Physics - Molecular Theory of the Living Cell - page 23

The supplementary and complementary relations defined above can be conve-
niently represented as triadic relations among three entities labeled A, B, and C.
Supplementarity refers to the relation in which the sum of a pair equals the third:

¼ þ

Supplementarity: C A B (2.30)

As an example of supplementarity, Einstein's equation in special relativity,

mc 2 (Shadowitz 1968), may be cited. Energy (A) and matter (B) may be
viewed as extreme manifestations of their source C that can be quantitatively
combined or added to completely characterize C. As already indicated there is no
common word to represent the C term corresponding to the combination of matter
and energy . Therefore, we will adopt in this topic the often-used term “mattergy”
(meaning matter and ener gy ) to represent C. Through Einstein's equation, matter
and energy can be interconverted quantitatively. The enormity of the numerical
value of c 2 , namely, 10 21 , justifies the statement that:
Matter is a highly condensed form of energy.

E ¼

(2.31)

In contrast to supplementarity, complementarity is nonadditive: i.e., A and B
cannot be combined to obtain C. Rather, C can be said to become A or B depending
on measuring instruments employed: i.e., C B, depending on measure-

ment. We can represent this complementary relation symbolically as shown in
Eq. 2.32 :

¼ AorC ¼

A ^ B

: ¼

Complementarity C (2.32)

where the symbol ^ is introduced here to denote a “complementary relation.”
Equation 2.32 can be read in two equivalent ways:

A and B are complementary aspects of C. (2.33)
C is the complementary union of A and B. (2.34)
Statements 2.33 and 2.34 should be viewed as short-hand notations of the deep
philosophical arguments underlying complementarity as, for example, discussed
recently by Plotnitsky (2006) and Camillieri (2007). The principles of complementar-
ity and supplementarity defined above may operate not only in physics but also in
biology as first suggested byBohr (1933; Pais 1991). In other words, itmay be said that:
Physics and biology are symmetric with respect to the operation of supplementarity and
complementarity principles. (2.35)

We will refer to Statement 2.35 as the Symmetry Principle of Biology and
Physics (SPBP). SPBP is supported by the symmetry evident in Table 2.5 .
In Table 2.5 , two new terms appear, “mattergy” (see Item 2) and “liformation”
(Item 7) whose meanings are explained in footnotes. One of the most significant
conclusions resulting from Table 2.5 is the assertion that life and information are
intimately related in biology just as matter and energy are related in physics (see
Items 1, 2, 6, and 7), leading to the coining of the new term “liformation” in analogy