Beauty Is Objective. Why the World Really Is Beautiful – and Why the Feed Is Lying to You About It

In 1993 two conceptual artists who had emigrated from the Soviet Union to the United States put to humanity the question art is usually too embarrassed to say out loud: what do you actually want from a picture? With money from the Nation Institute they hired polling firms and surveyed people in ten countries across several continents – extrapolated to the whole of humanity, the "People's Choice" claimed to report the preferences of close to two billion souls. The questions were plain and domestic. A landscape or an interior? Which animals, which colours, which people – famous or ordinary, clothed or nude? And then, and this is where the project becomes a spectacle, the two of them actually painted, for every country, its most-wanted and least-wanted picture – a pastiche built from each nation's favourite colours, shapes and subjects.

At first it looks like a joke, and in part it is one. America's Most Wanted came out like this: George Washington on a grassy bank by a lake, three clean-cut children who look like vacationers at Disneyland, two deer and a bellowing hippopotamus. Denis Dutton compares it to a poll about most-wanted food: people named ice cream, pizza and hamburger, so it would be logical to serve hamburger-flavoured ice cream inside a chocolate-coated pizza. That people want Washington, game animals and children in pictures does not mean they want them all in the same one.

But through the joke a fact appears that survives it. Everywhere, from Kenya to Iceland, people gravitated to the same kind of image: a landscape with water, trees, human figures and animals, and the favourite colour of the entire world was blue. Something stranger still came out of it. Kenyans preferred landscapes that resembled upstate New York more than they resembled the terrain of Kenya. It was as if, one of the artists remarked into a tape recorder, everyone has "this blue landscape in their head. It sits there… They can see it, down to the smallest detail." Kenya and Iceland – what could be more different in the whole world – and both want the blue landscape.

Dutton, a philosopher of art, reads this not as a story about taste but as a story about inheritance. The ideal landscape of the people polled is open ground with clumps of trees, water in view and signs of animal life – that is, the East African savanna where the hominids split off from the chimpanzee lineages. It is not a fancy trained into us by calendars, as the relativist would prefer; it is an attachment older than any culture. And the cleanest proof came from children. In a replicated experiment, Balling and Falk showed photographs of five kinds of terrain to six age groups. The youngest, the eight-year-olds, preferred the savanna above every older group – though none of them had ever been in a savanna, just as the Kenyans had never seen the Hudson River.

Hold that scene. It is the first hint of this lecture's thesis: that what we are used to calling private taste, a "vibe," each to their own, may in fact have an objective core, written into us deeper than fashion. That beauty may be something we read out of the world rather than something we cast onto it. And if so, then learning to see it means knowing something about reality, and not merely having a preference.

There is one place where you can watch beauty at work rather than merely admire it – mathematics. In 1940 the English mathematician Godfrey Harold Hardy, old now and certain his creative power had left him, sat down to write A Mathematician's Apology, a small sad book about what he had done all his life. And in it is the sentence on which this part of the lecture rests. "The mathematician's patterns, like the painter's or the poet's, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics."

Notice the exact logic. Hardy does not say beautiful mathematics tends to last longer. He says ugly mathematics has no permanent place at all. Beauty here is not a decoration laid over correct proofs. It is the filter that decides what survives. And the mathematician is the one maker whose material does not age: the painter works in shape and colour, the poet in words, and the mathematician, Hardy says, in "patterns made with ideas," which is why his patterns last the longest.

Hardy chose two Greek proofs that, in his words, "two thousand years have not written a wrinkle on," and that any intelligent reader can walk through in an hour. The first is Euclid's: there are infinitely many primes. Suppose instead there are finitely many, and 2, 3, 5 … P is the complete list. Form the number Q by multiplying all these primes together and adding one. Then Q, divided by any of them, leaves a remainder of one, so it is divisible by none of them; which means either Q is itself prime, or it is divisible by some prime not on the list. The list was not complete. Contradiction. Hardy loves the image of a game here: proof by contradiction is "a far finer gambit than any chess gambit: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game."

