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

First embryological development of an early chordate:
Some features regarded with aspects from the dimension model.

Elementary definitions in geometric and physical terms in the model with complementary poles in different dimension degrees (d-degrees):

            Fig Em-1

Whole 5 - Directions 4 - Volumes 3- Surfaces 2 - Lines 1 - Motions 0/00

Polarizing forces from 00-pole ~ from outside. Binding, integrating forces from the 0-pole, ~ from inside.
   If the dimensional model can be applied, one has of course to count on a multiple of processing steps at different levels of underlying and superposed dimension chains more or less simultaneously.

1. Forms in the first stages of development in an embryo of a lancelet:


Fig Em-2-11

- First embryo cell undergoes division into a filled ball - a "morula".
During continued cell-growth the filled ball get transformed to a spherical shell of cells, a "blastula". Its inside room gets filled with blastocoel liquid.
- A coordinate axis appears defined on the blastula in patterns of growth between animal pole (A) and vegetative pole (V).
- The following processes - the "gastrulation" - involves immigration of cell material at the V-pole into the cavity of the blastula forming a 2-layer bladder and further inner differentiations into tubes etceteras.
   The process can be interpreted in terms of steps in the dimension model:

2. Aspects on Morula →> Blastula:

The first step from morula to blastula is rather remarkable and it may really be asked what guides this transformation. It's mentioned in another context that outer cells of morula grows faster than the inner ones and it's is possibly one factor* but cannot explain why all cells of morula get "center-displaced" to a circumference.
   *Cf. in the dimension model velocity as corresponding to d-degree step 1 →> 0/00, represented in each d-degree step in the dimension chain outwards.

- It's an expression of Vdiv, of pole 4b in our model, divergence, a step center to anticenter, (c →> ac).

- In geometrical terms it's a step 3 →> 2 in d-degrees, from a volume, a 3-dimensional ball, the morula, to a 2-dimensional sphere, a surface, the one-layer blastula. (Each higher d-degree in relation to the lower one is a relation of the type c-ac, ~ 0 to 00: there is an infinity of surfaces in a volume etc.)

- In physical terms it's simultaneously a polarization of d-degree 3 into Mass - Space, as presumed in the dimension model, however inverted in relation to macrocosm: outer mass, inner space.
   (Cf. about the cell as an inverted atom. In atoms mass is concentrated to the center, space outside in the shell. Compare too the inversion of charge over a cell membrane in relation to an atom; negative charge inside, positive outside.)
- The polarity mass - space gets here the form of a step in phases between cellular (as "solid") phase (3) and the extracellular blastocoel liquid (2): note secreted inwards from anticenter.

- A third aspect on these first stages of embryo development is the relation between the properties Mass and Charge, presumed in the model to be related as d-degree 3 to 2 (although level of analysis is regarded as optional). Cf. gravitation, FG, connected with mass, assumed developed in step 4 - 3, and the electromagnetic force, FEM, in step 3 - 2.
   One application of this aspect is the mass of cells of the blastula sphere and the "ion balance" of the blastocoel liquid, appearing in experiments about exogastrulation, see below. (Cf. also gravity strongest at the surface of a body !).
   Another application concerns the poles A - V that develops or appear on the surface of the blastula.

3. Blastula to a 2-layer bladder and A-V-axis:

- In the dimension model the poles out of polarization of d-degree 3 have in elementary geometrical terms been presumed as circular (3a, with origin in the 00-pole and radial (3b, with origin in the 0-pole). These geometries show up in the growth of cell material: circular "downwards" from the A-pole towards the V-pole, radially "upwards" but inwards inner space from the V-pole.

Fig Em-3-12-1, Em-4-13-1

It confirms the identification of the two complementary poles, and concerns the blastula as a 3-dimensional volume polarized into mass - space in terms of physical quantities.
   Space in macrocosm is interpreted as expanding, an expression for the outward acceleration force (pole 4b, FA) as opposite mass connected with gravitation, and inward acceleration (pole 4a, FG). (With references here to files about forces.)

The pattern of growth reminds also of the M-field around Earth, divergent outwards at the North-pole, convergent inwards at the South-pole. (N-S-poles known through experiments to be asymmetric, hence the directions here.)

