As a belated Christmas gift to readers of my blog (thank you!), I thought I would help answer what is probably one of the nerd sniping-est comics from XKCD. It turns out the answer is more biology than physics. The girl in the comic is right in questioning her mother’s answer; violet is a shorter wavelength than blue (if you remember your Roy G. Biv acronym ordering the colors of the rainbow, you’ve also listed the colors in order of decreasing wavelength). It actually turns out that indigo and violet light is scattered well in the sky. You just don’t see it because your eyes aren’t ideal detectors of light wavelength. The reason you can observe different colors is because you have different cone cells in your eye, and each one reacts to a different part of the visible spectrum. We only have three though, and they don’t respond to all the colors equally.
The blue curve which represents the cone that picks up short wavelengths is really sensitive to light at around 450 nm. This wavelength represents the shorter end of what we consider “blue”, which goes up to about 500 nm. The shorter wavelengths are “violet”. As you can see, the response drops off really quickly on the shorter end. This means that while there might be violet in the sky, you register the blue more in a mix of purple and blue. The Georgia Tech researchers in the MSNBC article actually say you perceive a mix of blue and violet the same as a mix of blue and white. The article the graph comes from also talks more about how the combination of different color sources affects your perception.
How we see color is actually a very complicated subject and isn’t just a straight up application of optics. Spectroscopy is a branch of physics that studies how different wavelengths of light interact with matter. Photometry and colorimetry are branches of science that study how people can actually perceive these wavelengths. This includes factors like the structural aspects of your eye (like the chemical/physical behavior of the cone cells) as well as processes that go on in your brain, as seen in the famous checker shadow illusion.