Cell Language Theory, The: Connecting Mind And Matter

18 The Cell Language Theory: Connecting Mind and Matter

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

= - log 2 (1/6)

= log 2 6 = 2.6 bits. (2.8)

The meaning of the result in Eq. (2.8) is that the amount of uncer­

tainty that we have about which of the six numbers will show up upon

one throw of a dice is 2.6 bits. In other words, it will take 2.6 bits of

information to correctly predict which of the six numbers will appear

upon throwing a fair dice.

(2) The case of a “loaded” dice. Let us assume that the dice has been

tampered with so that the probability of each number showing up is

not equal but different as shown in Table 2.2.

Therefore, the result in Table 2.2 indicates that the average uncer­

tainty about the appearance of a number is less when the dice is loaded

than when it is fair (2.42 bits vs. 2.6 bits).

2.2.3 Planckian Information (IPl)

A new measure of information, denoted as IPl, was introduced in 2015 [26]

following the discovery of the universality of the Planckian distribution

equation (PDE) in [27] discussed in Section 8.1. One interesting difference

between Shannon information, ISh, and IPl , defined in Section 8.5.1, is sug­

gested to be that IPl is to organized complexity (studied in biomedical sci-

ences) what ISh is to disorganized complexity of Weaver (studied in

statistical mechanics) [366].

Table 2.2 Calculating the Shannon entropy, H, of a loaded dice.

ith Possibility pi Pi log 2 pi H (bits)

1 0.15 0.15 × (log 2 6.67) = 0.15 × 2.75 0.41

2 0.25 0.25 × (log 2 4) = 0.25 × 2 0.50

3 0.11 0.11 × (log 2 9.09) = 0.11 × 3.18 0.35

4 0.25 0.50

5 0.10 0.10 × (log 2 10) = 0.10 × 3.33 0.33

6 0.10 0.33

Spi = 1.00 –Spi log 2 pi = 2.42

Note: The Shannon entropy of a fair dice is calculated to be 2.6 bits; see Eq. (2.8).

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