It is remarkable that any one could read my commentary "Does Gender Matter?" and conclude that I said that there are not innate differences between male and female brains. Nothing could be further from the truth.

It is certainly not remarkable given the content of your article, which included many passages which referred to innate differences (and the proponents thereof) in disparaging terms, yet included no citations whatsoever to the voluminous literature on innate differences between male and female brains (Box 1 -- the only place where even an indirect nod is made to this research -- contains anecdotes, not citations). For example:

Barres: Last year, Harvard University president Larry Summers suggested that differences in innate aptitude rather than discrimination were more likely to be to blame for the failure of women to advance in scientific careers...Lawrence draws from the work of Simon Baron-Cohen4 in arguing that males are 'on average' biologically predisposed to systematize, to analyse and to be more forgetful of others, whereas females are 'on average' innately designed to empathize, to communicate and to care for others....I am suspicious when those who are at an advantage proclaim that a disadvantaged group of people is innately less able....there is little evidence that gender differences in maths abilities exist, are innate or are even relevant ...The comments of Summers, Mansfield, Pinker and Lawrence about women's lesser innate abilities are all wrongful and personal attacks on my character and capabilities...Mansfield and others claim that women are more emotional than men. There is absolutely no science to support this contention...There is no scientific support, either, for the contention that women are innately less competitive...

And on and on it goes. Almost every sentence in which the word "innate" appears is surrounded with dismissive, disdainful context. Both careful and casual readers alike could be forgiven for believing you to be rather hostile to the idea of innate differences between male and female brains.

But for the sake of argument let us agree that you do (now) grant that there are significant innate differences -- inborn differences -- on average between the genders, not just in terms of hormonal levels and secondary sexual characteristics, not just in terms of hardwired sexual preferences and physical strength, but also in terms of neurological properties and behavioral traits.

Your position, then, is that though such differences exist that they are *immaterial* to anything of importance regarding scientific or mathematical output. That is, brain differences between genders exist -- they just can't affect anything in the real world of importance, such as the likelihood of becoming a scientist (not to mention a construction worker or a nursery school teacher). It doesn't matter whether women are shown to have better verbal abilities on average than men or whether men are shown to differ from women by a full SD in average 3D visualization ability...all of this is ostensibly immaterial to the question of what professions they might choose to pursue.

This sort of airlock between theory and practice is reminiscent of the way fundamentalist Christians separate their use of antibiotics from their antipathy towards evolution. Somehow you wish to accept modern neuroscience -- complete with manipulation of sexual behavior in fruit flies and brain imaging of gender differences in cognition -- while walling it off from any real world relevance. As you say:

there is no convincing evidence that these innate differences are relevant to women's ability to advance in science.

So let's rebut this claim directly. For the sake of brevity, I will focus on one point.
Again from the original article:

Barres: there is no evidence that sexually dimorphic brain wiring is at all relevant to the abilities needed to be successful in a chosen academic career. I underwent intensive cognitive testing before and after starting testosterone treatment about 10 years ago. This showed that my spatial abilities have increased as a consequence of taking testosterone.

So, spatial abilities increase as a consequence of taking testosterone -- one of the biggest biochemical differences between males and females. Is it really plausible to state that spatial abilities are irrelevant to mathematical ability? Or that the ability to manipulate CAD/CAM drawings, to develop statistical visualization algorithms, and to calculate rotation matrices are irrelevant to scientific and engineering progress? The literature indicates otherwise:

Importance of Assessing Spatial Ability in Intellectually Talented Young Adolescents: A 20-Year Longitudinal Study

Proficiency in spatial ability has long been associated with success in cognitively demanding educational tracks and occupations such as engineering, architecture, physics, chemistry, and medical surgery...strong abilities in these areas are salient characteristics of physical scientists. Gardner (1993) agrees and suggests "it is skill in spatial ability which determines how far one will progress in the sciences" (p. 192). Others have made similar observations (Hedges & Nowell 1995; Humphreys, Lubinski, & Yao 1993)...Wide agreement exists that spatial ability distinguishes group membership and performance in cetain artistic, engineering, and scientific disciplines.

Utility of predicting group membership and the role of spatial visualization in becoming an engineer, physical scientist, or artist.

This article has two themes: First, we explicate how the prediction of group membership can augment test validation designs restricted to prediction of individual differences in criterion performance. Second, we illustrate the utility of this methodology by documenting the importance of spatial visualization for becoming an engineer, physical scientist, or artist. This involved various longitudinal analyses on a sample of 400,000 high school students tracked after 11 years following their high school graduation. The predictive validities of Spatial-Math and Verbal-Math ability composites were established by successfully differentiating a variety of educational and occupational groups. One implication of our findings is that physical science and engineering disciplines appear to be losing many talented persons by restricting assessment to conventional mathematical and verbal abilities, such as those of the Scholastic Aptitude Test (SAT) and the Graduate Record Examination (GRE).

