Between

If no one asks me

Around the years 397 to 400, Augustine, the bishop of Hippo in North Africa (the city is now Annaba, in Algeria), wrote a confession that included a famous puzzle about time. “What, then, is time?” he asks. “If no one ask of me, I know; if I wish to explain to him who asks, I know not” (in the 1876 English translation of J. G. Pilkington, in the public domain). The lecture uses the same move for beauty: most of us rarely make mistakes about what is beautiful, and almost none of us can say what beauty is. There is an older precedent than Augustine. The dialogue Hippias Major, traditionally ascribed to Plato (perhaps about 390 BC), has Socrates ask the sophist Hippias what the beautiful is, and then take apart each answer. Is it a beautiful girl? Gold? What is appropriate? What is useful? What is beneficial? Pleasure through the eyes and ears? Every answer fails, and the dialogue ends with Socrates saying that he now understands the proverb “beautiful things are difficult” (in H. N. Fowler’s Loeb translation of 1926). In Greek: chalepa ta kala.

Most attempts since have fallen into three families, which the lecture names and which this lesson takes in turn: that beauty lies in proportion, in unity within variety, or in use. The lecture presents them as eighteenth-century definitions, each soon refuted. Proportion and use are in fact far older, as the next sections show, and what the eighteenth century added was the attack on them, along with a new statement of the second.

Proportion

The idea that beauty is a matter of ratios goes back to the Greeks. Lesson 3 met Polykleitos’s Canon, reported by Galen as the fit of the parts to one another. The Roman architect Vitruvius, in the late first century BC, wrote that proportion is the fit of the parts “to each other and to the whole,” and that a temple needs it as much as a well-formed human figure does. The Renaissance writer Leon Battista Alberti, between about 1443 and 1452, defined beauty as a harmony of the parts in which nothing could be added, taken away, or changed without harm.

Music gave the idea its best evidence. Plucked strings whose lengths stand in the ratios 2:1, 3:2, and 4:3 sound an octave, a fifth, and a fourth. That much is solid, and Course 1 shows it on a one-string instrument: music is number you can hear. The famous story of how Pythagoras found it is false, though. Nicomachus, in the second century AD, says Pythagoras heard blacksmiths’ hammers ring in those ratios. It does not work: hammer weights do not map onto pitch like that. Around 1589 the lutenist and theorist Vincenzo Galilei, Galileo’s father, found that an octave needs a four-to-one ratio of string tensions, because pitch goes with the square root of the tension. The ratios are real for string lengths and not for hammers.

Edmund Burke, in A Philosophical Enquiry (1757), took proportion apart with nature. “How does the slender stalk of the rose agree with the bulky head under which it bends?” he asks, and answers that the rose is beautiful all the same. The swan, “confessedly a beautiful bird,” has a neck longer than the rest of its body and a very short tail, while the peacock has a short neck and a tail longer than all the rest together. He does not say, as the lecture has it, that the stranger the flower, the more beautiful; he says that apparent disproportion does not spoil the rose, and may even add to it. He attacked fitness and perfection the same way. If fitness were beauty, the wedge-shaped snout of the pig, so well made for digging, would be beautiful. And beauty, he writes, “almost always carries with it an idea of weakness and imperfection.” He ties beauty to smallness, smoothness, delicacy, and clear color, and he takes women as his chief model, a point to keep in mind when reading him.

Unity in variety, and use

Francis Hutcheson, in 1725, proposed that the figures that excite the idea of beauty “seem to be those in which there is Uniformity amidst Variety.” In 1753 the painter William Hogarth published The Analysis of Beauty and named a shape for it: the “line of beauty,” a gentle S-shaped curve. The lecture’s showpiece for unity in variety is the Laocoön, a marble group in the Vatican of a Trojan priest and his two sons caught by sea serpents. It was dug up early in 1506 in a vineyard on the Esquiline Hill in Rome, and Michelangelo was among those called to see it. Pliny the Elder had praised it as the work of three sculptors of Rhodes, Hagesandros, Athenodoros, and Polydoros. The lecture’s reading, in which the father’s body is balanced against his sons’, is a standard formal analysis. The eighteenth-century writers who made the statue famous were interested in something else. Winckelmann in 1755 saw in Greek art “noble simplicity and quiet grandeur,” and Lessing in 1766 argued that the sculptor held back the scream because Greek art served beauty.

