+> To this it might be objected that there are many different types of women. Clusters can internally have many subclusters: Pureto Rican women (or married women, or young women, or lesbians, _&c_.) don't have the _same_ distribution of traits as women as a whole, and yet are still women. Why should "trans" be different from any other adjective one might use to specify a subcategory of women?
+>
+> What makes this difficult is that—_conditional_ on the two-types hypothesis and specifically gender dysphoria in non-exclusively-androphilic biological males being mostly not an intersex condition—most trans women aren't just not part of the female cluster in configuration space; they're specifically part of _male_ cluster along most dimensions, which people _already_ have a concept for. [...] [T]he concepts of _women_-as-defined-by-biological-sex, _women_-as-defined-by-self-identity, and _women_-as-defined-by-passing are picking out different (though of course mostly overlapping) regions of the configuration space, which has inescapable logical [consequences](http://lesswrong.com/lw/nx/categorizing_has_consequences/) on the kinds of inferences that can be made using each concept.
+
+If that wasn't sufficiently clear, perhaps I have _failed as a writer_, and I can only beg that Ozy and our joint readership permit me the chance to try again.
+
+I don't want to _define_ gender based on psychology.[ref]Also, on a personal note, can I remark on how _weird_ and _uncomfortable_ it is that defending sex differences has now apparently become my thing? I'm an individualist/egalitarian androgyny fan, not a [complementarian](https://en.wikipedia.org/wiki/Complementarianism); I [_don't want_](http://unremediatedgender.space/2017/Dec/theres-a-land-that-i-see-or-the-spirit-of-intervention/) women and men to have incommensurable souls. But faced with an intellectual climate where brilliant, kind, otherwise-sane people seem to feel morally obligated to _destroy our collective ability to reason about sex using natural language_, I feel morally obligated to not let them get away with it. Not for love of the territory in its current state, but for the love of that property of maps that _reflect_ the territory.[/ref] ([Definitions are overrated](https://www.lesswrong.com/posts/cFzC996D7Jjds3vS9/arguing-by-definition), anyway.) I do think that biological sex is almost as close as you can get to being a _natural category_[ref]The [chemical elements](https://en.wikipedia.org/wiki/List_of_chemical_elements) would be an example of an even more robustly natural category. Atoms with more protons than nitrogen but fewer than oxygen _do not exist_, and thus there is no analogue in chemistry to the "Well, what about intersex conditions?" [challenge](http://geekfeminism.wikia.com/wiki/Derailment) to the concept of sex or the "Well, what about [ring species](https://en.wikipedia.org/wiki/Ring_species)?" challenge to the concept of species.[/ref] in something like the following sense. If we imagine a distribution of artificial intelligences studying life on Earth and humans in particular, but lacking any preconceived concept of _sex_,[ref]It would be more traditional to put aliens rather than AIs in the observer role of this genre of thought experiment, but evolved aliens probably _would_ already know about sex![/ref] different AIs would each invent [different concepts](https://www.lesswrong.com/posts/XeHYXXTGRuDrhk5XL/unnatural-categories) in order to model the aspects of reality relevant to their own individual values, but most of them would be forced to reinvent the category of _sex_ sooner or later, because sex category membership makes predictions about [_many_ different dimensions of observation](https://en.wikipedia.org/wiki/Sex_differences_in_humans)—although some with much larger [or smaller](https://www.apa.org/pubs/journals/releases/amp-606581.pdf) effect sizes than others—at least _some_ of which are likely to be relevant to the interests of any particular AI that's paying any attention to animal life at _all_.
+
+[I use the "bimodal multivariate distribution" frame a lot—it's even in the URL—but it's actually worse: sex-specific adaptations—functional adaptations and not just shifted distributions—are a thing https://thingofthings.wordpress.com/2017/05/05/the-cluster-structure-of-genderspace/]
+
+[if you have to do definitions, you go by physiology, because that's the part that's truly almost-completely-binary]
+
+That categories are clusters in a _high-dimensional_ space is relevant because of a statistical phenomenon perhaps most famously elucidated in [A. W. F. Edwards's critique of Richard Lewontin's critique of the concept of _race_](https://en.wikipedia.org/wiki/Human_Genetic_Diversity:_Lewontin's_Fallacy): groups that overlap along any _one_ particular measurement might be much more clearly distinguishable when you look at the conjunction of many different measurements.
+
+[TODO: the standard diagram]
+
+When discussing whether a proposed recreational basketball association[ref]I'm somewhat reluctant to choose a sports example, because sporting is such a comparatively small and unimportant part of life—at least from the perspective of non-athletes—but it's a good place to start pedagogically, because merely physical sex differences are relatively uncontroversial, and it's important to avoid the distraction of unnecessarily contentious issues in the presentation of a topic that's already so prone to [motivated misunderstandings](https://en.wikipedia.org/wiki/Straw_man).[/ref] should be sex-segregated or not, one fact that might come up during the discussion is that the sex difference in human height has a magnitude of Cohen's _d_≈1.7, which is relevant because it means that insofar as selecting for good basketball players implies some degree of selection for tall people, it also implies some degree of selection for men, which would detract from the goal of creating an atmosphere where people are socially rewarded for excelling at the [high challenge](https://www.lesswrong.com/posts/29vqqmGNxNRGzffEj/high-challenge) of their chosen sport rather than for the (preëxisting, uninteresting, mostly immutable[ref]Given current technology.[/ref]) brute fact of their sex.