- The vegetative - animal poles V-A reflect also the physical properties Mass versus Charge from d-degrees 3 and 2:
   Cell material at the animal pole gives a) the nervous system, operating mainly with electromagnetic signals, b) the outer surface (d-degree 2) of the embryo, the ectoderm.
   Cell material at the vegetative pole gives invaginated a) archenteron and b) much of the other intestines, hence the nutrition system that operates with chemicals, in this sense mass.
   The two poles represent the two main systems of the body and its dependence of the environment, its role as "a half", with inflows from the surroundings.

- Geometrically the step to a 2-layer bladder illustrates further the polarization of d-degree 2 into outside / inside (convex/concave), the complementary poles of d-degree 2 in the dimension model: 2a: ectoderm, 2b: endoderm.
   It's said also that long projections of threads develop from the inside layer of the bladder and draw this inner layer towards inside of the outer layer. Hence, there is also a structural development of d-degree 1 in this process in agreement with the model..

- The remarkable invagination of cell material at V-pole as a main feature of life implies a negative or rather antipositive curvature inwards, simply expressed as surfaces growing faster than the square of radii. (A necessity if we imagine that there has to be room for a 5-dimensional unit within a 3-dimensional space!)
   In macrocosm there is possibly a negative or rather antipositive curvature of Space, as expression for the outward acceleration force FA, and the positive curvature of mass as expression for gravitation FG inwards. It should in the dimension model appear as a polarization of Euclidean geometry in d-degree step 4 →> 3,
   In the multicellular animal the same antipositive "curvature" gets inward directed, yet as in Space of macrocosm expanding from V-pole radially into space, while enclosed through positive curvature of the A-pole.
   (In a certain sense it becomes an inversion of macrocosm also with regard to what has the curvature: V-pole as representing mass reveals the negative curvature, leading to multilayer formations in inner space. While the A-pole, as defining the enclosed space, gets the positive curvature.)

- In the loop version of the dimension model where debranched degrees from higher steps outwards meet "the other way around", the step 4→>3 of polarization into positive / antipositive curvature leads to the step 2←1, the polarity inside - outside, forming the 2-layer bladder.

      Fig Em-5

- Simultaneously the processes implies that primary force of divergence, pole 4b from 0-pole outwards from morula to blastula, in these next steps is replaced by the complementary force of convergence, pole 4a from 00-pole in agreement with directions in the figure above.

- One general aspect on further steps of gastrulation is that material at the V-pole as originating from center-pole 0 takes back its position as center within the material from A-pole, which represents the anticenter from 00-pole.

What happens with the blastocoel liquid in the two-layer bladder? It could be presumed that this early liquid contains extra potent - 'highdimensional' - substances . Formally at least it seems to land up between outer and inner layer of the skin, between ectoderm and endoderm. The very rich differentiation of sensory receptor cells that later develops in the skin could perhaps partially depend on the blastocoel liquid being an early opposite pole to cell tissue in the blastula?

The character of V- and A-poles as originating from 0- and 00- poles and how these are interpreted in the dimension model becomes affirmed through the experiment called exogastrulation.

4. Exogastrulation:

The experiment implied that the ion milieu was changed in the blastula, which had the effect that cell material at the vegetative pole didn't invaginate but nearly separated from that of the animal pole (= exogastrulation). It turned out that the isolated cell material from V-pole went through several normal differentiations anyhow, while the cell material from the A-pole remained a formless hollow mass.
   Interpreted in terms of the dimension model a center-pole implies outward and hence differentiating directions, and it has always some kind of anticenter, an outside, a surrounding with a certain polarizing effect, even if not the appropriate one. It represents also the integrating force. While a separated anticenter, the 00-pole, represent the polarizing force and without a center, something to work upon, remains a hollow mess.
   Biologists draw the natural conclusion that the cell material from vegetative pole is the governing power in embryo development - possibly depending on a richer or less specialized cytoplasm in these cells (here we could say a more highdimensional cytoplasm). Notice that this is an old interpretation from 1970th. There are surely more knowledge now of how these facts are expressed biochemically.

5. The neural tube:

The V-pole as the guiding one is further stressed by the condition for the forming of a neural tube. Not until the invaginated inner material of the V-pole - the archenteron - has reached up to the A-pole inside the 2-layer bladder, the central area of cells at A-pole invaginates to a neural tube. Biologists talk about induction. It's obviously an expression for a binding force.
   In terms of the dimension model the contact between the poles A-V implies a kind of momentary depolarization, hence a lowering to a deeper, higher d-degree in which the direction from the A-pole becomes "vertical" and inwards as in d-degree 4, while it in first stages was circular as in d-degree 3.
   This close dependence between A-V-poles, shown at the very creation of the neural tube, is reasonably one condition behind the fact that nerve cells through their long axons can find their special inner organs in the body during the later development.