The second is Pythagoras's: √2 is irrational. Suppose √2 = a/b, a fraction in lowest terms, so that a and b share no common factor. Then a² = 2b², so a² is even, so a is even; write a = 2c, substitute, and you get b² = 2c², so b is even too. But then a and b are both even and share the factor 2, which we forbade. Contradiction. And the consequence stunned the Greeks: the diagonal of a square is incommensurable with its side, there is no common unit that measures both.

So what is beauty in a proof, once you take it apart? Hardy gives an answer you can hand to a student: "a very high degree of unexpectedness, combined with inevitability and economy." The argument takes an odd, surprising form, the weapons look childishly simple next to the far-reaching result, and there is no escape from the conclusion. And an image tailored for this archive: "A mathematical proof should resemble a simple and clear-cut constellation, not a scattered cluster in the Milky Way."

Here beauty and objectivity are visibly the same thing. Mathematicians agree with one another about which proofs are beautiful as reliably as they agree about which are correct; "no other subject has such clear-cut or unanimously accepted standards." And the objects themselves do not depend on us. "317 is a prime, not because we think so, or because our minds are shaped in one way rather than another, but because it is so, because mathematical reality is built that way."

And last, a gift, bitter and beautiful. Hardy built his moral defence on the fact that his mathematics was useless, and therefore clean. "I have never done anything 'useful.' No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world." "Real mathematics has no effects on war. No one has yet discovered any warlike purpose to be served by the theory of numbers." He wrote that in 1940, on the threshold of the century that turned his words inside out. The theory of numbers – primes, factorization, the very "gentle and clean" mathematics Hardy prized for being good for nothing – is today the foundation of public-key cryptography. It secures every banking transaction, every encrypted message, and yes, military and intelligence communications. There is no gotcha in this. Hardy chose those theorems for their beauty, indifferent to use, and their beauty turned out to be inseparable from a depth so real it eventually bit into the physical world. The usefulness followed the beauty; it did not precede it. That is almost a proof of the lecture's thesis: the beautiful, objective structure was there first, waiting, mind-independent, and the world later found out it had teeth.

If beauty is written into pure mathematics, is it also written into the physical world that is made of mathematics? Frank Wilczek, a Nobel laureate in physics, gave a whole book to a single question: "Does the world embody beautiful ideas?" – and at once re-poses it: "Is the world a work of art? … is it a successful work of art?" The answer in the book is not asserted but earned, page by page, and comes at last as "a resounding – Yes!" The most daring hopes of Pythagoras and Plato to find purity, order and harmony at the heart of creation, Wilczek says, have not been met by reality but far exceeded by it.

The root of it all is Pythagoras, and here the lecture rhymes with the beginning of the course itself. Our first lesson on the [Pythagoreans](/en/lecture/daredevils) already told how calculation replaced prophecy; Wilczek shows the same figure from the physics side. Harmony is number. Two like strings sound good together precisely when their lengths stand in the ratio of small whole numbers: the octave when the lengths are as 1 to 2, the fifth as 2 to 3, the fourth as 3 to 4. These musical rules, Wilczek says, "deserve to be considered the first quantitative laws of Nature ever discovered." So beauty – harmony – turned out to be a fact about number, and number turned out to be a fact about the world. When Pythagoras proved his theorem he is said to have offered a sacrifice of a hundred oxen; when his school discovered that √2 is no ratio of whole numbers, it was a scandal inside a sect that worshipped number, and the man who found that incommensurability, Hippasus, soon drowned at sea.

But the deeper tool of physics is symmetry, and it can be explained in three minutes. An object is symmetric, Wilczek says, if you can perform a transformation on it that might have changed it but in fact does not. Rotate a circle – every point has moved, and it is the same circle; a hexagon coincides with itself only every 60°, and a lopsided shape never does. Then comes the leap: equations can be symmetric too. And so you can run it backwards – begin from the symmetry you demand, and the equations turn out to be almost forced. Maxwell's equations, Wilczek writes, "are the circles defined by their own highly evolved rotations." And then Emmy Noether arrives – a mathematician denied a paid Göttingen chair for being a woman (Hilbert defended her by saying, "After all, we are a university, not a bathhouse"), and who fled Nazi Germany. Her theorem is "the single most profound result in all of physics": every symmetry of a physical law gives rise to a conserved quantity. Energy cannot be created from nothing precisely because the laws do not care what time it is.

