Math is hard

Two dispatches this week from the “is our girls and women learning?” wars. Elizabeth Weil writes about the nascent movement for single-sex education in public schools, and Christina Hoff Sommers takes on efforts to socially engineer the equal representation of women in science and engineering PhD programs. (Charlotte Allen’s “Women are dumb” doesn’t make the cut.)

These arguments over the influences of innate cognitive differences (in the mean and in variability), socialization, hostile environments, and self-selection don’t seem to be going anywhere. Sommers has moved on from the crisis in boys’ learning to the crisis in men’s—women now earn the majority of PhDs, so academia must be hostile to men. Except in math, science, and engineering. And activists are now using Title IX to redress this last injustice.

As a high-school math nerd, I was on the school and county math teams, did national math competitions, and went to math camp. Needless to say, these were not overrun with girls. I taught math to very precocious twelve-year olds (in a program associated with a longitudinal study of very very precocious twelve-year olds), and to learning-disabled teens; lots of Y-chromosomes in both camps—and more so, the more gifted or disabled. I went to grad school in mechanical engineering, the most-heavily male of all technical fields. [In 2005, 12% of ME PhDs went to women, vs. 18% in all engineering fields, 27% in math and physical sciences, 34% in earth sciences, 49% in life sciences, and 68% in psychology.] Later, at a professional seminar I looked around the room and saw more than a hundred men, and not a single woman. I might as well have been on a nuclear-submarine crew, or at a Doctor Who fan convention.

I’m hardly an expert, but I’d followed the research on girls and women in math and science with some interest. It had led me to explain the preponderance of men mostly by social and attitudinal factors; fewer women are interested in spending their days solving differential equations and setting up lasers, whatever their capabilities—a view I came to before reading Steven Pinker or Simon Baron-Cohen. Maybe a few more would be interested but have been socialized to do something more “nurturing.” And a few more are put off by hostile or unappealing environments—macho [yeah, right—ed.] or nerdy. Larry Summers got a raw deal: Differences in innate cognitive abilities may account for some small part of the gap, and more so at the five-sigma level (I wouldn’t hold my breath waiting for parity in Fields Medalists) [or not—see Update below]. And cognitive abilities that don’t meet their potential, from understimulation during primary education, for a bit more. Add it all up, and it hardly surprised me that there were so few women getting PhDs in engineering, even as they came to dominate law, medicine, and other academic fields.

But I’ve been out of that world for some time, and my attention has lagged. Sommers cites and summarily dismisses a recent report, Beyond Bias and Barriers: Potential of Women in Academic Science and Engineering, from the National Academy of Sciences. She doesn’t like that Donna Shalala chaired the committee, and she objects to how others have used its findings, but she also takes careful aim at the studies it cites, and other allied literature:

The research emphasizing the importance of biological differences in determining women’s and men’s career choices is not decisive, but it is serious and credible. So the question arises: How have so many officials at the NSF and NAS and so many legislators been persuaded that we are facing a science crisis that Title IX enforcement and gender-bias workshops can resolve?

The answer involves a body of feminist research that purports to prove that women suffer from “hidden bias.” This research, artfully presented with no critics or skeptics present, can be persuasive. A brief look at it helps explain the mind-set of the critics and their supporters. But it is a highly ironic story. For the three recognized canons of the literature are, in key respects, travesties of scientific method, and they have been publicized and promoted in ways that have ignored elementary standards of transparency and objectivity. If they are auguries of how the STEM-equity activists intend to transform the culture of science, the implications are deeply disquieting.

The National Academies are not infallible, but they’re as close to a gold standard of objectivity and incorruptibility as we’ve got, and I’ll always put the burden of proof on those who’d discredit them. From Beyond Bias:

Biological explanations for the dearth of women professors in science and engineering have not been confirmed by the preponderance of research.

…

A substantial body of research demonstrates that women are underrepresented at higher levels of business and academe because of the influence of gender schemas and the accumulation of disadvantage that such schemas generate.

…

In addition to bias, systematic structural constraints built into academic institutions have impeded the careers of women scientists.

Still, the NAS study doesn’t consider the differences among S&T disciplines in much depth, and doesn’t do much to change my view that mechanical engineering will remain a boys’ club for…ever? But, what ho!

Women now account for twice the share of engineering PhDs as they did when I finished. Depending on the model specification, the data suggest that they’ll account for half sometime between 2024 and 2065, and for 110% about when the robot overlords come to power.

Talk of mathematics being “socially constructed” is arrant pomo nonsense (not to be confused with constructive mathematics), and the Navier-Stokes equations* are not written differently in men’s and women’s frames of reference. But women may yet change the culture of engineering. Maybe enough to lure me back.

Update: Catching up with some of the more recent research. In particular, Spelke, Elizabeth S. (2005). “Sex differences in intrinsic aptitude for mathematics and science? A critical review,” American Psychologist, 60(9):950—958. Spelke strongly concludes that there’s no greater variability in mathematical aptitude in males than in females, which is the usual explanation for why boys and men predominate more as you ascend the achievement ladder. I doubt that this will settle the matter, but it’s an eye opener.

Son of Update: Several readers have taken me to task for the heading. I thought the reference was familiar-in perhaps the biggest toy-marketing blunder until Fondle-Me Elmo, a talking Barbie was programmed to say “math is tough!” which has come to be remembered as “math is hard!” Or buy it and find out for yourself.

Return of the Son of Update: Nerts! For at least the second time in a week, I see that Matthew Yglesias has scooped me on the smug heading. And, h/t to one of his commenters, the last word on girls and math.

*Footnote: The Navier-Stokes equations are the fundamental equations of turbulent fluid flow, in which I did my PhD. My program was generally regarded as friendly to women, of whom we had many more than the national average (although only one out of about 70 professors was a woman). I’d thought that the subject was immune to pomo flapdoodle, even in satire. I was wrong:

The privileging of solid over fluid mechanics, and indeed the inability of science to deal with turbulent flow at all, she attributes to the association of fluidity with femininity. Whereas men have sex organs that protrude and become rigid, women have openings that leak menstrual blood and vaginal fluids. Although men, too, flow on occasion—when semen is emitted, for example—this aspect of their sexuality is not emphasized. It is the rigidity of the male organ that counts, not its complicity in fluid flow. These idealizations are reinscribed in mathematics, which conceives of fluids as laminated planes and other modified solid forms. In the same way that women are erased within masculinist theories and language, existing only as not-men, so fluids have been erased from science, existing only as not-solids. From this perspective it is no wonder that science has not been able to arrive at a successful model for turbulence. The problem of turbulent flow cannot be solved because the conceptions of fluids (and of women) have been formulated so as necessarily to leave unarticulated remainders.

(Hayles, N. K. (1992) “Gender encoding in fluid mechanics: masculine channels and feminine flows,” Differences: A Journal Of Feminist Cultural Studies, 4(2):16—44.)

Although this would have made Alan Sokal proud, it was not a hoax. Every woman fluid dynamicist I’ve shown this to has responded with an unladylike snort.