A PRIMER ON GEOMETRY AND VISION

(I have not included references in this post. They can each be found in the main of body of the work.. GCH)

The premise here for vision research is that a simple geometric explanation describing  the physics of  individual light interaction sites (or “pixels”) on the retinal surface leads to an entirely new understanding of the evolution of the eye,  the question: what is  “color”,  and the fundamental nature of the overall process of vision.

I have proposed that an entirely new and fundamental principle that combines geometry and the nanostructure of the retina of the eye is involved in light interaction with this surface. I have shown that this same principle and mechanism of light interaction applies to the photosynthetic organelles of plants and algae.

This principle  is totally at variance with the traditional (and abstract!) construction of quantum physics that has been unquestioningly carried over to  every textbook on vision, that “a light photon interacts with a pigment molecule contained within each cone or rod retinal receptor”.  How could this be wrong? But, this construction  has led, for example,  to such absurd  (i.e., without any theoretical or experimental basis) ideas as the “photon catch” hypothesis purported to explain the extended length of retinal light-accepting receptors. Utter nonsense accepted as gospel!

But most importantly, this  traditional line of thought is not (and can never be) consistent with the long accepted distribution of cone and rod on the retina (the measurements of Osterberg). That concept proposed that “classes of cones”  (the receptors that are thought to detect “color”) exist in some ordered  arrray on the retina. But this has never experimentally been shown to be true. AsI  have discussed (read the work!), cones  sensitive to “blue” have been almost vanishingly hard to locate. All of this in turn leads to the idea (again that cannot be justified) that the retina acts as the imaging plane where film is placed in a camera. All of this is totally irrational but has been propounded as fact for a hundred years!

As shown in Figure, I propose that each light interaction site on the retina is composed of two distinctly separate regions: A): a variable, wavelength-determinative space comprising the spatial distance between the centers of two adjacent cone or rod  receptors, and, B): a material-determined space of fixed dimension formed by a quantum-confined electron region of the ubiquitous (i.e., common to all receptors) retinal molecules contained within the body of each receptor. The result is a transition at the instant of light incidence from the classical wave nature of light entering the eye to a “particalized” electron that serving the electrical information processing function of the absorbing mass. THIS SINGULAR, INITIAL LIGHT INTERACTION EVENT OCCURS ON A TIME SCALE. OF FEMTOSECONDS (OR 10-15 SEC) AND HAS NOTHING TO DO WITH THE SLOWER “REACTION TIME” OF THE EYE. There is evidence for this in  the long established (but never explained) measurements of the isomerization (i.e. “signal producing”) time of the retinal molecule showing that this molecular “mechanical” event takes place in the same femtosecond time domain.

Figure 1 illustrates in the abstract the situation where the two adjacent receptors that comprises the two above described regions. As initially shown, these receptors have the same spatial diameter such as would be the case for two adjacent cones or rods. The retinal surface, however, actually contains chiefly (no quibbling!) two receptor diameters that have traditionally been termed  the cones and rods. As shown geometrically in Figure 2, and following many measurements over the years, the ratio of the diameters of these two types of retinal receptors has been determined to be very close to 1.8:1 with the larger diameter abstract circle representing  a cone and the smaller a rod.

Now to considerations of purely abstract geometry that directly follow from this retinal characteristic. First, this ratio of 1.8:1 corresponds to the width of the visual band, i.e., from 700 to 400 nanometers. Lest anyone doubt  the validity of this ratio it can easily be seen that this ratio results in exactly eight of the small circles fitting around one of the large circles and  that this is the motif found on the human retina at 8-9 degrees of retinal angle (see Osterberg). And even more surprisingly, this same “eight-around-one motif is seen in the visual organs of seemingly all species (see Snyder).

Therefore I would propose that the ratio of the sizes of the two circles (or two sizes of receptors if such appear on any retina) determines the width of a visual band.

Further,  it follows that the geometric (center-to-center) distance  corresponding to appositions of the larger circles (i.e., the “cones” that comprise the central fovea of the human retina) determines the exact long wavelength limit of the visual band. Correspondingly, this appositional distance of the smaller circles (the “rods”)  determines the exact short wavelength limit of the visual band.

Thus it is geometry that determines both the width and the exact endpoints of the visual band.

Again to quote Einstein “All is geometry”.

Then to perhaps the crucial factor that is geometrically determined – it  follows that the appositional distance of a large to a small circle (i.e., a cone-to-rod distance) must correspond to a geometrically determined exact mid-band wavelength, at 550 nm.

Thus a geometrical construction – or distance – is fundamentally associated with a specific light wavelength.

I would propose that this fixed geometrical reference corresponds to  Edwin Land’s  “fulcrum” wavelength that he deduced must be present in the eye. This is the reference that  the eye uses as to synthesize the hues of color from light intensities absorbed on either side (Land’s long and short wavelength “records”).  The term “color” enters here for the first time! The eye fundamentally detects three narrow band, geometrically determined wavelengths although in the history of vision science these have improperly been termed the “primary colors”.  They should  be termed primary “wavelengths” as they are not yet the hues of color!

These purely geometric considerations seem to explain Land’s brilliant deductions about the mechanism of color vision that he made from  measurements made external to the eye.

The central finding of this work follows directly from the above considerations.  Using Osterberg’s classic 1935 measurements of the distribution of cones and rods on the retinal surface (that no one disputes), the three primary wavelength peaks described above arise  simply “counting” the three types of receptor apposition (i.e., cone-cone, cone-rod, rod-rod) as a function of retinal angle. See Figure 3 in the main body of this work.  THESE ARE PEAKS OF THE DENSITY OF LIGHT SENSITIVE CENTERS. The central fovea that contains >99% of the large (i.e., cone) receptors is solely long wavelength sensitive and, as described above, exactly determines the long wavelength  limit of the visual band. The concept of the existence of “three classes” of cones has been a fundamental  error in the history of vision science! The wavelength peak defining the geometrically determined mid-band “fulcrum” is seen to exist at angles of 8-9 degrees where (see Osterberg!) the morphology consists of aNn entire area-encompassing motif of eight rods surrounding each cone. In viewing Osterberg’s data this is very striking!  Beyond this angle the retina consists almost solely of rod receptors with these rod-rod appositions  determining the exact short wavelength limit of the visual band. It seems that the retinal area from which the visual image is derived extends from the fovea to perhaps 20 degrees of retinal angle. I have proposed that the peripheral rod-containing retina functions as a “wide angle light meter” that controls constriction of the pupil of the eye.

Further, the plan of wavelength interactions on the retinal surface is totally consistent with computer simulations of light refraction within the body of the eye. It is almost ncomprehensible to me why this has not been seen!

And further, the lesson at the basis of these geometrical considerations is that the structure of the eye evolved in consonance with the physical principles of the refraction of light. There is no need for any “design”. I have written about this elsewhere on this webpage.

I would note finally that all of this is predictive that is the requirement of any new concept. I have noted some preliminary examples in the body of this work relating the retianae of fish and insects to the characteristics of their visual response.

Respectfully submitted,

GCH
Tucson, AZ
7.31.09

Tagged as: nanosptail geometry