And this pull toward beauty pays. "In beauty we trust, when making our theories," Wilczek says, and he keeps a box score in which prediction beat observation every time. Neptune: Uranus's orbit misbehaved, and Le Verrier, "trusting in the beauty of the theory," calculated an unseen planet and told astronomers where to look. Radio waves: Maxwell's equations foretold invisible colours of light, and Hertz produced and detected them. Antimatter: Dirac, "through a strange and beautiful equation," predicted antiparticles no one had yet seen. Hertz himself left a testimony that deserves a monument here: one cannot escape the feeling that these formulae are wiser than we are, wiser even than their discoverers, and that we get more out of them than was put in. That is the shortest way to say it: the beauty really was out there, and not in our heads.

The mathematician and the physicist show that beauty acts objectively; the philosopher has to say why, and in what exact sense. Roger Scruton, an analytic philosopher who asks the reader for no theological concessions, argues it through the front door of argument. Beauty, he writes, is "a real and universal value, one anchored in our rational nature." And here is the whole case for objectivity in one sentence, among his "platitudes" about beauty: "In describing an object as beautiful, I am describing it, not me." The judgement of taste is about the beautiful object, not the state of mind of the one who judges. It is a verdict, and one for which I can reasonably be asked to give a justification. Kant said that in such a judgement I am "a suitor for agreement," offering my verdict not as a private opinion but as a binding one for all rational beings. There is, Scruton concludes, "as much objectivity in our judgements of beauty as there is in our judgements of virtue and vice." The judgement is reasoned, though not deductive, as reasons in ethics are reasoned – they guide without compelling. The carpenter who has hung a door steps back and asks, "does that look right?" The question is real, and it cannot be answered in utilitarian terms, yet it is rational for all that.

The second witness reaches the same goal by another road. Dietrich von Hildebrand, a Christian phenomenologist and, as it happens, one of Europe's strongest anti-Nazi voices in the 1930s, builds everything on a single dividing line: what merely subjectively satisfies me has to be told apart from what is important in itself – with a middle case, what is objectively good for me, standing between them. A compliment matters exactly as much as it pleases me; take the pleasure away and it sinks back into grey neutrality. A generous act of forgiveness, by contrast, stands before us as important in itself, independent of any reaction of ours. Beauty belongs to the second kind.

His sharpest argument is the hedonist's self-refutation. Aristippus, who admits only degrees of pleasure, still warns against chasing our instincts "in a brutelike way" and calls reasonable moderation "the wiser attitude, the attitude we should have." But why should we be wise? If the merely subjectively satisfying is the standard, where did the obligation come from? He has quietly introduced another, objective norm: the value of wisdom. The relativist cannot state his own case without smuggling value back in through the side door. And language testifies against him: we say "this melody is beautiful," not "beautiful for me"; and when we do say "for me," we mean "in my opinion" – a claim about my judgement, which has discerned the beauty, and not that the beauty is a pleasant effect on me.

Here two witnesses converge. C. S. Lewis – whom the archive will treat in his own right elsewhere – noted the absurdity of the claim that, in calling a landscape sublime, we are really projecting an emotion onto it. For the emotion we feel in looking at the landscape is not itself sublime: we feel humility and reverence. The projected feeling has the wrong quality to be the thing we are naming. And a time-test of the same kind: I can say my enthusiasm was greater last year than today, but I cannot meaningfully say that the music itself was more beautiful a week ago. The response varies; the beauty does not.

