Beauty is back. Architects are designing harmonious skyscrapers for London, artists are producing works on the subject, and evolutionary psychologists are presenting evidence that canons of beauty are hard-wired into the nervous system. The latter studies challenge established taste. According to the facial canon of pulchritude, Audrey Hepburn is more beautiful than Sharon Stone. Marilyn Monroe may be the sexiest woman of the last 100 years, if polls in America are to be believed, but her physiognomic proportions are not up to those of Catherine Deneuve or Grace Kelly. Marilyn's chin is too big, cheekbones too low, and her eyes not big enough in proportion to the face. Hugh Grant may be handsome, according to the same kind of investigation, but he lacks the strong bone structure and masticatory muscles that make ugly men, such as Mick Jagger and John Travolta, so appealing to the female nervous system. Such points are well publicised on television and in popular books. Where facial science leads, plastic surgeons are sure to follow, and sure enough noses are getting smaller, lips bigger in LA.
All this is absurd, of course. And it is hard to keep a straight face when the discussion of beauty reaches the sort of propositions put forth in books called Survival of the Prettiest, or the BBC series, The Human Face, co-faced by John Cleese. Measurements of facial ratios or any simple formulae cannot capture this elusive subject, precisely because it is a compound made up of at least four incommensurable sources. The singular point of beautiful objects, and people, is that they are experienced not as parts, or ratios between cheekbones and chin, but as wholes. The experience of beauty is a perception, but it is one that mixes up various other sensations and makes them converge in a particular way. This convergence remains something of a mystery, as I will argue, but it is one illuminated by recent scientific insights which deal with what are known as "strange attractors."
Is anything as elusive as beauty open to scientific investigation? The hypothesis that there are universal codes of beauty has a delightfully funny history, in which evolutionary psychology is only the latest chapter. We know, from the arguments of Vitruvius and the drawings of Leonardo, that good facial and body proportions should be reflected in good buildings. The face, from the chin to the top of the forehead, is one-tenth the part of the whole body, and so too is the perfect ratio of the hand, from the wrist to the tip of the middle finger. Such body proportions became a standard for those of classical temples. The one-tenth ratio resonates with the inner neurones. This was a happy surprise in the 1st century BC, and it seemed to prove that our proportions reflected the harmonies of the universe. The architect Francesco di Giorgio was so fascinated by such arguments that he proved, in many drawings, that the body could generate excellent cathedral plans, and the ratios of the face could impregnate the capital of a column with its beauty. Cesariano took this ideal further: he put the perfectly proportioned man on a rack and gave him the perfectly proportioned erection. Inevitably, it was one tenth the size of his body: final proof that we reflected the harmony of the spheres.
The evolutionary psychologists (EPs) are as confident about measuring beauty as the classicists were. The EPs reveal to us the supposed secrets of female beauty-large eyes, high cheekbones, plump lips, small lower faces-and tell us the reasons for it. Men prefer characteristics which suggest health, good design, nubility or fitness for purpose-that is, fecundity. Darwinian sexual selection, they claim, does the rest. The same kinds of argument produce the nightingale's song and that paragon of incontestable beauty, the peacock's tail-the paradigm case for an absolute, hard-wired, foundational beauty.
To the female peahen the explosion of blue and green feathers shimmering in the wind is, as the EPs say, a powerful "fitness indicator." It says to her: "in spite of my encumbrance I can resist parasites, eat well, and survive predators-therefore, pick my extra-powerful genes. My tail is a true advertisement because, with all the apparent drawbacks, I have managed to survive. QED my other genes must be very fit indeed." According to selfish gene theory, the intelligent molecules do the decoding, not the conscious peahen. Such arguments now dominate evolutionary psychology, and as Geoffrey Miller wrote in his Prospect essay "Waste is Good" (elaborated in his book The Mating Mind) sexual display has helped to produce not only the human mind, but culture too.
