagonal model and says nothing about receptors, and the test from the other experiment shows it: run the dichromat construction backwards and CAT16 commits itself to a deuteranope confusion point a long way from the measured one. The transforms are good at the job they were fitted for, and the letters on their rows are the only claim that they are receptor sensitivities.
What settles it: CAT16 misses the deutan confusion point by 1.45 and the protan by 0.12, where the construction from the points themselves returns them to 1e-16. Argued in The cones an appearance model uses.
A camera matrix works under any light.
It is fitted under one illuminant and quotes its residual there. Fitted under a tungsten lamp and used under a cold sky the same matrix delivers eight times as much error, because a sensor that fails the Luther condition has a different best 3×3 under every light. What does work is the two-matrix scheme every real profile uses: a blend of a warm and a cool calibration reaches, at the right weight, exactly what a matrix fitted at the intermediate light reaches — and the weight comes from an illuminant estimate, which is itself a guess.
What settles it: 1.17 ΔE00 where it was fitted and 9.34 at the far end, while the best blend gives 1.153 against 1.153 for a matrix fitted there. Argued in A matrix is fitted under one light.
A chromatic adaptation transform's three axes are cone responses.
They are fitted axes wearing a physiological name, and the direction the fitting walks is away from the receptors rather than towards them. Minimising the residual over all nine free numbers gives a basis whose implied deuteranope confusion point is further from the measured one than Hunt–Pointer–Estévez's, than CAT16's and than the receptors' own — and walking in a straight line from the receptor basis to that optimum improves the residual at every stop, with no shoulder and no interior minimum. The diagonal model wants channels narrower and less overlapping than any eye has.
What settles it: the best axes leave 0.97 ΔE00 against the receptors' 1.65, and imply a deuteranope point 1.63 from the measured one. Argued in The best axes are not receptors.
A more cone-like basis is better for everything a colour model does with it.
Two objectives are written over the same nine numbers and they point apart. The basis that minimises what an adapted observer is left with after a gain is a disaster as a space to measure a colour difference in; the basis that makes the discrimination ellipses roundest adapts worse than the receptors do and worse than three of the four transforms in ordinary use. Each winner is beaten on the other objective by every published candidate. The basis built from the confusion points is best at neither and is one of three entries within a factor of two of both floors.
What settles it: the adaptation winner leaves an axis ratio of 7.70 against the floor's 1.61, and the discrimination winner leaves 1.79 ΔE00 against the floor's 0.97. Argued in No basis is good at both.
CIELAB's cube root is what makes it perceptually uniform.
The exponent is nearly irrelevant to that job. Minimised over every basis, the ellipse anisotropy floor barely moves above a square root: a cube root and a square root differ by about three per cent, and a tenth root buys another three. Almost the whole of what a compression buys arrives with the first departure from linearity. Meanwhile, at a fixed exponent, the choice of basis is worth a factor of two — and on CIELAB's own basis compressing harder makes the geometry steadily worse rather than better.
What settles it: floors of 2.33 at no compression, 1.66 at a square root and 1.57 at a tenth root, while CIELAB's own basis goes from 3.57 to 3.77. Argued in The exponent was never the argument.
A display's primaries are a gamut decision and nothing else follows from them.
Moving a display's white point is a gain on R, G and B, so a display adapts in the inverse of its own primary matrix, and three chromaticities agreed in a standards meeting decide how well every white-point change on that panel behaves. Posed as a design problem — choose three realisable primaries to minimise the adaptation residual, subject to a floor on coverage — the constraint turns out to cost about two per cent against a basis free to be any nine numbers, and the trade against coverage is nearly flat.
What settles it: 0.996 ΔE00 at 54% coverage and 1.018 at 64%, against 0.974 with all nine numbers free. Argued in Primaries chosen for their inverse.
A sensor satisfying the Luther condition exactly is a poor von Kries observer.
The condition asks that the sensitivities be *some* linear combination of the matching functions and says nothing about which, and which one is exactly what a colorimetric camera's adaptation basis reduces to once the illuminant has cancelled. So such a camera can have any basis at all, including the best one there is, with a drift of zero. This collection asserted the opposite for two phases on the strength of one control, whose mixing matrix was written to make three curves look like camera channels and was never chosen for anything else.
What settles it: four exactly colorimetric sensors leave 0.97 to 2.46 ΔE00, all with drift under 1e-6°. Argued in The condition chooses no axes.
A von Kries model has nine free numbers, of which six are fixed by dichromat data, leaving three to fit.
The three that remain are the row scales, and a gain cannot see them — which was already established as an identity. Measured as a rank it is a stronger statement: the second-derivative matrix of either objective this collection scores a basis on has rank exactly six at its own optimum, so there is no seventh flat direction anywhere in the nine. The three eigenvalues it drops fall as the square of the finite-difference step, which is what a truncation error on an exact zero does.
What settles it: rank 6 with a gap of 4.0e+3 between the sixth eigenvalue and the seventh, and a largest principal angle of 2.5e-2° to the row scalings. Argued in The rank is the invariance.
The shape of an optimum can be measured by walking outwards in random directions.
A random unit vector in nine dimensions carries an expected ninth of its length on every principal direction, so the curvature it feels is close to the mean of the nine eigenvalues and the radius it reports is close to the middle of the bowl. Twenty-four of them reported a bowl eight times longer one way than another where the eigenvalues say thirty. More samples do not help, and neither does measuring closer in: the same six eigenvalues predict every one of the twenty-four measured radii, so the sample added nothing the curvature did not already hold.
What settles it: 8.0 sampled against 29.8 exact, with the model predicting each sampled radius to a median of 8%. Argued in How long is the bowl.
A constraint that removes more parameters costs more.
The count predicts nothing. Requiring an adaptation basis to be the inverse of three realisable display primaries removes three degrees of freedom and costs two per cent; requiring it to hit three dichromat confusion points removes six and costs seventy. What decides it is the quadratic form in the direction the constraint points, and two of the nine directions carry most of every excess. The cheap constraint is cheap because it barely moves the basis in the six directions the objective can see at all.
What settles it: 0.022 ΔE00 at a displacement of 0.068 against 0.677 at 0.891. Argued in A constraint is a direction and a distance.
A pigment model good enough to predict cone catches is good enough to locate a confusion point.
A copunctal point is where two nearly parallel planes meet, so it is a quotient of small differences and a model accurate to a fraction of a per cent on catches is nowhere near accurate enough. Read straight off this collection's own template the protanope's point lands a quarter of the way across the diagram from the measured one, and the deuteranope's moves by more than the diagram is wide when the stimuli the fit was made over are changed. The construction runs cleanly the other way, which is what makes a transfer possible.
What settles it: a protan point at (0.99, 0.20) against a measured (0.75, 0.25), and a deutan point moving 23 units between two fitting sets. Argued in A template cannot place a point.
A display primary's tolerance is a distance.
It is a closed region, and none of the three is round: the red primary's free region at a one per cent rise is fifteen times longer one way than another, green's is nearly seven and blue's nearly six, and their areas differ by four and a half times. About half of red's boundary and half of blue's lie outside the region a real primary can occupy, where the cost does not rise and the primary cannot go. The objective's cheapest direction moves red and green together and leaves blue alone, which no per-primary tolerance can express at all.
What settles it: ratios of 15.1, 6.6, 5.9 with 23 of 48 boundary directions of the r primary outside the realisable region. Argued in A tolerance is a region.
A specification can state a tolerance as a limit on each parameter.
A list of intervals is a box, and a box contains an intersection rather than being contained by it. Where two requirements' regions are long, thin and crossed at an angle — which is what a display primary's adaptation and gamut regions are — what satisfies both is a small fraction of either, and the box's corners satisfy neither. The loss grows with how elongated the regions are and with the angle between them, which are exactly the two properties that make a tolerance worth stating.
What settles it: the region satisfying all four requirements is 5.0% of the smallest one alone, on a display's red primary. Argued in Two tolerances do not meet in a tolerance.
A colour management chain is as good as its profile.
