Changing Patterns using Transformation Pathways (Part #6)

These are of relevance to the quest for a meaningful configuration of the organization of the codon/hexagrams on the drilled truncated cube:

• distinctions made between the two "halves" of the pattern of 64 can be used to suggest a degree of correspondence between:
  • 32 codons organized into 8 families of 4 "whole" families and 32 organized into a second cluster of 8 "split" families
  • traditional organization of 64 hexagrams into 8 "houses" of 8 hexagrams each, readily split into two "halves" as indicated in the circular configuration of hexagrams (Organization of I Ching hexagrams in terms of traditional "houses", 1995)
• recognized "transformations" of those patterns noted with respect to the Kazakh report:
  • in the codon case, those conventionally distinguished are:
    • the transformation of Yuriy Rumer by which "whole" families can be transformed into "split" families (as indicated below left)
    • a second transformation based on Rumer's transformation, using the subset of codons with either three identical or three different bases. These give rise to two sets of 7 transformations (as indicated below right)
    • seven other transformations and symmetries are indicated by Kemp as having been recognized by the Kazakh research (but are less than evident from that report)
  • in the hexagram case, those traditionally distinguished are a primary feature of the I Ching as the consequence of transformations of any of the 6 lines of a hexagram (from broken to unbroken, or vice versa), thereby engendering another hexagram (as noted above)

Depiction of Rummer's transformations in relation to the circle of hexagrams	Depiction of transformations based on Rummer in relation to the circle of hexagrams

From within the "camp-us" modality, as noted above, there are remarkably few exceptions to the lack of exploration of the interplay between the codon and hexagram patterns -- most notably from the perspective of biosemiotics. One early exception -- in passing -- appeared in the pre-conference Abstracts for the First Gatherings in Biosemiotics (Copenhagen 2001) is that of Abir Igamberdiev (Semiokinesis **o Semiotic autopoiesis of the Universe, modified version of that published in Semiotica 135, 1-23):

A well-known biosemiotic structure, the genetic code, has its invariants (triplet structure, complementarity, four elementary letters) that could be derived from the model of reflection. The reflective structure may generate triads of binary compositions forming combinations which number is multiplied by four (Igamberdiev, Life as Self-determination, 1999) and this is directly deducted from the triadic reflective action.

The similar generalized structures (square matrices of grouping of pairs of opposites corresponding to the temporal progression of the phenomenal world) are present in Chinese 'I Ching' book and it may represent a general rule for establishing invariants through the unfolding of reflection (Merrell, 1992). It can be followed in the genetic code model as finite reflective structure of G**del numbers(that initially appears as a result of infinite reflection into finite). The letter (number) N (e.g., adenine) reflects in its complementary number N' (e.g., thymine), then duplication of signs leads to the appearance of additional letters N₁ (guanine) and N₁' (cytosine).

The combination of these letters satisfying the principles of consistency, simplicity and optimality generates the observed structure of the genetic code. It is arbitrary in the sense of the Saussurean arbitrariness of sign, but it satisfies optimality principles of construction of G**del numbers during Wittgensteinian language game. The pattern of genetic code can be explained on the basis of search of the optimal variant of reflective domain structure.

Thus we have Peircean trinitary structure in living system: a) metabolic network, b) genome as a signifying embedding within metabolic network, and c) superposition of genome rearrangements as an interpretante of the genomic system. Following Aristotle (De Anima, II, 1) metabolic network corresponds to hyle (matter) of living being, genome corresponds to **ythe entelechy as a possession of knowledge**O and language game generated by genome corresponds to **ythe entelechy as an actual exercise of knowledge**O

For Tidjani N**gad. (Rumer's Transformation, in biology, as the negation, in classical logic, International Journal of Quantum Chemistry, 94, 2003):

... we make a connection between the Rumer transformation, used in the study of the genetic code-doublets, and the negation of classic logic. A unified classification is given, relying on two Klein's 4-groups describing the symmetries of the 16 doublets of nitrogenous bases and those of the 16 binary connectives of classic logic, both groups being subgroups of a larger noncommutative group with eight elements we identify as the dihedral group D4.

Such arguments notably serve to frame the issue of how the binary code of the I Ching might be related to that of the DNA bases. This question is the subject of detailed exploration in a very remarkable study, supported by many illustrations, by Fernando Castro-Chavez (Defragged Binary I Ching Genetic Code Chromosomes Compared to Nirenberg**Os and Transformed into Rotating 2D Circles and Squares and into a 3D 100% Symmetrical Tetrahedron Coupled to a Functional One to Discern Start From Non-Start Methionines through a Stella Octangula, Journal of Proteome Science and Computational Biology, 2012). He notes:

The four nucleotides of the genetic code: T, A, C, G have specific physicochemical properties deserving a careful analysis, as also do the codons and amino acids produced by them; however, it is important to first recognize the value of binary systems in bioinformatics as applied to the DNA genetic code. The most ancient 64-grid representation seems to predate the Chinese civilization but somehow was preserved by them, representing faithfully the binary order of the genetic code through the most ancient or primeval pairs of trigrams that integrate each of the 64 hexagrams of the I Ching table, also called the Book of Changes or Book of Mutations. This article shows that some basic principles of software engineering can be applied to this ancient binary genetic code system.

From without the "camp-us" modality, however, as noted by M. Alan Kazlev (The I Ching and the Genetic Code. Kheper.net, 2005):

There are actually on the Internet a number of different correlations assigning the I Ching bigrams and hexagrams with the nucleotide bases. Different authors use different assignments to bases and numbers (6,7,8,9). Another assignment is the one used by Chris Lofting of I Ching plus who gives a detailed discussion. Still other correlations can be found. It is rather disappointing that there is no agreement on this matter.