Is the color wheel just an optical illusion? As a kid, I was taught that that blue and yellow make green, yellow and red make orange, and red and blue make purple - forming the subtractive color wheel. As an adolescent I was taught that blue and green make cyan, green and red make yellow, and red and blue make magenta - forming the additive color wheel. Somewhere in that time I was also taught that the colors of the rainbow are ROY G. BIV.
That last one is the only one that makes much sense to me in physics because perceivable light is not somehow a cycle, but rather a tiny segment of the EM spectrum.
Why do the colors at the top and bottom of the spectrum seem to be mixable? Is there anything in nature that indicates this should be the case? Is this just a psychological or physiological phenomenon?
 A: Light wavelengths are on a linear scale, but humans only measure "color" by the relative power in three regions of this linear spectrum.  A whole gamut of relative weights of these three color components is possible.  The possible colors (hue and saturation, normalizing out intensity) we can perceive can therefore be represented as a triangle in a plane, which is often simplified to a circle.
A: You see color based on which of your light receptors in your eye detect that particular wavelength of light and to what degree.  This is largely based on the size of the receptors but also on a lot of factors I don't understand.
Say:
Receptor A reacts most light with wavelength a.
Receptor B reacts most light with wavelength b.
Did you say that out loud? good!
Now Receptor A will react just a little with b and the closer b is to a, the more A will react.
If we see wavelength a as yellow and b as blue, there is some wavelength c between a and b which will trigger A and B equally and we will arbitraily call that green. (Note each receptor does not quite react exactly like this but this is an overly simplified analogy.)
You can imagine now that if we trigger A and B with a and b in the exact proportions that A and B are triggered by c, we will see green.  That is (by my understanding and I work with inorganic pigments for a living) my understanding why the color wheel works the way it does.  As to why it is fashionable to shown blue next to orange, I have no idea.
