As I’ve said before the existence of any innate statistical difference between men and women in mathematical/scientific ability is of no real practical importance. As far as public policy goes we should be looking at what would be most effective in increasing the number of capable graduates in math and science related fields. However, I blog about what irks me not what matters and articles like this one on arstechnica and this summary at science NOW that falsely suggest some study provides a clear cut answer to the nature/nurture debate really annoy me.

For starters I think it’s fairly irresponsible for a publication of the AAAS to offer a statement like this as unqualified commentary

The results “essentially confirm” earlier studies–and they should finally put to rest the idea that girls aren’t going into technical fields because they can’t do the math, says Ann Gallagher, a psychologist who studies testing at the Law School Admission Council in Newtown, Pennsylvania.

The casual reader will certainly understand this claim as saying that women are not innately disadvantaged relative to men in technical fields. Yet this research doesn’t even come close to proving this claim and in light of broader trends in male/female school performance that came up previously this result is perfectly compatible with girls being innately statistically worse at doing mathematics. Given that girls tend to outperform boys generally in academics before college we must either conclude that girls have greater innate intellectual talent or that some other factor, such as a greater willingness to study or pay attention to the teacher, accounts for this general academic superiority and must be accounted for to accurately compare innate ability. While the former hypothesis shouldn’t be dismissed out of hand the later one seems more likely¹ meaning that this study is essentially useless in comparing the innate abilities of boys and girls in math/science. While the authors of the research article might have reasonably expected their audience to be aware of the generally higher performance of girls in pre-college schooling leaving these considerations out of interpretive articles for the lay reader is at best unacceptable sloppiness.

True, the sentence I quoted is technically true. Girls have the literal capability to do technical fields but the obvious implication is that they have statistically equal innate ability which simply isn’t demonstrated by this piece of research. Unfortunately the article on ars is no better.

Thus, the gender gap in math performance seems to be insignificant in grade school, which is good news. Unfortunately, that does not help explain why the gender gap widens later in life. It is possible that pressure from society eventually catches up to women and makes it difficult to stay in certain fields, as the problem certainly doesn’t seem to be innate intellectual capability.

Once again this is a technically correct claim that is nevertheless extremely misleading. For starters, just like the piece in Science NOW this remark plays to the false idea that there is a sharp well-defined distinction between nature and nurture while also implying that whatever social effects cause the gender bias in the sciences must be negative. It’s equally possible that women are relatively more likely to be drawn away from math/science by other interests (child rearing, law, other non-technical pursuits). Even discouraging social pressures aren’t necessarily bad. If women leave technical subjects because they find math/science nerds less hot or simply don’t like hanging out with them that’s not a harm against women². Moreover, there are a vast number of explanations that don’t fall clearly on either the socialization nor innate differences side, e.g., suppose women are innately less rebellious and more eager to please authority figures and thus our educational system is more likely to snuff out their interest and ability to think critically. Fallaciously suggesting that social effects must be harmful barriers to women is almost as bad as what the sexist individuals on the nature side of the debate do when they conflate evidence of innate differences with female incapacity.

As if this wasn’t enough the arstechnica article casually dismisses the results from the article about greater male variation in performance and the Science NOW article ignores them entirely. Interestingly the study found that different races favored different genders at the high end of the tests, e.g., more Asian girls than Asian boys scored at the very high end while more white boys than white girls scored at the top. Still, while both ars and the original journal article dismiss the effects found as small in a discipline requiring mathematical ability at the 99th percentile these data suggest we should find 67% women and only 33% men. Pointing out that some engineering fields have only 15% women as the journal article does only tells us there are other factors at work but it doesn’t downplay the significance of this one. In fact given that math and physics Ph.D.s are probably almost exclusively chosen from the top half percent in mathematical ability this effect on it’s own might account for much of the observed gender gap. Moreover, in combination with the normal tendency of people to clump with others of the same gender and the role of friends/acquaintances in determining classes and majors it’s certainly plausible that even relatively minor differences in gender ratio could be magnified into something larger even if everyone acted in a fair and reasonable fashion.

Ultimately, however, any conclusions you might have been tempted to draw from the results in this article are undone by the fact that none of the questions asked in the standardized tests required serious thought. I stand with the researchers in bemoaning the sorry state of standardized testing in pre-college education but unfortunately for them this undermines any conclusions they might wish to draw about gender and innate ability. Quite simply how well you can memorize the quadratic formula and plug in numbers is totally irrelevant to your ability to do higher mathematics. I’m about to get my Ph.D. in mathematics despite being almost held back a grade because I wasn’t fast enough at my multiplication tables and regularly losing a fair number of points on math tests in high school because I didn’t memorize their stupid rules.

