Category: Politics

Why Feminists Are Bad at Math

The recent push to promote the notion of gender equality in mathematical aptitude, contrary to the overwhelming bulk of psychometric data, is itself ironically a demonstration of mathematical illiteracy. Just as it is horrible scientific practice to cherry pick studies indicating the desired result while ignoring all others, so it is terrible mathematics to make inferences about statistical variance from facts about the mean. Allow me to clarify.

Large-scale psychometric analyses have consistently found a stable discrepancy between males and females in cognitive test performance. The difference in the statistical mean or average is small, favoring men by about 2.5 IQ points according to the best analysis, but the most marked difference is not in the mean, but in the variance. There is significantly greater variance among males than among females. This means males outnumber females at both ends of the spectrum, so there are more male dullards and geniuses, a fact consistent with most people’s recollection of their classmates.

Distribution of general intelligence factor by sex; for math ability, the gender disparity is slightly greater, in both mean and variance.

The current Science study touting gender equality actually confirms that male variability in math ability is greater, by a factor of 1.11-1.21, consistent with results back in 1960 (variance factor: 1.20, mean difference 0.12 std dev, N=73,000 15-yr olds). This aspect of the study is downplayed by the media, even among scientific journals, since it leads to some politically undesirable facts.

As the authors of the Science paper admit, the gender discrepancy in variance means that at about two standard deviations above the male mean, there should be twice as many males as females. So if the threshold for performance in a science or engineering program was at two standard deviations above the mean, we should expect there to be twice as many males as females, based on mathematical aptitude alone. In reality, the most demanding physics and engineering programs only accept people three to four standard deviations above the mean, which would make the male to female ratio even greater, consistent with the 85%-15% male-female split in most top science and engineering programs. Harvard President Larry Summers made precisely this point in the infamous speech that cost him his job, at the instigation of feminist faculty who ironically displayed their own mathematical ineptitude.

All of this contradicts contemporary social dogma, yet is entirely consistent with common sense. It is far more credible that the consistent discrepancy in variability, seen across cultures and time periods, is the result of a real difference in aptitude rather than the product of discrimination. Indeed, gender stereotyping is more likely to take place in the home than at liberal institutions of learning, especially at the highest levels. If social factors were the cause of gender disparity, we should expect this to diminish as students progress to higher levels of university education, becoming further removed from their family’s influence and more engaged with socially liberal university culture. In fact, we see the exact opposite, as the gender disparity becomes more pronounced as students progress to higher degrees. Thus feminists are left with the absurd accusation that science and engineering departments are biased against females. Anyone familiar with university life should know better than to believe such nonsense, as faculty and administrators take special care to offer opportunities to females and minorities.

The disparity between male and female mathematical aptitude is barely noticeable at the median level. A little extra industriousness would be enough for females in the middle of the pack to perform equally with males in math class or even a bit better. In fact, in cultures where girls are academically industrious, we do see slightly better average grades for females in primary and secondary math class, probably owing to better study discipline, again consistent with common observation. However, at the highest levels, the aptitude disparity is too great for very many females to compensate with greater effort. The gifts of mental quickness and astute intuition are needed in order to do math at a high level with the facility required in a fast-paced working environment. The difference in gender variability may be used to calculate the expected male-female split among mathematicians in the National Academy, Fields medalists, and Putnam competition top performers. The computed values correspond closely with reality, comporting with the hypothesis that membership in these categories is indeed merit-based.

It is striking that the Science study still shows the same discrepancy in variability by gender, despite the fact that it uses the SAT, which was redesigned in 2002 to be less of an aptitude test and more of an achievement test. Verbal analogies were eliminated, since minorities performed poorly on these, and the math section now places less emphasis on speed and intuition, instead focusing on mastery of course material. This emphasis on achievement gives industrious females an advantage at the middle of the pack, accounting for the disappearance of the difference in mean, which still persists on true cognitive tests. Yet extra study is no substitute for genius, so there is still a pronounced gender discrepancy at the high end of SAT math performance, as the mathematically gifted can breeze through the exam with ease.