- In following steps of gastrulation, se below, the growth of material at A-pole becomes again circular but now along the inside of the surface, and the growth from V-pole becomes "radial", expressed in evaginations from archenteron: laterally to coeloms and upwards to cells for a notochord. Thus in accordance with geometries of d-degree step 3-2.

      Fig Em-6-14-1b

6. The tip over of the bladder:

The two-layer bladder "tips over", which implies that a second coordinate axis gets defined, the Front - Back one (F - B). By biologists this has been explained as a result of a "displacement of the center of gravity" through a change in the storing of cell material. It sounds as a rather vague explanation and it's natural to ask: Why this rearrangement of cell material, if so?

Fig Em-7-16

The tip over is a partial rotation, and in our model rotation is proposed as the 2-dimensional character of external motions in d-degree 3. That's one reason while we here assume that the tip over is an expression for the d-degree step 4 →> 3. The connection with changes of gravitational center and mass - as these concepts are interpreted in the model - agrees with the same view (gravitation as a force from pole 4a).
   Obviously the development of this new axis Front - Back is not a result of outer gravity and position or related to an external source of nourishment but endogen. The same should be valid for the A-V-axis, the development of which has been assumed by biologist to depend on a richer cytoplasm at the vegetative pole. Thus, reference to concepts as gravity and mass reappear here about the F-B axis.
   (Another reason to regard the axes as given from inside, of endogen nature, is that also unicellular flagellates include a central axis in direction of flagella.)
   If the A-V-axis could be said to represent d-degree 4 or step 5 →> 4, the new axis Front - Back may be seen as representing d-degree 3 or step 4 →>3. In angle steps as halvings it's a step 180° →> 90°, which has been assumed in this step in the hypothesis about dimension chains as angular polarizations.
   With the F-B-axis defined the inner, enclosed volumes turn to the lengthwise, tube-formed growth.

7. Mesoderm - the further development;

- The subsequent process of gastrulation implies the mentioned invagination of animal pole to the neural tube - and evaginations from the ventral pole, i.e. from archenteron: an opposition in agreement with our definitions of inward and outward directions from 00- and 0-poles respectively.
   In general terms the differentiation of inner V-pole material implies laterally secondary polarizations mass - space into creation of a true body cavity (enterocoelom) with enclosed tubes.

- The circular - radial polarity of growth from original A-V-poles characterizes also the further process as shortly mentioned above. Material around the A-pole and neural tube invaginates too (inward direction from anticenter) and spreads circular (from pole 4a to pole 3a in the model) along inside of ectoderm - while the evaginations of endoderm from central V-pole have radial and upward direction and becomes tied off parts. The "vertical" one becomes the notochord (and in further historic evolution replaced by vertebrae that comes to enclose the neural tube), and laterally (or in an angle as ¨45°") to coelom, mesodermal material.  
      Fig Em-8(6)-14-1b   

With the coelom and tube-formed growth along the F-B-axis the 3rd coordinate axis Left-Right (L-R) inevitably gets defined.

- One opposition of the type center - anticenter between V- and A-poles appear in their different contribution to mesoderm: from A-pole material it's in the form of mesenchyme, i.e. individual, immigrating cells; from V-pole material it has the form of cell layers: a difference in d-degrees of structure that shows on the more highdimensional force of integrating V-pole.

- Another step in d-degrees, 3 →> 2, is illustrated by the first development of coelom from archenteron in the form of lateral plates: 2-dimensional screens that grow to surround archenteron as a 3-dimensional volume (and also notochord and neural tube as volumes).

- A corresponding step in lower d-degrees, 2→>1, can be identified at the animal pole in the creation of a neural 1-dimensional wall from border of the 2-dimensional neural plate when this invaginates to the neural tube. A fold that also defines the central line between right and left sides. On a tissue level the process can geometrically be described in d-degree steps 2 →> 1 →> 0, with the last step represented by neural wall material invaginating to disintegrate into individual mesenchyme cells.
   The process as such could further illustrate what in the model here is the "pole exchange" in d-degree 0/00 of motions: pole 1a, "motions to each other" is shown by convergence of folds to the neural wall and then inwards. It defines according to the model a new 0-pole (0') from which we get outward direction, "motions from each other", as shown by the divergence of cells from neural crest inside ectoderm.

