Science. It Works. #11

Theodore P. Hill published a paper entitled An Evolutionary Theory for the Variability Hypothesis. The abstract reads:

An elementary mathematical theory based on “selectivity” is proposed to address a question raised by Charles Darwin, namely, how one gender of a sexually dimorphic species might tend to evolve with greater variability than the other gender. Briefly, the theory says that if one sex is relatively selective then from one generation to the next, more variable subpopulations of the opposite sex will tend to prevail over those with lesser variability; and conversely, if a sex is relatively non-selective, then less variable subpopulations of the opposite sex will tend to prevail over those with greater variability. This theory makes no assumptions about differences in means between the sexes, nor does it presume that one sex is selective and the other non-selective. Two mathematical models are presented: a discrete-time one-step statistical model using normally distributed fitness values; and a continuous-time deterministic model using exponentially distributed fitness levels.

Such mathematical theorizing was too much for activists and so Theodore Hill has now written an article about how his paper was sent down the memory hole: Academic Activists Send a Published Paper Down the Memory Hole.

In the highly controversial area of human intelligence, the ‘Greater Male Variability Hypothesis’ (GMVH) asserts that there are more idiots and more geniuses among men than among women. Darwin’s research on evolution in the nineteenth century found that, although there are many exceptions for specific traits and species, there is generally more variability in males than in females of the same species throughout the animal kingdom.

Evidence for this hypothesis is fairly robust and has been reported in species ranging from adders and sockeye salmon to wasps and orangutans, as well as humans. Multiple studies have found that boys and men are over-represented at both the high and low ends of the distributions in categories ranging from birth weight and brain structures and 60-meter dash times to reading and mathematics test scores. There are significantly more men than women, for example, among Nobel laureates, music composers, and chess champions–and also among homeless people, suicide victims, and federal prison inmates.

Darwin had also raised the question of why males in many species might have evolved to be more variable than females, and when I learned that the answer to his question remained elusive, I set out to look for a scientific explanation. My aim was not to prove or disprove that the hypothesis applies to human intelligence or to any other specific traits or species, but simply to discover a logical reason that could help explain how gender differences in variability might naturally arise in the same species.

I came up with a simple intuitive mathematical argument based on biological and evolutionary principles and enlisted Sergei Tabachnikov, a Professor of Mathematics at Pennsylvania State University, to help me flesh out the model. When I posted a preprint on the open-access mathematics archives in May of last year, a variability researcher at Durham University in the UK got in touch by email. He described our joint paper as “an excellent summary of the research to date in this field,” adding that “it certainly underpins my earlier work on impulsivity, aggression and general evolutionary theory and it is nice to see an actual theoretical model that can be drawn upon in discussion (which I think the literature, particularly in education, has lacked to date). I think this is a welcome addition to the field.”

The bold sentence highlights the fact that Hill is merely hypothesizing a mathematical model to account for the GMVH, he is not trying to prove the GMVH.

Once we had written up our findings, Sergei and I decided to try for publication in the Mathematical Intelligencer, the ‘Viewpoint’ section of which specifically welcomes articles on contentious topics. The Intelligencer‘s editor-in-chief is Marjorie Wikler Senechal, Professor Emerita of Mathematics and the History of Science at Smith College. She liked our draft, and declared herself to be untroubled by the prospect of controversy. “In principle,” she told Sergei in an email, “I am happy to stir up controversy and few topics generate more than this one. After the Middlebury fracas, in which none of the protestors had read the book they were protesting, we could make a real contribution here by insisting that all views be heard, and providing links to them.”

You already know the Intelligencer ultimately backed down despite the tough talk.

Sergei Tabachnikov, Hill’s co-author, faced intense pressure from Penn State’s Women In Mathematics (WIM) chapter. We are told:

A female colleague had then instructed Sergei that he needed to admit and fight bias, adding that the belief that “women have a lesser chance to succeed in mathematics at the very top end is bias.”

As noted above, the original paper was not an argument in support of the GMVH. But if it was, the proper response is to challenge the GMVH with evidence and reason, not accuse the authors of bias. Hill’s request for constructive feedback from WIM was left unanswered. Also note there is no concern that if the GMVH is true men have a greater chance than women of scraping the bottom of the barrel.

Hill goes on to say that the National Science Foundation (NSF) requested the acknowledgment of NSF funding be removed from the paper. Tabachnikov’s Penn State colleagues had worked behind his back:

However, a Freedom of Information request subsequently revealed that Penn State WIM administrator Diane Henderson (“Professor and Chair of the Climate and Diversity Committee”) and Nate Brown (“Professor and Associate Head for Diversity and Equity”) had secretly co-signed a letter to the NSF that same morning. “Our concern,” they explained, “is that [this] paper appears to promote pseudoscientific ideas that are detrimental to the advancement of women in science, and at odds with the values of the NSF.”

Once again, the paper was not an argument in support of the GMVH. But I think it is worth noting that the truth of the GMVH is quite relevant to what “diversity” and “equity” proponents want to achieve. Perhaps the reality of the matter is that only 30% of high-end mathematicians can be women (this number is purely hypothetical). If that’s the case then attempting to make 50% of high-end mathematicians women is an unachievable goal that will waste time and resources.

As noted above, you know the Mathematical Intelligencer folded.

But, that same day, the Mathematical Intelligencer‘s editor-in-chief Marjorie Senechal notified us that, with “deep regret,” she was rescinding her previous acceptance of our paper. “Several colleagues,” she wrote, had warned her that publication would provoke “extremely strong reactions” and there existed a “very real possibility that the right-wing media may pick this up and hype it internationally.”

. . .

She replied that she had received no criticisms on scientific grounds and that her decision to rescind was entirely about the reaction she feared our paper would elicit.

And so now the “right-wing media” will broadcast the existence of this paper far and wide and also note the cowardice of academics. Apparently the “left-wing media” doesn’t care about scientific integrity.

At this point, faced with career-threatening reprisals from their own departmental colleagues and the diversity committee at Penn State, as well as displeasure from the NSF, Sergei and his colleague who had done computer simulations for us withdrew their names from the research. Fortunately for me, I am now retired and rather less easily intimidated–one of the benefits of being a Vietnam combat veteran and former U.S. Army Ranger, I guess. So, I continued to revise the paper, and finally posted it on the online mathematics archives.

Keep examples like this in mind when you’re told how scientists advocate for free inquiry for the truth. True open-minded thinkers at Penn State would have countered the paper with rational argument, not threats to a man’s career. Also note how calls for “diversity” and “equality” can conflict with the search for the truth. And don’t be surprised if standards need to be lowered to achieve “diversity” and “equality”.

Hill continued trying have his paper published. It looked like the New York Journal of Mathematics (NYJM) was going to publish it, but then they backed out too. Amie Wilkinson, senior professor of mathematics at the University of Chicago and wife of NYJM editorial board member Benson Farb, who sabotaged the publishing of the paper in the Mathematical Intelligencer, struck again. Half the NYJM editorial board threatened to resign and harass the journal until it died unless the paper was pulled. And so the paper was pulled.

Cases like this will and should lead the general public to be skeptical of consensus findings in fields like differences between the sexes, differences between races, sexual orientation, transgenderism, and other fields whose results may not be politically correct.


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