The only reason to protest these findings is political, not scientific. The gender disparity in math performance is no less well established than a reverse disparity favoring females at reading. No one questions the latter finding, in fact many feminists are proud to point to it, evincing their strange notion of equality. Similarly, race-based cognitive differences, which are even more pronounced than gender differences, even after controlling for socioeconomic status, are strictly taboo, unless perchance they are in favor of the supposedly oppressed minority.

This deep hostility to any finding that contradicts the contemporary myth of equality of aptitude across demographic categories is misguided. Gender- or race-based disparity in math and science aptitude is no cause for dismay or bigotry, if we understand what statistical statements about groups signify. We are making general statements about groups via statistical averages and variances; there will still be many individual women who do well in math and science, and even some geniuses. It would be a mistake to judge an individual based on that person’s demographic group; individuals are the basis of statistics, not the product of statistics. However, it is disastrous social policy to try to “correct” aptitude-based inequalities, not only because it results in unjustified accusations of discrimination, but because it may direct individuals away from the field they would have chosen for themselves based on their aptitude and inclination. Once outside of academia, graduates will find that performance is what matters, and they will be ill-benefited by having been protected or coddled by grade inflation or some other esteem-building measure to impose a false equality.

I understand that the desire to prove equality of aptitude by race and gender is motivated by the belief in the moral equality of all people, yet neither of these equalities implies the other. Even if we admitted that all races and genders were equal in every aptitude, with the same mean and standard deviation for all groups, we would still be faced with a real variation of aptitude among individuals within each group. What then of human equality? Does a genius have greater moral, social, or political rights than a dullard? If not, then it is clear that moral equality does not depend on equality of aptitude.

The confusion between equality of human worth and equality of ability can only come about in a society that values people primarily for their abilities. This instrumentalist notion of humanity, so unworthy of human dignity, can be a constant temptation for capitalist societies, where people are valued based on what they can produce. This perverse moral philosophy can be given a social Darwinist rationale, declaring that the only attributes with value are those that have some adaptive advantage. Only when we move beyond this crass instrumentalism will people be able to face their congenital inequalities with maturity and not be perturbed by them, nor use them as an excuse to lord over one’s fellow human being, for we have human worth for who we are, not what we can do.

Keeping and Bearing Arms: A Pre-Constitutional Right?

In the landmark case D.C. v. Heller, the U.S. Supreme Court has held that the Second Amendment right “to keep and bear arms” is an individual right. This reading is consistent with the unanimous sentiment of the late eighteenth and nineteenth centuries, as well as the language of the amendment. In a scholarly tour de force that dissects the Second Amendment grammatically, logically, and historically, Justice Scalia’s majority opinion argues that the purposive clause regarding a “well-regulated militia” cannot be construed as contradicting the operative clause: “the right of the people to keep and bear Arms, shall not be infringed.” He then eloquently shows the logical, grammatical and linguistic incoherence of the contrary interpretation, which would effectively mean that this right shall be infringed, even to the point of banning handgun ownership as in D.C.

Notwithstanding Scalia’s painstaking dissection of the issues, gun control advocates and leftist legal scholars have raised their usual canards when attacking a decision grounded in originalist jurisprudence. These themes include (1) accusing the originalist of judicial activism; (2) claiming that the Constitution has always been “dynamically interpreted;” and (3) complaining that the decision ignores “precedent,” usually some controversial twentieth-century activist decision that itself disregarded a century of prior precedent.

The laughable assertion by liberal journalists that the court majority is practicing “judicial activism” by virtue of striking down a DC statute betrays an ignorance that would shame some high school students. By that standard, anyone who supports Marbury v. Madison (1803) is a judicial activist. It is true that this decision might be considered “activist” by some hard-core originalists who do not accept “incorporatism,” the century-old doctrine that the rights enumerated in the Constitution also apply to the states by virtue of the Fourteenth Amendment. This doctrine allows federal courts to rule on whether local statutes violate constitutionally guaranteed rights. As mainstream liberals and conservatives alike accept this doctrine, that cannot be the basis for the accusation of activism.