The profile's interpolation between its nodes is the smallest term in the delivered error by a wide margin, and the whole range from a coarse grid to a fine one moves the total by less than the viewing condition does by existing. What dominates is the room — the one stage nobody controls — and what has the most reach is the rendering intent, which contributes nothing at its usual setting and can move the total by more than any other choice. A budget stated without naming the viewing conditions has left its largest term unwritten.
What settles it: the room carries 97.1% of a delivered difference of 4.43 ΔE00 and the profile 0.13. Argued in A delivery tolerance is three tolerances.
A ΔE of 1 means the same thing whichever formula computes it.
A tolerance is not a distance, it is a boundary drawn through the space of pairs, and six defensible formulae draw six different boundaries enclosing different sets. Pairs built to sit at exactly 1.0 in CIEDE2000, then read in the other five after each has been scaled onto the same footing, come back anywhere between two thirds of a unit and nearly two. The appearance formula rejects every one of them. Two laboratories can both measure correctly, both use a published formula, and disagree indefinitely about individual batches.
What settles it: pairs at exactly 1.0 ΔE00 read from 0.69 to 1.93 elsewhere, and 0.0% of them pass in CAM16-UCS. Argued in A tolerance is a boundary through pairs.
Which colour-difference formula is used changes the numbers but not the conclusions.
The levels move by a factor of two, which changes nothing, and the ordering moves too, which changes a great deal. Recomputing this collection's census of chromatic adaptation under five alternative formulae, each first scaled onto the published one's footing so that only real disagreement survives, reverses between two and ten of the ninety-one pairs of rows. The two ends of the ranking are immovable and the middle is not, so a conclusion about the extremes is safe and a conclusion about an adjacency is not.
What settles it: 2 to 10 of 91 pairs of census rows change places, depending on the formula. Argued in The census in six units.
A reflectance curve is a property of the sample.
It is a property of the sample and of what was done to it. Two constructed slabs whose bulk reflectance agrees at every wavelength to fifteen figures — the same colour to every observer under every light — read as different colours through a four-millimetre aperture, because a reflectance is the integral of a kernel and an aperture collects only part of it. Nothing about the two samples is exotic, and nothing about the disagreement involves an observer.
What settles it: identical to 4.6e-15 of a reflectance unit at every band, and 6.25 ΔE00 apart through a four-millimetre radius. Argued in A pair the aperture separates.
Measuring with the ultraviolet cut out measures the sample not fluorescing.
A cut filter at 400 nanometres removes most of what excites a brightener and not all of it, because the excitation band has a long tail reaching into the visible. What is left is not a rounding: the dye is still absorbing about a sixth of what a full lamp gives it, so the condition measures a partially-fluorescing sample. That is why the four standard measurement conditions are four different quantities rather than four degrees of care.
What settles it: 17.7% of what the full lamp excites survives a cut at 400 nm. Argued in The ultraviolet is half the product.
Two systematic measurement errors on the same sample add.
They add only when they act on the same part of the reading in the same direction. An aperture removes light that entered the material and came back too far out; an interface returns light that never entered at all — so on a glossy translucent sample the two partly cancel, and each measured alone overstates what both together do. The cross term is larger than the smaller of the two effects on every material tested, which makes an additive budget conservative by about a factor of two and therefore uninformative.
What settles it: on candle wax, 17.55 alone and 1.12 alone against 15.46 together — a cross term of -3.21 ΔE00. Argued in Two departures that partly cancel.
Right about one quantity, wrong about another
56 claims
The chromaticity diagram shows every colour a person can see.
It encloses every chromaticity a person can see, and almost every printed copy of it is filled edge to edge with colours the printing could not reach — so the picture makes its own claim false in the act of being reproduced. Most of the area cannot be shown on any ordinary display. Here every cell is tested before it is drawn and the unreachable region is hatched rather than clipped to the nearest available lie.
What settles it: 15.0% of the visible diagram is reachable in sRGB at Y = 0.55 — 349 cells drawn in their own colour against 1970 that cannot be. Argued in Most of this diagram cannot be shown.
CIELAB is perceptually uniform.
It is the claim the space was built to make, and it is settled by measurement rather than by argument: MacAdam's discrimination ellipses re-plotted in a candidate space would be circles of equal size if the space were uniform. CIELAB equalises their *size* well — the spread falls from a factor of ten in xy to about three — and it does not make them round. That leftover anisotropy is exactly what ΔE2000's weighting functions and rotation term exist to correct, which is why the field has a complicated formula over a simple space rather than the reverse.
What settles it: mean anisotropy 3.42 in CIELAB (1 would be uniform), against 2.95 in xy and 2.27 in Oklab — and CIELAB's size spread is 3.24 against xy's 10.42. Argued in MacAdam measured it.
A ΔE of 1 is a just-noticeable difference.
It is what the formula was constructed to mean and it is not what the data it was fitted to says. MacAdam measured discrimination at twenty-five places in the diagram and the ellipses differ in area by nearly two orders of magnitude, so a step of a fixed size is a comfortable margin in one region and invisible in another. A tolerance written as a single number is therefore a statement about where in the space it will be applied, whether or not it says so.
What settles it: MacAdam's largest discrimination ellipse has 74.2 times the area of his smallest. Argued in A threshold is not a unit.
Blue and yellow make green.
True of paint and false of light, and the two are not variations on one rule. Paints subtract: what comes back is what neither pigment absorbed, and a blue that passes some green plus a yellow that passes some green leaves green standing. Lights add, and blue light plus yellow light is a pale, unsaturated white. The everyday version is a fact about the mixing arithmetic, and stating it without the arithmetic makes an additive display look broken.
What settles it: the subtractive mixture lands at hue 153.1° with chroma 32.0; treating the same two as filters in series gives hue 149.4° at chroma 20.0 — two models, one of which is the arithmetic the claim is actually about. Argued in Why blue and yellow make green.
Colour temperature tells you what colour a lamp is.
A correlated colour temperature is the nearest point on the Planckian locus, and *nearest* is a projection: it says which way along one curve, and nothing at all about how far off it the lamp sits. Two lamps at the same stated temperature can be visibly different, one greener and one pinker, and the number that would have said so — the distance off the locus — is routinely dropped from the specification. A lamp is not a blackbody, and the one number quoted is the one that assumes it is.
What settles it: a white LED at 4900 K sits 18.23 × 10⁻³ off the Planckian locus in u′v′, against 3.20 × 10⁻³ for D65 — the same number of kelvin, and a different colour. Argued in A lamp is not a blackbody.
A high colour rendering index means a lamp renders colour well.
It is an average of shifts on a set of test samples, and how saturated those samples are decides the verdict. Two lamps can score within a point of each other and then differ by more than twofold on how much they distort a saturated surface — which is the case anybody buying a lamp for a fabric, a painting or a face actually has. The index is not wrong; it is a mean over a sample set that the claim then quotes as though it were a guarantee about all surfaces.
What settles it: a narrowband source distorts saturated samples 2.36× as much as desaturated ones, a smooth LED only 1.47× — at indices of 82.9 and 81.6, which are within two points of each other. Argued in What a lamp cannot give back.
Automatic white balance recovers the light in the scene.
Every estimator is an assumption about the scene wearing the costume of a measurement. Grey-world assumes the average surface is neutral, max-RGB assumes something in frame is white, and each is close to exact when its premise holds and badly wrong when it does not — so a camera that has chosen one has chosen which photographs to be wrong about. No estimator wins on every scene, which is a statement about the problem rather than about any of the algorithms.
What settles it: grey-world is 2.5° from the true illuminant on a balanced scene and 43.1° on a scene that is mostly foliage, while max-RGB is 0.00° on a scene containing its own premise. Argued in The algorithms that guess the light.
Converting a picture to CMYK means losing colours.
It loses a great many and gains some, and the second half is never mentioned. Measured as CIELAB solids by one estimator, more than half the sRGB solid is outside a four-colour press — which is the half everybody means — and about a ninth of the press's solid is outside sRGB, concentrated in the cyans, where a printed colour is more saturated than any screen has ever shown. The instruction to expect loss is sound advice about a conversion that is not a reduction.
