My Faults My Own

…willing to sacrifice something we don't have

for something we won't have, so somebody will someday.

(Not really) About Math

This post brought to you by a lovely dinner conversation with a non-biological aunt and a dear friend who I definitely don't see enough, given that we've known each other for almost precisely our entire lives.

note: this is not the post on vegetarianism that I promised. I got distracted in the middle of drafting that one. It's sort of complicated, and I haven't quite yet figured out how I want to put what I want to say, but I promise that I'll get back to it, and to China, eventually. In the mean time, just enjoy this ramble on a very important thing.

Girls are bad at math. It's a simple matter of statistics. Statistically sound double-blind studies done in the US in the last twenty years clearly indicates that girls perform significantly worse on tasks related to math and logical-reasoning than their male counterparts, controlling for, well, everything. The evidence is embarassingly conclusive. Even the former president of Harvard University is on record saying that, biologically speaking, women suffer from a lack of "intrinsic aptitude".

Unless you test children in any country besides the United States, where girls match -- and outperform -- boys in math, sciences, and technology. (No, I don't have links on hand. As always, I'm convinced that I've read most of these facts somewhere. Just roll with me here.)

Or if you test US students before middle school (oh, that regrettable, awful hell-masquerading-as-education...), where math ability is not at all linked to sex. Or in single-sex schools, where, controlling for private-school weirdness, students at all-female schools tend to outperform those at all-male schools. I haven't seen a serious study of home-schooled students, but I'd expect it, too, to demonstrate a significantly lower (or absent?) disparity.

The popular conclusion drawn is that the disparity in mathematical ability is that, sometime in US middle schools, girls are societally pressured away from mathematical fields. They begin to fall behind in the sixth and seventh grades because they don't want to be 'weird' or 'unpopular', and by the time they graduate high school, the young women bound for post-secondary education are overwhelmingly humanities-focused (except for the holdouts that are still studying biology -- at rates still slightly higher than young men. If we're serious about closing the gender gap in the sciences, we need to rethink the messages we -- as a society -- send girls in their middle school years, because something is driving them away in droves.

Well, maybe. That's still not quite right, either. The societal-pressures narrative makes a lot of sense, but doesn't quite explain why more-detailed studies find that more boys than girls are really bad at math. One more time: more boys than girls are really good at math, and more boys than girls are really bad. Huh? (caveat: in the US, after middle school, in traditional education settings)

The point, as Larry Summers was actually trying to get at, is that we see, not so much a higher mean aptitude among boys, but a higher variability in aptitude. (If you know literally no statistics, then what I mean is that on a plot like this, boys are more like the red curve -- more likely to deviate from 'normal' -- and girls are like the blue -- still as good, 'on average', but more closely clustered together)

And so, on tests that are relatively challenging, when asking "How many {boys, girls} are this good at math?", it consistently appears that more boys are at least X good (for X > average). Because that's how normal distributions work. And when you ask "How many {men, women} have a PhD in {science, math, engineering, CS}?", what you're really asking is "How many {men, women} are at the 99.7th percentile in their field?"

Okay, why? Let's try two takes:


disclaimer: I am not a biologist; this might all be a load of bunk.

From an evo-devo perspective, high-variability, as a meta-trait, is more beneficial to men than women. In the men-impregnate-as-many-women-as-possible model, male competitors have much to gain by 'beating the field' -- especially if they can do it by a substantial margin -- than do females. After all, a male who 'wins' the mating game can give birth to substantially more than one offspring in nine months, whereas females are rather rate-limited. Add in the fact that being 'just a little bit better' than the competition is likely to net the victorious male more than 'just a little bit more genetic reproduction', on average, and it suddenly becomes obvious that it is very much to the male's benefit -- on average, probabilistically -- to take a chance at being 'better', even at risk of ending up 'worse'.

It's a fine just-so story, but doesn't exactly explain why the disparity is so aggravated by the American middle-school social experience in particular, and not seen abroad, or in different environments, or beginning from birth. Which brings us to...


disclaimer: Neither am I a sociologist.

Girls/women are under great social pressure to conform, whereas boys/men largely enjoy the privilege of self-determination.

Almost. But. Men are driven to suicide at a rate almost four times that of women. (My good friend Rachel Hall deserves credit for digging this statistic up for me.) And so they're apparently under greater, not lesser societal pressure.

The heck?