However, unlike the EPs, most people believe that beauty is subjective, simply in the mind or eye of the beholder. It is the rare artist or architect, such as Le Corbusier, who believes that there is objective beauty in nature, or in objects, which resonates with our inner being; "the axis which lies in man" he called it. But do such natural orders really exist and if so are they beautiful? Pick up a sunflower and count the florets running into its centre, or count the spiral scales of a pine cone or a pineapple, running from its bottom up its sides to the top, and you will find an extraordinary truth: recurring numbers, ratios and proportions. On these and many other growths there are typically five scales spiralling to the left, and eight spiralling to the right; or 13, 21, 34 and so on. These numbers follow the famous Fibonacci sequence, where each term is the sum of the previous two (named after the 13th-century Florentine who discovered it). When laid out in grids, the harmonic patterns form what are known as golden section rectangles. The recurrent pattern is a form of robust self-organisation, the most probable way the leaves or pinescales can occupy space given the rate at which they grow. The explanation, which eluded botanists for hundreds of years, has recently been discovered to lie in the close-packing of space. It turns out that one floret of the sunflower grows after another at the key angle of 137.5 degrees, because this is the angle best suited for occupying space over the growing time of the plant. The structural elements of a pine cone, daisy, pineapple and so many other spiralling plants can support each other most efficiently in this way.
Here the truth of close-packing leads to what I, and many others, find beautiful: the unfolding proportional spiral forms, an objective aesthetic in nature's patterns. Contrary to the EPs' explanations, many similar spiral patterns exist before there is life and natural selection (for instance, in galaxies and hurricanes). And the notion that certain forms are inherently beautiful recurs when strong artists suddenly have an insight. In the 18th century, William Hogarth argued in The Analysis of Beauty that gently undulating lines would always be more beautiful than angular ones. The s-shape or serpentine line he found to reveal "the utmost beauty of nature" and he backed up his insight not only with illustrations of flowers and dairymaids but also man-made objects such as chairs, tools, corsets, ships and castles-those objects that had a functional naturalism. Whatever we think of this pronouncement, there have always been exponents of the curved, (most recently Prince Charles), and by contrast those who are in favour of the angular, such as the expressionists.
Also, a few scientists, besides the EPs, keep faith in objective beauty. An insight into nature, such as E=mc2, is called a beautiful discovery because it brings together two different areas, energy and mass, in a new, simple way; mathematicians notoriously find good proofs exquisitely aesthetic. C?zanne found what he took to be the underlying geometry of nature-the Platonic solids of spheres and tetrahedra-to be eternally attractive. And because most people grant that the cosmos is beautiful, at least in some parts, it is not true to say that scepticism is universal.
Indeed, these shifts in opinion over natural beauty lead to an eternal flip-flop. Like our attitude to love, truth and goodness, we seem to be confident about knowing what beauty is-certain, even dogmatic-until we think hard about the idea, whereupon all confidence flies away. The flip-flop is everywhere today, even among the experts and curators. Why is this? When you investigate any set of canons closely enough-Hogarth's curves, Vitruvian proportions, or the recent face measurements of the EPs-they may turn out to be only local orders within a greater pattern of culturally shaped variance. For instance, the body type of Marilyn Monroe, the hourglass figure preferred since the Victorians and perhaps for 2,000 years, is quite different from the one preferred for the previous 25,000 years: that of the Venus of Willendorf. The pear-shaped woman, with fat buttocks, hanging breasts and large stomach, characterises good taste in hunter-gatherer societies and Neolithic ones. Even one or two courtly painters in a later era, such as Rubens and Boucher, celebrated cellulite, fleshy bottoms and excessive thighs.
The rule seems to be that there are no absolutes, that what is rare is prized. Thus, in times of relative affluence thin models become dominant. But do any norms or canons transcend these vagaries of history and taste? Can there be a non-subjective theory of beauty. This brings me to my four-part argument.
