1. Relation between organs for equilibrium and hearing:


   

Fig H-1-117-1

We have assumed that gravitational waves, if they exist, are of the longitudinal, linear type: → ← → ← → ← So are sound waves, conveyed through variations in pressure on the tympanic membrane in cochlea. Pressure is a quantity F/m², the force F here an inward directed one as is gravitation. Thus, it's rather natural that the sense of hearing is developed in close relation to the sense of equilibrium, even though it sometimes has been called a 'mystery'. (Cf. 'pressure' as increasing 'Density', proposed as only term for first physical quantity defined in step 5 - 4 in the model here, before gravitation gets defined in next step.) 

The organ of equilibrium concerns own position and movements of the individual, in this sense referring to outward activity from the organism as center, a 0-pole. Hearing is primarily an organ for input, impressions from outside the environment, from the 00-pole. Hence, the two organs may be interpreted as representing a polarization in directions outwards →> ← inwards, which may be one factor behind the differences in developed structures.

Hearing is also "time displaced", later developed during evolution. A small canal from saccula in the organ of equilibrium develops to a tube which grows during evolution, becomes a bent tube in reptiles and then the convoluted spiral in cochlea of mammals (figure above).

In the dimension model the outward direction for dimension degree (d-degree) of structure: 5 →> 4 →> 3 →> 2 →> 1 →> 0/00 gives the opposite chain from 0/00 stepwise inwards to 5 in d-degrees of motions.    The development of the organ for hearing from first a "linear" tube to rotating spiral could be apprehended as a substantiation of the pattern of motions of increasing d-degrees. (In opposition to the structures in organ of equilibrium, from sacs as volumes to half circle bows with functional steps towards increased d-degree of motional reaction from linear to rotational movements.)

Fig H-2-117-2

2. Number 3 in structure appears in cochlea too:

- Spiral turns - like shell of a mollusk - are nearly 3. In cross-section it gives number 5 in-out as 1-2-3-2-1.
- The auditory ossicles in middle ear are 3 in mammals (Reptiles have only 1 but already among ray-finned fishes one finds 3 small bones on each side of the 4 first vertebra that convey pressure changes from swim bladder to the labyrinth (Kz).
- The inner of cochlea tube becomes divided in 3 canals.

3. Cochlea and organ of equilibrium as one dimension chain:

In the spiraled tube of cochlea the anticentric canals with perilymph are those in which the pressure waves from outside are transmitted in - out. The middle, central canal with basilar membrane contains enclosed endolymph, the same as in the sacs of equilibrium organ.
   Cochlea and organ of equilibrium are joined through the mentioned very small canal for endolymph from saccula to the middle canal of cochlea.
   If we identify parts of the equilibrium organ as expressions of d-degree steps, saccula with step 5 →> 4, then the small connecting canal could be identified with the debranched degree in that step: hearing as derivative of static pressure formed by that debranched degree in opposite direction?

Fig H-3

Cochlea as from debranched d-degrees.
Figure above broken to positioning of right part straight above the left:

      Fig H-4

Two other small canals connect endolymph and perilymph respectively to the brain:
- One departing from between saccula and utricle (as in step 4 →> 3, marked in the figure above) for endolymph, going to the dura,a layer near the space for CSF around it. (Cf. CSF departing as a side branch from 4th ventricle to circulation around the brain.)
- One, containing perilymph, departing from cochlea (?, divergent information in sources), going parallel with the preceding one to the subarachnoid space between membranes of the brain, in closer contact with the CSF liquid.
   The three canals seem to illustrate ramification (polarization) of degrees and join the two organs as to one dimension chain.

If the ducts of equilibrium organ only contains perilymph (according to Nf p. 396) or, which seems more probable, in similarity with sacs and cochlea includes endolymph too as later illustrations show, is left here as an open question.

It seems possible also to describe the opposition between the two organs in terms of centric - anticentric lymph:
- It's motions of the centric endolymph that directly activate the hair cells in organ of equilibrium.
- It's pressure waves in the anticentric perilymph that Via a membrane effect the endolymph and hair cells in cochlea.

