Endless Summers

Responding to the critics of the critics of Harvard president Larry Summers, i.e., those who claim that political correctness has silenced debate at Harvard and elsewhere, a father and his two daughters, all of whom have math-related advanced degrees from Harvard, attempt to explain “How Summers Offended” in today’s Washington Post.

Did the media treat Summers’s critics fairly? We are Harvard-educated mathematical scientists and university educators — a father and two daughters — and we think not.

The essay begins with some strong points:

Academic freedom does not protect any professor from having his or her ideas scrutinized. And in this case Summers’s comments, while provocative, sorely misrepresented the research. Girls’ scores on standardized tests have consistently improved with strides against discrimination and social bias. This fact alone counters the notion that the differences are “innate.” Standardized educational tests such as the SAT were, in fact, not designed to measure innate differences, and overwhelming research points to social phenomena as underlying the differences in scores between the sexes. If innate differences play a role in SAT scores, how do we explain the mathematics scores in countries such as Iceland, where girls outshine boys on standardized international and national exams?

Those are interesting and relevant points, and if the essay had continued in this vein I wouldn’t be writing, for I have no particular knowledge, or even opinions, about the degree to which intelligence is innate or what standardized tests do or don’t measure. Unfortunately, however, at this point the father-daughters team abandoned a discussion of the allegedly misrepresented research and turned to what they regard as “the real reason Summers’s comments offended.”

The real reason Summers’s comments offended … is because they were made in the context of a history of discrimination that has hurt scientific and mathematical progress immeasurably. And unfortunately, Harvard is a part of this history….

Summers’s remarks offended because they echoed the sex biases with which we grew up — and whose psychological consequences we strive daily to counter in our educational work. These were biases that Harvard helped to perpetuate….

What follows is a conventional (except where it is anecdotal) discussion of the bad treatment of women in science, especially at Harvard. I have no trouble assuming that everything they say is true, but even if it is true that truth is not relevant to the question of whether or not Summers “misrepresented the research” about women in science.

In short, what the father and daughters team has done here is to confirm and highlight what we Summers critics critics have been saying all along: that in the view of many Summers critics any discussion of comparative math abilities is illegitimate and beyond the pale because it (inevitably) occurs “in the context of a history of discrimination.”


Now, since so much of their essay was personal and anecdotal, let me conclude with a personal anecdote (or two). (And, for once, this will not involve my math-and-science-talented daughter.) A number of years ago, when I still had many feminist friends, one of them sent me a draft of an essay criticizing Carol Gilligan’s influential book, In A Different Voice: Psychological Theory and Women’s Development (Harvard, 1982). Her essay was cogent and well-written, but I was disturbed, as I told her, that the substance of her critique was not that Gilligan’s argument (that women and men follow different paths of moral development) was wrong because it was wrong, but that it was wrong because its acceptance might place an obstacle in my friend’s preferred path to women’s equality. Pointing out the potentially negative effects of an interpretation, I argued (to no avail), was not the same as arguing that the interpretation was wrong.

I didn’t realize it at the time of this correspondence with my friend, but because of my long involvement in the EEOC v. Sears case (discussed at length here) I soon came to realize, in spades, that politically engaged scholarship, or political commentary about scholarship, often (but certainly not always) substitutes instrumental for scholarly standards: in this mode, it asks not whether a particular argument or interpretation is true or persuasive but rather whether or not it is Good For the Jews or Blacks or Women or …. In Sears, for example, politically engaged historians worked up a froth arguing that even if it were true (even if?!) that very, very few female job applicants were qualified, available, and interested in, say, installing home heating and cooling systems, no historian should say so in public.

For me, the Summers debate is déjà vu all over again.