There remains the darkest and deepest note. Hildebrand calls it "beauty of the second power." A melody is ontologically small – a sequence of notes; and the beauty it carries is comparable only to the beauty of high virtue or holiness. "There is a total discrepancy between the ontological dignity of these bearers of beauty and the beauty which appears in them." And this connection, he honestly warns, "is not in the least an intelligible connection; rather, it is a mystery." Here the classical spine the course already owns comes back. [Plotinus](/en/lecture/plotinus-ascent) told of the ascent from the beauty of bodies to the beauty of the soul, and Diotima of her ladder. This lecture does not re-teach them; it only adds a modern proof to an old one.

If beauty is objective, then ugliness is objective with it, and an honest lecture has to give the opponent his best cards first. The best opponent here is Umberto Eco, and his book On Ugliness stands openly on relativism. "Concepts of beauty and ugliness are relative to various historical periods or various cultures," he writes. Xenophanes of Colophon, whom Eco quotes approvingly: had the oxen and the lions hands, they would draw the gods as oxen and lions. Voltaire's toad: ask a toad what true beauty is, and he will describe his mate, "with her two fine round eyes protruding from her small head"; ask the devil, and he will describe horns, claws and a tail. And Fredric Brown's little tale "Sentinel": a soldier fifty thousand light-years from home, caked in mud, guns down the enemy – "cruel, repulsive, hideous creatures, horrible monsters"; and the last line turns the mirror, for they were disgusting creatures "with only two legs, two arms, two eyes, that sickening white skin and without scales." The monster is us. A strong card.

Now the break, and Eco makes it himself. He is a relativist who cannot stop documenting constants. His book set out to prove that ugliness is period-relative, and instead compiled the catalogue of its recurrence: hell, the devil, monsters, decay, the obscene – the same things, century after century. He notes the asymmetry of synonyms himself: the words for "beautiful" express a disinterested appreciation, while almost all the words for "ugly" carry disgust, if not violent repulsion, horror or fear. Language encodes ugliness as an involuntary recoil, not a taste. And Darwin, the relativists' most-cited authority, Eco is obliged to quote at the point where Darwin concedes that the movements expressing disgust "prevail throughout a large part of the world."

And at the centre is an image worth retelling. The diabolus in musica, the augmented fourth, C to F-sharp. The Middle Ages called it "the Devil in music" and banned it. It sounds in Bach, in Mozart's Don Giovanni, in Liszt, in West Side Story, in Hendrix's "Purple Haze," and on a Slayer album literally titled Diabolus in Musica. For eight hundred years it has meant the same tension every time. And in his final chapter Eco openly moves "to correct the relativist perspective": the diabolic interval came to be accepted over time not because it became pleasant, but precisely because of that whiff of sulphur it never lost. The relativist's own last page hands the lecture its thesis.

And here [Aquinas](/en/lecture/aquinas-house-of-faith) stands. Eco recalls his definition: beauty is the result not only of due proportion and clarity but of integrity – a thing must have all the characteristics its form has imposed on the material. So ugliness is a real defect of integrity: a diminishment, as when a limb is missing, or an excess, as with a third eye. It is not a neutral option; it is a defect of being. Augustine put it more sharply: evil and ugliness have no existence of their own, they are privatio, the loss of a prior good, a dark patch that gives the order of the cosmos its chiaroscuro. However you frame it, the conclusion is one: ugliness is real, and to call a thing ugly is not a whim.

Now for honesty, because this archive does not sell clean victories. Three things hold the thesis in check, and you should hold all three.

First: the objective core is a foundation, not a dictation of every taste. Dutton, whose blue landscape opened this lecture, in his chapter on "the contingency of aesthetic values" himself grants that our most cherished preferences are "'ours' only through accidents of when and where we were born." "Beauty is objective" does not mean "all taste is the same." There is a cross-cultural floor – landscape, skill, narrative, the features that recur in every documented society – and on it is built an enormous, genuine cultural variety. And even thinkers sympathetic to evolution disagree about how deep that floor goes. Steven Pinker, himself an adaptationist, holds that the arts are largely a by-product, "cheesecake for the mind": we enjoy strawberry cheesecake, but not because we evolved a taste for it. Dutton disputes him, and the dispute is unresolved. The Pleistocene left us stones and bones, not its songs.