First principle: patterns squared. Vitruvius, evolutionary psychologists, William Hogarth, even Prince Charles, all have a point. Catherine Deneuve is stunning, the curves and whiplashes of Art Nouveau are devastating, the cubes of C?zanne and the cubists are a knockout. Remember the peacock's tail: if you don't find it beautiful, either something is wrong with you or you're not a peahen. Visual forms are coded into the nervous system, but the problem with the "beauty is objective" theorists is that they take these partial codes for the whole artwork.
The obvious truth is that perceiving beauty is a total experience and concerns more than one or a few things, like facial measurements. Psychological studies of how we rate beauty over time bring this out. Strangers, who were brought together for one hour a day over four days, changed their view of who was beautiful based on other qualities such as likeability and character. It is obvious that an animated face-talking, laughing-is different from a frozen face considered in the abstract, and this dynamic quality of beauty is why conventionally ugly women, such as Cleopatra, can become the most seductively beautiful.
The second problem with the "beauty is objective" theorists is that they consider only a few codes of perception beautiful, instead of all codes. It is not that Hogarth's curving line is not beautiful, nor that any system of aesthetics-gothic, modern, grotesque-cannot lead straight to beauty. No, the proposition is that all patterns, in the right context, can produce beauty. This is perhaps more easily granted with patterns of nature: we can experience all of them as aesthetically pleasing-not just the spheres, cones and cylinders of classical and modern aesthetics, not just the Platonic archetypes. The truth is that the eye and mind respond to every conceivable pattern-spirals, crinkles, blobs, folds, fields, zigzags, dots or those which Benoit Mandelbrot characterised in his book as The Fractal Geometry of Nature. Most of nature is, counter to C?zanne and the classicists, fractal in form and irregular. It is also true, as Mandelbrot pointed out in his seminal work, that the maths of fractals were rejected as pathological by scientists for 80 years because they did not conform to the western paradigm of beauty and order.
Yet the question of beauty is deeper than mere pattern formation: the formal aspect of beauty, its foundation, concerns the intensification of patterns. Put in a nutshell, this first principle of beauty is patterns about patterns, or patterns squared. By this I mean the way in which the artist plays with patterns-cubes, curves, fractals, blobs or any forms-so that they refer to themselves. The self-referential notion of the aesthetic sign makes us attend to the plane of expression as if it were the content. It heightens sense perception, whether it is information coded as sound, taste, smell, touch or visual form.
Excessive sensual pattern-apprehension, through one of our five senses, is the general foundation for the experience of beauty. It sounds harmless but it contains a surprise-it means that conventionally ugly patterns may be beautiful too, even repugnant things such as gargoyles, or brutalist buildings, or Chinese yellow wax rocks. These last have been loved and collected by the Chinese for centuries, in spite of being repulsively slimy, like overripe pustules or lugubrious stomach-parts. Indeed, through developing a taste and then connoisseurship for such monstrosities, even their repugnant qualities are turned into virtues, just as we have turned the mannerist terribilita or the frightening work of Francis Bacon into a new form of beauty. What makes the Chinese rocks so fascinating is not only the way they challenge received notions of beauty, but also the way they show that nature herself can be the artist. They lend support to the argument that beauty is "out there," not just in our nervous system, or the eyeball of the beholder. Patterns about patterns, patterns squared or heightened, are produced by nature.
I may seem a bit hung up on this notion of patterns as the foundation for an objective beauty, and indeed I am: the reason is that, as mathematicians are telling us, they are the most basic things in nature. They are deeper than the maths (which only discovers their algorithms) and much deeper than our eye or mind. At the beginning of the universe supersymmetry reigned, the primeval symmetrical fireball misnamed the big bang. From then on it is symmetry-breaking, all the way down to the present. More and more interesting patterns arise-which is not to say they are all beautiful. It is only those which call attention to themselves through some rhetorical means, some aesthetic manipulation or accidental heightening, which pass the minimum foundational test. Beyond that I would argue that heightened patterns which are highly interrelated and more complex than simpler patterns are more sustaining; they allow deeper and more different readings, and for that reason are more long-lasting. They "stand the test of time," that old arbiter of beauty, although perhaps for reasons which are not usually given.
