  A recent paper in a prominent science magazine claims to show that humans can
discriminate at least 1 trillion odors. The authors reached that conclusion
after performing just 260 comparisons of two smells, of which about half could
be discriminated. Furthermore the paper claims that the human ability to
discriminate smells vastly exceeds our abilities to discriminate colors or
musical tones. Here I show that all these statements are wrong by astronomical
factors. A reanalysis of the authors' experiments shows they are also
consistent with humans discriminating just 10 odors. The paper's extravagant
claims are based on errors of mathematical logic. Further analysis highlights
the importance of establishing how many dimensions the perceptual odor space
has. I review some arguments on the topic and propose experimental avenues
towards an answer.
