Update #1 at Bottom of the post.

Update #2: We have followed up with a briefer rejoinder here. PLoS Blogs has linked to both posts responding to the commentary by Ben Barres.

In my view, when faculty tell their students that they are innately inferior based on race, religion, gender or sexual orientation, they are crossing a line that should not be crossed - the line that divides free speech from verbal violence - and it should not be tolerated at Harvard or anywhere else. -- Ben Barres

Good god, not again! There's a current buzz in parts of the blogosphere about potential discrimination against women in science, initially sparked by a commentary letter (pdf, also available in our GNXP forum -- under the Frappr ad) to Nature by female-to-male transgendered Ben Barres, a professor of neurobiology at Stanford. It's mostly a rehash of the innate sex difference denial, an extreme viewpoint that is not only false, but by this point in time, annoying. We've covered the issue here at GNXP before (see here, here, and here), and in response to the Larry Summers fiasco of 2005, Steven Pinker debated Elizabeth Spelke here (slides which contain his references here; another list of relevant literature compiled by Pinker here in pdf form). As I consider this issue decided in favor of the camp that believes the contribution of innate biological factors is greater than zero, I won't waste any more space repeating what others like Pinker have already said; I'll consider them background reading. So then, let me turn specifically to the charges that Barres brings up, as well as some other points relevant to the debate but which Pinker did not specifically address in his debate or popular writings -- namely sex differences in personality that are relevant to scientific creation, as well as the nature of scientific creation itself.

Before getting to the hard data, allow me to voice my utter disgust for the exploitation of personal information in Barres' commentary, as well as in any other difference-denying writing. No readers of Nature, or any other journal, are interested in anecdotal evidence -- and given how brief the articles are in top-tier journals, even a single sidebar or consistent parenthetical musings constitute disproportionate allotment of space to the anecdotal compared to the data-driven. [1]

First, Barres defines the "Larry Summers Hypothesis," which he ascribes to Summers, Pinker, and Peter Lawrence, in this way: "women are not advancing because of innate inability rather than because of bias or other factors" (my emphasis). Already we've constructed a straw man, as none of these fellows, nor I, nor anyone else who believes innate sex differences play a role, assume that they are the only role, leaving no room for bias or "other factors." On the contrary, the claim is merely that innate factors are non-trivial, not that they account for 100% of the variance in career outcomes. He then proceeds to review irrelevant literature showing that the average test scores in math for males & females from ages 4-18 are the same -- in Pinker's debate against Spelke, he covers the relevant literature that addresses greater male variance, which leads to increasingly disproportionate male representation in both the upper and lower tails of the bell curve: "more prodigies, more idiots," as he says. And indeed, it's the far upper tail that we're interested in -- to become a tenured math prof at Harvard, no one cares if you can do long division; at a very minimum, they care about your ability to quickly solve those brain-teaser problems at the end of the SAT math sections (for example, if you take a grapefruit and make 3 slices all the way through it, what's the most number of pieces you could end up with?). [2]

However, not only does the different variance matter for IQ or some other measure of cognitive ability -- it matters for every single variable that is involved in eminence in the world of science. Here I reviewed the relationship between g and creativity / eminence (scientific or artistic) -- the punchline is that the distribution of eminence in science and art is log-normally distributed, meaning that whatever factors are involved interact multiplicatively rather than additively [3]. The difference, recall, is that in an additive mix of things, the components don't "see" or "talk to" the others, whereas in a multiplicative mix, the components interact in a "synergy," mutually enhancing each other. Subtract a high score on one variable from an additive mix, and the overall score isn't affected that much -- since all the pieces are working blind of one another's doings. Subtract a high score on one variable from a multiplicative mix, and the whole thing crashes since the pieces are mutually reinforcing -- as if a Miss Universe contestant had ideally proportioned eyes, full pouty lips, neotonous facial geometry, lustruous hair, pearly white teeth ... as well as boils encrusting the majority of her face. It's difficult for us to isolate each component feature, assign it a score, and then add them up (in which case this contestant might score quite high). Facial perception is more of a gestalt process, so we can't help but view it as a synergistic entanglement of features, and hence this contestant wouldn't stand a snowball's chance in hell of winning.

