Fads and Fallacies in the Social Sciences by Steven Goldberg: Part II

Part I

We now discuss the first two of Goldberg’s main claims. Both of them are contentious, are bitterly contested, and passion inducing. Try to keep a cool head; certainly read the caveat in Part I. Remember, too, that I will not be able to present all of Goldberg’s book-length evidence.

Environmentalism cannot explain all behavior

It is obvious and true that one’s environment influences one’s behavior. A Chinese will tend to act differently than a Russian; for example, they will tend to celebrate different holidays and show variation in respect to their elders, purely because of socialization. No one disputes this.

It is also true and obvious that one’s physiology and biology, one’s neurochemical makeup, influences one’s behavior. A 250-pound, muscle-bound man is more likely to play for the NFL than is a short, 150-pound, desk-bound man. Goldberg is fond of repeating, “an adult male’s ability to grow a moustache is not caused by our telling little girls that facial hair is unfeminine” (emphasis in original).

Bizarrely, however, many dispute this. Not about all aspects of behavior, of course—there are only a few (but still they exist) that deny that the anatomical differences between males and females lead to differences in behaviors, even in reproductive terms—but usually in those behaviors related to intelligence. That is, a sociologist might allow that men taller than six feet would, on average, make better professional basketball players than men shorter than six feet, but she would dispute that some men might, say, evince greater mathematical aptitude than others except that those differences are caused by differences in socialization and not innate ability. Even stronger would she deny that there could be any differences in intellectual ability between males and females, or between other groups.

Before we get to that, let’s take care of a common statistical argument against the importance of group differences. People often say that “within-group differences are almost always greater than between-group differences” and so the between-group differences do not matter. Goldberg offers this brilliant analogy (all emphases in the original):

It is, of course, true that the difference between the means of two groups is usually much smaller than the range within either group, but this casts no doubt on the importance of the between-group differences. No one could doubt that the mean difference in height between men and women (four or five inches) is less than the four or five foot difference between the shortest man and the tallest man or between the shortest woman and the tallest woman. But no one could reasonably use this fact to deny that it is meaningful to say that men are taller than women, that the reason is primarily hereditary, and that the difference is important in some contexts.

Men and women exhibit different behaviors (Please read all of this section before reacting.)

On “virtually everything measurable” men exhibit more variability than do women. Often, the mean of the measures will be the same for the sexes, as it does in tests of mathematical ability, or even higher for women, but the variability has always shown to be greater in men. A typical consequence of this (without getting too deeply into this) is that at the extremes more men than women will be found. That is, in any collection of the “world’s greatest” mathematicians, poets, writers, musicians, or whatever, more men than women will be and are found. But it also means that in any collection of “world’s worst” “murderers, traitors,” etc., more men than women will be and are found. The exceptions to this are obvious and well known: maternal abilities are greater in women, paternal abilities in men. It is extremely important to emphasize that these facts are true not just in the U.S.A. in 2009 but in every culture and throughout history.

A consequence when the means are equal, as regarding mathematical ability, is that men and women are equally probable in being better than average (and worse than average). You cannot say “men are better than women at math” without adding “because they have a higher probability of exhibiting extreme brilliance” and “because they have a higher probability of exhibiting extreme stupidity.” To just say “men are better than women in math” is meaningless without those additions—as is saying “men and women are equally good at math” without them (see this example).

Now, you might want to believe that, in most areas, there are no innate differences between men and women on average, but you do so based on faith, or, rather, in exact opposition to the evidence. This is because there is no and has been no evidence that men and women are the same. Sometimes, this fact is accepted (the men and women differ) but sociologists argue that the differences are caused by socialization. Whereas this explanation might be plausible in one culture at one time (ours) it becomes highly implausible when regarding all cultures and times.

Pay attention: Sally is a professional, tenured mathematician and has four papers each with eight citations in the Journal of Topology. Bill is also a mathematician in the same department as Sally and also has four papers each with eight citations. Is Bill a better mathematician because he is male? No. Can Bill take pride that he is a mathematician because he is a man? No. (If you like, swap “top grades in math class” for “papers.”)

As asked in Part I, if Sally is over six feet tall and Bill is over six feet tall, are both Sally and Bill over six feet tall? Even though Sally is a woman and Bill a man? What irks the leftist in questions like this, and what motivates her to deny the obvious differences, is that Sally might be treated differently than Bill even though she has the same abilities as him because people foolishly and incorrectly conclude that because more men will be exceptional each man will.

Instead, it is true that any woman might be better (intellectually) than any man. Knowing a person is a woman does not allow you to conclude that she will not exceed any man in ability. In fact, the true statement that more men will be found in the extremes of behavior says absolutely nothing about any individual man or woman, and so the fact that men are more variable is of little use, especially political use. The only way to tell whether Sally is better than Bill, or vice versa, is to put them to the task and see.

Importantly, men have nothing whatsoever to crow about because more of them will be in the extremes—of which, it shouldn’t be necessary to remind ourselves, there are two. Nor should any woman suffer pangs of diminished self-esteem. Nor should she not apply herself to discover whether she is a Sally. Equally, however, neither should we create programs that mandate equal percentages of intellectual jobs go to men and women—unless we are prepared, in the name of fairness, to mandate equal numbers of men and women at the bottom of society1 (we’ll need to dramatically boost the number of women in prison, for one).

Obviously, we have barely touched on this subject (such as how the male/female ratios change from culture to culture, but with the men ever greater in the extremes; nor have we discussed why men and women are different), but we have already gone on too long. Again, I beg that you read Goldberg on this before becoming too exercised.