   Fig Em-9-14-1a

Further development of coelom:
The whole process looks roughly like repetition on the mesodermal level of steps from underlying, more elementary steps of gastrulation in 1- to 2-layer organisms. However reversed.
   With the conditions of a circular growth from A-pole and all new material having to enter through invagination from ventral side, the development of mesodermal coeloms seems to imply a kind of "pole exchange", a secondary "A-V"-axis turned upside down relative the original one:

Upwards - Ventral pole

Downwards - Animal pole
Fig Em-10

Material nearest first V-pole, "south of the equator" of a blastula sphere, should at it seems evaginate to front part of the lateral plates. After a split into 2 layers, the inner tissue layer thickens and becomes the somites that develop to striated musculature, shoulder skeleton among other things.
   Material "north of the equator", closer to A-pole on a blastula sphere, should invaginate later and with this view form the ventral, back part of mesoderm. After split of the plates the inner layer of these coeloms seems to be the origin of smooth, visceral muscles.
   Regarding directions, the striated muscles from front part serve outward locomotion, the visceral ones intestines etc. direction inwards with this functional aspect. A reversed A-V-axis could explain such data and also why striated muscles grow to an essential part of body mass.
   Below an effort, indeed very rough and approximate, to illustrate the outgrowth, separation and and split of lateral plates to coelom:

Fig Em-11-017-2

Geometrically the split of the 2-cell layer of lateral plates implies other kinds of inversions too in chordates who get a true body cavity:
- Directions outwards/inwards (step 4 →> 3) of layers get reversed - of natural reasons: Inner layer get the inward direction, becomes outside of intestines, while outer layer gets the direction outwards and becomes inside of skin or the abdomen.
- Layers of plates versus cavity can be regarded in terms of the primary polarity mass - space in d-degree step 3 →> 2 according to the model. Inner central cavity as divergent space becomes reversed to space as anticenter in relation to all intestines, which become more or less centralized masses. (Biologists explain the split of lateral plates as caused by "anti-affinity", which probably is chemically expressed in some terms of charge (a property assumed of d-degree 2 in our model). Anti-affinity corresponds to "motions from each other" in the model, pole 1b, which implies divergence and thus can redefine space as anticenter.

- The first split of the 2-cell layer of plates (d-degree 2 as the one of surfaces) to 2 layers can simultaneously illustrate the polarization in d-degree step 2 →> 1 in the model, into poles 2a - 2b as outside - inside. This should imply a definition of d-degree 1 according to the model, which here seems to be nonsense, if not the first rupture between the layers may be seen as such
   Another possibility is to regard the thin, small "bridge" between front and back part of the plates as a bit more substantiated expression for 1-dimensional linear connection. In this case the polarization would concern another direction, the F - B axis
   We have also that longitudinal "ridges" - as "linear" formations - develop in the neighborhood of these bridges, ridges which give material to organs for excretion of fluids (kidneys) and for gonads, the reproductive system; hence possible to see as the last step 1 →> 0/00 (~5') in our model.

Real development of the proposed steps above is mainly the opposite to descriptions above. 

A special question is why mesoderm gets so clearly divided lengthwise along the F-B axis in a front and a back part with only a thin bridge connecting front somites and back coeloms(In humans marked by the diaphragm.) It's a polarization to a certain degree complementary too. Do the lateral plates eventually grow out in 2 opposite directions? It looks as if the imagined "equator plane" of a blastula stage became more than virtual.    One aspect perhaps: Development of coelom implies that the Left - Right axis gets defined. Together with the primary A-V-axis (dorsal - ventral) it defines a plane that divides the Front-Back axis. Dimensionally it should in d-degree 3 be d-degree 2 as a potential surface that act as polarizing force.
   This third halving implies a mix of the earlier to complementary poles in two opposite directions, a division in 4 poles, hence the clear opposition between somites and back coelom.

8. Coordinate axes:

Coordinate axes become defined as results of polarizations between complementary "poles" (the poles also equivalent with partial structures).
   Each new coordinate axis is regarded as polarized into next one.
      Fig Em-12-18-2

The 3 coordinate axes developed as from angle steps between d-degrees:
- First axis A-V defined through d-degree step 5 →> 4, angle step 360°→180°.
- Next axis F-B defined through d-degree step 4 →> 3, angle step 180°→ 90°.
- Third axis L-R defined through d-degree step 3→> 2, as an angle step 90°→+/- 45°.

