TITLE: Four questions on color
QUESTION [2 upvotes]: First, I apologize for being a mathematician and having no scientific background in physics. The following questions on color came up in a discussion at lunch and I would be very happy to get some answers or corrections of my understanding.

The first question is, what a color the human eye can see is in the first place. According to this wikipedia article, the human eye has three cone cells $L$, $M$ and $S$ responsible for color vision which can be stimulated each in a one dimensional way, i.e. ''more'' or ''less''. Combining the stimulation of all three, one gets a $3$-dimensional space called the LMS color space. Is a color the human eye can see just a point (in a specific range) in this LMS-space? A negative answer could be that time plays a role (switching between e.g. two points of the LMS-space with a certain frequency defines a color). The model is made in the way that only one point in the space at a time represents a state of the eye at that time and not many.

For the following questions, I suppose that the answer to the above question is positive, e.g. a color the human eye can see is defined by a specific point in the LMS-space. By experiments, one could possibly determine the body in the LMS-space, the human eye can see (this is what I meant by the ''specific'' point). Of course, this may differ from person to person but perhaps one can average over some and get an average body $AB$ in the LMS-space. Points inside are now exactly the colors the human eye can see.

Now there is this CIE color space which is vizualized by this $2$-dimensional picture looking like a sole of a shoe. As far as I understand, there is a bijection (continuous?) from the LMS-space above to this CIE-space where two axes describe the so called chromaticity and one axis describe the so called luminance. What is the figure shoe sole now exactly? Is it a certain hyperplane in the $3$-dimensional CIE color space to which the luminance-axis in perpendicular? (Perhaps one can say something like ''it is the color at full luminance''. Note, that black isn't in here.)
The RGB color space has the drawback of having a gamut not filling the whole visible range. Why doesn't one use the frequencies of the $L$, $M$ and $S$ cone cells as the primary colors for technical devices like screens? Couldn't one describe the whole visible range then (i.e. wouldn't the gamut be the whole shoe sole then)?
My last question concerns this old painters belief, that every color can be obtained by mixing red (R), yellow (Y) and blue (B) or the belief that every color can be obtained by mixing cyan (C), magenta (M) and yellow (Y). Both models, the RYB and the CMY model, are subtractive. When one mixes these colors, doesn't one ignore the luminance? I.e. don't the painters want to say that they can obtain each chromaticity by mixing these colors? (Of yourse, if they want to say this, it is also not really true since the gamut of these three colors determine a certain region in the shoe sole plane from the previous questions which is not the complete sole.)

REPLY [1 votes]: My last question concerns this old painters belief, that every color can be obtained by mixing red (R), yellow (Y) and blue (B) or the belief that every color can be obtained by mixing cyan (C), magenta (M) and yellow (Y). Both models, the RYB and the CMY model, are subtractive. When one mixes these colors, doesn't one ignore the luminance? I.e. don't the painters want to say that they can obtain each chromaticity by mixing these colors? (Of yourse, if they want to say this, it is also not really true since the gamut of these three colors determine a certain region in the shoe sole plane from the previous questions which is not the complete sole.)

Chromaticity only is not interresting for painters, one has to know the level of luminance associated to a given chromaticity to correctly represent a color.
For example, a dark green and a "lemon" yellow can have the same (or almost the same) chromaticity, but they are certainly not the same colors.
There is an ambiguitiy in the word "color" itself that cannot be understood by the sole concept of chromaticity : there is nothing "dark yellow", no material is at the same time of an "intense blue" AND light (blue paints are always dark, the more blue the darker...)
Chromaticity is practical when you want to characterize the "color" of light sources, if you want to talk "real colors" (light sources on a screen or material colors), you need a 3D space.
The CIELAB colorspace gives you a more intuitive picture for this.
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