Update: I hope readers can see that I only placed one “ought” in this entire article; in the last sentence in the penultimate paragraph. Everything else is an “is.” See Part I.

Update: Friday morning. Reader Stephen Dawson reminds us of La Griffe di Lion’s analysis of the male/female math gap. Highly recommended. Pay attention to the shift in the axis limits of Figure 3 and to the cross-cultural analysis.

Still to come: race, patriarchy, homosexuality, capital punishment, abortion.

Part I

———————————————-

1This statement implies that mathematicians properly belong at the top of society.

Comments

Fads and Fallacies in the Social Sciences by Steven Goldberg: Part II — 60 Comments

  1. “Boys are better than girls at math.” Stereotype and empirical generalization are not at all arbitrary. This statement was indeed backed by statistics in the 90s. Evidence now has suggested that girls have achieved gender parity in math performance on average (or, as Briggs said, men have a higher probability of exhibiting extreme stupidity).

    Mr. Briggs, has Mr. Goldberg addressed possible explanations for such change in his book?

  2. Sally—I mean, JH, he has. Also, as you know as well as I, mean parity does not imply parity everywhere. Men are more variable while also having same mean as women. From this, it follows that a greater number of men will be—and are, and always have been—found in the extremes.

    Also, we should be clear. Nowhere does Goldberg ever say “boys are better than girls at math.” Nor do I say so. Actually, Goldberg points to many studies that show that before puberty girls are better than boys at math.

  3. I find none of the above surprising, perhaps because I grew up in a less politically correct age: and perhaps one which took it’s science more seriously too so that well educated people were expected, if not to be experts, to have a general grasp of what was going on in Science. And the Scientific journalists of the day usually had good science degrees and wrote clearly, concisely and well. Unlike today.

    Moreover in the 1950′s and 60′s I think both the Oxford school, Huxley jr, or the London school, after Malinowski, although they fought like Kilkenny Cats over most things, would have broadly endorsed the above.

    They would I imagine have also said that in mammals it is usual for the males to be bigger and heavier than the females and that the ratio in humans, from memory, is about 5 to 4 across all races whether they be Han Chinese or South Sea Islanders.

    They would also I think have said that the ratio of exhibiting extreme behaviour is about ten times greater in men than women, but would have added that whilst very rare some women can and do exhibit much greater extremes of behaviour than men.

    Mind you in that latter statement they would have had, indeed did have, very different views about the respective roles of genetics and social conditioning.

    Against that they would have been united in the view that the entire science of Sociology could be written on the back of a postage stamp IN CAPITAL LETTERS.

    Well it was Sociology back then but I believe in the USA you have something called Ebonics or such like.

    Kindest Regards

  4. Mr. Briggs,

    Thank you. I would need in a pair of x-high pumps though. Thanks also for the clarification about girls and boys. Oh, I didn’t mean to bash men…uh…maybe, just you. Picking on you has become my new hobby.

    I am interested in knowing the impact of stereotyping on society and vice versa. Think of women’s suffrage and slavery in U.S. and many events in Chinese history. Society and culture seems to be important factors in stereotype formation. Maybe I can validate/invalidate my ignorant thinking in the book, which I have requested vie E-Library and it shall arrive within a week.

  5. I mean to say that maybe I can validate/invalidate my ignorant thinking by reading the book.

  6. Don’t be silly, Sally, you’re quite mentally tall.

    But you reminded me that I want to clarify what I mean by “extremes.” The differences between men and women are such that you will not, on average, be able to discern differences in behavior for more than 99% of the population: in everyday life there just is no real, on average, difference between men and women. Extremes are just that—extreme; in statistical speak, people at the very tails of the distribution. Very crudely, extremes are people who end up as tenured math professors, or, even more so, those who end up in history books (those prepared by sex- and race-blind historians, that is).

  7. Quite right, Joy. But the vast majority of “feminist” sociologists are female.

    Say! That’s my kind of Sally! Sorry I missed the show.

  8. No argument here, Briggs. I often get into disputes about why there are so few women engineers, and what we must do to correct this social ill. My antagonists are a small group of puritanical fanatics from a nearby university (not one sociologist among them–educators all) who are unfun beyond the 99th percentile. Our latest encounter occurred in a large gathering where we were being lectured about the “chilly climate” for young women in engineering–and that all one needed to do was examine the numerical disparity between men and women in the field to prove its existence. I have no tolerance for BS and asked them, “How does this chilly climate work? Who is involved, and what role does each play in it? How does it operate? What is your theory?” and so forth. No response at all on these questions. Soon, though, I was accused of saying that women were not a smart as men, and in mathematics in particular. The trump card. Never mind that I never said any such thing.

    However, to be a good engineer does not require either high intelligence nor much mathematical ability. People who reside between the 75th and 90th percentiles in math, and who attain SAT results above the 60th percentile make great engineers. So I will soon counter the “trump card” my antagonists always use with your argument that one cannot demonstrate any difference between men and women in math (or science I presume) with a sample between the 1st and 99th percentiles. Excellent!

    By the way, in education we are trying to correct the social ill of not enough engineers (a claim I don’t buy into) by recruiting heavily among women. But my experience with this, and my experience is pretty extensive in both education and industry, is that it is darned difficult to hold the interest of women in a field like mechanical engineering–its a little easier in a field like civil engineering, but still not easy. I swear we are battling a biological “difference in interests” where there is a mean disparity–a lot of the women who drop engineering do so when they are doing well in their studies. Through pressure recruiting, heaps of opprobrium for dropping out of one’s programs or non-retention, and easy claims of “chilly climate”, we are making for lots of unhappy students, professors, and maybe employers too.

