+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 like me (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 (given some suitably exhaustive parsing and factorization of the human design into individual "traits"), 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? 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_.)
+
+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.
+
+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.
+
+And knowledge about the distribution is genuinely informative. Occasionally you hear progressive-minded people dismiss and disdain simpleminded transphobes who believe that chromosomes determine sex, when actually, most people haven't been karyotyped and don't _know_ what chromosomes they have. (Um, with respect to some sense of "know" that doesn't care how unsurprised I was that my 23andMe results came back with a _Y_ and would have bet on it at very generous odds.)
+
+Certainly, I agree that almost no one interacts with sex chromosomes on a day-to-day basis; no one even knew that sex chromosomes _existed_ before 1905. [(Co-discovered by a woman!)](https://en.wikipedia.org/wiki/Nettie_Stevens) But the function of [intensional definitions](https://www.lesswrong.com/posts/HsznWM9A7NiuGsp28/extensions-and-intensions) in human natural language isn't to exhaustively [pinpoint](https://www.lesswrong.com/posts/3FoMuCLqZggTxoC3S/logical-pinpointing) a concept in the detail it would be implemented in an AI's executing code, but rather to provide a "treasure map" sufficient for a listener to pick out the corresponding concept in their own world-model: that's why [Diogenes exhibiting a plucked chicken in response to Plato's definition of a human as a "featherless biped"](https://www.lesswrong.com/posts/jMTbQj9XB5ah2maup/similarity-clusters) seems like a cheap "gotcha"—we all instantly know that's not what Plato meant. ["The challenge is figuring out which things are similar to each other—which things are clustered together—and sometimes, which things have a common cause."](https://www.lesswrong.com/posts/d5NyJ2Lf6N22AD9PB/where-to-draw-the-boundary) But sex chromosomes, and to a large extent specifically the [SRY gene](https://en.wikipedia.org/wiki/Testis-determining_factor) located on the Y chromosome, _are_ such a common cause—the root of the [causal graph](https://www.lesswrong.com/posts/hzuSDMx7pd2uxFc5w/causal-diagrams-and-causal-models) underlying all _other_ sex differences. A smart natural philosopher living _before_ 1905, knowing about all the various observed differences between women and men, might have guessed at the existence of some molecular mechanism of sex determination, and been _right_. By the "treasure map" standard, "XX is female; XY is male" is a pretty _well-performing_ definition—if you're looking for a [_simple_ membership test](https://www.lesswrong.com/posts/edEXi4SpkXfvaX42j/schelling-categories-and-simple-membership-tests) that's entangled with a lot of information about the many intricate ways in which females and males statistically differ.
+
+Take faces. People are [verifiably very good at recognizing sex from (hair covered, males clean-shaven) photographs of people's faces](/papers/bruce_et_al-sex_discrimination_how_do_we_tell.pdf) (96% accuracy, which is the equivalent of _d_ ≈ 3.5), but we don't have direct introspective access into what _specific_ features our brains are using to do it; we just look, and _somehow_ know. The differences are real [(a computer statistical model gets up to 99.47% accuracy)](https://royalsocietypublishing.org/doi/10.1098/rspb.2015.1351#d3e949), but it's not a matter of any single, simple measurement you could perform with a ruler (like the distance between someone's eyes). Rather, it's a high-dimensional _pattern_ in many such measurements you could take with a ruler, no one of which is definitive. [Covering up the nose makes people slower and slightly worse at sexing faces, but people don't do better than chance at guessing sex from photos of noses alone](/papers/roberts-bruce-feature_saliency_in_judging_the_sex_and_familiarity_of_faces.pdf).
+
+Notably, for _images_ of faces, we actually _do_ have transformation technology! (Not "magical", because we know how it works.) AI techniques like [generative adversarial networks](https://arxiv.org/abs/1812.04948) and [autoencoders](https://towardsdatascience.com/generating-images-with-autoencoders-77fd3a8dd368) can learn the structure of the distribution of facial photographs, and use that knowledge to synthesize faces from scratch (as demonstrated by [_thispersondoesnotexist.com_](https://thispersondoesnotexist.com/))—or [do things like](https://arxiv.org/abs/1907.10786) sex transformation (as demonstrated by [FaceApp](https://www.faceapp.com/), the _uniquely best piece of software in the world_).
+
+If you let each pixel vary independently, the space of possible 1024x1024 images is 1,048,576-dimensional, but the vast hypermajority of those images aren't photorealistic human faces. Letting each pixel vary independently is the wrong way to think about it: changing the lighting or pose changes a lot of pixels in what humans would regard as images of "the same" face. So instead, our machine-learning algorithms learn a [compressed](https://www.lesswrong.com/posts/ex63DPisEjomutkCw/msg-len) representation of what makes the tiny subspace (relative to images-in-general) of faces-in-particular similar to each other. That [latent space](https://towardsdatascience.com/understanding-latent-space-in-machine-learning-de5a7c687d8d) is a lot smaller (say, 512 dimensions), but still rich enough to embed the high-level distinctions that humans notice: [you can find a hyperplane that separates](https://youtu.be/dCKbRCUyop8?t=1433) smiling from non-smiling faces, or glasses from no-glasses, or young from old, or different races—or female and male. Sliding along the [normal vector](https://en.wikipedia.org/wiki/Normal_(geometry)) to that [hyperplane](https://en.wikipedia.org/wiki/Hyperplane) gives the desired transformation: producing images that are "more female" (as the model has learned that concept) while keeping "everything else" the same.
