Biology / An elementary 5-dimensional model applied in different sciences
- some general aspects on life as such based on the dimension model -

What characterizes life?

Life may be seen as a natural continuation of fusion in the sun, outsourced to the planet (an "A-Z-illustration" .here). The force that binds protons gets replaced by the complementary force binding electrons. It's noteworthy that it's the unsaturated atoms with shared lack in their electron shells that build the main structures of life, not the self-sufficient ones with surplus.
   Life as continued fusion is not a merely banal aspect. The covalent electron bonds as complementary seems to follow the similar scheme as shown on this site:
- The genetic code shows astonishing numeral connections with the 2x2-chain (x = 5-4-3-2-1-0) behind the periodic system, with half this chain times 25 of some unknown reason. (Scientists with interest in the field of applied mathematics are invited to search for explanations!)
- The nearly universal genetic code agrees numerically still closer with a variation of half the same chain: the cubic roots of 5-4-3-2-1 squared times 100 (the ES-chain).
- It could be remembered too that flowers have 5-4-3 number plans - surely of some fundamental genetic reason.

Life from inversions is another aspect proposed here. It could be mentioned first that 2 times inversion of sum of all integers 1-110 (110 = the sum of the 2x2-chain) gives the sum of the amino acids from the genetic code as periodic number.
- The cell appears as an inversion of an atom (H, hydrogen) - both regarding forces and charge but also as it may be in a basic number of its the genetic code from the inverted mass quotient proton/electron.
- As pointed to in files about biochemistry the inversion of number 7 seems able to give a code for synthesis of substance as fatty acids and collagen.
- One suggestion is that life could have its ultimate root in the 7 so-called "undeveloped" dimensions calculated with in the String theory.
   About geometries, biologists of profession often give descriptions in geometrical terms. The same views here are thus partly about highlighting and formalizing these aspects.

Biologists' explanations have most often been of the teleological type: "Why 4 feet?" They are practical for land living animals. (Yet some fishes got them already in the sea.) It's naturally assumed here that the evolution contains more than random mutations and "natural selection", and the fundamental view sides with theories about a hidden "black box", here suggested to contain a scheme of the background model type or the like if simplified to fundamentals.
   The individualization of life remains perhaps the most difficult to understand Cells appear as a kind of "singularities", as points of Zero and Infinity in the same place, 0 and 00

Some numbers:

- 5 - 4 bases (from 2, hypoxanthine - orotic acid): G, A, U, C + T
- 5 x 4 amino acids (ams) with 4 x 3 x 2 x 1 = 24 different codons
- 5 histones (proteins on which DNA-chain is rolled upon in chromosomes)

- Valences for essential elements of life: 5 - 4 - 3 - 2 - 1; P - C - N - O/S - H
- 5 C atoms in the A- and G-bases, 4 in U- and C-bases.
- 5 C in ribose, part of nucleotides.
- 4 - 5 rings in the porphyrins.

- 4 - 5 - 6 cyclic processes have been considered necessary for "life":
Marquand asked how many chemical processes that a system should be able to catalyze for it to count as life. Haldane suggested at least 4, Marquand himself says 5 - 6.

Perhaps the most obvious and essential character in the structure-building for life is the fact that it is performed by nonmetal atoms, characterized by mutual lack in relation to the octet rule; this in opposition to self-sufficient atoms and those with a surplus of e-. It's mainly constructed of C-N-O, as if the carbon-nitrogen cycle of nuclear fusion in the sun just continued, outsourced to planets for transformation into external relations.

1. Life as the antithesis of entropy:

The way outwards in a dimension chain implies that structure gradually gets translated into motions, ties as potentials get broken; it's a trend toward increasing "disorder" according to views in physical mechanics, equivalent with direction towards increasing "entropy". (Yet, it may be discussed if the released motions of macro- and microcosm in reality are disordered?)
   Life implies a shift towards more structure, synthesis, creation of links, well recognized as the antithesis of entropy. However, it demands energy from outside to uphold its life.
   Life processes involve both synthesis and disintegration and can be illustrated by double-direction within the dimension chain (with development of new levels proposed as perpendicular to the basic chain).

