Weekend Essay Links: Beauty is Truth, Truth Beauty. . . Or is it?

When old age shall this generation waste,

Thou shalt remain, in midst of other woe

Than ours, a friend to man, to whom thou say'st,

'Beauty is truth, truth beauty,--that is all

Ye know on earth, and all ye need to know.'

-John Keats, "Ode on a Grecian Urn"



On rereading the whole "Ode," this line strikes me as a serious blemish on a beautiful poem, and the reason must be that either I fail to understand it, or that it is a statement which is untrue. And I suppose that Keats meant something by it, however remote his truth and his beauty may have been from these words in ordinary use. And I am sure that he would have repudiated any explanation of the line which called it a pseudo-statement. . . the statement of Keats seems to me meaningless: or perhaps the fact that it is grammatically meaningless conceals another meaning from me.

-T.S. Eliot, "Dante," Selected Essays, 1932



To emphasize only the beautiful seems to me to be like a mathematical system that only concerns itself with positive numbers.

-Paul Klee

In the NYT Magazine, economist Paul Krugman blames his fellow economists for falling in love with an idealized model of markets, and mistaking beauty for truth:

It will be a long time, if ever, before the new, more realistic approaches to finance and macroeconomics offer the same kind of clarity, completeness and sheer beauty that characterizes the full neoclassical approach. To some economists that will be a reason to cling to neoclassicism, despite its utter failure to make sense of the greatest economic crisis in three generations. This seems, however, like a good time to recall the words of H. L. Mencken: "There is always an easy solution to every human problem -- neat, plausible and wrong." (source)

Sean Carroll responds with this perceptive critique of Krugman's hypothesis:

Sure, people can fall in love with beautiful theories, to the extent that they overestimate their relationship to reality. But it seems likely to me that the correct way of understanding all this, once it's properly understood, will look pretty beautiful as well. General relativity is widely held up as an example of a beautiful theory -- and it is, when understood in its own language. But if you put the prediction of GR in the Solar System into the language of pre-existing Newtonian physics (which you could certainly do), it would look ugly and ad hoc. Likewise, Newton's theory itself is quite elegant, when phrased in the language of potentials on a fixed spacetime background; but if you express the theory in terms of differential geometry (which you could certainly do), it looks like a mess. Sometimes the beauty/ugly distinction between theoretical conceptions is more a matter of how well we understand them, and less about their intrinsic qualities.

So my counter-hypothesis would be that it wasn't beauty that was the problem, it was complacency. If you have a model that is beautiful and works well enough, you're tempted to take pride in it rather than pushing it to extremes and looking for problems. I suspect that there is a very beautiful theory of economics out there waiting to be developed, one that understands perfectly well that individuals aren't rational and markets aren't perfect. One that has even more impressive-looking equations than the current favored models! Beauty isn't always a cop-out.(source)

I agree with Carroll: "beauty" depends not merely on the eye of the beholder, but on the language of the beholder - the way in which the beholder conceptualizes and describes their world. You might even argue that an equation is only as beautiful as the notation in which it's written, or that a significant component of "beauty" arises from intellectual inertia.

But Carroll also does something else here: he invokes a faith shared by many scientists (and if I dare, physicists in particular) - that when the final answer is found, it will be beautiful. Is that a safe bet?

Krugman says in his essay that economists were seduced by the vision of a (necessarily) elegant "Theory of Everything." Some would argue string theorists are skipping blithely down the same path. It's tempting to expect that the world will eventually yield up beautiful, elegant solutions to its mysteries - that Keats, whether or not you like his poem, was right about truth and beauty being one and the same. I want to believe that - it feels right. My experience with biology tells me that systems often turn out to work in beautiful, elegant ways. But I also can't help entertaining serious doubts that a concept as malleable as "beauty" is necessarily going to map onto the ultimate "truth" of our reality. So much depends on how we construct and define beauty. And intellectual dead ends can be beautifully ingenious and complex in their own way - consider the epicycles cunningly crafted on the stunning astrolabe at the top of this post. Epicycles turned out to be a complete mess. They were wrong. But weren't they beautiful at the time?

Here's a thought: maybe when we get to the end of our pursuit of truth (assuming we do), we'll find a messy solution that reflects neither our sociobiological preferences nor our intellectual ones. If so, do we rework the concept of beauty?

Krugman responds:

. . . won't we eventually have a true theory that's as beautiful as the full neoclassical version? Well, one thing's for sure: we don't have that beautiful final theory now, so the current choice is between ideas that are beautiful but wrong and a much messier hodgepodge. But my guess is that even in the long run it won't be all that neat. Discover suggests general relativity versus Newtonian physics; but a better model may be meteorology, which as I understand it starts from some simple basic principles but is fiendishly complex in practice.

Who knows. We might be moving towards beauty, or towards disorder. Perhaps disorder is the new beauty (see my previous post on beauty and dereliction). Regardless, let's just hope we're moving towards truth.

Image credit: Museum of the History of Science, Astrolabe and Equatorium, southern France or Italy, late 15th century. The three prominent discs reflect the 'epicycles' used by Ptolemy.