Putting the case for objective beauty on its foundation in patterns about patterns has the advantage over previous positions, such as the Platonic, the classical or the psychological, in being very general. And it is so abstract as to include the other definitions as special cases. But this is only a foundation. It does not encompass the other aspects which play a role in our perception of beauty.
Second principle: the pleasure of the new. The notion of what is beautiful has swung back and forth between classical and expressionist aesthetics, while at the same time inventing new categories of experience. Little is clear from this history except the anti-classical insight that beauty is not one thing, nor can it be captured by one set of canons, nor even by a loose set of overlapping concepts or language games. For instance, with turn of the century art movements there is no set of definers that will unite the impressionists to the fauves, or either of these to the cubists, dadaists, and surrealists. There are some continuities here, but no congruent set of qualities. Lautr?amont's definition, "beauty is the fortuitous encounter of an umbrella and sewing machine on a dissecting table," or Andr? Bretons's pronouncement, "beauty will be convulsive, or it won't be at all," or Picasso's remark, "I race ahead of beauty," characterise the artists' divergent attitudes. Duchamp's readymades were intended as anti-art, against beauty, but they have been found over time to be beautiful, as he reluctantly admitted at the end of his life. It would be vain to seek an essence connecting all this work, some hidden thread, beyond the minimum, patterns heightened, and the fact that it has all been recognised as art.
But a lesson of modernism, learned over the last two centuries, is that perceiving the new can be sensual, akin to the Marquis de Sade's view that children love nothing so much as a surprise, a "shock to the nervous system." By contrast, repeated patterns lose their activating potential, because of what is called Hebbian Learning, after Canadian psychologist Donald Hebb. He showed that brain cells which repeatedly fire in the same learning sequence become hard-wired into the long-term memory: cells which fire together, wire together. The conclusion has negative as well as positive implications. An old beauty is not as exciting as one perceived for the first time-caught on the wing. This insight-the second principle of beauty-may have been overdone, the new may have been fetishised, but today some resetting of tradition has come to be bound up with our experience of the beautiful.
This explains why, when an innovation occurs within the avant-garde-Picasso's Les Demoiselles d'Avignon, Stravinsky's Le Sacre de Printemps, TS Eliot's The Waste Land, to name three shocks which established the modern canon-it has such an impact. When the mind perceives a new idea, and new formal pattern, it is aroused by its own transformation. It is as if the mind received a natural pleasure in feeling its dendrites coalesce in new ways, feeling its glial cells send little nodules spinning down the neuronal highways to meet up with those on a different path. We can now watch such micro-growth on film, and literally see new ideas linking up with old ones. This may be too physical an explanation but every time one hears a new joke, and finds it funny, the mind bristles with new connective tissue, and the feeling of pleasure and laughter signals the construction of new pathways. Hence our delight at the shock of the new when it is a real breakthrough, not something merely different or clever. Innovating art creates new ways of seeing, feeling, experiencing the world, a new kind of knowledge, and this cognitive extension is an essential part of the experience of beauty.
Third principle: symbols of perfection. The first two components of beauty (the intensification of patterns and the delight of the new) may be in tension with the third-the imaginative projection by the perceiver on to the object, investing it with attributes of perfection, love and transcendence. Of course, the object must be suitable for such projection, classical beauties such as the Taj Mahal are typical in this respect. The moon, before Galileo showed it to be a dead lump of matter, was also a suitable object of projection; and it remains so for many, even after astronauts played golf on it. But when it became a clich?, a stereotype of transcendence 90 years ago, the futurists declared "a war on moonlight." The ocean also went through several phases of acceptance and rejection. The wide sea is seemingly endless, infinitely ambiguous, and like a Rorschach figure, a good receptacle for articulating wishes; until so many Bayswater Road seascapes kill it off. Suggestive figures vaguer than the moon, enigmas as de Chirico argued, may escape this exhaustion. "Always suggest, never name" was an injunction of symbolist poets in the 19th century. Much subsequent art has stayed fresh through this truth.