2. Life a coincidence?

Life is here naturally postulated as a given result from "laws of Nature", a virtual, built-in possibility under certain conditions, not a random coincidence. It's assumed as a given result from the development along the main axes through the level chain towards increasing complexity. (See figure at end of this file.)

3."Negative curvature":

It's proposed that the most characteristic feature of Life could be regarded in terms of "negative curvature inwards" (cf. "involvement"). This in opposition to the eventual negative - or rather antipositive - curvature of expanding vacant space outwards in macrocosm, (This simply expressed as surfaces growing faster than the cube of the radius.) About curvature of macrocosm, see file here.)
   Most obvious is this feature of antipositive curvature turned inwards in the development of multicellular animal organisms (see file Embryology) but also in eukaryotic unicellular ones. The fast growth of surfaces occurs inwards and results in multi-shell structures. Cf. the outward growth of crystals for instance

(If a 5-dimensional unit, developing towards growing superposed levels, shall get spatial form within 3 dimensions, much has to happen internally out of this contradiction or tension.)

We could associate to the String theory and its 7* so called "undeveloped" dimensions. As a guess they could relate to the ordinary 4 developed ones of ordinary physics in a similar way as mathematical "conjugates" to each other. Perhaps be the very root of life!?
   *(There are many ways to count dimensions.)

How the single cell first was created is still unknown but it may be assumed that some kind of a substantiated center - anticenter polarity between complex molecules had to be defined within which the positive — negative curvatures developed, expressed in very general terms.

The turn inwards of the antipositive curvature could eventually be connected with the pole exchange in last step of our model in the dimension degree (shortened here d-degree) "0/00" of Motion. This redefines d-degree 5 in terms of pure kinetic energy and may simultaneously imply a kind of feed back mechanism.

4. Life as self mobility:

The "negative curvature" inwards, the expansion internalized, means more and more enclosed motions according to the model. One characteristic of life. (Life to regard as time-loops internally stored into spatial units - or spatial units transformed and fragmented into "ten thousand" times?)
   However, this would be only one part of the answer to the "self mobility". The other has to do with the relation between the single cell and its environment, center - anticenter, 0- and 00-poles of the whole.

5. Life as ½:

A living organism as the single cell is "haploid" (½) relative the environment - as a center versus anticenter in the big level chain leading to birth of a cell. This essential haploid character concerns all internal levels and stages of development in the cell. It's expressed as "needs".
   "Needs" become potentials originating from the primary polarization: cell - environment: potentials that have been differentiated internally in a lot of different directions, an intricate network of roads. Referring to our dimension model, the elementary polarity cell - environment as 0- and 00-poles define Direction, d-degree 4, polarized inwards/outwards; that's forces for the interaction of living cells with the surroundings such as inorganic matter, energy, water, air…
   Incorporating of elements from the surroundings into the cell may be regarded as one aspect on life as developed through negative curvature inwards. In another context we have expressed the general principle as a stepwise building-in of the anticenter pole into the unit defined as center.
   One example is the incorporation of metal ions in cell structures of non-metals, e.g. Mg in chlorophyll. Compare too our hypotheses that such a principle also may concern atoms, their structure depending on built-in vacant space. (If so, the negative curvature inwards should perhaps not be a feature regarded as restricted to what we generally call life.)
   "Vacant" space can be defined as antimatter on the atomic level, the environment becomes antimatter on the biological level.
   In general terms the stepwise building-in of the anticenter is a natural expression for the binding force between complementary poles.

The chemistry of life is characterized by more or less closed, "cyclic" processes in communication with the outside world, and a cyclic process, similar to rotation, means geometrically more of one-way direction. Increasing one-way direction is assumed in our model as one main feature in the development outwards of dimension chains. It implies that directions become more and more specified.
   It's a remarkable fact that not only cells but also individual molecules can wander between others towards given addresses - as people in a city on their way towards certain destinations.
   The addresses of pathways can be interpreted as a complex network of potentials from previous polarization steps, which means that the molecules are linked on large distances via underlying levels of space and time - similar to human memories of past acquaintances and contacts in the past. Wandering of molecules, governed by needs, becomes in this way also an expression for the cell being "one half" on its plentitude of internal levels.

