Solution (source code)

= Solution

\b[Individual differences show that <color vision> depends on receptor signals, their neural interpretation and the task used to measure them.] They provide natural perturbations of the system, but differences in genes, matching, discrimination, naming and subjective appearance must not be treated as interchangeable.

A useful starting point is the <principle of univariance>. For a <cone cell> class $j$, a simplified <receptor quantum catch> is $Q_j=\int N(\lambda)a_j(\lambda)\,d\lambda$, where $N$ is the incident photon distribution, including optical filtering, and $a_j$ is effective absorptance. One receptor's absorption count does not uniquely identify <wavelength>: increasing <intensity> can compensate for a change in <spectral sensitivity>. Comparing classes supplies spectral information. With three classes, distinct spectra can satisfy three equal-catch constraints and therefore be <metamers>. This is information loss: if a spectrum is represented by more than three independent <wavelength> bins, its three-channel sampling matrix has a nontrivial <kernel>. Around a strictly positive spectrum, sufficiently small changes along that <kernel> preserve nonnegative stimulus values and all three catches. Thus the observer, not <wavelength> alone, defines a <color> match. With <luminance> fixed, three independent receptor coordinates leave at most two independent chromatic coordinates.

Inherited differences test that account. <Dichromacy> removes one independent class of cone input; <anomalous trichromacy> retains three classes but with altered spectral separation, often weakening particular discriminations. L and M are overlapping long- and middle-wave sensitivities, not detectors that individually label light “red” and “green.” Molecular work by <Jeremy Nathans> and colleagues identified cone pigment genes, then related inherited red–green variation to changes in the corresponding gene arrays.<Molecular genetics of human color vision: the genes encoding blue, green, and red pigments by Jeremy Nathans and others>[Science 232, pp. 193–202, pigment-gene identification]{ref}<Molecular Genetics of Inherited Variation in Human Color Vision by Jeremy Nathans and others>[Science 232, pp. 203–210, genotype–phenotype comparison]{ref} The important inference is a relation between biological variation and available spectral signals, not a claim that all observers with one label have identical vision.

A <Rayleigh color match> makes that inference measurable. An observer adjusts a mixture of two narrowband lights to match a comparison light, with brightness adjusted separately. The accepted mixture and matching range constrain pigment sensitivities and discriminability. A <color discrimination> task instead measures whether two stimuli can be distinguished, ideally with <luminance> cues controlled and a fitted <psychometric function>. Plate tests and everyday <color> names are less specific: learned labels or a brightness difference can support a correct response without normal chromatic discrimination. Conversely, reduced discrimination does not imply a world without <color>.

Individual differences also reveal compensation. <Heidi Hofer> and colleagues used <adaptive optics> retinal imaging with selective pigment bleaching and retinal densitometry to classify <cone cells> in living eyes. In their small sample, men passing normal color-vision tests had L:M cone ratios spanning approximately 1.1:1 to 16.5:1; the paper's corrected abstract supplies the lower value. The ratio was not fixed even within the normal category.<Organization of the Human Trichromatic Cone Mosaic by Heidi Hofer and others>[Methods and abstract, eight observers; corrected L:M ratio; J Neurosci 25, pp. 9669–9679]{ref} This rules out a simple requirement for one universal cone proportion. For example, <opponent color processing> could compare gain-adjusted cone signals rather than raw cell counts. It is compatible with post-receptoral gain adjustment and <chromatic adaptation>, but normal test scores do not prove identical <subjective experiences> or one uniquely identified compensatory mechanism.

A stronger question is whether more receptor classes create more perceptual dimensions. Heterozygous carriers of certain X-linked pigment variants can, through <X-chromosome inactivation>, have a <retina> containing more than three spectrally distinct cone types. Yet four types need not supply four functionally independent signals to behavior. <Gabriele Jordan> and colleagues combined forced-choice matching, multidimensional scaling and genetic analysis. One of 24 obligate carriers of deuteranomaly showed behavior consistent with <tetrachromacy> across their tests; most did not.<The dimensionality of color vision in carriers of anomalous trichromacy by Gabriele Jordan and others>[Abstract and behavioral/genetic tests, J Vis 10(8):12]{ref} This distinction between potential and demonstrated extra dimensionality is crucial. The selected sample cannot establish population prevalence, and additional <opsin> variants alone cannot establish enhanced discrimination or richer experience.

Finally, optical and experiential differences must be controlled. Lens and macular filtering change the spectrum reaching the <cone cells>; age, adaptation, illumination and task <learning> can therefore mimic or modify receptor differences. Repeated measurements should separate within-person variability from stable between-person variation. Matching should be compared with discrimination, naming and appearance judgments rather than assuming that one measures all the others. <Color> naming can change without changing the receptor information; matching can change without entailing a particular verbal category.

The strongest conclusions arise when genetics, retinal measurements and controlled behavior converge. \b[Variation establishes both the constraints imposed by receptor sampling and the flexibility of later processing; it does not directly disclose another person's <color> qualia.]