The d-degree steps represent also development of the three layers of 3-layer organisms:
- A-V-axis the 1-layer stage of the blastula,
- F-B-axis the 2-layer stage of the bladder that tips over,
- L-R-axis the 3-layer stage with developed mesoderm.

With the loop version of the dimension model (figure 4 above) we get the number of tissue layers connected with angle steps and coordinate axes in this way:

5 → 4: 1-layer stage: morula →> blastula: in opposite direction 1← 0/0 , the 1st axis A-V.
4 → 3: 2-layer stage: blastula →> bladder: in opposite direction step 2 ← 1, the 2nd axis F-B.
3 → 2: 3-layer stage: mesoderm develops: in opposite direction step 3←2, the 3rd axis L-R.
   (A halfway meeting of directions in this 3rd polarity: 90°→ 45°. One aspect on the approximately bilateral symmetry developed in this stage?)


s-p-orbitals in electron shells:
The evolution of coordinate axes from the blastula resembles how the "circular" s-orbitals of electrons in atomic shells are followed by the orientation of electrons along three coordinate axes in the p-orbitals. There is the similar process from s- to p-orbitals as in the embryo from 360° to 180° to 90° of polarities in orientation.
   In the next, higher d-orbitals, representing the middle step 3 - 2 in the 2x2-chain behind the periodic system, there are also electrons divided along axes in the plane quadrants, i.e. in angles of 45°.
   The axes correspond also to cleavages of cells at first stages of fertilized eggs in many organisms.

The A-V-axis, the first defined, mark as pointed to above the positions of invaginations, the primary inflows from the surroundings: 1) inflow of material (cf. Mass at V-pole, archenteron as first mouth) and 2) sensory inflow (cf. conducted through Charge, at A-pole). In this sense it represents the cell as "a half" in relation to its total environment as the other half, as the angle step 360° to 180° is a halving
   F-pole represents a secondary form of animal A-pole after tip-over of the bladder. Here an invagination occurs in this type of organisms, Deuterostomia: the secondary mouth opening, (inward direction from anticenter): an analogy to invagination of neural tube at first animal pole.
   The F-B-axis implies in relation to the A-V-axis a step from two-way direction to one-way direction mouth — anus in chordates.
   The direction of external motion gets defined, at least for most fishes and land living species apart from Homo Erectus, where the original A-V-axis dorsal - ventral give the direction A → V.
   The 3rd L-R-axis gives the approximately bilateral symmetry that also characterizes many 3-merous flowers.

The polarizations of mesoderm can be described as more or less parallel to the primary ones:
- inner versus outer layer of split sideplates analogous to polarization ectoderm / endoderm,
- somites versus ventral coelom parallel to front - back axis and
- later partial segmentation of e.g. striated muscles parallel to the lateral axis L-R.
(Paired organs as e.g. kidneys and ovaries seem to be the result of this 3rd coordinate axis, not otherwise necessary in themselves. Material from mesoderm takes part in these paired organs.)

9. A summary of dimensional views:

It seems surely too easy to identify the elementary geometrical forms proposed in the dimension model in this complex embryonic development. Yet, it's hard to explain the "invelopments" without a similar model.
   We have the polarization Mass - Space from morula to blastula, defining a surface, the circular versus radial growth during invagination from V-pole, a polarization outside - inside, which also implies the long projections between these as of d-degree 1 that draws the layers towards each other. (In d-degrees: Morula (3) to blastula (2) to projections (1). And behind these processes, necessary to assume, a field level of forces, guiding in first step the outward direction, in next step the invagination, equivalent with directions outwards / inwards. In all steps and further on expressed in d-degree 0/00 as motions from/to each other.


Fig Em-13

10. Some more general aspects:

a) Affinity:

Why do cells in the blastula keep together? Biologists refer to "affinity" between the cells and the formation of tubes is for instance explained as result of an especially strong affinity. Cracks or splitting of a cell material is referred to as anti-affinity. However, it's hardly an explanation.
   It's naturally another word for acting forces. These are certainly expressed in some biochemical substances but here these are assumed as just expressions for and "carrier" of underlying forces - polarizing/binding ones - in the same sense as photons are called carriers of the electromagnetic force.
   In the dimension model we have convergence from anticenter. (Cf. gravitation, strongest at the surface of a body.) On the chemical level there is the hydrophobic bond, corresponding to the nuclear force and appearing in cell membranes.
   We ought to imagine the atomic forces reappearing here, "extrapolated" to this multicellular level in reversed forms. (See further The Cell.)
   It could be observed that the embryological step morula to blastula have a certain correspondence already on the elementary molecular level with the step from tetrahedrons to molecular carbon rings, through sp-hybridization.