Finally, asymmetries become one result of complementary halvings of dimension chains in steps towards more of one-way direction. One example is the selection of L-amino acids among the genetically coded ones in most organisms. An optical activity that involves polarization - polarized light.

6. "Instinct" of self-preservation":

That which usually is described as the self-preservation force of life can simply be the result of and expression for the binding force between the organism and the environment as poles out of an original whole: the organism as center one "half" with navel string downwards the staircase of levels in Nature with bond to the other half, environment as anticenter. The lower level is binding force on the superposed one according to postulates in in the model.
   Fig Li-4-6-2

7. Reproduction:

As is proposed about light beams through empty space, the chromosomes (as "lumosomes") complete themselves from environment, that's from what on their level is "antimatter", i. e. the manifold of separate complementary nucleotides, followed by polarizations. It's on this level an expression for the same pattern as in an L-wave: → ← → ← → ←... Generations of cells appear as propagating waves, propagation of quantified energy packages.

Besides this aspect on reproduction as succession, it's simultaneously a manifolding of one cell to many, a repetition of the process with divisions 1-2-4-8... in all directions. If it would be possible keeping to the analogy of propagating waves, it would be necessary imagining not only L-waves, in a certain sense linear, or T-waves as in the same sense 2-dimensional but waves of a higher dimension. (Compare perhaps where a photon exists on its way to a screen in quantum mechanics? In some descriptions "everywhere".)

As far as scientists know, so far, all life springs from other life - nowadays at least. Does then all life on earth derive from a single first cell 3-4 billion years ago? It is a rather curious thought that only a single point on the entire surface of the Earth would give birth to a cell, assuming that the cell is a consequence of laws of Nature. Similar chemical conditions must have existed in many places. Amounts of cells can have come into existence that were similar because the same natural laws were applied and the same surrounding conditions. If so, it would be changes in the environment that later made life depending on heredity. (Theoretically however, the initial conditions for emergence of an entire cell should be possible to produce in laboratories. )

8. Life as demarcated units

Demarcation, individualization, is a vital condition for life and perhaps the most difficult problem in explaining the occurrence of cells.
   There is in fact the same problem with the creation of atoms from Big Bang (protons as packets of the assumed 3 quarks, the 3 divided 2 plus-charged, one minus-charged, 5 → 4 →  3, the 3 divided 2 + 1). Hardly easier to "explain".

Atoms and cells are building stones on very different levels. Underlying levels represent higher d-degrees than the superposed ones and are binding forces in relation to these (general view in the model).
   It's logical that the H-atom becomes the original first integrating force of the cell as polarized into H+ and e- (as d-degree 5 polarized into 0- and 00-poles in the model, secondary binding and polarizing forces)..
   A cell may in several respects be interpreted as inversion of n atom (see further The Cell).

Inner, underlying level unity gets also according to the model "inverted" to outer potentials, expressed as bonds, in lower d-degree (as "polarized" photons in quantum mechanics?) It's like the more fundamental history when fusion in the sun gets outsourced and "inverted" to molecular constructions on the Earth. The big step from the atomic level to a cell and outer atomic relations implies an immense increase in degrees of freedom, even if already a C-atom has several (cf. CO2 and the steps between sp3- and sp2-hybridizations).
   One aspect on the problematic demarcation of cell units becomes the negative curvature inwards as a reversal of the relations mass - space, between elementary forces FA - FG in macrocosm, Mass built-in into Space, to Space into Mass in microcosms of cells. Cf. in Embryology the "blow up" of morula to a demarcating surface as a step center to anticenter, followed by involutions.

About forces, protons and electrons, H+ and e- that represent most of mass and most of space respectively in the atom, become "carriers of forces", in the same sense as bosons on the physical level (the assumed gravitons and photons etc.) As responsible for elementary chemical processes and bonds in cells they appear as poles 1a — 1b (+ / - ½) in last step of the model, defining the d-degree of motions in the dimension chain. The "pole exchange" in d-degree 0/00 implies also a kind of inversion in fundamental directions.
   With increasing complexity molecules as enzymes and coenzymes become forces in the same physical sense on superposed levels, polarizing - binding ones, "carriers" of the vital force.

