Wavelength is physical. Color is a construction of the visual cortex. Most people nod at that and then keep talking as though a tomato is red the way it is round. I want to make the distinction actually bite, because once it does, a lot of things about screens, paint, and arguments over dresses stop being mysterious.

Three numbers

Light arriving at your eye has a spectrum: some amount of energy at every wavelength from about 380 to 700 nanometers. That is, in principle, infinite-dimensional. A function.

Your retina reduces it to three numbers. There are three kinds of cone cells, called L, M, and S for long, medium, and short, each with a broad, overlapping sensitivity curve. Each cone reports one number, the total light it absorbed, weighted by its curve. It does not report which wavelengths did it. It integrates and forgets.

So the entire spectrum, the whole function, becomes a point in a three-dimensional space. Everything you will ever call color is a location in that space. The projection from spectra to LMS is enormously many-to-one, and the collisions have a name.

Metamers

Two spectra that produce the same LMS triple are metamers. They look identical, by construction. There is no way to distinguish them with your eyes, because your eyes are the thing that made them the same.

This is the entire basis of every color display ever built. A screen does not emit the spectrum of a lemon. It emits three narrow spikes, red, green, and blue, at intensities chosen so that your cones report the same three numbers a lemon would have produced. The "yellow" on your screen has no yellow wavelength in it whatsoever. It's a red spike and a green spike, and your cortex, receiving the same three numbers it would get from a 580 nm photon, says yellow.

Point a spectrometer at the screen and at the lemon and the graphs look nothing alike. Point your eyes at them and they are the same color. Color isn't on the graph. It's on the far side of the cones.

Magenta has no wavelength

Here's the cleanest demonstration. Take the visible spectrum, red at one end, violet at the other. Every hue in the rainbow corresponds to a wavelength. Now find magenta.

It isn't there. There's no wavelength that looks magenta. Magenta is what you see when L cones and S cones are both firing and M is not, which no single wavelength can do, because M's curve sits between them. Magenta is your brain's answer to "red and violet at once," and rather than reporting "two things," it fabricates a hue that closes the line into a circle.

The color wheel is a circle because the brain bent it. The physics is a line.

Opponency: the brain's second projection

The cones are only the first stage. The signals get recombined almost immediately, in the retina itself, into three new channels: roughly light versus dark, red versus green, and blue versus yellow. This is Hering's opponent-process theory, and it explains things the cone model cannot.

You can't see a reddish green. Not "it would be muddy," you can't imagine it, because red and green are opposite ends of a single channel that can only be at one value. Same for bluish yellow. This is also why afterimages come in complementary colors: stare at red, fatigue the channel toward red, look at white, the channel rebounds toward green.

So by the time color reaches anything you'd call perception, it has been through two different coordinate transforms, neither of which preserves the physics.

Constancy: the brain lies on purpose

The third stage is the one that started fights online in 2015. Color constancy is the visual system's habit of discounting the illuminant. A white shirt looks white in sunlight, in shade, and under a tungsten bulb, even though the light actually reaching your eye is blue-ish, blue-er, and orange in those three cases. Your cortex estimates the lighting and subtracts it, so that you perceive the surface rather than the light.

This is a very good idea for a system that needs to recognize a ripe fruit at dawn and at noon. It's a bad idea for a system looking at a photo of a dress with no lighting cues. Some brains assumed a blue-ish shadow and subtracted blue, and saw white and gold. Others assumed warm light and subtracted yellow, and saw blue and black. Both were doing exactly what they're built to do. The pixels had one value. The color had two, because the color was never in the pixels.

Brown is the everyday version of this. There's no brown light. Brown is dark orange in a context that includes brighter things. Show a "brown" patch in isolation against black and it looks orange. Surround it with white and it goes brown. The wavelength didn't change. The neighborhood did.

Gamut, and why your screen can't do that

A consequence of the three-number reduction is that any display with three primaries can only produce a triangle of colors in the chromaticity space. Colors outside the triangle exist, you can see them in the world, but no mixture of those three primaries can make your cones report them. That triangle is the gamut. sRGB, the one nearly everything uses, covers about a third of what your eyes can distinguish. The saturated cyans and greens in a real forest are simply not representable. The screen shows you the nearest point on its triangle and you accept it, because you've been trained by thirty years of screens.

Wider-gamut displays push the triangle out. They can't make it a circle. Three points make a triangle.

The people who see four

About 12% of women carry a gene for a fourth cone type with a slightly shifted curve, and a small number of them appear to be functionally tetrachromatic: they can distinguish spectra that are metamers for everyone else. To them, two "identical" swatches of paint can be visibly different. Their color space is four-dimensional. There is no way to show them the color they see on any screen ever made, because all screens are built for three.

I bring them up because they settle the argument. If color were a property of light, everyone with working eyes would see the same colors. Instead, the number of colors that exist depends on how many kinds of detector you were born with. The world doesn't get a vote. The observer does.

So what is red

Red is a name for a region of a three-dimensional space that your nervous system constructs from an infinite-dimensional input, then rotates into opponent channels, then corrects for guessed lighting, then compares to its neighbors. It is a very good model of surface reflectance. It's stable enough that we can build entire industries on it. And it's entirely, without exception, inside your head.

The tomato reflects a spectrum. You supply the red. Somebody has to.