All primary physical quantities, regarded as a dimension chain, should naturally be expected as expressed and involved in the embryonic differentiation, with density, added as only conceptual quality in step 5 → 4: forces (d-degree 4), distribution of mass (d-degree 3), ion balance (charge, d-degree 2 according to suggestions here) as well as distances (d-degree 1) and time (d-degree 0/00 of motions) as in relative velocities of growth.
   Invelopment as such could in generalized terms be the effect of binding forces from higher d-degrees (2←1←0 from 5 → 4 → 3). The ultimate binding force behind the invaginations at animal and vegetative A-V-poles would be the binding forces from d-degree 5 between 0 and 00 leading to the creation of a multilayer organism within first poles.

On superposed levels similar "affinities" between individual multicellular organisms can form groups that may function as more or less one single organism, as among cnidarians: a 40 meter long "worm" of jellyfishes where position in the row defines their different organic function!
   Cf. human clans as well!

The polarizing force, the "anti-affinity", appears very early, as it's said that first cell division is initiated from cytoplasm of the fertilized egg cell. One to several divisions occur also within a first embryo cell of different species before the whole cell divides.
   It's said too that eukaryotic cells, even without nuclei (artificially picked out), odd enough can divide (one reference:
    What in membrane or cytoplasm induces this polarization? In any case a force from anticenter, a 00-pole in our model.
   The blocking of genes in DNA that differentiates activities of cells may also be regarded as a kind of polarization and occurs through molecules from outside.

(If we regard DNA as a kind of piano and should translate the 24 codons to two octaves of tones, perhaps the 5 G1-codons and the 5 C1-codons to the black tangents and the 7 U2-codons and 7 A2-codons to the white tangents, how should the melody of e.g. insulin or substance P sound? But DNA is sooner like a string instrument where blocking defines a tone, than a piano)

One factor behind the fundamental "affinity" that differs multicellular organisms from unicellular ones could perhaps be identified in terms of what is called "neoteny": a branch of evolution starting from a deeper, preceding level of embryonic development. Translated to the dimension model it would imply a start from e.g. level of d-degree 4 instead of 3, a still less differentiated one, where the binding force would be stronger.

Communication over distances in the developed body - such as nerves finding their special targets or hormones their receptor cells - is in reality the same kind of mystery as the old one how gravitation can act over distances in macrocosm. It could also be seen as an expression of "affinity". As in macrocosm, it's the forces in development of space that create the distances.

At some first cell divisions the individual cells can develop to complete organisms and obviously contain all information. Later cell divisions imply specializations.
   Hence, it seems necessary to assume that the division of a cell at this stage gives daughter cells that in some respect are complementary. Hardly in the genetic code itself. Perhaps in which genes that becomes blocked, although pre-decided somewhere in DNA and rooted in geometries. (Cf. Epigenetics.) Some essential information seems lacking about how such a differentiation between daughter cells is realized (at least here in used sources).
   Anyhow, such polarities at cell divisions could be suspected to be one factor behind communication over distances.

With the dimension model the distant connections could be apprehended in more abstract terms: an inner relation, represented by a higher d-degree get when polarized "inverted" to outer connections into next lower d-degree as a new potential, including new directions and a new distance. 
      Fig Em-14

Another aspect on the question is level chains. It's assumed in the dimension model that each step in a fundamental first chain can develop to whole new chains of 2nd order, steps in these to whole chains of 3rd order etceteras., which leads to a "level chain". (In the figure below illustrated as simple loops in each first chain steps.)