Now, the exact same thing applies to the factors involved in becoming a top scientist (or artist). First, and probably most important, is an IQ of roughly 125 to 130 (so, roughly +2 SD), and again males are overrepresented here due to greater variance. Francis Galton, the first modern psychologist to study genius, suggested that another key factor is a disposition for "doing a great deal of very laborious work" [4] -- slaving your butt off to discover or create something. In slide 25 of Pinker's debate, there is a convenient graph of how many hours per week a group of 33 year-old males vs females desired to work. They (n = 1,729) were pre-selected to have math skills in the top 1%. In the range of 60-69 hours a week, males outnumber females by about 2 to 1, and ditto for the range of 70+ hours a week. If for no other reason than that women on average are more likely to be wired to want to raise a family or take care of elder relatives, the biological contribution to this discrepancy in slavish commitment to work is non-trivial.

Another key personality trait, in the estimation of researcher of genius Dean Simonton [5], is the Big Five factor called Openness to Experience -- specifically, its lower-order facets called Openness to Fantasy and Openness to Ideas, which the Big Five manual describes, respectively, as: "receptivity to the inner world of imagination" and "intellectual curiosity." The other facets of Openness measure Aesthetics "appreciation of art and beauty," Feelings "openness to inner feelings and emotions," Actions "openness to new experiences on a practical level," and Values "readiness to re-examine own values and those of authority figures." The latter four may make one more cultured, in touch with one's feelings, willing to vacation in strange lands, and search for further moral improvement by questioning received moral values -- but surely "imagination" and "intellectual curiosity" are what matter for making a good scientist (though arguably Openness to Feelings would matter for artists in addition to Fantasy and Ideas). But is there any evidence of male advantage in these two facets of Openness? Indeed, that is exactly the case.

The best meta-analysis of sex differences in personality traits is Costa, Terracciano, & McCrae's (2001) review [6] (available in GNXP forum), which specifically measured differences in the Big Five factors and their facets, an improvement on Feingold's (1994) meta-analysis [7]. Across cultures (N = 21,642) and in the US (N = 1,000), males scored higher on Ideas (= "intellectual curiosity"), with a difference in means of roughly 0.165 SD outside the US and 0.32 SD inside the US. Now, "outside the US" is a big place, and their data show that the other Western, Individualist countries show differences quite similar to those of the US, with most of the non-Western, Collectivist countries showing differences under 0.2 (thus, considered "weak" effects). As for Openness to Fantasy, data from the rest of the world is quite weak, while in the US the male-female difference in means is 0.16 SD -- still considered "weak" but significant. In fact, the cross-cultural data are so consistent that the authors developed a new construct called "feminine Openness" which added the scores of Aesthetics, Feelings, and Actions, and subtracted the score for Ideas because it turns out the stereotype about women being more likely to explore their feelings and men more likely to explore ideas is true. And remember, we're really interested in the tails -- even a difference of 0.32 SD between means has a more appreciable consequence when we look at the level of people who are very intellectually curious. Let's operationally define "very intellectually curious" as 2 SD above the male mean (like "very intelligent" might be set at IQ 130). Then males would outnumber females by 2.2 to 1.

Moving on, another key personality trait (or traits) is mild psychopathology, not only on Simonton's (1999, 2004) account, but Eysenck's (1995), Rushton's (1997), as well as the whole tradition that views genius as intricately linked with madness [8]. Keep in mind we don't mean someone so schizophrenic that they're non-functional but rather someone with schizotypal traits who can still function -- in plain English, someone nutty enough to think up novel ideas or approaches but composed enough to develop them to fruition. In Eysenckian terms, the relevant trait is Psychoticism, which is likely the multiplicative result of the Big Five terms Agreeableness and Conscientiousness (namely, a person who is disagreeable and lacks conscientiousness). The Costa et al. meta-analysis shows that there are no appreciable cross-cultural sex differences in any of the facets of Conscientiousness; in the US, there are no differences except a weak one of 0.2 SD between men and women for Competence, which measures "belief in own self-efficacy" -- in the US, males score higher than females.

However, for Agreeableness, there is a significant moderate effect size at the factor level of 0.57 SD, where women are more agreeable than men across all facets. That means women will tend to excel as social workers, teachers, and in other professions that involve getting along well with others. But it also means that in careers that require a certain level of tough-mindedness, and often callousness towards the feelings of others -- say, when delivering criticism of another's work -- men will be at an advantage. Again, a scientist (or artist) can't be too much of a son-of-a-bitch to others, so let's define "tough-minded" as 1 SD above the male mean. Then men would outnumber women by 2.7 to 1. If we think "tough-minded" scientists should instead be 2 SD above the male mean, then men would outnumber women by about 4.5 to 1.