  9. I have ordered Goldberg’s books. Alas the local libraries do not have either of them. So trusting Briggs’ summary it seems that the meta points are (a) just as we know less than we think we do, we frequently confuse what we think ought to be with what is and (b) because we frequently confuse what we think ought to be with what is, we will continue to know less that we think we do.

    I suspect that if Steven Goldberg had been President of Harvard and said a fraction of what he has ostensibly written at a Harvard faculty meeting he would have been vilified, harassed and ultimately fired. There is empirical evidence to support this proposition.

    As for the women in engineering issue, it strikes me that this is an area for some careful empirical work. I suspect that whatever accounts for the difference in both entry and completion rates in Engineering, if they actually exist, occurs in other disciplines as well. Similarly there may be disciplines where fewer men enter and more fail to complete – though I have no idea what these might be. This is the research that should be undertaken before anybody pronounces what ought to be and tries to make it so.

  10. A number of years ago, Mattel recalled a generation of Barbie dolls. It spoke ten phrases or so, one of which was “Math class is hard.” This of course led to a feminist charge omitting only the pitchforks and torches.

    There is a societal pressure on women to not be as smart as men, and that doll represented it well. Mating games matter. Add in the higher male variability (biological), and much is explained. Add in that females on average really are different than males – and that must extend to preferred activities – and that about covers it.

    My wife is in general smarter than me. We are in part together because I respect her intelligence.
    Yet most men seem to prefer the ‘dumb blonde’, and you can count on that kind of sexual selection to have an effect, even if only a social one.

  11. One of the things that has always bothered me about these issues is the assumption (sometimes implicit; sometimes explicit) that “abilities”, be they musical, artistic, mathematical, or otherwise have a symmetric distribution.

    Maybe it’s just because I have so little experience with the lower extreme of these distributions, but it seems to me that while it may make perfect sense for height to follow a normal distribution, that musical ability follow a very skewed distribution, and that skewness my differ by genetic factors.

  12. A bulk of this argument is being made from the use of standardized math exams. When data from early years of education was included ‘grades 2-11’ there was no difference between girls and boys found. But of course this cannot be true, so we must exclude pre-high school/prepuberty data. Now everything looks in order.

    But wait. Prepuberty/Pre-high school boys and girls are taught and motivated the same. Learning for learning’s sake. It is not until high school where expectations and motivations of girls and boys differ. Not unequivocally true, but generally, boys in high school showing academic promise are encouraged to excel, are expected to perform well and get accepted to university, get a degree, get a good job and provide for their family. Girls in high school are encouraged to learn, only as much as it takes to get accepted to a university where they can either perform well or at least find a boy who is performing well and will get the good job and provide for the family. Expectations of girls in high school are lower. Many girls excel through self motivation or from a family/teacher expressing an uncommon interest, but in general both boys and girls will only do as well as expected. When an exceptional girl is expected to be average, she will fall somewhere in the middle. When an exceptional boy is expected to become one of the greatest minds his hometown has ever seen…. To quote a comment from one of your earlier topics “It is so hard to learn to be good at math when a voice in my head says “There´s no use. You are a girl”. My grades say I´m good at it. But the thoughts are still there.” Phoenix

    As for the bottom of the extreme being weighted down with boys, how many of the poor performers on college prep math/SAT are male athletes who took these exams because it was required for entrance to State College? Female athletes are not provided the luxury of scoring a 300 SAT math score and hope to gain college admittance. As such, poorly educated female athletes don’t bother taking college entrance tests if it is forgone they will not qualify. I’ve seen high school transcripts of DivII football players with a 9/36 ACT math score. Plenty of high school girls would have scored as poorly, except high school girls who would score that low wouldn’t take the exam in the first place.

    Interestingly, the link to La Griffe du Lion’s page stumbles upon the ‘Iceland anomaly’ but more or less dismisses it as such. In fact, it mentions that no explanation for this is known. This is not true. In Reykjavik the distribution looks similar to progressive western culture because the situation in this one urban city in Iceland mimics western culture. The rural setting in Iceland offers a clear cultural explanation and is well documented. Iceland is one of the few rurally dominated countries which offers women the same opportunities as men. It guarentees availability of education to anyone who seeks it.

    The rural expectation of education for boys in Iceland is they will do only as well as is necessary to get by. The value of male education is downplayed because the vast majority of rural Icelandic men will become financially stable as commercial fishermen or similar, where secondary education is not needed. Icelandic females without quality secondary education go jobless or take mundane low skill/low pay jobs. There is little opportunity to ‘marry up’, and as such girls are expected to study hard and excel in school since the financially stable jobs available for women generally require a degree.

    My favorite part was [Ergo a link between cultural barometers like the GGI and sex differences in mathematics performance. The link, however, is entirely accidental.] This reeks of AGW models which attribute 100% of global warming to CO2, and then dismiss any other possible influence because their model already accounts for everything. The other connections/trends must be accidental because you can throw them out and the CO2 model holds strong.

    Aside:
    The inability of the Goldberg to distinguish between intellectual development and the ability to grow hair on your face speaks volumes.

  13. John:
    Can you summarize your points? I think you are saying – Not so fast on that assumption of greater variability among males compared to females especially with regards to math skills?

    If so, and again not having read either Goldberg book, I do think this is an interesting empirical question. My guess is that “feminists” would argue that this is an inappropriate question. Goldberg would probably disagree.

    Given the findings of Christina Hoff Sommers, I think that whatever it might have been, it is no longer an inappropriate question.

  14. Bernie, part of my post is definitetly saying just that.

    I am also saying that just because it is possible to find a correlation when excluding a subset of evidence (ie cultural biases, discrimination practices, solar forcing, ENSO), it doesn’t mean the excluded evidence is irrelevent or even that your correlation is real.

