Cell Language Theory, The: Connecting Mind And Matter

386 The Cell Language Theory: Connecting Mind and Matter

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

The two numbers involved in the golden ratio can represent either line

segments (see Figures 9.3 (a)–(k)), or two-dimensional areas as shown in

Figures 9.3(d), (h), and (l).

9.4.2 The Fibonacci Numbers

Fibonacci numbers, F = {1, 1, 2, 3, 5, 8, 13, 21, etc.}, can be repre-

sented as

F(n + 1) = F(n) + F(n – 1), (9.13)

where F(n) is the nth Fibonacci number, counting from the second number

of the first triplet of the Fibonacci numbers, i.e., 1, 1, 2, so that F(n – 1) = 1,

F(n) = 1, and F(n + 1) = 2. The basic unit of the Fibonacci series is the adja-

cent or contiguous triplet, F(n + 1), F(n), and F(n – 1), which will be referred

to as the “Fibonacci triplet”.

The Fibonacci triplet embodies an ITR in the senses that (a) replacing

any one of them with other integers will destroy the Fibonacci series and

(b) the triplet constitutes a commutative triangle as shown in Figure 9.5,

and hence a mathematical category.

The Fibonacci series, in the form of rectangles, can be generated by

iterating two simple operations; (a) squaring the longer side of a Fibonacci

rectangle and (b) adding to it the old Fibonacci rectangle. Repeated applica-

tion of these two operations (to be referred to as the Replication with

Variation (RV); see Figure 9.7) generates a series of Fibonacci rectangles

that harbor what may be called the Fibonacci spirals found in nautilus shells

f g

DS ES DS’

h

Figure 9.4 A postulated universal molecular mechanism underlying semiosis (UMMS)

that satisfies the thermodynamic and enzymological requirements. DS = dissipative struc-

ture of Prigogine [57, 248]; ES = equilibrium structure; DS′ = a partial replica of DS. f =

information production or encoding based on PMETM [384], Process (9.11); g = informa-

tion utilization or decoding based on CMMF [65], Process (9.12); h = information flow,

representation, self-replication, inheritance.

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