Biology / An elementary 5-dimensional model applied in different sciences

Most data here concerns the human eye.

1. Geometry of analysis:

A geometrical analysis of received pictures is performed by the eye. It appears to be much of the same kind as the elementary geometrical definitions of the complementary poles in our dimension model.
   Scientists have been able to distinguish 5 different types of ganglion cells, sensible for different geometrical features (Nf p. 373), in number also the same as degrees in the model.
   There are for instance cells sensible for direction of linear structures, others sensible for round forms, others for curves, convex or concave, others for straight lines in different angles, others for motions of geometrical elements in certain directions.

         Fig S-1-113-2

Cf. in the model proposed geometries of polarized dimension degrees (shortened here d-degrees) d-degrees:

Fig S-2

Direction (4): Vdiv - Vconv, Volumes (3): radial - circular structure, Surfaces (2): concave - convex, inside - outside. Distances (1): motions to - from each other (0/00).

2. Number of cell layers:

There are 5 layers of cells in the retina (compare number 5 in the many other cases of arrangements in the human body):
   3 cells in 'vertical' direction, from receptors of photons, the cones and rods, via bipolar cells to ganglion cells, leading the signals to the optic nerve and visual cortex in the brain.
   2 intermediate transverse layers of cells, at right angle to the other ones, the layer of horizontal cells and the layer of amacrine cells.
   It's a number relation as in step 3-2 in the dimension chain, where the polarization 3 → 2 was defined in elementary geometry: radial versus circular, outer poles of d-degree 2 in the model, that of surfaces.
   An outline of the layers without any precision:


Fig S-3-111-1

Here the cells in 'vertical' lines are the integrating ones. Cf. the relation between d-degrees 3 and 2 as corresponding to a 0-00-relation: the 0-pole as integrating, the 00-pole as differentiating. Bipolar cells gather signals from many receptors, ganglion cells from many bipolar ones.
   Cells in the transverse, 'horizontal' layers have a similar function of lateral inhibition or stimulation as corresponding cells in the general nervous system: facilitate or inhibit the sensitivity of propagated light signals: it's the polarization we have suggested as d-degree step 2-1 in the chain of polarities in the nervous system.

 5 —> 4 —> 3
     \ 1      \ 2 → debranched

meeting the other way around

Fig S-4

3. Center - anticenter polarity in d-degree 2:

Structure of the eye is on a macro-scale 3-2-dimensional with the globe (3) and the retina (2): pictures principally 2-dimensional. We could note that the eye-globe really can rotate, the "external motion" assumed in d-degree 3 in our model (!). A rotation through its 6 muscles (m.), a number that happens to be sum of the poles 3a + 3b out of polarized d-degree 3.


Fig S-5 (after Mf p. 335)

(Cf. muscles in the dimension chain of organs identified in d-degree step 3 - 2 and angle steps 180°→>90° →> 45°.)

A general, structural feature on a more detailed level regard surfaces (d-degree 2) and the polarity between a central area and an anticentric one; not explicitly included before in the model among the polarizations of d-degree 2 (concave / convex, inside / inside...).

      Fig S-6-111-2

The same polarity appeared among types of corpuscles for general senses in the skin but only as smaller and bigger fields for reaction. In the eyes this opposition becomes much more obviously a polarity. (Embryologically the differentiation of cells around animal pole in the blastula is of the same kind.)

- The pupil of the eyeball is of course a first example of this center - anticenter (c - ac) structure. The center as just an opening, a hole (!) could be regarded as one kind if inversion, cf. the cell interpreted as inversion of an atom.
   Area of this center, the pupil, is governed by radial and circular muscles, the geometric poles 3b and 3a out of d-degree 3 and outer poles of d-degree 2 in the dimension chain.
   These muscles are in their turn governed by the sympathetic and parasympathetic nervous system respectively for outward and inward directions, The fact that the pupil not only functions as an aperture but also chronically "oscillates" a little in size (Nf p. 353) could perhaps be traced back to the vibrational moment assumed in d-degree 4 of Direction, origin of these muscles?

- Next example is the organization of cones and rods in the retina, with cones in the central region and fovea, a central shallow depression, and rods in the anticentric area. While cones have more own pathways, signals from up to 1000 of rods (Aph) may converge to one ganglion cell: it shows the typical convergence = direction inwards from an anticenter. The whole system for analyses of signals seems built on processing steps of convergence / divergence (Mf p. 363), the forces from 00- and 0-poles.
   1/3 of the fibers in the optic nerve comes from the fovea, 2/3 from the surrounding area (also a noteworthy division) as numbers of steps from d-degree 3 (?).

About P and M in the figure, see below.

      Fig S-7- 112-1

In cortex however, it appears that these threads occupy equal parts of the primary visual cortex (Mf p. 310), a division 1/1 which could support the view on a c-ac-polarization of the same d-degree.
   We could note the number 3 too in the different kinds of cones creating all colors.

White light is all wavelengths gathered together: the eye shows the generalized peripherally in the sensitivity of rods, the separated wavelength, the colors, centrally, which reflects the polarity unity - manifold between 0- and 00-poles.

- The "P-M-system" is a third example of the c-ac polarity in d-degree 2. The reception areas of the ganglion cells are usually circular with a center field and surrounding anticenter field:
   Ganglions for cones are called P-cells: they have small reception areas, mostly in the center.
   Ganglion cells for rods, called M-cells, have larger reception fields, mostly peripherally.
   That this division corresponds to a polarization becomes evident too from the fact that they have synapses in different cell layers in the visual cortex and get projected to different secondary areas (TA p. 106).

