Biology Reference
In-Depth Information
postulate may be expressed alternatively as:
The Boltzmann constant k is to biology what the Planck constant h is to quantum
mechanics.
(12.48)
Statement 12.48 may be referred to as the
k-h isomorphism postulate
.
The universal property inherent in the last two categories of Table
12.13
is
suggested to be
communication
or
information exchange,
for which both
information
(I) to be transferred and the energy (E) to drive the transfer process are absolutely
required according to Shannon's channel capacity equation, Eq.
4.29
. Since the
complementary union E and I is referred to as gnergy (G) (Sect.
2.3.2
), it would
follow that communication absolutely requires (or is synonymous with) gnergy.
The selection of I (not I
gt
), E, and G as the universal properties of the associated
categories in Table
12.13
is motivated by the
information-energy complementarity
I, E, and G, are postulated to form a higher-order category, to be designated as C
2
(from “CC” or the “cosmological category”), which is a 9-tuple consisting of four
objects (denoted with capital letters) and five morphisms (denoted with lower-case
letters) as follows:
CC
¼
(E
;
I
;
G
;
U
;
f
;
g
;
h
;
j
;
k)
(12.49)
Equation
12.49
can be represented graphically using the “commutative diagram”
as shown in Fig.
12.33
. A commutative diagram can be viewed as a network
g
E
U
j
f
k
G
I
h
Complementarity
(
G
E
U
)^(
GI
)
or (
g
°
f
)^(
k
°
h
) =
j
(12-50)
Supplementarity
: (G
E
U) = G
I
U)= (G
U)
or
f
°
g
=
h
°
k
=
j
(12-51)
Therefore
j
is both
complementary
and
supplementary
!
Fig. 12.33 The
commutative diagram
for the cosmological category (CC or C
2
) consisting of four
objects, energy/matter (E), information (I), gnergy (G), the universe (U) and five morphisms,
tentatively identified as
f
(physical interactions),
g
(quantization),
h
(biological evolution), j
(cosmogenesis), and
k
(communication) embodying/reflecting/ organized by two universal