  15. John:
    I absolutely agree. Many models of significant and complex phenomena like climate (and most human phenomena, e.g., suicide and mathematical ability) are grossly underspecified. There is a huge amount of unexplained variance and the addition of a new variable could well diminish or augment the importance of existing explanatory variables. We seem to share the same viewpoint on the explanatory power of increasing levels of CO2.

  16. Bernie, John,

    Quick reply. La Griffe’s analysis in this instance is indeed based on standardized tests. Goldberg’s arguments and evidence are not solely so based. Goldberg asks us to (mentally) compile a list of he world’s (all-time) greatest mathematicians. In anybody’s list no more than two females appear (one of them Nother; the other is escaping me; will look it up when I have a moment).

    In any case, even though La Griffe’s analysis is based on standardized tests, it’s interesting, is it not, that the same male/female difference is found in all other cultures—the exception is Iceland, where the difference of the difference is unusual when compared to a normal model. That means, as Bernie suggests, the normal model isn’t ideal.

    Mike B makes this same point: why expect symmetry? Too, no model of ability, say IQ, can ever be perfectly modeled by a normal. Stone dead, your IQ is 0, but the normal model will still give (trivial) probability of IQ less than this.

  17. A list if the greatest mathematicians of all time is irrelevant as formal higher education offered to females is unique to the modern era.

    It’s interesting, is it not, that the difference is less and less significant when the individual country analyzed is shown to be less male dominated and average IQ of the region is higher. That the difference is less significant within the same country when you compare older data with data many years after equal opportunities have become available. That when you run across 1 culture who overemphasizes female education you see the opposite result. And when you look at an age group where there is little pressure for males to excel and expectations of girls and boys is equal (grades 2-8) you see absolutely no difference at all.

  18. One can name many males who have had zero formal education, yet reached the apex of mathematical or scientific achievement. It still may be cultural, or environmental, but yet…

  19. Of course the all-time-across-all-cultures-all-forms-of-government-organization-and-socialization-types list is relevant, John: that is the extreme data of which we speak. The burden is on you to explain why it should not be. And you can’t just say something like “it might be true than in some future enlightened civilization, men and women will be exactly, distributionally-speaking—the same.” That of course is a true statement, but all the observed evidence so far has been against it.

    I think (a) you first have to read Goldberg on this, and (b) pay stricter attention to du Lion’s analysis of how much of the male/female difference is likely a cultural component and how much is likely innate. And in any case, Goldberg, and I, are mainly discussing adults. du Lion’s analysis is for younger people, yes; but the real differences pop in the extremes, which occur during adulthood.

    And even with the young-adults and kids that du Lion analyzes, the GGI is only slightly lower for countries with “low IQ”: from 0.66 average in the low IQ group to 0.77 in the high IQ group. Now, I won’t defend that GGI as an ideal measure, but that it changes so little, says something. And the cross-cultural analysis shows that in every instance the gap between m/w is there (even for Iceland).

    So does culture matter? Certainly: as Goldberg (and I) say, nobody disagrees with this. But it doesn’t matter completely. Any reading of the data shows that.

    And let’s also recall that we’re not just discussing mathematics, here, but m/f differences in behavior in general. Compile any “all time” list (physicists, playwrights, musical composers, philosophers) and calculate the fraction of women on that list. Of course, the “things might get better for women” statement is still, and always will be, true.

    But here is the kicker: if you agree that it was not better for women in the past, you have to explain why. Men’s domineering, threatening, hold-them-backness? Ok, I’ll accept that. Then it must mean, if that is true, that, since women, on average, have never been able to master this art of holding-them-backness, men at least excel at this and women don’t. And therefore we have demonstrated what was at issue: men and women evince different behaviors.

    And before I get accused: of course there are plenty, multitudes of instances where men have held women back, in many times and in many places. But they have not always done so in all times and at all places.

  20. 1) At 3 AM I wrote something here about F = F0(Δ, ρ) + α (1-GGI) + β (1-GGI)2 + γ (1-GGI)3 + O([1-GGI]4) , but when i reread it i was so tired I couldn’t make sense of it.

    2) Iceland isn’t even in his GGI data because he only uses the top 12 and bottom 12 PISA countries. Iceland was not in either group so it’s excluded. However if you look at the Gap Scatter figure (fig.4) Iceland is at -4/-14 which conflicts with your statement:
    “And the cross-cultural analysis shows that in every instance the gap between m/w is there (even for Iceland).”

  21. On “virtually everything measurable” men exhibit more variability than do women.

    It strikes me that there is an anthropological significance in this. Man has succeeded and populated the corners of the planet because of his adaptability. Now in order for a people to grow and thrive (before modern medicine) it was necessary to employ the genetic contribution of all of the women but only a portion of the men. If the men exhibited varying abilities (speed in the hunt, cleverness in trap-making, body more suited to a harsh climate) for coping with a new environment, a wider variability would enable a faster evolution of the essential skills for the entire group. Variability amongst the women would be less significant.

    This observation might have sociological significance today, although I doubt there will many social scientists motivated to study it.

  22. Maybe the exams in Iceland (where, I point out again, the boys still do better than the girls in math) are like this: “Boy, 15, gets an exam pass – just for using the bus“.

    Or like this one. Iceland, after all, is a very enlightened place.

    And then there is this story, where we have an academic sociologist displaying the fretting tendency:

    For comparison purposes, Bobbitt-Zeher divided majors into four categories: business; math, natural sciences, and engineering; education; and the social sciences, arts and humanities. Men are more likely than women to major in the first two categories and women more likely than men to major in the latter two.