Of course there is nothing here to suggest that the gender differences we see in technical fields are the result of any innate differences but this research certainly doesn’t show otherwise so it shouldn’t be presented as doing so. Frankly I’m quite disturbed at the persistent bias in lay scientific articles about this subject. While I wholeheartedly agree about the importance of disabusing the public about their simpleminded stereotypes about gender differences and strongly support efforts to root out remaining discriminatory treatment covering up the complexities of the issue as these articles do feels too close to being propaganda for the desired answer for my taste.

So I often find myself trying to make the case that people are especially irrational when it comes to voting and other activities where the emotional content is large but individuals have little influence over the outcome or aren’t very affected by it but I’m stymied by a lack of a good example. I can point them at “The Myth of the Rational Voter” for good theoretical and empirical arguments but a good example is worth a lot. I ran across a good one today listening to the KQED discussion about the proposed golden gate suicide barrier. Now I think a suicide barrier is almost certainly unjustified at the cited cost for reasons I give below but what’s interesting/scary isn’t that people disagree with me. If you think there are substantial third party benefits from a suicide barrier or even just make different plausibility judgments from me in a way that consistently favors the barrier you could reasonably think it is a good idea. What’s both scary and interesting is the sorts of motivations people have for thinking a barrier is obviously a good idea and their failure to even indulge in the sort of cost/benefit analysis that would be appropriate for this kind of question.

During the debate the mental health professional opposing the barrier offered rational responses and citations pointing out the faulty reasoning used in arguments for the efficacy of the barrier those who wanted the barrier would call in to say something like, “you admit a barrier might save some people so how many lives is enough?” or, “If you just say we will always have suicides your saying we will always have poverty and…” and those callers at least were making cogent arguments. Many others simply related their personal knowledge of people who had tried to commit suicide and otherwise used emotional ploys (likely unconsciously) to frame the question as whether you were for or against suicide. One caller even went so far as to explicitly express her outraged amazement that someone in the mental health profession would be so cold and unfeeling as to not want to stop suicides.

What is notable about these remarks is that the guest opposing the barrier was arguing that it simply wouldn’t be effective and that we should put our resources into mental health services rather than barriers. The only role these arguments, or the anecdotes offered in the SF gate series promoting the barrier could have in the argument is to make people feel bad for not supporting the barrier. Indeed, despite the fact that at some point we must trade off cost against lives saved (a billion dollars would not be a cost effective price to pay to save one person) some of these arguments derive their force only by pushing the opponent to bite the bullet and admit that these lives aren’t worth X dollars.

To be fair, the callers opposing the barrier were no better. Their arguments seemed to be little more than thinly glossed resentment at being forced to accomodate suicidal individuals. Also the lady supporting the barrier did make reasonable points by citing several studies that on their face would seem to suggest a barrier would be effective. These studies were pretty much the same ones mentioned in this article and fairly easily rebutted. For instance, showing that survivors of one attempt have good prospects for survival is almost totally useless and may even work argue against the barrier. Not only do the survivors constitute a biased sample containing few of those most intent on killing themselves but this statistic, if valid, argues for ensuring that people first attempt suicide in a fashion that is likely to be prevented. Yet, unless you believe a large portion of people who jump off the golden gate bridge do so on impulse while crossing the bridge for unrelated reasons, you would expect that putting up a suicide barrier on the golden gate that is known to be nearly foolproof would drive people contemplating suicide to focus on another location that may not be so easily monitored. Moreover, making it impossible to jump off a particular bridge seems much more akin to taking a single gun off the street or blocking access to one type of barbiturate while leaving others on the market than the wholesale elimination of one convenient method of killing yourself, e.g., putting your head in a coal-gas stove. Not to mention the fact that a single historical data point about gas stoves is highly suspect, likely involves plenty of confounding factors and the rise in suicides 15 years hence is inconsistent with the supposed claim.

Still, even if you generously believe that the barrier will prevent a number of deaths approximately equal to the 34 confirmed suicides that occur some years this simply doesn’t get you to the conclusion that a suicide barrier is justified. For instance economic studies suggest that we implicitly trade off a single life for about 1.5 million dollars. Importantly even if our individual choices in terms of risks and rewards would place a higher dollar value on a statistical life it’s the choices implicit in government decisions that are really relevant since if we could use the 50 million that it will likely cost to build the barrier to save more lives some other way surely that would be preferable. Thus not even counting the loss of utility that might occur from a degradation of the bridge aesthetics nor the fact that the life of a suicidal person is likely to be less enjoyable and thus contribute less utility than an average member of society (suicidal people really do feel more unhappy than most of us) the barrier is a close call. With these factors considered it seems to me that the costs outweigh the benefits.