Activism means more than voiding an unconstitutional state or local law, or prescribing some course of remedy, as such powers have been regarded as proper to the judiciary since the founding. The contrary of judicial activism would not be to uphold every state law, but to exercise “judicial restraint,” judging only whether the law is valid under the Constitution, not whether it is a good or bad policy. When a law is struck down because it is considered a bad law, even though it is constitutionally valid, we enter the realm of judicial activism. The archetype of such activism is Brown v. Board of Education, which did not even attempt a constitutional rationale, but was based on the supposed sociological effects of segregated schools. Miranda v. Arizona is another activist decision, prescribing a procedure of reading a suspect his rights, grounded more in the Court’s sense of fairness than in any constitutional requirement.

It would be hard to classify DC v. Heller as an activist decision, as the ruling makes no appeal to the prudence or justice of gun control laws, but judges only whether it infringes the Second Amendment right to bear arms. The majority opinion is not concerned with policy outcomes, but with establishing the construction of the Second Amendment text based on relevant historical and legal documents. One may disagree with the construction, but that does not make the decision remotely activist.

The accusation of activism is in any case insincere, as the same charlatans who complain that (1) the Court has departed from the meaning of the Amendment also claim that (2) we shouldn’t strive for original meaning, but accept that the meaning of the Constitution changes with time. Simultaneously holding both points is inconsistent and petty. Scalia presents evidence showing that the right to bear arms would have been worthless if it applied only to organized militia, since the federal government controlled the militia and the Bill of Rights was intended to restrain the federal government. Even without his exhaustive argument, the meaning of the Second Amendment should be obvious to anyone remotely familiar with the time, where the individual right to bear arms was widely assumed, and never contradicted. In 150 years of American jurisprudence, no one ever dared suggest that bearing arms was only a “collective” right; indeed, it was a symbol of free citizenship, and awarded even to blacks after their emancipation. Only those disingenuous enough to project their modern liberal views onto eighteenth-century men could deny the Court’s assessment of the original meaning of this right.

Opposing originalism is the idea of a “living Constitution” or “dynamic interpretation” or whatever Orwellian term one prefers to describe the position: “the Constitution means what we say it means.” If the Founders intended the Constitution to be easily changed in its meaning, it is hardly understandable why they took pains to make its amendment so difficult. Anyone familiar with the political philosophy of the time knows that a constitution was considered to be the most fundamental and least-changing aspect of a political state. Chief Justice Marshall likened constitutional interpretation to interpretation of a statute, and there certainly was no theory of dynamic interpretation of statutes current at the time. The law expresses the will of the legislators, which must be respected in its execution and interpretation.

The idea that the meaning of the Constitution changes (based on ideas of people who have read a little philosophy and understand even less) makes a mockery of written constitutions and laws; we would indeed be ruled by the arbitrary will of judges. What saves us from such tyranny is concern for original intention and meaning, which was the common approach of all jurists for most of this country’s history (read Justice Harlan’s dissent in Plessy v. Ferguson). The Constitution may be applied to different circumstances, and jurists may disagree as to how its principles apply to those circumstances, but the principles remain the same.

To be “progressive” often entails having a myopic view of history and contempt for the remote past. History before the social revolution is to be forgotten, except as an object of derision. After ignoring the unanimous sentiment of the eighteenth and nineteenth centuries, liberal scholars contend that the 1939 case U.S. v. Miller deserves a special reverence, disregarding all earlier jurisprudence. Even if such a legal theory were valid, it would not prove what they wish. Miller does not even attempt to construct the Second Amendment, much less did it define the right to bear arms to be a purely collective right. The brief ruling upheld the constitutionality of the National Firearms Act, requiring registration of firearms crossing state lines. No reading of the Second Amendment (not even that of Heller) would invalidate such a law. The Court even noted that the various States have different provisions for the right to bear arms, but “none of them afford any material support for the challenged ruling”.