Say What? (20)

  1. Laura February 21, 2005 at 10:31 pm | | Reply

    It actually could be Good for Women to ask these questions. I have a theory, and I may be 100% wrong, but here it is: On average, the brain maturity required for language happens earlier for females than for males, and for math it happens earlier for males than for females. I didn’t enjoy math at all in high school, but in college it suddenly all made sense. It’s why I’ve told my daughter not to worry about the fact that she doesn’t like math now; it doesn’t mean she’s not suited to a career in the sciences. I wonder if the tests that show that males do better on spatial blah blah are administered only to high-schoolers or to older people too. I can see how girls might not think they’re suited to math, and therefore science, if they’re frustrated because it just hasn’t kicked in yet. Maybe single-sex education starting in elementary school is the answer after all. If we ask these questions and dig a little harder, we might end up with more rocket scientists and brain surgeons.

    I’ve told this story before, but what the heck. A couple of years ago the kids at my daughter’s school who had high scores on the PSAT were invited to take a prep course for the SAT. (These are offered year-round at her school; this was a special session.) We got there a bit early and she noticed that all the kids standing around waiting were Asian males. I told her that Asian males are going to be over-represented in that top group, and she told me sternly that there was a stereotype in there somewhere. When she came out of that first session she said, laughing, “Talk about stereotypes!” She was the only girl at her table. There was one Asian boy at her table. The kids took a practice SAT, and she got the highest verbal score and the lowest math score at her table. The boy with the highest math score was the Asian.

  2. John Rosenberg February 21, 2005 at 10:50 pm | | Reply

    Laura – Interesting points. I know nothing about math, and less than that about how people learn it. But from watching Jessie grow from a kid for whom learning the multiplication table (later, by the way, than I thought it should be taught) was not a piece of cake to someone, it turned out later, was quite good in math, it struck me that being good in arithmetic and being good in higher math are not at all the same thing. In fact, Jessie still makes arithmetic mistakes.

  3. Richard Nieporent February 22, 2005 at 12:07 am | | Reply

    On the surface, the argument presented in the Washington Post op-ed piece seems plausible. After all, in the past women were prevented or discouraged from going to college let alone going into the sciences. So now isn

  4. Gabriel Rossman February 22, 2005 at 12:28 am | | Reply

    Aside from confusing moral/political standards with scientific/empirical standards, another problem w the Post essay is that like most of the criticism of Summers, it misrepresents his argument. Summers didn’t claim that women have lower mean innate ability in math or anything else, he claimed that they have the same mean and a lower variance. In laymen’s terms, this claim means that men are fairly likely to be good or bad, whereas women tend to be in the middle. The problem with this is that he generalized well beyond the range of the data, and in effect, made overly heroic assumptions about the shape of the distribution, which may in fact be only approximately normal. That doesn’t mean he’s necessarily wrong, just that he strayed excessively into the realm of idle speculation.

    But his mathematical sins pale in comparison to those of the op-ed. As statisticians, the three authors obviously know the difference between mean and variance. The question is whether their indignation blinded them or whether they decided to mis-characterize Summers’ argument for polemical effect. Unfortunately, I’m inclined to think the second since when they do paraphrase him, they do so accurately by referring to differences in the “top tier,” but later on switch to speaking about means. Unless mean differences were so large as to be two or three standard deviations in girls’ favor (they’re not, even in Iceland), evidence about group means is a non sequitur in this debate.

    Likewise, they mention the history of discrimination affecting girls’ performance and it’s pretty easy to imagine how discrimination could either shift the distribution (reduce the mean) or truncate it (a ceiling effect). But I lack the imagination to see how it could compress a distribution. If some social phenomena suppressed both incompetence and genius, I don’t know if discrimination would be the right term for it.

  5. Nels Nelson February 22, 2005 at 1:53 am | | Reply

    Very interesting comments, Laura and John, in regards to how math is taught, or of what math consists. I hope you won’t mind if I add my personal experiences to the bunch. I know nothing about the subject of math education, and what follows is all about me, so anyone who doesn’t want to read rambling has been warned and should please feel free to skip to the next comment.

    I don’t at all intend for this to sound like bragging, but based on my K-12 math performance one would think that I had great math aptitude: straight A’s for as long back as I can remember, perfect score on the math SAT, perfect scores on two other College Board math tests that I believe gave college credit, and the highest possible grade on the AP Calculus test.