Next, top scientists and artists tend to be introverted rather than extraverted [9]. The Costa et al. meta-analysis shows a pattern in Extraversion similar to that in Openness, where the sex difference is at the level of facets: women score higher on Warmth "interest in and friendliness towards others," Gregariousness "preference for the company of others," and Positive Emotion "tendency to experience positive emotions;" while men score higher on Assertiveness "social ascendancy and forcefulness of expression" and Excitement Seeking "need for environmental stimulation." There is no sex difference in Activity "pace of living." The authors again develop the novel construct "feminine Extraversion" which adds the scores of the female-typical facets and subtracts the male-typical ones. This is particularly instructive as it gives a good measure of which facets of Extraversion matter for scientific or artistic achievement -- most of the work is more solitary (as opposed to a career in sales), despite the occasional chat, but in order to get one's voice heard (and thereby to somewhat boost one's self-confidence) one must be socially dominant rather than submissive. On this measure of "feminine Extraversion," Costa et al. found a difference of 0.25 SD between men and women in the US (again, similar figures hold for other Individualist countries, while in Collectivist countries the difference dwindles below 0.2). Again adopting the convention of 2 SD above the male mean (that is, preferring solitary work and remaining cool towards others, while being socially dominant), then men would outnumber women by 1.9 to 1.

Last of the Big Five is Neuroticism, and as with Agreeableness, there is a clear factor-level sex difference around the world: 0.55 SD difference between the US male and female means, with equal or higher figures in other Individualist countries, and more modest or even weak differences in Collectivist countries. This trait has to do with how prone one is to negative emotions, anxiety, depression, and so on, and I know of no studies linking it to scientific achievement. Presumably for scientists, a more emotionally stable temperament leads to greater success -- though this could well go the other way for the revolutionary scientists. Given how prone artists are to mood and affective "disorders" [10], this would actually be a strength in artistic creation. Let's say for science the optimal level is exactly the male mean -- not incredibly stable but not very unstable either. At this level, men would outnumber women by 1.7 to 1. (For poets, though, the optimal level might be 2 SD above the female mean, in which women would outnumber men by 4.2 to 1.)

As an aside, let's note that the Costa et al. and Feingold meta-analyses thus thoroughly refute Barres' lazy claim that "There is absolutely no science to support this contention," i.e. "that women are more emotional than men." Women across cultures are score significantly higher on all facets of Neuroticism and are more Open to Feelings. What Barres should have said in noting, correctly, that most violent crimes are committed by men, is that men are more likely to behave violently when something pisses them off -- as shown by the cross-cultural tendency for men to score significantly lower on Agreeableness -- not that they're more emotional (we already saw that they are more Open to Ideas). He also dismisses the notion that men are more competitive on average, suggesting that such a sex difference wouldn't matter anyway because he believes "powerful curiosity and the drive to create sustain most scientists far more than the love of competition." I quite agree. But we already saw that if we define "power [intellectual] curiosity" as 2 SD above the male mean, there would be more than twice as many men as women. And as Pinker pointed out in he debate against Spelke, citing the Benbow et al (2000) study of mathematically gifted youngsters, the variable of "inventing or creating something" was more important to males than females [11].

Barres then claims that most of the reason why female scientists leak out of the pipeline is due to lack of self-esteem -- perhaps, but a National Science Foundation study [12] found that females more than males were likely to report dissatisfaction with their doctoral field, explaining that they felt pressured into the sciences by others and felt the need to respect these others' wishes rather than follow their own desires. And if lack of self-esteem, despite equal qualifications as a confident male, were the root of the problem, that predicts that females could never make any headway into the sciences, arts, or professions at all -- rather than the reality in which, once the artificial barriers were removed, they flooded in, even if not constituting 50%. The same could be said for Ashkenazi Jews -- though anti-Semitism is largely absent in the top levels of Anglo society today, earlier in the 20th Century and before, Jews suffered not just discrimination but vilification as well. And yet, rather than be crushed by lack of self-esteem, they poured into the arts, sciences, and professions at a rate far disproportionate to their number in the population [13].

