It almost always involves “mirror image” (horizontally bilateral) symmetry—two matching lamps on either side of a room, or maybe bookends. But, in William Blake’s famous verse

“Tyger, tyger, burning bright

In the forests of the night,

What immortal hand or eye

Could frame thy fearful symmetry?”

he was surely talking about something deeper than the similarity between the right and left sides of the tiger. Dictionary definitions of symmetry often mention correspondence of parts on either side of an axis, after the idea of pleasing proportion, beauty, and harmony… more likely the idea that Blake had in mind. Consider that standing up from the couch in the living room, sitting at the dinner table, and then returning to the couch an hour later is symmetry of movement– one’s dining room chair is an axis of sorts in space, but so is the middle of dinner an axis in time.

Mineral crystals are among the most easily visible of nature’s tendencies towards mathematical regularity and predictability, but scientists of all kinds – from chemists and nuclear physicists to sociologists and behavioral scientists observe and take advantage of the countless examples of symmetry in the workings of the world and universe around us. Crystallography expands our ideas of “bookend” symmetry to include symmetries not only based on two axes, like most mandala art, but three axes, four axes, and more. All symmetries take place around a center point. Two identical pencils, placed at right angles with their points touching, demonstrate a symmetry of 90 degree rotation. Most ambigrams demonstrate 180 degree rotational symmetry.

In both scientific and the artistic symmetries, an often overlooked phenomenon is the concept of “dissymmetry.” Quite different from “asymmetry,” dissymmetry is a state of *almost* perfect symmetry. As beautifully proportioned as they are, few mineral crystals achieve perfect symmetry. One might look at the system of tributaries that feeds a river, or the shape of a tree, observing at a glance the impression of symmetry. Of course, neither of these examples, or any of a myriad of other natural occurrences is perfectly symmetrical—far from it. But the apparent symmetries are critical to an understanding of those systems. In the graphic arts, perfect symmetry is usually considered static, and thus less interesting than an almost perfect symmetry. Even if subtle, the departures from the regularity are said to invigorate the design as a whole. As an example, consider the importance of the differing treatments of the yin/yang symbols on the cover of *Wordplay*—how much less interesting the cover would have been had they treated identically. When we include not only symmetries with multiple axes, rotational symmetries, symmetries in time, and the universe-full of dissymmetries, there is a lot more symmetry around than we might think. In his book, *Das Energi*, Paul Williams puts it this way:

“Truth is what sounds right.

Beauty is what looks right.

Beware of Symmetry.

Beware means aware.”

It almost always involves “mirror image” (horizontally bilateral) symmetry—two matching lamps on either side of a room, or maybe bookends. But, in William Blake’s famous verse

“Tyger, tyger, burning bright

In the forests of the night,

What immortal hand or eye

Could frame thy fearful symmetry?”

he was surely talking about something deeper than the similarity between the right and left sides of the tiger. Dictionary definitions of symmetry often mention correspondence of parts on either side of an axis, after the idea of pleasing proportion, beauty, and harmony… more likely the idea that Blake had in mind. Consider that standing up from the couch in the living room, sitting at the dinner table, and then returning to the couch an hour later is symmetry of movement– one’s dining room chair is an axis of sorts in space, but so is the middle of dinner an axis in time.

Mineral crystals are among the most easily visible of nature’s tendencies towards mathematical regularity and predictability, but scientists of all kinds – from chemists and nuclear physicists to sociologists and behavioral scientists observe and take advantage of the countless examples of symmetry in the workings of the world and universe around us. Crystallography expands our ideas of “bookend” symmetry to include symmetries not only based on two axes, like most mandala art, but three axes, four axes, and more. All symmetries take place around a center point. Two identical pencils, placed at right angles with their points touching, demonstrate a symmetry of 90 degree rotation. Most ambigrams demonstrate 180 degree rotational symmetry.

In both scientific and the artistic symmetries, an often overlooked phenomenon is the concept of “dissymmetry.” Quite different from “asymmetry,” dissymmetry is a state of *almost* perfect symmetry. As beautifully proportioned as they are, few mineral crystals achieve perfect symmetry. One might look at the system of tributaries that feeds a river, or the shape of a tree, observing at a glance the impression of symmetry. Of course, neither of these examples, or any of a myriad of other natural occurrences is perfectly symmetrical—far from it. But the apparent symmetries are critical to an understanding of those systems. In the graphic arts, perfect symmetry is usually considered static, and thus less interesting than an almost perfect symmetry. Even if subtle, the departures from the regularity are said to invigorate the design as a whole. As an example, consider the importance of the differing treatments of the yin/yang symbols on the cover of *Wordplay*—how much less interesting the cover would have been had they treated identically. When we include not only symmetries with multiple axes, rotational symmetries, symmetries in time, and the universe-full of dissymmetries, there is a lot more symmetry around than we might think. In his book, *Das Energi*, Paul Williams puts it this way:

“Truth is what sounds right.

Beauty is what looks right.

Beware of Symmetry.

Beware means aware.”