Koen De Paus originally shared this post:
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1) An imprecise sense of harmonious or aesthetically pleasing proportionality and balance; such that it reflects beauty or perfection.
2) A precise and well-defined concept of balance or "patterned self-similarity" that can be demonstrated or proved according to the rules of a formal system: by geometry, through physics or otherwise.
When we think of symmetry, we tend to think of option 1, which relates more to our human world of feeling and beauty. When we look at a face we see symmetry but this is an illusion caused by the scale on which we view things and the lack of detail our eyes can pick up. The symmetry we see in our day to day lives is an approximation. If you were to zoom in on a complex object, let's say a face, there will always be flaws, a scar or even a stray molecule is enough to to break perfect symmetry.
Perfect symmetry is almost impossible to attain for complex objects but remarkably, there exists a realm of physics where simple symmetries in real objects cease to be approximations and become perfect. That is the domain of quantum physics, which for the most part is the physics of very small, very simple objects such as electrons, protons, light, and atoms.
Why is it that we find symmetry so attractive? Asymmetry can surprises you while symmetry offers you a nearly identical data set. Don't we like surprises? Perhaps the brain likes simplicity? If it anticipates symmetry, it doesn't need to process as much information, it can figure out what the right side of a face looks like even if it only gets to see the left side. Which is pretty amazing but also causes quite a bit of trouble when the revealed side of the face differs from our expectations…