High Concept

Beauty’s Truth

A defense of scientific elegance.

Thomas Kuhn, who died last month, was famous for accusing science of “irrationalism.” He argued that scientific change occurs by revolution–one “paradigm” overthrows another–but he was never too clear about what triggers these revolutions, beyond a sort of mob psychology among scientists. Nor could he make up his mind as to whether there were absolute standards of evidence that would permit one to judge, for example, that the Copernican paradigm was superior to the Ptolemaic one.

In other words, Kuhn’s ideas were woolly. This probably enhanced his stature among the ruck of intellectuals, but few philosophers of science take him very seriously. Kuhn’s charge of irrationalism is worth lingering over, though. If scientists were utterly rational, they would invariably plump for the theory most consistent with the evidence, the one that yielded the most accurate predictions, the one with maximum explanatory power. They would pursue only empirical truth.

But did Einstein arrive at relativity theory in this way? Hardly. He was not trying to account for celestial observations that were anomalous from the Newtonian point of view. His motives were aesthetic. He was troubled by the fact that, in Newton’s theory of gravity, an object’s resistance to force (it’s inertial mass) just happened to be the same as its power of attraction (its gravitational mass). Newtonian physics offered no explanation for this; it was fortuitous and, to Einstein, ugly. So he worked up a theory that, by identifying gravity with the curvature of space-time, merged these two masses into one. It was a construction of unexampled elegance, simplicity, and symmetry. It captured the gross workings of the cosmos in a tensor equation that takes up less than a line of text.

Relativity theory is not only beautiful; it also happens to be empirically true (although its predictive success is too meager to account for the theory’s widespread acceptance). Einstein does not appear to have been irrationally subordinating truth to beauty. But consider his reaction to quantum theory, the other great achievement of 20th-century physics. Though quantum theory predicted quite accurately how things work in the small, it offended his aesthetic sensibilities. It was indeterministic, so he rejected it (as did the original discoverer of the quantum, Max Planck).

Other notable physicists have been even more cavalier about letting truth and beauty diverge. “My work always tried to unite the true with the beautiful,” remarked Hermann Weyl, the perfecter of both relativity theory and quantum mechanics, “but when I had to choose one or the other, I usually chose the beautiful.” Yet when Weyl thought he was sacrificing truth to beauty–by developing a theory of gravitation based on a whole new concept of symmetry even after he became convinced of its empirical falsity–his decision was vindicated by that concept’s surprising fruitfulness over the last couple of decades.

Today the religion of beauty is confessed almost universally among theoretical physicists. “You can recognize truth by its beauty and simplicity. When you get it right, it is obvious that it is right,” said Richard Feynman, one of physics’ most intuitive geniuses. I have always thought that the sentiment on Keats’ urn, “Beauty is truth, truth beauty” refuted itself: It is beautiful but untrue. But is it really so preposterous? Suppose your aesthetic creed were Renaissance classicism, and you believed that a human creation was beautiful insofar as it was a just representation of a noble subject. Then you would have to say that the scientist, in seeking to depict nature’s harmonies through mathematics, was after beauty by definition. Even if you rejected this mimetic view of beauty and opted instead for the 17th-century neoclassical notion of beauty as “uniformity in variety,” you’d still have to say that the scientist, whose pursuit of truth is a matter of getting facts to hang together in a logical network, was aiming for beauty despite himself. Uniformity in variety is precisely what Kepler found when he subsumed the vast and meticulous observations of Tycho Brahe under three concise laws of planetary motion. It is what the Nobel laureate Leon Lederman had in mind when he said that the goal of physics was “to explain the entire universe in a single, simple formula that you can wear on your T-shirt.”

At the moment, though, physicists are not doing so well in the simplicity department. Their so-called Standard Model is a stick-and-bubblegum contraption. It crudely splices together three of the fundamental forces of nature (the strong and weak nuclear forces and the electromagnetic force), leaving out the fourth (gravity) altogether. The 36 quarks or fundamental particles it posits come in six flavors and three colors. It needs 12 Yang-Mills fields to govern the interaction of subatomic particles and a large number of “Higgs” particles to explain why it all looks so distorted to an observer. Worst of all, it needs no fewer than 19 arbitrary constants to describe the masses of the particles and the strengths of the various interactions. (In an elegant theory, constants can be deduced from first principles.) Empirically it works just fine, but it is unlovely in the extreme. It needs a makeover.

The Holy Grail of contemporary physics is unity through beauty, a spare mathematical formalism that would disclose how the four forces are all manifestations of a single primordial force regnant at the instant of the big bang. Such theories could only be tested at big-bang energies–which happen to be a hundred trillion times greater than those attainable in the most powerful particle accelerators. In other words, they are beyond the reach of empirical confirmation.

Does this mean the end of science? John Horgan has recently suggested as much in a book of that title. Horgan is unimpressed by superstring theory, currently the only plausible candidate for a Theory of Everything. He visits Ed Witten, the smartest man on superstrings, who rhapsodizes about the theory’s “wonder, its incredible consistence, remarkable elegance, and beauty.” But it generates no testable prediction, so Horgan dismisses it as “ironic science”: It cannot be literally true.

If, as T.H. Huxley once quipped, the great tragedy of science is “the slaying of a beautiful hypothesis by an ugly fact,” then physics has entered a post-tragic era. There are no fatal facts lurking about, ugly or otherwise. And this was true long before the push for unification began. Physicist Steven Weinberg observed in his Dreams of a Final Theory that it has been more than 100 years since an experiment has refuted a well-accepted theory.

This raises the question of how the next revolution in physics might break out: Will it be an episode of Kuhnian irrationalism, as hordes of rank-and-file physicists jump aboard the superstring bandwagon for shabby reasons of professional politics? Or an aesthetic revolution?

In his forthcoming Beauty and Revolution in Science, the philosopher James W. McAllister argues that all revolutionary episodes in science have really been of the aesthetic variety. Consistency with evidence, predictive success, explanatory power–these criteria for scientific truth have survived revolutions unscathed. It is an idea of beauty, even of simplicity itself (a terrifically complicated notion), that is toppled and replaced. “Every property that has at some date been seen as aesthetically attractive in theories has at other times been judged as displeasing or objectively neutral,” McAllister writes.

This is no whim of intellectual fashion. Scientists fancy some aesthetic feature of a theory to the extent that it is linked with empirical success at the time. For instance, René Descartes, Pierre Gassendi, and Robert Boyle, all rivals to Newton, found “corpuscularism” attractive. This was the doctrine that all phenomena should be explained as the motion and collisions of solid corpuscles that possess no occult properties. Newton, however, could find no corpuscularist story that accounted for celestial motion. So, hearkening back to Renaissance magic, he appealed to gravitational “action at a distance.” This was at first a serious blemish in a theory that was eventually viewed as the soul of beauty.

Looking back through the history of science, it is plain that beauty is a harbinger of probability only in retrospect. Most aesthetic convictions held by scientists–like the Aristotelian notion that uniform circular motion is the loveliest of all–ended up impeding the advance of knowledge. Innovations like Kepler’s ellipses or quantum mechanics usually come surrounded by an aura of ugliness, which predictive success replaces with the splendor of truth. The great exception is Einstein’s relativity theory, a singularly heroic discovery that set the tone for the rest of the century. Today’s physicists have returned to the classical Greek project of understanding the cosmos by thought alone. The beautiful Final Theory will be the true one, not because it accords with the empirical evidence, but because it reflects the mind of God–a God who geometrizes or arithmetizes, depending on your taste.