Olfactory category/topos theory sensory articulations (warning: far out)

Let Ξ be some mathematical entity — be it topos or category or whatnot — with morphisms. 

To each morphism of Ξ, assign a spring constant k (in practice, I’m hoping there are more or less canonical spring constants for each Ξ)

We could obtain a vibrational spectrum of Ξ (this is done in practice with small molecules, in which the vibrational spectrum is determined by the application of group theory) , and if Luca Turin’s theory of olfaction is correct

(http://en.wikipedia.org/wiki/Vibration_theory_of_olfaction), one could with the right 

olfactory prosthesis (which is well beyond current technology) , smell the difference between FinSet, Grp, and nCob.

More to the point, the whole enterprise would no longer have the sensory qualia of a child in the 1950s playing with an erector set which contains morphisms and objects, and some flashlights (functors)

When you read about the olfactory sense of dogs, http://www.pbs.org/wgbh/nova/nature/dogs-sense-of-smell.html, I wonder just what exotic structures might exist that we could only get a whiff of if we could olfactorize Ξ and its congeners

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3 responses to “Olfactory category/topos theory sensory articulations (warning: far out)

  1. coming from the other direction. What is the mathematical structure of the olfactory sense?

    Molecule-shape (or whatever a molecule-shape maps to in our/dogs’ mental maps of sense-able smells), like the space of consumer products or the space of organisms, is full of starkly different things but which are partitioned by Aristotelian categories. As far as I know we just put them in set-bags and not in informative categories.

    ———-

    on your post. why would there be spring constants? and, isn’t this in a sense what the grothendieck project is about–fuzzing up the precise in order to see the broader structure?

    Maybe I’m off base.

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