Title: Beyond the Binary
-Date: 2021-06-01 05:00
+Date: 2023-12-12 13:00
Category: commentary
Tags: categorization, epistemology
-Status: draft
> Do not at the outset of your career make the all too common error of mistaking names for things. Names are only conventional signs for identifying things. Things are the reality that counts. If a thing is despised, either because of ignorance or because it is despicable, you will not alter matters by changing its name.
>
-> —[W. E. B. duBois](http://www.virginia.edu/woodson/courses/aas102%20%28spring%2001%29/articles/names/dubois.htm)
+> —W. E. B. duBois
A common misconception about words is that they have definitions: look up the definition, and that tells you everything to know about that word ... right?
But if you saw this person on the street or even slept in their bed, you wouldn't want to call them a woman, because everything about them that you can observe looks like that of an adult human male. If you're not a reproductive health lab tech and don't look at the photographs in biology textbooks, you'll never _see_ the gametes someone's body produces. (You can see semen, but the individual spermatozoa are too small to look at without a microscope; people [didn't even know that ova and sperm _existed_ until the 17th century](https://onlinelibrary.wiley.com/doi/full/10.1111/j.1439-0531.2012.02105.x).) Does that mean this common definition of _female_ isn't perfectly serviceable after all?
-No, because humans whose gonads produce eggs but appear male in every other aspect, are something I just made up out of thin air for the purposes of this blog post; they don't exist in the real world. What this really shows is that the cognitive technology of "words" having "definitions" doesn't work in the world of the imagination, because _the world of the imagination_ encompasses (at a minimum) _all possible configurations of matter_. Words are [short messages that compress information about the world](https://www.lesswrong.com/posts/mB95aqTSJLNR9YyjH/message-length), but what it means for the world to contain compressible information is that some things in the world are more probable than others.
+No, because humans whose gonads produce eggs but appear male in every other aspect, are something I just made up out of thin air for the purposes of this blog post; they don't exist in the real world. What this really shows is that the cognitive technology of "words" having "definitions" doesn't work in the world of the imagination, because the world of the imagination encompasses (at a minimum) _all possible configurations of matter_. Words are [short messages that compress information about the world](https://www.lesswrong.com/posts/mB95aqTSJLNR9YyjH/message-length), but what it means for the world to contain compressible information is that some things in the world are more probable than others.
-To see why, let's take a brief math detour and review some elementary information theory. Instead of the messy real world, take a restricted setting: the world of strings of 20 bits. Suppose you wanted to devise an efficient _code_ to represent elements of this world with _shorter_ strings, such that you could say (for example) `01100` (in the efficient code, using just 5 bits) and the people listening to you would know that what you actually saw in the world was (for example) `01100001110110000010`.
+To see why, let's take a brief math detour and review some elementary information theory. Instead of the messy real world, take a restricted setting: the world of strings of 20 bits. Suppose you wanted to devise an efficient code to represent elements of this world with shorter strings, such that you could say (for example) `01100` (in the efficient code, using just 5 bits) and the people listening to you would know that what you actually saw in the world was (for example) `01100001110110000010`.
-If every length-20 bitstring in the world has equal probability, this can't be done: there are 2<sup>20</sup> (= 1,048,576) length-20 strings and only 2<sup>5</sup> (= 32) length-5 codewords; there aren't enough codewords to go around to cover all the strings in this world. It's worse than that: if every length-20 bitstring in the world has equal probability, you can't have labels that compress information at all: if you said that the first 19 bits of something you saw in the world were `0110000111011000001`, the people listening to you would be completely clueless as to whether the whole thing was `0110000111011000001`**`0`** or `0110000111011000001`**`1`**. Just _locating_ a book in the [Jose Luis Borges's Library of Babel](https://en.wikipedia.org/wiki/The_Library_of_Babel) is mathematically equivalent to writing it yourself.
+If every length-20 bitstring in the world has equal probability, this can't be done: there are 2<sup>20</sup> (= 1,048,576) length-20 strings and only 2<sup>5</sup> (= 32) length-5 codewords; there aren't enough codewords to go around to cover all the strings in this world. It's worse than that: if every length-20 bitstring in the world has equal probability, you can't have labels that compress information at all: if you said that the first 19 bits of something you saw in the world were `0110000111011000001`, the people listening to you would be completely clueless as to whether the whole thing was `0110000111011000001`**`0`** or `0110000111011000001`**`1`**. Just locating a book in the [Jose Luis Borges's Library of Babel](https://en.wikipedia.org/wiki/The_Library_of_Babel) is mathematically equivalent to writing it yourself.