If you disagree that’s fine but it’s disturbing that people support these projects merely to avoid thinking of themselves as cold because they weigh the cost against the value of the lives lost. That doesn’t make you warm and caring, it makes you a moral monster. Deciding that someone’s life isn’t worth the amount of money it costs to save may seem cold but it’s not as horrific as letting people die because you wanted to feel warm and fuzzy so you couldn’t be bothered to balance the lives this money could save if used to improve road safety with those that might be saved via a suicide barrier.

So a couple days ago there was a hysterical story on slashdot saying we were running out of rare earth elements. Apparently this whole thing was started by Armin Reller, a materials chemist at the University of Augsburg, whose predictions of mineral extinction dates inspired an article by Robert Silverberg in Asimov’s science fiction magazine and reported in a new scientist story that was in turn picked up by one of the Wall Street Journal blogs. Already we should be pretty skeptical. We have a panicked warning driven by multiple commentaries on a single scientists remarks and, going by the failure of any of these stories to cite a journal article for Reller’s remarks, they may not even beer peer reviewed¹.

There is certainly a kernel of truth in these stories as in most of the misleading articles New Scientist publishes. However, these articles make it sound as if we are going to run out of various rare earth metals the way you might run out of toilet paper at home, i.e., we used it all up and have to make do without it. Indeed the article in the Asimov magazine explicitly analogizes this ‘crisis’ to a science fiction scenario of a world without usable iron. True, the prices of many rare earth metals and even Zinc are rising rapidly and for many of them we are currently using them faster than they are being mined. But does that mean we will ‘run out’ or even have to give up our flat screen TVs with Indium based transparent transistors or fancy new Intel CPUs with Hafnium based high-k dielectric? Certainly not. Moreover, we most certainly won’t ‘run out’ of these metals the way these stories suggest.

The idea that the Indium on Earth is just going to be used up in 2017, Terbium in 2012 and Zinc in 2037 is just absurd from both a geological and economic point of view. As an economic matter the market won’t simply let us keep increasing our consumption until we suddenly run out. Rather, when demand increases relative to supply the price rises and decreases consumption. If companies really believed zinc was going to simply run out in 2037 do you think they would be selling it cheaply enough to make it cost effective to make pennies with it or use it in many other trivial ways? There isn’t any great crisis ahead, merely a rise in price for these metals that will cause other metals to be substituted where possible and wasteful uses to be eliminated (eliminate the damn penny!) while essential uses (LCD displays, CPUs) continue. If you don’t believe me put your money where your mouth is. If you think we will simply run out of Terbium in 4 years buy up some Terbium or Terbium futures and you’ll make a fortune.

It’s an even more absurd proposal from a geological perspective. Neither Indium or Gallium occurs naturally in high concentrations in any mineral. Rather small quantities of both these minerals are isolated from Zinc deposits (Sphalerite) and in the case of Gallium Bauxite and coal as well. Already then something seems fishy about the suggestion we would run out of Indium in 9 years but wouldn’t run out of Zinc for another 20 years after that. Surely companies aren’t going pull all of the worlds Zinc deposits out of the ground so they can isolate the 50ppm of of Gallium and then pay to store the Zinc for another 20 years. Moreover, some simple math shows how absurd the suggestion is that we will simply run out of Zinc.

Zinc makes up .0004% of the Earth’s crust and the continental crust in turn accounts for .374% of the earth total mass. Wikipedia tells us the Earth has a mass of 5.97 * 10²⁴ kilograms and doing the math gives us 8.910¹³ metric tons of Zinc in the continental crust. Given a current consumption rate of about 7.110⁶ metric tons a year we could continue at this rate for 10 million years before we depleted the Zinc in the crust.

Of course we can’t efficiently extract anywhere near all the Zinc in the crust and it’s the notion of efficient extraction that’s central to this issue. Unlike the toilet paper you keep in your bathroom mineral deposits aren’t all equally easy to extract until you suddenly run. If we were willing to pay more for minerals like Zinc companies would start mining locations that were formerly unprofitable. Conversely if the amount of Zinc we have sitting around in storage shrinks the price of Zinc will rise and consumption will decrease. Likely the numbers quoted in the New Scientist article describe the point at which current rates of usage will deplete the proven reserves of these various minerals in the ground. In other words they tell us how long these metals would last if mining companies didn’t bother to go look for more, didn’t start extracting ore from regions currently unprofitable when prices increased and people kept using them at the same rate despite increased scarcity. We might as well assume the Martians are stealing our metal with ray guns to predict future catastrophic shortages. Now I’m just guessing at what these numbers are supposed to actually mean (the articles couldn’t be bothered to tell us that) but there is no doubt that none of these articles gives cause to be anxious.