Antiquity and After. “Symmetry” is a Greek term
and a Greek conception, and, as Pliny already sensed,
there is perhaps no proper verbal equivalent for it in
any European idiom. However, the term does not occur
in Homer, and it may have indeed been post-Homeric
by formation. Homeric terms have a peculiar verbal
strength, and they also have a central meaning which
they usually retain even if their later connotations are
spread over variant possibilities. But the term sym-
metry was not of this kind. Rather, in the classical
Hellenic era, the term belonged to a group of terms
and locutions that designated harmony, rhythm, bal-
ance, equipoise, stability, good proportions, and even-
ness of structure.
When translating from the Greek for the general
reader it is best to follow Pliny's (and Vitruvius') exam-
ple and let the term symmetry stand as it does, rather
than render it by a locution that, for a scholar, might
perhaps better fit the context. It is true that the dic-
tionary meaning of the term symmetry has shifted since
antiquity, but none of the original connotations has
become obsolete, certainly not entirely so. What has
seriously changed is this, that one of the connotations
that originally was barely there—in a dictionary sense,
that is—has gradually grown to prominence, and even
paramountcy. It is the connotation of “bilateral”
symmetry, or, what is the same, of mirror symmetry.
This symmetry allows a strictly geometric definition,
which can be applied to a visual tableau of any dimen-
sion. If the tableau is spatial, that is, three-dimensional,
a “mirror” is any (two-dimensional) plane in its entire
extension, and it decomposes the tableau into two
half-spaces, such that a design in one of the half-spaces
has, by reflection, a mirror image in the other. A design
and its image are geometrically congruent, except that
they differ in a sense of orientation, as a right-hand
glove differs from its left-hand mate.
In a two-dimensional tableau a “mirror” is a straight
line, any straight line, and on a one-dimensional axis
it is a point. Right and left, above and below, front
and back, when paired in a three-dimensional tableau
refer to mirror reflections with respect to three mutu-
ally perpendicular planes. “Before” and “after” corre-
spond to a bilateral symmetry on the time axis, if, as
usual, this axis is represented by a (Euclidean) straight
line.