4. Oval - round window and upper - lower canals:

Pressure waves from tympanic membrane are conducted to the oval window into perilymph, upper canal. Through a small hole in apex of the cochlea the pressure can turn to outward direction in perilymph in lower canal and to the round window.
   Here is once again the polarity between round and oval forms, as a step of polarization one to two focal points, connected with the polarity outward - inward direction (and ultimately with 0-00-poles):

- ac - oval window →> inward direction - upper canal.
- c - round window←outward direction - lower canal.

"Upper" versus "lower" as between distal versus ventral sides in the whole nervous system. This latter polarity is defined through the features of the middle canal:
- basilar membrane with hair cells on the wall to lower canal,
- the flap of a membrane (tectorial membrane) that lies over the hairs and affect these from the wall to upper canal.

5. Cochlea as illustration of forces:

a. It's the difference between the pressure forces inwards on the oval window and outward on the round window that decides the effect on the receptor cells in the middle canal (AM), hence a kind of derivative.
   Suppose that we associate the force in pressure (F/m²) inwards on the oval window as derived from gravitation (FG) and the opposite direction of pressure outwards on the round window as derived from the outward acceleration force (FA). The change of directions inwards - outwards in the small hole at apex of cochlea have the character of a "pole exchange", presumed occurring in last d-degree 0/00, equivalent with 5' in the dimension mode. (Cf. what happens in the "bottom" of black holes!)
   From apex an d-degree 0/00 of motions the growing spiral of cochlea illustrates the substantiated 4-dimensional motion assumed in the model of a linear 1-dimensional structure.

      Fig H-5

b. Association to magnetic fields - and d-degree of motions:
The whole cochlea along the length axis gives in cross-section the picture of anticentric motion of canals and pressure waves around the central axis with its nerve fibers from the hair cells.
      Fig H-6-118-1

It reminds also of the magnetic field around an electric cable. In files about forces and electromagnetic waves the magnetic factor is suggested as "the son of" gravitation in the following d-degree step 3 - 2. (FG as one of the two forces in d-degree 4 and step 4→> 3.)
   Then, a magnetic field around the electric nerve fibers could be partly responsible for the structure of cochlea?
   However, the graded radii of circles demonstrate simultaneously what we in file about motions have suggested as a 4-dimensional motion in d-degree 1 as "pumping".

6. Two gradients:

The form of the bony cochlea, from the outer broad base towards its inner apex corresponds to inward direction from anticenter to center, 00 →> 0. The basilar membrane with hair cells in its middle canal has the opposite structure: most narrow at the broad entrance of cochlea, widening toward its inner, narrow apex as direction 0 →00. It gives the principle structure of two opposite gradients in each other:

   Fig H-7-117-3

Breadth of the basilar membrane furthest out in relation to furthest in is 1/5 (Nf) - which perhaps could be seen as expression for relations in a dimension chain?
   The construction feels odd* with regard to space but reveals and underlines the clear, complementary polarity of type center — anticenter, receptor structure versus the surrounding bony cochlea..
   * (Is explained by the smaller size of central axis nearer apex.)

The figure of gradients could be compared with directions in the production of lymph, fluids in opposition to structures a phase relation of the type 00 to 0:
- The endolymph is produced and secreted by specialized cells in the middle canal of cochlea (Aph p. 578): hence in direction inwards with the dimensional interpretation above, from organ of hearing to that of equilibrium.
- Perilymph has the similar content as CSF and it would be logical to presume that it derives from the other end, outwards, perhaps from CSF in the brain? (No information available.)
   It should imply opposite directions of currents in accordance with the c-ac polarity but as motions of fluids reversed in directions in relation to structures of the organs.
   A similar reversal appears in relative charge compared with the inner of a cell and its extracellular environment: Central endolymph is positive (+80 mV) in relation to the anticentric perilymph. It doesn't depend on the ion balance; endolymph as central contains much K+ as the inner of cells, perilymph much Na+ as the fluid outside cells, but here it's the perilymph that contains most proteins, responsible for most negative charge within cells.
   Both these reversals could be regarded as results of the opposite directions in the structure according to the suggested interpretation - and most likely as phenomena on different levels.

