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Changing the triangle inequality to a strict one and claiming that the result is non-Riemannian is a bit dubious. First of all the difference between a strict

Changing the triangle inequality to a strict one and claiming that the result is non-Riemannian is a bit dubious. First of all the difference between a strict and a non-strict inequality is not that big, stating two things are never exactly equal is nigh impossible to measure, especially for something subjective. Secondly that could happen simply by reporting distances in some non-linear fashion, and who cares if the unit of distances is non-linear? If there is a metric that correctly identifies which colour is closer then we're in business, nobody ever said this had to correspond linearly to whatever measure of perceptual distance someone came up with.

yccs27 2y ago
Yes, it's important to note the measure of distance used. Quoting from the paper: Humans are not good at judging questions of the type “How big is the difference?” that form the basis for many large difference experiments. Instead, the authors use data from decisions of "which color step is larger". They find that as the steps get larger, you need a higher difference in color steps to reach the same certainty. This is not that surprising, since people generally get worse at noticing small differences as the absolute quantities get larger. Unfortunately, the model of perception uncertainty used in the paper (Thurstone’s theory of Gaussian perceptual process) does not take this effect into account.
- mannykannot 2y ago
  Thanks, that clears up one thing I was puzzling about: if I were asked to give a quantitative value to how different two colors seem to be, my first problem would be to figure out what a number - any number - would mean in this context. While 'barely perceivable difference' seems like a reasonable unit of measure, I don't think I could judge multiples of that unit with any degree of accuracy or consistency, or, indeed, in any meaningful way. On thinking about this issue, it seems to me that I think of large differences categorically (red vs. green, for example) while thinking of small differences as being on a continuum, even when the colors in question lie in the borderlands of the above categories.

yccs27 2y ago

Yes, it's important to note the measure of distance used. Quoting from the paper: Humans are not good at judging questions of the type “How big is the difference?” that form the basis for many large difference experiments. Instead, the authors use data from decisions of "which color step is larger". They find that as the steps get larger, you need a higher difference in color steps to reach the same certainty. This is not that surprising, since people generally get worse at noticing small differences as the absolute quantities get larger. Unfortunately, the model of perception uncertainty used in the paper (Thurstone’s theory of Gaussian perceptual process) does not take this effect into account.

mannykannot 2y ago
Thanks, that clears up one thing I was puzzling about: if I were asked to give a quantitative value to how different two colors seem to be, my first problem would be to figure out what a number - any number - would mean in this context. While 'barely perceivable difference' seems like a reasonable unit of measure, I don't think I could judge multiples of that unit with any degree of accuracy or consistency, or, indeed, in any meaningful way. On thinking about this issue, it seems to me that I think of large differences categorically (red vs. green, for example) while thinking of small differences as being on a continuum, even when the colors in question lie in the borderlands of the above categories.