The Court in Miller viewed the purposive clause of the amendment as defining the scope of arms to be borne. A ‘shotgun having a barrel of less than eighteen inches in length’ did not have any “reasonable relationship” to the legislative purpose of preserving a militia. Yet it does indicate, in its discussion of early American militias, that men were to purchase and maintain their own arms, so this is by implication an individual right, though it is granted for the sake of the common defense. Without debating the merits of Miller, we can see it falls short of denying an individual right to bear arms, though it does circumscribe that right by a “reasonable relationship” to the common defense.

Heller goes further, and includes a common law right of self-defense, citing Blackstone, as the basis of the right to bear arms. This ruling goes deeper than interpreting the Constitution, for it indicates that the rights enumerated in the Bill of Rights are prior to the Constitution, not granted by it. The right to bear arms belongs to the people, not as a gift from the federal government, but as something they held before it existed. The idea that civil rights are morally and temporally prior to the Constitution is an important step toward grounding American jurisprudence in something like natural law. Yet if Scalia scorns jurists who try to be moral philosophers interpreting natural law, he avoids this only by appealing to English common law tradition, which is our last link to the Catholic world and natural law theory, codified as an unquestioned given.

Cultural Amnesia and the Marriage Question

Four leftist judges in California have substituted their confused moral philosophy for judicial precedent and popular sovereignty in order to advance a nonsensical definition of marriage. This act reflects the ill-founded presumption that the Weberian state has the authority to re-define pre-existing institutions such as the family, from which the state’s own authority is derived. The absurdity of applying a twenty-first century leftist interpretation to a nineteenth-century constitution is lost among those who value the end over the means.

For the moment, let us not concern ourselves with the incoherence of liberal jurisprudence, nor with the usual arguments regarding same-sex attraction. The popular misconceptions surrounding these issues do not admit of a simple, pithy response, though at least one attempt has been made to summarize the relevant arguments from a Catholic and natural law perspective. Instead, I should like to turn attention to the extraordinary fact that most defenders of the California court’s decision seem to be wilfully unaware of the fact that this position was recently considered extremist even among liberals, yet no account has been made of the reason for this sea-change of opinion.

Only fifteen years ago, the idea of same-sex unions constituting a marriage in a sense fully equivalent to conventional marriage was not mainstream opinion, even among social liberals. Indeed, the anthropologist searches in vain for a precedent, finding at best some rites of friendship or clandestine practices. Even the numerous ancient societies that approved of homosexual acts did not pretend that this had anything to do with marriage, which was irrevocably tied up with the rearing of children. As recently as forty years ago, the weight of scientific opinion, even among atheists, was that homosexuality was a psychological disorder, and numerous case studies indicated that it could be cured. Of course, the classification of a behavior as a mental disease involves a normative moral judgment. As mores changed, so would the definition of health.

The de-classification of homosexuality as a mental disorder in the 1970s was likely a reflection of changes in attitudes toward sexuality rather than the result of any scientific breakthrough, since to this day our understanding of same-sex attraction remains rudimentary and speculative. The influence of social attitudes on scientific inquiry could be seen in the 1990s, when there were several premature claims to have found a genetic basis for the attraction, evincing a desire to find such a basis. Given the lack of scientific progress, and the further fact that most people are scientifically illiterate, we cannot invoke science as a primary reason for the recent sea-change in opinion regarding same-sex unions.

Changes in modern social mores are dictated by two main arbiters of propriety: the state and the cultural media. Church, family and ethnicity tend to conserve values rather than fabricate new ones, while the liberal state constantly creates new mores via legislation and judicial rulings, and the cultural media, especially through the verisimilitude of television and film, have the power to shape impressions about what is normal behavior. We have just seen the power of a compact judicial majority of four over three to dictate mores to a state of 50 million people. Television, film, and journalism have also shaped mores, thanks to the effective nullification of decency standards in the 1990s, promoting a progressively vulgar and sexually hedonistic ethos, in which there is, understandably, nothing remarkable about same-sex attraction.

