“What is Beauty?”

Very little has surprised me more, in my years as a public intellectual, than how often I get collared on the street by some desperate pedestrian demanding an answer to this most fundamental question. Almost never. It hardly ever happens.

Which is odd, because people still care about Beauty—quite a lot in fact—especially here in Southern California, if I can be the first to make that observation. Last night in my room at the Sunset Marquis I reached out for what I assumed was the room-service menu and passed a few fleeting surreal moments trying to imagine what “Upper Leg with Bikini” might taste like, for a mere $100. It turned out that I had grabbed the Beauty Menu by mistake and that for $240 someone was prepared to come to my room and give my skin a “Firming Renovateur.”

But while people may care about being beautiful as much as they ever did, it seems they have largely stopped trying to figure out what Beauty actually is.

It wasn’t always thus. The ancient Greeks, for their part, were convinced that an explanation of, and definition for, Beauty was as concrete and discoverable as the answer to why the days got shorter in winter or why your toga weighed more after you’d gone swimming in it. Indeed, no less a thinker than Pythagoras, he of hypotenuse fame, logged some impressive early results. In music, Pythagoras showed that the notes of the musical scale were not arbitrary but reflected the tones produced by a lute string—or any string—when its length was subdivided precisely into such simple ratios as 2:1 or 3:2. In architecture and design, similarly, he managed to show that the shapes people found most pleasing were those whose sides were related by the so-called golden ratio.

The golden ratio, briefly, is the proportional relationship between two lines a and b such that (a + b) is to a as a is to b; in other words, the ratio between the whole and one of its parts is the same as the ratio between its two parts. This doesn’t sound like much in algebra form (a/b = (a + b)/a) and still less when expressed as a decimal (1:1.61814). But draw a rectangle—or build a Parthenon—with sides of a and b, and the sheer cosmic rightness of the thing leaps out at you. If you were to be stranded on a desert island with one particular rectangle, that’s the one you’d go with. Palpably, it’s the first rectangle that occurred to God when he realized he needed another four-sided, right-angled shape to complement his juvenile masterpiece, the square.

This was good enough for Plato, the 800-pound gorilla of ancient Greek intellectual life, to include Beauty as one of his famous forms: those transcendent, invisible archetypes of which this reality is nothing but a set of blurry ramshackle imitations. Beauty was not in the eye of the beholder. On the contrary, to borrow Plato’s legendary cave metaphor, the beholder had his back to Beauty, able to see only its flickering shadows on the grimy cave wall of reality.

In short, the Science of Beauty was inaugurated by the two classical thinkers upon whose shoulders the science of pretty much everything else would eventually come to rest. Among historians of science, that’s what is known as a rollicking and auspicious start.

Imagine the surprise, therefore, of one Dr. Stephen Marquardt, a plastic surgeon working in Southern California at the tail end of the 20th century, who checked in on the progress of the Science of Beauty since Pythagoras and found that very little had been made.

As Los Angeles plastic surgeons go, Marquardt (now retired from clinical practice) was the serious, unsleazy sort. His patients weren’t the standard Valley girls and divorcées whose breasts a doctor could breezily augment to the tinkle of a Japanese water feature before checking his teeth in the shine of his scalpel and heading off for cocktails at Skybar. His patients were deformed. They were people who were born without chins or who had taken a speedboat turbine to the face. And they came to him with dreams not of gorgeousness or superstardom but of one day being able to ingest food orally.

Yet herein lay a paradox. The fact that aesthetic perfection was the last thing on his patients’ minds meant that Marquardt had to think about it all the time, far more than if he’d been just another surgeon slinging collagen up in Beverly Hills. People didn’t come to him wanting a cleft in their chin; they came to him wanting a chin, and they generally left it up to Marquardt to decide what the thing was actually going to look like.

Which was harder than it sounds. Often Marquardt would walk out of surgery thinking he’d gotten someone’s chin exactly right, only to find weeks later, when the bandages came off, that the thing just didn’t work on an aesthetic level.

The solution, Marquardt decided, was to ramp up the degree of proportional precision. But he could find nothing useful in the literature. After Pythagoras with his golden ratio and Plato with his forms, the mathematics of Beauty went largely untouched until Leonardo da Vinci. Da Vinci’s Vitruvian Man, that famous sepia sketch of a nude, spread-eagled person touching a square and a circle with his extremities, asserted the eerie proportional coincidences of the ideal human form (arm span = height; height = hand length x 10) but said nothing about the face.