The lecture gets the story behind the statue wrong. In Virgil’s Aeneid, Laocoön was not the one man who knew the secret of the wooden horse. He distrusted it (“I fear the Greeks, even bearing gifts”) and threw a spear at it. A Greek spy, Sinon, then lied to the Trojans, and two serpents came from the island of Tenedos and killed Laocoön and his sons. The Trojans took this as punishment for harming the horse and dragged it inside. Cassandra, too, had warned them, and was not believed.

Use is the third family. In Xenophon’s Memorabilia (3.8), Socrates tells a friend that a dung basket is beautiful and a golden shield ugly, “if the one is well made for its special work and the other badly” (in E. C. Marchant’s translation, 1923). It is Xenophon’s Socrates who defends use. Plato’s Socrates in the Hippias Major takes the same idea to pieces, so the lecture merges two different Socrateses. And the lecture’s assertion that nobody admires mathematical formulas fails: the mathematician G. H. Hardy wrote in A Mathematician’s Apology (1940) that “beauty is the first test” and that there is no permanent place in the world for ugly mathematics.

The golden ratio

The most famous proportion is a number: 1.6180339887…, written φ and called the golden ratio. Euclid describes it in his Elements about 300 BC, as dividing a line “in extreme and mean ratio,” so that the whole is to the larger part as the larger is to the smaller. It is tied to the Fibonacci numbers (1, 1, 2, 3, 5, 8, 13, …), whose consecutive ratios close in on it; Kepler is credited with noticing this in print in 1611. Luca Pacioli’s De divina proportione (Venice, 1509, with drawings by Leonardo da Vinci) calls it “divine” for theological reasons, not for beauty. The name “golden” is far later: one early use in print is in a German physics dictionary of 1789, and the Greek letter φ was adopted only about 1910, reportedly in honor of the sculptor Pheidias.

Does anyone prefer the golden rectangle? Gustav Fechner tried it in the 1860s and described it in 1876: he showed people ten rectangles and asked which pleased them most. Of 347 responses, the golden rectangle drew 35.0 percent, the 3:2 rectangle 20.6, and the 1.77:1 rectangle 20.0, and nobody chose the golden one as the least pleasing. That is a lean result, and later studies went both ways: in 1995 the psychologist Christopher Green concluded that the effect may be real but is fragile, and a 1997 paper was titled “The golden section hypothesis: its last funeral.” The honest summary is that since 1865 the effect has been weak, shaky, and dependent on method. You can run the test yourself.

The claims about where the golden ratio appears are another matter. Take the Parthenon. Its base is 69.5 by 30.9 meters, and its front is 30.9 meters wide and 13.72 high, so both proportions are about 9 to 4, or 2.25, and not 1.62. In 2014 the archaeologist Foutakis surveyed temples, tombs, sarcophagi, and steles and found the golden ratio “totally absent” from the architecture of the fifth century BC. A later tale says the sculptor Pheidias used it; the symbol φ itself was chosen only about 1910, reportedly in his honor, so it is no evidence of Greek practice. The Great Pyramid’s height of 280 cubits and half-base of 220 cubits stand in the ratio 14 to 11; the claim that it encodes φ goes back to John Taylor in 1859, who misread Herodotus. Dividing the slant height by half the base does give 1.6186, but the same numbers give π equally well, so a pyramid holding both is numerology. For the Mona Lisa the astrophysicist Mario Livio wrote that no documentation exists to show that Leonardo used the golden ratio consciously. The chambered nautilus does not grow in a golden spiral: one study measured a growth of about 1.33 per quarter turn, against 1.618 for a golden spiral.

Some golden-ratio claims are true. The spirals of sunflower seeds and pine cones follow Fibonacci numbers, and the angle between successive seeds, 137.5 degrees, is the golden angle. In 1992 Stéphane Douady and Yves Couder showed that droplets of magnetized fluid dropped one at a time onto oil, each repelling the others, arrange themselves into Fibonacci spirals with no knowledge of φ at all. Some artists and designers have used it on purpose. Le Corbusier built his Modulor system (1948) on a man 1.83 meters tall with a series of golden-section measurements. Salvador Dalí painted The Sacrament of the Last Supper (1955) on a canvas 267 by 166.7 centimeters, a ratio of 1.602, so “close to” φ, with a dodecahedron floating over Christ. The Cubist group that called itself the Section d’Or, whose Paris show opened in October 1912, took its name from the idea; by Duchamp’s account, and Livio’s, the idea was not actually used. And the lecture’s other proportion claim, that Renaissance buildings were made from musical ratios, has a real history behind it, since Alberti and Palladio wrote about it and Rudolf Wittkower made the case in 1949, but how far builders followed the ratios is still argued.

