Mrs. Laquedem asked me, with a dangerous glint in her eye, what I thought of the January 15 remarks of Lawrence Summers, the president of Harvard College, to the NBER Conference on Diversifying the Science & Engineering Workforce.
More bravely than sagely, I told her what I thought. After the resulting discussion [omitted here purely for the sake of brevity] I read his actual remarks, available here. A few things stand out. First, Mr. Summers said that he was speaking to provoke discussion and not to report on what Harvard is doing to address gender equality in the sciences. Second is that he described his specific topic as "women's representation in tenured positions in science and engineering at top universities and research institutions," not as a general survey of women and mathematics.
Top universities don't have a lot of women holding tenured positions in science and engineering. The question is why. Mr. Summers described three competing theories: (1) the "high-powered job hypothesis," that men are more willing than women to work at 80-hour-per-week jobs, (2) innate biological differences, the theory that got him into trouble, and (3) discrimination and socialization.
If you read his remarks (and I hope that you will), you may notice something interesting about how he described theory no. 2. He said that possibly men and women have different standard deviations (not means) in their aptitude for science, and that this results in more men than women at the extremes.
For example, suppose that science ability can be measured on a IQ-like scale, with 100 as the mean, and that a science quotient (SQ) of (say) 130 is required to achieve tenure at Harvard. If men and women have a mean SQ of 100 (that is, the same average ability), but men have a standard deviation of 15 and women have a standard deviation of 10 and both are normally distributed, then about 2.5% of the men will have an SQ above 130, but only 0.25% of the women will have an SQ above 130, even though the average abilities of men and women are identical. So even though the two populations have identical average abilities, at the high end men will outnumber women by about 10 to 1. (If this is true, then men will outnumber women at the low end by 10 to 1 also.)
The controversy that he stirred up (which he said was his goal in giving the speech) brought to mind another story of women and mathematics, this one involving Marilyn vos Savant, who claims to have the highest IQ of any living person and who writes a column in Parade magazine called "Ask Marilyn." In her September 9, 1990 column, she included a brain-teaser that's now called the "Monty Hall problem," after the original host of Let's Make a Deal. You must choose among three doors. Behind one door is a car; behind the other two are goats. You choose one door. Before the door is opened, Mr. Hall opens a second door to reveal a goat, and then asks if you want to swap the door you picked for the third door. The question is whether you should switch. Ms. vos Savant said that you should switch: you have a 1/3 chance of winning the car if you stick with your original choice, and a 2/3 chance of winning the car if you switch.
Professional mathematicians (all men) were outraged. . .
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