Biology Reference
In-Depth Information
Fig. 5.4 The Yin-Yang
symbol visualizing the
concept of
embeddedness
(i.e., the
black dot
in the
white
background
, and the
white dot
in the
black background
)
and the
intertwining
(between
the
white
and
black tear-drop
shapes)
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where n is a natural number greater than or equal to 2. As can be seen, Eq.
5.13
defines the (n + 1)th Fibonacci number in terms of two previous Fibonacci num-
bers. A linguistic example of recursivity is provided by the acronym GNU whose
definition implicates itself: “
G
NU is
n
ot
U
nix.” A biological example of
recursivity
may be suggested to be the self-relication of the DNA double helix, since it
implicates replicating the DNA double helix using the original DNA as the tem-
plate: Self-replication of the DNA double helix is
self-referential
,or
recursive
. The
growth of an organism from a fertilized egg cell can be viewed as recursive process
in the sense that the fertilized egg serves as a template to form its daughter cell, the
daughter cell in turn serving as the template for the production of the next genera-
tion cell, etc. The cell division is recursive or results from a series of recursive
actions. On the basis of these analyses, it may be concluded that life itself is
recursive.
Many physical, chemical, biological, engineering, and logical principles are
mutually
inclusive
and
intertwined
in the sense that it is impossible to separate
them completely. This principle is represented in the familiar Yin-Yang symbol of
the Taoist philosophy (Fig.
5.4
): The dot of the Yin (dark) is embedded in the sea of
the Yang (light) and the dot of the Yang is embedded in the sea of the Yin. The
embeddedness of the Yin in Yang (and vice versa) is reminiscent of the
embeddedness of a sentence within a sentence in human language or the
embeddedness of an algorithm within an algorithm in computer programming,
both of which exemplify the
recursivity
(or the recursion and self-similarity) widely
discussed in computer science (Hofstadter 1980).
The complementarity principle of Bohr seems to embody the principle of
recursivity as the following argument shows. As is well known, Bohr in 1947
inscribed on his coat of arms the following motto:
Contraria sunt complementa. or
(5.14)
Contraries are complementary.
(5.15)