Incidentally, Barres himself notes that after his 10 years of testosterone treatment, three salient consequences have emerged: "my spatial abilities have increased," largely losing "the ability to cry easily," and being able to "complete a whole sentence without being interrupted by a man." Perhaps it is this trio of better spatial reasoning (important in scientific problem-solving), increased emotional stability, and increased social dominance that led a faculty member of his to remark that, "Ben Barres gave a great seminar today, but then his work is much better than his sister's.” Barres is under the impression that spatial abilities and personality traits couldn't make much of a difference in the quality of work one produces as a scientist, but as we've seen, that's not the case. Maybe his new work really has, in part, benefited from his more male-typical profile, a hypothesis he doesn't see fit to entertain.

Returning to the data, to get an idea of how such tail-end sex differences, together with the multiplicative rather than additive nature of scientific eminence, can have drastic consequences when mixed together, consider the following crude illustration. We actually don't know how strongly weighted each of the variables is -- well, we're sure IQ matters more than Neuroticism, but does Openness matter more than Extraversion, and if so how much? Let's assume they all are equally weighted, and see how the moderate male advantages in each variable "percolate up" to the top when we consider the whole mix. Moreover, let's put IQ aside for the moment and just consider the differences in the desire to slave away at work and the four personality traits that show sex differences. In an additive scenario, we could just add up the male to female ratios (again, just a crude way of looking at it): conservatively, 2 + 2.2 + 2.7 + 1.9 + 1.7 = 10.5. Now instead, multiply them and get 38.4. This conveys how a synergistic scenario creates skew that would favor males even more than a non-interactive scenario would. Remember we left out the male advantage in the high-tail of the IQ distribution, so more realistic account would skew it more for scientific careers -- obviously, women would be favored in a career that requires one to be Agreeable, Neurotic, femininely Extraverted, and femininely Open to Experience (teaching?).

Returning to our Miss Universe contestant, if each of 4 facial features is scored from worst to best as 0 to 4, the distribution of total scores in an additive scenario would range from 0 to 16 and would be roughly normal, while they would range from 0 to 256 in a multiplicative scenario and would be highly skewed -- crucially, she could score perfect 4s on 3 features but a detestable 0 on the last one, making her total score 0. Lykken et al. (1992) call such traits that are close to all-or-nothing, requiring interactions among many independent traits, "emergenic" [14]. The population geneticists will see this as a new word for epistatic interactions among genes, and this is likely the reason why the progeny of top-caliber scientists and artists (say, Nobelists) tend to be rather mediocre scientists or artists at best, on average, leagues below their parent. As far as purely additive effects of genes go (say, just considering IQ), the children will tend to regress toward the mean, and so be noticeably above-average in IQ (though still less so than their parents). But for traits that require one to luck out in the epistatic lottery, the regression toward the mean is rather fierce since failing to meet the threshold for just one of the component traits will produce near nil results.

So the question now is to what extent are these traits due to genetic and other factors? I won't rehearse the by now large behavior genetic literature which shows that all personality and cognitive ability traits are moderately to strongly heritable, where additive genetic variance (or the "narrow-sense" heritability) is typically around 0.35, non-additive genetic variance (such as epistasic variance) is typically around 0.15 (making the "broad-sense" heritability ~0.5), shared environmental variance (what's typically called "nurture" -- anything that two siblings reared together would share) is typically around 0 to 0.05, with the rest comprising non-shared environmental variance and errors of measurement [15]. Judith Rich Harris has already done a fine job synthesizing the literature and offering her own interesting viewpoints in The Nurture Assumption and No Two Alike [16].

Hopefully, the arguments and references from Pinker's debate, as well as the above discussion, have built the case for biological factors accounting for a non-negligible portion of the variance in outcomes in scientific careers. But that still leaves open the question of whether bias operates also -- well, does it? Let's look at the specific claims that Barres makes, aside from the purely anecdotal or self-serving (such as MIT professor Nancy Hopkins heading the very inquiry board investigating her claims of discrimination -- can someone say "conflict of interest?"). The only hard data he mentions is a study done in Sweden on potential sex discrimination in awarding of post-doctoral grants. In his words: "one study found that women applying for a research grant needed to be 2.5 times more productive than men in order to be considered equally competent (Fig. 2)." Oddly enough, Razib here at GNXP blogged on this awhile back.

