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Systems Biophysics Set Eusystem Generic Model-Form.


The ontogenic discipline of Systems Biophysics Set (abbreviated here 'SBS') deploys minimum systems integrity (MSI) models to demonstate COMPONENTS, BIOFORMS, ECOLOGIES, EUSYSTEMS and other ENERGY-EVENTS and TOPOLOGICAL conveyances and correspondences in elementary Euclidean Space-Time (S3). These fundamental notions can be extended, in theory, to any number of alternative more abstract alpha-numeric set conceptioning strategies.

[annoted Equilateral 4-Hedron Volume]

One-Half of the Elementary Eusystem's Model is an EQUILATERAL TETRA-HEDRON (or 'Volumetric Tetrahedron, Vt') Demonstrating minimally complex inside-out-sided-ness in the
EUCLIDEAN GEOMETRIC FIELD.

    The CONSTRUCTUAL Sub-ELEMENTS of the MODEL are:

    • EDGES (Partitionable Euclidean Lines).
    • VERTICES (Euclidean Points).
    • FACETS (Triangular Areas).

      We can imagine the sub-elements 'to assemble' (action) to define a volume-idea.
      The The Primary Componential compounding defines the alpha-numeric resolutions which co-define:

      • SIX Distinct EDGES (Line-Element 'CA' is one example).
      • Four Distinct VERTICES ('Pz' is always uniquely named the 'APEX' vertex).
      • Four Distinct FACETS (Triangular Areas,... the 'BASE FACET' is always a triangle called 'ABC').
      • One Distinct CENTROID LOCUS (Geq or Gi is uniquely named the 'CENTROID of VOLUME') .

      The assembled elements enclose a volume.
      As a single Vt is associated with 'one-half' of the SBS Model-form, DYADS of forms are associated with a higher resolution of the model. This is useful in biophysics because we can often think of the binomial dyads (dynamical-compositions of two 4-Hedron in association) as existing in a sort of 'Head-and-Body' relation for which we should like to define an evermore efficient alpha-numeric set processing. For example, as the Biological energy-event called the 'METAZOAN CELL' may implicate a well-bounded 'body-model' aspect,...it may be useful and interesting to have the idea of the 'MITOCHONDRION' as the associated 'head-model' aspect. Another potential for the ever-present dichotomocity-binomialism (hardly ever symmetric as with a pairing of equilateral forms made co-vertexial) might be somehow correlated to more refined resolutions of biophysical systems,...the complexing of biochemical purines and pyrimidines, e.g. More about this and a potential to make the model evolutionary 'DYNAMIC' is presented later.

      OBSERVATIONS:

      [001.]
      We can associate the symbol 'Ø' with the equilateral tetrahedron. Other symbols can be associated with any non-equilateral tetrahedron.

      [002.]
      All 4-Hedra have a centroid center-of-volume (or 'mass') aspect. Here this is denoted Gi for the i-th identity. In physics and bio-physics these conceptual space-time loci are imbued with gravitational relevance. The alpha-numeric symbol 'G' is often associated with gravitation in the SBS theoretics and other physical theories as well. In the example of the EQUI-LATERAL 4-Hedron, there are also FOUR EQUAL (in measure) lines which can be constructed from 'G' to each VERTEX.
      Historically these have been called 'RAYS'. (See Figure)

      [003.]
      Just as the ancient geometers found that ANY THREE POINTS can be assoctiated-with (or define) a single CIRCLE;....
      Given any Vt ('Volumetric Tetra-hedron'), ...its four vertices can ALWAYS be made continuous with the surface of a single SPHERE.
      This fact plus the fact that any sphere of RADIUS R or r can have only one unique locus on its surface which can be named "AØ" or "Ak" (one of the four vertices of an equilateral 4-Hedron)__ means that any other locus, point or structural element in the Euclidean Field can be uniquely ORIENTED with respect to this single point which can be called 'THE COORDINATE ORIGIN'of the Field or system. Since these resolutions have a sort of 'fractal-manifold' property or character because of the infinite values we can assign the RADII of the encompassing sphere,...We can define SETS of model-forms which are unique because all FORMS can be held 'CO-RELATIVE' (or 'correlative') with respect to a single equilateral form and its 'R-Value'. This is useful in biology because we can correlate the mathematicl-geometric model with the on-going systems to taxonomize the bioforms and other entities. Thus Phyla can be associated with an R-value, and the taxa sub-summed by a phylum in R, can be asigned to the sets of 'r', and so on. More about this later.

      [004.]
      As the BASE FACET of the en-sphered Vt defines a Euclidean PLANE, it also defines an action called 'DISSECTION' of the SPHERE. And in this case the dissection-partioning defines Two Sub-Volumes of the sphere of which only one contains the 'extinct centroid' of the Vt-4-Hedron.

      To Be Continued.

      "Knowledge is the small part of ignorance that we arrange and classify."
      Ambrose Gwinnett Bierce

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