In physics, something has a symmetry if you can do something to it, and after you've done it the original thing hasn't changed. It can be shown that symmetries of the laws of physics are deeply connected to conservation laws. In quantum mechanics it becomes possible to build entire theories by looking at the symmetries they have to satisfy. The models of elementary particles are built this way.

The Symmetry of an object is defined in terms of the symmetry operations that can be performed upon it.

The symmetry of a particular object can be defined in terms of this set of operations which gives a classification known as the point group of the object. Because of the interrelationships between the operations there are only a small number of different point groups (at least in Euclidean space).

Symmetry is also the idea that the laws of physics apply to all observers identically, i.e. that regardless of your acceleration, velocity, or position in space and time the same laws of physics apply. You might recognize that symmetry with respect to velocity is sometimes called special relativity, and that symmetry with respect to acceleration is sometimes called general relativity. This is a pretty important concept, since it would make physics a LOT harder if you had to find different laws of physics for different observers. The laws of physics are also symmetric with respect to orientation, that is, it doesn't matter from what angle you are observing something, the same laws apply. There are also symmetries with respect to forces that are called gauge symmetries that are a lot more abstract, and which I only vaguely understand, so I'm not going to try and explain them. There is at least one more kind of symmetry that I really don't understand, which has to do with the spin of the elementary particles. Basically, there are a lot more kinds of symmetry than you might expect, and a lot of them have nothing to do with what something looks like if you look at it in a mirror.

At one point TPC symmetry or time-parity-charge -symmetry was considered to be one of the most fundamental laws of physics. The basic idea is that any elementary event can happen forwards or backwards (symmetrical in time), left- or righthandedly (symmetrical in parity) and with a negative or positive charge (symmetrical in charge). More recently (late last century) a case was however found in which a certain particle will, as it decays, emit a smaller particle in a certain direction relating to the axis around which it is spinning. This, as far as I understand, is in violation with parity symmetry.

The human love of symmetry is a biological part of us, because it helps us to choose genetically more advantageous mates, with fewer genetic abnormalities and better nutritional upbringing. Both genetic abnormalities (such as Marfan's Syndrome) and severe nutritional deficiencies (such as Vitamin D deficiency also called Rickets when severe) can cause abnormal fetal and developmental growth patterns resulting in bodily asymmetry, both gross and subtle.

While what we consider beautiful can be modified by culture, at least some characteristics of beauty are very much cross-cultural. A love of symmetry in the body generally and the face in particular, is not restricted to this culture - and it's not surprising that a contrary love of mutations hasn't prevailed instead. Most mutations, most of the time are pernicious, and sexual selection for abnormality in bilateral symmetry in particular would raise the probability of miscarriage and early death in the offspring of organisms with this preference, selecting them out of their species, in time.

Which is just to say that this love of symmetry is unlikely to be merely human, but present in animals which choose mates (during the day at least, so frogs maybe not so much). First posted June 25, 2004

A stream of multicolored light fills the Eastern sky
early, before the alarm buzzes
giving us time to make you late.

Afternoons are spent mostly apart
you, to and from offices
me, to and from appointments
leaving each other messages, checking in

Evenings are for errands
you with a list in one store
me without a list, in another
calling to remember what I forgot

The light of a single streetlight fills our bedroom
late, long after other lights are extinguished
a few minutes before midnight,
giving me time to watch you sleep.

Sym"me*try (?), n. [L. symmetria, Gr. ; with, together + a measure: cf. F. sym'etrie. See Syn-, and Meter rhythm.]

1.

A due proportion of the several parts of a body to each other; adaptation of the form or dimensions of the several parts of a thing to each other; the union and conformity of the members of a work to the whole.

2. Biol.

The law of likeness; similarity of structure; regularity in form and arrangement; orderly and similar distribution of parts, such that an animal may be divided into parts which are structurally symmetrical.

Bilateral symmetry, or two-sidedness, in vertebrates, etc., is that in which the body can be divided into symmetrical halves by a vertical plane passing through the middle; radial symmetry, as in echinoderms, is that in which the individual parts are arranged symmetrically around a central axis; serial symmetry, or zonal symmetry, as in earthworms, is that in which the segments or metameres of the body are disposed in a zonal manner one after the other in a longitudinal axis. This last is sometimes called metamerism.

3. Bot.

(a) Equality in the number of parts of the successive circles in a flower.

(b) Likeness in the form and size of floral organs of the same kind; regularity.

Axis of symmetry. Geom. See under Axis. -- Respective symmetry, that disposition of parts in which only the opposite sides are equal to each other.