But first, notice what Barres leaves out: any descriptive statistics -- he leaves the impression that the authors of the Nature sex bias study had access to thousands of data points on post-doctoral grants, whether from a single study or by conducting a meta-analysis. In reality, the study only looked at the awarding of just 20 post-doctoral grants, 16 of which went to men and 4 of which went to women. Four words folks: lack of statistical power! As Razib pointed out, the claim that women would have to be "2.5 times more productive" than equally qualified men to be judged equally competent commits the authors to a reductio ad absurdum proof that their model is dead wrong. It makes the prediction that, in addition to the already insane quality of work a male would have to generate to get funding, females would have to generate either an extra 3 Nature or Science articles or 20-30 articles in the top journal in a specific field. That's all but impossible to accomplish in the same amount of time, and thus women shouldn't be getting funding or professorships at all! Moreover, the authors were unable to determine whether the sex of the judge correlated with whether they favored a male or female applicant.

A better gender-blinding study (pdf) was conducted in the US in 1999 to see whether the hiring practices for psychologists at two different levels -- first-time job applicants and those being awarded tenure -- showed sex bias [17]. The CVs for job applicants and tenured profs were identical, with only stereotypical male & female names making the difference. The sample size included 238 judges, both male and female, and the authors, who are at pains to uncover insidious discrimination, conclude that there was no difference in how males and females were judged for the tenured prof position, though males were favored over females for the entry-level position -- but both male & female judges showed this favoring. As the Larry Summers debate is over the top tier of the science world, it's really the datum on tenured profs in this study that merits attention, and there was zero evidence of sex bias. The favoring of males over identical females at the lower level could be parsimoniously explained by the judges' using Bayesian reasoning to infer that the females are more likely to burn out and leak out of the "science pipeline" at the earlier stages, and so are a less safe bet when all other data is the same. Once we reach the late stages, though, the judges may infer that the tendency to burn out should have already manifested itself, and therefore males and females are equally safe bets.

One source of potential bias that I find more credible, and which Pinker moots in his debate against Spelke, is that the tenure process makes ridiculous demands on women at the stage in their lives when their biological urges are pushing them to start a family, raise children, or look after other family members. Men in their 20s or early 30s, however, might find it easier to single-mindedly focus on their career over potential family concerns. This suggests a possible fix: namely, tweak the tenure process so that women aren't penalized for wanting to follow any desire they may have for family relationships. But again, this can't be the only source of the "leaky pipeline," for if biological factors weren't involved, then the degree of leakiness should track the degree to which females in particular fields desire to have children and take after their family. So, the prediction would be that female psychologists are the least likely to focus on family, biologists more so, and physicists & mathematicians are the most likely to want to start a family. To my knowledge, there is no data establishing this pattern, and it certainly goes against the typical disposition of the average scientist in these fields -- surely it's psychologists who show greater interest in other people, feelings, and family, and not physicists or engineers.

Nevertheless, I should temper this proposal for making the tenure process more family-friendly by noting the costs -- every choice has both costs as well as benefits. One cost would surely be the drop in quality of the woman's scientific output -- indeed, it would impact a man's output as well, should he have to face the same crisis. The reason is simple: in the most mathematical and abstract sciences such as physics and math, scientists tend to make their first major contribution in their late or mid-20s, respectively; their seminal contribution in their late 30s; and their final major contribution in their early 50s [18]. A likely explanation for this ruthlessly ageist pattern compared to, say, geoscience, is that original research in math and physics makes a greater demand on an individual's fluid intelligence (Gf), or the raw pattern-discerning / abstract reasoning ability, as contrasted with crystallized intellgience (Gc), or the store of ideas accumulated by applying one's reasoning skills to particular problems and disciplines. (g is considered isometric with Gf [19].) So, physics and math are fields in which one doesn't progress by having to read thousands of several-hundred-page books filled with words, but instead by doing difficult reasoning gymnastics through fewer books and articles made up of fewer words. Still difficult, but it doesn't take as long to digest the relevant background material. Simonton (2004) relates the following witticism from physicist and former Lucasian Professor Paul Dirac:

Age is, of course, a fever chill
that every physicist must fear.
He's better dead than living still
when once he's past his thirtieth year. [20]

