Why does he conclude that we need 4 primary colors? He knows that our eyes have three kinds of 'sensors', which roughly correspond to [R, G, B]. How the brain processes the initial perceptions, allegedly [R-G, (R+G)-B, R+G+B], doesn't change the fact that you can approximate all colors by mixing quantities of R, G and B.

What I'd find more interesting is a proposal (or a mention) of a color space that's based on what are, according to him, the 'computed' values. Something like NTL (tiNt/Temperature/Luminance), where N is R-G, T is (R+G)-B, and L is R+G+B. (The names 'tint' and 'temperature' are taken from photo editing software, as they are the only tools I can think of that come close to this system.)