    Bobbitt—dash—Zeher is nervous because of this “discrepancy.” She also worries because the former categories are more highly remunerated than the later two.

    Pay attention to the academic (no doubt tenured) “anthropologist” commenter who offers as evidence the guess that a female cop would not have arrested H. Gates. Non sequituriol fantasy, anybody?

  23. Matt:
    I could not resist commenting on the Inside Higher Ed article as follows:

    “I have monitored salary data by major since contributing to a National Science Foundation study of Engineers in the early 80s. The differences by major and differences by major over career are readily available. The relative rewards have not shifted in the last 25 years. On average they are vast. At the same time I am not surprised that students who are in the process of selecting majors do not know them. In many instances the salary information by major would generate significant cognitive dissonance among those who should be providing students with this information. I can hardly fathom how an English or Art History professor could talk to a student of average ability in their field without pointing out the low return they are likely to receive on their investment in their education. If there is any conspiracy, it is a conspiracy of silence on the part of those who do not provide those choosing majors with the basic realities of earning power based on major. It is on the same level of dubious ethics as the athletic recruiter who does not accurately state the probabilities of (a) career limiting injuries; (b) chances of earning a living as an athlete; and (c) consequences for success in a major that will match the athlete’s interests, capabilities and economic goals. It is like a doctor not revealing to a patient the chances of success of and the risks inherent in a procedure.

    “I would also reinforce criticism of the last comment about differences between men and women police officers. It is a silly, gratuitous and trivializing statement without any empirical basis. It raises in my mind questions as to the Professor’s critical thinking capabilities.”

    We will see if it gets posted.

    My guess is that if it is posted, it will lead to a series of fairly trite statements about the value of an education beyond it’s impact on earning power. But hopefully, unlike Prof Bobbitt-Zeher, I am open to being pleasantly surprised by comments from reflective practitioners to the effect that they are caught in a dilemma when it comes to advising students as to their major.

  24. Matt:
    To follow up and elaborate. I recognize that the above comment is a bit off-thread. I do think, however, that it addresses one of Goldberg’s important issues: the discussabillity of key issues that peope ho;d strong beliefs about. It is many years since I hung around a faculty lounge but I suspect starting salaries by college major is a subject one would not raise among liberal arts types basically for the reasons stated above.

  25. Speaking on the different variability of males and females, I remember from Arthur Jensen’s
    “Bias In Mental Testing”, that in the 1930s just about all of the school children in Scotland were tested. Using a “16″ IQ scale, the average for males and females was the same, but
    the standard deviation for males was 16.5, for females it was 15.5.

  26. I hate to keep bringing it up since it is only 1 of many parts of this topic, but i will so long as you keep posting wrong information. For both datasets, 2003 and 2006, girls in iceland performed better than boys IN MATH, as noted by the ability gaps -4 and -15 (approximations).

    “Each country that took part in both PISA years, 2003 and 2006, contributed a single point to the plot giving its gender math gap in both years. ” Fig. 4

  27. I wonder how Goldberg, Briggs or anyone would explain the finding that Asian American girls’ math scores are just as variable as boys. I know I will like all the answers to this question. :)

    “The facts that male mathematical advantage does not manifest itself on tests until adolescence…. Preadolescent boys and girls have the same (in)ability to grow facial hair; this does not imply that the adult males’ ability to grow a moustache is owing to social factors. “ ~S. Goldberg

    Who knows, maybe just maybe, the testosterone or other hormone could be shown important in the development of mathematical reasoning ability… I am trying to be open minded here. I wish Goldberg had discussed his perspectives based on the lower extreme, but then a statement such as “There are more extremely stupid men than women” sure is no consolation to me.

    Bernie, speaking of the earning power, I read somewhere that women have become the majority in veterinary medicine. One of the reasons is that a veterinarian is just not paid as much as other medical professions. I think men tend to measure their success in terms of their earnings, which could affect their career choices. Well, I thought one of the reasons was that women were just better at…. ^_^

  28. Feministsgive women a bad name.
    If anyone’s held me back, it’s me. I gave up maths at sixteen despite it being my strongest, being top of the class and it was my favourite subject.

    I would not argue with any observation of a decline in girl’s maths ability after puberty because I believe from my own experience that there is something interesting to learn about how our brains change around this age. It’s just a feeling I have always had and do remember starting to think differently.

    Bernie, your comment reminds me of a classmate at school who whilst waiting in the classroom with me pulled a very fat book off the shelf. She could read normal print up close with her nose touching the book. I can see her now looking through the contents at the list of careers by salary.
    “That’s what I’m going to be, an “actuary!” and laughed. What’s one of those, says I,
    “I dunno, but they get more money than anyone else, so that’s what I’m doing.” She is now a solicitor.
    Too late for me, I’d already chosen the daftest subjects.

  29. Joy:
    I am all for people making their own decisions on whatever criteria they want to use. However, I believe like the patient being told they need an operation that the teacher/career counselor/guidance counsellor/professor need point the person in the direction of something akin to the large book your friend had the good sense to use.
    By the way, being an actuary is pretty demanding so the fact that she ended up a solicitor is pretty good.

    As for your personal experience – my general belief is that in order to understand the dynamics of career and major selection decisioms, the correct unit of analysis are individual decisions just like yours. The Professor of Anthropology is going to add nothing to understanding the dynamics.

  30. Joy,

    Feminists give women a bad name?

    What does “feminist” mean to you? What is feminism really about nowadays?

