Extended Data Fig. 8: Perceptual independence of metamers.

We wondered whether metamers are simply instances of ‘olfactory white’. This would imply that the difference between (not within) the 3 metamer pairs would be under 0.05 radians. To address this question, we measured the distances between the 3 metamer pairs, which are as follows: pair 1 and pair 2, 0.11 radians; pair 1 and pair 3, 0.13 radians; pair 2 and pair 3, 0.07 radians. In other words, each metamer is a distinct odour. Moreover, we next compared the metamers to ‘olfactory white’. We selected the ‘best’ white from a previously published study⁸ and measured its distance from each of the metamers. The obtained minimal distances were 0.25, 0.24 and 0.24, all of which are much higher than 0.05 radians. One may note that the white in the previous study⁸ may not have been ‘true White’, as indeed that study did not have the underlying computational framework developed here. Moreover, that study was restricted to about 30 components. To address this, we generated 1,000 virtual versions of white odours, by combining different sets of 100 components. We observe that all mean distances between the metamers and these whites are above 0.1 radians, and that the minimal distance of any pair to any white is larger than 0.05 radians. a–c, Histograms show distances between current metamer pairs to the 1,000 different white odours that we generated. Distance between one odour (of the metamer pair) to the whites is shown in blue, and distance between the other odour (of the metamer pair) to the whites is shown in red. Circular points show distances of each odour in the pair to the three previously described white odours⁸. Each panel shows one of the three metamer pairs reported in this paper.