Then: beauty can mislead even in physics, the place where it works best. Wilczek is scrupulous about the failures. Kepler's geometric Solar System and Plato's geometric atoms were "beautiful theories that, as descriptions of Nature, utterly failed." And Wilczek himself made a live bet – that a beautiful symmetry called supersymmetry would close the last gap, and that the Large Hadron Collider would find it "within the next five years." It did not. Beauty wrote a check that reality declined. He knew it might: "Beauty is precious. We must not give up too easily." His honesty is the point. Beauty is a reliable compass, and a fallible one at the same time. And Wilczek installs the caveat that keeps the whole thesis from swelling into a lie: "Many varieties of beauty are underrepresented in Nature's style… Science isn't everything, thank goodness." What is at stake is the beauty of law, not the beauty of everything under the sun.

And third: taste is not character. Hildebrand, of all people the most confident that beauty can be ranked, is also the one who insists that a trivial person may have exquisite taste and a noble soul a terrible one. Thérèse of Lisieux admired "the ghastly tombs in the cemetery in Milan." A good eye is not a good heart. Anyone tempted to read this lecture as a licence for aesthetic snobbery has misread it. Ranking is an act of reason, and there is no contempt in it: even the toad and the hippopotamus, Hildebrand says, carry an aesthetic value, and "the world would be poorer if they did not exist."

Now let us make the armour explicit. You carry a device that shows you a thousand images a day and, in its whole grammar, suggests that all of them are the same kind of thing – content, a stream, each as worthy and as worthless as the next, because "it's all subjective." Scruton saw the mechanism as early as 2009, before the phones had won. Kitsch, he wrote, "is not an excess of feeling but a deficiency… a heartless world, in which emotion is directed away from its proper target towards sugary stereotypes, permitting us to pay passing tribute to love and sorrow without the trouble of feeling them." That is the filtered selfie, the performative grief, the eternal #blessed. And the twin of kitsch is desecration. "Beauty makes a claim on us: it is a call to renounce our narcissism and look with reverence on the world" – and precisely because it makes that claim, there arises "a desire to spoil beauty." Desecration is "a defence against the sacred… in order to escape that judgement we destroy the thing that seems to accuse us."

Here is why it matters that beauty is real, and not a vibe. If beauty were only subjective, then the word "desecration" would carry no sense: you cannot profane what was never sacred, you cannot destroy a value where there was none. The cynicism of the feed is not neutral. It disarms you. It tells you there is nothing there to defend, and therefore nothing being taken.

Von Hildebrand earned his right to this point with his own life. When the Nazis dragged a noble Haydn melody into the anthem of a murdering state, that was a desecration – and the word has weight only if the beauty of that melody was really the melody's, and really beauty. Hildebrand said it aloud, and then fled the Gestapo for having said it. You are reading this in a country at war, where a neighbour that levels cities calls the ruin peace and styles itself the defender of a higher culture against a decadent West. The claim that beauty and ugliness are only opinions is exactly what such a power needs you to believe: that there is no difference between the cathedral and the bomb-crater except the one you happen to prefer.

So the armour is this. Learn to see. The mathematician sees that some proofs are beautiful, and agrees about it with every other mathematician; the physicist reads symmetry out of the world, and it foretells particles no one has yet seen; the philosopher shows that "this is beautiful" is a verdict you can be asked to justify, exactly like "this is just." To learn to see beauty is to gain knowledge, and not to indulge a preference. And the archive this course keeps carries the older witnesses too, whom you can go to yourself. Let the last word be Wilczek's, for it is the one thing that keeps this lecture from turning into its own kitsch. He ends a whole book on a single balance: the physical world embodies beauty; the physical world is home to squalor, suffering and strife; forget either aspect and you betray them both. Beauty is objective. So is the crater. To see the first clearly is exactly what gives you the standing to refuse the second. That is not consolation. It is a weapon.