Gender differences in advanced mathematical problem solving.

Strategy flexibility in mathematical problem solving was investigated. In Studies 1 and 2, high school juniors and seniors solved Scholastic Assessment Test-Mathematics (SAT-M) problems classified as conventional or unconventional. Algorithmic solution strategies were students' default choice for both types of problems across conditions that manipulated item format and solution time. Use of intuitive strategies on unconventional problems was evident only for high-ability students. Male students were more likely than female students to successfully match strategies to problem characteristics. In Study 3, a revised taxonomy of problems based on cognitive solution demands was predictive of gender differences on Graduate Record Examination-Quantitative (GRE-Q) items. Men outperformed women overall, but the difference was greater on items requiring spatial skills, shortcuts, or multiple solution paths than on problems requiring verbal skills or mastery of classroom-based content. Results suggest that strategy flexibility is a source of gender differences in mathematical ability assessed by SAT-M and GRE-Q problem solving. Copyright 2000 Academic Press.

Moreover, the male-female difference on this particular variable (spatial visualization) is one of the largest on any mental test known to date:

Sex Differences in the Brain, Scientific American, May 13 2002

In examining the nature of sex differences in navigating routes, one study found that men completed a computer simulation of a maze or labyrinth task more quickly and with fewer errors than women did. Another study by different researchers used a path on a tabletop map to measure route learning. Their results showed that although men learned the route in fewer trials and with fewer errors, women remembered more of the landmarks, such as pictures of different types of buildings, than men did. These results and others suggest that women tend to use landmarks as a strategy to orient themselves in everyday life more than men do.

Although it used to be thought that sex differences in problem solving did not appear until puberty, the accumulated evidence now suggests that some cognitive and skill differences are present much earlier. For example, researchers have found that three- and four-year-old boys were better at targeting and at mentally rotating figures within a clock face than girls of the same age were. Prepubescent girls, however, excelled at recalling lists of words.

Sex differences in visuospatial ability: do performance factors play such an important role?

This study was designed to analyze some performance factors as a possible source of sex-related bias in psychometric tests of visuospatial aptitude. Goldstein, Haldane, and Mitchell (1990) explored the effect of two response styles-slowness of performance and reluctance to guess-by using a 3-D mental rotation test (the task showing the largest cognitive sex difference) and found that time limits and raw scores contributed substantially to the male advantage. We applied two tests in the speed-power continuum to a representative sample of 621 males and 821 females in their last year of high school in a 2 x 2 (gender x time) full factorial design. Reluctance to guess was similar for males and females. Males obtained more correct responses on both tests, and for both time conditions, than did females. These results are not only statistically significant but also are of substantial practical consequence.

And at least part of the molecular mechanism is known -- namely testosterone:

Sex hormones affect spatial abilities during the menstrual cycle.

The aim of this study was (a) to show that different measures of spatial cognition are modulated by the menstrual cycle and (b) to analyze which steroid is responsible for these cognitive alterations. The authors collected blood samples in 3-day intervals over 6 weeks from 12 young women with a regular menstrual cycle to analyze concentrations of estradiol, progesterone, testosterone, luteinizing hormone, and follicle-stimulating hormone. The performance on 3 spatial tests was measured during the menstrual and the midluteal phases. A significant cycle difference in spatial ability as tested by the Mental Rotation Test was found, with high scores during the menstrual phase and low scores during the midluteal phase. Testosterone had a strong and positive influence on mental rotation performance, whereas estradiol had a negative one. These results clearly indicate that testosterone and estradiol are able to modulate spatial cognition during the menstrual cycle.

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The point of all these references, in sum, is this:

1) spatial visualization ability is one of the largest average cognitive differences between men and women
2) this cognitive difference is known to be at least partly based in biochemistry (namely testosterone)
3) and reams of literature support the fact that such ability is a strong predictor of scientific ability in general.

Hence this is but one of many known sex differences in the brain which are partially responsible for the observed pattern of sex differences in professional choices. I should probably reiterate at this point that stating that A and B have *different* inclinations and aptitudes is clearly *not* equivalent to stating that A is "inferior" to B.

Note also that the references cited above are but a drop in the ocean of literature on this topic; I have specifically limited my remarks here to sex differences in spatial visualization and their consequences for professional choices, one of the most cut & dried issues in the sex difference literature -- a cut & dried issue whose manifest relevance to scientific achievement you nevertheless deny.