Some paradoxes, errors, and resolutions concerning the spectral optimization of human vision

The peak brightness of the solar spectrum is in the green when plotted in wavelength units. It peaks in the near-infrared when plotted in frequency units. Therefore the oft-quoted notion that evolution led to an optimized eye whose sensitivity peaks where there is most available sunlight is misleading and erroneous. The confusion arises when density distribution functions like the spectral radiance are compared with ordinary functions like the sensitivity of the eye. Spectral radiance functions, excepting very narrow ones, can change peak positions greatly when transformed from wavelength to frequency units, but sensitivity functions do not. Expressing the spectral radiance in terms of photons per second, rather than power, also causes a change in the shape and peak of the distribution, even keeping the choice of bandwidth units fixed. The confusion arising from comparing simple functions to distribution functions occurs in many parts of the scientific and engineering literature aside from vision, and some examples are given. The eye does not appear to be optimized for detection of the available sunlight, including the surprisingly large amount of infrared radiation in the environment. The color sensitivity of the eye is discussed in terms of the spectral properties and the photo and chemical stability of available biological materials. It is likely that we are viewing the world with a souvenir of the human evolutionary voyage.