Light is a spectrum — a whole curve, effectively infinite-dimensional. Your eye answers it with three numbers. Everything strange about colour is one consequence of that single collapse.
Six layers of this place each circle one strange fact about colour, and each holds only its own corner. There is no magenta in the rainbow. Your screen's yellow contains no yellow light. Your dog can't tell its red ball from the green grass. The sky should be violet and isn't. And Homer, who could see perfectly well, called the sea wine-dark and never once blue.
None of them says the load-bearing thing, because each only sees its own face of it. They are one theorem, watched from six angles.
Here is the theorem. The light reaching your eye is a spectral power distribution — how much energy sits at each wavelength, a value for every point along the rainbow. That is a curve, an object with effectively infinite degrees of freedom. Sampled even coarsely — every 5 nm across the visible band — it is a vector with 65 independent dials. Your retina reads that whole curve through exactly three kinds of cone. So the map from light to colour is a projection: it takes those 65 numbers (really infinitely many) and returns three. Three numbers wide. That is the entire width of human colour.
A projection throws things away. The space of differences it cannot see — its kernel — has dimension 65 − 3 = 62. You are constitutionally blind to a sixty-two-dimensional space of light. Watch the collapse happen.
Pick a light, or paint your own spectrum by dragging across it. The eye folds the whole curve down to three numbers — and those three numbers are the colour. Nothing else survives.
If the eye keeps only three numbers, then any two lights that share those three numbers are, to you, the same colour — no matter how differently their energy is spread across the spectrum. The set of differences that vanish is the kernel, and it is enormous. Here is a light, and a second light built to be physically different everywhere yet land on identical numbers.
Why three? Because you grow three kinds of cone. The width of colour is not a fact about light — it is a count of receptors, and it varies from eye to eye and species to species. Turn the dial and watch the same world gain and lose dimensions of colour.
Plot, for every single wavelength, the two ratios its three numbers reduce to. They trace one curve — the famous horseshoe, the spectral locus. The colours your eye can possibly report are everything enclosed by it. But the curve does not close. The straight chord that seals it into a wheel — the line of purples — is crossed by no wavelength at all. Magenta, fuchsia, every rose and hot pink, lives there: a band of hue the eye manufactures to join two ends the spectrum leaves open. And a screen, having only three primaries, can fill only the triangle pinned to its three corners.
It would be too tidy to say colour is "only in your head." The light is real, and physics fixes it hard: gold is yellow because its electrons run at half the speed of light, a strontium firework emits its red at a wavelength you could read off a chart, the sky really does scatter more violet than blue. The spectrum arriving at your eye is not invented. What is invented — or better, computed — is the step from that spectrum to a colour. The world hands you a curve. Your eye hands you three numbers. The gap between them is where every member of this portal lives.
And there is a third projection stacked on top, looser than the first two and just as real. Even once the eye has its three numbers, where you draw the names across them is not given by physics or biology — it is given by your language. Homer's Greek had no common word for blue, so his sea is wine-faced, violet, grey — and a 19th-century Prime Minister mistook the gap in the vocabulary for a gap in the eye. Sappho calls fear "greener than grass," where the Greek χλωρός means green and pale and fresh all at once, and every translator must choose. The world's light becomes three numbers (physics into biology); the three numbers become a handful of names (biology into culture). Three collapses, each lossy, each true.
research/three-numbers-wide/verify.mjs — 17/17. It proves: the matching map has rank exactly 3 (Gram determinant > 0), so the kernel is 62-dimensional; a metameric black makes two spectra with sup-distance 1.0 share an identical XYZ to 1e−12; dropping to two cones hides a real colour change (ΔL = 4.65, ΔM = ΔS = 0); a model fourth receptor splits a three-cone metamer (∫M·Q = 5.95 ≠ 0); the gamut boundary has one 319 nm non-spectral edge; sRGB covers 33.5%; and the nearest wavelength to white is 577 nm, a quarter of the diagram away. The fourth-receptor curve is a labelled model — its shape sets the size of the split, never its existence. Cone fundamentals are the standard Hunt–Pointer–Estevez transform of the same data; dichromat appearance uses the cone-projection method (Viénot, Brettel & Mollon, 1999).
Portal — the kind of layer whose job is to make the whole exceed the stack. Companion portals: The Common Measure, Any Loop You Can Draw, Every Number Honest, The Limits of Knowing.