Cell Language Theory, The: Connecting Mind And Matter

The Universality of the Planckian Distribution Equation 363

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

we assume that GLE is associated with random processes due to its sym-

metry with respect to the sign reversal of the (x - μ) term in Eq. (8.9). This

measure of order will be referred to as the Planckian information (IP)

defined quantitatively as shown in Eq. (8.10) or (8.11):

IP = log 2 (AUC(PDE)/AUC(GLE)) bits (8.10)

or

IP2=log()()∫∫P x dx / G x dx (8.11)

where P(x) and G(x) are, respectively, the Planckian distribution equa-

tion and the Gaussian-like equation.

Applying Eq. (8.10) to Figures 8.6(b), (d), (e), (g), (i), (m), (o), and (q)

generated the IP values given in Table 8.1. The Planckian information

represents the degree of organization of physical (or nonphysical) sys-

tems in contrast to the Boltzmann or the Boltzmann–Gibbs entropy

which represents the disorder/disorganization of a physical system,

whether the system involved is atoms, enzymes, cells, brains, human

societies, or the Universe. The organization represented by IP results

from symmetry-breaking selection processes applied to some randomly

accessible (and hence symmetrically distributed) processes, whether

the system involved is atoms, enzymes, cells, brains, languages, human

societies, or the Universe [26, 27].

8.5.2 The First Law of Informatics: Information Can but Entropy

Cannot Be Negative

There is a great confusion in science and philosophy concerning the rela-

tion between the concepts of information and entropy as succinctly

reviewed by Wicken [369]. A large part of this confusion may be traced

back to the suggestions made by Schrödinger in 1944 [545] and others

subsequently (e.g., von Neumann, Brillouin, etc.) that order can be meas-

ured as the inverse of disorder (D) and hence that information can be

measured as negative entropy (see the second column in Table 8.3).

As I pointed out in [546], the concept of “negative entropy” violates

the Third Law of Thermodynamics and hence cannot be used to define

“order” or “information”. However, Planckian information, IP (see the

third row in Table 8.3), can be positive, zero, or negative, depending on

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