FRACTAL AESTHETICS

Symmetry in Western Art

The dichotomous nature of Western discourse is evident in the Chamber's Dictionary (1994) definition of the word 'symmetry':

'symmetry n exact correspondence of parts on either side of
a straight line or plane or about a centre or axis; beauty of form'
(p. 1747)

The first definition here refers to an actual geometric concept. Yet, 'beauty of form' fails to denote any symmetrical properties at all. The quotation reveals that 'beauty' - a socially constructed connotation of symmetry - has actually come to signify the word itself. As Hermann Weyl wrote:

'Beauty is bound up with symmetry. Thus Polykleitos ...
[was] praised for the harmonious perfection of his sculptures.'
(Symmetry, p.3, 1952)

                      
Seated goddess of symmetry, from Taranto or Locri, c480.
Fig. 5 Seated goddess of symmetry,
from Taranto or Locri, c480.

Due to an initial semantic linkage with 'beauty' and 'harmony', 'symmetry' has occupied the positive pole of a binary opposition since the beginning of Western civilisation (Fig. 5). Only able to occupy the perjorative pole, asymmetry has become negated. The word has thereby suffered an oppositional semantic linkage with 'ugliness' and 'discord'. Undermining the notion that 'the beautiful thing is essentially symmetrical' (Aesthetics, p.80, 1975) has not been a solely twentieth century phenomenon. Plotinus argued against the legitimisation of such a master narrative in the third century. He maintained that if symmetry - a compound artifact - was necessary for beauty then apparently simple artifacts, such as lighting, must be devoid of aesthetic quality. Compound artifacts which are composed of apparent simplicities cannot be beautiful because:

'Beauty in an aggregate demands beauty in detail.'
("On Beauty" Enneads, I, vi, 400/10)

Plotinus's conditions for beauty depend on the existence of self-similairity in an artifact, and their consequent unification:

'The Ideal-Form ... has grouped and coordinated what from a
diversity of parts was to become unity: it has rallied confusion into
operation ... there is beauty of all a house with all its parts, and the
beauty which some natural quality may give to a single stone [of that house].'
(I, vi)

> Plotinus overcomes the duality of 'compound' and 'simple' artifact by suggesting neither is a necessity of beauty. Each artifact is composed of multiplicities ('diversity of parts'); and beauty occurs through a 'unification' of these parts to create a whole, 'as far as multiclicity may'(I, vi). But how are these diverse parts united? Through the continuity of self-similairity operating at different scales in the artifact - because each scale heightens the aesthetic quality of another scale, each scale emphasizes the aesthetic quality of the artifact as a whole. Like Briggs, Plotinus conveys aesthetic intensity as a process ordered by a fractal-like complexity; a dynamic process which refuses habituation. I believe that the duality of symmetry and asymmetry inherent in much of Western Art, dilutes this tension between unity and diversity - a conditon of aesthetic intensity. I will seek to illustrate through a discussion of Picasso's Les Demoiselles d'Avignon (Fig. 6, 1907) how reflectaphoric tension or aesthetic intensity is acheived through a 'unification' or deterritorialization of the symmetry/asymmetry dichotomy. Out of the painting's structure then 'illuminating ambiguities' are able to thrive, which are indelibly representative of its meaning. Therefore, Les Demoiselles d'Avigon's meaning is indelibly linked with aesthetic intensity.

                      
Picasso's Les Demoiselles d'Avigon, 1907 .
Fig. 6 Picasso's Les Demoiselles d'Avigon, 1907

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