Aggregations of micells as P-lipids during different degrees of density has been studied in search for an answer on demarcation of cells. Actually, inversions seem to characterize lipid layers according to studies of lipids in later decades, different structures with P-groups of the lipids inwards or outwards (Wikipedia). 
This ability for inverting the structure seems connected with the P-group, phosphorus with valence 5. With a dimensional interpretation of valences the d-degree 5 is polarized in center and anticenter and directions outwards/inwards of d-degree 4 in our model. On the deep, atomic level the phosphorus atom P with valence 5 could represent the basic integrating force.
   Cf. the similarity between bilayers of P-lipids and DNA-structure, see file The Cell.

9. Pure geometrical views on demarcation:  

With the view that dimensions and geometries make up the basis of Nature, the laws for quantification and demarcations become endogenous. There is for instance such things as the observed and unexplained polarizations in H2-clouds in macrocosm between hotter and colder regions. In nuclei of atoms it's said that the positive charge at fusion toward heavier atoms is built as in layers from outside inwards. It could be examples of the anticenter pole 00 and inward direction (pole 4a), representing the polarizing and quantifying force in the basic definitions of our dimension model,

a. In simple geometrical terms the step 3 →> 2 in the model (2 as the d-degree of surfaces) implies a polarization of 3-dimensional volumes to enclosed/excluded room.
   With a "haploid" view on a dimension chain as developed between poles 0 and 00, the anticenter pole 00 of d-degree 4 may be regarded as debranched, (figure a below) meeting "the other way around" from the end of the chain in inward direction. 
   Postulated in the model is that pole 4a, inward direction get "circular" structure when transformed to d-degree 3.

a) b)  

Fig Li-5-1, Li-5-2, Li-3-6-1

b. The hypothesis that a dimension chain can correspond to angle steps of halvings towards increasingly narrow angles leads also to a nearly closed unit. Figure b. Cf. directions of potential bonds as decreasing angles: C→>N →> O →> (H). Such development of the 0-pole outwards in angle steps may also illustrate life as "½" of the whole and the living unit's communication with the environment.
   (One could also assume such a process as endogenous within single atoms, involving processes and structural changes at the molecular level. One example is the sp3 → sp2-hybridization of carbon.)

c. A different aspect on the creation of a demarcating cell membrane concerns general conditions for level developments: It's suggested in files about physics to regard level development occurring through the middle step 3-2 in the dimension chain (see figure at end of this file). One hypothesis is that such a development should demand counter-direction from another, equivalent 5-dimensional center for saturation to a superposed, more substantiated level (figure c). Without such counter-direction the process 2 → 1 → 0/00 should only lead to repetition or energy lost to the external world.
   It would be an interpretation in agreement with Haldane's hypothesis about the cell as a fusion of two "half-organisms".
In a double cell-membrane the lipids meet with directions outwards/inwards, that's of Direction, d-degree 4. (Compare that orbitals of the same sign bind to each other. Overlapping of inward directed magnetic circular fields may eventually define a new center?)

10. Substantiation:

A gradual substantiation through increasing complexity is of coarse a necessary complement to geometrical models. What's only "field lines", potentials or motions as pathways are to regard as stepwise substantiated to molecular chains, to pipes, to organelles etc. Foldings of "linear" proteins to globular, 3-dimensional ones can illustrate increasing complexity. Saturation through incorporation from other units is another factor that builds structures of high d-degrees from lower ones (as 1 + 1 = 2, 2 +2 = 3!).
There is the similar processes on the level of human society: That which begins as wanderer's pathway through trackless terrain, becomes gradually a track, becomes a carriageway with inns, becomes a highway through communities with entrances and exits, etceteras.
   The need to get from suburbs to inner city, to and fro, becomes a drawing that gets materialized in a subway.
   One example could be the periodic, linear arrangement of filaments in collagen. Exactly how this works, in scientifically accepted terms, is another question.

