Why are highway signs large squares or rectangles? Why do we set up cubicles the way we do? Why are buildings symmetrical pillars that arise from the ground? Why is beauty tied to symmetry?
Alan Lightman, American physicist, writer, and author of The Accidental Universe: The World You Thought You Knew, explores in one of the chapters why we as humans are drawn to symmetry, and more importantly, how we can start understanding this pattern in our lives by studying nature first.
Lightman begins by saying:
“The deep question is: Why does nature embody so much symmetry? We do not know the full answer to this question. However, we have some partial answers. Symmetry leads to economy, and nature, like human beings, seem to prefer economy. If we think of nature as a vast ongoing experiment, constantly trying out different possibilities of design, then those designs that cost the least energy or that require the fewest different parts to come together at the right time will take precedence, just as the principle of natural selection says that organisms with the best ability to survive will dominate over time. On the other hand, as far as we know, the symmetries in the electroweak theory and relativity and chromodynamics did not evolve from ongoing experiments with different designs. Rather, they were apparently built in at the origin of the universe, by whatever processes and principles determined the fundamental laws of physics. … One physical principle that governs nature over and over is the “energy principle”: nature evolves to minimize energy. If you place some marbles on a flat table, after some time has passed you will find most of the marbles on the floor. That’s because a marble on the floor is closer to the center of the Earth and has lower gravitational energy than on the table. Snowflakes have six-sided symmetry because of the angles that the two hydrogen atoms make with the oxygen atom in each water molecule. Those angles minimize the total electrical energy of the water molecule. Any other angles would produce greater energy. Large bodies, like the planet Saturn, are round because a spherical shape minimizes the total gravitational energy.”
This is also why our brain creates habits—to expend less energy in our daily life. It’s why our minds are hardwired for biases, stereotypes, and self-delusions—quick decisions based on our memories allows for easier decisions versus sitting there and contemplating the pros and cons.
Alan Lightman provides an elegant example for the thought above by studying bees and the honeycomb [emphasis mine]:
“A beautiful illustration of some of the ideas above is the beehive. Each cell of a honeycomb is a nearly perfect hexagon, a space with six identical and equally spaced walls. Isn’t that surprising? Wouldn’t it be more plausible to find cells of all kinds of shapes and sizes, fitted together in a haphazard manner? It is a mathematical truth that there are only three geometrical figures with equal sides that can fit together on a flat surface without leaving gaps: equilateral triangles, squares, and hexagons. Any gaps between cells would be wasted space. Gaps would defeat the principle of economy.[…]But why hexagons? Here unfolds another fascinating story. More than two thousand years ago, in 36 BC, the Roman scholar Marcus Terentius Varro conjectured that the hexagonal grid is the unique geometrical shape that divides a surface into equal cells with the smallest total perimeter. And the small total perimeter, or smallest total length of sides, means the smallest amount of wax needed by the bees to construct their honeycomb. For every ounce of wax, a bee must consume about eight ounces of honey. That’s a lot of work, requiring visits to thousands of flowers and much flapping of wings. The hexagon minimizes the effort and expanse of energy. But Varro made only a conjecture. Astoundingly, Varro’s conjecture, known by mathematicians as the Honeycomb Conjecture, was proven only recently, in 1999, by the American mathematician Thomas Hales. The bees knew it was true all along.[…]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 us 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.”
This makes sense when considering the fact that our nervous system and ultimately our nature is hardwired to organize chaos into order. Whether something happens to us for good or ill, there’s always a story—it’s a way for us to make sense of our lives, because it’s difficult for the mind to accept something as meaningless.
Perhaps our love for symmetry, as Lightman suggests, stems from not just the idea of nature but the fact that we come from nature [emphasis mine]:
“Perhaps in asking why the pervasive symmetries in nature are found appealing to the human mind 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 hundreds of millions of years of sensory response to sunlight and sound and tactile connection to the world around our bodies. And the architecture of our brains was born from the same trial and error, the same energy principles, the same pure mathematics that happens in flowers and jellyfish and Higgs particles. Viewed in this way, our human aesthetics 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 inside too.”
The Accident Universe: The World You Thought You Knew is a deeply enriching read on “the emotional and philosophical questions raised by recent discoveries in science.” Lightman shares the various theories of how our universe came to be, and how this molded the human species. He does it with grace and humility, arriving at a point that is existentially difficult to accept: what we understand of the world is perhaps a mere fraction of what is seemingly an unfathomable yet beautiful accident.