What settles it: 54.5% of the sRGB solid is unreachable on the press, against 11.0% of the press's solid unreachable on the display. Argued in Neither gamut contains the other.
This display has a contrast ratio of 1000:1.
It has that ratio in a dark laboratory, which is where it was measured and is not where anybody uses it. Light falling on the screen comes back off it and adds the same luminance to every pixel — nothing beside a white and several times a black — so the ratio in an ordinary room is a small fraction of the published one, and the code that means black arrives at the lightness of a dark grey card. No calibration can remove it, because the added light is not in the signal.
What settles it: 1000:1 in the dark becomes 137:1 at 300 lux, with black arriving at L* 6.6 rather than 0.9. Argued in The screen is not the room.
Chroma subsampling is visually lossless.
It is lossless on the edges the eye resolves best and ruinous on the ones it resolves worst, and the two are the same edge to an encoder. An achromatic edge survives exactly, because everything it contains is in the luma plane, which is not subsampled. An edge between two colours of nearly equal luminance is carried entirely by the planes that are averaged, and arrives with a stripe of a third colour along it.
What settles it: worst ΔE00 = 0.00 across a black-to-white edge against 43.4 across a magenta-to-green one at the same sampling. Argued in Colour thrown away on purpose.
CIEDE2000 is a distance between colours.
It is an excellent measurement of how different two colours look and it is not a metric. Searching triples finds arrangements where the detour is shorter than the direct route — by half, between colours far apart, and still by a fraction of a per cent inside a five-unit ball, which is the scale a tolerance is written at. ΔE94 additionally fails symmetry, by up to forty-seven units, because its weighting is built from whichever colour is named first. ΔE76 keeps every axiom and is not accurate enough to use, which is the trade the whole subject has been making since 1976.
What settles it: a detour 51.0% shorter than the direct route under ΔE2000, and a 47.6-unit asymmetry in ΔE94. Argued in A difference is not a distance.
A colour difference means the same thing wherever it appears in a picture.
A difference formula answers a question about two large uniform patches, because that is the experiment it was fitted to, and it carries no extent at all. The same colorimetric difference spread as a fine chromatic pattern is filtered away by the eye's own chromatic channels, which give out four to six times sooner than the luminance one. A per-pixel colour difference over an image is therefore a number about a file rather than about a picture, and the ratio between the two depends on nothing but how finely the difference is divided.
What settles it: the same ΔE00 14.22 pattern is seen as 0.92 at 2 px per cycle and 11.11 at 32. Argued in A difference has no size.
A lamp modulating above about a hundred and twenty hertz does not flicker.
It is right about a stationary observer looking at a stationary field, which is the only condition the number was measured in. A modulation seen on something *moving* is written onto the retina as a spatial pattern at the modulation frequency divided by the speed — so a kilohertz drive during an ordinary saccade lands within a factor of two of the spatial frequency the eye is most sensitive to, and is plainly visible as a dotted trail. The ceiling is not a frequency at all; it is a ratio, and the denominator is a speed.
What settles it: a 1 kHz drive is 2.0e-70× threshold standing still and 312× during a saccade. Argued in A lamp has a waveform.
A halftone screen is set at forty-five degrees because it looks less obtrusive.
The practice is right and the reason has a size nobody quotes. Contrast sensitivity is lower on the diagonals than on the cardinal axes at high spatial frequency — the oblique effect, a measurement of people rather than of ink — and a square screen at 45° puts *both* of its fundamentals there. The radial part of the eye's filter cannot tell the two arrangements apart at all: same ruling, same coverage, same frequency, and one is twice as loud.
What settles it: 2.00× quieter at 45° than at 0°, with nothing about the ink changed. Argued in A pattern has a direction.
Colour matching is linear.
Grassmann's four laws are exact for a fixed set of cone sensitivities — the residuals are floating point — and they are what makes colorimetry an integral at all. What fixes the sensitivities is a light level. Below a few candelas a square metre the rods contribute and a pair matched for three cone classes is not matched for the fourth receptor; above a few thousand a share of the cone pigment is bleached, the fundamentals narrow, and the observer is a different observer. Colorimetry has an operating band, and no standard states it.
What settles it: exact to half a per cent of a cone excitation from 4.5 to 6,310 cd/m² — 3.15 decades. Argued in The laws that make colour add up.
Colour vision is simply worse away from the centre of gaze.
It is worse, and it is not uniformly worse: the three channels' thresholds rise at three different rates, so a colour difference presented off-axis has its parts divided unequally and what is left points somewhere else. And the centre of gaze is the exception rather than the best case — a disc a third of a degree across contains no short-wavelength cones at all, so a small blue–yellow difference presented exactly where a reader is looking vanishes.
What settles it: 33% of a difference left at 10° and its hue turned by 24.4°, while a short-wavelength pair at fixation collapses from ΔE00 20.1 to 0.000. Argued in Colour stops at the edge of sight.
A colour name is roughly a colour.
It is roughly a colour the way a postcode is roughly an address. Two colours have to move about ten just-noticeable differences apart before people stop calling them the same thing, and how far varies threefold across one plane of the space — so a word resolves colour an order of magnitude more coarsely than the eye does, and every quantity colour science computes lives in the gap. The eleven basic terms of English also divide what a display can show into territories differing by a factor of 4.6, which no metric accounts for.
What settles it: a name changes at 8.3 ΔE00 at the nearest boundary, and the eleven territories differ by 4.5×. Argued in A name is not a threshold.
Languages cut the colour space where the eye discriminates best.
There is a correlation in that direction and it is moderate — boundaries do sit nearer the hues where a degree of hue angle buys the most colour difference, at about −0.4 to −0.6 on three rings, and it survives computing the partition in a different metric so it is not circular. What it does not explain is how *unequal* the arcs are. Measuring them in ΔE00 rather than in degrees removes only fifteen per cent of the inequality: green takes four and a half times as much colour difference as yellow after the metric has been given every chance to account for it.
What settles it: 5.3× in degrees against 4.5× in ΔE00 — 15% accounted for. Argued in A colour has a name.
A lower mean colour difference means a better reproduction.
The mean reads the bulk of a reproduction's error and a high percentile reads its tail, and real reproduction error has both — accurate nearly everywhere and poor at the gamut boundary. The two statistics rank two candidate reproductions differently in thirty per cent of cases. Both numbers are honest; only one of them matches what a viewer does, which is to find the part that is wrong rather than to integrate.
What settles it: the mean and the 95th percentile disagree about the winner in 30% of 2000 candidate pairs. Argued in A mean is not a difference.
The eye's own drift is what keeps a stabilised image from fading.
Both edges of the drift band are luminance numbers. Luminance temporal sensitivity is band-pass, so a stationary luminance pattern falls into a dip and needs motion; chromatic temporal sensitivity is low-pass, so a stationary chromatic pattern sits at the top of its own sensitivity and needs no eye movement at all. The chromatic bands have no slow edge. And in a stabilised image colour is the first thing to go, which is the opposite of what the argument predicts.
What settles it: the luminance band closes at 0.018°/s and neither chromatic band has a slow edge at all. Argued in The drift is a luminance mechanism.
An afterimage is a neural effect.
Indoors it is, because a display bleaches one and a half per cent of the pigment and leaves a fifth of a ΔE00 behind. Outdoors the pigment is the story: a minute on snow bleaches ninety-four per cent of it, the three cone classes bleach by different fractions because they catch different numbers of photons from the same white light, and what is left is a tint of ΔE00 10.4 that is still above half a unit nearly two minutes later — on a chemical clock twice as slow as any neural one.
What settles it: ΔE00 10.4 at once and 0.54 at 110 s, on a 120 s time constant. Argued in The slowest clock is chemical.
A stabilised retinal image disappears.