Pretty, and worth a look

The lecture’s own way out is to split the word. Some things are pretty, and others are worth looking at without being pretty at all. Philosophers have long held something close to this. Frank Sibley noted in 1959 that beauty and ugliness are the general verdicts, while words such as unified, balanced, serene, dynamic, delicate, moving, and tragic pick out narrower aesthetic qualities, and each needs taste to apply. The lecture’s contrast is Ingres’s La Source, a smooth nude begun in 1820 and finished in 1856 (now at the Musée d’Orsay), against Edvard Munch’s The Scream, which exists in several versions from 1893 to 1910. Munch’s diary entry of 22 January 1892 mentions “an infinite scream passing through nature.” The Scream is not pretty, and that is the point: a pastel version sold at Sotheby’s on 2 May 2012 for $119,922,500.

Between

The lecture’s most distinctive idea is that beauty is found neither in a definite shape nor in the lack of one, but between them. It turns to a seventeenth-century Chinese writer for the best description. Li Yu (李渔, 1611–1680) wrote Xianqing ouji (闲情偶寄, roughly “casual jottings of leisure,” 1671), a book about the pleasures of leisure, and in its section on selecting women he asks what makes someone move us. His answer is not good looks. 古云：「尤物足以移人。」尤物维何？媚态是已: the old saying is that an “extraordinary thing” moves people, and what is it? Allure (态, tài). Beauty of face, however fine, is still a thing, he says, and a thing cannot move anyone; but add allure and the thing becomes extraordinary. Allure is like the flame of a fire, the glow of a lamp, the luster of pearls and gold: 是无形之物，非有形之物也, a thing without form, not a thing with form. Because it is a thing that is not a thing, formless yet seeming to have form, it is called 尤物 (yóuwù), and it “cannot be explained.”

The lecture picks up two more of his lines. Allure is born, not made: forced allure only makes plainness worse, as the same frown is lovely in Xishi and ugly in Dongshi. And 学则可学，教则不能: it can be learned, but it cannot be taught. A woman without allure who lives day and night beside one who has it may, perhaps, be changed, as a wild plant growing among hemp stands straight without support. Li Yu’s final turn is wry: if he tried to drill it into her, where in the twenty-one histories would he begin? Two cautions. The passage is written for men choosing concubines, and its “extraordinary thing” slides between an enchantress and a monster. The lecture’s switch to men is its own move. And Li Yu, who left Hangzhou for Nanjing in 1662 partly because pirate printers were copying his books, is one of the first authors known to fight piracy loudly, though not the first: a Southern Song book reportedly carried a printed notice against copying nearly five centuries earlier.

A saying attributed to the painter Qi Baishi (齐白石, 1864–1957) turns the same idea into advice for painters: 作画妙在似与不似之间，太似为媚俗，不似为欺世 (zuòhuà miào zài sì yǔ bù sì zhī jiān, tài sì wéi mèisú, bù sì wéi qīshì). The charm of painting is between like and unlike; too like is pandering, and not like is fraud. Its source is not documented, and the line appears everywhere without a citation, so “attributed” is the careful word. Qi Baishi was born in Hunan to a farming family, worked as a carpenter from the age of fourteen, and became a painter of shrimp, crabs, and frogs observed closely. The older Chinese background is Laozi’s 大象无形 (dà xiàng wú xíng), “the great image has no form” (chapter 41).

The West has its own versions. Joseph Kosuth’s One and Three Chairs (1965, in the Museum of Modern Art since 1970) is a folding chair, a photograph of a chair, and an enlarged dictionary definition of “chair.” Plato’s Republic (book 10) gives the old version: there is the bed that God makes, the bed that the carpenter makes, and the bed in the painter’s picture, which stands “thrice removed” from the truth. The order differs: Plato’s is the Form, the carpenter’s bed, the painter’s image, while Kosuth’s is object, picture, word. Calling it a gulf between idea and object is an interpretation. The Chinese artist Xu Bing (born in Chongqing in 1955) plays with the gulf in The Living Word. Its first version was reportedly made in 2001 for the Arthur M. Sackler Gallery in Washington, and the third and largest hung at the Morgan Library and Museum in New York from 19 July to 2 October 2011: more than four hundred laser-cut acrylic characters, rainbow-colored, rising from a dictionary definition of 鸟 (niǎo, “bird”) on the floor and changing from modern script into the ancient picture of a bird. The lecture claims that only Chinese writing can play this game. That is a thesis, and a debatable one, since Egyptian hieroglyphs and Maya writing are also picture-based, and most Chinese characters are not pictures but compounds of meaning and sound.

