Are you as hot as you think you are?

Megan McArdle of The Atlantic says that You're not as hot as you think you are. (From Marginal Revolution.)

What they don't say is that you're probably hotter than you look in photos.

McArdle writes:

A cognitive scientist at the University of Chicago explained why to me last winter. When we look at ourselves in the mirror, in any given session we tend to anchor on the time slice image that makes us look our best. That, we decide, is the "real" us.

Photographs, however, are a random sample of the various arrangements of light, angle, and facial expression that we can be found in. The median photograph of you is probably the best approximation of your physical attractiveness. But that wars with your self image, which is anchored on other, better combinations.

I don't know if I'd call photographs a "random sample". I don't like being photographed, so I probably look less happy in photographs than I do on average, and happiness makes you look good.

But what's more, evolutionarily we're not used to looking at people at a single moment in time. At the time when our cognitive machinery evolved, there were no still photographs. (It's the reverse of the semi-early Internet, where there were still photographs but no video.) Even a person who you meet for a second will get more information about how you look than they would from a photograph. And perhaps photos look repulsive because they're not moving, and for a long time anybody who wasn't moving was dead.

McArdle also writes:

Which, by the way, is probably the best gauge of how attractive you are; how attractive are the hottest people who want to go out with you? They're probably only slightly more attractive than you are.

This is tempting, but basically impossible. I agree that it's true, among heterosexuals, and in percentile terms -- a man who's more attractive than 60% of men is probably most likely to be with a woman who's more attractive than 60% of women. (I'm assuming that there are an equal number of heterosexual men and heterosexual women.) But we don't think in these terms. Do you have any idea what these hypothetical 60th-percentile people look like? Furthermore, in looking at who people actually are in relationships with a lot more things than just their appearance come into play.

The only thing to do is the following: say you're a man. Then think "what if I were gay? Then who is the most attractive man who would be willing to go out with me?" That might work... but it tells you how hot you are as a gay man, and gay men have different standards for attractiveness than straight women. (Similarly for women; straight men and lesbians have different standards.) For the sake of simplicity I have assumed in this paragraph that there are exactly two genders and everyone belongs to exactly one of them.

Perhaps you could also go to hotornot.com (wow, I haven't looked at that site in years!) -- where people post photographs of themselves and other people rate them on a scale of 1 to 10 -- but we don't know how the scores are distributed there, and more importantly these are photographs.

If you buy the "best time-slice" theory, this also explains why you might find your friends more attractive than the average person. (I know I do.) I spend more time with my friends than with a random person I see on the street (if I didn't, they wouldn't be my friends) and I probably anchor on to their best time-slices. The times when they looked good are stuck in my brain even when they don't actually look good. If you figure that how good one looks at any given moment is normally distributed around their "true" attractiveness, then the "perceived attractiveness" -- the maximum attractiveness I've ever seen them at -- should grow without bound. After I've seen the person n times, the most attractive they've ever been is around the 100n/(n+1) percentile. This sounds ridiculous; the quantitative truth of how we determine someone's attractiveness is probably more like averaging the top √k or so of the k timeslices we have of a person. You still get the "attractiveness growing without bound" problem, but it takes a lot longer to come. (It's probably a normal distribution, because attractiveness is a sum of many different things, so I wave my hands and say the magic words "Central Limit Theorem", but that doesn't matter.) Also, your friends probably share the same cultural affinities that you do, meaning that what they do to make themselves seem attractive is probably similar to what you do to make yourself seem attractive. To avoid cognitive dissonance, then, you have to assume they're hot in order to be hot yourself.

Beauty is in the eye of the beholder

Ben Goldacre, writing in Bad Science, tells us the story of how he was contacted by a PR firm which wanted him to concoct some equations that would "prove" that certain celebrities had sexier walks than certain other celebrities, as part of a promotion for Veet hair removal cream. I am not making this up. It's an extended version of his column in the Guardian.

The press release seems to have beeen reproduced by about a zillion British newspapers, usually in a shortened version; the longest version I could find is here, and I'll be quoting from it.

JESSICA Alba, the film actress, has the ultimate sexy strut, according to a team of UK mathematicians. Beauty is no longer in the eye of the beholder - it can now be worked out using a simple mathematical formula.

Bullshit! And this isn't just me being bitter that I might not fit some social standard of beauty. It's me being bitter that mathematics is being "used" in this way. In Goldacre's column, we learn that there was no team. Richard Weber at Cambridge is the mathematician who's mentioned there, but only after Goldacre was contacted -- and Goldacre as far as I can tell is a medical doctor. (By "there" I mean Goldacre's blog post; I can't find a version of the press release that mentions Weber.)

The academics found that it is the ratio between hips and waist that puts the sway into a woman's walk - and the nearer that ratio is to 0.7, the better.

No they didn't! This seems like the stuff you see out there every so often about the Golden Ratio making things more beautiful -- and in fact that ratio's been used to sell pants! -- where there's some "magic number". There's at least some justification for the 0.7 number, though, in that Real Scientists have done studies, although the preferred ratio varies by culture. And it never seems to be given to more than one decimal place, which suggests that a few inches don't matter. Apparently Weber made a more nuanced comment that got cut down to this.

This ratio provides the body with the right torso strength to produce a more angular swing and bounce to the hips during the walking motion.

Furthermore, the waist-to-hip ratio might actually be important for physical attractiveness, but nobody said that had anything to do with the walk. I don't know much about biomechanics, though. But it looks like the causality just isn't there.

Oh, and they screwed the survey up so badly that it doesn't even mention anything that hair removal cream could actually do. You'd expect a study by a hair removal cream company to say that having smooth, shiny, hairless [insert body part here] was an important part of beauty.

Fortunately, they're just using this to sell hair removal cream. Recent studies have also shown that studies which are funded by pharmaceutical companies are far more likely to say that drugs do something goodthan studies which are not funded by pharmaceutical companies; that sort of hijacking of the scientific apparatus is a lot more insidious, as people could actually die.

I'm not saying that beauty can't be encapsulated in some sort of formula. But it'll be a lot more complicated than this one. (In fact, it might not be a "formula" at all, in the sense that you put in numbers which describe the person and get out a numerical rating of their beauty; much more feasible would be a recommendation system like that on Netflix or Amazon. As I understand it, those systems work by recommending books or movies to you that people who have bought the same books or rented the same movies as you also liked.)

And I'm skeptical of any formula that says that the same people will seem beautiful to everyone, because that's simply not true. I think someone could come up for a formula that will tell them who I am likely to find beautiful -- there are definitely patterns. But my tastes are not the same as yours. And don't try to tell me they should be.

P. S. I moved into my apartment a year ago today. As I sit here, I look out my kitchen window and see a truck from the movers I used. This is probably not a coincidence, though, as September 1 is kind of a big moving day in my neighborhood.