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