On the dimensionality of olfactory space

Abstract

We recently presented an estimate of the number of mutually discriminable olfactory stimuli at one trillion (1). Subjects were asked to sniff mixtures of molecules with increasing component overlap selected from a panel of 128 isointense structurally and perceptually diverse monomolecular odorants (2). We considered stimulus pairs discriminable when the majority of subjects could significantly discriminate them at p=0.05, a conventional statistical threshold given our sample size. From these empirical data, we estimated that human discriminative capacity exceeds one trillion olfactory stimuli. Several readers have pointed out that such extrapolations are sensitive to underlying assumptions about the chosen significance threshold (3) and the dimensionality of olfaction (4). It is important to note that any exponential function will be sensitive in this way, and the goal of our model was not to identify the exact number of discriminable olfactory stimuli, or even the exact mathematical bounds, but an estimate of the order of magnitude of human discriminatory power across a population of human subjects. This was not clearly stated in our paper, and we agree that contradictory references to a “lower limit” and an “upper bound” were confusing. The central argument in (4) is that our estimation method assumes that the dimensionality of olfactory space is large. We agree that the high-dimensional nature of olfaction is indeed an assumption, and we should have stated this explicitly in our paper (1). Even if we follow this logic of the models presented in (4), purely geometrical calculations show that our results hold if the dimensionality of olfactory representations is D≥25. The dimensionality of olfaction is a question of interest to everyone, and while we do not know for sure, all available evidence suggests that olfaction is a high-dimensional sense. The olfactory system is wired to keep information from the ~400 odorant receptors strictly separated, so it is plausible that olfaction operates at least in 400-dimensional space. This is an important topic of discussion in olfaction, and we welcome continued debate of the dimensionality of smell and how this impacts human olfactory perception.