The Mathematics of Beauty

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 Here in L.A., everyone thinks they understand the mathematics of beauty. You know, Clothes. Faces. Legs. Our eyes expertly rove an afternoon mall or a midnight bar, evaluating the smooth, the tight...or at least, the fashionable.

Tonight the Urban Man finds himself standing in line outside a dance club just off Hollywood Boulevard. It's about 11:30, and the line is composed mostly of women 22 to 26, all trying hard to look beautiful. Strangely, they have each decided to wear the same tiny black dress, riding high above the hip, along with loose hair, dangerously high heels, and dark eye makeup.

All the women are pretty...I mean, they aren't getting in if they're not pretty...but tonight their efforts seem, well, too obvious to be called "beauty." And for a moment, I consider getting the attention of everyone in line so I can explain the aesthetic theories of leading Swiss mathematician, Jürgen Schmidhuber.

I mean, what better way to kill the time?

"What is beauty," asks this thinker. Certainly it implies regularity and predictability. Even Darwin observed that if you merge a lot of human faces together photographically, so that you get an average of all faces, the result seems...pretty. It's the call of the herd, and I see that surely, in their attempt to look exactly alike—not to mention sexually available—the women in line have accomplished this minimum task.

But Schmidhuber says that true beauty requires an additional element he mathematically defines as "interestingness."* "Interestingness" means a set of data which does not immediately explain itself, but which is nevertheless data we think we could compress into a clearer and hence more beautiful statement if only we stared long enough: you know, the way we stare at fine art, trying to figure it out. His algorithm quantifies the way the eye makes a number of saccades, that is, rapid motions across an object — collecting info for a fresh understanding of the world.

And here I pause to look at a giggling woman adjusting her spaghetti straps, and I think...no.

According to Schmidhuber's algorithm, the interestingness of data D to Observer O over time equals the potential compression of new data multiplied by beauty, divided by the change in time. In other words, quote: "A beautiful thing is interesting...only as long as the algorithmic regularity that makes it simple has not yet been fully assimilated by the adaptive observer."*

When you look at a truly beautiful woman, you can understand how this process might never cease. Consider, like, Cate Blanchett. Your eye makes its many saccades, but your perception is a hyperbolic curve which approaches, but never quite reaches an asymptotic value. Something's there you can never quite grasp.

And surely, the same is true of mere mortals. I mean, relationships often end when one person believes they have grasped the totality of the other person; when they decide that person, no matter how symmetrically arranged, can be too easily paraphrased. Sometimes it happens in one night.

Now a nearby couple begins to argue. Because she's so tall, she looks especially absurd in her tiny black dress. He wears worn jeans with shirt-tails hanging out. Her clothing says, "I am easy to understand." His says, "I am unconcerned."

Aloud, the woman says, "Why should I do that?"

Aloud, the man replies, "Because you're not the only woman on the streets tonight."

At which, of course, she storms off as fast as anyone wearing stiletto heels can storm. Which is not, actually, very fast.

Me, I laugh and I turn to look with new appreciation at my...wife, who has, yes, been standing next to me in line this whole time. She is no doubt unaware that I have been looking at all these other women; and once again, I see in her face the many complex data points of a beauty I know I will never fully explore. An algorithm kicks in, and the Urban Man says, "Let's get the hell out of here."

Copyright © 2009 Marc Porter Zasada. All rights reserved.

*Schmidhuber. Simple Algorithmic Theory of Subjective Beauty, Novelty, Surprise, Interestingness, Attention, Curiosity, Creativity, Art, Science, Music, Jokes. Journal of SICE, 48(1):21-32, 2009. PDF.

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