What disappears is everything coarser than the adaptation pool that cancels it, which gives out at about a quarter of a cycle per degree — a feature four degrees across. Every channel of the eye resolves more than an order of magnitude finer than that, so a stabilised eye loses the *fill* of a picture and keeps its outline. That is why the phenomenon needed a contact lens and a projector to demonstrate rather than being obvious to anybody who stares at a wall, and it is why a stabilised disc takes the colour of its surround instead of going grey.
What settles it: a patch fades above 1.8° across and stays below it, with the pool giving out at 0.37 cycles per degree. Argued in What a still eye stops seeing.
The CIE has two standard observers because industrial samples are larger than two degrees.
That is why the second experiment was run and it is not what makes its answer different. The macular pigment is a filter over the fovea and nowhere else, so a two-degree field is measured through it and a ten-degree field mostly is not. Fitting a single macular absorption to the ratio between the two tabulated luminous efficiency functions gives an optical density close to the measured population median — a number arrived at from psychophysics on different people, for a different purpose, decades apart.
What settles it: the implied macular density is 0.400 against a measured median of 0.35, and a match made at the fovea fails 10° out by ΔE00 5.9. Argued in One person is two observers.
A minute is long enough for an observer to settle into a room.
It is long enough for the observer and not for the room. A switched-on luminaire takes four hundred seconds to reach nine tenths of its colour change, which is slower than every clock in the eye — so a minute in, most of what is left is the lamp rather than the observer, and three quarters of that survives an eye that adapts perfectly and instantly, because a warming lamp changes the shape of its spectrum and no adaptation of any speed removes a change of shape.
What settles it: ΔE00 6.08 still to go after a minute, of which 4.65 could not be adapted away by any observer. Argued in The room settles after the eye does.
A camera profile's colour error is the camera's.
Its error against the observer it was fitted to is the camera's, and that is the number every comparison of sensors reports. Its error against a *person* is nearly four times larger, and a camera with no spectral error whatever — one reporting the standard observer's tristimulus values exactly — would carry very nearly all of the same error, because the standard observer is an average and nobody is an average.
What settles it: ΔE00 0.92 against the standard observer, 3.35 against a person, and 3.47 for a camera with no spectral error at all. Argued in Fitted to an eye nobody has.
A halftone patch looks like the reflectance a spectrophotometer measures on it.
It does once the screen is too fine to resolve, and not before. An aperture averages the patch and reports the lightness of the mean; an eye blurs it first and compresses afterwards, and the mean of a concave function is below the function of the mean. So a resolvable screen looks darker than it measures — by about as much as the tone value increase a press does correct for, and by an amount that depends on how far away the reader is standing.
What settles it: ΔE00 11.1 at 4 cycles per degree and 0.61 at 35, with the coarse patch looking 14.3 lightness units darker than it measures. Argued in Measured with an aperture, seen with an eye.
A fourth display primary is for reaching more colours.
It can be, and at a fixed gamut it buys something else: agreement. Held to the same chromaticity area, a four-primary design optimised against a population leaves two hundred eyes materially closer together than the best three-primary design can — because the extra emitter lets the other three be broader, and a broad emitter averages over the differences between people instead of sampling them.
What settles it: at 1.4× sRGB's area, 95th-percentile ΔE00 1.20 with four primaries against 3.08 with three. Argued in A fourth primary is a design.
A chromatic adaptation transform scales the three cone signals, so which transform is used is a detail.
Every one of them scales three signals, and which three is the whole content of the transform. A diagonal is only diagonal in some particular set of axes, and the published transforms differ from each other by up to fifty-eight degrees on their first axis. Applied to the same census of light changes they leave residuals that differ by a factor of two, and the ordering between them reverses inside the range of lamps a person meets in an ordinary week.
What settles it: mean ΔE00 2.37 scaling XYZ against 1.14 for the best of them, a factor of 2.1. Argued in A gain needs a basis.
A camera that satisfied the Luther condition would get colour right, so it would white balance properly too.
It would get colour right and it would white balance worse than a real sensor does. Satisfying the condition means the raw channels are a linear combination of the matching functions, and a per-channel gain on the matching functions is a von Kries adaptation in the XYZ basis — which is last in every comparison this site has run. The property that makes a sensor a good colorimeter makes it a bad adapting observer, and no design has both.
What settles it: mean ΔE00 2.52 left by a colorimetric sensor against 1.70 by a silicon one, and 1.41 by an eye. Argued in Only one of these devices adapts.
Media-relative colorimetry normalises to the substrate, which is bookkeeping rather than a model of anybody.
It is a model of an observer — it says the reader adapts to the sheet, which is correct — and it implements that model as a von Kries adaptation in the XYZ basis. On the near-neutral stocks a press uses that costs a few hundredths of a unit, because a sheet of paper-mill white is the smoothest change of light there is. On a tinted sheet it costs ten times what the same rule costs in a cone basis, and a tinted sheet is an ordinary thing to print on.
What settles it: ΔE00 1.72 against 0.17 on a blue sheet — a factor of 10.2. Argued in Dividing by the paper.
A reflectance describes what a surface does to light.
It describes what a *reflecting* surface does, which is a special case that stopped being universal when optical brighteners went into nearly every white sheet sold. The general description has two wavelength indices rather than one — how much leaves at each wavelength for light arriving at each — and a reflectance is that matrix's diagonal. The off-diagonal block is why a brightened sheet returns more light in the blue than reaches it there, which no reflectance can do and every instrument reports as a reflectance anyway.
What settles it: radiance factor 1.21 at 430 nm, above one from 420 to 460 nm — a reflectance cannot exceed 1. Argued in A reflectance is a diagonal.
Optical brighteners make paper brighter.
They make it bluer. The emission lands at 435 nanometres, where the luminous efficiency function is 0.017 against 1.0 in the middle of the band, so a sheet returning fifteen per cent more light than arrives in that band gains three tenths of one per cent of luminance — and seven units of b*. The whole commercial effect is chromatic, which is also why the whiteness formula weights chromaticity so heavily and why over-brightening produces a visible blue cast rather than glare.
What settles it: 0.3% of luminance against 7.45 units of b*, for the same sheet with and without the excitation. Argued in The eye weights where the light is not.
A caveat saying the numbers are lower bounds is as good as computing them.
It is as good as computing them only when the bound is tight enough to be used. This collection carried exactly that caveat about its own fluorescence numbers from its first year — the excitation band ran off the short end of the grid, so the emission could only be understated. The sign was right. Widening the range to where the CIE actually publishes the daylight basis shows the floor sitting between two and three times below the value, which is a bound nobody could put in a specification.
What settles it: the truncated grid understates the emission by 2.10× to 3.20×, worth ΔE00 6.82. Argued in The tables do not stop together.
The eye cannot see ultraviolet because the retina does not respond to it.
The receptors respond perfectly well; the light does not arrive. The cornea is opaque below about 295 nanometres and the crystalline lens takes nearly everything between 300 and 400, so the short-wave limit of colour vision is a piece of optics in front of the receptors — which is why it moves by a factor of twenty across a working life and why people whose lens has been removed report seeing further into the violet.
What settles it: 18.4% of the short-wave band reaches a twenty-year-old retina, 0.9% a seventy-year-old one, and 99.6% one with no lens. Argued in The eye stops at the lens.
A colour match that holds under one light can be restored under another by changing the light back.
True of metamers, which is what the sentence is normally about, and false of a pair that differs in fluorescence. A dyed sheet built to a brightened one's ultraviolet-excluded measurement has the same reflectance everywhere the eye can see; their disagreement is a fixed direction in tristimulus space scaled by how much excitation the light supplies, and a light with negative power does not exist. The only repair is a light with none.
What settles it: ΔE00 0.00 with the ultraviolet excluded, 7.10 with it included and 10.64 under daylight. Argued in Two sheets that match until the window.
The cone fundamentals are a measurement of the three receptors.
Colour matching is a measurement, and what it measures is a three-dimensional subspace rather than three particular curves in it. Apply any nonsingular 3×3 to the matching functions and every match anybody has ever made survives unchanged, so nine numbers are left entirely free. What fixes them is a different experiment — the three dichromat confusion points, six numbers, plus three choices of unit — and the published curves are the output of that construction rather than a direct reading from a receptor.
