Cell Language Theory, The: Connecting Mind And Matter

242 The Cell Language Theory: Connecting Mind and Matter

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

structures) to the dynamic functions of the living cell (i.e., cell-language

texts; see the lower right corner; dissipative structures), thus in part sup-

porting the concept of the cell language (Chapter 4).

One example of the “deep structures” of the genetic code is demon-

strated in row 1 in Tables 5.2 and 5.3. Hidden under the usual genetic

alphabets, A, C, G, and T, are the deep structures, called subalphabets

shown in Table 5.3, which may be viewed as embodying the doctrine of

the Yin–Yang opposites of the Daoist philosophy [382]. Note that there

are three Yin–Yang pairs that can be generated from the four Watson–

Crick nucleotides (see 1)–3) in the middle of row 1 in Table 5.2 or rows

1–3 in Table 5.3). One of these three yin–yang pairs, i.e., 2) divides the

four nucleotides into two opposite groups, namely A and C, on the one

hand, and G and T, on the other (see the second row of the 3 × 4 matrix

located on the right-hand side of row 1 in Table 5.2).

Petoukhov has uncovered close relations between genetic phenomena

and classical matrix mathematics of oscillators with many degrees of free-

dom [158]. He represented these two pairs of Yin–Yang opposites as two

(2 × 2) diagonal matrices as shown in row 2 of Table 5.2. He then applied

the rules of tensor multiplication of matrices (symbolized as ⊗) recur-

sively three times to generate the (8 × 8)-matrix of 64 elements shown in

row 3 in Table 5.2. Now comes the miraculous coincidence: The 64-

element matrix thus generated from the (2 × 2)-matrix formed from the

four Watson–Crick nucleotides exactly overlaps with the 64 elements of

the codons (as shown in row 4 of Table 5.2)! The unique arrangement of

the 64 triplets shown in row 4 of Table 5.2 is one out of the 64! or 10^89

possible arrangements and hence carries about log 2 (10^89 ) = 89 × 3.32 =

295 bits of Shannon information. To emphasize the potential significance

of this coincidence and anticipating the future references to this important

finding, I am suggesting that we refer to this surprising finding as the

“Petoukhov coincidence”.

Petoukhov [158] suggests a possible “mechanism” underlying the

phenomenon of what is here referred to as the “Petoukhov coincidence”,

and the suggested mechanism is based on the principle of “resonance”

between vibrating or oscillating systems that can be described using the

same mathematical language, i.e., the tensor algebra. In other words,

Petoukhov views nucleotides and their higher structures including genetic

codons, genes, and DNA as resonance signal generators that self-organize

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