Philip Ball who is one of my favorite science writers has a thoughtful rumination on the constant tussle between beauty and truth in science. Ball argues that the expectation of beauty as a guide to scientific truth is quite uncertain and messy and successes are anecdotal, and I tend to agree with him. There are undoubtedly theories like general relativity which have been called 'beautiful' by both their creators and their followers, but for many other concepts in science the definition is much more tricky. Ball again raises the question asked by Keats: is beauty truth? And is truth beauty?
To begin with it's clear to me that the definition of beauty depends on the field. For instance in physics it's much easier to call the Dirac equation beautiful based on the fact that it can be written on a napkin and can explain an untold number of phenomena in a spare, lucid line of symbols. But as I pointed out in a previous post, appreciating beauty in chemistry and biology is harder since most chemical and biological phenomena cannot be boiled down to simple-looking equations. In a previous post I have also noted how simple equations in chemistry can look beautiful and yet be approximate and limited, and how complicated equations can look ugly and yet be universal, giving answers precise to six decimal places. Which equation do you then define as being the more ‘beautiful’ one?
It's also apparent to chemists that in chemistry, beauty resides significantly in the visualization of chemical structures. Line drawings of molecules and 3D representations of proteins are recognizable as beautiful, even to non-chemists. Yet this beauty might be deceptively seductive. For instance many ‘impossible’ or highly unstable molecules look beautiful when sketched out, and many beautiful-looking protein structures are actually imperfect models, built from uncertain and messy data and subjects to the whims and biases of their creators.
I have always suspected that 'beauty' is more of a place-card or a proxy for something else, and in his article Ball quotes the well-known physicist Nima Arkani-Hamed to this effect. It's a sentiment which sounds like a cogent guideline for defining beauty:
It’s not fashion, it’s not sociology. It’s not something that you might find beautiful today but won’t find beautiful 10 years from now. The things that we find beautiful today we suspect would be beautiful for all eternity. And the reason is, what we mean by beauty is really a shorthand for something else. The laws that we find describe nature somehow have a sense of inevitability about them. There are very few principles and there’s no possible other way they could work once you understand them deeply enough. So that’s what we mean when we say ideas are beautiful.
In his quote Arkani-Hamed is alluding to many criteria of beauty cited especially by physicists and mathematicians; concision, universality, timelessness and inevitability. That's a worthy listing of qualities. Nobody expects the basic theorems of general relativity or quantum mechanics to be upended any time soon. However, Arkani-Hamed's quote also makes me suspect that it is precisely the connection of beauty with these other qualities that makes it accessible only to the most penetrating minds in the field. For instance Einstein, Paul Dirac and the mathematician Hermann Weyl are often quoted as thinkers who perpetuated howlers declaring their allegiance to beauty over truth. But another way to interpret these anecdotes is to wonder if Dirac, Weyl and Einstein were precisely the kind of superlative minds that could actually see beauty as the manifestation of these more subtle and deep qualities. If this were indeed true, then the mundane conclusion would be that beauty is indeed truth, but only when proclaimed by an Einstein, a Weyl or a Dirac.
There is one criterion among those described by Arkani-Hamed that does apply to the 3D representations of proteins that I discussed above - timelessness. For instance, Nobel Prizes have been awarded to many crystal structures of important biomolecular assemblies like the ribosome and the potassium ion channel. There is no doubt that more detailed explorations will uncover unexpected details of the structures, but the basic architecture of these fundamental molecular machines will likely never have to be revised; it is, for many purposes, timeless.
Other qualities that underlie beauty can be more controversial. For instance Ball says that the whole concept of symmetry which is not only regarded as a great test of beauty in physics but which has also led to many of the field's most fundamental advances, is also a poor guide in other fields like art and poetry. There are numerous instances of art (Picasso) and poetry (T. S. Eliot for instance) which lack elements of symmetry, and yet they are considered important classics. But that's where Ball points out that unlike the equations of relativity, art and poetry are much more subjective and therefore much more subject to the changing currents of society and fashion. But are they, really? We do consider Einstein’s field equations to be timeless, but what about ‘The Wasteland’?
Ultimately notions of beauty and its connection to truth are always going to be murky, of uncertain merit, even dubious. And yet I completely agree with Ball that scientists and artists should not give up their quest to find beauty in nature and in their works, if only because it serves to propel ideas forward and stimulate them to think in new ways. The one thing he asks is that they make their intentions and thought processes clear.
Despite all this, I don’t want scientists to abandon their talk of beauty. Anything that inspires scientific thinking is valuable, and if a quest for beauty – a notion of beauty peculiar to science, removed from art – does that, then bring it on. And if it gives them a language in which to converse with artists, rather than standing on soapboxes and trading magisterial insults like C P Snow and F R Leavis, all the better. I just wish they could be a bit more upfront about the fact that they are (as is their wont) torturing a poor, fuzzy, everyday word to make it fit their own requirements. I would be rather thrilled if the artist, rather than accepting this unified pursuit of beauty (as Ian McEwan did), were to say instead: ‘No, we’re not even on the same page. This beauty of yours means nothing to me.’