Cell Language Theory, The: Connecting Mind And Matter

Matrix Mathematics of Genetics 249

“6x9” b2861 The Cell Language Theory: Connecting Mind and Matter

bonds between G and C. The numbers 0 and 1 in Table 5.5 are symbols

that differentiate between the two groups of bases whose traits are

more or less opposite, e.g., two vs. three hydrogen bonds in the first

row, purine and pyrimidine bases in the second row, and the amino and

keto groups in the third row. It is not necessary to use numbers 0 and

1 for the purpose of making a binary distinction: They can be replaced

by any pair of unequal symbols such as + and −, yes or no, Yin or

Yang, etc.

The three sets of the “Yin–Yang” pairs in the first column can be con-

veniently represented as a pair of diagonal matrices, each matrix denoted

as [X, Y]d, where X and Y are the DNA bases and “d” indicates “diago-

nal” (see the third column of Table 5.5).

If one carries out the tensor multiplications [158] among all the possible

triplets that can be formed from the amino-keto yin–yang pairs, e.g., [C, A]

d*[C, A]d*[C, A]d; [C, A]d*[C, A]d*[T, G]d; [C, A]d*[T, G]d*[C, A]d; etc., one

obtains the eight 8 × 8 diagonal matrices with 8 × 8 = 64 elements, each

element being a nucleotide triplet, as shown in row 3 in Table 5.2.

The 64 triplets thus generated exactly correspond to the 60 nucleo-

tide triplets coding for 20 amino acids and four nucleotide triplets cod-

ing for the stop signal in vertebrate mitochondria, as shown in row 4 of

Table 5.2, which has been referred to as the Petoukhov coincidence in

Section 5.1.

A simple combinatorial calculation shows that there are 20^64 or ~ 1083

possible ways of assigning the 20 amino acids into the 64 boxes and the

Table 5.5 The three sets of the yin–yang doublets embedded in the four DNA bases.

Yin–Yang Pairs

(or Sub-alphabets)

DNA Bases

2 × 2 Matrix Representation

G A T C of the Yin–Yang Pairs

1. 2H–3H pairs (also called the
   Watson–Crick paira)

1 0 0 1 [C, G]d; [T, A]d

2. Purine–pyrimidine pairs 0 0 1 1 [G, A]d; [T, C]d


3. Amino-keto pairs 0 1 0 1 [C, A]d; [T, G]d
   Note: aIn addition to the Watson–Crick pairs, there are the Hoogstein pairs that have the same
   chemical formula but different conformations, i.e., the 3D structures that can be altered without
   breaking any covalent bonds (https://en.wikipedia.org/wiki/Hoogsteen_base_pair).

b2861_Ch-05.indd 249 17-10-2017 12:01:17 PM