MIGHT THERE BE AN OVER-ARCHING SPATIAL ORDER ON THE RETINA ?
Tuesday, August 25th, 2009Very early in my study of the retina it became apparent that, if one assumed three classes of color sensitive cones (THAT SHOULD NOW BE APPARENT IS AN INCORRECT ASSUMPTION!), these receptors were not arranged in any logically spaced order on the retina but rather seemed to be distributed randomly. If one assumed, as vision textbooks portrayed (and still do), that the retina was located at the image (i.e., intensity-only sensitive) plane of the optics of the eye then some type of spatial order would be necessary to accept the image. This situation is akin to that obtaining on the image plane of a digital camera where the silicon chip contains a logically spaced array of tri-color sensitive light detecting centers (”pixels”) to accept and electronically process the incoming image. But, the three types of cones (!) were spaced randomly!
I could not, and still do not, understand how the vision field could reconcile this random distribution of light detection centers (or pixels) with any logical image-forming process!
(Incidentally, I do in this work reconcile the distribution of receptors with an image-forming process explaining directly from Osterberg’s historic retinal topology measurements, without any doubt, that the retina is the Fourier (or focal) plane of the eye with each pixel having the necessary capability for processing both the intensity and phase of incoming light as the Fourier equation demands).
So, a dilemma - the historically found statistical distribution versus the logical requirement for some sort of ordered array of receptors? ( and I didn’t even mention that in measurements of the statistical distribution of “color sensing” receptors there is always a paucity of blue sensitive things - blue cones are very difficult to find! All of this is explained in this work.
Examples of recent work demonstrating the statistical distribution of receptors are the experiments of Roorda et al that I have previously referenced.(over and over!) This group developed a method for microscopically imaging and identifying individual retinal receptors. Their initial measurements focused on a region of the retina near one degree of eccentricity. This is a transition region where the density of cones is rapidly decreasing and where the introduction of rods is rapidly taking place . The rods being introduced crowd and fill the spaces between the diminishing number of cones. (it is the statistically small number of rod-to-rod appositions that form “blue” centers that are misrepresented as cones). In summary, the centers defined as cones in this region was totally random.
(I would be derelict in my duty if I did not insert here the thought that what they found was in exact accord with my explanation! Their “red-sensitive” cones were actually cone/cone apposition centers that were still dominant in this region. What they termed “green sensitive” cones were cone/rod appositions that were beginning to statistically appear. The few (very few!) centers that they labeled “blue sensitive” were the small number of rod/rod appositions. All is geometry!).
One can read in my preceding Comments on this page where I repeatedly suggested that if the Roorda group, or some other group using their methods, would make the same type of measurement at a larger retina angle - near 8 degrees of eccentricity - they would find that, in their terms, “green cones” would predominate. I heard no direct acknowledgement to my request but another group ( A paper (3832/A375) was presented at the ARVO 2008 Annual Meeting “Arrangement of the Human Trichromatic Cone Mosaic in Peripheral Retina” authored by O. Masuda, H. Hofer, J. Carroll and D.R.Williams) did make such measurements at larger retinal eccentricities. They reported (surprisingly!) finding what they chose to term a “clumping” of green cones in this region - in accord with what I had predicted although there was no acknowledgment of this.
This second group, apparently still seeking some spatial order buried in the random distribution, employed statistical sampling tests to locate some degree of order. -They found none (other then the “clumping of green cones”).
In this work the only spatial order of the retina is contained in the three diffractive regions (the long wavelength limit, the exact geometrically defined midband wavelength, and the short wavelength limit). I had assumed that these regions were circularly symmetric on the retinal surface. I recently came upon something, however, that indicates that perhaps there may be a larger “over-arching” order to retinal structure.
In reading “THE GOLDEN RATIO” by Mario Livio (published in 2002 by Random House) about this fascinating number (1.618…..), the author introduces the “Wonderful (or logarithmic) Spiral”. I’ll not go into this (one can read the book), but looking at the structure of the head of a sunflower that displays such a spiral (p.36) I remembered a plate from Pirenne (VISION AND THE EYE), specifically Plate 7. This figure from a drawing by Schultz in 1866 (!) is titled the “mosaic of the cones in the fovea centralis of human retina” and is abstracted in the following:
There is certainly a spiral motif when viewed from this larger perspective.
GCH
Ojai, CA
8.25.08
From Wikipdia on the sbject of Phyllotaxis and Physics - the “Wonderful Spiral” in biology”
“Physical models of Phyllotaxis date back to Airy’s experiment of packing of hard spheres. Douady et al. also have shown experimentally and theoretically that phyllotactic patterns
emerge as self-organizing processes in dynamic systems.[4] In 1991, Levitov proposed that lowest energy configurations of repulsive particles in cylindrical geometries reproduce the spirals of botanical phyllotaxis.[5] More recently (2009), Nisoli, Gabor et al. have shown experimentally and numerically that indeed that was the case, by constructing a “magnetic cactus” made of magnetic dipoles mounted on bearings stacked along a “stem”.[6] They also revealed that these interacting particles can access novel dynamical phenomena beyond what botany yields: a family of highly non local novel topological solitons emerge in the nonlinear regime of these systems, as well as purely classical rotons an maxons in the spectrum of linear excitations. They named these novel phenomena “Dynamical Phyllotaxis”, as they appear in physical systems whose statics is dictated by the number theoretical laws of Phyllotaxis.”

