September 30, 2018
Eric Rasmusen, [email protected]
Last revised: October 7, 2018
The Ted Hill Male Variability Paper that the Math Journals Suppressed
One lesson my field, game theory, teaches is how useful it is to put yourself in the place of someone else and try to figure out what they should do to maximize their objective function given their possible actions, available information, and prior beliefs. Another idea much used in mathematics, economics, and philosophy is to look at extreme cases to better understand real, more moderate, situations. Let’s try applying those ideas to the Ted Hill Male Variability Affair.
First, let’s go over the situation.
Retired Georgia Tech math professor Theodore Hill put together an evolutionary model of the male variability regularity with Penn State’s Sergei Tabachnikov. [1] The model explains the well-known regularity that human males (and males of many animal species) are more variable in their traits than females, using the idea that if all females find mates but not all males, male genes ought to “roll the dice” because being a moderately attractive is no better than being entirely unattractive, but a small chance of being highly attractive is better than either. The male variability regularity is one explanation for why there are so many more men than women who are math professors, though the particular evolutionary explanation would not seem relevant to that. They submitted the paper to Mathematical Intelligencer, an outlet mainly for expositions of existing ideas. Editor Marjorie Senechal (of Smith College, retired) accepted their article for the Viewpoint column, which is “for any issue of interest to the mathematical community. Disagreement and controversy are welcome.” The publication process went as far as the article being sent to India for typesetting. Then feminists found out and started exerting heavy pressure. These feminist included University of Chicago math professor Amie Wilkinson, her father, statistician/psychologist Leland Wilkinson, and many people at Penn State, Tabachnikov’s department. The National Science Foundation, having heard from some enemies of the paper (Penn State’s WIM administrator Diane Henderson, Professor and Chair of the Climate and Diversity Committee” and Nate Brown, Professor and Associate Head for Diversity and Equity, as Hill later discovered using a FOIA request), asked that Tabachnikov remove his thanks to the NSF for support of his research. Tabachnikov then asked that he be removed as co-author. Finally, Editor Senechal rescinded her acceptance for fear that “the right-wing media may pick this up and hype it internationally.” She proposed instead “to convene a Round Table to discuss and debate the VH hypothesis per se, including the authors’ toy model, and publish the proceedings in The Mathematical Intelligencer.”[2] Hill was very unhappy with this, though he discussed how such a Round Table might be organized and offered to personally provide $10,000 in funding. [3]
In Act Two, Igor Rivin, one of many people with the title “editor” at the well-respected online journal, the New York Journal of Mathematics (the NYJM), heard about the paper and asked Hill if he’d like to submit it to his journal. He quickly got two referee reports (rather than the usual one), which were favorable, and checked with the chief editor for approval (which was highly unusual and not required of editors at Rivin’s level). The paper was published online. Amie Wilkinson’s husband, Benson Farb, was also on the editorial board of the NYJM and heard about this. He and other editors threatened to resign and blackball the journal unless the editor-in-chief retracted the paper. The paper was removed from the website and replaced with another of the same length without explanation to Hill or the public. Amie Wilkinson mounted a Facebook campaign against Rivin, telling her “Facebook friends” they had to unfriend him or she’d unfriend them.
In Act Three, Hill tried to find out what happened. He is a West Point man and a Vietnam veteran who, like Igor Rivin, is well-known in mathematics for his eccentricity. Hill also has a special interest in the federal FOIA (Freedom of Information Act) and state Open Records acts. He found out that Amie Wilkinson was acting behind the scenes and formally requested that the University of Chicago discipline her, which the University refused to do. He wrote a long article in the online magazine Quillette laying out the affair, and then posted 41 pages of emails and other supporting documents on the Web. Amie Wilkinson and Benson Farb posted short statements denying they did anything wrong. Three well known mathematicians, Timothy Gowers (Cambridge, Trinity College), Terence Tao (UCLA) and Andrew Gelman (Columbia) posted about the affair in their blogs, talking about it in reasonable tones but generally being more critical of Hill than of Wilkinson. Their comment sections filled with pushback, which Gowers and Gelman engaged with but Tao did not. Mathematicians Lior Pachter (Cal Tech) and Igor Pak (UCLA) also blogged, Pachter heavily critical of Hill and Pak with a lengthy essay on proper behavior of journals in the abstract, but without directly applying it to this affair. And so here we are.
http://rasmusen.org/papers/hillmath1.png
To fully understand the situation, one must also understand this diagram. [4] It shows two distributions of mathematical ability. The horizontal axis is a person's ability, with the average taken as 0, so -2 means the person is worse than average at math. The vertical axis is the number of people in the population, so the peak at 0 means what's most common are people of average ability. Suppose women followed the red distribution and men the blue, so they both have the same average ability, but men are more variable. Then there would be hardly any women with abilities of less than -4 or more than +4. If it takes ability of at least +4 to be a math professor, would expect to see hardly any women math professors. The Hill paper is not about measuring the variability of math ability in men and women, just about why males and females in animal species and humans might have different variabilities. Nonetheless, it is related to an idea that would explain the small number of female math professors in a way that displeases many people.
