Engineering - Molecular Theory of the Living Cell - page 128

Fig. 5.5 A diagrammatic
representation of the
complementarity
of complementarities, or the
“recursive complementarity”

B-C

C/P

KEB-C J-C

It is interesting to note that Statement 5.15 can be interpreted as either of the
following two contrary statements, P and not-P:

All contraries are complementary. (5.16)

Not all contraries are complementary. (5.17)

Statement 5.17 is synonymous with 5.18:

Only some contraries are complementary. (5.18)
Statement 5.16 reflects the views of Kelso and EngstrØm (2006) and Barab (2010)
who list over 100 so-called complementary pairs in their topics. I favor Statements
(5.17) and (5.18) based on the complementarian logic discussed in Sect. 2.3.3 .
Since 5.16 and 5.17 are contraries, they must be COMPLEMENTARY to each
other according to 5.15. That is, defining the relation between 5.16 and 5.17 as
being complementary entails using Statement 5.15. This, I suggest, is an example of
“recursive definition,” similar to the definition of the Fibonacci sequence 5.13. To
rationalize this conclusion, it appears necessary to recognize the three definitions of
complementarities as shown below (where B, KE, and J stand for Bohr, Kelso and
Engstrom, and Ji, respectively):
B-Complementarity (B-C)

¼ Contraries are complementary. (5.19)

KEB-Complementarity (KEB-C) ¼ All contraries are complementary. (5.20)

Not all contraries are complementary. (5.21)
Since, depending on whether or not the complementarian logic is employed, the B-
complementarity can give rise to either the KEB-or the J-complementarity, respec-
tively, it appears logical to conclude that the KEB- and J-complementarities are
themselves the complementary aspects of the B-complementarity. This idea can be
represented diagrammatically as shown in Fig. 5.5 .
After formulating the idea of the “recursivity of complementarity,” I was
curious to find out if anyone else had a similar idea. When I googled the quoted
phrase, I was surprised to find that Sawada and Caley (1993) published a paper
entitled “Complementarity: A Recursive Revision Appropriate to Human Science.”
This paper may be viewed as an indirect support for the conclusion depicted in
Fig. 5.5 . However, upon further scrutiny, there is an important difference between
the perspective of Sawada and Caley (1993) and mine: Sawada and Caley believe
that, in order to introduce the idea of recursivity to complementarity, Bohr's
original complementarity must be revised (by taking the observer into account
explicitly). In contrast, my view is that Bohr's original complementarity is

J-Complementarity (J-C) ¼