Red + yellow = orange. Orange sits between red and yellow in the rainbow. It makes sense mixing them provides an “average”
Yellow + blue = green. Green sits between yellow and blue in the rainbow. Same as above.
Purple does not sit between red and blue in the rainbow. Why do they combine to make purple?
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You might have seen an image [like this](https://tutorials-cdn.pixelmator.com/gradient-tool/top.jpg) before. If you notice, its bordered by two ends of Red, one turning into purple and the other turning into orange.
The reality is that the color spectrum is more like a continuous gradient. It’s not like the traditional cartoon “Reading Rainbow” type rainbow where it hard starts with Red and hard ends with Violet. In reality, the violet eventually gradients into red, and repeats etc.
Your eyes have three types of color receptors – what we’d call Red, Green and Blue.
The level of activation of each type results in what we perceive as colors. Some wavelengths of light activate multiple types of receptors, resulting in blends that we perceive as mixes of the three primary colors.
As you go off the blue end of the spectrum you detect blue, the green receptors mostly don’t pick up anything, but the red ones have a small uptick in sensitivity [graphical representation](https://midimagic.sgc-hosting.com/eyespect.jpg).
So you are detecting “red” at the very end of the “blue” end of the spectrum, giving a warp-around effect to your color perception, which makes purple appear to be between blue and red.
Edit: [A lot more info here, with nice accessible graphics](https://midimagic.sgc-hosting.com/huvision.htm)
It’s all made up by your brain
your eyes only sense 3 different colors (red, green, blue) any natural light will ‘tingle’ the closest sensors, example: if some yellow light reaches your eye, the red sensor will ‘tingle’ moderately and the green one just a bit; the brain read those signals and goes “hey, that’s yellow”. When you have blue light and red light mixed, your brain will receive those signals and has to interpret a color from them, and so purple is created, although there is no real purple light (as seen in the rainbow)
If you’ve ever taken an art class chances are you’ve seen a color wheel (https://images.app.goo.gl/ewQjHAhNbRjuGnua8) notice how purple does sit between blue and red. This is because visible light is a spectrum and loops in a sense. For example, if you take a glass prism and hold it up to a light source, with the right angle you could see the rainbow repeat itself
The same reason we can’t distinguish yellow light from mixed red and green light. The eyes don’t tell the brain what wavelength light it’s receiving, just the intensity of light triggering the different receptors. Sometimes you get red and blue light without green light, and purple is how you interpret that input.
If we had eyes more like a mantis shrimp or spectrometer, we might interpret colors as wavelength, be able to tell the difference between yellow light and mixed green and red light, or be able to tell that purple is really red and blue mixed together. Or we might just see more distinct colors and not inherently know about wavelength.
There are people with four types of cones, but in order for everybody’s eyes to work that way you need some strong selection pressure benefiting people that can see more colors. For example, if that was the only thing that let you distinguish a poisonous plant from a nutritious plant during a famine. The people that could tell the difference would have an advantage and more of them would survive.
I can’t believe no one has said this yet, but using your own analysis (which is pretty good, honestly) purple actually is between red and blue. You’re just used to looking at colors in a spectrum that goes left-to-right following wavelengths, but if you look at a color wheel (how our eyes actually see colors irrespective of what wavelengths they are) you’ll see that purple actually is between blue and red, just as you’d suspect.
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