A Geometric Principle at the Heart of Non-Rigorously Geometric Biology
June 16th, 2006 | No Comments »Perhaps the most fundamental aspect of this explanation of the process of vision is that pure, rigorously geometrical or dimensional, factors effect the exact determination of wavelength in the certainly non-rigorously geometrical realm of biology. Geometrical nanostructure is at the heart of (I want to use the term ‘overlays’) a biological process.I refer here to my proposal that it is retinal receptor dimensionality and interreceptor dimensionality that is the specific wavelength determining factor of the retina. The maximum intensity of the ‘green’ (or 550 nm) wavelength, for example, is detected at 7-8 degrees of retinal angle in accordance with light refraction within the eye by the maximum density of cone/rod appositions that geometrically occurs at this point. And further, this wavelength-determining apposition geometrically forms the location where the exact midpoint of the visible band interacts on the retinal surface. In addition to validating Land who deduced that such a fixed point must be present, it provides the basis for an understanding of the historically mysterious color constancy of the vision process.
The principle is that an admixture of two dimensions (as the cones and rods are intermixed on the retina according to Osterberg) results in the specification of an exact, geometrically defined midpoint. Receptor size itself determines wavelength sensitivity and, importantly, the ratio of the difference in size of two dimensions determines where this midpoint occurs.
I have noted that the specific size ratio of cone and rod receptors comprising the retina is 1.8:1 (cone/rod) corresponds to the visible band (700-400 nm). And herein, in addition to defining a symmetrical midband point on the retina, enters the greater idea of geometrical (nanostructural) symmetry. Back in the recesses of this work (search the term ‘epitrochoid’) I noted that this size ratio is unique to defining a spatially symmetrical epitrochoidal shape (the same necessarily symmetrical epitrochoidal shape that Felix Wankel used in his internal combustion engine). Who knows?
But the idea of symmetry…and following the Olive Sacks comment (see previous) that ‘Landian’ correlations seem to take place in the vision centers of the brain…..might the concept of a spatial ‘nanostructural symmetry’ follow onward from the retina to perhaps new insights into the functional mechanisms of the brain? The unexpected occurrence of a ‘geometrical spatial symmetry’ in the biological realm…..??????
I am reminded here of a quote that I have used from Roger Penrose:
“There is, in fact, at least one clear place where action at the single quantum level can have importance in neural activity, and this is the retina (recall that the retina is a part of the brain).”
GCH
