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PhilGoetz comments on Seeing Red: Dissolving Mary's Room and Qualia - Less Wrong
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I figured it out. An ideal perceptual representation of sound would only need 2 hair cells - if hair cells, like cones, reported a distance from the stimulus. A cone cell gives a signal whose intensity indicates how far the wavelength of the light it sensed is from its preferred frequency. 1 cone cell lets you order colors along a ray. 2 cone cells lets you order them along a line. 3 cone cells lets you order them on a plane.
A hair cell is specific to a frequency, so you can't combine the output from n hair cells to give an n-1 dimensional picture.
That's true if you're talking about a stimulus that only contains a single frequency at a time, but real sounds and colors are mixtures of an entire spectrum of frequencies, each frequency having its own distinct amplitude.
For example, 2 hair cells, even if they had a wider frequency response, would not be enough to understand speech; for that you need at least 4 to 8 frequency bands.