When I received the invitation to speak as part of the Darwin College lecture series on Beauty, I was deeply conscious of the honour paid me, but apprehensive. I was afraid I had nothing new or original to say, because both beauty and happiness have been discussed or represented by philosophers and artists at different times and places throughout human history. As I prepared my lecture, I also remembered what Walter Pater wrote in 1893 in his preface to The Renaissance: Studies in Art and Poetry: ‘Beauty, like all other qualities presented to human experience, is relative; and the definition of it becomes unmeaning and useless in proportion to its abstractness.’

As a postgraduate fellow at the Freer Gallery of Art in Washington in the late 1970s, every day I had to use an entrance hidden behind one of the walls of the Peacock Room (Figure 6.1) to reach my small office. The Peacock Room was designed by James Whistler (1834–1903) as the dining room for his patron, Frederick Richards Leyland (1831–92); it was later dismantled and was sold eventually to Charles Lang Freer (1854–1919). In 1923 it was reinstalled in the Freer Gallery of Art. Seeing the Peacock Room daily gave me ample opportunity to think about beauty and happiness. First of all, it compelled me to contemplate what the French writer Stendhal wrote on several occasions: beauty is nothing other than the promise of happiness. It also reminded me of John Ruskin’s assertion in Stones of Venice: ‘Remember that the most beautiful things in the world are the most useless; peacock and lilies, for instance.’ The blue and white porcelains in the Peacock Room also evoked the ‘china-mania’ initiated by Whistler and his contemporaries. The fact that blue-and-white porcelain, most of it mass produced in Chinese factories for export and considered quite unremarkable by Chinese connoisseurs, caused such a sensation in Europe from the seventeenth century onward made me wonder if there is such a thing as universal beauty.

When I was asked to talk about quantum beauty I was a little startled, because the beauty of quantum theory is something that practising physicists, in the course of their work, rarely think about or mention. But when I gave the idea a chance, it really caught my imagination. And that’s why I’m here. Quantum beauty really is a wonderful, true thing to talk about.

I’m going to sneak up on quantum beauty by putting it in historical context. The right context, I think, is a broader question:

That is a question that people have thought about for a long time. Its intellectual history deserves volumes and syllabi. Here, though, I want to keep things brief and entertaining, so I shall spin a simple tale of heroes.

Pythagoras and Plato intuited that the world should embody beautiful ideas; Newton and Maxwell demonstrated how the world could embody beautiful ideas, in specific impressive cases. Finally, in the twentieth century in modern physics, and especially in quantum physics, we find a definitive answer: Yes! – the world does embody beautiful ideas.

Envision some visitors who have travelled to Kenya to observe wildlife (Figure 5.1A). They first encounter a pair of baboons mating. The visitor group quickly drives away muttering, perhaps after covering their children’s eyes. Coming upon a ranger or a field scientist, the parents splutter their outrage at such an X-rated sight. A pair of mating lions or elephants is encountered next; cameras roll, and if a tour guide is present he is given an extra tip for such a wonderful sighting. A male baboon kills and feeds on prey, perhaps a gazelle; the visitors recoil, and may even seek a wildlife ranger to complain about the horrible scene that they have witnessed: can’t somebody stop the baboons from doing this terrible thing (see Figure 5.1B)? A lion kills and feeds on prey, perhaps a gazelle, wildebeest or baboon; again cameras roll, and more visitors are attracted to the awesome sight, delighted to have witnessed one of the highlights of anyone’s African safari. These scenarios or slight variations on them occur frequently in African wildlife reserves.

What diverse responses there are to similar behaviour exhibited by three mammal species, each large, group-living and highly social! When and why are humans variously repulsed, nonplussed, or attracted to ostensibly similar events? Why is sexual or predatory behaviour by lions but not by baboons attractive to many people? The answer seems to lie primarily in our obvious similarity to baboons, more similar than to lions and to elephants, and perhaps the consequent embarrassment that comes from watching behaviour that would not be comfortable to watch if it were people performing. This kind of differential response to various species is familiar to conservation biologists, who regularly deal with people’s differential willingness to work for the survival of some species versus others; large, furry, round-faced and large-eyed mammals are particularly appealing. Outside the conservation community, however, relatively little attention is paid to these biased responses.

