The CIE chromaticity diagram
Here's another way to organize all colors so that similarity and proximity correlate...and all possible perceived colors are mapped.  It's the CIE chromaticity diagram.  All monochromatic spectroscopic colors are on the horseshoe-shaped rim.  The bottom, straight line is the pure purples: mixtures of monochromatic violet and red of wavelengths at the farthest limits of human sensitivity.  They are not in the rainbow.  The "C" region ("centroid") is what we call "white." 
Each inside point represents some combination of hue and saturation.  The farther from "C" the greater the saturation.  The z-axis (which isn't shown) is intensity, the necessary third dimension.

It's a "nomograph"!

This is the choice of arrangement for the color theoretician.  Here's why:  To find what color is produced by the additive mixture of two colors, simply locate each of the two colors on the diagram, then draw a line between those two points.  The new, mixed-light color is on that line at a position proportionally located according to the relative intensities of the two source lights.  (The proportion is inverse, of course.  The stronger the light, the closer the mixture is to it.)

The red lines are colors that a protanope cannot distinguish between.  (This remarkably clear way to "see" the two dimensionality of protanopia comes from The Feynman Lectures on Physics I, p 35-8.)  That line which goes through the centroid is—for a "normal"—brilliant, 100%-saturation blue-green at the left, becomes less and less saturated as we move toward C, and then shifts into the red and becomes less and less detectable as we approach the corner of the diagram.  For the protanope these are all variations of white ("shades of gray" if on the printed page).  For the protanope, the two-dimensional chromaticity diagram has all the dimensions of color collapsed into its two dimensions.  Something resembling "hue" is the angle of those red lines.  Or perhaps its closer to "saturation."  Protanopic color does not have three distinct parameters of color for which the Munsell choice of parameters is meaningful.

A color "normal" person has difficulty understanding what colors a protanope sees, colors which the protanope then solves the arrangement puzzle with only two dimensions—and it is correct for him while not correct for the "normal" person.  Nevertheless, a protanope has much more difficulty understanding what "normal" color  looks like.

A color "normal" person is no more able to comprehend what a bird sees.  Four-component color must have a fourth Munsell-like parameter in addition to hue, saturation and intensity.  That fourth "dimension"  must be as unlike all of the familiar three as those three are different from each other.  Since what experiencing it would be like would depend on how evolution developed our brain circuitry to interpret it, we probably cannot imagine the experience: it simply doesn't exist.

Nevertheless, it represents real-world phenomena at the edge of human comprehension.  To explore beyond the edge, we need our most powerful modern tool kit.  The one that so often seems to be just a little out of reach:

Mathematics.

If you understand a couple of elementary points from calculus, understanding how "white" arises in our vision is easy.  If you are not familiar with calculus, here is a relatively easy way to begin to understand a couple of its elementary principles.

Take the plunge.

 
 
 
 
  
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