“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.

“什么是美丽？”

在我作为一个公众知识分子期间，没有什么事比我在街上被一些绝望的行人拦住询问这个最基本的问题答案的频率更让我惊讶的了。几乎从来没有。那样的事几乎没有发生过。

这很奇怪，因为现在还有人关心美丽-事实上关心的人还很多-特别是在这里在南加州，如果我是第一个观察的人的话。昨天晚上在Sunset Marquis酒店的房间里，我拿了一本我以为是房间服务菜单的东西读了起来，并花了短暂的梦幻般的时间试图想象所谓仅售100美元的“穿着比基尼的后小腿”会什么什么味道。结果才知道我误拿了美容菜单，而花240美元就会有人到房间来为我的皮肤来一次“紧致美化”。

但当人们与从前一样多地关心着自身美丽时，似乎他们也不再尝试找出美丽到底什么。

然而事情不总是如此。对于古代希腊人来说，他们坚信美丽的解释和定义就如冬天白昼变短或是穿着衣服游泳后外袍会变重一样浅显易懂。确实，没有一个思想家比毕达哥拉斯这个发现了勾股定律的人得出了更早更令人印象深刻的结论。在音乐方面，毕达哥拉斯指出音阶的音符并不是任意的，而是反映了当一根琵琶弦-或是任何弦-其长度被精确细分成2：1或是3：2时发出的音调。在建筑和设计方面，他同样指出了人们认为最赏心悦目的形状是那些边线被分割成所谓的黄金比例的。

黄金比例简单说来就是两条线段a和b之间（a+b）/a等于a/b的比例关系，换句话说，整条线段与其中一部分的比率与两个部分的比率是相同的。这听上去与代数形式（a/b=(a+b)/a）不太一样，与小数形式（1：1.61814）就更不一样了。但画一个矩形-或造一个帕台农神庙-边为a和b，它的完美和谐的直角就会吸引你的注意。假如你被困于一个有着一个特殊矩形的孤岛上，那就是你要与之伴随的。显然它就是当上帝意识到他需要另一个四边直角的图形来补足他初期的杰作正方形时想到的第一个矩形。

对于柏拉图，这个重800磅的古希腊智者来说，将美丽包括在他的思想中是相当好的：那些先验的无形的理论基础，而现实不过是这些理论的模糊的、摇摇欲坠的模仿罢了。美丽不在旁观者的眼中。相反，借用柏拉图传奇般的洞穴比喻，旁观者对美丽转过身去，只看到了现实肮脏的墙壁上的闪烁的影子。

简而言之，美丽的科学由两个古代思想家创造，美丽的科学以及其他所有的事最终都落在他们的基础上。在科学历史学家中，这就是所谓的快乐而幸运的开始。

所以，想象一下整形外科医生史提芬·马夸特博士的惊呀吧，他于20世纪末工作于南加州，他研究了自毕达哥拉斯以来的美丽科学的进程并发现取得的进展很少。

根据洛杉矶整形外科医生所说，马夸特（现已不再做临床手术）是那种严肃而廉价的整形医师。他的病人不是那些标准的山谷女孩或是那些期望医生在动手术刀或到空中酒廊喝一杯之前就能轻松地增加她们的魅力离婚妇女。他的病人是那些身有畸形的人。他们是那些出生就没有下巴或是那些被高速游艇的涡轮毁了脸的人。他们到他那里就医不是为了美丽或是成为超级巨星，他们只是希望有一天他们能够咽下食物。

然而这里却存在着一个矛盾。在他的病人的脑海里美学上的尽善尽美是排在最后的，这一事实就意味着马夸特医生必须始终想着这一点，要比那些在比弗利山上弄着胶原质的医生想的多得多。人们来到他这里不是想在下巴上弄个褶子，他们来是想要一个下巴，他们通常指望马夸特医生来决定他们的下巴看上去会是什么样子的。

