On Symmetry I

“Symmetry is what we see at a glance; based on the fact that there is no reason for any difference, and based also on the face of man; whence it happens that symmetry is only wanted in breadth, not in height or depth.” (Blaise Pascal, “Pensées”, 1670)

“Symmetry is evidently a kind of unity in variety, where a whole is determined by the rhythmic repetition of similar.” (George Santayana, “The Sense of Beauty”, 1896)

“By the word symmetry […] one thinks of an external relationship between pleasing parts of a whole; mostly the word is used to refer to parts arranged regularly against one another around a centre. We have […] observed [these parts] one after the other, not always like following like, but rather a raising up from below, a strength out of weakness, a beauty out of ordinariness.” (Goethe)

“In everyday language, the words 'pattern' and 'symmetry' are used almost interchangeably, to indicate a property possessed by a regular arrangement of more-or-less identical units […]” (Ian Stewart & Martin Golubitsky, “Fearful Symmetry: Is God a Geometer?”, 1992)

“In the one sense symmetric means something like well-proportioned, well-balanced, and symmetry denotes that sort of concordance of several parts by which they integrate into a whole. Beauty is bound up with symmetry.” (Hermann Weyl, “Symmetry”, 1952)

“A thing is symmetrical if there is something you can do to it so that after you have finished doing it, it looks the same as before.” (Hermann Weyl, “Symmetry”, 1952)

“[…] a symmetry isn't a thing; it's a transformation. Not any old transformation, though: a symmetry of an object is a transformation that leaves it apparently unchanged.” (Ian Stewart & Martin Golubitsky, “Fearful Symmetry: Is God a Geometer?”, 1992)

“A symmetry is a set of transformations applied to a structure, such that the transformations preserve the properties of the structure.” (Philip Dorrell, “What is Music?: Solving a Scientific Mystery”, 2004)

“Symmetry is the representation of two or more equivalent or balanced elements with respect to a common origin, position, or axis.” (David Smith, “The Symmetry Solution: A Modern View of Biblical Prophecy”, 2009)

“Symmetry is basically a geometrical concept. Mathematically it can be defined as the invariance of geometrical patterns under certain operations. But when abstracted, the concept applies to all sorts of situations. It is one of the ways by which the human mind recognizes order in nature. In this sense symmetry need not be perfect to be meaningful. Even an approximate symmetry attracts one's attention, and makes one wonder if there is some deep reason behind it.” (Eguchi Tohru & ‎K Nishijima , “Broken Symmetry: Selected Papers Of Y Nambu”, 1995)