What settles it: every match survives a change of basis to 2.8e-15 relative, and the construction that closes the freedom has rank 9 of 9. Argued in The matches do not name the cones.
The 1931 diagram is a bad ruler and a better one would be uniform.
It is a bad ruler, and the improvement available is bounded. Every chromaticity diagram is a projective picture of the same measurement, so how badly MacAdam's ellipses fail to be circles can be minimised over the whole family — and the best plane there is still leaves the average ellipse twice as long as it is wide. The 1976 revision took most of the available improvement in the sizes and rather less in the shapes; the residual anisotropy is invariant, and is therefore a property of the eye rather than of anybody's primaries.
What settles it: axis ratio 2.95 in CIE xy, 2.37 in u′v′, and a floor of 2.02 that no diagram beats. Argued in No diagram makes them circles.
A camera profile's quoted error is how accurate the camera is.
It is the residual on the patches the matrix was fitted to, and those patches decide it. On a chart with no chromatic range the design is badly conditioned, the fit reports two tenths of a unit and the same matrix delivers more than eight times that on surfaces it never saw. Worse, a second matrix indistinguishable on the chart delivers more again — least squares makes the residual flat in exactly the directions the data left free, so a residual is guaranteed to be silent about them.
What settles it: 0.19 ΔE00 reported against 1.65 delivered, at a design conditioning of 178:1. Argued in The chart decides the profile.
A printer profile built from a big enough target is exact.
It is exact at every patch that was printed and interpolated everywhere else, which is where every job lives. The interpolation error falls with the square of the node spacing while the patch count rises with its cube, so twenty-seven times the patches buys about eight times the accuracy — and past a certain grid the residual is smaller than the press's own sheet-to-sheet variation. None of that is visible from the target: a profile checked on its own patch set reports zero for ever, because a table reproduces its nodes by construction.
What settles it: 2.93 ΔE00 worst at 135 patches against 0.35 at 3645 — 27× the work for 8.4× the accuracy. Argued in A profile is a fit between its nodes.
CIECAM16's axes were chosen to make the space it produces uniform.
They were chosen to fit corresponding-colour data and to stop CAT02 going negative on saturated colours, and both of those are about adaptation or about numerical hygiene. The same matrix then carries the model's compressive nonlinearity, so it decides the geometry of small differences as well — a job it was never scored on. It happens to be the best published transform at that job, because backing off CAT02's sharpening to fix the negativity moved it towards the second objective's optimum. The good outcome is an accident of a fix for something else.
What settles it: CAT16 leaves an axis ratio of 2.71 against CAT02's 4.29 and a floor of 1.61. Argued in One matrix doing two jobs.
No coordinate system makes MacAdam's ellipses much rounder than an axis ratio of two.
No chromaticity diagram does, and that floor of about two is invariant under the whole nine-parameter group acting on diagrams, which is what made it worth calling a property of the eye. It is a property of the eye seen through a projective picture. Divide by a white point instead of by a sum and apply a cube root, and the same twenty-five ellipses measured the same way reach substantially below it. The clause matters because the space everybody uses already contains the nonlinearity; what it does not contain is a basis chosen for this.
What settles it: the best chromaticity diagram leaves 2.02 and the best basis for a cube root leaves 1.61, on the same twenty-five ellipses. Argued in A compression goes below the floor.
A gap in a contour lets the surround leak into the region it encloses.
A gap removes two things and only one of them costs anything. Open a hole in the *barrier* and leave the border signal unbroken and the interior does not move at all, because a ring of driven cells encloses a centre whatever the wall outside it is doing. Break the signal too and the shortfall goes as the square of the fraction missing. So the reason a dashed outline fills in as though it were solid is the dashes rather than the gaps, and the approach to completeness is quadratic rather than merely approximate.
What settles it: a third of the perimeter open in the wall alone costs 4e-16, and open in the drive as well costs 12.0% — an exponent of 2.02. Argued in A gap in the drive, not in the wall.
The axis ratio of a discrimination ellipse can be measured by mapping its boundary and dividing the longest radius by the shortest.
It is the definition read as a recipe, and the recipe is accurate exactly where the answer is boring. The image radius has two broad maxima and two very narrow minima, and the width of a minimum is the reciprocal of the axis ratio — so a fixed sample resolves the answer when the answer is small and steps over it when it is large. The sample size a ratio needs is proportional to the ratio, at a log–log slope of 0.94 against a predicted 1. The replacement takes no sample: an ellipse is a quadratic form and the image's semi-axes are singular values.
What settles it: a forty-eight-point sample reads 18.59 where the ratio is 40.76, and the points a ratio needs rise with the ratio at a slope of 0.94. Argued in An ellipse is not a ring of points.
Adapting well and discriminating well trade against each other symmetrically.
They trade, and not symmetrically. At the basis that adapts best, one per cent of adaptation spent in the right direction moves the ellipse anisotropy nearly half the way to its floor, because the first objective is quadratic there and the second is linear. At the basis that discriminates best, the same one per cent buys under two per cent of the other gap. The direction to spend it in is the flattest of the six rather than the one the second objective most wants, by a factor of twenty.
What settles it: an anisotropy of 7.70 falls to 5.02 for one per cent, while a residual of 1.793 falls only to 1.778. Argued in The trade only runs one way.
Bradford is the best chromatic adaptation transform available.
It has the lowest mean residual over the census of illumination changes, which is why colour management uses it. Inside the family that census was drawn from, its middle row's reading of the adapting white passes through zero, so the gain is a division by nothing and the model stops being defined rather than merely doing badly. CAT02 does the same less violently; CAT16, which exists because CAT02 was withdrawn for going negative, does not. A transform that is worse on the average is better at the edge, and the two rankings disagree.
What settles it: Bradford leaves 1.140 ΔE00 on the census mean and a middle gain of -1.0e+19 at the searched worst, where CAT16 leaves 1.312 and 500. Argued in Best on the average, undefined at the edge.
The receptor construction costs seventy per cent above the unconstrained floor.
It costs that for the one observer whose confusion points are published. Propagated across a population of eyes the same construction runs from a quarter above the floor to a hundred and thirty per cent above it, and the population's own spread is wider than the entire gap between the published transforms the seventy per cent was being compared against. Seventeen per cent of members are better served by their own receptors than by a matrix built to make a gain behave.
What settles it: 1.22 to 2.24 ΔE00 across two hundred members, against a single quoted 1.65 and a floor of 0.97. Argued in The price is also the person.
The published adaptation transforms are demonstrably not cone responses.
They are not, and the evidence is two confusion points out of three. Measured in a population's own standard deviations, every published transform sits two to fourteen out on the protanope's point and four to twelve on the deuteranope's — and between half a standard deviation and two and a half on the tritanope's, which is indistinguishable from a member of the population. The raw chromaticity distances rank the opposite way, because one of the three points is off the diagram and a distance near infinity is not a distance.
What settles it: the nearest on the protan point is CAT02 at 2.2σ, and the furthest on the tritan point is XYZ scaling at 2.6σ. Argued in Two points out of three.
A camera's colour filter array is specified by three centre wavelengths and three bandwidths, each with its own tolerance.
The six numbers are right and the six independent tolerances are not. The adaptation objective over them has a condition number in the hundreds, its stiffest direction is almost entirely where the blue dye sits, and its flattest is the three bandwidths moving together — a combination no per-parameter tolerance can express. A budget spent holding the centre wavelengths buys twenty-five times what the same budget spent holding the widths does, against this criterion.
What settles it: a condition number of 623, with the blue dye's centre carrying 0.96 of the stiffest direction. Argued in Where a camera is blind to itself.
A sensitivity analysis tells you which input to measure better.
It tells you which input the answer responds to most, which is a different question from which one is worth improving and a third question again from which one is nearest to breaking something. Over four declared widths of this site's population model the three rankings differ: the lens carries most of the answer, the macular pigment carries most of the doubt once each width's own uncertainty is counted, and the pigment peaks are the width that takes two published statements nearest to failing. Only the third names an experiment, because only the third names a claim as well as a measurement.
