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

1. The sense of equilibrium builds on the gravitational force (FG) as the sense of sight on the electromagnetic one (FEM). Early forms of chordates as tunicates had one receptor cell for electromagnetic waves and one "statocyst" as "gravitational organ" (Kz). In the history of evolution these organs could be regarded as the "first" specialized senses for external orientation. (The forces obviously still more decisive for plants!)
   Already in cyclostomes this organ for equilibrium has developed to sacs with 1-2 ducts, and sharks have the two sacs saccula and utricle plus the 3 semicircular canals in three directions as all later species and human beings.
   The organs for equilibrium originates obviously from the lateral line system of fishes, depressed canals along the sides with sensory hair cells.
    Hence, this is a further example of how the environment (the 00-pole in our model) is successively built-in into an organism as a center versus the surroundings, a 0-pole: one general principle view in the dimension model.
   A specialization of that lateral line system becomes the receptors for electric fields among species of fishes, which implies a step between forces FG/FA →> FEM

2. The organ of equilibrium becomes divided in 5 structural parts, differentiated in functions.


Fig Eq-1-115

Receptors are hair cells that react mechanically on the movements of the fluid endolymph in sacs and the 3 ducts at changes of body and head positions. They are embedded in christae (called macula in the sacs), one in each duct, one in utricle, one divided in saccula, hence 5 to 6.

There is a first polarization between sacs and ducts: while the sacs register static forces, the ducts register changes in velocity and directions of rotation, also a relation of the kind between a function and its derivative.
   The christae in the sacs react on motions along gravitational axis up-down and on linear acceleration. Compare our interpretation of outward acceleration (FA) as complementary pole to gravitation (FG) as inward acceleration. The hair cells in the ducts (the semicircular canals) react on different kinds of rotation of the head.
   This polarization agrees with our interpretation of external motions in dimension degree (shortened here d-degree) step 4 →> 3 of structure: a 1-dimensional motion developed to a 2-dimensional one (rotation) in d-degree 3. Simultaneously this opposition implies a step from the whole body to the part, the head.
   (Hence, hair cells in the sacs register linear acceleration, those in the ducts angular acceleration. This could also be illustrated with a figure of a dimension chain as angle steps, a polarity of 180° in d-degree 4, 90° in d-degree 3 as a transition to rotation.)

A functional differentiation between maculae in the two sacs should reasonably exist but isn't noted in the references here. It's only said (Mf p. 318) that the function of saccula is less known but eventually reacts on both linear acceleration and falling - possibly then both FA and FG in our terms? It's left as an interesting question.

3. There is however
in external form and in arrangement of the ciliated receptors (hair cells) in the sacs features of partial polarizations.
   In forms the sacs differ as "round" and "elliptic". An ellipse may be described as a circle, the center of which has been polarized into two focuses. (Cf. about the sense of hearing, the "round" and "oval windows" in cochlea.) The longer coordinate axis of the oval utricle sac becomes also to a certain degree tangential to the round saccula sac. The oval sac seems in this sense as an expression of the very transitional step 4 →> 3, to rotation. Followed by the breaking up of "volumes" into three perpendicular 2-dimensional planes, designed as "halved circles" of tube-shaped canals as one expression for d-degree step 3 →> 2. (2 vertical ducts, 1 horizontal.)
   Cf. 3-dimensional motion as "translation in 3 dimensions".

4. The arrangement of the receptors in the sacs differ too according to a figure in a reference (Zf p. 284): in the "round" saccula they are positioned both vertically and horizontally with a separate bundle of nerves from each, in the oval utricle only horizontally, showing on a step towards one-way direction.
   The higher d-degree of maculae in the sacs may also be seen in the mineral grains of calcium carbonate (the statoconia) that lie on cilia of the hair cells and through pressure and motions affect them. This in opposition to only fluid streams that affect hair cells in the ducts. It's a d-degree step in phase too of influencing matter.
   Further in details: in sacs the relation between the influencing crystals and cilia is vertical, in the ducts the influence of fluid streams on cilia is horizontal.

5. The "hairs" of the individual cells
are cilia polarized in two kinds: one big, single kinocilium on each hair cell, always at one end, and up to 100 smaller stereocilia in parallel rows. Essential for reaction of the receptor cell is if the stereocilia are bent towards the single kinocilium or from it.
   Here we have both the polarity unity - manifold of the poles 0 and 00 in our model and simultaneously the directions outwards - inwards, translated to a linear projection.
   In ducts the polarity of directions appears between vertical and horizontal ducts through opposite arrangements of the cilia: in vertical ducts the kinocilium is placed outwards from utricle, in the horizontal duct inwards utricle. Since a reaction giving a nerve signal is always the result of stereocilia bending in direction towards the kinocilium, it gives that vertical ducts in this sense represent outward direction, the horizontal one inward direction.

Another feature: in the sacs the hair cells give hardly any signals at ordinary position of the head. In the ducts they have a basic frequency which varies at different motions of the head. It seems as an expression for the increasing motional moments towards lower d-degrees of structure in our model.

6. Signals from hair cells in the 3 ducts
correspond to rotation of head in 3 planes, in at least northwest countries signs for "Yes", intermediate "Njae" and "No":
- Vertical plane = Front - Back | Dorsal-Ventral axes: posterior duct, rotation for Yes.
- Vertical plane = Front-Back | Left-Right axes: superior duct: tilting of head for "Njae",
- Horizontal plane = Dorsal - Ventral |Left - Right axes: horizontal duct: rotation for No.
   It may be noted that the half or decisive 'No' in these cases include the Left-Right axis, suggested to represent d-degree 2 according to number of polarization steps in embryos' development (Embryology, No. 8): a 'No' also connected with "inhibition", polarization step 2-1 in the nervous system.

7. The bundles of nerves become 6 with two from saccula, one from utricle and one from each duct (Zf p. 284). They join two and two, which implies 3 polarizations from the aspect of a main tract.
   The bundle from horizontal cells in saccula joins with the posterior vertical duct: this plane is defined by the primary two coordinate axes of an embryo, which we have interpreted as representing d-degree 4 and 3, the A-V- and F-B-axes. Some geometry guides surely this bundling. Could the horizontal saccula cells represent linear acceleration outwards, the vertical ones gravitation? Or the horizontal one both of these forces, the vertical as secondary one of them? Only guesses.

We can observe in the figure below that the 3 bundles are paired vertical (V) with horizontal (H) in ducts or relations of macula and ducts. Saccula as of higher d-degree has both types, a kind of double-direction.

Posterior duct V-1, superior duct V-2, horizontal duct H:


Fig Eq-2-116-2




© Åsa Wohlin
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Texts are mostly extractions from a booklet series, made publicly available in year 2000

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