Human response to light is not particularly well-modeled by a logarithmic response. It's --- no big surprise --- better modeled by a power law.
This stuff is confusing because there's two perceptual "laws" that people like to cite: Fechner-Weber, and Stephens's. Fechner-Weber is logarithmic; Stephens's is a generalized power-law response.
"Human response to light is not particularly well-modeled by a logarithmic response. It's --- no big surprise --- better modeled by a power law.
This stuff is confusing because there's two perceptual "laws" that people like to cite: Fechner-Weber, and Stephens's. Fechner-Weber is logarithmic; Stephens's is a generalized power-law response."
Neither would seem that useful, given the very uneven weighting of the eye towards certain wavelengths, and the fact that women have different color perception versus men (and that doesn't get into those who have had cataract surgery and can now see into the UV range, which throws perception off dramatically from what most people consider 'normal.') Those generalizations are outdated with any current science from roughly the 1970s on. Steven's power law was shown to not hold up very well when considering individual respondents.
f(x+eps)/f(x) ~= eps f'(x)/f(x) + 1
f(x) = x^2.2 f'(x) = 2.2x^1.2
f(x+eps)/f(x) ~= 1.2 eps/x + 1
Human response to light is not particularly well-modeled by a logarithmic response. It's --- no big surprise --- better modeled by a power law.
This stuff is confusing because there's two perceptual "laws" that people like to cite: Fechner-Weber, and Stephens's. Fechner-Weber is logarithmic; Stephens's is a generalized power-law response.