+
+Two-dimensional _images_ of people are _vastly_ simpler than the actual people themselves in the real physical universe. But _in theory_, a lot of the same _mathematical principles_ would apply to hypothetical future nanotechnology-wielding AI systems that could, like the AI in "Failed Utopia #4-2", synthesize a human being from scratch (this-person-_didn't_-exist-dot-com?), or do a real-world sex transformation (PersonApp?)—and the same statistical morals apply to reasoning about sex differences in psychology and (which is to say) the brain.
+
+Daphna Joel _et al._ [argue](https://www.pnas.org/content/112/50/15468) [that](https://www.pnas.org/content/112/50/15468) human brains are "unique 'mosaics' of features" that cannot be categorized into distinct _female_ and _male_ classes, because it's rare for brains to be "internally consistent"—female-typical or male-typical along _every_ dimension. It's true and important that brains aren't _discretely_ sexually dimorphic the way genitals are, but as [Marco del Giudice _et al._ point out](http://cogprints.org/10046/1/Delgiudice_etal_critique_joel_2015.pdf), the "cannot be categorized into two distinct classes" claim seems false in an important sense. The lack of "internal consistency" in Joel _et al._'s sense is exactly the behavior we expect from multivariate normal-ish distributions with different-but-not-vastly-different means. (There aren't going to be many traits where the sexes are like, _four_ or whatever standard deviations apart.) It's just like how sequences of flips of a Heads-biased and Tails-biased coin are going to be unique "mosaics" of Heads and Tails, but pretty distinguishable with enough flips—and indeed, with the right stats methodology, [MRI brain scans can predict sex at 96.8% accuracy](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6374327/).
+
+Sex differences in the brain are like sex differences in the skeleton: anthropologists can tell female and male skeletons apart (the [pelvis is shaped differently](https://johnhawks.net/explainer/laboratory/sexual-dimorphism-pelvis), for obvious reasons), and [machine-learning models can see very reliable differences that human radiologists can't](/papers/yune_et_al-beyond_human_perception_sexual_dimorphism_in_hand_and_wrist_radiographs.pdf), but neither sex has entire _bones_ that the other doesn't, and the same is true of brain regions. (The evopsych story about complex adaptations being universal-up-to-sex suggests that sex-specific bones or brain regions should be _possible_, but in a bit of _relative_ good news for antisexism, apparently evolution didn't need to go that far. Um, in humans—a lot of other mammals actually have [a penis bone](https://en.wikipedia.org/wiki/Baculum).)
+
+Maybe this should just look like supplementary Statistics Details brushed over some basic facts of human existence that everyone knows? I'm a pretty weird guy, in more ways than one. I am not prototypically masculine. Most men are not like me. If I'm allowed to cherry-pick what measurements to take, I can name ways in which my mosaic is more female-typical than male-typical. (For example, I'm _sure_ I'm above the female mean in [Big Five Neuroticism](https://en.wikipedia.org/wiki/Big_Five_personality_traits).) ["[A] weakly negative correlation can be mistaken for a strong positive one with a bit of selective memory."](https://www.lesswrong.com/posts/veN86cBhoe7mBxXLk/categorizing-has-consequences)
+
+But "weird" represents a much larger space of possibilities than "normal", much as [_nonapples_ are a less cohesive category than _apples_](https://www.lesswrong.com/posts/2mLZiWxWKZyaRgcn7/selling-nonapples): a woman trapped in a man's body would be weird, but it doesn't follow that weird men are secretly women, as opposed to some other, _specific_, kind of weird. If you _sum over_ all of my traits, everything that makes me, _me_—it's going to be a point in the _male_ region of the existing, unremediated, genderspace. In the course of _being myself_, I'm going to do more male-typical things than female-typical things, not because I'm _trying_ to be masculine (I'm not), and not because I "identify as" male (I don't—or I wouldn't, if someone could give me a straight answer as to what this "identifying as" operation is supposed to consist of), but because I literally in-fact am male in the same sense that male chimpanzees or male mice are male, whether or not I like it (I don't—or I wouldn't, if I still believed that preference was coherent), and whether or not I _notice_ all the little details that implies (I almost certainly don't).
