Engineering - Molecular Theory of the Living Cell - page 151

CS are found in TS. Thus, at both these levels, more elements of TS are found to be
the elements of CS than the other way around, which may be expressed as
Inequality (5.57):

<

TS CS (5.57)

Inequality 5.57 may be interpreted as reflecting the relative complexities of TS
and CS in the sense that

It takes a longer bit-string to describe a system viewed as a CS than as a TS. (5.58)

Based on the content of the third row of Table 5.10 , it is clear that:

All control systems are thermodynamic systems; but not all thermodynamic systems are
control systems. (5.59)
We may refer to Statement 5.59 as the “Principle of the Insufficiency of
Thermodynamics for Controlled Processes” (PITCP). Statement 5.59 establishes
that there are more thermodynamic systems than there are control systems or that
CS is a subset of TS, leading to Inequality 5.60 :

TS > CS (5.60)

On the surface (i.e., on the syntactic or formal level), Inequalities 5.57 and 5.60
appear contradictory. However, on the semantic level, that is, if we take into
account the different contexts under which the TS and CS sets are defined, no
contradiction appears. There are two ways of defining a set - (1) extensionally ,by
listing sample members of a set, and (2) intensionally , by listing the characteristics
of, or the rules obeyed by, the members of a set. It is here claimed that
If A is a subset of B, A is less complex than B extensionally and more complex than B
intensionally. (5.61)
We may refer to Statement 5.61 as the “Complementarity of the Extensional
and Intensional Definitions of a Set” (CEIDS), or, more briefly, the “Extension-
Intension Complementarity” (EIC). Since the extensional definition of a set is akin
to viewing a set globally and the intensional definition akin to viewing a set locally ,
EIC may be regarded as a species (or token) of what is often referred to as the
“Forest-Tree Complementarity”. Based on EIC, we can now account for the
apparent contradiction between Inequalities 5.57 and 5.60 as a natural consequence
of the complementarity between the extensional and intensional definitions of a set.

5.3.2 The Law of Requisite Variety

One of the most useful laws to be imported from engineering into biology is what is
known in cybernetics as the Law of Requisite Variety (LRV). There are many ways