Western philosophy has its own “between.” Kant’s beauty has “purposiveness without purpose” and a “free play” of imagination and understanding that settles on no concept. Friedrich Schiller, in On the Aesthetic Education of Man (1795), put a play drive between the drive of the senses and the drive of form, and wrote that a person is fully human only when playing.

How to learn it

The lecture ends with a method. One kind of learner, it says, works from experience: you cannot teach aesthetics in a classroom but only in front of works, in museums, concert halls, and theaters. The other works from study, reflecting on what others have said about art, a “study of studies.” The lecture’s own diagram has three layers: art practice, art criticism, and the theory that studies the criticism. Monroe Beardsley’s Aesthetics: Problems in the Philosophy of Criticism (1958) names the top layer as the philosophy of criticism, and the lecture’s scheme tracks his.

On the first side, the lecture names the Chinese aesthetician Zong Baihua (宗白华, 1897–1986). He went to Germany in April 1920, studied philosophy in Frankfurt and then aesthetics in Berlin, and returned home in 1925. His essays are collected as 美学散步 (Měixué sànbù, “Aesthetic Strolls” in our rendering, 1981), named for a 1959 essay in which he writes that a stroll is a free, unconstrained action whose weakness is that it has no plan and no system: 散步是自由自在，无拘无束的行动，它的弱点是没有计划，没有系统. The title is a manner of learning, not a school. The lecture’s American example is Arthur Danto. In the spring of 1964 Danto saw Andy Warhol’s Brillo Box sculptures at the Stable Gallery in New York, and in October that year his essay “The Artworld” argued that seeing something as art “requires something the eye cannot descry”: a knowledge of art’s theories and history. Danto taught at Columbia from 1951 and wrote for The Nation from 1984 to 2009. He described the sixties in New York as “a period of extraordinary experimentation.”

On the second side, Kant is the lecture’s model of the thinker who worked from study. He was born in Königsberg in 1724 and died there in 1804, and the lecture says he never left it. He did leave the city for about five years from 1748, as a tutor in country houses, but the farthest he is reported to have gone is somewhere between 65 and 95 kilometers, since accounts differ. When he wrote about the sublime in 1790, he drew on a traveler’s report of the Egyptian pyramids, which he never saw. Both kinds of aesthetician exist, and the lecture’s advice is to do both.

It helps to know how people actually look. In 2001 Jeffrey Smith and Lisa Smith timed visitors to the Metropolitan Museum of Art in New York: the mean time at a work was 27.2 seconds, the median 17.0, and the most common 10. A repeat in 2017 at the Art Institute of Chicago found a mean of 28.63 seconds and a median of 21.00. Slow Art Day, founded in 2010, invites people to spend ten minutes on each of five works and then talk about them over lunch. A 2014 study of more than ten thousand students on guided field trips to the Crystal Bridges Museum in Arkansas found small gains, such as 0.09 of a standard deviation in critical thinking about art.

A Saturday list

1. Look longer. The typical viewer spends under half a minute. Try five works, ten minutes each.
2. Compare two similar works. Hume listed comparison, with practice and delicacy and freedom from prejudice, among the habits of a good judge.
3. Try Clive Bell’s lens, then argue with it. In Art (1914) he proposed “significant form” as what provokes aesthetic emotion. The usual objection is that the test is circular.
4. Stroll without a plan. Take Zong Baihua’s stroll as a model of free, unhurried looking. His essay of 1959 also admits the stroll’s weakness: no plan and no system.
5. Finish the experience. John Dewey, in Art as Experience (1934), held that an experience that has a beginning, a development, and a fulfillment is the aesthetic one.

If you want to read, start with Zhu Guangqian’s Talks on Beauty (谈美, 1932), then Zong Baihua’s essays and Li Zehou’s The Path of Beauty (美的历程, 1981; English translation by Gong Lizeng, 1994). In English, Roger Scruton’s Beauty: A Very Short Introduction, Elaine Scarry’s On Beauty and Being Just (1999), Alexander Nehamas’s Only a Promise of Happiness (2007), and Denis Dutton’s The Art Instinct (2009) are readable, and Paul Guyer’s A History of Modern Aesthetics (2014) is the full history.

To close the circle: what relation does the study of beauty have to its subject? Neither the philosopher’s nor the criminologist’s. It is the singer’s. You will study best by doing both, looking and reading, and the person who has only read, or only looked, is at half strength.