So Marquardt went it alone. He collected photographs of faces the world deemed beautiful and began measuring their dimensions. Whereupon something peculiar and thrilling presented itself: the golden ratio. Beautiful people’s mouths were 1.618 times wider than their noses, it seemed, their noses 1.618 times wider than the tip of their noses. As his data set expanded, Marquardt found indeed that the perfect face was lousy with golden ratios. Even the triangle formed by the nose and the mouth was a perfect acute golden triangle.

Marquardt went public, making a splash with his unveiling of the Golden Mask, his understandably grandiose name for what was, if he was right, nothing less than a blueprint for the perfect face—and more than enough reason, you would think, for this reporter, passing through Los Angeles, to check in with Marquardt to see where his work has gone from there.

So I did, and I have to say I left Marquardt’s comfortable home in Huntington Beach not entirely convinced. Gunning my rented Ford Escape back to Los Angeles, I couldn’t help but think that the good doctor was overreaching—perhaps quite a lot—with this whole Golden Mask thing.

society and culture may call us ugly, but that’s only because society hasn’t yet gone to the trouble of comparing our faces to the golden mask.

The iris, in particular, gave me pause. Marquardt contends that the golden ratio can be detected in the iris, the colored part of the eye. Take 10 golden triangles, arrange them with their sharp points touching, and you have a golden decagon, fitting perfectly within the iris of the eye, vertices neatly touching the rim. But surely, so would a square, if you sized it right. Or an equilateral triangle. Or a bull’s-eye.

Then there was the way the Mask did not quite fit supposedly beautiful faces as well as Marquardt told me it did, while he helpfully talked me through the images on his Web site (beautyanalysis.com). As well as the way it seemed to fit supposedly ugly faces much better than you’d expect. Marquardt conceded this last point and hailed it as proof that the human race has evolved to the point that—hooray!—most of us, in objective terms, are actually rather attractive. Society and culture may call us ugly, but that’s only because society hasn’t yet gone to the trouble of comparing our faces to the Golden Mask, which was derived by studying faces that society deems beautiful . . . which would seem to me to invalidate the whole ball of wax.

It was only later that I changed my mind—a gradual, nay, ineffable process I should probably describe, for the sake of Beauty, as an epiphany at the end of a pier in Santa Monica while watching the sun go down through my Ray-Bans.

So what if Marquardt’s overreaching? I suddenly realized. If he’s right only in his assertion that the most pleasing faces have mouths that relate to the noses above them by the ancient and mysterious golden ratio, that’s not nothing. That’s a lot. And if he’s also right, as he once told The Washington Post, that the width of the front two teeth in a supermodel’s smile is 1.618 times the height of each tooth, then he is actually really onto something.

Maybe Plato was right as well: that nothing in this world is perfect, be it a table, a face, or the life’s work of a California scientist, until you tune out the noise and break through to what is true—and even a whiff of mathematical insight into Beauty gets the job done. For as John Keats once said, frantically overachieving en route to his glamorous early grave, “Beauty is truth, truth beauty—that is all ye know on earth, and all ye need to know.”

Other scholars can debate whether Keats, at 24, dying, working in the anything-goes medium of poetry, actually knew what he was talking about when he wrote those words. But I think perhaps that I, peering through the faux-deep shallows of Southern California to its faux-shallow depths, finally do.

“什么是美麗？”

在我作為一個公眾知識分子期間，沒有什么事比我在街上被一些絕望的行人攔住詢問這個最基本的問題答案的頻率更讓我驚訝的了。幾乎從來沒有。那樣的事幾乎沒有發(fā)生過。

這很奇怪，因為現(xiàn)在還有人關(guān)心美麗-事實上關(guān)心的人還很多-特別是在這里在南加州，如果我是第一個觀察的人的話。昨天晚上在Sunset Marquis酒店的房間里，我拿了一本我以為是房間服務(wù)菜單的東西讀了起來，并花了短暫的夢幻般的時間試圖想象所謂僅售100美元的“穿著比基尼的后小腿”會什么什么味道。結(jié)果才知道我誤拿了美容菜單，而花240美元就會有人到房間來為我的皮膚來一次“緊致美化”。