+
+Okay, maybe I'm _not_ completely over my teenage religion of psychological sex differences denialism?—that belief still feels uncomfortable to put my weight on. I would _prefer_ to believe that there are women who are relevantly "like me" with respect to some fair (not gerrymandered) metric on personspace. But, um ... it's not completely obvious whether I actually know any? (Well, maybe two or three.) When I look around me—most of the people in my robot cult (and much more so if you look at the core of old-timers from the _Overcoming Bias_ days, rather than the greater "community" of today) are male. Most of the people in my open-source programming scene are male. These days, [most of the _women_](/2020/Nov/survey-data-on-cis-and-trans-women-among-haskell-programmers/) in [my open-source programming scene](/2017/Aug/interlude-vii/) are male. Am ... am I not supposed to _notice_?
+
+Is _everyone else_ not supposed to notice? Suppose I got the magical body transformation (with no brain mods beyond the minimum needed for motor control). Suppose I caught the worshipful attention of a young man just like I used to be ("a" young man, as if there wouldn't be _dozens_), who privately told me, "I've never met a woman quite like you." What would I be supposed to tell him? ["There's a _reason_ for that"](https://www.dumbingofage.com/2014/comic/book-5/01-when-somebody-loved-me/purpleandskates/)?
+
+In the comments to [a post about how gender is built on innate sex differences](https://web.archive.org/web/20130216025508/http://lesswrong.com/lw/rp/the_opposite_sex/) (of which I can only link to the Internet Archive copy, the original having been quietly deleted sometime in 2013—I wonder why!), Yudkowsky opined that "until men start thinking of themselves _as men_ they will tend to regard women as defective humans."
+
+From context, it seems like the idea was targeted at men who disdain women as a mysterious Other—but the same moral applies to men who are in ideologically-motivated denial about how male-typical they are, and whether this has implications. [At the time, I certainly didn't want to think of myself _as a man_.](https://www.greaterwrong.com/posts/FBgozHEv7J72NCEPB/my-way#comment-7ZwECTPFTLBpytj7b) And yet ...
+
+For example. When I read things from the [systematizing–empathizing](https://en.wikipedia.org/wiki/Empathising%E2%80%93systemising_theory)/"men are interested in things, women are interested in people" line of research—which, to be clear that you know that I know, is [only a mere statistical difference at a mere Cohen's _d_ ≈ 0.93](http://unremediatedgender.space/papers/su_et_al-men_and_things_women_and_people.pdf), not an absolute like genitals or chromosomes—my instinctive reaction is, "But, but, that's not _fair_. People _are_ systems, because _everything_ is a system. [What kind of a lame power is empathy, anyway?](https://tvtropes.org/pmwiki/pmwiki.php/Main/WhatKindOfLamePowerIsHeartAnyway)"
+
+[But the map is not the territory](https://www.lesswrong.com/posts/np3tP49caG4uFLRbS/the-quotation-is-not-the-referent). We don't have unmediated access to reality beyond [the Veil of Maya](https://web.archive.org/web/20020606121040/http://singinst.org/GISAI/mind/consensus.html); system-ness in the empathizing/systematizing sense is a feature of our _models_ of the world, not the world itself.
+
+So what "Everything is a system" _means_ is, "I _think_ everything is a system."
+
+I think everything is a system ... because I'm male??
+
+(Or whatever the appropriate generalization of "because" is for statistical group differences. The sentence "I'm 5′11″ because I'm male" doesn't seem quite right, but it's pointing to something real.)
+
+I could _assert_ that it's all down to socialization and stereotyping and self-fulfilling prophecies—and I know that _some_ of it is. (Self-fulfilling prophecies [are coordination equilibria](/2020/Jan/book-review-the-origins-of-unfairness/).) But I still want to speculate that the nature of my X factor—the things about my personality that let me write the _specific_ things I do even though I'm [objectively not that smart](/images/wisc-iii_result.jpg) compared to some of my robot-cult friends—is a pattern of mental illness that could realistically only occur in males. (Yudkowsky: ["It seems to me that male teenagers especially have something like a _higher cognitive temperature_, an ability to wander into strange places both good and bad."](https://www.lesswrong.com/posts/xsyG7PkMekHud2DMK/of-gender-and-rationality))
+
+Of course there are women with an analogous story to tell about the nature of their own uniqueness—analogous along _some_ dimensions, if not others—but those aren't _my_ story to tell.
+
+I can _imagine_ that all the gaps will vanish after the revolution. I can imagine it, but I can no longer _assert it with a straight face_ because _I've read the literature_ and can tell you several observations about chimps and [congenital adrenal hyperplasia](/images/cah_diffs_table.png) that make that seem _relatively unlikely_.
+
+I was once told by a very smart friend (who, unlike me, is not a religious fanatic), "Boys like games with challenges and points; girls like games with characters and stories."
+
+I said, "I like characters and stories! I think."
+
+He said, "I know, but at the margin, you seem suboptimally far in the challenges and points direction. But that's fine; that's what women are for."
+
+And what evidence could I point to, to show him that he's _bad and wrong_ for saying that, if he's not already religiously required to believe it?