    But starting with algebra I never really understood what it was that I was doing, or why anything worked. This got much worse with trigonometry, and by the time I was acing calculus tests I couldn’t have explained to you even the very basic principles of calculus; to this day I have no idea what calculus is; how or when someone would know to use it; or why I was being taught it. What I could do well, and our education and testing systems seem to feed right into this, is identify what type of math question was being asked, remember how I’d been taught to solve that type, and plug in the numbers. I didn’t know how or why it worked, but it did. When I occasionally couldn’t figure out how an entire type of question was to be tackled – as for example I recall happened with those “here are two equations, each with an x and y; solve for both x and y” problems – I’d just guess at numbers and work backwards, which never failed to get me the right answer in short time.

    Compounding this lack of real math understanding, I’ve always had great difficulty retaining the most basic numbers in my short term memory. I do addition and subtraction like a 2nd grader, crossing out numerals when subtracting and writing down the new, superscripted numerals. When adding I still have to write down the carried ones. Division for me is always done with the long method, where for big problems the numbers cascade down the page. My work is highly accurate, however, as long as I keep everything on the paper. And in regards to practical matters, if I were to pick up a phone and you then told me a number, I guarantee you I would have forgotten the first digit, and everything after, by the time you reached the seventh; it’s embarrassing but I have to ask people to wait for me to dial each digit before saying the next one – even two in a row is too much.

    Sorry about going on and on about myself – what’s my point? It’s that as best I can tell I’m very poorly suited for math, and would have failed miserably if I’d tried to major in something like Mathematics or Physics. Eventually, I assume, one is required to create rather than just regurgitate, and I couldn’t have done that if I didn’t understand 9th-grade math principles. Presumably it is also very helpful to be able to think of solutions in one’s head, or perform basic operations with speed, things I can’t do.

    But because as a student I was an excellent problem solver I was pushed onto a high-achieving math track, assumed by everyone to be destined for a math-related career, hurt my classmates when we were graded on a curve, and perhaps led someone else to believe that math wasn’t their field because she couldn’t keep up with me. So maybe the tests are doing a poor job of testing math aptitude, and some folks who have what is needed for college math are being convinced, from early on, that they don’t.

  6. Dom February 22, 2005 at 11:41 am | | Reply

    Rossman made the comment that needed to be made, in my opinion.

    I have one further point. I did a little research in Math education, and it is pretty clear that, in early years, boys and girls need to be taught differently. There is an obvious innate difference at work, but it is not on the order of superior/inferior differences, it is just a difference.

    “Discrimination” is not the word here. You can work at improving a woman’s education in math and sciences, but it has nothing to do with removing biases.

  7. Sandy P February 22, 2005 at 12:10 pm | | Reply

    Arnold Kling has an interesting response via Instapundit.

  8. John Rosenberg February 22, 2005 at 12:40 pm | | Reply

    From the ridiculous to the sublime…. I was recently experiencing feelings of despair about my comment section (because of the nature of comments on another post), but these have hit a new high. I think I’ve learned more from Gabriel and Nels above than for everything else combined I’ve read about the Summers affair. Thanks to all.

  9. Laura February 22, 2005 at 1:01 pm | | Reply

    Nels, you may have a point. My child insists on understanding everything before she goes on. You can’t just show her how to work a problem, she’s got to feel it. I used to have to draw pictures to explain how to add fractions, for instance; she wouldn’t just take my word for it. (School was worthless there, before you ask.) I used to joke that we should have named her “Missouri”. But I’m that way too. It’s a good way to be if you’re not too slowed down or outright paralyzed. I’ve had people I supervised turn in really stupid results, like 10 billion parts per million, because they thought they were following the formula or because that’s what the computer said. “Can’t you see that that has to be WRONG?” makes no sense to some people. Others just have to be encouraged to listen to their gut telling them a number doesn’t seem right. But it’s very feasible that her taking-up of math has been slowed down in middle and high school from being that way. It’s another reason not to despair of her catching up. (She didn’t exactly bomb the SAT when she took it for real; 750 verbal, 640 math. I think she could have pulled the math up, but for what she wants to do the scores are adequate.)