Nobody disputes that Hill’s model is mathematically correct, or accuses him of plagiarism. What is in dispute is
(a) Whether the model is so distant from reality as to be useless,
(b) Whether he should have related his model to the existing biology theoretical literature (not just the empirical literature), where the basic idea is well known,
(c) Whether any model of evolutionary biology would be appropriate for Mathematical Intelligencer or the NYJM, and
(d) Whether the model, even if valid, would have pernicious social consequences such as discouraging women from becoming professional mathematicians.
So much for background. Let’s now apply the “extreme case” technique. Consider two hypotheticals.
Case 1. John Doe submits an article to a math journal that purports to be a theoretical model of male variability. It is, but it also conceals within it a coded message to Neo-Nazis saying that Hitlerism will rise again. His plan is to get the article published and then to disclose the code, so everybody will see that this reputable journal has endorsed Hitlerism. The editor of the journal does accept the paper, which contains no mathematical errors. The editorial board finds out. What should they do?
In Case 1, I think it right to retract the paper, even though it has no errors. The author intentionally deceived the editor about the most important feature of the paper. The editor himself should want to retract it, and if he didn't, the board of editors would be justified in forcing him to retract it and in firing him if he continued in his refusal.
Case 2. John Doe submits an article to a math journal that contains a theoretical model in which employers reject a black job applicant over a white job applicant when both appear exactly equal except for race, but are justified in doing so if they want to employ the best candidates, regardless of race. This article will give comfort to racists if they read it. The editor accepts the article, which contains no mathematical errors. The editorial board finds out. What should they do?
In Case 2, I think it would be wrong to retract the paper, even if the board of editors believed it would have pernicious social consequences. In my own field of economics, a large number of papers have potential social consequences and editors will normally disagree with the policy implications of many of the papers they publish, perhaps even most of the papers. My own belief, for example, which is not unusual and perhaps is the consensus, is that the great majority of theoretical papers on monopoly could easily be misinterpreted and misused by policymakers, because most of them deal with special situations and find flaws in markets that would only be made worse if the government tried to remedy them, even if an ideal government composed of economics professors might possibly use them to make good laws. But scholars should publish ideas even if some people might misuse them. Scholars should not suppress the truth because they think the public should believe "noble lies". We should not imitate the Roman Catholic Church, which until roughly 1900 looked dimly on vernacular translations of the Latin Bible and discouraged Bible reading by the laity for fear the laity would misunderstand what they were reading and be led into heresy.[5]
Case 2 is a good example because it is a real one. It describes the idea of "statistical discrimination". Suppose ability is not directly observable, but the average black has lower ability than the average white. Employers observe indicators of ability such as education and experience, but these are not 100% correlated with ability. Bayes's Rule tells us that with the prior that the white applicant has higher ability and the signals that both applicants are equal, the posterior must be that the white has higher ability.
Statistical discrimination is a well-known idea in economics. I remember that I came across it on my own when I was a young scholar and wondered, trembling, if I dared publish it. Then I found everybody knew it already. It isn't clear who came up with it first. It is usually attributed to Edmund Phelps, whose 1972 paper in economics's top journal, the American Economic Review, was titled "The Statistical Theory of Racism and Sexism." Phelps won the Nobel Prize in Economics in 2006. The Economics Prize is for a scholar's entire body of work, not just one discovery, but that article is his second most highly cited, with 3,625 cites in 2018 (his most-cited paper, with Richard Nelson, is a 1966 AER paper on education and innovation, with 4,939 cites). Kenneth Arrow (Nobel winner in 1972) had a 1972 paper with the idea, as did John McCall and Melvin Reder, top economists at big-name schools.
I don't think any economist would say that these papers on statistical discrimination shouldn't have been published. Statistical discrimination is a valid mathematical theory, a simple one, to be sure, but we in economics believe simplicity in a theory is a feature, not a bug. Obviously, for application it is important (a) whether the average ability of blacks differs from whites, (b) the extent to which observable indicators are correlated with ability, and (c) whether there are alternative factors at work such as racial animus and government regulation. But the idea is a useful one, and has implications far beyond racial discrimination.
