What is symmetry? | ||

## Symmetry |
||

is a | ||

phenomenon, | class of properties, | concept |

which is present in | ||

all scientific disciplines |
and | all kinds of the arts |

Symmetry bridges | ||

different disciplines, |
and sciences,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:

*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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