Okay, so here's my take. I've not seen any serious scientific inquiry here, so this is speculation, based on subjective, anecdotal experience. (Unlike, say, scientific inquiry, which is not at all subjective nor anecdotal...)

The traditional understanding of middle-school gender roles is something like "boys play sports, do science, and win things" / "girls like clothes, aren't too smart, and make artsy things".

And yet. I can clearly recall, from middle school, 'cool' boys who did none of these things. There were plenty who were 'nerdy', or 'dumb', or 'chill'... so it's not a matter of "fill all of these roles"; it's more like "Here are some different things you might do. Pick one."

But all the 'popular' girls I can recall did all of the 'girl things' to at least some degree, and more often than not did all of them very well. So it's not just a matter of do-one-of-these-things; the 'girls should...' pressures are the conjunction of expectations, not the union of available paths...

In other words, boys are told what not to be; girls are told what to be. There are clear societal taboos applicable to males -- most of which indicate being 'less of a man' -- but besides those, males enjoy relative freedom to be, well, whatever, just so long as you aren't (1) a dancer, (2) a cheerleader, or (3) a (girly) romantic. Homosexuality was, of course, unthinkable. (It was 2007. Things were the way things were.) There were many things that you could do right, but you only really needed to hit one of them (and avoid the fatal traps) to be accepted as a 'normal' person.

By contrast, the model for what's 'okay' for girls is much, much narrower. You're supposed to be pretty (or at least not ugly), artsy (in some way), (some amount) social, and (approximately) nice. It's not okay to just 'not care' about one category; you have to be doing decently well at all of them before being considered 'normal'. Miss one, and you're dead.

The pattern continues into adulthood, of course. Men can be (1) dads or (2) businessmen or (3) leaders or (4) geniuses or (5) artists or or (6) athletes, and even if they fail miserably at the other five, still be considered to be a 'great man' (or at least, a 'great guy'). It's just a few things -- homosexuality or subservience to a female partner -- that are really unacceptable.

On the other hand, if a woman is any of (1) single, (2) not interested in kids, (3) don't-care-how-I-look, (4) strong-willed, (5) smart, or (6) athletic, people very quickly begin to ask "What is wrong with her?" (Heaven forfend that she combine any two!)

The effect? Any given population has only a few 'abnormal' males, and many 'abnormal' females. The females receive a sort of general pressure to conform (which I am not discounting as trivial -- it's pernicious and evil and the reason for most things wrong in this world), but the attention focused on the queer* males is, by dint of being so concentrated, that much stronger, violent, and personal. And so we see men pilloried -- at the least, grossly, intentionally offended** [tw: Fox News] -- by the media and a more general, distributed media attack on women's agency. (i.e. the traditional media-against-women's-agency narrative)

And so, men are free to be (almost) anything. They can't quite "have it all", as the saying goes (see: "logistical impossibility"), but they can pick what they want to be in life (If you didn't click that link, you really should read it. It made my day. In a good -- no, awesome -- way. But I digress...), and be that, and be well respected, but the few that transgress societal norms get smacked down pretty hard. Women, for the most part, are constrained to very small 'acceptable' patches in possible-identity-space, and suffer from a more general 'pressure-towards-normal' societal compulsion.

So men go to the moon and launch computing revolutions and become the nine highest-paid people in the world (I was shocked that there was even a woman at #10...) and get elected president and play sports and make art and do, well, anything and everything. And women, when they try to do any one of those, are fighting against a society which asks: "Why don't you do [the normal-woman thing] instead?"

...where did I start this post? Oh, right.


Well, high-aptitude-variance is likely in part genetic. I'd certainly be surprised if there was literally no relation between sex and average variance of phenotypic traits, seeing as how biological asymmetries are likely to set up differences in genetic-fitness incentives. But given how fond our society is of trying to move past inequalities of birth, it seems like it's not the right thing to do to just throw up our hands and say "oops, that's the way it is." At the very least, it's worth taking a serious look at how our society (implicitly? explicitly?) informs its citizens how they are (not) supposed to live, and just what disparities are coded there. It's about thinking broadly, and realizing that we need to generally unthink the girls-should-X/boys-shouldn't-Y narratives that underly 21st-century misogyny/homophobia/transphobia/etc. But first, maybe we should realize that this is about so much more than just being "bad at math" -- whatever that means -- and ask ourselves what people are really saying.