A thing of beauty

A thing of beauty: even when the evidence was going against them, Nobel prize-winners Murray Gell-Mann and Richard Feynman clung on to cherished theories just because they thought they were "beautiful".

Are beauty and science compatible? Do scientists have the right to use the word beauty? For physicists and mathematicians, at least, the answer is an emphatic "yes". Back in the 1960s, Paul Dirac famously asserted that: "It is more important to have beauty in one's equations than to have them fit experiment" Richard Feynman, too, insisted on believing in one of his theories even when it seemed to contradict experimental data.

So what makes an equation or a theory beautiful? For most art theorists and artists, beauty is subjective, but not for scientists. To scientists symmetry is beauty and therefore objective: scientists seek out mathematical equations that retain their form no matter how they are transformed. The mathematical equation for a sphere, for example, does not change when its coordinates are inverted. A sphere is still a sphere when viewed from any perspective, even in a mirror.

And if experiments on the decay process of elementary particles produce the same results when viewed in a mirror, they exhibit "mirror symmetry" associated with the law of the conservation of parity. Call it what you will, there is a basic element in most scientific theories that scientists believe they can quantify objectively as "aesthetics" or "beauty".

Why is symmetry so important? Why is it the term that scientists use synonymously with beauty? For many, it goes back to that fraction of a second after the big bang, some 13.7 billion years ago, when there was only one force − an instant of purest symmetry. When this symmetry was broken, the four forces of the physical world emerged: the gravitational, electromagnetic, nuclear and weak forces. The universe is now seen as being made up of broken symmetries. What scientists are trying to do is to find this primordial symmetry by hypothesising other symmetries that unify these four forces. When scientists look for explanations for what "breaks" these symmetries, they discover particles. Theories which exhibit the maximum symmetry − such as those unifying fundamental forces, like the electroweak theory − are considered "beautiful theories", and they usually turn out to be correct, which seems to justify the hunt for symmetry.

Symmetry need not be tied to visual imagery − the need could reflect an intuition about how nature ought to be. This was Einstein's starting point in 1905 when he introduced aesthetics into 20th-century physics. His discovery that light could also be a particle emerged from his minimalist aesthetic. Einstein's formulation of the theory of relativity also sprang from this aesthetic. The electromagnetic theory of the day offered two radically different explanations of how a current is generated in a wire moving relative to a magnet, depending on whether the current was observed by someone riding on the wire or on the magnet. To Einstein the two explanations were redundant: worse, they were asymmetrical. Having unmasked this asymmetry, he could extend the principle of relativity to electricity, magnetism and light.

Arthur I. Miller