These types show simultaneously a relation of higher d-degree to lower ones in two respects, as such a relation always is of the kind 0 to 00:
   The P-cells react especially on colors,a property connected with surfaces (~ d-degree 2) and wavelengths (~ d-degree 1 as distance), the M-cells especially on motions, the last degree 0/00 in the dimension chain; cf. the figure above.
   Further, M-cells adapt fast in opposition to the P-cells. Such fast adapting cells can be regarded as "derivative cells", illustrating changes in the same way as the derivative of a mathematical function illustrates changes of directions in a curve and implies a decrease in d-degree.

4. On-off-center cells:

The polarization of the derivative M-cells show the complementary feature of poles in our model very clearly.
   The receptor fields of the ganglion cell becomes through different connections in the net polarized in two kinds, on- and off-center cells:
   One type gets active when light hits the center, and inhibited when it hits the circumference of its receptive field.
   The other type is the inverse: gets active when light hits the surrounding area, inhibited when it hits the center of its receptive field.


Fig S-8-112-3 after Nf p. 370

We may compare with polarization of a derivative in an inclination upwards of a curve and an inclination downwards, with polarization of signs plus/minus as in the physical property of charges.
   According to a principal sketch (Nf) inhibiting pathways go to centers in the one kind, to the anticenter in the other kind.

The arrangement could be interpreted in terms of the final step 1 →> 0/00 with "pole exchange" in the dimension model: Pole 1b, "motions from each other" out of divergence and 0-pole, define an anticenter, a new 00-pole, and "motions to each other", out of convergence and 00-pole, define a new center: With 00-pole representing inhibition, 0-pole excitation we get following scheme:

Fig S-9-113-1

The approximate number of cells reacting in different ways seems to include 3 steps of divisions in percentage:: 100 →> 50-50, 50 →> 30-20, 20→>(10-10 ?, no figures given):
- 50 % of them react both when light is turned on and when it's turned off, on-off-cells,
- 30 % react when light is turned off, off-center cells,
- 20 % react when light is turned on and during lighting, on-center cells.
These 20 % are further divided in such that only react initially, and those that also react during continuous lighting.

Fig S-10-112-2

Since vision is built on light, on electromagnetic waves and the electromagnetic force (FEM), it is a reasonable question if the polar arrangements in the retina in some way could reflect the continuous changes between electric and magnetic factors in EM-waves. (In the interpretation of forces we have assumed the EM-force defined in d-degree step 3 - 2 with E and M as the complementary poles or fields.) One association goes to the light and dark rings on a detector screen when photons pass a small hole in a screen in experiments showing the double nature of light.

5. Several inverse features appear in the sense of vision:

  • The nerve cells get hyperpolarized (from ~ 40 mV to ~ 70 mV) when excited - instead of depolarized as in other nerve cells.
  • The photoreceptors secrete transmitters in darkness. (A condition for the sight signals is a continuous own activity in the cells.)
  • The receptor cells with their extensions are turned inwards in the retina of mammals.
       Besides that the pictures the eye delivers to the brain are upside-down.

Such properties could eventually be connected with the turn in main directions in the loop version of the dimension chain in step 3 - 2.

      Fig S-11

(Or with "the pole exchange" in d-degree 0/00 of our model where pole 1b from 0-pole defines a new anticenter 00' and pole 1a from 00-pole defines a new center 0'. See file General senses, figure Gs-6.)

6. Direction and distance to viewed objects:

These to properties in the visual field are registered in different columns in primary visual cortex.
   Direction seems defined through a difference in the storage of cells that receive signals from the two eyes: those from opposite eye lie gathered or tightly over one another in the column, those from the same eye are more horizontally spread (Nf p. 385).
   In other terms, the opposite eye seems to represent a center or the vertical axis, the eye from the same side the horizontal one. It corresponds to first polarization in d-degree step 4 →> 3 in our model. The differentiation becomes horizontal for directions as along a circle..
   Distance in the depth columns seems defined through equal, horizontal distribution of signals from both eyes (a bit vague expressed in the reference). Differentiation hence vertical. (It should also represent a step from vector to scalar.) An own interpretation of the reference below:

Fig S-12-114-1

Texts in this figure concerns actually cells in one single column. It's said in more general words that the vertical organization in a column concerns details and orientation, the topographic picture of retina the "place"; cf. in this sense directions (d-degree 4) - of lines and other details too - versus 3-dimensional space.

7. Layers in columns of cortex;

The deeper the research towards a detailed level, the more a stringent geometrical organization within biology is revealed. There is for instance also a strict order of fibers in the optic nerve. At first station where fibers cross over from one eye to the other side (lateral geniculate nucleus) the cells are arranged in 6 layers. Fibers from the opposite side go to layer 6 and 4 + 1, fibers from the same side to layers 5 and 3 + 2. (Nf p. 375).

Numbers from reference.

Fig S-13-114-2

Cf. 3 polarizations of 5 in a dimension chain, 0/00 (~ "6th" d-degree) as one of them.


Fig S-14-7-3

8. About number of cells in the human retina:

Human beings have about 125 million rods and about 6 million cones. (Also about 6 million bipolar cells) and about 1 million ganglion cells and fibers in the optic nerve (Aph). An interpretation of the very numbers:

Levels as in a dimension chain = 6.
5 radii on each level.
Gives 125 crossing points.
+ 6 along the central axis = 131

Suppose each level represents a 10-power.

We get the number 125 x 106 rods
and 6 x 106 cones.



Fig S-15-114-3



© Åsa Wohlin
Free to distribute if the source is mentioned.
Texts are mostly extractions from a booklet series, made publicly available in year 2000

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