    Where would you be today without feminism? Without the right to vote, educational rights, vocational rights and sexual rights…

    Many men consider themselves feminists who treat women as equals. It’s about equality, not sameness. Feminists are not feminazis. It’s unfortunate that some women rather accept the negative stereotypes associated with the word and willingly admit women are inferior to men in every way.

  31. I don’t think feminism is about anything worthy of attention in the civilised world. It is a gaping yawn. There are people who have real problems and who don’t complain. Always the ones who shout the loudest are in the best position to help themselves.

    The vote was the most important first step, the contraceptive pill had a much greater effect on women’s role in the workplace in my view. Obviously a medical breakthrough, not a result of feminist activism.
    What are sexual rights, seriously?

    Everyone has the same rights to an education, irrespective of sex and has never been otherwise. I have one man to thank for ensuring that I received the best secondary education in the country. I am grateful for that.

    “willingly admit they are inferior to men? Do you mean admit some sort of inherent advantage? That’s not a matter of admission, it’s a matter of fact in many areas.
    If you consider this is synonymous with inferiority then that’s where I would disagree. If a man told me he was a feminist I’d think he was after something! Or having a laugh.
    How about feminine role models? Who is there? Who are we supposed to want to emulate?

  32. I refrained from commenting on Z Berg’s post on the assumptrion that Joy would provide a more “legitimate”, full and appropriate response. I am pleased to say that I was right!

  33. I don’t think any of the “theory” espoused above contradicts my empirical assessment of fat, 40-ish women in the previous post.

  34. “…inherent advantage? That’s not a matter of admission, it’s a matter of fact in many areas.”
    “Or having a laugh.”
    “How about feminine role models?”

    You don’t seem to get my point or have any understanding of the history of the feminist movement. You only see the negative side of feminism, laugh at and doubt a man like me who shows support for equal status for women, and BELIEVE that men have an inherent non-biological advantage in many areas. Judging from what you said, you appear to have high pride but not a healthy self-esteem. I will not challenge you anymore. Be positive, be humble but confident, and have a happy life.

  35. Concerning Iceland and extremal variability .
    There is no difference between Iceland or Iraq or China or any other country or culture for that matter as far as the gender composition of math extrema is concerned .
    An excellent statistically significant sample of extremal behaviour are the Mathematical Olympics .
    All countries participate and the duration of the sample extends over 50 years .
    The participants are arguably the extremal mathematical performers of each country and they compare all to each other via an identical set of tests .
    Some observations :
    - more than 90 % of contenders are male . This is independent of continent , culture or race .
    - the best performers (medals) are also males with a percentage that exceeds their percentage in the overall population of participants .
    .
    As for Iceland :
    In 25 participations , the selections allowed 130 Icelandese participants out of which 117 male and 13 female .
    That makes a female percentage of about 10 % what is perfectly equivalent to the overall average as well as the average for any other country .
    On a particular note , this percentage (about 1 girl for 9 boys) didn’t significantly vary in 50 years .
    This shows that the extrema (in this case the top math performers) overrepresents males by a factor of about 9 and this factor is constant through all cultures , educational systems and time .
    A factor 9 is certainly significant enough .
    These facts strongly support the thesis of higher extremal variability for men and generalises it to any socio-cultural environment that could have been met on Earth over the last 50 years .
    .
    P.S for William
    Emmy Noether was indeed a genius . And it is not (only) me who says so but Einstein .
    About every physicists willl agree that the Noether’s theorems belong to the top 10 of most brilliant and beautiful pieces of research ever .
    Obviously despite the fact that she was jewish and woman in the Germany of end 19th century she was not prevented to do maths and do it very well what tends to show that if somebody is brilliant at something , he or she can always do it regardless of culture and environment .
    Sure it has not been easy for her but the intelligent men (in this case the Great Hilbert himself) were bound to notice her ability and helped her in all possible manners .

  36. Z. Berg:
    Whoaa! You have no data from any of the above to suggest that anyone here does not support equal status for women – if by that you mean equal rights, as opposed to equal outcomes. I have no idea what precisely is meant by an “inherent non-biological advantage”. If by that you mean something along the lines that by definition men have great cognitive aptitude for highly complex mathematics – I am not sure anyone has claimed anything beyond that which the data indicates. What I see the debate about is the possibility that inherent differences do exist and that it is legitimate to explore the facts. One stream of feminist ideology is that such questions and explorations are inappropriate. That is what Matt is highlighting in Goldberg’s books – which I have yet to read.

  37. John, According to du Lion’s Figure 3, only in 2003 were the girls in Iceland better than the boys. In 2006, the boys were better. (I wish that figure had a one-to-one line to make it easier to read.)

  38. Fig. 3 is presumably % gender [total PISA] scores over 5 and Fig. 4 is the gender gap of [PISA math].

    If this is not the case, it brings the entire (inaccessible from the website) data set into question since the data points are not the same.

    Figure 4. It plainly shows a gap of ~(-4 and -15) for MATH. Negative values for both 2003 and 2006.

    It doesn’t help that the figure legends are bad, the data isn’t linked anywhere, and the labels of the graphs are selective. Figure 4 is the worst actually because only one data point is labled and there are no units on the numerical values.

  39. Tom,

    Solving questions on the Math Olympiad exam does require high-level math and problem-solving skills. I accept the fact that there are more male Math Olympians. However, can we scientifically conclude, based on the top <<0.01% extreme group, that men have a higher math reasoning ability AND that the difference is rooted in physiological difference?

