I guess if you _didn't_ grow up with a quasi-religious fervor for psychological sex differences denialism, this whole theoretical line of argument about evolutionary psychology doesn't seem world-shatteringly impactful?—maybe it just looks like supplementary Science Details brushed over some basic facts of human existence that everyone knows. But if you _have_ built your identity around [quasi-religious _denial_](/2020/Apr/peering-through-reverent-fingers/) of certain basic facts of human existence that everyone knows (if not everyone [knows that they know](https://www.lesswrong.com/posts/CqyJzDZWvGhhFJ7dY/belief-in-belief)), getting forced out of it by sufficient weight of Science Details [can be a pretty rough experience](https://www.greaterwrong.com/posts/XM9SwdBGn8ATf8kq3/c/comment/Zv5mrMThBkkjDAqv9).
-My hair-trigger antisexism was sort of lurking in the background of some of my comments while the Sequences were being published (though, again, it wasn't relevant to _most_ posts, which were just about cool math and science stuff that had no avenue whatsoever for being corrupted by gender politics). The term "social justice warrior" wasn't yet popular, but I definitely had a SJW-alike mindset (nurtured from my time lurking the feminist blogosphere) of being preoccupied with the badness and wrongness of people who are wrong and bad (_i.e._, sexist), rather than trying to maximize the accuracy of my probabilistic predictions.
+<a id="hair-trigger-antisexism"></a>My hair-trigger antisexism was sort of lurking in the background of some of my comments while the Sequences were being published (though, again, it wasn't relevant to _most_ posts, which were just about cool math and science stuff that had no avenue whatsoever for being corrupted by gender politics). The term "social justice warrior" wasn't yet popular, but I definitely had a SJW-alike mindset (nurtured from my time lurking the feminist blogosphere) of being preoccupied with the badness and wrongness of people who are wrong and bad (_i.e._, sexist), rather than trying to maximize the accuracy of my probabilistic predictions.
Another one of the little song-fragments I wrote in my head a few years earlier (which I mention for its being representative of my attitude at the time, rather than it being notable in itself), concerned an advice columnist, [Amy Alkon](http://www.advicegoddess.com/), syndicated in the _Contra Costa Times_ of my youth, who would sometimes give dating advice based on a pop-evopsych account of psychological sex differences—the usual fare about women seeking commitment and men seeking youth and beauty. My song went—
You might think this is "unfair": some women—about 7 per 1000—are 5′11″, and we don't want to say they're somehow _less female_ on that account, so why can't I keep my height? The problem is that if we refuse to adjust for every trait for which the female and male distributions overlap (on the grounds that _some_ women have the same trait value as my male self), we don't end up with a result from the female distribution.
-The typical point in a high-dimensional distribution is _not_ typical along each dimension individually. [In 100 flips of a biased coin](http://zackmdavis.net/blog/2019/05/the-typical-set/) that lands Heads 0.6 of the time, the _single_ most likely sequence is 100 Heads, but there's only one of those and you're _vanishingly_ unlikely to actually see it. The [sequences you'll actually observe will have close to 60 Heads](https://en.wikipedia.org/wiki/Asymptotic_equipartition_property). Each such sequence is individually less probable than the all-Heads sequence, but there are vastly more of them. Similarly, [most of the probability-mass of a high-dimensional multivariate normal distribution is concentrated in a thin "shell" some distance away from the mode](https://www.johndcook.com/blog/2011/09/01/multivariate-normal-shell/), for the same reason. (The _same_ reason: the binomial distribution converges to the normal in the limit of large _n_.)
+<a id="typical-point"></a>The typical point in a high-dimensional distribution is _not_ typical along each dimension individually. [In 100 flips of a biased coin](http://zackmdavis.net/blog/2019/05/the-typical-set/) that lands Heads 0.6 of the time, the _single_ most likely sequence is 100 Heads, but there's only one of those and you're _vanishingly_ unlikely to actually see it. The [sequences you'll actually observe will have close to 60 Heads](https://en.wikipedia.org/wiki/Asymptotic_equipartition_property). Each such sequence is individually less probable than the all-Heads sequence, but there are vastly more of them. Similarly, [most of the probability-mass of a high-dimensional multivariate normal distribution is concentrated in a thin "shell" some distance away from the mode](https://www.johndcook.com/blog/2011/09/01/multivariate-normal-shell/), for the same reason. (The _same_ reason: the binomial distribution converges to the normal in the limit of large _n_.)
Statistical sex differences are like flipping two different collections of coins with different biases, where the coins represent various traits. Learning the outcome of any individual flip, doesn't tell you which set that coin came from, but [if we look at the aggregation of many flips, we can get _godlike_ confidence](https://www.lesswrong.com/posts/cu7YY7WdgJBs3DpmJ/the-univariate-fallacy-1) as to which collection we're looking at.
projects / Ultimately_Untrue_Thought.git / blobdiff