For example, Dirac won the Nobel Prize in Physics in 1933 when he was only 31 years old, the work which won him the prize having begun when he was just in his mid-20s at Cambridge! Einstein's extraordinary year papers on the Photoelectric Effect, Brownian Motion, Special Relativity, and Matter-Energy Equivalence won him the 1921 Nobel Prize in Physics -- he was just 26 when he published these four seminal papers in 1905. I'll leave it to the reader to check how much their favorite Canonical poet, painter, or composer had accomplished by their 30th year, to show that this pattern is not restricted just to top scientists. The upshot of all this is that delaying a scientific career in a field that makes demands on abstract reasoning, or apparently in an fine arts field as well, brings quality costs as well as the benefits of following one's desire to start a family. Moreover, let's say this hypothetical female scientist "drops out" of full-time, slavish work for roughly 10 years (whether dropping out altogether, or doing only occasional part-time work). That's 10 years of work that could have been done, just in sheer quantity, regardless of quality. And as strange as it may seem, the best predictor of how eminent a scientist will become is the sheer quantity of output -- in the real world, those who produce the best also produce the most, though clearly that means they produce a lot of ignored work as well [21]. Again, if an individual faces the dilemma of whether to plow full steam ahead in science / art or to delay doing so to start a family -- regardless of whether this person is male or female -- it's up to them to decide how to trade off the competing goods. But it's clear that choosing a family will have non-trivial consequences for quantity and quality of lifetime output, which is what the tenure committees should focus on the most, assuming they want to hire the best and most promising individuals.

A possibility worth considering is acknowledging largely biological differences between men and women that predispose the latter to want to start a family more than the former, as well as the blow this would deal to their future careers as scientists, but presenting them with research that suggests that their personal happiness is unlikely to skyrocket, or even increase, once they start a family. To be sure, having raised a family gives one the sense of satisfaction to see the children grown up and ready to strike it on their own in the world, as well as the happy memories of their childhood that we tend to remember more selectively than the miserable ones. Yet on a day-to-day level while the kids are actually growing up, a mother's happiness actually declines, reaching a nadir when the children reach adolescence [22] -- a sure shock to anyone who's raised kids through adolescence without killing them, or to anyone who's honestly reflected on how undeservedly bratty they behaved toward their parents during adolescence. Happiness only reaches it's pre-child-rearing level once the kids have gone off to college.

So, a partial solution could be to present bright, motivated female scientists with this research, which they can digest and decide how to respond. Maybe some will say, "OK, so day-to-day happiness goes down the toilet for 18 years -- but I want to look back when I'm older and have fond memories, a sense of fulfillment, and so on, so I'll take family over maximizing scientific output." Some, though, might say, "Wow, nuts to rosy retrospection in old age -- full steam ahead in my science career!" These latter could still enjoy the good parts of being around kids by volunteering with youngsters, becoming a godmother, and so on, without having to change diapers or be yelled at to "Get outta my room, Mom!" Now, the right thing to do here is present all the evidence in an unbiased way and let the individuals decide their own course of action according to their own temperaments -- a rather different approach from that of the gender warriors whereby fence-sitting women are all but badgered into feeling ashamed for having let down their gender in the crusade to stick it to The Man.

Lamentably, Barres ends with an exhortation to "enhance leadership diversity in academic
and scientific institutions" -- in other words, quotas. Open the doors to anyone who's qualified and motivated, and let the chips fall where they may. And as we've already seen in the Steinpres et al (1999) gender-blinding study of how judges would award tenure to hypothetical candidates, neither male nor female judges showed a preference for men or women, and even at the lower-level of first-time applicants, the female as well as the male judges preferred men. Therefore, simply increasing the number of females would do nothing in itself -- what Barres must have in mind, therefore, is to inflate the number of gender warriors in powerful positions to rig the outcomes in advance rather than render disinterested appraisals. Perhaps this is what is meant by his suggestion for "special hiring strategies"? As already discussed, his seemingly commonsense proposal that "merit be decided by the quality, not quantity, of papers published" runs into trouble with reality, as sheer quantity of output is the best single predictor of a scientist's rank in eminence.

So, to recapitulate: the contribution of biological, partly genetic, factors to the sex disparity in science is greater than zero, and likely substantial since the variables are multiplied rather than added together. Thus, we're not talking about overlapping normal distributions when we talk about scientific research -- we're talking about overlapping log-normal distributions, where the weak or moderate male advantages in the component normal distributions (e.g., for IQ above 130, for Openness to Ideas, the male-typical pattern of Introversion, etc.) are compounded and thus skew the distributions even more. However, that doesn't mean women will be absent, just underrepresented. The source of these weak or moderate male advantages are partly genetic, partly due to non-shared environmental factors, but not at all to shared environmental factors. For this reason, we can label the causes as "intractable," comprising both genetic and chance factors in development. There is no clear evidence of irrational sex discrimination at the highest levels of science, although one could argue that the way tenure is structured discriminates indirectly against those who want a family, who are overwhelmingly women. Still, modifying the tenure system would bring costs of quantity & quality of output, along with whatever benefits it might also bring for increasing sex diversity. Equal opportunity should be given to all, and the only differences in outcome that show up should reflect underlying statistical differences in talent and temperament between the sexes. And last, but perhaps most importantly, honest discussion cannot proceed when gender warriors like Barres label contrary viewpoints as "verbal violence," and neither should participants indulge whatever desire they may have to focus on the personal rather than the data-driven.

