Symmetry (from Greek συμμετρία symmetria “agreement in dimensions) refers to a sense of harmonious and beautiful proportion and balance. In mathematics and physics “symmetry” is when an object stays the same, in some way, even if it undergoes reflection, rotation or scaling.
The opposite of symmetry is asymmetry.
Why symmetry matters in Physics, Mario Livio
Universal laws are symmetric under translation in space and time — they don’t change from place to place or from today to tomorrow. As astronomers know, hydrogen atoms billions of light years away are subject to the same physics as on Earth.
Because physics has no preferred direction, natural laws are also symmetric under rotation. Whether we measure orientation with respect to the farthest quasar or the nearest coffee shop, the rules are the same. Such symmetries are true of Newton’s laws of gravity and motion, which he applied in the seventeenth century to falling apples, ocean tides, the Moon and planetary orbits.
They are also true of those laws’ twentieth century successors: Albert Einstein’s special and general theories of relativity, with their revolutionary ideas about the constancy of the speed of light, the equivalence of acceleration and gravity, and the warping of space-time by masses. Imposing symmetry on all frames of reference was Einstein’s motivation for developing relativity theory. He wanted to find a way of describing the laws of nature that would look the same to all observers, whether at rest, moving at a constant velocity or accelerating.
In looking for symmetries, Einstein was following in the footsteps of James Clerk Maxwell, a physicist who died the same year Einstein was born, in 1879. Purely for mathematical balance, Maxwell added to equations describing electromagnetism an extra term that related electrical currents to a resulting magnetic field. In doing so, he unified all electric and magnetic phenomena then known, as well as the laws of optics.
from Nature V.490, 25 Oct 2012.
Symmetry and physical beauty
Aesthetic judgements of physical attractiveness – beauty – are not arbitrary. Scientific studies show that they are are related to biology and health, which is often manifested as facial symmetry and “averageness.’
In scientific studies, averageness describes the physical beauty that results from averaging the facial features of people of the same gender and approximately the same age. The majority of averageness studies have focused on photographic overlay studies of human faces, in which images are morphed together. The term “average” is used strictly to denote the technical definition of the mathematical mean. An averaged face is not unremarkable, but is, in fact, quite good looking. Nor is it typical in the sense of common or frequently occurring in the population, though it appears familiar, and is typical in the sense that it is a good example of a face that is representative of the category of faces.
A possible evolutionary explanation for averageness is koinophilia, in which sexually-reproducing animals seek mates with primarily average features, because extreme and uncommon features are likely to indicate disadvantageous mutations. – Wikipedia
Science College Board Standards for College Success
Standard: Form and function are complementary aspects of objects, organisms and systems in the natural and designed world. The form (i.e., shape, composition, symmetry, orientation in space) of an object or system is frequently related to use, operation or function.
Enduring Understanding 5E: The conservation of angular momentum is a consequence of the symmetry of physical laws under rotation, which means that if everything relevant to an experiment is turned through some angle, the results of the experiment will be the same.
Benchmarks for Science Literacy, American Association for the Advancement of Science
Constancy and Change. …Because scientists are always looking for the simplest possible accounts (that are true), they are always delighted by any aspect of anything that doesn’t change even when many other aspects do. Indeed, many historians and philosophers regard conservation laws in physics (such as for mass, energy, or electric charge) to be among the greatest discoveries in science. Somewhat different aspects of constancy are described by the terms stability, conservation, equilibrium, steady state, and symmetry. These various ideas are interrelated in some subtle ways. But memorizing the distinct meanings for these terms is not a high priority. More important is being able to think about what is happening.
Symmetry is another kind of constancy—or more generally, invariance—in the midst of change. Equilibrium, steady states, and conservation might all be thought of as showing symmetry. But more typically, symmetry implies a pattern whose appearance stays the same when it undergoes a change such as rotation, reflection, stretching, or displacement. The symmetry can be geometrical or more general, as in a social order, set of computer operations, or classification of atomic particles.
Symmetry (or a lack of it) may determine properties of many objects, from molecules and crystals to organisms and designed structures. 11C/H13** (BSL)