  10. Stephen February 22, 2005 at 1:37 pm | | Reply

    “Summers’s remarks offended because they echoed the sex biases with which we grew up — and whose psychological consequences we strive daily to counter in our educational work. These were biases that Harvard helped to perpetuate….”

    What are called “sex biases” here are the traditional values of a religious society.

    Harvard, and all colleges, are arrogating to themselves a function that is none of their business, in indoctrinating women that they must be the same as men. Feminism is a political ideology, not revealed truth.

    Less than a quarter of women identify themselves as feminists. NOW is dying for lack of a constituency. And, yet, not a single women’s studies department actively recruits traditional and religious women. You will note, interestingly, that my loathing of feminism expressed in my posts yesterday earned me the moniker “misogynst.”

    Oddly, I have raised two daughters, both with advanced degrees and I was married to a woman who was a phenomenal artistic and business success. In my weblog, I write at great length about the women that I know, and every one of them is quite a remarkable woman. Calling me a misogynst is yet another rendition of the old song “if you’re not a feminist, you’re not a women.” Since 3/4 of women are not feminists, I gather that we have a lot of imposters on our hands.

    This issue all about indoctrination in what feminist women want other women to do. Harvard needs to cease these strong arm tactics of indoctrination of young women, mind its own business, and go about the business of education. Harvard is brutality violating the simplest notions of educational ethics by using its facilities for this ideological brow beating. Those who are responsible for it should simply be canned.

    I’m not holding my breath.

  11. David Nieporent February 23, 2005 at 3:38 pm | | Reply

    What are called “sex biases” here are the traditional values of a religious society.

    So you’re actually agreeing with Summers’ critics; you simply don’t see a problem with it where they do.

    You’re certainly not agreeing with Summers’ hypothesis, which is that these are in large part biological, not the result of “values,” traditional or otherwise.

    Feminism is a political ideology, not revealed truth.

    As are “traditional values of a religious society.”

  12. Stephen February 23, 2005 at 4:33 pm | | Reply

    Thanks for telling me what I think. How did you acquire this omniscience?

    I said something very simple. Harvard has no business concerning itself with indoctrinating young women. I said nothing about Summers. He doesn’t interest or concern me.

    Harvard engages in political indoctrination of young women. It does not, as far as I know, engage in religious indoctrination. In fact, I imagine that it ridicules traditional religious indoctrination.

    Women and men are different and they should be. The drive to make them the same will fail because they are different and reality cannot be overturned. It will also fail, because as I noted, the vast majority of women reject feminism. Shall I play the omniscient sage and say that you think that only feminist women are actually women?

    Young women will benefit far more from a traditional religious indoctrination than from a political indoctrination. Religious indoctrination works. It’s time tested. It serves real human needs. And it produces good results, particularly in marriage and family. Feminism indoctrination produces human misery.

  13. Michelle Dulak Thomson February 23, 2005 at 4:48 pm | | Reply


    Who called you a “misogynist,” and in which thread? I can’t find it.

  14. Stephen February 23, 2005 at 5:02 pm | | Reply

    The accusation was made indirectly in “More Deanly Invective”:

    “Your position is that the world is full of Stephens, and therefore there’s a need for black solidarity, including nasty language towards black kids who aren’t sufficiently, shall we say, solidaritous? You might just as well say that in a world full of misogynists any woman who defends any man in any context is a ho.”

  15. Michelle Dulak Thomson February 23, 2005 at 5:24 pm | | Reply

    Ah, I see.

    Stephen, I wasn’t calling you a misogynist. I was analogizing. Cobra, obviously, considers you a racist. He thinks that with such as you in the world, the Dean Turners of the world have every right to force racial solidarity among minorities, even on minority individuals who don’t like the idea, even by harsh invective of the kind we were discussing. I likened calling blacks “Uncle Toms” just because there exist racists to calling women who defend men in any context “hos” just because there exist misogynists.

