The geometric origin of the aminoacids
Bifurcation 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
Updated April 11, 2021
The Four Causes in cyclic creation through bifurcation:
 In the groundstate, the Four Causes are indistinguishable, only bifurcation makes them distinguishable.
 After bifurcation, the Formalis (formal cause) represents the whole groundstate, and so on.
 The bifurcation becomes recursive if the number of permutation groups equals the number of causal factors.
 The bifurcation 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 demicycle, the recursiveness naturally forms as there are 4 causes mapped to 4 permutations  there are no constraints, therefore the bifurcation is spontaneous.
 For the full dual phased creation cycle (of biosynthesis) the permutations are constrained as follows:
 there must be a prescribed bifurcation axis for each phase
 there must be a specific number of concurrent cycles
making the bifurcation more arduous.
Ref: "Fundamentals of Tetralogic"  http://science.trigunamedia.com/fundamentalsoftetralogic/
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:
cccc/i 
ccc/ic 
cc/icc 
c/iccc 
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 bifurcation into the Four Causes through the dual phased creative cycle. The grouping based on the NH2CCOOH groups matches the axiomatic grouping as follows (once sorted, the groups are randomly matched):
Groupings, axiomatic 
Groupings, NH2CCOOH morphologically identical 

4 indistinguishable causes, extroversial 
GLY  VAL  ASN  THR 

1 Formalis / bifurcation identifier 
ASP 


4 Indistinguishable causes, introversial 
TRP  CYS  GLU  SER 

1 Formalis / bifurcation 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 bifurcates through bisection (systaltic, vector, multisymmetrical, divergent)
 The icosahedron restores symmetry through "Phisection" (synergetic, scalar, "Phifurcated", omnisymmetrical, 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 possible symmetry axes
Geometrization of proteinogenic aminoacids, at first showing the 2 main groups, forming one of the 5 concurrent creation cycles,
with resp. bifurcation / symmetry restore axes.The tetras bisected by the octa during the extroversial phase, are "Phisected"
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 singlestranded whole human genome DNA are fractal and finetuned by the Golden Ratio 1.618"  J.C. Perez, https://www.ncbi.nlm.nih.gov/pubmed/20658335
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© All rights reserved, Frank van den Bovenkamp, TrigunaMedia / TGMResearch, 20172021