I think Amie Wilkinson, Benson Farb, and Leland Wilkinson would disagree with me, though, about whether Phelps’s paper should have been published. I'd be interested in their reaction. I wonder what Andrew Gelman, Terence Tao, and Tim Gowers would say. They all have good math blogs on which they've discussed the Hill affair in a moderate tone, but with a clear preference for Wilkinson over Hill. I’m sure they wouldn’t like it if the American Economic Review retracted the Phelps paper. Would they say that the journal shouldn’t have published it?
Case 3.
Now let’s return to the Hill case, but in a version where I speculate beyond what we know--- so you may wish to treat this as a hypothetical too, because my Case 3 narrative is conjecture. Suppose Hill wrote his paper because he wanted mathematicians to be conscious of the male variability regularity as one explanation for why there are so few female math professors. The pattern is part of biology rather than mathematics, so he wrote up a mathematical model explaining why we'd expect to observe such a pattern.
Suppose Mathematical Intelligencer’s editor Marjorie Senechal agreed that mathematicians should be conscious of the idea, and even suggested to Hill that he play up the math-department implications of his model. Suppose NYJM editor Igor Rivin agreed too, as did the chief editor of NYJM, and, besides, they were outraged at Hill's treatment by Senechal. If that is true, then at both journals the purpose of publishing the paper was to bring the attention of the profession to an already-known empirical regularity more than to propose a mathematical explanation of that regularity. At Mathematical Intelligencer, the opposition was from people who did not want mathematicians to be aware of the regularity; at NYJM it was not only that, but also because its other editors believed the journal should not publish applied mathematical models, only pure theory.
But we don’t really believe the fuss was about the applied nature of the article or its irrelevance to mathematicians. I doubt even the most infuriated of the editors would have threatened to resign over say, an article using differential equations to model mortgage-backed securities. Moreover, the very existence of this controversy shows that mathematicians care more passionately about male variability than they do even about ergodicity and prime numbers. The reason people were outraged was not that they thought it was too removed from what mathematicians care about, but that they disagreed with its implications for hiring.
A better argument is that NYJM should not have accepted the paper because even though it is of great interest to mathematicians, the NYJM is not the appropriate outlet because it is more about the mathematics profession than mathematics itself. It is like a paper giving a new methodology for ranking math departments, the kind of paper that would attract far more readers than most math articles, but only because of its real-world implications. Such papers get published in top journals in my field routinely, but math’s customs don’t have to be the same as economics’s.
Anyone who makes this argument, however, has to say what math journal is appropriate. Mathematical Intelligencer, the first journal Professor Hill thought of, immediately comes to mind as appropriate. But I doubt that the people at NYJM who threatened to resign were saying, “This isn’t appropriate for NYJM: it should be published at Mathematical Intelligencer.” If they were, they would have been outraged at Mathematical Intelligencer’s retraction and would have said so in their own retraction.
[6]
This also applies to Amie Wilkinson, whose statement implies that she didn’t suggest that the paper be retracted, only that it be published with a response.
[7]
Why, in her statement, doesn’t she call on The Mathematical Intelligencer to hold the proposed Round Table and publish Hills’s article with rebuttals (and supporting comments too), now that the NYJM doesn’t want it? Or, there’s another way the NYJM could have dealt with the paper. If the other editors thought Rivin accepted a paper containing gratuitous political points they could require the author to remove them. The Hill paper is mainly a theoretical, mathematical, model. If the introduction, literature survey, and conclusion digress to irrelevancies, simply ask the author to reduce the length of those sections. Keep the math and discard the applications. But this is premised on the idea that the editors object to the paper on the grounds that its subject matter is inappropriate. I’m afraid a more likely explanation is that they thought was correct but would make people think that discrimination against women is not a problem in math departments, so the bad guys will win instead of the good gals. A lie is much less awkward than a truth that hurts your side, because you can't refute it. Thus, we may here have an application of Lenin's principle of "Kto, Kovo?", "Who will beat whom?", but is often applied to the identity-politics idea of looking to see who is on which side of an issue to decide which side you’re going to say is right.
[8]
“Tout est politique,” “Everything’s political,” says Marxian philosopher Gramsci and the Spirit of ’68.
