Symmetry in Nature: Fundamental Fact or Human Bias?

image of peacock. (Image credit:

Women have more orgasms during sex with men who are more symmetrical. Does this penchant for order cloud our ability to see the universe accurately? A new book by theoretical astrophysicist Mario Livio explores the question.

DURING THE EARLY PART OF THE 20TH CENTURY, the famous Harvard mathematician George David Birkhoff developed a mathematical formula which he believed could be used to gauge how beautiful and appealing a work of art was.

Birkhoff's formula relied on two abstract concepts: complexity and order (or symmetry). According to Birkhoff, if something is complex, it will be more appealing if it is less symmetrical. Alternatively, if something is highly-symmetrical, it is better if it is less complex.

The formula seemed to make sense in theory, but there was one major problem: how to measure complexity and symmetry? Birkhoff claimed there was a way to do this, but his methods were too subjective for most people's tastes and his formula was soon forgotten.


Despite his failed effort, Birkhoff's idea that symmetry is a crucial determining factor for an object's aesthetic appeal is once again gaining credence in science, but in a slightly different form. In biology, recent studies have found that humans and other animals are highly attuned to symmetry in each other and often use it to gauge beauty and health during mate selection. Sensitivity to symmetry, it seems, is ingrained into our behavior.

Leonardo Da Vinci modeled his perfect human form after the proportions laid out by Vitruvius, an ancient Roman architect. Da Vinci's Best Ideas

Mario Livio, a senior astrophysicist at the Space Telescope Science Institute in Baltimore, wonders if our biological preference for symmetry is biasing our perception of the world, influencing what humans find beautiful or even affecting the way we conduct science.

Livio is the author of "The Equation That Couldn't Be Solved" (2005, Simon & Schuster Trade), a book that explores symmetry in everything from biology and physics to music and the visual arts.

"Because our brains are so fine tuned to detect symmetry, is it possible that both the tools that we use to determine the laws of nature and indeed our theories themselves have symmetry in them partly because our brains like to latch onto the symmetric part of the universe and not because it's the most fundamental thing?" Livio wonders.

Symmetry and sex

The body plans of most animals, including humans, exhibit mirror symmetry, also called bilateral symmetry. They are symmetric about a plane running from head to tail (or toe).

Bilateral symmetry is so prevalent in the animal kingdom that many scientists think that it can't be a coincidence. After all, there are infinitely more ways to construct an asymmetrical body than a symmetrical one. And yet, fossilized evidence shows that bilateral symmetry had already taken hold in animals as early as 500 million years ago.

Therefore, bilateral symmetry must have evolved for a reason, the thinking goes. And over the years, scientists have come up with a number of hypotheses about what that reason might be. According to one, a body that is bilaterally symmetrical is easier for the brain to recognize while in different orientations and positions, thus making visual perception easier.

Another popular hypothesis is that symmetry evolved to help with mate selection. Experiments with birds and insects revealed that females prefer to mate with males possessing the most symmetrical sexual ornaments. Peahens, for example, prefer peacocks with more extravagant and symmetrical tails, and female barn swallows prefer males with long, symmetrical tail feathers.

Human experiments also show similar patterns.

Experiments have found that women are more attracted to men who have features that are more symmetrical than other men. One study even found that women have more orgasms during sex with men who were more symmetrical, regardless of their level of romantic attachment or the guys' sexual experience.

The connection between body symmetry and mate selection began to make sense when researchers started finding correlations between symmetry and health. One study found that men with asymmetric faces tend to suffer more from depression, anxiety, headaches and even stomach problems. Women with facial asymmetry are less healthy and more prone to emotional instability and depression.

Another study found that the more asymmetric a person's body was, the more likely they were to show signs of aggression when provoked.

Symmetry is also prevalent in the physical sciences and is woven into the very laws that govern our universe.

Symmetry in physics

In mathematics, the language of physics, symmetry has a more precise meaning. Livio defines it as an immunity to change. "Namely you do a certain operation and something does not change, you call that a symmetry," he told LiveScience.

This definition takes into account bilateral symmetry but it also includes other symmetries as well:

  • Time translation symmetry: Physical laws do not change with time.
  • Translational symmetry: The laws of physics are the same whether they are acting in our solar system or at the far end of the universe.
  • Rotational symmetry: The laws of physics don't change if we turn around.

These symmetries are crucial for understanding science, especially physics. If the laws of nature were not symmetrical, there would be no hope of ever discovering them. In a universe where the natural laws were not symmetrical, experimental results might change depending on where and when and in what direction an experiment was performed.

Here's an example of the importance of all this: One way astronomers are able to determine the material composition of stars that are millions of light-years away is to examine the chemical signatures encoded in the light they emit. In order for the astronomer's conclusions to be of any value, the atoms in those stars must obey the same laws that govern our corner of the universe.

Symmetry is so integral to the way the universe works that Albert Einstein used it as a guiding principle when he devised his General Theory of Relativity.

Einstein firmly believed that the laws of physics should be the same for all observers, regardless of how they were moving. Through various thought experiments, Einstein discovered another fundamental symmetry in nature, called general covariance. Under this symmetry, physical laws act the same regardless of whether an object is accelerating or at rest. In other words, the force of gravity and the force resulting from acceleration are two facets of the same force—that is, they are symmetrical.

Scientists have glimpsed other symmetries in nature as well.

A positron, for example, can be thought of as a mirror image of an electron. And James Clerk Maxwell, a 19th century mathematical physicist, demonstrated symmetry between electric and magnetic fields. Through a series of equations, Maxwell demonstrated that electricity and magnetism are actually two complementary aspects of a more fundamental force, called electromagnetism.

Many scientists suspect that there may be more natural symmetries waiting to be discovered. Some think that the so-far elusive "Theory of Everything," which physicists have spent decades searching for, will contain some type of universal symmetry that fully explains and knits all the known laws of physics together.

Are the two connected?

Livio wonders if our biological preference for order might be an example of what scientists call selection effects, which are unrecognized biases that distort our sense of reality. For example, our eyes are only able to perceive visible light, so it's no surprise that human didn't discover the other types of electromagnetic radiation—x-rays, infrared rays, gamma rays—until relatively recently in human history.

"If it's true that our insistence of symmetry in the laws of nature is largely a selection effect because of how our brain works, it may mean that there are completely different ways to formulate the laws of nature in which symmetry is not the most fundamental thing," Livio said.

But just as humans learned to develop detectors that could see things in the universe that our own eyes can't, Livio thinks that in time scientists might be able to see past our biological preference for symmetry.

"In this case, because we are talking about the truly fundamental theories of the universe, it's a bit harder," Livio said. "Nonetheless, the more that we learn about what the ultimate theory might be, we might understand what [are] the most fundamental principles to the laws of nature and get past this selection effect."