Engineering - Molecular Theory of the Living Cell - page 132

Table 5.4 The question
and answer (QA) matrix.
1

Answers Binary questions

1

2 3 ... N

¼ Yes; 0 ¼ No

1 0 1 1 ... 0

2 0 0 1 ... 1

3 1 0 0 ... 0

. . . . . .

. . . . . .

. . . . . .

2 N 0. 0 0 ... 1

which in Chinese can be written with just six characters that read in Korean thus:

Doh Gah Doh, Bee Sahng Doh.
We may refer to Statement 5.22 as the “Principle of Ineffability,” probably one of
the most important principles of the Taoist philosophy.
The purpose of this section is to formulate an “algebraic geometric” version of
the Principle of Ineffability, which will be referred to as the “Knowledge Uncer-
tainty Principle (KUP)” in analogy to the Heisenberg Uncertainty Principle (HUP)
in quantum mechanics. For the purpose of the present discussion, I will differentiate
“knowledge” from “information” as follows: Knowledge refers to actuality and
information to potentiality, just as physicists differentiate between the probability
wave function C symbolizing “possible information” and its square C

2 referring to
measured information or probability (Herbert 1987; Morrison 1990). It may well
turn out that KUP subsumes HUP as suggested by Kosko (1993). The KUP is based
on the following considerations:

1. All human knowledge (including scientific knowledge) can be represented as
sets of answers to N binary questions (i.e., questions with yes or no answers
only), where N is the number of questions that defines the universe of discourse
or the system plus its environment under observation/measurement. This
resonates with Wheeler's “It from bit” thesis (1990) that information is as
fundamental to physics as it is for computer science and that humans participate
in producing all scientific information by acquiring the apparatus-elicited
answers to yes-or-no questions as in the game of 20 questions (Sect. 4.15 ).
Recently Frieden (2004) has claimed that all major scientific laws can be
derived from maximizing the Fisher information of experimental data.
2. As shown in Table 5.4 , each answer in (1) can be represented as a string of N
0's and 1's, for example (0, 1, 1, ... , 0 ) for Answer #1, and (1, 0, 0, ... , 0) for

Answer #3, etc.
3. There will be a total of 2 N N-bit strings as the possible answers to a set of N
questions (see the last row in Table 5.4 ).
4. The N-bit strings in Table 5.4 can be represented geometrically as the vertices
of an N-dimensional hypercube (Kosko 1993, p. 30). An N-dimensional
hypercube is a generalization of an ordinary cube which can be viewed as a