    Well, “Genius is 1% inspiration and 99% perspiration.” So, yeah, men do achieve a higher status because it’s been shown scientifically that men tend to produce more sweat than women. Maybe this is the physiology difference Goldberg was talking about. ^_^

  40. JH

    You will have noticed that I carefully used several time the words “extremal performance” .
    That means that we have a sample at one of the tails of the distribution .
    And this sample has a huge merit that it spans all races and socio-cultural systems over a long period of time .
    So obviously while it doesn’t allow any conclusion about AVERAGES (because average performers are not included in the sample) it demonstrates with a very high statistical significance (a factor 9 is not some small number) that at least one tail of the distribution largely overrepresents males .
    And this overrepresentation is the same for all environments – Icelandese as well as Chinese or Nigerians etc .
    So this fact indeed supports the thesis according to which males have a higher VARIABILITY in mathematical abilities , e.g a male has a higher probability to be VERY good in maths than a female .
    In other words the female distribution would look like a narrow gaussian while the male distribution would look like a broader gaussian , both gaussians may (but must not) have a similar average .
    To complete the symmetry it would be necesary to organise “anti math olympiad” where would be selected the WORST performers .
    Then it would be interesting to see if the males overrepresent the females by a factor 9 also in the worst math performers .
    If yes then chances are that the averages are similar if no then chances are that even in average the males would be better performers .
    The problem with the low end tail being that that here we would see a big environmental impact which doesn’t exist at the high end tail – obviously f.ex the percentage of children attending school would be the governing parameter of the low end tail . So it would be necessary to remove the environmental influence from the sample what would very difficult . Etc .

  41. Tom,

    I did notice that your comments were carefully worded. That’s why I asked you the question.

    I have found what I wanted to hear from you. One cannot conclude that, ON AVERAGE, men have a better inherent math/analytic ability based on the extremal performance. In my opinion, the two statements “men are better than women at math” and “men have a higher chance of exhibiting extreme brilliance” have totally different meanings and implications.

    I suspect that more women believe that men are better than women at math. I could be wrong and it won’t be the first time. Our society subtly genderizes, for example, quantitative cognitive styles as masculine and qualitative cognitive style as feminine. I don’t know how this genderization affects anyone, and what really matters to me is that my two smart daughters don’t think so! :)

    Thank you for your thoughtful response.

  42. JH,

    Actually, and by now not surprisingly, Goldberg has anticipated your comment about “genderizing” (he calls it “socialization”). He accepts that it might be true that we socialize men more than women in math, but this does not prove that men and women are equal, distributionally speaking, because we then have to explain why this socialization occurs. Is it because men are better (in the sense we have been using) at math, and that we all recognize it? Or it is entirely arbitrary? You can claim total arbitrariness, but then the burden is on you to explain the empirical results.

  43. Briggs, ooOh, I am patient and probably could live another 35 years or so. I shall inform you when the percentage of PhD degree in mathematics or statistics granted to female exceeds 50% in any year. In the mean time, please help me promote the “Smart Is Sexy” slogan. ^_^

  44. “I am patient and probably could live another 35 years or so. I shall inform you when the percentage of PhD degree in mathematics or statistics granted to female exceeds 50% in any year.”

    In continuation of the subject this is typically impossible because 35 years are not enough for some evolutionnary process to take place .
    PhD degrees are typically included in the “extremal performance” sample where men outnumber women by a factor 9 or so .
    As we have seen that this is independent of all imaginable external factors (like socio cultural environment , educational or political systems etc) it has internal causes of genetic and/or epigenetic origin .
    These internal factors may change (in either direction) but if they do , it takes a very long time .
    The only way to achieve such a result in a short time without natural evolution is by artificial constraints (e.g double standards) .
    But that would concretely mean that women’s PhD would be worth much less than men’s and people who pay money to obtain mathematical performance , would employ male PhDs rather than female PhDs .
    So in order to “fix” that , farther artificial constraints would be necessary .
    It is a devil’s circle where the only thing that would happen is destroyed value and nobody wishes to deliberately destroy value (intellectual or monetary) .
    However even if a scenario where a society deliberately destroys value has a low probability , it can’t be excluded – after all it already happened in the past and the communist societies are an excellent example .
    If what you describe ever happened in some subset of the societies within a short period of time , it would say more about the value management in this subset than about mathematical performances sorted by gender .
    Ah and this subset of societies would have to stop sending its mathematicians to the mathematical Olympiads because they would become a laughing stock of the rest of the world :)

  45. Z.Berg,
    All women have a different way of tackling the sexism that is part of normal life. Some have fun with it, some turn a blind eye, Nelson style.
    I happen to dislike the feminIST way. I find it rude, ungracious and demanding.

    When I come across sexism from men, I make a mental note that the individual is not as bright as they seem. If they cannot recognise a person for who they are and only judge by superficial markers then they are lacking in some important mental faculties, however good their maths skills. The opposite is also true.

    I don’t doubt that JH will live to see her 50% female PhD’s. I hope she does, but I believe that women can achieve this type of success by determination and resilience, both traits abundant in women. Essentially it is not a matter of whether women can achieve PhD’s but whether they want to. The PhD question is a different one to the extreme brilliance question. This does not mean it will come naturally to them. I speak of the narrow maths arena.
    When women have the grades or the ability and go in another direction there is something else at play there.

    The narrow topic on this post does not allow for deviation into subtlety. This does not make men better, or “more brilliant”, they are just different in my view. After all, the evidence presented concerns the tail-enders, and is shown to make the point about why more men than women appear at top levels in industry etc. That’s all.

    Of course we would never read on this blog about how men are the most violent, cruel, stupid, insane, narcissistic. This does not suit our aesthetic idea of “man”.

    The method employed by most wise women who you might call the “willing admitters” is simply to do what you were going to do anyway.

