Larry Summers' Math

"We're Different. Get Over It." - My op-ed for the National Post of Toronto on what Larry Summers actually said:

In fact, it's precisely because the presentation by Summers, one of the world's leading economists, was lacking in crude misstatements that it was so threatening to feminists. When finally published, it turned out to be humbly argued, open-minded, well-informed, logically rigorous, and, in sum, cumulatively devastating to the feminist orthodoxy from which many of Summers' female critics have professionally and financially profited...

Hopkins and company want to drive Summers out of polite society to prevent his insightful skepticism from undermining their special privileges.

This is not to say that Summers' sophisticated attempt "to think systematically and clinically about the reasons for underrepresentation" would instantly convince those unfamiliar with the issues. But over the years, the example of the President of Harvard getting away with speaking the subversive truth about gender inequality would embolden others to point out that the feminist empresses have no clothes.

Let me try to outline Summers' unusual approach to "underrepresentation."

He tends to view people relativistically, employing that most useful of all conceptual tools for thinking about both the similarity and the diversity of human beings: the probability distribution (more roughly known as the bell-shaped curve).

In contrast, most intellectuals today think in absolute, black and white categories, and thus they get irrationally upset by mention of any facts they can denigrate as a "stereotype." Many seem unable to distinguish between perceptive observations about the average traits of a group and blanket assertions about each and every group member. Thus, even carefully worded summations of the obvious like, "More men than women find mechanical engineering interesting," are indignantly countered with, "So, you're saying no woman likes engineering? Huh? Huh?"

As a bell curve aficionado, Summers noted a widely observed tendency: "It does appear that on many, many different human attributes -- height, weight, propensity for criminality, overall IQ, mathematical ability, scientific ability -- there is relatively clear evidence that whatever the difference in means … there is a difference in the standard deviation and variability of a male and a female population."

In other words, as any woman could testify, there are more stupid men than women; likewise, at least in math and spatial reasoning, there are more brilliant men than women.

Summers stated, "… if one is talking about physicists at a top twenty-five research university, one is not talking about people who are two standard deviations above the mean. [In a normal bell curve, only one out of 44 individuals is that much above average.] And perhaps it's not even talking about somebody who is three standard deviations above the mean [or one out of 741]. But it's talking about people who are three and a half [one out of 4,299], four standard deviations above the mean [one in 31,574] …"

Observing that among the top five percent of twelfth-graders in math and science, it's common to see two boys for every girl, Summers estimated that the variance in ability is about 20 percent greater among males. He went on, "If you do that calculation -- and I have no reason to think that it couldn't be refined in a hundred ways -- you get five to one [males per female], at the high end."

Actually, by my calculations, although perhaps I'm wrong, Summers was being a bit politically correct with his math. At three standard deviations above average (the equivalent of a 145 IQ, although he's just talking about the quantitative/visual portion of IQ), there would be over seven males for every female. At four standard deviations (a stratospheric 160 IQ), there would be more than 30 men for each woman.

This also implies, correctly, that there are a lot more retarded men than women, but they don't come up much for tenure at Harvard.

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