Gah. A thousand-word answer and I didn't actually answer the question posed.

Quote Originally Posted by Sathurn View Post
I was watching Sesame Street with my son and had a kind of weird thought. We as humans see red, yellow and blue as primary colors.
Actually, we see red, green, and blue. The red, yellow, and blue that we learn in school are (close to) the primary subtractive colors (as Midgardsormr points out). The difference is that paint works by removing colors from white (the color of the paper); removing blue gives yellow, removing green gives magenta (which is close to red), removing red gives cyan (bluish-green).

Quote Originally Posted by Sathurn View Post
Is this a rule for humans? i.e. the structure of our eye, or is this a rule of optical physics.
I think I answered this one in the previous answer; it's completely dependent on what frequencies of light our three kinds of photocells are most sensitive to.

Quote Originally Posted by Sathurn View Post
Could you design an alien that sees orange, green and purple as primary? And what would the consequences of such a difference?
In general, you could have any different set of photocells with different sensitive frequencies, even more than three of them! (Which would give you more than three primary colors, but would also have big effects on how color is perceived in general.) Let's stick with three, so we don't have to speculate about alien physiology. So, orange, green, and purple. The orange cell is sensitive to light with sorta-low frequency, while the green cell is sensitive to light with mid-range frequency. But the "purple" cell? The problem here is that there's no single frequency of light which is "purple"; purple is what we call light with a mix of low and high frequencies but no mid-range frequencies. But let's say that this is what your "purple" cell is sensitive to: light of high and low frequency, but not mid-range frequency.

This is actually kind of interesting. First, could our alien distinguish red light from blue light? The purple cell would respond the same way to red light or blue light. In order to distinguish them, we would require that the sensitive range of the orange or green cells overlaps the purple cells' range at the top or bottom. If there is overlap between orange and red and between green and blue, for instance, then red light would produce a high orange and purple response but no green response, while blue would produce a purple and green response but not an orange. There is very little overlap in humans, though; the reason we have primary colors at all is that green light (for example) strongly stimulates the green cells but barely stimulates the red or blue cells at all. If there was overlap in the aliens between purple cells and both green and orange, then there would be no "purple" primary color! If there was no overlap on one or both ends, on the other hand, the primary color would be either red or blue (or both)!

Orange is still pretty close to red, so let's say that it overlaps purple, except maybe at the very lowest frequencies (which would then be indistinguishable from blue). Then the primary colors, the three kinds of dots in the aliens' TV sets, would be orange (which stimulates only the orange cells), green (which stimulates only the green cells), and blue. Why blue? Because red light will stimulate both purple and orange, while blue light will only stimulate purple. Their TVs would probably look a lot like ours, then, except the red dots would be a little more orange. The colour combinations would look weird, though. A picture of a red apple would use the orange and blue dots; that is, it would be intended to activate the orange and purple photocells, because that would look like what we call "red". To a human, though, the display would look fuchsia (which is how we perceive the combination of orange and blue). In fact, such a display would be incapable of producing anything we'd recognize as "red". To them, our displays would also look strange: the color our TVs display for "orange" wouldn't look at all orange to them, for example.

I'm going on about our TV screens (though similar differences would be found for all color combinations, including paint and ink) because that's where I think the greatest difference would be. They'd probably still have the same color wheel as us, for example, for reasons I explained in the previous post. That is, unless they really can't distinguish red from blue, in which case they wouldn't have anything we would recognize as purple; anything we call "purple" they'd see as the same color as red or blue.