    To quote a very clever lady in her eighties who I was speaking to on Wednesday, about her life,
    “men don’t like a clever woman”…when men speak down to me or treat me like a silly old lady, I just think to myself, I had my day”. She was referring to her work which sadly I can’t divulge because it’s not my secret.

    However, here’s aleftist feminist misbehaving, and I love her because she doesn’t take herself too seriously.
    (and I’m with her on the curtains.)

  46. And the part about the bad men was the tail-enders at the other extreme. Of course this is not true of men as a rule. I Probably didn’t make that clear.

  47. Joy:
    Well, I do not think I am a “tail ender” on any of the dimensions you identified. But I do believe that Stephen Fry deserves to be seen as … He is extremely bright and very funny!

    Along somewhat the same lines you describe above, I have a strong reluctance to assign traits or characteristics to groups that are not actual or potential empirical statements, e.g., Football fans tend to engage in more fights and law breaking than Cricket fans. (Though if we win the Ashes in the next few days, I might be proven wrong!) I still believe that people act, not groups. I try to judge people by what they do, not by the group to which they ostensibly belong – I know many polite and law abiding football fans and a few obnoxious and loud cricket fans.

    It would be interesting to see the extent to which individuals who ascribe to many of Goldberg’s fads or fallacies have a “collective” versus “individual” mind-set.

    One interesting set of data comes from the Lemon-Sommers debate that Matt provided a link to. It is almost funny as the commenters begin to lose it when trying to respond to Christina Hoff Sommers criticisms of Nancy Lemon’s misuse of information and data on the tragedy of Domestic Violence (http://chronicle.com/article/Domestic-Violence-a/47940/).

  48. Joy, you’ve made my Saturday. I think I’ve gotten my point across.

    Tom, yes, my optimistic genes might be over-expressed… you are being a party pooper. Unlike our polite Miss Joy, I do resort to name calling. ^_^

  49. Bernie,

    Hope the men in my family who have all gone to the oval today don’t provide you with any reason to review your summary of cricket fans. I’ll watch on TV. My Dad’s wearing his panama.

    Also, given that I do think there are clear differences in the sexes, this makes non-sexism almost an impossible state for me or anyone. A point, I think,made elsewhere on this or another thread.

    Had missed Matt’s link but your summary is fair. It’s sad that these women have lost faith in the opposite sex. Some of them really sound neurotic. I am tempted to try and ‘help’!

    Lemon’s figures Smack of “unless we announce disasters no one will listen.” The thirty something percent is way off the mark, obviously. It must be more like a fraction of a percent of presentations.
    I have rarely, if ever, seen an acute case.

    Of the two hundred different people I saw in an eight-week period recently, there were two victims of violence. One was a boy of nine, the other, a six foot four thirty-something year old male who looked like he might be carrying something worth taking who was set upon by six black men with baseball bats ( from behind. They took everything he had. He came round with one of their feet on his head as they rummaged in his pockets. He ran in front of a car with an elderly couple in. As they were driving off, the assailants were chasing and trying to get in the car to finish him off. He had a head injury and was p-ing blood. (His Doctor said “You’ve got whiplash”.)

    The police know who they are but the fellow can’t pick them out of the line up because they were behind him, it was dark, and he has lost some memory. So, these fine specimens of “man” are still on the loose. They were after his blackberry. These are the other tail-ender types I had in mind, the Neanderthals.

  50. Joy:
    Nasty story. I am not sure I would hang around the Oval too much after dark – unless it has changed since I was a kid.

    As for the Lemon Sommers debate, I would add that many whose comments were from left field were (a) male and (b) from left field! And the latter is part of the issue. Though I would hasten to add that I think the misrepresentation of data is the hallmark of all political extremists.

    It sounds like you may have access to actual UK data on Domestic Violence? Matt was going to check some of his data sources since there are some questions on the data that “estark” presented. Evan Stark is apparently an “expert” but it is unclear as to the weight that should be given to his data.

  51. Sorry about that,
    Although I know some who have access to that data I’m not sure how forthcoming it would be.
    I only have my own clinical experience to go by. Of course cuts and bruises don’t make it to physio unless those have caused some other problem. So twenty-eight women required ‘major medical treatment’. I’m not sure what point the writer is trying to make there, but I would consider that a low number out of the original 218 in the study mentioned from August 1991.
    It would be interesting to hear about the other 190.

    Doctors Evan Stark and Anne Flitcraft, prominent researchers in this field, announced similar findings in their 1996 book Women at Risk: Domestic Violence and Women’s Health: “The initial conclusion of our research was that more women sought medical treatment for injuries resulting from domestic violence than for any other cause.” I don’t believe that. I think the quote is missing the words,
    “violent cause of injury.” Otherwise it seems to imply that domestic violence is more common that other types of injury. In which case, tell us something we didn’t expect or know already.

    There’s some dodgy misquoting which ought to be easily verified and checked from the original text, without even the need to argue about who said what or even looking at the data because aside from Lemon’s alarm and error in quoting, the numbers seem unsurprising.

  52. Joy:
    Your Dad must have enjoyed himself immensely.

    WRT Domestic Violence data, I agree there are missing words. The question is what led to the missing words and why the refusal to accept the fact that it was an error. Sommer’s primary point is that academics like Lemon and Stark repeatedly make mistakes that benefit their agenda and are averse to issuing corrections. I think Sommer wins the argument both on the actual facts and the fact that her opponents do not stay on point and resort to ad hominem arguments.

  53. Bernie,
    Thank you, he did. It was a surprise, he didn’t know until twenty to ten this morning!
    “They couldn’t have done it without us” he reckons.
    I agree on the Lemon Vs Sommer thing,I’ve given it some thought and there doesn’t seem to be a plausable excuse for Lemon.