Are beauty and truth two sides of the same coin? It is charming to believe so. As Nobel Prize laureate Paul Dirac, who helped lay the mathematical groundwork for quantum mechanics, put it:
It seems that if one is working from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress. If there is not complete agreement between the results of one's work and experiment, one should not allow oneself to be too discouraged, because the discrepancy may well be due to minor features that are not properly taken into account and that will get cleared up with further developments of the theory.
The poet John Keats expressed it more concisely:
Beauty is truth, truth beauty – that is all
Ye know on earth, and all ye need to know.
But, in science, does a beautiful hypothesis necessarily lead to deep truth about nature?
Several famous success stories suggest that it does, at least in physics:
James Clerk Maxwell arrived at his celebrated system of equations for electromagnetism by codifying what was thought to be known experimentally about electricity and magnetism, noting a mathematical inconsistency, and fixing it. In doing so, he moved from truth to beauty. The Maxwell equations of 1861, which survive intact as a foundation of today's physics, are renowned for their beauty. The normally sober Heinrich Hertz, whose experimental work to test Maxwell's theory gave birth to radio and kickstarted modern telecommunications, was moved to rhapsodize:
One cannot escape the feeling that these mathematical formulae have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers, that we get more out of them than was originally put into them.
Albert Einstein, on the contrary, arrived at his equations for gravity—the general theory of relativity—with minimal guidance from experiment. Instead he looked for beautiful equations. After years of struggle, in 1915 he found them. At first, and for decades afterwards, few testable predictions distinguished Einstein's new theory of gravity from Newton's venerable one. Now there are many such tests, and it is amply clear that Einstein moved from beauty to truth.
Yet even in physics, the record is more mixed than is commonly known. Despite Keats and Dirac, beauty's seductions don't always give birth to truth. There have been fascinating theories that are both gorgeous and wrong: Beautiful Losers.
Like surgeons, physicists bury their failures. But the most beautiful of the Beautiful Losers deserve a better fate than oblivion, and here they'll receive it. I've written brief accounts of three Beautiful Losers: Plato's Geometry of Elements, Kepler's Harmonic Spheres, and Kelvin's Vortex Atoms.
Plato’s Geometry of Elements: Plato believed that he could describe the Universe using five simple shapes. These shapes, called the Platonic solids, did not originate with Plato. In fact, they go back thousands of years before Plato; you can find stone models (perhaps dice?) of each of the Platonic solids in the Ashmolean Museum at Oxford dating to around 2000 BC. But Plato made these solids central to a vision of the physical world that links ideal to real, and microcosm to macrocosm in an original, and truly remarkable, style. Read more
Kepler’s Harmonic Spheres: Like Plato, the German astronomer Johannes Kepler believed that five Platonic solids provided an essential blueprint for our universe. Six planets were known to Kepler, and he believed that they were carried around on nested globes that he called the celestial spheres. Kepler reasoned that five solids could correspond to six planets, if the solids—or more precisely, their bounding surfaces—marked the spaces between planetary spheres. He described this elegant construction in his Mysterium Cosmographium in 1596. Read more
Kelvin's Vortex Atoms: A tornado is just air in motion, but its ominous funnel gives an impression of autonomous existence. A tornado seems to be an object; its pattern of flux possesses an impressive degree of permanence. The Great Red Spot of Jupiter is a tornado writ large, and it has retained its size and shape for at least three hundred years. The powerful notion of vortices in fluids abstracts the mathematical essence of such objects, and led William Thomson, the 19th century physicist whose work earned him the title Lord Kelvin, to ask: Could atoms themselves be vortices in a ether that pervades space? Read more
It's wonderful, and comforting, that each of my Beautiful Losers, though wrong, was in its own way fruitful. Today more than ever physicists working at the frontiers of knowledge are inspired by beauty. In the alien realms of the very large, the very small, and the extremely complex, experiments can be difficult to perform and everyday experience offers little guidance. Beauty is almost all we've got!