Update by Darth Quixote: I do not have access to the study cited as Figure 1 in Barres's commentary. You can read what GC has to say about it in the comments. But it is clear to me that at best this study is an outlier with respect to a now-massive body of evidence on sex differences in mental abilities. For analyses of relevant (and typical) data, see these two pieces (this and this) by La Griffe du Lion. The most recent results that I know of, an analysis of sex differences in the Minnesota Study of Twins Reared Apart (Johnson & Bouchard, 2006), also clearly bear out the consensus; note the extremely large male advantage on tests of mental rotation. Another very recent paper by Arden and Plomin (2006) confirms the greater male variance in mental test scores. I also urge readers to check out an analysis of the 2000 Program for International Student Assessment (PISA) on p. 232 of the Handbook of Measuring and Understanding Intelligence: the Varimax-rotated principal component scores on the reading achievement portion of the PISA favor females in all 29 countries; the Varimax-rotated PC scores on the math achievement portion favor males in all 29 countries; and the Varimax-rotated PC scores on the science achievement portion favor males in 28 countries (in Iceland females come out on top by 0.01 standard units).

For whatever it is worth, the lead investigators of the papers that I have cited (the psychometrician Wendy Johnson and the behavioral geneticist Rosalind Arden) are both women. End of update.


Notes:

[1] To illustrate the pointlessness of navel-gazing: the summer before my senior year of college, I did my student internship at my school's laboratory for child language acquisition, a field which, as Pinker notes in his debate, is dominated by women. While other guys were striking it rich high-fiving their frat dude buddies in Wall Street investment banks, or else soaking up the sun hitting on topless girls in South Beach, there I was in a windowless basement room for hours transcribing videotapes of a mother and infant linguistically interacting. But I find precocious baby babble to be cute, so I didn't mind. Of the 7 or 8 people working on this project (from undergrad up to tenured prof), I was the only male. My senior year, I took two upper-level seminars on child language acquisition: one that focused on theoretical connectionist modeling, and another that focused on empirical studies of how children develop linguistically. All four participants in the former seminar were male, reflecting the greater male interest in machines and doo-hickies, while in the latter seminar, only 2 of the 14 or so participants (including me) were male, reflecting the greater female interest in people and children in particular. Now, I could write up this personal anecdote as an article, ascribing this state of affairs to discrimination against males in child language acquisition -- no doubt unconscious and not deliberate, but persistent and insidious nonetheless -- but I would be wrong. I would also be wrong in assuming that anyone else cared, a point that eludes others.

[2] Pretend the answer didn't jump out at you (it didn't for me anyway). If we start simply, take a 1-dimensional line -- if we make 1 cut, we can end up with 2 1-D pieces. If we take a 2-D circle and make 2 cuts, we can end up with 4 2-D pieces if we make the cuts perpendicular to each other (and just 3 pieces if we made the cuts parallel). So, when we move to 3-D grapefruit, the pattern should continue -- we make 3 cuts, but they should be perpendicular to maximize the number of pieces, as we learned with the circle. That makes 8 3-D pieces. (The apparent pattern is that if we make n cuts through an n-sphere, we can produce at most 2^n chunks.) It's this sort of "figuring out weird, unfamiliar stuff by analogy or sequence pattern" that matters more for doing real science than the mere ability to repeat back what your math teacher taught you by solving a problem that's exactly like what you've practiced a gajillion times in class before the test.

[3] Shockley (1957). On the statistics of individual variations of productivity in research laboratories. Proceedings of the Institute of Radio Engineers 45, 279-90.

[4] Galton (1869), Hereditary Genius: an inquiry into its laws and consequences. London: Macmillan. Quoted in Simonton (1999). Origins of genius: Darwinian perspective on creativity. New York: OUP.

