Knocking on Heaven's Door (41 page)

Initially, no one knew how to organize calculations among these complicated strongly bound states. However, today’s physicists think quite oppositely about the strong force. We now understand it much better than we did when the idea was first proposed. David Gross, David Politzer, and Frank Wilczek won the Nobel Prize for what they called “asymptotic freedom.” According to their calculations, the force is strong only at low energies. At high energies, the strong force is not much more powerful than other forces, and calculations work just as they should. In fact, some physicists today think theories such as the strong force, which become much weaker at high energies, are the
only
well-defined theories, since the interaction strength won’t grow to infinite strength at high energy as it might otherwise do.

Gell-Mann’s theory of the strong force is an interesting example of the interplay between aesthetic and scientific criteria. Simplicity was his initial guide. But hard scientific calculations and theoretical insights were necessary before everyone could agree on the beauty of his suggestion.

This, of course, isn’t the only example. Many of our most trusted theories have aspects so superficially ugly and uncompelling that even respected and well-established scientists rejected them initially. Quantum field theory, which combines quantum mechanics and special relativity, underlies all of particle physics. Yet the Nobel Prize—winning Italian scientist Enrico Fermi (among others) rejected it at first. For him, the problem was that although quantum field theory formalizes and systematizes all calculations and makes many correct predictions, it involves calculaional techniques that even some of today’s physicists view as baroque. Various aspects of the theory are quite beautiful and lead to remarkable insights. Other features we just have to put up with, even though we aren’t so enamored with all their intricacies.

This story has repeated itself many times since. Beauty is often agreed on only a posteriori. Weak interactions violate parity symmetry. This means that particles spinning to the left interact differently from those spinning to the right. The breaking of such a fundamental symmetry as left-right equivalence seems innately disturbing and unattractive. Yet this very asymmetry is what is responsible for the range of masses we see in the world, which is in turn necessary for structure and life. It was considered ugly at first, yet now we know it is essential. Although perhaps ugly in itself, parity symmetry breaking leads to beautiful explanations of more complicated phenomena essential to all the matter we see.

Beauty is not absolute. An idea might appeal to its creator but be cumbersome or messy from someone else’s perspective. Sometimes I’ll be quite taken with the beauty of a conjecture I’ve come up with largely because I know of all the other ideas people had thought of before that hadn’t worked. But being better than what came before doesn’t guarantee beauty. Having made my share of models that satisfied this criterion, but were nonetheless met with skepticism and confusion from colleagues who were less familiar with the topic my model addressed, I now think a better criterion for a good idea might be that even someone who never studied the problem can recognize its appeal.

The reverse is sometimes true as well—good ideas are rejected because their inventors consider them too ugly. Max Planck didn’t believe in photons, which he thought to be an unpleasant concept, even though he initiated the train of logic that led to their conjecture. Einstein thought the expanding universe that followed from his equations of general relativity couldn’t be true, in part because it contradicted his aesthetic and philosophical predispositions. Neither of these ideas might have seemed the most beautiful at the time, but the laws of physics and the universe in which they applied didn’t really care.

LOOKING GOOD

Given the evolving and uncertain nature of beauty, it’s worth considering some of the features that might make an idea or an image objectively beautiful in a way that has some universal appeal. Perhaps the most basic question about aesthetic criteria is whether humans even have any universal criteria for what is beautiful—in any context—be it art or science.

No one yet knows the answer. Beauty, after all, involves taste, and taste can be a subjective criterion. Nonetheless, I find it hard to believe that humans don’t share some common aesthetic criteria. I often notice a striking uniformity in people’s opinions about which piece of art in a given exhibit is the best or even which exhibits people choose to go see. Of course this doesn’t prove anything since we all share a time and place. Beliefs about beauty are difficult to isolate from the specific cultural context or time period in which they originate so it’s difficult to isolate innate from learned values or judgments. In some extreme cases, people might all agree that something looks nice or appears unpleasant. And in some rare instances, everyone might agree on the beauty of an idea. But even in those few cases, people don’t necessarily agree about all the details.

