+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. 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-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 they're 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 all Heads, but there are vastly more of them.