What settles it: the answer says lens, the doubt says macular, and what breaks a claim soonest is peaks at 1.34× its declared width. Argued in Which measurement is worth making.
An adapted observer removes the change of light.
The model everybody computes with removes it completely, and the same standard's own formula says a real observer does not: the degree of adaptation is a function of the surround and the adapting luminance, and in an ordinary room it is 0.94 rather than 1. That is not a rounding. Every adaptation residual on this site is computed at complete adaptation and is therefore a floor, with the number for somebody in a lit office larger by three quarters.
What settles it: a mean census residual of 1.31 ΔE00 at complete adaptation, against the standard's own D of 0.941 in an average surround at 100 cd/m². Argued in A discount nobody measured.
A curvature at a matrix describes the shape of the objective there.
It describes the second-order term, and at every adaptation transform anybody uses the first-order term is the larger one over almost the whole distance to the best matrix. The radius at which the curvature catches the slope is a few per cent of that distance, so a table of eigenvalues taken at a published transform describes a bowl no reader meets on the way anywhere. It also hides a sign: three or four of the nine directions at each of those points curve downwards, which a decomposition returning magnitudes cannot show.
What settles it: at Bradford the curvature catches the slope at 3.2% of the way to the optimum. Argued in The slope arrives before the bowl.
CIEDE2000 is a more uniform measure than the space it is built on.
Measured on the discrimination ellipses the whole question was settled by, each step of chroma weighting makes an ellipse rounder and makes the ellipses more unequal in size across the diagram. Dividing a difference by the chroma at which it was measured equalises directions at a point, which is what improves; it also shrinks every difference in the saturated part of the diagram against every difference in the pale part, which is what degrades. Every published account reports the first number and none reports the second.
What settles it: anisotropy 3.42 → 2.89 → 2.74 while spread 3.24 → 3.59 → 4.12. Argued in A unit rests on a space that was ranked.
A von Kries gain is a crude approximation to chromatic adaptation.
It is crude as a piece of arithmetic and it is close to the best a bounded observer can do. Three numbers read off the room — the white, in a fixed basis — remove most of what a change of light costs an unadapted observer, and the exact answer that would remove the rest is a matrix whose nine numbers are the change of light itself, which is the quantity adaptation exists to discount. A model whose parameters cannot be obtained is not a better model of the same thing.
What settles it: three numbers about the room remove 91.6% of a change of light and one number removes 2.6%. Argued in Three numbers the scene supplies.
An integrating sphere averages out gloss, so a glossy and a matte sample of the same pigment read alike.
A sphere does not average and does not need to. Under a hemisphere of constant radiance, Helmholtz reciprocity makes the detector's reading the sample's directional-hemispherical reflectance for the detector's own angle — an exact quantity about the sample, whatever the surface is. That is a much stronger property than averaging, and it is not the property the slogan describes: the reading sits at the bottom of the range the surface's reflectance takes over incidence, not in the middle of it, and moving the detector moves it.
What settles it: a sphere reads 0.54 at eight degrees, against a bihemispherical albedo of 0.58 — the reading is exact and is not an average. Argued in A room is not a sphere.
Use the largest aperture the specimen allows, because light leaks out of the lit spot.
The instruction is right and the reason given is only half of it. What decides the error is a product of two apertures — the lit disc and the measured one — and widening either of them recovers the whole of the sample's reflectance. Measuring a larger area than is lit works exactly as well as lighting a larger area than is measured, which is not what the usual explanation predicts and is often the cheaper of the two to arrange.
What settles it: both discs at 2 mm recovers 51.8%; lighting wide recovers 100.0% and measuring wide recovers 100.0%. Argued in Either disc can be the wide one.
Mixing two paints correctly means working in K/S rather than in reflectance.
It is the right operation in the wrong variable unless somebody says which reflectance. Kubelka-Munk is additive in the reflectance of the pigment layer, and what an instrument reports is that layer seen through an interface — related by a Mobius function rather than by a constant offset. Mixing in the reported variable instead of the internal one moves the answer by several units, always towards less chroma, and no published curve says which of the two it is.
What settles it: 3.35 to 7.86 ΔE00 between the two mixtures, with the internal-variable one more chromatic at every concentration. Argued in A mixture in the variable nobody named.
Outside the mechanism
5 claims
A reflectance is a property of the surface, so measure it once.
Not for anything fluorescent, and paper, detergent-washed cloth and safety clothing are all fluorescent by design. An optical brightener absorbs in the ultraviolet and re-emits in the blue, so what comes back is not a fraction of what arrived at that wavelength and the reflectance model has no term for it. Multiplying a once-measured spectrum by a new illuminant then predicts the wrong colour, and predicts it confidently.
What settles it: predicting the colour under illuminant A from a measurement under D65 is off by ΔE = 5.38, almost all of it in b* — 5.33 units of blue that the reflectance model cannot represent. Argued in Some paper is brighter than white.
This is what a colourblind person sees.
No method supports the sentence. A simulation projects a stimulus onto the two remaining cone axes and returns a colour a *typical trichromat* would confuse in the same way — which is an argument about the geometry of the collapse, not a report from inside somebody's visual experience. It also has no severity built in unless one is stated, and the common deficiencies are anomalous rather than absent. The figures here name the model and the severity for that reason, and neutrals are asserted to survive the transform because a simulation that tints greys is broken in a way that looks plausible.
What settles it: a red and a green ΔE00 = 70.9 apart collapse to 17.1 (protan), 6.2 (deutan), 50.5 (tritan) — and 2 of 3 of those simulations leaves the display gamut, so the picture of the deficiency cannot itself be shown. Argued in Simulating what cannot be simulated.
No surface can lie outside the MacAdam limits.
True of reflecting surfaces, which is what the limits are derived for — the derivation assumes only that a reflectance lies between zero and one, and that inequality is the whole of it. A brightened sheet has no reflectance, so the derivation does not apply, and the sheet sits measurably outside. The proof is a supporting hyperplane rather than a hull: for a stated direction the largest value any reflectance can reach is one integral, and the sheet exceeds it.
What settles it: 2 of 6 stocks exceed the bound, the worst by 4.0%, and none of them does with the ultraviolet removed. Argued in A white that is not a reflectance.
A better algorithm would recover the illuminant of a photograph.
The count forbids it. Three sensors give three numbers per surface and the scene asks for three per surface plus the light, so the problem closes only when reflectances lie in a linear model of dimension at most two — and each further surface adds three equations and three unknowns, so a larger scene never helps. At three dimensions the alternative scenes can be written down explicitly: a family of illuminants, each with reflectances reproducing every sensor response to machine precision. Every constancy algorithm is a rule for choosing among them, which is a prior rather than a measurement.
What settles it: 5 alternative daylights spanning 4500 K reproduce the image to 1.8e-15 relative. Argued in An image does not determine the light.
An eye is a compromise between adapting well and discriminating well.
Nothing in a population of observers behaves that way. The trade-off is a property of the nine-dimensional space of matrices somebody could choose; across the five-dimensional sliver of it that actual eyes occupy, the two costs correlate weakly and positively, so an observer whose receptors adapt badly tends to discriminate badly as well. One measurement does trade the two off — the macular pigment, which correlates one way with adaptation and the other with anisotropy — and the lens trades neither, being worse for both.
What settles it: the two costs correlate at 0.29 across two hundred observers, where a trade-off would be negative. Argued in A trade between matrices, not people.
Underdetermined
26 claims
The human eye can distinguish about ten million colours.
The recipe is a gamut volume divided by the volume of a just-noticeable difference, so the answer inherits whatever the difference formula says a JND is — and the two formulae this site implements disagree by a factor of nearly five on the same solid and the same lattice. Both are upper bounds, because no arrangement fills space with non-overlapping ellipsoids at unit density. The useful content is the ratio, not either magnitude, and the number in circulation is one model's output quoted without its model.