How could enzymes emerge, the very long protein chains that effectively reduces the energy needed for a certain reaction? An analogy to the industrial revolution of manual work as it seems. The energy needed for a certain reaction without enzymes is often illustrated as a curve, a hill. Rather than believe enzymes as preexisting, it's easier to imagine them as substantiation of this very curve, taken as a real mold, then inverted to a hole for the key and lock relation to substrata. Enzymes are forces in the cell, As substantiated to proteins they are a "matrix" to substrata, in that sense complementary poles, the "antimatter" on this level. (Something like magnetic fields in relation to electric fields.)
    To store such a protein chain in the long term memory of DNA should of course need a backward process from amino acids to codons. (Or already, in some potential form, existed within DNA.

11. DNA coding amino acids:

Unique to life is DNA (or RNA) and the coding system DNA →> proteins. See The Genetic Code and The protein synthesis and file The Cell. Here only a couple of annotations.

As molecules amino acids represent a higher d-degree than the bases: the tetrahedrons with a central C-atom may be regarded as center-displaced (or "inverted") to the ring-bound C- and N-atoms in the codon bases; a step from sp3- to sp2-hybridization of the C-atom. It corresponds to a step d-degree 3 → 2 (or 4 to 3) outwards, from radial to circular structure. Conceptually codes are also secondary in relation to what is coded, as the written alphabet relative to spoken sounds.

With regard to the molecular structures, the relation could perhaps be illustrated in a dimension chain as in the figure below: bases as from intervals equivalent with debranched degrees meeting in synthesizing direction the other way around

Fig Li-5-DNA


In valences, the phosphorus atom P represents d-degree 5 (or rather something like a step 5-4 with one double-bonded oxygen).
   N and O with valences 3 and 2 represent opposite ends of backbone chains in amino acids (and opposite polarity in charge*) - and bonds through H-bridges between complementary bases in DNA (here also such N - N bonds, 3--3, in our model outer poles in d-degree 2).
   *(Cf. EM-force supposed developed in step 3 - 2 in our model.

In directions there are proteins outwards in the cell, structure-building and transporting, RNA-, DNA- nucleotides inwards the center, towards less mobility. (Cf. principle of stepwise building-in of anticenter, the 00-pole, and the similar building in of the animal pole to a nervous system in embryological development.)

One of the subject classes can serve as reference to the other because they originate from the same basic structure (of the type our 5-dimensional model here).

The figure above could be compared with numbers in the "ES-chain" (from file The genetic code")

Fig Li-7

259 circa sum of 2 bound DNA-bases (G + C 262 - 2, A + T 261 - 2)
752 x 2 = sum of side-chains of amino acids for 20 + 4 codons.
2(5 + 4 + 3) = 24 amino acids.

We have also that 292 = P~P-ribose bound (2 x 98 + 150 - 3 x 18) and 252 + 208 = 2 x P~ ribose at which codon bases get attached when constructed. Cf. a figure in S. Copley et al* (2005) where such a pair of nucleotides are bound to a P~P-ribose group. Their hypothesis is that amino acids originally were constructed at the inner ribose which should imply at the center of the chain in the figure above.)

*Copley S D, Smith E, Morowitz H J: A mechanism for the association of amino acids with their codons and the origin of the genetic code. Proc. Natl. Acad. Sci. 2005, 102:4442-4447.

12. Additional remarks:

- The physical quantities (rather qualities) and their transformations into one another as a dimension chain are naturally given as aspects:
   density - forces - mass/space - charge - distance - time,
in accordance with definitions proposed in files on physics..
   "Density" seen as the primary quality in d-degree step 5 →4, polarized in mass/space in step 4 →3. (Mass numbers become an underlying level in relation to charge numbers for instance.)

- The underlying scheme and geometrical, mathematical rules that is assumed with the model here, guiding the building of molecules and organs on superposed levels could be imagined as changing between d-degrees and levels in agreement with these. (And the processes go further and further perhaps just because relations and numbers don't become integers!)

Chemical processes could be apprehended as efforts of a fragmented matter to solve the demand of the Whole, the "Entirety", the ultimate binding force.

A level chain:


Fig Li-10-017



© 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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