    It does not follow from the fact that your name was in the paragraph that every sentence in it was about you, Stephen. I never said, nor alleged, nor thought that you are a misogynist. Indeed, you read more like a “difference feminist,” if you don’t mind my saying so ;-)

  16. Stephen February 23, 2005 at 6:20 pm | | Reply

    I think the problem is the perception that, if you are not a feminist, you oppose women achieving.

    This is patent nonsense.

    I grew up in poverty, in a small farming town in Illinois. The women I knew in my youth worked, just like the men, at dirty, dangerous jobs for very little money. The feminists I met when I went away to college were uniformly soft, suburban women.

    I am not any kind of feminist. I reject the notion that women ever suffered an inferior status to men. This is the core lie of feminism. Poverty, and hard work were the lot of both men and women in my family until very recently, and this is the reality of almost all of humanity.

  17. Michelle Dulak Thomson February 23, 2005 at 6:40 pm | | Reply

    Oh, Stephen. You are overreaching, badly.

    I am not any kind of feminist. I reject the notion that women ever suffered an inferior status to men.

    No? Not under the Taliban? Not in Saudi Arabia today? Is it that the trifling discomforts of not being allowed to drive, or appear in public without approved clothing, or without a suitable male escort, is compensated by that mysterious, private erotic power that’s the real wellspring of the world?

    If you really think that such trifles as the right to own property and the right to vote (both, in historical terms, given to women only recently) are negligible, or compensated by other rights women had that men did not, I should like to read a fuller explanation.

    And I say this as one who really does agree with you in some fashion on this subject. Men die younger than women; they disproportionately do the most dangerous jobs; they get murdered far more often; they get imprisoned far more often; they kill themselves far more often; and they generally spend much of their income supporting women who make less than they do. But to represent that women have never “suffered an inferior status” to men is . . . well, silly.

  18. Stephen February 23, 2005 at 7:31 pm | | Reply

    So, we disagree.

    Have you ever thought of how many of those members of the Taliban were teenage boys dragooned into military service? Or of how many of them died before they reached maturity?

    Property rights are of very little value to those who have none. No man in my family owned property until well into the 20th century. This was the common experience of men.

    No man in my family had the franchise until the 1890s. Before that, men in my family were desparately poor serfs. Women in my family acquired the vote 30 years after their men.

    Feminist history is lie on top of lie. Nope, the history to which you are referring is the history only of the very wealthy and powerful, a very tiny class. Until the expansion of the middle class in the U.S., the common lot of humanity was desparate poverty and miserable work. That is where I come from. I gather you come from somewhere else?

  19. Richard Aubrey February 24, 2005 at 1:12 pm | | Reply

    It would be odd if men and women were exactly the same in math/physics capabilities. Why should they be?

    When one considers all the talk about multiple intelligences and how women are more nurturing and men are Gaia-raping monsters, that being gay is not a choice, the idea that the math/physics area must be a place where differences do not exist is rather odd.

    One anthropologist said, hyperbolically, that the only bigger difference than between male and female is the difference between dead and alive.

    We are required to forget all the other talk of innate differences for this issue only?

  20. Laura February 24, 2005 at 8:49 pm | | Reply

    A bigger difference than between male and female is that between any two individuals, in my opinion.

    I don’t have a problem hypothesizing that there are more men than women who excel at physics and math because of innate ability. I do have a problem (1) assuming that’s the case, and (2) allowing that assumption to keep us from asking questions like the brain maturity question I posed earlier. I think that as long as any woman can reach the limit of her ambition and ability, there’s not a discrimination problem, regardless of the statistics at the end of the day. But I also think that although of course it’s true that if people want to kill themselves working in the lab 80 hours a week they ought to be able to do that, it’s not right for anyome, male or female, to be coerced into working like that just to show how committed they are. It’s not healthy for individuals or for families.

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