Spectacular astronomical images of clusters of blue stars deeply embedded in vibrant clouds of dusty gas have become abundant over the last decade. Collected using space telescopes and a new generation of ground-based instruments, these pictures awe us with their glorious landscapes of multi-coloured gas sculpted to form swirls and filaments. Black misshapen blobs and tenuous drifts of dust are seen in silhouette against the glow of the gas, and the whole is peppered with aggregations of brilliant, bright blue stars. Many of these vistas are by now familiar to the layperson (for example, the ‘pillars of creation’ shown in Figure 8.1), who is able to appreciate their beauty without necessarily requiring comprehension of what is being portrayed. In this chapter I shall revisit such images with the aim of deconstructing them in order to explain the science that underlies the beauty.

The interstellar medium

We live in a spiral galaxy, flattened out to form a giant frisbee slowly wheeling in space, with our own Sun just one of two hundred thousand million stars all bound together by their mutual gravity. A central bulge of stars is surrounded by an extended flat disc that contains the spiral arms, which are traced by conspicuous clusters of young blue stars (see the Whirlpool Galaxy, shown in Figure 8.2). We live within such a spiral arm, about halfway from the centre to the edge of our own galaxy, the Milky Way. The clusters of stars most apparent in our night sky – such as the Pleiades, or the double star cluster in Perseus – are prominent because they are physically close to us, located in neighbouring spiral arms. As we will learn later, blue stars such as those seen in these clusters are hot, massive, and the most recently formed. But whilst they are the most obvious feature to draw the eye and delineate the structure, a galaxy does not consist solely of stars. It is easy to dismiss the void between the stars as being only empty space; even though it might be millions of times emptier than the best vacuum that we can achieve in a laboratory on Earth, it is not completely devoid of matter. Interstellar space abounds with atoms and molecules of gas, alongside tiny solid particles that we refer to as ‘dust’.

Beauty, truth and the sublime

In December 1817 John Keats wrote to his brothers, George and Tom, after dining with the English artist William Hayden: ‘The excellence of every Art is its intensity, capable of making all disagreeables evaporate, from their being in close relationship with Beauty & Truth.’ Two years later, Hayden’s articles on Classical and medieval art, published in the Examiner in May 1819, inspired Keats’s ‘Ode on a Grecian Urn’ in which the poet famously gives the ‘Attic shape’ words to comfort man: ‘Beauty is truth, truth beauty, – that is all/ Ye know on earth, and all ye need to know.’ The Modernist poet T. S. Eliot dismissed Keats’s equation of truth and beauty as ‘meaningless’, but scholarship in science and mathematics holds fast to the accuracy of Keats’s assertion. The simplicity of the equation, which was so objectionable to Eliot, reflects the Classical search for purity of form, which produced the beautifully clear mathematics of Pythagoras and Euclid that Frank Wilczek and Bob May celebrate here in their chapters, ‘Quantum beauty’ and ‘Beauty and truth’.

If ‘beauty is truth’ then beauty cannot be purely pleasurable. Yet if the intensity of a work of art is sufficient, Keats argues, it enables the subject to transcend its ‘disagreeable’ elements and provide access to truth through the observer’s experience of the sublime. As W. P. Albrecht explains in ‘The Tragic Sublime of Hazlitt and Keats’, the sublime for these writers was not the delightful horror of Edmund Burke and William Wordsworth, to which Evgeny Dobrenko refers in his chapter, ‘Terror by beauty’. Keats defined the sublime as a moment in which the ‘imagination excited by passion . . . selects and combines sensory details to catch the “verisimilitude” which an object or experience has for him at that moment’. For the artist José Hernández, beauty is something that can be manifested in the external world once the imagination has done its work, both in the process of creation and perception: a process that he explores in his chapter on the relationship between ‘Beauty and the grotesque’.