This implies that there might be an abstract code of beauty at some deeper level of perception, a point put to me by the sculptor Anish Kapoor when I mentioned the importance of the first principle, patterns heightened. He countered with the intriguing idea that beauty is the presence of the absence of any pattern, and pointed out the positive way we respond to "all-overness," a quality that his own work exploits. It often consists of an all-over colour, a single pigment such as deep red or dark purple, and a continuously varying shape which seemingly has no beginning, end, dimensionality or pattern. In his sculptures boundaries are vague; depth is impossible to determine. They draw us into an experience because we cannot figure them out: mind-teasers, sense-teasers, impossibility-teasers. All these works engage the viewer in a speculative activity, they invite the projection of inner sensations on to a void. Most people find the work, or activity of projection, "beautiful."
This returns us to eastern notions of nothingness and the idea in physics today of the plenum void: the idea that the perfect vacuum is full of possibility, quantum events which jump into and out of existence very quickly (entailed by the principle of uncertainty). In Zen aesthetics, the void, has been understood as a positive part of existence, while in western art the blank canvas, Malevich's "white on white" series or Rodchenko's and Reinhardt's "black on black," have also become canonic. Often these objects are perceived as symbols of perfection, of the divine. However, as with the second principle-the shock of the new-this brings in belief, taste and culture.
Fourth principle: significant content. By admitting the importance of taste it looks as if I have fallen back into the subjective view of beauty. But there are distinctions to be made. First, although the eye is an extension to the brain, and does indeed pre-code certain perceptual states which are learned, it is not the thinking, feeling mind. We may, as psychologists claim, pre-judge a person or object in the first microsecond we come upon them, but with beauty it is the second glance that really counts; it involves an oscillating state of mind which includes, and balances, many perceptions and ideas. Beauty is thus more in the mind than the eye of the beholder. Second, this active mind is having a complex holistic experience, not the kind implied by faces on a chart in a laboratory of pulchritude. The reductive measurement of parts interferes with attentiveness-just as the Hollywood director who concentrates on lining up beautiful actors may take his eye off the script.
If we grant that there are a few naturally beautiful forms, such as the Fibonacci spiral, in which truth and beauty are reconciled, it may mean that there is a positive aesthetic in nature, but it does not follow that all definitions of beauty must be based on it. Foundations are not superstructures. The peacock's tail is beautiful, and so are all patterns heightened, but this is still not the paradigm case for more complex social and cultural beauty. In a few cases, Keats' famous line, "Beauty is truth, truth beauty," does summarise the matter, but in much great art they can be opposed or in conflict. Yet in a deep and successful work of art, truth, beauty, goodness and many other things do seem to converge in our minds. The experience of beauty is a unitive perception in which contradictions are balanced, and these conflicts produce an even greater whole: deep as opposed to shallow beauty. Into this complex equation comes the fourth principle-the content or subject matter or beliefs expressed in a work of art.
We bring to our experience of art what we know, believe and value about life. Seeing and knowing, as EH Gombrich has pointed out, cannot be separated. For example, I find Leni Riefenstahl's film of the 1936 Olympics very beautiful, and the way it unites the moods of nature, the clouds, sea and mountains with the exertions of the athlete's body entirely convincing; but knowing its purpose as Nazi propaganda colours my perception. While I can suspend my disbelief in Nazi ideology, and partly enjoy the film, a deeper pleasure results when ideas, beliefs and expression can draw near. This truth forces subject matter into consideration. Content matters. Beauty thrives on an emotion, or condition, which we find significant, or on an idea we find fundamental to life: love, quite obviously, and first and last things, and our relation to the rest of humanity and nature.
