Queen prodigy

Queen Izabella is trying her hand at film criticism, and her main complaint boils down to the movie not being about her. (When a woman was awarded the Fields Medal for the first time, you could sorta read between the lines of Laba’s sourpuss post that it was basically sexism that kept her from getting the prize.)

Let’s lay down some markers. Laba, unlike the motha functor and mathbabe, really is a world-class mathematician  (something we’ve previously noted). For non-mathematician readers, it is difficult to convey a sense of just how unevenly mathematical talent is distributed among humans. Take the most abstruse, technical mathematical concept you learned (complex numbers? Riemann integrals?) and try to explain it to an intelligent eight year-old. You’ll see that he probably gets some vague gist, but doesn’t come close appreciating the full depth. This is how an average professional mathematician, from an ordinary backwater school, feels like when explaining advanced math to a layman. This is how a world-class mathematician feels when talking to an average mathematician about his specialized field. Beyond that, at even higher eschelons, I don’t know if the gaps continue to grow exponentially. (I recall reading somewhere that people have a good understanding of the class interactions below but not above their socioeconomic class; something similar is true for math.)

Being a strong mathematician does not make one immune to wandering way out of one’s depth in unfamiliar areas of knowledge. This is worse than political stupidity: In the linked post, Laba is not merely proposing naive or authoritarian social engineering schemes. She is actually dismissing an entire area of study (psychometry) from first principles, based on the central limit theorem and the uneven rate of convergence at the hump vs. the tails. (There’s actually a lot more; sample: “How do we measure for example “math ability” independently of the social and economic context?” Try looking up controlling for a variable, lady.)

Now PTT being a “first principles” rather than “raw data” blog, we can sympathise to some extent with such blissfully uninformed arguments. However, we have a first-principles counter-argument, summarized here. In a nutshell, whenever you discover some trivial gotcha reason why an established area of scientific inquiry is based on false premises and hence entirely wrong, pause to consider that perhaps the luminaries of the field are acutely aware of the difficulties, and have addressed them in copious literature. I was going to leave it at that, but a friend of a friend, Mike Berman, pointed me to the Lotka curve (pp. 87-106 in Charles Murray’s Human Accomplishment). Turns out PTT wasn’t the first to take note of human talent’s extremely uneven distribution. This would be the place for Laba to start if she did not wish to perpetuate the ignorant ditz stereotype threat.

Well, two can play this game. Quoth Laba:

Let me tell you about a layman’s version of Szemeredi’s theorem that I like: given any desired statistical pattern, one can always find data to support it, provided only that a large enough pool of data is available to pick and choose from. […] Szemeredi’s theorem doesn’t take sides, so if you’re looking for data to contradict the same pattern instead, you should be able to find that as well. In either case, you’ll be ignoring the vast majority of the data available to you.

Watch me mansplain Szemerédi’s theorem to this math-broad. See here, babe, I know you think it was clever to name-drop a deep and difficult theorem in an attempt to refute the very premise of The Bell Curve, but Szemerédi has absolutely nothing to do with hypothesis testing. Yes, you’re allowed to choose any wacky “statistical pattern” as your initial hypothesis, but then you must obtain a bunch of new data and check if the hypothesis is in agreement with it. The more attempts at refutation a fixed hypothesis survives, the lower its odds of being a completely spurious “statistical pattern”. This is how science works.


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