Information Technology Reference
In-Depth Information
aesthetic measure proposed the simple ratio
M
O/C
where
M
is the measure of
aesthetic effectiveness,
O
is the degree of order, and
C
is the degree of complexity.
But what is complexity? And what is order? Birkhoff suggested that these are
proxies for the effort required (complexity) and the tension released (order) as per-
ceptual cognition does its work. As a practical matter Birkhoff quantified complex-
ity and order using counting operations appropriate to the type of work in question.
For example, in his study of polygonal compositions complexity was determined by
counting the number of edges and corners. His formula for order was:
=
O
=
V
+
E
+
R
+
HV
−
F
(10.2)
Here he sums the vertical symmetry (
V
), equilibrium (
E
), rotational symmetry
(
R
), horizontal-vertical relation (
HV
), and unsatisfactory or ambiguous form (
F
).
These notions of complexity and order at first appear to be formulaic and objective,
but they nevertheless require subjective decisions when quantified.
In an attempt to add conceptual and quantitative rigour, Bense (
1965
) and Moles
(
1966
) restated Birkhoff's general concept in the context of Shannon (
1948
)'s in-
formation theory creating the study of
information aesthetics
. Shannon was inter-
ested in communication channels and the quantification of information capacity and
signal redundancy. From this point of view an entirely unpredictable random signal
maximises information and complexity, and offers no redundancy or opportunity for
lossless compression. In this context disorder or randomness is also called
entropy
.
Extending this, Moles equated low entropy with order, redundancy, compressibility,
and predictability. High entropy was equated with disorder, complexity, incompress-
ibility, and surprise (see Chap. 3 for further discussion of information aesthetics).
As previously noted, Machado (
1998
) has updated this approach by calculating
aesthetic value as the ratio of
image complexity
to
processing complexity
. Processing
complexity refers to the amount of cognitive effort that is required to take in the
image. Image complexity is intrinsic to the structure of the image. This lead them
to propose functional measures where image complexity is inversely proportional to
JPEG compressibility and processing complexity is directly proportional to fractal
compressibility.
With the advent of complexity science as a discipline defining order and com-
plexity has become much more problematic. This account begins with
algorithmic
complexity
or
algorithmic information content
as independently developed by Kol-
mogorov (
1965
), Solomonoff (
1964
), Chaitin (
1966
). In this paradigm the complex-
ity of an object or event is proportional to the size of the shortest program on a
universal computer that can duplicate it. From this point of view the most complex
music would be white noise and the most complex digital image would be random
pixels. Like information complexity, algorithmic complexity is inversely propor-
tional to order and compressibility.
For physicist Murray Gell-Mann the information and algorithmic notions of com-
plexity don't square with our experience. When we encounter complex objects or
situations they aren't random. Despite being difficult to predict they also have some
degree of order maintaining integrity and persistence.
