As anyone following this work will have noted, I assert that light interacts on the retina in three distinct geometrically defined regions formed by appositions of the intermixture of cone and rod receptors and not within the receptors themselves. It even becomes possible to view the retina abstractly as a logically ordered array of generic quantum confined electron centers. It may even be helpful to completely do away with the terminology of “cones” and “rods” and view them simply as elements that provide the proper logical “geometric spacing” between the generic (essentially retinal molecule) energy absorbing electron centers.
The three interactions are as follows:
a.) With the hexagonal matrix of cones that form the fovea with this interaction defining the exact long wavelength (“red”) limit of visual response. The fovea is “blue blind” as Wald correctly found!
b.) With the admixture of cones and rods where, at 7-8 degrees of eccentricity, the density of rods is sufficient to completely surround each cone to form a perfect octagonal symmetry. This, again exactly and geometrically, defines the center (“green”) wavelength of the visible band. This geometrically fixed point provides a fixed reference on the retinal surface from which all other wavelengths can be compared in the visual image formation process. This array of octagonal “rods-around-cone” assemblies have been mistakenly termed “M cones”.
c.) With the, again, hexagonal symmetry of the predominantly rod-containing region of the peripheral retina that defines the exact short wavelength limit of visual response.
(I must parenthetically note: 1.) no one as yet seems to have seen my point that the only geometric basis for the octagonal symmetry of the mid band centers is a receptor size ratio (i.e., the diameter of cones to rods) of 1.8:1. This is the only ratio that can result in the octagonal symmetry that is observed and this ratio corresponds to the visible band, i.e., from 700 to 400 nanometers and, 2.) a reminder that the three wavelengths detected as above are “primary” (as deduced early in the history of vision) but are not yet “colors”. The hues of color are determined by comparing these wavelengths in the manner deduced so brilliantly by Edwin Land. Through all of this I am reminded again of the quote attributed to Einstein that “All is Geometry”)
Thus… three narrowly tuned wavelength-receptive regions are defined on the retinal surface.. What is the parameter that varies across each region? At first thought it is the density of receptor sites. But secondly, it is the perfect symmetry of each region that in addition to defining density of sites is related to the point of peak light absorption. One moves from the perfect (large receptor) hexagonal symmetry of the fovea to a perfect octagonal symmetry at 7-8 degrees to a perfect (small receptor) hexagonal, symmetry of the rod containing peripheral retina.
Thus the retina progresses at increasing eccentricity from hexagonal to octagonal to, again hexagonal symmetry.
It is then perfect geometric symmetry that defines the peak of each wavelength absorptionregion.
A diagram from Pirenne that I have previously used showing the perfect octagonal motif at the 7-8 degree retinal eccentricity. I again humbly submit that this is the basis for the “clumping of M cones” that Masuda et al have recently reported (see previous Comments for the reference).
I have not time to go into it here but geometrical perfection combined with the sub-optical wavelength dimensionality of these receptor centers results in a density that precludes overlap of photon (read “quantized”) interactions at each center resulting in the high (nearly perfect) light interaction efficiency in these regions. This in turn leads to an explanation for the ability of vision to detect single photons (or, again, quantized interactions.
GCH
5/21/08
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