       Fig Em-15

An original close relation of a d-degree step in a basic chain can in this way develop to a very far one.
   Compare how mRNA is cut on its way to ribosomes: a way to reestablish the original basic relation in the hierarchy through cutting off the loops?

b) Processes of design as waves:

Tube-forms as archenteron and neural tube, which also were explained as results of extra strong affinity between cells, may be regarded in the same way as in- and evaginations of a cell membrane in a single cell, cut off to vesicles, serving import and export of material. (Cf. about the cutting of mRNA above.)
   They can be interpreted as the 3-dimensional external motion attributed to a 2-dimensional structure - the tissue level - in the dimension model.
   With addition of a 4th motional moment, the growth lengthwise along the front-back axis F-B the forms become "1-dimensional" canals on a macro-scale.

The wavy character reminds of the problematic turbulence of water streams where bigger whirls get translated into smaller and smaller circular whirls: a way to store a surplus of energy?
   Another parallel is found in meteorology: how high- and low-pressure "cells" are tied off from the Rossby waves around the North Pole. Why are they tied off? It seems necessary to assume that a certain area on the surface gets defined and demarcated with the border defined as anticenter, from which convergence leads to the tied off "loops" - as occurs with neural tube from neural wall.
   Tubes can also get designed another way as from d-degrees 0/00 inwards 1 and 2 from single mesenchyme cells when it concerns a fluid as blood.

In the dimension model it's a general hypothesis that the d-degree of motions increase towards lower d-degree of structure. Internal structural relations are stepwise released to external motions. Simplified: The opposition waves versus particles are seen as lower d-degrees of structure in relation to higher ones.

Segmentation could also be regarded in terms of waves. As previously mentioned the inner front part of somites gets segmented. Segmentation in the form of transverse bands takes also place of the neural tube during its embryonic development. That's quantification in rows of similar units, a linear repetition in first phase, which later may be more or less differentiated. (Cf. Evolution and segmented animals.)
   It should be noted that segmentation concerns typically front and dorsal part of the embryo, representing the earlier A-pole (00), corresponding to primary polarizing force in the dimension model.
   This feature of segmentation has the character of longitudinal L-waves lengthwise:
→ 0 ← 00 → 0 ← 00 → 0 ←... , a variation in density, assumed as first physical quantity in the model in step 5→4. Such linear, 1-dimensional L-waves are suspected on the field level, in d-degree 4 (as in gravitational waves if they exist). Cf. that they in typical, segmented species demarcate whole units of essential organs.
   In synthesizing directions, inwards from end of a dimension chain, motions to and from each other, it becomes one way to build 1-dimensional lines. On a molecular level it could be compared with the way globular proteins or units of collagen line up after one another.

Neural tube - vertebrae give in their relation another example of how elementary waves can be applied as aspect on design:
   The vertebrae come to enclose the spinal cord as magnetic field lines surround an electric conductor. There is a phase displacement too between vertebrae and segments of neural tube as between M- and E-components in an electromagnetic light wave, in this case a transversal T-wave.
   First notochord and the neural tube derive from opposite poles V-A in the embryo, which could underline the complementary polarity in this later design vertebrae - neural tube.

A general view could probably be to see the whole embryonic development as materialized processes, substantiated motional structures, or formulated as "captured internalized waves", whatever to mean by that.

c) Geometry:

It seems obvious that the position of cells in the blastula decides their later roles and functions. It could be taken as evidence for geometry as the guiding principle.
A general aspect from the dimension model is also steps towards more and more differentiations of directions, i.e. towards increasingly specialized ones. Cf. about level chains above.

The c-ac polarity center - anticenter appears not only in the first phases of whole embryo and the polarity along diametrical axes. Such polarizations occur obviously also within regions on the tissue surface, i.e. in d-degree 2
   Best known example seems to be the area around the animal pole, where the neural plate gets defined as center and surrounding circles of cells immigrate and come to differentiate in 8-10 separate cell types (Kz p. 116) - as from circles of different radii from the center (?). They include more peripheral types of nerve cells, glial cells that surround nerve cells, cells for membrane around the brain, cells for teeth, for cartilage and bone in cranium...

Fig Em-16-22-2

How position of a cell in morula - or generation number? - is translated to its position at surface of the blastula has perhaps been clarified during later decades (?) - but what decides the angle, demarcating the neural wall as border between immigrating cells and those remaining ectoderm?
   (Material that becomes mesoderm from archenteron is also anticentric around the vegetative pole.)

