The geometric origin of the aminoacids

Symmetry breaking in biosynthesis may be the driving force of evolution, and explain why
there are only 20 proteinogenic aminoacids, out of 64 possible base combinations

By Frank van den Bovenkamp, TrigunaMedia / TGMResearch, Nov. 24, 2017, frank@trigunamedia.com

The Four Causes in cyclic creation through symmetry breaking:

• In the groundstate, the Four Causes are indistinguishable, only symmetry break makes them distinguishable.

• After symmetry break, the Formalis (formal cause) represents the whole groundstate, and so on.

• The broken symmetry becomes recursive if the number of permutations equals the number of causal factors.

• Recursive symmetry break generates a cyclic mode, consisting of an extroversial creation phase (in the present context the phenotype), and an introversial creation phase (genotype).

• For a single phase or demi-cycle, the recursiveness naturally forms as there are 4 causes mapped to 4 permutations - there are no constraints, therefore the symmetry break functions spontaneously.

• For the full dual phased creation cycle (of biosynthesis) the permutations are constrained as follows:

• there must be a prescribed symmetry break axis for each phase
• there must be a specific number of concurrent cycles

making the symmetry break more arduous.

Ref: "Fundamentals of Tetralogic" - http://science.trigunamedia.com/fundamentals-of-tetralogic/

Counting the elements
must
equal..
Constraining the permutations
makes..
Solving the number of cycles
4 Indistinguishable causes, extroversial

"c" = indistinguishable cause
"i" = symmetry axis identifyer

4 partial permutations:
 c-c-c-c/i c-c-c/i-c c-c/i-c-c c/i-c-c-c

n concurrent cycles
n = 5

and

total permutations
after constraint =

total elements =
1 Symmetry axis identifier
n Concurrent cycles
4 Indistinguishable causes, introversial
1 Symmetry axis identifier
n Concurrent cycles
10 + 2n = Number of elements = 4 x n >>> 20

Axiomatic and molecular grouping

The morphology of the set of proteinogenic aminoacids is naturally grouped in such a way that it reflects the symmetry breaking of the Four Causes through the dual phased creative cycle. The grouping based on the NH2-C-COOH groups matches the axiomatic grouping as follows (once sorted, the groups are randomly matched):

 Groupings, axiomatic Groupings, NH2-C-COOH morphologically identical 4 indistinguishable causes, extroversial GLY - VAL - ASN - THR 1 Formalis / symmetry break identifier ASP 4 indistinguishable causes, introversial TRP - CYS - GLU - SER 1 Formalis / symmetry break identifier ARG Cycles - extroversial, introversial idential pairs 1 - 1 PHE - TYR 2 - 2 ILE - LYS 3 - 3 THR - HIS 4 - 4 LEU - GLN 5 - 5 ALA - MET * http://www.biotopics.co.uk/jsmol/aa_categories.html Total groups: 9, total elements: 20 Total groups: 9, total elements: 20

Geometry of the aminoacids in extroversial and introversial phase

• The octahedron breaks symmetry through bi-section (systaltic, vector, bi-furcated, multi-symmetrical, divergent)
• The icosahedron restores symmetry through "Phi-section" (synergetic, scalar, "Phi-furcated", omni-symmetrical, convergent)
• The 20 axiomatic / molecular permutations are 20 permutations of the octahedron in the icosahedron
• The 5 x 2 cycles are 5 x 2 icosahedral angles, the 2 x 4 causes are 2 x 4 octahedral spins, the 2 identifiers the 2 symmetry break axes

Geometrization of proteinogenic aminoacids, at first showing the 2 main groups, forming one of the 5 concurrent creation cycles,
with resp. symmetry break / restore axes.The tetras bisected by the octa during the extroversial phase, are "Phi-sected"
during the introversial phase.

Adding the 5 concurrent cycles - the geometry brings the 20 elements
and their 20 causal permutations in one model together

The octahedron and its 20 permutations in the icosa, assuming a given symmetry axis.
The 20 elements have become 20 permutations - the recursion is solved.

Further proof: Fibonacci genome

"Codon populations in single-stranded whole human genome DNA are fractal and fine-tuned by the Golden Ratio 1.618" - J.C. Perez, https://www.ncbi.nlm.nih.gov/pubmed/20658335

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