What settles it: 195,914 cells under ΔE76 against 41,948 under ΔE2000 — a factor of 4.67. Argued in How many colours are there.
A wide-gamut display can show more colours than any real surface.
The usual comparison draws a display's primary triangle over the diagram and compares areas, which compares a *projection* against a *slice* and is meaningless without a luminance. Fixed at one, the answer changes with which one: no display comes close at low lightness, and at mid lightness a Rec. 2020 display exceeds what any physically realisable surface can do. The satisfying version of this comparison — sRGB's triangle is 2% off the surface bound — is an artefact of comparing two incomparable quantities, and a suspiciously satisfying result deserves the scrutiny a suspicious one gets.
What settles it: matched at a luminance factor, sRGB reaches 39.8% of the physically possible at Y = 0.6 and 21.3% at Y = 0.9, while Rec. 2020 reaches 106.4% at Y = 0.6 — above everything a surface can do. Compared the usual way, sRGB's triangle (0.11205) and the surface bound at Y = 0.6 (0.11455) agree to about 2%, which is a coincidence between a projection and a slice. Argued in No surface can be that colourful.
Daylight is 6500 K.
Daylight is not one illuminant and is not a blackbody. D65's chromaticity is measurably off the Planckian locus at its own correlated temperature, and outdoors the light arriving at a surface is a mixture of direct sun and scattered sky in a ratio set by geometry — so an open patch and a shadowed one a metre away are lit by different spectra. The sky is the reason a shadow is blue, and it is a fact about scattering rather than about perception.
What settles it: D65 sits at (0.3127, 0.3290) where a blackbody at D65's own 6505 K sits at (0.3135, 0.3236) — a gap of 3.2 × 10⁻³ off the locus in u′v′ — and open ground against shadow is ΔE00 = 5.4 apart under the same sun. Argued in The sun is not one illuminant.
A colour has a CMYK value.
Four inks against three numbers leaves a degree of freedom, so a printable colour has a one-parameter family of separations rather than a value. Every member matches under the illuminant the separation was computed for, because that is what the arithmetic was asked for; they are metamers of one another, so under a tungsten lamp they come apart by more than any printing tolerance. Which member a file contains was decided by a prepress setting chosen for ink cost.
What settles it: 11 separations of one colour agree to ΔE00 = 0.003 under D50 and spread to 6.75 under illuminant A. Argued in The separation is not unique.
A lamp sold as a D65 simulator is D65.
D65 is pinned by a chromaticity, which is three numbers, and a spectrum on this site's grid has eighty-one degrees of freedom. A source built from five emission bands can hit the chromaticity to about a part in a billion with a third of the visible band nearly empty — and pairs of reflectances that match exactly under D65 come apart under it by several units. That is why a simulator is graded by a metamerism index rather than by a colour difference: the whites agree by construction, so what separates the two sources is everything else they fall on.
What settles it: chromaticity matched to 8.5e-10, and pairs that match under D65 separate by a mean of ΔE00 4.98 under it. Argued in There is no D65 lamp.
Eight bits per channel is enough to avoid banding.
Whether a gradient bands is set by where in the tone scale it sits, how sharp each step is, how wide it is drawn and how far away the reader is — and a bit count contains none of the four. The same eight-bit encoding leaves a shadow ramp thirty times over threshold and a mid-grey one under three, because the eye's threshold is a contrast and a code step near black is a much larger fraction of the light it is a step of. Ten bits is enough at mid grey and not in the shadows, which is the argument that produced the threshold-shaped transfer functions.
What settles it: 29.8× threshold in the shadows against 2.76× at mid grey, at the same bit depth. Argued in Banding is not a bit depth.
A colorimetric match is a match.
It is a match for the observer it was solved against and an acceptance rate for everybody else. Three primaries two nanometres wide, driven so their sum has exactly D65's tristimulus values — residual four parts in ten thousand billion billion — are seen as a different colour by half a population of two hundred eyes at ΔE00 9.3 and by the worst-off at 20. How much of a person is in the number depends on how far apart the two spectra are, which is a quantity no specification records.
What settles it: exact to 4.3e-16 for the reference, and ΔE00 9.3 at the population median. Argued in A tolerance is a probability.
ΔE00 ≤ 1.0 is a specification.
The formula is defined with three parametric factors in it that the CIE leaves to the industry using it, and the two settings in ordinary use differ by a factor of two in one of them. Twenty-nine per cent of pairs change verdict between graphic arts and textiles at a tolerance of one unit, the rate stays between a quarter and a third at every tolerance from half a unit to five, and it is more than twice the disagreement between two different formulae about which of two pairs is worse.
What settles it: 29% of 4000 pairs change verdict between kL 1 and kL 2. Argued in Three constants nobody quotes.
A lamp has a colour.
It has one in each direction, one at each drive level, and a different one for the first several minutes after it is switched on. A conformal phosphor converter makes light leaving at an angle cross more of it, so the beam is ΔE00 16 warmer at seventy-five degrees than on its axis; a dome geometry removes that exactly. 'Dimmed to a tenth' names three colours up to twenty-six units apart. And the warm-up moves the white 2.6 units over seven minutes — longer than every clock in the eye.
What settles it: ΔE00 16.4 across the beam, 25.9 between dimming methods, 2.6 over the warm-up. Argued in A lamp has a direction.
A colour rendering index says how well a lamp renders colour.
It says how well a lamp renders colour *for the 1931 standard observer*, and no published method presents that as a choice. Scored by a population instead, one lamp's spread across observers is wider than the whole range the standard observer puts several lamps in — so a ranking quoted to a tenth of a point is a statement about one set of tables rather than about the lamps.
What settles it: one lamp spans 3.8 points across 120 observers, against 1.8 points between the lamps themselves. Argued in The index is one observer's opinion.
A colour tolerance is a property of the pair it is written about.
It is a property of the pair and the room. The light multiplies both members, and the difference between two products is not the product of the difference — so pairs constructed at exactly one unit under D65 measure something else under every other light, even for an observer who has adapted completely to it. Most of them get smaller, which makes a test enforced under the wrong lamp systematically lenient.
What settles it: pairs built at ΔE00 1.000 measure between 0.64 and 1.57 across 14 changes of light. Argued in One unit in another room.
Two spectrophotometers that agree on a white tile are measuring the same thing.
Not until they agree about where they were standing. A 45°/0° instrument throws away the four per cent a surface returns at its interface and a sphere with its gloss port closed collects it, so the two report the same sample differently — by a constant added to every band, which is nothing on a white sample and more than doubles the reflectance of a black one. Removing the interface component makes the two agree exactly, which is the check that this is the whole of the difference.
What settles it: ΔE00 11.46 between the two geometries on the darkest sample and 1.15 on the lightest. Argued in An instrument has a geometry.
A display's gamut is the set of colours it can show.
It is the set of colours it can show to somebody, and the somebody is in the answer. Whether a non-negative mixture of three emission spectra reproduces a paint depends on whose cones are integrating them, so the boundary is a band rather than a curve — and the narrower the primaries, the wider the band. A laser projector's triangle is the largest of any technology here and the least agreed on.
What settles it: 2 of 28 boundary surfaces are displayable for the standard observer and not for everybody on an LCD, and 10 on a laser projector. Argued in A gamut has a population.
A spectrophotometer measures a property of the sample.
Not until it says which lamp it used. For a reflector the instrument's own source divides out and any lamp gives the same answer; for a fluorescent one it does not, because the sample returns light in proportion to how much ultraviolet it was offered. The four measurement conditions a printing standard names are four different quantities, and on an unbrightened sheet they agree to a hundredth of a unit.
What settles it: ΔE00 7.66 between two conditions on one brightened sheet, against 0.01 on the unbrightened control. Argued in An instrument brings its own light.
Whiteness is a property of a sheet of paper.
It is a property of a sheet and a lamp, and on the samples the scale is used for the lamp is the larger term. Take the ultraviolet out of the instrument and the spread between an ordinary stock and a premium one collapses, because what separates them is the part the brightener contributed and a brightener needs a source to work. The measurement condition can also change which of two sheets ranks higher, which is a failure no tolerance absorbs.