Induction, the term biologists use for certain processes, includes also special geometrical features in design. It's the same term used for how E- and M-factors influence each other in a magnetic field. Thus, it concerns how complementary biological poles influence each other, expressed with views in the dimension model.
   One essential example is the mentioned invagination of a certain area around the animal A-pole to a neural tube through induction by the invaginated vegetative V-pole when it reaches the inner "ceiling" of the early 2-layer bladder at A-pole. It represents a partial or momentary depolarization to higher d-degree of primary A-V-poles, where the upward direction of V-pole induces downward direction from A-pole. The induction should go via the higher d-degree as binding force and underlying, deeper level - as d-degree 4 in relation to poles 4b-4a of d-degree 3.
   More or less simultaneously (?) the "ceiling" cells of archenteron from V-pole develop to the germ for a chord or notochord, also straight upwards. It could point to induction as eventually mutual.

There is however something more in this process, perhaps from mutual induction. Vertebrae come to enclose enclose the neural tube. Material with origin from V-pole, principally radial and outward directed, become anticenter around material from A-pole, principally inward directed, which thus gets the role of a center.
   Another example is how the eye lens is formed: it requires the meeting between the eye cup from inside the brain with ectoderm from outside, which through this induction gets formed to the lens.
      Fig Em-17-23-2

In these and other cases it is not only a question of chemistry but of geometry, a center - anticenter polarity in the design and a "pole exchange". Divergence from some centers inside, convergence from outside leads to a structure where inner material become anticenter around outer material. Pole exchange" is in the model assumed to occur in last d-degree of motions 0/00, and a step 1 - 0/00 in either direction should be involved - as it is by definition in every d-degree step in a dimensions chain.

A question is how the surface area for invagination in these examples is defined, through a certain solid angle of virtual radii from inside?

Other examples of a similar geometry in the human body:
- Hypophysis from a pharyngeal pouch that come to enclose nerve material from the brain.
- Adrenal glands with the bark (ac) from intestines (vegetative pole, ~ 0) and their marrow (c) from the nerve tissue (animal pole, ~ 00).
- Oviducts in relation to ovaries.
- In skeleton ball and socket joints in hips and shoulders.

The aspect on the eye lens and its construction could be extended to the meeting between the whole organism as 0-pole and direction-specific environment as 00-pole: new complex centers could be expected defined at this pole-meeting on the surface of the organism and be built-in into new structures (as it occurs at the psychological level).
   Examples of course are sense organs but maybe also fin rays, where bottom, ground contact could induce rudiments of legs, of new skeleton parts under the skin...? (A geometric approach to the evolution...?)

      Fig Em-18-24-1

Gradual incorporation of the 00-pole is a more general formulation of the corresponding principle (cf. inward direction from the 00-pole):
- the incorporation of sperm chromosomes into the egg,
- the incorporation of surrounding space in neural tube and archenteron,
- the incorporation of external nourishment,
- on chemical level also the building-in of metal ions (00-poles in relation to non- metals etceteras.
   (Universe as a camel trying to pass through the needle eye of a cell!)

Number of cells becoming the human, amniotic embryo after a certain amount of cell divisions is said to be 4 - 5. All the other become coverings, some with the function to penetrate into uterus. Apart from the interesting number, it shows obviously that it is the geometrical position as center that indeed decides the potential for development. It confirms too what was find in experiments with exogastrulation described above.


d) Mass - Space:

Masses are built-in into vacant space in macrocosm and "vacant" space as primary antimatter built-in into atomic structure in microcosm. We could see gastrulation and multilayer structures as a similar double process at a size level between micro- and macrocosm.
   Surrounding space gets built into cavities as "negative mass" within closed cell layers in neural tube and archenteron, coelom etceteras., and these get built-in as positive mass in the cavities of the embryo.
   And as presumed in text about physics atoms "breathe vacuum" and are depending on surrounding "vacant space" for maintaining their structure as atoms, so the embryo with archenteron and neural tube supports itself on its environment.
   *(File about the atom in Physics not yet translated.)

A multilayer creature from repeated positive - negative curvature:

      Fig Em-19-22-1

A note:
It's easier to visualize the whole embryological process in d-degrees 3 - 2, and perhaps we should imagine the process as a stepwise "inversion" of deeper levels through step 3 — 2 to superposed ones?

The cello string - an association:

A speculation, without any knowledge, about vibrations in a cello string:

Fig Em-20-28-2

Quantification of waves with obscure allusions to biology:
   Fig Em-21-28-3

Displacements of side-waves through new vibrations as "serial inlays" from the middle. With half-steps: in every second step bellies in the middle, in every second nodes, witch imply tied off centers.



© 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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