[9]
“Kto-Kovo” has an another, distinct, application: to the idea that when there is disagreement, you support your friends and oppose your enemies, or, more mildly, you support the good guys and oppose the bad guys. Loyalty to friends is indeed a virtue--- but so is justice, and truthfulness. They often come into conflict. When your friend is in the wrong, you cannot stick to the principle of loyalty without rejecting the principles of justice and truth. For Neo-Marxists this is not a problem; they don’t believe in justice or truth anyway. Having to choose makes life hard for the rest of us, though. We want to stick by our friends, and we want to be on the side of the good people. But we can’t always. Everyone is uncomfortable when a married couple, both friends and nice people, get divorced. We want to be on both sides. Thus, we start avoiding the two of them, or we start telling them different things while hoping they never reconcile and tell each other what we’ve said to each of them. One hopes that scholars would choose truth over allies, but that is not always the case.
[12]
I’ve heard through the grapevine that Amie Wilkinson and Benson Farb are nice people as well as first-rate mathematicians. Farb is very helpful to young mathematicians and generous with his time. Amie Wilkinson’s speech at a graduation ceremony for Berkeley math students shows her human qualities. I have also heard--- and it is easy to see from their public writings, that Ted Hill and Igor Rivin are gadflies with sharp tongues who don’t suffer fools gladly. A person can have two reactions to this. One reaction is that Wilkinson and Farb must be in the right in this dispute. The other reaction is that in evaluating what third parties say, we should realize that they will tend to support Wilkinson and Farb out of loyalty, so we should discount that support if we’re interested in justice. I, of course, have the second reaction. Fiat justitia ruat caelum. If we were choosing a moral examplar, or even just who should be chairman of the math department, we would look at the whole person. We are not, though. We are looking at a single dispute, and it is quite possible for a nice person to be entirely in the wrong once in a while. [13]
Being a nice person isn’t all that is work here, however. There’s also status and power. I included university affiliations earlier on in this essay for a reason. Amie Wilkinson is at the University of Chicago. She is on the editorial boards of Chaos (2002--), Transactions of the AMS (2006--2007), Journal of Modern Dynamics (2006--2014), Algebraic and Geometric Topology (2007--2014), Ergodic Theory and Dynamical Systems (2007--), Commentarii Math Helvetici (2014 --), Journal of the European Math Society (2016 --), and Compositio Mathematica (2017 -- ). Hill is a retired Georgia Tech professor, currently a visiting scholar at California Polytechnic. His CV notes that he has done a lot of refereeing. No editorial boards are listed. Benson Farb is also at Chicago, but Igor Rivin is at Temple and Marjorie Senechal is a retired Smith professor. They’re all active in research, but the power and status disparity is huge. When Terence Tao, Andrew Gelman, and Timothy Gowers, all reasonable people, pull their punches on Wilkinson and criticize her critics, “Kto, Kovo” seems like a reasonable theory to explain it. Those three don’t have to worry about power, I think, but in academia we are very very conscious of status. We’re terrible snobs, me included. We’re as conscious of the gradations between Journal A and Journal B as any German princeling in the 18th century was of the differences between a margrave, a burgrave, and a landgrave, and, within each rank, the difference in centuries of ancestry. When a peasant insults a margrave with sixteen quarterings of nobility, what is one to think? “I guess the peasant is right, but he should have been more polite.”
[14]
This is something of a fight between insiders and outsiders. That’s important in understanding the social context. Insiders work inside, using connection. Outsiders work outside, using publicity. Thus, we see Hill’s 41 pages of documentation, but very little from the other side--- and Hill had to use the FOIA law to extract some of that information. Hill’s opponents worked inside, in secret emails and secret meetings. Hill published an article online, in Quillette. One sees this in politics generally, where by “politics” I mean people in disagreement interacting to persuade others to adopt their position. There is, however, a very important exception here. I was critical earlier of Gelman, Gowers, and Tao, but they are insiders who opened up discussion to outsiders, and even responded to their arguments, sometimes in agreement, sometimes in disagreement. Not all margraves will talk to peasants, but some will, and that has long been a feature of the academic pecking order. Academics are obsessed with rank, but we also believe in noblesse oblige. A graduate student can point out the flaw in a proof, and the Fields Medalist is obliged to respond. If a graduate student ends up at the beers table after a conference talk, the Great Man talks to him kindly and like an equal (which both know he’s not, but the Great Man pretends anyway, as a matter of academic good manners). Not all fields in academia are this way. I note a distressing trend in law professor blogs to eliminate comment sections, which prevents outsiders from correcting embarassing mistakes. And most of those supporting Hill in blog comments do not dare post their real names—though I am sure that it is not Gelman, Gowers, and Tao themselves whose vindictiveness they fear. But I am glad to see healthy discussion in big-name blogs does happen in math, as it does in economics, and I hope that is true of most fields within academia.