From the picture of two gradients it follows that basilar membrane with divergence inwards has its origin at anticenter of the body. Generally, receptor cells represent the inward direction in the main polarization of the nervous system in the sensory - motor pathways, thus could be said to have their starting point as 0-pole furthest out at the surface. (They derive obviously also like the organ of equilibrium from the lateral line system of fishes.) In this sense the anticenter becomes built-in into center, the central, endolymph canal in cochlea.
   The bony cochlea becomes the inverse, produced from inside out from temporal skull bone. Diverging outwards it encloses the basilarmembrane and inner canals.
   Such a feature of design, where tissue material from inside becomes anticentric to invaginating material from outside, recurs in several cases in embryology (No. 10 c).

The basilar membrane has its highest density as stiffness at its "0-pole", nearest the entrance, making it a gradient of density. Cf. "density" regarded as first physical property defined in d-degree step 5 →> 4 in our model.

   Fig H-8-121-2

Highest frequencies are registered nearest the entrance, the "0-pole" of membrane as gradient.. It's partly depending on the higher density of membrane here. Cf. EM-waves where higher, more energetic frequencies originate from center of an atom. Long wavelengths, lower frequencies reach their maxima further in towards apex where membrane are broader.
   
 In musical terms we get the deepest "fundamental tones" at apex of the cochlea, the center of other gradient, its "overtones" further out in cochlea; in this apprehension in opposite direction from deeper levels to superposed. What's fundamental and depth must obviously here be seen as decided by the waves in perilymph, not the membrane in itself.
   In agreement with this latter aspect, signals from apex (lower tones) are registered by centers in the brain at the ventral side, signals of higher frequencies from the entrance at distal side, sides corresponding to 0- versus 00-poles in the embryo (Nf p. 409).

7. Arrangement of hair cells:

The arrangement of hair cells on the basilar membrane seems to reflect the construction of the whole cochlea: 3 outer rows of hair cells, with cilia in V- or W-form turned inwards the central axis, as mirroring the 3 spiraled canals, and one inner, linear row of cells with linearly arranged cilia along the central axis with ganglions and nerve fibers. In cross-section of the cochlea it appears as one version of the radial / circular poles 3b-3a in the dimension model.

Fig H-9-119-1

Cilia, the "hairs", of the outer cells are also arranged in 3 rows on each cell, in 2 rows on inner row of cells. Number of cilia on each of the outer 3 rows is about 100, on inner row about the half, a relation ~ 2/1 (Nf p. 398).
   
Outer hair cells are more sensitive to motions inwards the central axis, the inner ones more sensitive to lengthwise motions along the axis (Nf p. 399): another expression for the same geometry.   

There are also nerve fibers of two kinds, transversal ones from outer to inner cells and to the central axis, and lengthwise spiraling ones.
   
The polarity center - anticenter is expressed in many ways.

- It seems as if the outer hair cells "activate" the inner ones (AM), if so just as well as it is the pressure waves in anticentric canals that activate all hair cells. It should be logical with the sensory nervous system as inward direction and anticenter pole as the polarizing force in our model.

- A further example is the polarity converging - diverging signals in the coupling of nerve fibers: signals from about 10 outer hair cells converge to one nerve fiber (convergence from anticenter), and the signal from each inner hair cell is spread to about 20 afferent nerve fibers (Nf p. 402), i.e. diverge. (Divergence from a center pole.)
   These relations should imply that outer rows of cells summarize impulses over a broader part of the basilar membrane and that it chiefly is the inner ("linear") row of cells that discriminate between frequencies in sounds.
   It looks like the polarity in every nerve cell is transformed to this whole multicellular system: amplitude modulation (summarizing) of incoming signals and frequency modulation of outgoing signals: principally perpendicular entities.