[5] Simonton (2004). Creativity in Science: chance, logic, genius, and Zeitgeist. Cambridge: CUP.

[6] Costa, Terracciano, & McCrae (2001). Gender differences in personality traits across cultures: robust and surprising findings. J of Pers and Soc Psych 81(2), 322-331. Available in pdf form in the GNXP forum.

[7] Feingold (1994). Gender differences in personality: a meta-analysis. Psychol Bull 116(3), 429-56.

[8] Eysenck (1995). Genius: The natural history of creativity. Cambridge: CUP. Rushton (1997). (Im)pure genius--intelligence, psychoticism, and creativity. In Nyborg (Ed.), The Scientific Study of Human Nature: Tribute to Hans J. Eysenck at Eighty (pp. 404-21). New York: Elsevier.

[9] Cattell (1965). The scientific analysis of personality. Baltimore: Penguin. A group of "eminent researchers" he studied using his 16 PF personality questionairre showed a tendency to be unsociable, emotionally stable, dominant, brooding, undependable, bold, sensitive, trusting, radical, self-sufficient, and self-disciplined. Also, Simonton (1999), Ch. 3. The literature on information-processing and Extraversion is reviewed in Ch. 12 of Matthews, Deary, & Whiteman (2003). Personality traits, 2nd Ed. Cambridge: CUP. On p. 343, their Figure 12.4 synthesizes the cognitive strengths and weaknesses of introverts and extraverts, suggesting that the real-world contexts that extraverts are best suited to are "Dating and mating" and "'High-pressure' occupations," while introverts are best suited to "Artistic/literary/scientific occupations." Presumably "high-pressure" refers to jobs like sales.

[10] For a (not necessarily exhaustive) compilation of top scientists and artists alleged to have suffered from Schizophrenic, Affective, and Personality disorders, see Table 3.1 in Simonton (1999), p. 96. His lengthy list of references for this catalogue is on p. 253, under the bolded heading "Empirical findings."

[11] Benbow, Dubinski, Shea, & Eftekhair-Sanjani (2000). Sex differences in mathematical reasoning ability at age 13: their status 20 years later. Psychol Sci 11(6), 474-80.

[12] Strenta, Elliott, Matier, Scott, and Adair (1993). Choosing and leaving science in highly selective institutions: General factors and the question of gender (Report to the Alfred P. Sloan Foundation). New York, NY: Alfred P. Sloan Foundation. Cited in Ch. 3 of National Science Foundation, Women, Minorities, and Persons with Disabilities in Science and Engineering: 1998, http://www.nsf.gov/statistics/nsf99338/.

[13] Murray (2003). Human Accomplishment: The Pursuit of Excellence in the Arts and Sciences, 800 BC to 1950. New York: HarperCollins.

[14] Lykken, McGue, Tellegen, & Bouchard (1992). Emergenesis: genetic traits that may not run in families. Amer Psychol 47, 1565-77.

[15] Eaves, Heath, Neale, Hewitt, & Martin (1998). Sex differences and non-additivity in the effects of genes on personality. Twin Research 1, 131-137.

[16] Harris (1998). The nurture assumption: Why children turn out the way they do. New York: Free Press. Harris (2006). No two alike: Human nature and human individuality. New York: Norton.

[17] Steinpreis, Anders, & Ritzke (1999). The Impact of Gender on the Review of the Curricula Vitae of Job Applicants and Tenure Candidates: A National Empirical Study. Sex Roles 41, 509-528.

[18] Simonton (1991). Career landmarks in science: Individual differences and interdisciplinary contrasts. Dev Psychol 27, 119-130.

[19] Gustafsson (1988). Hierarchical models of individual differences in cognitive abilities. In Sternberg (Ed.), Advances in the psychology of human intelligence, vol. 4 (pp. 35-71), Hillsdale, NJ: Erlbaum.

[20] Originally reported in Jungk (1958). Brighter than a thousand suns (J. Cleugh, Trans.). New York: Harcourt Brace.

[21] Simonton (1997). Creative productivity: A predictive and explanatory model of career trajectories and landmarks. Psychol Rev 104, 66-89.

[22] Walker (1977). Some variations in marital satisfaction. In Chester and Peel (Eds.), Equalities and inequalities in family life (pp. 127-39). London: Academic Press. Cited in Gilbert (2006). Stumbling on happiness. New York: Knopf.