On Symmetry V (Symmetry vs. Asymmetry I)

“Symmetry may have its appeal but it is inherently stale. Some kind of imbalance is behind every transformation.” (Marcelo Gleiser, “A Tear at the Edge of Creation: A Radical New Vision for Life in an Imperfect Universe”, 2010)

“Rut seldom is asymmetry merely the absence of symmetry. Even in asymmetric designs one feels symmetry as the norm from which one deviates under the influence of forces of non-formal character.” (Hermann Weyl, “Symmetry”, 1952)

“[…] in all things that live there are certain irregularities and deficiencies which are not only signs of life, but sources of beauty. No human face is exactly the same in its lines on each side, no leaf perfect in its lobes, no branch in its symmetry. All admit irregularity as they imply change; […]” (John Ruskin, “The Stones of Venice: The Sea Stories”, 2013)

“Nature is never perfectly symmetric. Nature's circles always have tiny dents and bumps. There are always tiny fluctuations, such as the thermal vibration of molecules. These tiny imperfections load Nature's dice in favour of one or other of the set of possible effects that the mathematics of perfect symmetry considers to be equally possible.” (Ian Stewart & Martin Golubitsky, “Fearful Symmetry: Is God a Geometer?”, 1992)

“In every symmetrical system every deformation that tends to destroy the symmetry is complemented by an equal and opposite deformation that tends to restore it. […] One condition, therefore, though not an absolutely sufficient one, that a maximum or minimum of work corresponds to the form of equilibrium, is thus applied by symmetry.” (Ernst Mach, “The Science of Mechanics: A Critical and Historical Account of Its Development”, 1893)

“Symmetry is a fundamental organizing principle of shape. It helps in classifying and understanding patterns in mathematics, nature, art, and, of course, poetry. And often the counterpoint to symmetry — the breaking or interruption of symmetry - is just as important in creative endeavors.” (Marcia Birken & Anne C. Coon, “Discovering Patterns in Mathematics and Poetry”, 2008)

“An asymmetry in the present is understood as having originated from a past symmetry.” (Michael Leyton, “Symmetry, Causality, Mind”, 1992)

“Approximate symmetry is a softening of the hard dichotomy between symmetry and asymmetry. The extent of deviation from exact symmetry that can still be considered approximate symmetry will depend on the context and the application and could very well be a matter of personal taste.” (Joe Rosen, “Symmetry Rules: How Science and Nature Are Founded on Symmetry”, 2008)

“[…] asymmetry can be defined only relative to symmetry, and vice versa. Asymmetric elements in paintings or buildings are most effective when superimposed against a background of symmetry.” (Alan Lightman, “The Accidental Universe: The World You Thought You Knew”, 2014)

“Chaos demonstrates that deterministic causes can have random effects […] There's a similar surprise regarding symmetry: symmetric causes can have asymmetric effects. […] This paradox, that symmetry can get lost between cause and effect, is called symmetry-breaking. […] From the smallest scales to the largest, many of nature's patterns are a result of broken symmetry; […]” (Ian Stewart & Martin Golubitsky, “Fearful Symmetry: Is God a Geometer?”, 1992)