但當(dāng)人們與從前一樣多地關(guān)心著自身美麗時，似乎他們也不再嘗試找出美麗到底什么。

然而事情不總是如此。對于古代希臘人來說，他們堅信美麗的解釋和定義就如冬天白晝變短或是穿著衣服游泳后外袍會變重一樣淺顯易懂。確實，沒有一個思想家比畢達哥拉斯這個發(fā)現(xiàn)了勾股定律的人得出了更早更令人印象深刻的結(jié)論。在音樂方面，畢達哥拉斯指出音階的音符并不是任意的，而是反映了當(dāng)一根琵琶弦-或是任何弦-其長度被精確細(xì)分成2：1或是3：2時發(fā)出的音調(diào)。在建筑和設(shè)計方面，他同樣指出了人們認(rèn)為最賞心悅目的形狀是那些邊線被分割成所謂的黃金比例的。

黃金比例簡單說來就是兩條線段a和b之間（a+b）/a等于a/b的比例關(guān)系，換句話說，整條線段與其中一部分的比率與兩個部分的比率是相同的。這聽上去與代數(shù)形式（a/b=(a+b)/a）不太一樣，與小數(shù)形式（1：1.61814）就更不一樣了。但畫一個矩形-或造一個帕臺農(nóng)神廟-邊為a和b，它的完美和諧的直角就會吸引你的注意。假如你被困于一個有著一個特殊矩形的孤島上，那就是你要與之伴隨的。顯然它就是當(dāng)上帝意識到他需要另一個四邊直角的圖形來補足他初期的杰作正方形時想到的第一個矩形。

對于柏拉圖，這個重800磅的古希臘智者來說，將美麗包括在他的思想中是相當(dāng)好的：那些先驗的無形的理論基礎(chǔ)，而現(xiàn)實不過是這些理論的模糊的、搖搖欲墜的模仿罷了。美麗不在旁觀者的眼中。相反，借用柏拉圖傳奇般的洞穴比喻，旁觀者對美麗轉(zhuǎn)過身去，只看到了現(xiàn)實骯臟的墻壁上的閃爍的影子。

簡而言之，美麗的科學(xué)由兩個古代思想家創(chuàng)造，美麗的科學(xué)以及其他所有的事最終都落在他們的基礎(chǔ)上。在科學(xué)歷史學(xué)家中，這就是所謂的快樂而幸運的開始。

所以，想象一下整形外科醫(yī)生史提芬·馬夸特博士的驚呀吧，他于20世紀(jì)末工作于南加州，他研究了自畢達哥拉斯以來的美麗科學(xué)的進程并發(fā)現(xiàn)取得的進展很少。

根據(jù)洛杉磯整形外科醫(yī)生所說，馬夸特（現(xiàn)已不再做臨床手術(shù)）是那種嚴(yán)肅而廉價的整形醫(yī)師。他的病人不是那些標(biāo)準(zhǔn)的山谷女孩或是那些期望醫(yī)生在動手術(shù)刀或到空中酒廊喝一杯之前就能輕松地增加她們的魅力離婚婦女。他的病人是那些身有畸形的人。他們是那些出生就沒有下巴或是那些被高速游艇的渦輪毀了臉的人。他們到他那里就醫(yī)不是為了美麗或是成為超級巨星，他們只是希望有一天他們能夠咽下食物。

然而這里卻存在著一個矛盾。在他的病人的腦海里美學(xué)上的盡善盡美是排在最后的，這一事實就意味著馬夸特醫(yī)生必須始終想著這一點，要比那些在比弗利山上弄著膠原質(zhì)的醫(yī)生想的多得多。人們來到他這里不是想在下巴上弄個褶子，他們來是想要一個下巴，他們通常指望馬夸特醫(yī)生來決定他們的下巴看上去會是什么樣子的。

事實比聽上去的難得多。馬夸特醫(yī)生通常會丟開手術(shù)想想他是否整好了病人的下巴，而只有到幾周后，當(dāng)拆除繃帶的時候，他才會發(fā)現(xiàn)手術(shù)在美學(xué)水平上并不成功。

馬夸特醫(yī)生認(rèn)為解決方法是提高相對精確度。但他發(fā)現(xiàn)文獻資料里幾乎沒什么有用的。在畢達哥拉斯的黃金比例和柏拉圖的理論之后，直到達芬奇之前美麗的數(shù)學(xué)一直處于毫無進展的狀態(tài)。達芬奇的維特魯威人，這個著名的草圖畫了一個赤身裸體的伸展的男子，他手腳觸摸著一個正方形和一個圓，顯示了理想的人體比例驚人的巧合（臂展=身高；身高=手長的10倍），然而這幅畫卻為提及臉。