   Fig H-10-119-2

8. Wave forms:

Frequency and amplitude as complementary energy forms become translated in different ways in the pressure waves and basilar membrane:
   Higher amplitudes increase the bandwidth (~ lengthwise) of frequencies, however most for high frequencies (Nf p. 408). Low amplitudes give more narrow maxima. It could illustrate the principally perpendicular relation between these forms of energy as between circular and radial poles out of d-degree 3, originating from anticenter and center respectively in our model.
   An illustration of the principle:

      Fig H-11-121-4

The increase in bandwidth at high amplitude of sounds and the inverse at low sounds could be compared with the relation between high and low temperature, another form of energy that seems analogous:
   High temperature (to compare with high amplitudes of sound) corresponds to great spread of particle velocities, low temperature to more equal velocities of the particles. Principally it gives heat and cold as properties at straight angle to one another:

   

Fig H-12-122-1:

As mentioned above, density (~ stiffness) as a factor behind the frequency distribution on the basilar membrane is in the dimension model proposed as first "physical quality" defined in d-degree step 5 - 4. Temperature as motion of quanta is as "physical quantity" defined in last step 1 - 0/00. A correspondence seems natural with the loop version of the model in mind.

About frequencies (f), there is the other polarity between high and low f:
- Long sound waves (low f) have long rise times, i.e. reach their maxima further in, nearer apex, but have steep, short fall times.
- For short waves (high f) it is the reverse: short rise times, longer fall times. (High f at the entrance = "0-pole" of basilar membrane.)

      Fig H-13-122-2

Rise and fall times correspond in this way with the main direction of basilar membrane in the illustration of gradients above.

9. Inhibition.

Inhibition of the lateral type between receptor cells isn't found in the cochlea. There are instead efferent nerve pathways from higher nuclear centers in the brain whose axons have synapses with the hair cells. (It seems to imply that hearing is an active, discriminating process!) This "antiparallel" inhibition from higher centers could in terms of the dimension model show hearing as a sense of higher d-degree than for instance sight with lateral inhibiting cell layers - or just on hearing as a later sense in the history of evolution, geometrically less developed?
   Inhibiting nerve fibers from higher centers go to the outer rows of hair cells (TA p. 88), whose activation of inner row of cells consequently should be hampered. If so, an example of indirect inhibition in two steps, inwards in a level chain:

   

Fig H-14-120-2

In the sensory system as inward directed, the outward directed activity from inside, (fundamentally associated with the motor system), thus becomes inhibiting. In its function also serving contrast:
   Activation through these efferent pathways on tones just above or under a certain tone can have inhibitory effect on the frequency of this tone (AM-Hf), in this sense an indirect "lateral" inhibition between receptors.
   Certain cells in cochlear nuclei are inhibited by tones with frequencies on both sides of its own frequency, other cells only by frequencies on one side, above or under its own (Nf p. 410), a differentiation corresponding to further polarizations and increasing "one-way-direction". (Cf. similar polarizations among on-off-cells of ganglia in retina.)

   (Hearing impairments often occur ½ - 1 octave above the frequency of the injurious sound but can also spread to lower frequency areas (AM-Mb). Thus, it becomes a natural question if such injuries depend on too strong (killing) inhibiting activity from inner, higher centers (?).   )

Fig H-15-121-1)

Another observation is that signal answers from hair cells depend on velocity of changes in stimulating tone frequencies. Fast changes give higher, narrower spikes, more distinct discrimination of frequencies (Nf p. 412) in cells of higher centers (nucleus cochlearis). It shows on their property as derivatives, developed in many senses, one feature that reveals d-degree steps - as in mathematics. (Velocity tentatively presumed in the model here as the physical entity for the very d-degree steps, distance/time.)

10. Number of hair cells and nerve fibers:

Data vary but one reference says hair cells in a human ear are ca. 15000, nerve fibers from cochlea 25000 - 30.000 (Nf p. 398, 400), thus up to twice the number of cells. (Ca. 12000 in outer rows, 3000 in inner row, a relation 4 to 1 - or 4 to 3 in individual rows of cells.) The number of cells happen to be ~ 10³ times the sum of a dimension chain, number of nerve fibers sum of the poles in this chain:

     

Fig H-16-120-1