The dangers associated with the sound of beauty are all too apparent in one of the earliest texts in the Western literary canon. On his way back from the Trojan war Odysseus is able to hear one of the most famous sounds of beauty in literature: the song of the sirens. Unlike the unfortunate sailors who had gone before him, however, cunning Odysseus is prepared. Earlier in the story, Circe had given him a detailed warning about the trials to come.

The wise Odysseus, famed for his cunning, obeys these instructions to the letter and gets to hear the song of the sirens in safety. Unlike every traveller who had gone before him, Odysseus experiences the sound of irresistibly enticing beauty and lives to tell the tale.

I find myself in something of a quandary, not only because of the essential differences between the Spanish and English languages but also because writing is not, and never has been, the natural mode of expression for a painter, and I am no exception to the rule. My translator, moreover, has had to cope with my personal linguistic quirks, perhaps a trifle baroque, and this has been a further source of complication. You are, therefore, regretfully forewarned. I shall do everything in my power to convey to you as accurately as possible my feelings, rather than ideas, concerning ‘beauty and the grotesque’.

Despite all the obstacles, and believing as I do that what really counts is communication, whether by means of words or signs, I think that the best thing I can do, to start with, is to tell you something of my personal experience as an artist: that is to say, of the insatiable curiosity that has driven me all my life to try my hand, albeit timidly, at other disciplines. These disciplines have turned out to be complementary to my principal activity as a painter: engraving, the illustration of literary texts, the production of sets for theatre, and sculpture. To conclude this preamble, I must insist that I am not writing as a specialist in beauty, aesthetics or semiotics. To pose as such would be to indulge in impersonation, hypocrisy and pedantry, all of which vices I detest. As for my views on the ‘ugly’ or ‘the grotesque’, I hope that they will become clear later in my comments on their paradoxical relation to beauty.

It is hard to admit, but even talking about beauty is a challenge to the present status quo, as the subject of beauty, which was earlier so urgent and widely discussed (even if it was in an acutely negative context, as, for example, in the era of modernism) and became the basis of an entire discipline – aesthetics – has lost its former popularity. The subject of beauty became unfashionable, even a sign of aesthetic (and political) retrogression. Why did this happen? There was, of course, a tradition, formulated back in the modernist era that linked beauty to the past, and therefore considered an interest in it to be a manifestation of obscurantism. However, another reason that is much later and much more acutely felt by us today is that beauty was inextricably linked to the terrible totalitarian experience of the twentieth century.

This is why many consider it fundamentally blasphemous to use positive aesthetic categories (and the most hallowed among them, beauty) in the description of totalitarian cultures. Poetry, and beauty right along with it, is impossible after Auschwitz. It seems even more impossible, so to speak, during Auschwitz. And was it not right of Umberto Eco simply to omit these dark alleyways of twentieth-century history from his landmark anthology On Beauty: A History of a Western Idea – which is neither a history of art nor a history of aesthetics but rather an attempt to draw on the histories of both these disciplines to define the ideas of beauty that have informed sensibilities from classical to modern times? Starting with the aesthetic ideal of ancient Greece and ending with the beauty of machines, abstract forms, provocation and consumption, Eco does not even mention ‘totalitarian beauty’, as if the revival of Beauty and the production of totalitarian kitsch in Nazi Germany, Franco’s Spain, Stalinist Russia or Eco’s native Italy of 1932 (when he was born) never happened, or as if this painful period of history did not constitute an epicentre of Western history of the twentieth century.

Introduction

In putting together the programme for the 2011 Darwin Lectures with their theme of Beauty, the organisers aimed to begin with a lecture on Beauty and Mathematics. I believe it would indeed be possible to produce a riveting lecture or chapter strictly confined to this topic, narrowly construed. I have, however, taken the liberty of widening the discussion, to ask about the part played by considerations of elegance and aesthetics – by beauty – in humanity’s age-old quest for understanding how the world works.

This being said, the chapter nevertheless begins with a discussion of what I hope is a persuasive account of the interplay between Beauty and Truth in purely mathematical contexts. Against this background, I go on to consider the extent to which Beauty has guided, and still does guide, our advances towards understanding how the real world actually works. The chapter concludes with a brief look at the more complex landscape of intersections among beliefs and values, beauty, truth and tomorrow’s world.