To this day, the majority of male homosexuals have little interest in monogamous marriage, yet they have advocated this issue strenuously, in order to achieve their ideological goal of full equivalence with “traditional” marriage, or marriage as it has always been known. Already aided by leftist judges and the increasingly libertine media, some have sought to indoctrinate children via public schools. Some U.S. federal judges have actually ruled that parents do not have a right to be notified of such indoctrination, which includes explicit references to same-sex “marriage”. Unable to produce children in their sterile relationships, the more militant homosexuals and their defenders insist on the right to shape the mores of other people’s children.

This act of violence against the family is not peculiar to this issue, but reflects a broader presumption that the state has greater rights over a child than a family. The proper response to this assault on familial rights is to resist such forms of state control, with force if necessary, to make clear that the state is but a servant of the households that formed it. The state that loses sight of this fact deserves to be dismantled until it returns to its proper role in society.

Vast resources of the state and private media have been directed (though not always consistently) toward shaping public opinion in precisely the form it has taken, often using unscrupulous tactics to suppress contrary evidence. Yet this trick could never work upon people who have a cultural memory independent of what is served through mass discourse. For such people, it would not suffice to assent to some vague sense that this is the “modern” or “progressive” thing to do, without any notion of how we got here. Here we come upon the most stunning aspect of such social changes: the complete cultural amnesia that makes it possible to forget the state of affairs of only fifteen years ago.

Fifteen years ago, the West was socially liberal and highly literate, yet by no means advocated the current paradigm of same-sex unions that is now proffered as a standard of liberalism, rationality, and open-mindedness. To regard anyone who differs on this issue as a hidebound conservative evinces a breathtaking ignorance of the recent past, where one could be liberal, secular and rational, yet regard same-sex “marriage” as bunk. I recall the famous words of Cicero:

Nescire autem quid ante quam natus sis acciderit, id est semper esse puerum. Quid enim est aetas hominis, nisi ea memoria rerum veterum cum superiorum aetate contexitur?
– Cicero, Orator ad M. Brutum (XXXIV, 120)

Not to know what occurred before one was born, that is to remain always a child. For what is the lifetime of man, if it is not connected with the remembrance of the histories of previous generations?

I wonder what Cicero would have said of those who cannot even remember what happened in their own lifetime, but are so faddish that they must disavow memory even of their recent past. As Cicero observes, the importance of recalling the past is that our lives are irrevocably connected to and derivative of the deeds of our predecessors. In other words, we need to know the past in order to understand where the present came from. In this way, we could see through many of the rhetorical tricks and misdirections that would-be opinion-makers cast at us, for we could see that they are not grounded in any substantive rational or empirical development. Knowledge of the past keeps liars honest, for they must be forced to account for why what they say now differs from what they said yesterday. Who remembers that, in the early nineties, “gay rights” advocates would deny that they sought the right to marry, dismissing such claims as alarmist fear-mongering? Yet why should we be surprised if no one remembers this, or makes nothing of it, when we permit a president to re-invent his reasons for invading Iraq in a matter of months?

We cannot expect the mass media, or even liberal academia, to place much emphasis on the past, since that would divest them of their cultural authority. The manufacture of an ignorant yet educated populace has been the work of a hundred years, beginning with the elimination of the classics from grammar school, so that today most university graduates wouldn’t know Cicero from Adam. Yet, as time goes on, the horizon of our collective memory shrinks ever further, so that “modern” only means the last twenty years or so, often even less. We surrender this collective memory only at the expense of our sovereignty against the encroachments of the state and the shallow intelligentsia who do not wish us to learn how flimsy is their philosophy.