Philip Ball explores the tension of the historical scientist’s pursuit of truth and beauty. 23/01/2023

The scientist, French mathematician Henri Poincaré wrote, does not study science because it is useful. Rather,

He studies it because he takes pleasure in it; and he takes pleasure in it because it is beautiful. If nature were not beautiful, it would not be worth knowing and life would not be worth living.

OK, two things. First, what most obviously jars the modern ear is the gendering – reflexive, of course, for Poincaré at the end of the nineteenth century, but made all the more uncomfortable here when we recognize how routinely scientists and natural philosophers have conversely gendered nature, the object of study, as female: beautiful, yes, but also passive and needing to be seduced, if not coerced, into revealing her secrets. 

Second, this seems a mere whisker away from St Augustine: “How can we love anything but the beautiful?” But whereas for Augustine, as for Aristotle and Confucius, beauty was allied to goodness and virtue, for scientists it has often become a signpost to truth. If, as Poincaré says, nature is inherently beautiful, then true theories cannot but reflect that.

This is just what Albert Einstein (whose work on the geometry of spacetime was indebted to Poincaré) thought too: “the only physical theories that we are willing to accept are the beautiful ones.” Scientists often like to quote Richard Feynman’s view that “it doesn’t matter how beautiful your theory is… if it doesn’t agree with experiment, it’s wrong.” But Paul Dirac, one of the few twentieth–century physicists whose brilliance arguably outshone Feynman’s, flatly disagreed, saying in 1963 that “it is more important to have beauty in one’s equations than to have them fit experiment.” That’s quite some responsibility for beauty to shoulder in science.

But was Poincaré right – is nature beautiful? There is probably no more universal a source of perceived beauty than the natural world, with its sunsets, coral reefs, alpine vistas. Yet this is not quite what he had in mind. His was a conceptual beauty revealed in the deep laws that scientists aim to discern. Commenting on Poincaré’s remark in 1919, the science writer J. W. N. Sullivan said that  

Since the primary object of the scientific theory is to express the harmonies which are found to exist in nature, we see at once that these theories must have aesthetic value. The measure of the success of a scientific theory is, in fact, a measure of its aesthetic value.

In other words, the true beauty of nature lies in its harmonious principles, and theories that express these are then bound to share that aesthetic appeal. The allusion to music here is not incidental, for it has long been seen as a model for theories of the world. The simple proportions that Pythagoras identified in the vibrations of harmonious musical intervals were also those said by Plato to govern the structure of the cosmos. Neoplatonic thinking anchored Johannes Kepler’s cosmological model in his 1619 treatise Harmonices mundi. It is to Beethoven that the Indian astrophysicist Subrahmanyan Chandrasekhar turned for analogy in his 1979 essay on “Truth and Beauty” in the sciences.

Rather few physicists today would side with Dirac in choosing beauty over conformity with experiment, but they retain a belief that beauty in a theory is at least a good guide to its veracity. That case was put by string theorist Brian Greene in The Elegant Universe (1999), and it is made too by Nobel laureate Frank Wilczek in A Beautiful Question (2015) – tellingly subtitled “Finding Nature’s Deep Design”. This “design” is not that which Kepler perceived, but the impulse is the same.

But what then is the nature of this theoretical “beauty” – which few non–experts are likely to experience in Dirac’s gnomic equation of quantum field theory or Einstein’s equations of general relativity that so delighted Chandrasekhar? For physicists it comes from a sense of rightness: a fitting together of the conceptual ingredients in a manner that can be concisely expressed, mathematically if not colloquially. Symmetry is typically central to this aesthetic, meaning an equivalence of this with that. The most generalized physical laws typically encode such symmetries: they tell us “what is the same”. 

Many consider James Clerk Maxwell’s equations of electromagnetism from 1865 to have such beauty because they reveal electricity and magnetism to be two sides of the same coin: two aspects of the same fundamental electromagnetic force. Wilczek explains in his book why a theoretical construct called supersymmetry is so attractive to many particle physicists, even though experimental evidence for the idea has remained perplexingly elusive. Not only does it promise to resolve some outstanding puzzles in high–energy physics but it does so by positing a symmetry – an equivalence now deeply hidden but which should become evident in immensely energetic particle collisions – between two hitherto distinct classes of fundamental particle. It is this sense of “rightness” that has kept many particle physicists faithful to the idea of supersymmetry (rightly or wrongly) even as empirical verification has repeatedly failed to materialize. It seems pertinent, however, that such symmetries are hard to discern precisely because they have become hidden in the world we experience: the story modern physics tells of the evolution of the universe is a story of progressively broken symmetries. If there was once a paradise of perfect Platonic symmetry, our own existence is possible only because it is now lost.

This Platonic sense of beauty as harmony and symmetry is not really to be found in theories of aesthetics or art. Immanuel Kant felt that too much regularity (of the kind that mathematics can describe) is “repugnant to taste”, and Francis Bacon saw beauty in departure from symmetry: it must have “some strangeness in the proportion.” Yet Wilczek identifies another aspect of beauty in scientific theories that perhaps allies more with that in art: you get out more than you put in. A theory is beautiful, he says, when it surprises you with its fecundity. You intended it to account for this, but found it will explain or predict that too. Einstein never anticipated that general relativity would also predict the expansion of the universe, black holes, and gravitational waves (and indeed had crises of conviction about all three).

I said there are two things, but there are three. I have talked only of physical sciences, and in particular of what is conventionally (if misleadingly) called “fundamental physics”, which tends to be highly mathematical, abstract, and general. The further you wander from this field, the less likely you are to hear talk of beauty in science. Most of physics itself itself grapples with messy particulars – of materials, fluids, optics. Chemists are usually too busy making molecules to wax philosophical about beauty. For biologists, nature is unpredictable, contingent, horribly complicated and often downright obtuse. Beauty can’t help or guide them. That’s the reality of the world at human scales, and perhaps we make our own beauty precisely because natural philosophy in the mundane sphere has precious little to offer.     

Philip Ball is a science writer and author. His latest book is The Book of Minds (2022)

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