4 ms·
Hey, so gamma is not a logarithmic response. You claim that the delta you use in Figure 2 is a ratio, but your code, https://github.com/johnnovak/johnnovak.site
by cscheid 10y ago
Hey, so gamma is not a logarithmic response. You claim that the delta you use in Figure 2 is a ratio, but your code, https://github.com/johnnovak/johnnovak.site/blob/master/blog/files/2016-09-21/src/gammaramp.nim#L64 https://github.com/johnnovak/johnnovak.site/blob/master/blog... uses a fixed power. These are not the same thing.
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.
- mark-r 10y agoA power law plotted on a logarithmic scale will be a straight line. log(x^2.2) == 2.2*log(x).
- cscheid 10y agoYou need log transformations on both axes for this to work.
- Coding_Cat 10y agoFor those whose algebra is rusty: Let y = ax^n Then log(y) = log(ax^n) = log(a)+log(x^n) = log(a) + log(x)*n i.e. and equation for a line when plotting log(y) vs. log(x).
- mark-r 10y agoYeah OK, after a little reflection I see where my mistake was. I wish there was a way to delete my comment.
- johnnovak 10y agoYour exactly right, my bad... I'll correct the article later today (and I'll also remove the word 'logarithmic' from a few places). Thanks!
- lightedman 10y ago"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 Those generalizations are outdated with any current science from roughly the 1970s on.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.
- cscheid 10y agoYou are right, of course, but from the perspective of an engineer, these two (admittedly broad) laws are very good things to have around. "Essentially, all models are wrong, but some are useful" and all that.