is a
phenomenon,
class of properties,
concept
which is present in
all scientific disciplines
and
all kinds of the arts
Symmetry bridges
different disciplines,
sciences
and arts,
different cultures
The term symmetry is of ancient Greek origin. Its meaning is in close association with the related terms of
a
symmetry, dis
symmetry, anti
symmetry. Symmetry and the lack of symmetry characterise the
phenomena in our natural and artificial environment, as well as our ideas about the world.
Traditional meaning of symmetry
The meaning of this term went through a fabulous transformation during its use for dozens of centuries.
The proper translation of the Greek term
symmetria
- (from the prefix
syn [common] and the noun
metros [measure])
- is 'common measure'. The Greeks interpreted this word, as the
harmony
of the different parts of an object, the good
proportions between
its constituent parts. Later this meaning was transferred to e.g., the
rhythm
of poems, of music, the
cosmos ('well-ordered system of the universe as contrast of chaos').
Therefore the Latin and the modern European languages
used its translations like
harmony, proportion until the Renaissance.
In wider sense,
balance, equilibrium belonged also to this family of synonyms.
Some way symmetry was always related to
beauty,
truth and
good.
(These relative meanings determined its application in the
arts, the
sciences, and the
ethics, respectively.)
Symmetry was not only related to such positive values, it became even a symbol of seeking for perfection.
Common meaning of symmetry
In its
everyday use symmetry is associated with its
most frequent manifestations, like
reflection or, in other words,
mirror-symmetry,
rotation (rotational symmetry), and
repetition
(translational symmetry). A few further geometrical appearances of symmetry
belong also to this class of interpretations, like
glide reflection,
similitude, affine projection, perspective, topological symmetry.
All they are associated with the observation, that one performed
a certain
geometric operation (a transformation) on an object;
and during that transformation one (or more)
geometric properti(es)
of that
geometric object did not change (were conserved).
That/those property/ies proved to be
invariant under the given transformation.
They are called '
symmetry' in everyday life.
Generalised, contemporary meaning of symmetry
In generalised meaning
one can speak about symmetry if
- under any (not certainly geometric) kind of
transformation (operation),
- at least one (not certainly geometric)
property
- of the (not certainly geometric)
object
is left invariant (intact).
Thus we made a generalisation in 3 respects: to
-
any transformation,
-
any object, and its
-
any property.
This
generalised meaning of symmetry made possible to apply symmetry
to materialised objects in the physical and the organic nature, to products
of our mind, etc. Over geometric (morphological) symmetries, we can discuss
functional symmetries and
asymmetries (e.g., in the human brain),
gauge symmetries (of physical phenomena);
properties, like colour, tone, shadiness, weight, etc. (of artistic objects).
Asymmetry: The lack of symmetry
Dissymmetry: The observed object is symmetric in its main features,
but this symmetry is slightly distorted
(e.g., an arabesque ornament)
Antisymmetry: The observed object is symmetric in one of its properties,
but one of its other properties changes to its opposite
(e.g., a chess-board)
(G. Darvas © )
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