But why are we attracted to symmetry?  Why do we human beings delight in seeing perfectly round planets through the lens of a telescope and six-sided snowflakes on a cold winter day?  The answer must be partly psychological.  I would claim that symmetry represents order, and we crave order in this strange universe we find ourselves in.  The search for symmetry , and the emotional pleasure we derive when we find it, must help is make sense of the world around us, just as we find satisfaction in the repetition of the seasons and the reliability of friendships.   Symmetry is also economy. Symmetry is simplicity.  Symmetry is elegance.

And however we define the mysterious quality that we call beauty, we associate symmetry with beauty.  Both Darwin and Freud have argued that our sense of beauty and the appeal of beauty originated with the imperative for sexual reproduction and the association of beauty with vibrant mate.  As Darwin wrote in the Descent of Man,

Clearly, human-made art and architecture abound with symmetry.  The Taj Mahal has a central dome and arch, two identical side domes, and four identical towers, symmetrically places.  Leading to the building is a rectangular pool with equally spaced cypress trees on both sides of the pool and symmetrical gardens beyond.  The octagon on Roosevelt Island in New York, designed by Alexander  Jackson Davis, is shaped like a you-know-what.  Leonardo da Vinci’s famous ‘Vitruvian Man’ depicts a figure with two identical sets of outstretched and equally spaced arms and legs, one set inscribed within a circle and one within a square.  The mosaic floor of the great cathedral at Cologne has a stunning set of nested circles filled with symmetrically placed flowers.  A widely reproduced image of Lakshmi shows the Hindu goddess sitting in the center of a circular flower with two identical arms raised  upward and holding identical yellow flowers, two more identical arms lowered releasing flower petals, and two identical elephants on each side of her pouring water from identical jugs.  However, if one looks at the image closely, it will be seen that there is a slight departure  from perfect symmetry.  Lakshmi has a red scarf draped over her left shoulder but not her right.  

In fact, human-made art, especially in painting, it sees that a slight bit of asymmetry is desirable and found to achieve a higher aesthetic satisfaction.  Ernst Gombrich, one of the leading (Western) art historians of the twentieth century, believes that although human beings have a deep psychological attraction to order, perfect order in art is uninteresting.  “However we analyse the difference between the regular and the irregular,” he writes, “we must ultimately be able to account for the most basic fact of aesthetic experience, the fact that delight lies somewhere between boredom and confusion.  If monotony makes it difficult to attend, a surfeit of novelty will overload the system and cause us to give up.”  My wife, a painter trained in the tradition of the Boston School dating back to the early 1900s, always tells me that a well-designed painting should have some off-center and asymmetrical accent.  Of course, asymmetry can be defined only relative to symmetry, and vice versa. Asymmetric elements in paintings of buildings are most effective when superimposed against a background of symmetry.  Perhaps nature is being the painter when she occasionally violates complete symmetry with irregular coastlines and the amorphous shapes of clouds.  

We should also point out that the association of symmetry with beauty in art is partially cultural.  In some non-Western cultures, asymmetries can be as lovely as symmetries.  No obvious symmetry can be found in the great wall of China, for example.  Instead, it was built to conform to its natural terrain.  The wall wanders and curves with the shape of the land, and its towers are irregularly spaced.  It blends with its surroundings.  The Chinese sense of beauty is, in some ways , more subtle, ambiguous, and less articulated  than that of the West.  For example, the world of the living is considered to be in symmetrical balance to the world of the dead.  On the other hand, even in the Chinese artistic tradition, we find some obvious symmetries, such as the couplet in classical Chinese poetry, where verb is aligned with verb, noun with noun, rhyme with rhyme.  

I find myself now looking at an old photograph taken in 1949.  I am a baby, held in my mother’s lap.  Standing directly behind her is her mother, and on her right and left are her two grandmothers, my great-grandmothers-a symmetrical arrangement of five people.  I study faces, looking for more symmetry, or lack of it.  Of course, , there are the familiar symmetries of the human head.  I look more closely.  One of my great-grandmothers, called Oma, has a mouth that droops slightly on the left side, breaking the symmetry of her face.  I associate that droop with the sadness of losing her husband only a few years into her marriage.  If I look even more closely at the photograph, I can see a blemish on her right cheek, possibly an age spot, also breaking the symmetry.  But these slight asymmetries announce themselves only against the background of symmetry.  

In the end, it is easier to explain why bees construct honeycombs shaped like perfect hexagons than why human beings place identical towers on the side of the Taj Mahal.  or the two grandmothers on equal sides of the mother.  The first is a result of economy and mathematics, the second of psychology and aesthetics.  Perhaps in asking why the pervasive symmetries in nature are found appealing to the human mind and and imitated in our human-made constructions, we are making an erroneous distinction between our minds and the remainder of nature.  Perhaps we are all the same stuff.  After all, our minds are made of the same atoms and molecules as everything else in nature.  The neurons in our brains obey the same physical laws as planets and snowflakes.  Most important, our brains developed out of nature, out of hundred s of millions of years of sensory response to sunlight and sound and tactile connection to the world around the bodies.  And the architecture of our brains was born from the same trial and error, the same energy principles, the same pure mathematics that happen in flowers and jellyfish and Higgs particles.  Viewed in this way, our human aesthetic is necessarily the aesthetic of nature.  Viewed in this way, it is nonsensical to ask why we find nature beautiful.  Beauty and symmetry and minimum principles are not qualities we ascribe to the cosmos and then marvel at in their perfection.  They are simply what is, just like the particular arrangement of atoms that make up our minds.  We are not observers on the outside looking in.  We are on the insdie too.

-The Accidental Universe

Alan Lightman