Even so, some aesthetic criteria do appear to be universal. Any beginning art class will teach about balance. Michelangelo’s
David
in the Accademia Gallery in Florence exemplifies this principle.
David
stands gracefully. He’s never going to tip over or fall apart. People search for balance and harmony where they can find it. Art, religion, and science all promise people the opportunity to access these qualities. But of course balance might also be simply an organizing principle. Art is also fascinating when it defies our notions of balance, as we see in early Richard Serra sculptures. (See Figure 47.)

[
FIGURE 47
]
These early Richard Serra sculptures illustrate that sometimes art is more interesting when it appears to be slightly off balance. (Copyright © 2011 by Richard Serra/Artists Rights Society [ARS], New York.)

Symmetry is also often considered essential to beauty, and art and architecture frequently exhibit the order that it generates. Something has symmetry if you can change it—for example, by rotating it, reflecting it in a mirror, or interchanging its parts—so that the transformed system is indistinguishable from the initial one. Symmetry’s harmoniousness is probably one reason that religious symbols often have it on display. The Christian cross, the Jewish star, the dharma wheel of Buddhism, and the crescent of Islam are all examples and are illustrated in Figure 48.

[
FIGURE 48
]
Religious symbols frequently embody symmetries.

More expansively, Islamic art, which forbids representation and relies on geometric forms, is notable for its use of symmetry. The Taj Mahal in India is a magnificent example. I haven’t spoken to anyone who’s visited the Taj Mahal and wasn’t taken with its masterful orderliness, shape, and symmetry. The Alhambra in southern Spain, which also incorporates Moorish art and its interesting symmetry patterns, may be one of the most beautiful buildings still standing today.

[
FIGURE 49
]
The architecture of the Chartres Cathedral and the ceiling of the Sistine Chapel both embody symmetry.

Recent art, such as the work of Ellsworth Kelly or Bridget Riley, exhibits symmetry explicitly and geometrically. Gothic or Renaissance art and architecture—see the Chartres Cathedral and the roof of the Sistine Chapel, for example—exquisitely exploited symmetry as well. (See Figure 49.)

However, art is often most beautiful when it is not completely symmetrical. Japanese art is notable for its elegance, but also for the well-defined breaking of symmetry. Japanese paintings and silk screens have a clear orientation that draws one’s eye across the pictures as one can see in Figure 50.

[
FIGURE 50
]
Japanese art is interesting in part because of its asymmetry.

Simplicity is another and sometimes related criterion that might help when evaluating beauty. Some simplicity arises from symmetries, but underlying order can be present, even in the absence of manifest symmetry. Jackson Pollock pieces have an underlying simplicity in the density of paint, though the impression might first seem chaotic. Although the individual splashes of paint seem completely random, his most famous and successful pieces have a fairly uniform density of each color that enters the work.

Simplicity in art can frequently be deceptive. I once tried to sketch a few Matisse cutouts, his simplest works, which he created when he was old and frail. Yet when I tried to reproduce them, I realized that they weren’t so simple—at least not for my unskilled hand. Simple elements can embody more structure than we superficially observe.

In any case, beauty isn’t found only in simple basic forms. Some admired works of art, such as those of Raphael or Titian, involve rich complex canvases with many internal elements. After all, complete simplicity can be mind-numbing. When we look at art, we prefer something interesting that guides our eye. We want something simple enough to follow, but not so simple as to be boring. This seems to be how the world is constructed as well.

BEAUTY IN SCIENCE

Aesthetic criteria are difficult to pin down. In science—as in art—there are unifying themes but no absolutes. Yet even though aesthetic criteria for science might be poorly defined, they are nonetheless useful and omnipresent. They help guide our research, even if they provide no guarantee of success or truth.

Aesthetic criteria that we apply to science resemble those that were just outlined for art. Symmetries certainly play an important role. They help us organize our calculations and often relate disparate phenomena. Interestingly as with art, symmetries are usually only approximate. The best scientific descriptions frequently respect the elegance of symmetric theories while incorporating the symmetry breaking necessary to make predictions about our world. The symmetry breaking enriches the ideas it encompasses, which thereby yield more explanatory power. And, as is often true for art, the theories that incorporate broken symmetries can be even more beautiful and interesting than those that are perfectly symmetrical.