> I don’t understand why we can’t teach the color wheel as a true wheel.

Is it even a wheel though?

It’s not, it’s a weird loop shape: https://en.wikipedia.org/wiki/CIE_1931_color_space

You can distort this shape into a circle but you lose the geometric relationship between chromaticities—two points an equal distance along the circumference of the color wheel don’t necessarily feel “as different” from each other.

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Tuna-Fish 4 days ago | parent [-]

Even this is a simplification. The color space you see is three-dimensional, because that is the physical reality of how your eyes work. Any representation of the color space in two dimensions involves choosing a projection that distorts reality.

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dcrazy 4 days ago | parent [-]

Sort of. Your photoreceptors are sensitive to overlapping frequencies, which means they’re not linearly independent and therefore cannot form the basis vectors of a 3D space.

CIE XYZ accounts for this by projecting SML excitations down to a 2D plane (XY) and making the third dimension a color-independent luminosity (Z). Since it’s luminosity-independent, the 2D slice is directly analogous to the color wheel.

	▲	jsmith45 2 days ago \| parent [-]
		I'm not sure that it necessarily follows from the overlap they are not linearly independent. As far as I can tell that alone would simply make them non-orthogonal basis vectors. The issue is more that there isn't really any frequency that only stimulates the M cones. There are some that more or less only stimulate the L cones, but as we get bluer, the stimulation curves of the M and L cones mostly converge, so we can't really get fully independent M cone stimulation (at least not without tricks like locating specific cones and using lasers to stimulate just the M ones, while missing the L ones.) This does indeed make them not linearly independent, so your overall point still stands.