Two recent buildings, often regarded as beautiful, show the contribution of ideas to the equation: Frank Gehry's new Guggenheim Museum in Bilbao, (see previous page) 1997, and Daniel Libeskind's Jewish Museum in Berlin, 1999. Both clearly have patterns which are heightened and extend architectural knowledge, thus exemplifying the importance of my first two principles. They both elicit extraordinary metaphors: Gehry's waves have been seen as a constructivist artichoke; or, by contrast, a swimmer bursting out of her sequinned bathing suit. Libeskind's angles have been called a frozen lightning bolt. Patterns heightened, which are new, invariably spark off bizarre comparisons-how else can we communicate amazement? As to the third principle, the sense of perfection, the all-over material, the reduction to essential forms on to which we can project ideas and fantasies, the two buildings seem purpose-built for this. Gehry's 50,000 sheets of titanium and Libeskind's zinc diagonals are omnipresent.
But aside from the sensuality, invention and functional fit of the forms, what makes these two buildings beautiful is the way they play with significant ideas. Gehry's building takes the basic shift in value of our time-the museum as cathedral, art as religion-and faces up to this problematic mutation. His building "performs" the city just as the gothic cathedral performed the city and the countryside around Chartres. It becomes the urban focus, sends out explosive rays to the surrounding hills, pulls in views down grimy streets, reflects the Nervi?3n river in its brilliant skin, relates to the metallic trains which slip behind it, or vehicles which pass on the bridge over one of its galleries. No building since the Sydney Opera House celebrates so well the tough urban realism of machines and the spectacular effects of nature. To see a sunset, storm or fog in its surfaces is much more than to see them in a mirror: it is to perceive them-because of double reflections-glowing out of the titanium. As with a cathedral, there is a cosmic reference to this museum, the content is the city, hills, weather and machines, taken up and made part of its dramatic forms.
No matter how spectacular and moving these forms are they would not have the resonance they do without their relationship to ideas. The fact that they have been derived and manufactured by computer and are fractals, self-similar petals rather than repetitious squares, gives them added relevance. These extensions of architectural knowledge, and knowing this content, is an essential part of perceiving the building as beautiful. So it is with knowing the content behind Libeskind's Jewish museum: the way it relates to the six-pointed star, references to the void down the middle, and the Holocaust. Significant content deepens the experience of beauty and cannot be disentangled from the perception.
The big question is how, and if, the four components fit together to create the experience of beauty-an oscillating state of mind, rather like the weather. The parallel may be illuminating. The weather is now understood, by chaos science, to emerge in a phase space determined by many variables. Yesterday's weather, temperature, air pressure, wind currents, and so on, fold into a whole to produce what is called a strange attractor. These forces limit and form today's weather, give it coherence, although the slightest change in one condition-the butterfly effect-may push the weather into another part of the phase space. Nevertheless, the strange attractor has a shape and various limits. It does not usually freeze in the desert or go above freezing in the Arctic circle. It oscillates around its limit cycles like a planet pulled to a sun which wobbles around. No two days are exactly the same, but there is still a general summer and winter, a fuzzy coherence. Today, informed by chaos science and a computer which can handle over 1m variables, meteorologists predict roughly what this strange attractor will look like: the weather report. It is not always right, but it is right often enough to remain a staple of the daily news. Moreover, most human organs oscillate like strange attractors around an attractor basin-the heart, the brain-indeed, all growth exhibits this self-similarity and slight variation.
Could the experience of beauty, in an individual or a culture, show the same coherence and slight variation? Information theorists showed, in the 1950s and 1960s, that the beautiful is a judicious mix of a) what was beautiful yesterday plus b) a significant variation from it-a "swerve" in the formulation of Harold Bloom. Artists knock beauty into a different regime. Changing sensibilities push it around, fashion claims its victims, but it wobbles forward and back with some consistency. This coherence is caused by the interaction of many variables, the way they come together to limit experience within a loose but expanding regime. No, we cannot predict exactly tomorrow's beauty but, yes, when these various components come together they give it shape. Beauty is that strange attractor of experience, attracted in its shape by the influence of exaggerated patterns, new knowledge, the idea of perfection and significant content. By definition, therefore, no one will have the last word on this mysterious drive, and goal, of life. n