所以馬夸特醫(yī)生獨自研究著。他收集了那些世人公認(rèn)的漂亮的臉孔的照片并開始測量他們的尺寸。于是一些獨特的令人興奮的結(jié)論浮現(xiàn)出來：黃金比例。美麗的人的嘴的寬度是他們的鼻子的1.618倍。隨著他的數(shù)據(jù)組的擴大，馬夸特醫(yī)生發(fā)現(xiàn)完美的臉確實有著黃金比例。即使是鼻子和嘴形成的三角也是一個完美而精確的金三角。

馬夸特走到公眾面前，用他揭示的黃金面具震驚了世人，假如他是對的，那么他的這個易于理解的富麗堂皇的名字無疑將是完美臉孔的設(shè)計圖，而你們就更能理解我這個穿越洛杉磯來拜訪馬夸特醫(yī)生，看看他研究進展的記者了。

我確實這樣做了，并且我還要說我當(dāng)我離開馬夸特醫(yī)生位于亨廷頓海灘舒適的家的時候我還未全然信服。開著我租來的福特車回到洛杉磯的時候，我不由自主的想這個醫(yī)生太沉迷于這整個黃金面具的事-可能太過了。

社會和文化可能會說我們世俗，但那僅是因為社會還沒有碰到將我們的臉與黃金面具相比的麻煩。

特別是虹膜讓我陷入了思考。馬夸特醫(yī)生認(rèn)為黃金比例在虹膜里能被檢測出來，這個瞳孔中有色的部分。畫10個金三角，把它們的頂點挨著排好，然后你就得出一個金十邊形，與瞳孔中的虹膜完美地一致，十邊形的最早點正好在眼眶。但是當(dāng)然正方形也可以假如你算好它的大小的話。等邊三角形也可以，牛的眼睛亦然。

這樣當(dāng)他通過他的網(wǎng)站（beautyanalysis.com）上的圖片向我解釋的時候，有些情況黃金面具就不再像馬夸特醫(yī)生所說的那樣符合想象中的漂亮臉蛋了。而有些情況下黃金面具似乎比想象的更符合丑陋的臉。馬夸特醫(yī)生承認(rèn)了這最后一點，并說明這證明了人類已經(jīng)進化到了這種程度-萬歲！-我們中的大多數(shù)人，客觀說來事實上都很吸引人。社會和文化可能會說我們世俗，但那僅是因為社會還沒有碰到將我們的臉與黃金面具相比的麻煩，這些黃金面具是由研究社會認(rèn)為美麗的臉孔而得出的、、、對我來說他們使得所有的細(xì)節(jié)都不再重要了。

到了之后我才改變了想法-為了美麗起見，我最好還是描述一下這個漸進的，不，全然無法形容的過程，就當(dāng)是當(dāng)夕陽從我的太陽眼鏡里落下去時，圣塔蒙尼卡碼頭上我的頓悟。

所以如果馬夸特醫(yī)生研究過頭了呢？我突然明白。即便僅僅馬夸特醫(yī)生的聲明是正確的，即最討人喜歡的臉其嘴巴與之上的鼻子之間有著這種古來而神秘的黃金比例的關(guān)系，這也不會全無意義，而是有著很多意義。并且如果他曾在華盛頓郵報上所說的也是對的話，即超級名模微笑時前面兩顆牙齒的寬度是沒課牙齒高度的 1.618倍，那么他就確實得出了一些結(jié)論。

也許柏拉圖也是對的：世界上沒有什么是完美的，無論是一張桌子，一張臉還是一個加州科學(xué)家的一生的研究工作--即使是對美麗的一點點的數(shù)學(xué)研究也是有意義的。正如約翰·濟慈在他快要不如死亡時曾經(jīng)所說，“美就是真，真就是美-這就是我們在人間知道和應(yīng)該知道的一切。”

其他的學(xué)者可以辯駁濟慈在他24歲將死的時候，在研究任何事都是詩的媒介的時候，當(dāng)他寫下這些話時，他是否真正知道他在說什么。但是我認(rèn)為，或許當(dāng)我凝視著由這南加州看似很深的淺灘看到它看似很淺的深度時，我最終明白了。