What settles it: 81.8% of the whiteness these stocks have above an unbrightened sheet disappears when the ultraviolet is removed. Argued in Whiteness is mostly the lamp.
A screen can show about a third of the colours a person can see.
It is a ratio of two areas on a chromaticity diagram, and which diagram decides the answer. Across twelve coordinate systems the discipline has actually published, the sRGB triangle covers anything from 8.5 to 38.4 per cent of the enclosed visible region — the same observer and the same display throughout, because area is not preserved by the projective maps that carry one such diagram to another. The invariant version of the question counts stimuli instead, and gives 92 per cent of this collection's constructed surfaces and none of the monochromatic lights.
What settles it: 8.5% to 38.4% across twelve published diagrams — against 92.1% of surfaces and 0% of spectral lights, which do not move. Argued in Two thirds is not a property of the eye.
A spectral measurement of a lamp is a measurement of its spectrum.
It is a measurement of the projection of that spectrum onto the span of the instrument's filters, and the complement is a null space no care recovers. On daylight that costs little; on a fluorescent tube three broad readings leave three quarters of the lamp unreached, twelve leave two thirds, and a ten-nanometre bank of forty-one still leaves a fifth, because mercury lines are narrower than any usable filter. The colour of the reconstruction is right long before the spectrum is, which is the condition under which a prediction made from it will be confidently wrong.
What settles it: at 12 readings the tube's colour is right to ΔE00 0.48 with 66% of its spectrum outside what the readings determine. Argued in The colour is right first.
A ΔE00 is a property of the two colours it is computed between.
It is a property of the two colours and of the basis the space was built on. A linear change of the observer's coordinates leaves every match untouched; a cube root does not commute with one, so CIELAB — divide by a white, take a cube root, difference the results — is a different space for every basis it is applied after. Measured on MacAdam's ellipses the mean axis ratio runs from about 2.6 in a cone basis to 3.4 in CIELAB's own and nearly 10 in a display's primaries. CIELAB's choice was made in 1931 to make matching functions non-negative.
What settles it: axis ratio 2.60 in LMS (confusion points) against 3.44 for CIELAB itself and 12.45 in sRGB rgb. Argued in A difference needs a basis too.
An adaptation transform's basis is a free parameter, to be fitted like any other.
It is free until a dichromat is measured, and then it is not free at all. A von Kries gain is `B⁻¹ diag(d) B`, and scaling a row of B cancels exactly between the gain and the inverse — so three of the nine numbers a colour match leaves free do nothing whatsoever to an adaptation model. The three copunctal points supply the other six. The receptor basis is therefore not a starting point for a fit; it is the answer to a fit with no free parameters, and what remains to be decided is which experiment to believe rather than which values to choose.
What settles it: scaling the rows by 3.7, 0.21 and 11 moves the residual by 2.0e-15 ΔE00, against a residual of 1.65. Argued in The three numbers a gain cannot see.
A wider-gamut display shows more colours.
It covers more of a chosen diagram, and a share of a diagram is not a count of anything: the same triangle covers between 8.5 and 38.4 per cent of the visible region across twelve published coordinate systems. The invariant question is how many stimuli fall inside, and for this collection's family of smooth matte reflectances under D65 the answer is all of them, for all three published primary sets. What the widening did change is a quantity nobody measured — the display's own adaptation basis, which improved by a factor of more than two.
What settles it: sRGB and Rec. 2020 both show 100% of the constructed surfaces, and leave 2.36 and 1.09 ΔE00 after a white-point change. Argued in The gamut race chose the basis.
A colour space's ellipse anisotropy is one number.
It is three, and they differ by up to a factor of two. A coarse sample of the boundary is an artefact; a converged sample of a contour of stated size is a real quantity that moves with the size, by seven to twenty per cent between the tabulated ellipses and the tenfold magnification they are printed at; and the derivative of the map is the local metric, which is what the phrase about making contours circles is asking about. A table that does not say which of the three it holds is under-specified.
What settles it: 9.84 sampled coarsely, 12.45 from the derivative and 14.99 for the contour at the magnification it is drawn at. Argued in Three numbers for one ellipse.
The worst change of light an adapted observer meets is a corner painted a strong colour.
That is the worst of fourteen changes on a list, and a maximum over a list is not a maximum. Searching the family those fourteen were drawn from — a wall with a centre wavelength, a width, a depth and a base, applied one to three times — reaches six times further under a box restricted to ordinary paint, and eight times further under one restricted only by the arithmetic. The search ends against the wall of whichever box it is given, so this family has no worst case at all and any number quoted for one is a number about somebody's constraint.
What settles it: 3.37 ΔE00 listed against 21.3 searched under a paint box and 28.4 under a wider one, with 2 of four parameters against a bound. Argued in The worst case is where the box stops.
A ranking of colour spaces by how uniform they are is a ranking.
The score is a mean over twenty-five ellipses, so it carries a sampling error those twenty-five determine, and the comparison between two spaces is paired because the same ellipses score both. Three of the seven adjacent pairs in this site's own table clear two standard errors of their gap and the other four do not — one of them crosses zero in more than a third of resamples. The ends of the table are ordered and its middle is a cloud of four bases whose relative positions the data do not settle.
What settles it: 3 of 7 adjacent pairs ordered — the worst crosses in 35.3% of resamples. Argued in Twenty-five is a sample of the diagram.
There is a worst case for how far a painted room can move a colour.
There is one, and it is at a band six nanometres wide — narrower than any pigment can cut, and narrower than the floor of the box the previous search was given, which is why nobody had seen it. Above that width the answer falls as a power of the narrowest band anybody is willing to allow, so a worst case quoted for a room is a statement about a pigment. What binds is the band's width and not, as anybody would guess, how saturated the paint is: the worst wall is dark rather than colourful and never approaches a purity ceiling.
What settles it: a maximum at 6.02 nm of band width, and 28.38 → 21.91 ΔE00 between the arithmetic bound and a pigment's. Argued in A notch a pigment cannot cut.
A model of colour vision should be built on the measured cone fundamentals rather than a pigment formula.
It depends entirely on whether the model has one observer or many. A tabulated fundamental is one curve measured once and has no peak wavelength to move, so a collection of observers who differ — which is what a population of real eyes is — cannot be built from it at all. A pigment template takes the peak as an argument, which is precisely why it is used, and among the templates actually available the choice between the two published ones is a small term against the choice to use a real pigment shape at all.
What settles it: two published nomograms differ by 0.05 ΔE00 on the median observer, against 0.79 for a Gaussian of the same width. Argued in The population rests on a template.
A room lit more evenly reads a glossy sample closer to its true colour.
Evenness is a magnitude and the error is a pairing, so the size of a field's departure from uniform does not decide the size of the reading's error, and does not decide its sign either. A viewing booth lighting mostly from overhead reads a gloss sample high; a window at thirty-five degrees reads the same sample low, at a comparable departure from uniform. What decides it is whether the light arrives from where the surface's lobe points, which no summary of the field's evenness carries.
What settles it: across twenty-four surface-and-field pairs the error uses between -0.10 and 0.36 of the bound a product of magnitudes promises — 6 positive and 18 negative. Argued in Either factor being zero.
What this index is not
two things it is easily taken for
It is not a list of things people get wrong about colour. Every claim here is one a competent person says, and most are shorthand for something true — the trouble is that the shorthand travels and the domain does not. A rule of thumb with its conditions stripped off is indistinguishable, in a sentence, from a measurement, and this subject strips conditions unusually fast because the everyday word colour is doing the work of at least three technical ones.
Nor is it a claim that the computations here are the last word. Each rests on a model, and the model is named on the page where the argument is made: a colorimetric calculation knows nothing about appearance, an appearance model knows nothing about what a particular person sees, and a simulation of colour vision deficiency is a statement about the geometry of a collapse rather than a report from inside anybody's experience. Where a number depends on which model produced it — the count of distinguishable colours is the clearest case — both are given rather than blended.