Truth and beauty

Do we need another Newton, or do we just need a different aesthetics?

December 21, 2011

In a 2009 New York Times article entitled How Did Economists Get It So Wrong? Paul Krugman wrote that “The economics profession went astray because economists, as a group, mistook beauty, clad in impressive-looking mathematics, for truth.”


Most non-economists, or even economists, would not associate economics with beauty. But a sense of aesthetics plays an important role in many branches of science. Bertrand Russell wrote that “Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty cold and austere, like that of sculpture.” The same kind of beauty is sought and appreciated by researchers in more applied areas as well – not just for its own sake, but because it often seems to indicate that one is on the right path.


The French mathematician and physicist Henri Poincaré wrote that the “true aesthetic feeling that all real mathematicians know” acted as a “delicate sieve” which allowed the scientist to discern the truly useful patterns in nature. The British physicist Paul Dirac went so far as to argue that “It is more important to have beauty in one’s equations than to have them fit experiment.” He proved it by using an elegant equation to infer the existence of anti-matter before it had been physically detected.


Three key aesthetic properties are elegance, unity, and symmetry. Perhaps the archetype of a beautiful theory is Newton’s law of gravity. The equation is mathematically simple and elegant. It unifies a broad range of phenomena – everything from the motion of the Moon around the Earth, to an apple falling to the ground. And it is highly symmetric, both spatially (it is the same in every direction), and in the sense that it produces a symmetric force. When the Earth pulls on the Moon, the Moon pulls back on the Earth (and produces tides).
Physicists seek out symmetries in nature because these allow simplified mathematical representations.


In areas such as physics, beauty and truth have come to be regarded almost as two sides of the same coin. But does the same approach work in a social sciences like economics?


Broken mirror
One of the great appeals of neoclassical economics is the physics-like way in which it reduces a complex world to a set of elegant equations. For example, some of the key planks of neoclassical economics are rationality, stability, and uniformity (a large number of consumers and producers with similar characteristics). These were originally evoked as computational simplifications, but have taken on a life of their own. And each represents a kind of symmetry in the system.


Rationality is a symmetry, because any rational person will make the same decision given the same information. If completely rational people look at one another, it must be like looking in the mirror. Stability is symmetry in time. If markets are in equilibrium, then the future looks like the past. And if markets are uniform in the sense that market participants have similar power and other characteristics, then that means transactions are symmetric.


Of course, no one thinks that people are perfectly rational, or that markets are perfectly stable or uniform. Much work has been done exploring deviations from these assumptions. But when it comes to what Krugman called the “impressive-looking mathematics” used in economic models, the world is a very rational, stable, and uniform place.


For example, the General Equilibrium Models beloved by policy makers look at how market equilibrium will rationally adapt to changing conditions. Risk models used by banks also assume rational behaviour and an underlying equilibrium. And as economist Norbert Häring notes in his book The Economics of Power, power discrepancies “are defined away by standard assumptions of mainstream economic models.”


As shown by the recent crisis, though, markets rely as much on emotions such as trust and confidence, as they do on rationality. There is no guarantee that the future will resemble the past. And the idea that power is not important will seem risible to the scores of economic protestors camped out in cities around the world. The mirror of symmetry isn’t just a little distorted – it is completely warped.


So do we need another Newton to come along with an aesthetically pleasing formula to explain it all? Or do we just need a different aesthetics?


A new aesthetics
While economics has traditionally modelled itself after physics, biologists have tended to see beauty in the complexity of life rather than the neatness of symmetric equations. For example, Louis Pasteur discovered in the mid-19th century that many organic chemicals can appear in two reflected versions. Artificially synthesised compounds will have a mix of both, but ones produced by living organisms always have the same handedness. He concluded that asymmetry and life were intimately related, and wrote that “Life as manifested to us is a function of the asymmetry of the universe … I can even imagine that all living species are primordially, in their structure, in their external forms, functions of cosmic asymmetry.”


Biological systems typically operate at a state which is best described as far from equilibrium, in the sense that the components are constantly being churned around. Stability, where it appears, is provisional, approximate, and subject to change. There is no symmetry in time – organisms are born, evolve, die, and decay. And as Darwin knew, evolution is driven not by uniformity, but by the infinite variation of the natural world.


Many of the new mathematical methods being applied in economics also do away with the symmetry assumptions of neoclassical economics. For example, behavioural economists allow people to be inelegantly human and flawed rather than perfectly rational. Complexity economics follows the non-linear, far-from-equilibrium dynamics of evolving economic systems. Network theory studies the non-uniform networks which characterise the financial system.


In order to develop a new vision for economics, perhaps we first need to develop a new sense of aesthetics, which takes its inspiration from biology rather than physics. The poet John Keats wrote that “Beauty is truth, truth beauty.” But there are different kinds of beauty – and like Marilyn Monroe’s mole, not all of them reduce to symmetry or neat equations.


David Orrell is a mathematician and author of Economyths: Ten ways economics gets it wrong