+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](https://archive.is/y5V9i), when actually, most people haven't been karyotyped and don't _know_ what chromosomes they have. 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 provides 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 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, apprently 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). 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 becuase 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 the core of old-timers from the _Overcoming Bias_ days, rather than the greater Berkeley "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 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/)?
+
+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 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))
+
+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 fantatic), "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?
+
+_Alright_. So _in principle_, you could imagine having a PersonApp that maps me to a point in the female region of configuration space in some appropriately structure-preserving way, to compute my female analogue who is as authentically _me_ as possible while also being authentically female, down to her pelvis shape, and the proportion of gray matter in her posterior lateral orbitofrontal cortex, and—the love of a woman for a man. What is she like, concretely? Do I know how to imagine that?