+I think I have just enough language to _start_ to talk about what it would mean. Since sex isn't an atomic attribute, but rather a high-level statistical regularity such that almost everyone can be cleanly classified as "female" or "male" _in terms of_ lower-level traits (genitals, hormone levels, _&c._), then, abstractly, we're trying to take points from male distribution and map them onto the female distribution in a way that preserves as much structure (personal identity) as possible. My female analogue doesn't have a penis (because then she wouldn't be female), but she is going to speak American English like me and be [85% Ashkenazi like me](/images/ancestry_report.png), because language and autosomal genes don't have anything to do with sex.
+
+The hard part has to do with traits that are meaningfully sexually dimorphic, but not as a discrete dichotomy—where the sex-specific universal designs differ in ways that are _subtler_ than the presence or absence of entire reproductive organs. (Yes, I know about [homology](https://en.wikipedia.org/wiki/Homology_(biology))—and you know what I meant.) We are _not_ satisfied if the magical transformation technology swaps out my penis and testicles for a functioning female reproductive system without changing the rest of my body, because we want the end result to be indistinguishable from having been drawn from the female distribution (at least, indistinguishable _modulo_ having my memories of life as a male before the magical transformation), and a man-who-somehow-magically-has-a-vagina doesn't qualify.
+
+The "obvious" way to to do the mapping is to keep the same percentile rank within each trait, but take it with respect to the target sex's distribution. I'm 5′11″ tall, which [puts me at](https://dqydj.com/height-percentile-calculator-for-men-and-women/) the 73rd percentile for American men, about 6/10ths of a standard deviation above the mean. So _presumably_ we want to say that my female analogue is at the 73rd percentile for American women, about 5′5½″.
+
+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? But 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. 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 which set the 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.
+
+A single-variable measurement like height is like a single coin: unless the coin is _very_ biased, one flip can't tell you much about the bias. But there are lots of things about people for which it's not that they can't be measured, but that the measurements require _more than one number_—which correspondingly offer more information about the distribution generating them.
+
+[TODO (somewhere around-ish this section): chromosomes at the root of the causal graph: https://www.lesswrong.com/posts/hzuSDMx7pd2uxFc5w/causal-diagrams-and-causal-models ]