Information Technology Reference
In-Depth Information
Fig. 10.1
Information and
algorithmic complexity
increase monotonically with
increasing disorder. Effective
complexity peaks where there
is a mix of order and disorder
such as is found in biological
life
Consider two situations, one where there is a living frog and another where there
is a long dead and decaying frog. The decaying frog has greater entropy because
relative to the living frog it is more disordered, and over time it will become more
even more disordered to the point where it will no longer be identifiable as a frog at
all. Intuitively we would identify the living frog as being more complex. It displays
a repertoire of behaviours, operates a complex system of biochemistry to process
food, water, and oxygen to generate energy and restore tissues, maintains and ex-
changes large amounts of genetic information in the course of reproduction, and so
on. Along with these orderly processes the frog remains flexible and unpredictable
enough to be adaptive and avoid becoming easy prey. In terms of entropy our highly
complex living frog is somewhere between simple highly ordered crystals and sim-
ple highly disordered atmospheric gases.
To better capture our intuitive sense of complexity Gell-Mann has proposed the
notion of
effective complexity
, a quantity that is greatest when there is a balance of
order and disorder such as that found in the biological world (Gell-Mann
1995
). Un-
like information and algorithmic complexity, effective complexity is not inversely
proportional to order and compressibility. Rather both order and disorder contribute
to complexity (Fig.
10.1
, please note that this graph is only meant as a qualitative
illustration with somewhat arbitrary contours).
Complexity science continues to offer new paradigms and definitions of com-
plexity. In a 1998 lecture by Feldman and Crutchfield at the Santa Fe Institute well
over a dozen competing theories were presented (Feldman and Crutchfield
1998
)—
the debate over complexity paradigms continues. Measuring aesthetic value as a re-
lationship between complexity and order is no longer the simple proposition it once
seemed to be. (For an alternate view of complexity and aesthetics see Chap. 12.)
Artists working in any media constantly seek a balance between order and disor-
der, i.e. between fulfilling expectations and providing surprises. Too much of the for-
mer leads to boredom, but too much of the latter loses the audience. It is a dynamic
that applies to visual art, music, and the performing arts alike. And it helps dif-
ferentiate genres in that styles that cater to established expectations are considered