事实比听上去的难得多。马夸特医生通常会丢开手术想想他是否整好了病人的下巴，而只有到几周后，当拆除绷带的时候，他才会发现手术在美学水平上并不成功。

马夸特医生认为解决方法是提高相对精确度。但他发现文献资料里几乎没什么有用的。在毕达哥拉斯的黄金比例和柏拉图的理论之后，直到达芬奇之前美丽的数学一直处于毫无进展的状态。达芬奇的维特鲁威人，这个著名的草图画了一个赤身裸体的伸展的男子，他手脚触摸着一个正方形和一个圆，显示了理想的人体比例惊人的巧合（臂展=身高；身高=手长的10倍），然而这幅画却为提及脸。

所以马夸特医生独自研究着。他收集了那些世人公认的漂亮的脸孔的照片并开始测量他们的尺寸。于是一些独特的令人兴奋的结论浮现出来：黄金比例。美丽的人的嘴的宽度是他们的鼻子的1.618倍。随着他的数据组的扩大，马夸特医生发现完美的脸确实有着黄金比例。即使是鼻子和嘴形成的三角也是一个完美而精确的金三角。

马夸特走到公众面前，用他揭示的黄金面具震惊了世人，假如他是对的，那么他的这个易于理解的富丽堂皇的名字无疑将是完美脸孔的设计图，而你们就更能理解我这个穿越洛杉矶来拜访马夸特医生，看看他研究进展的记者了。

我确实这样做了，并且我还要说我当我离开马夸特医生位于亨廷顿海滩舒适的家的时候我还未全然信服。开着我租来的福特车回到洛杉矶的时候，我不由自主的想这个医生太沉迷于这整个黄金面具的事-可能太过了。

社会和文化可能会说我们世俗，但那仅是因为社会还没有碰到将我们的脸与黄金面具相比的麻烦。

特别是虹膜让我陷入了思考。马夸特医生认为黄金比例在虹膜里能被检测出来，这个瞳孔中有色的部分。画10个金三角，把它们的顶点挨着排好，然后你就得出一个金十边形，与瞳孔中的虹膜完美地一致，十边形的最早点正好在眼眶。但是当然正方形也可以假如你算好它的大小的话。等边三角形也可以，牛的眼睛亦然。

这样当他通过他的网站（beautyanalysis.com）上的图片向我解释的时候，有些情况黄金面具就不再像马夸特医生所说的那样符合想象中的漂亮脸蛋了。而有些情况下黄金面具似乎比想象的更符合丑陋的脸。马夸特医生承认了这最后一点，并说明这证明了人类已经进化到了这种程度-万岁！-我们中的大多数人，客观说来事实上都很吸引人。社会和文化可能会说我们世俗，但那仅是因为社会还没有碰到将我们的脸与黄金面具相比的麻烦，这些黄金面具是由研究社会认为美丽的脸孔而得出的、、、对我来说他们使得所有的细节都不再重要了。

到了之后我才改变了想法-为了美丽起见，我最好还是描述一下这个渐进的，不，全然无法形容的过程，就当是当夕阳从我的太阳眼镜里落下去时，圣塔蒙尼卡码头上我的顿悟。

所以如果马夸特医生研究过头了呢？我突然明白。即便仅仅马夸特医生的声明是正确的，即最讨人喜欢的脸其嘴巴与之上的鼻子之间有着这种古来而神秘的黄金比例的关系，这也不会全无意义，而是有着很多意义。并且如果他曾在华盛顿邮报上所说的也是对的话，即超级名模微笑时前面两颗牙齿的宽度是没课牙齿高度的 1.618倍，那么他就确实得出了一些结论。

也许柏拉图也是对的：世界上没有什么是完美的，无论是一张桌子，一张脸还是一个加州科学家的一生的研究工作--即使是对美丽的一点点的数学研究也是有意义的。正如约翰·济慈在他快要不如死亡时曾经所说，“美就是真，真就是美-这就是我们在人间知道和应该知道的一切。”

其他的学者可以辩驳济慈在他24岁将死的时候，在研究任何事都是诗的媒介的时候，当他写下这些话时，他是否真正知道他在说什么。但是我认为，或许当我凝视着由这南加州看似很深的浅滩看到它看似很浅的深度时，我最终明白了。