-However, in the world of a _non-uniform probability distribution_ over strings of 20 bits, compression—and therefore language—_is_ possible. Say, if almost all the bitstrings you actually saw in the world were either all-zeros (`00000000000000000000`) or all-ones (`11111111111111111111`), with a very few exceptions that were still _mostly_ one bit or the other (like `00010001000000000000` or `11101111111011011111`), then you could devise an efficient encoding.
+However, in the world of a _non-uniform probability distribution_ over strings of 20 bits, compression—and therefore language—is possible. Say, if almost all the bitstrings you actually saw in the world were either all-zeros (`00000000000000000000`) or all-ones (`11111111111111111111`), with a very few exceptions that were still _mostly_ one bit or the other (like `00010001000000000000` or `11101111111011011111`), then you could devise an efficient encoding.
To _be_ efficient, you'd want to reserve the shortest words for the most common cases: like `00` in the code to mean `00000000000000000000` in the world and `01` to mean `11111111111111111111`. Then you could have slightly-longer words that encode all the various exceptions, like maybe the merely-eleven-bit encoding `10110101110` could represent `00100010000000000000` in the world (`1` to indicate that this is one of the exceptions, a following `0` to indicate that _most_ of the bits are `0`, followed by the [Elias self-delimiting integer codes](https://en.wikipedia.org/wiki/Elias_omega_coding) for 3 (`110`) and 7 (`101110`) to indicate that the 3rd and 7th bits are actually `1`).
Then if you wanted an efficient encoding to talk about the two and only two _clusters_ of bitstrings—the mostly-zeros (a majority of `00000000000000000000` plus a few exceptions with a few bits flipped) and the mostly-ones (a majority of `11111111111111111111` plus a few exceptions with a few bits flipped)—you might want to use the first bit as the "definition" for your codewords—even if most of the various [probabilistic inferences that you wanted to make](https://www.lesswrong.com/posts/3nxs2WYDGzJbzcLMp/words-as-hidden-inferences) [on the basis of cluster-membership](https://www.lesswrong.com/posts/gDWvLicHhcMfGmwaK/conditional-independence-and-naive-bayes) concerned bits other than the first. The majoritarian first bit, even if you don't care about it in itself, is a [_simple_ membership test](https://www.lesswrong.com/posts/edEXi4SpkXfvaX42j/schelling-categories-and-simple-membership-tests) for the mostly-zeros/mostly-ones category system.
-Unfortunately—_deeply_ unfortunately—this is not a math blog. I _wish_ this were a math blog—that I lived in a world where I could afford to do math blogging for the greater glory of our collective understanding of greater reality. ("Gender?" I would say, confused if not slightly disgusted, "I barely _know_ her.") It would be a better way to live than being condemned to gender blogging in self-defense, hopelessly outgunned, outmanned, outnumbered, outplanned [in a Total Culture War](/2020/Feb/if-in-some-smothering-dreams-you-too-could-pace/) over [the future of](/2023/Jul/blanchards-dangerous-idea-and-the-plight-of-the-lucid-crossdreamer/) [my neurotype-demographic](/2021/May/sexual-dimorphism-in-the-sequences-in-relation-to-my-gender-problems/). But since I _do_, somehow, go on living like this—having briefly explained the theory, let's get back to the dreary, how do you say?—_application_.
+Unfortunately—_deeply_ unfortunately—this is not a math blog. I _wish_ this were a math blog—that I lived in a world where I could afford to do math blogging for the glory of our collective understanding of greater reality. ("Gender?" I would say, confused if not slightly disgusted, "I barely _know_ her.") It would be a better way to live than being condemned to gender blogging in self-defense, hopelessly outgunned, outmanned, outnumbered, outplanned [in a Total Culture War](/2020/Feb/if-in-some-smothering-dreams-you-too-could-pace/) over [the future of](/2023/Jul/blanchards-dangerous-idea-and-the-plight-of-the-lucid-crossdreamer/) [my neurotype-demographic](/2021/May/sexual-dimorphism-in-the-sequences-in-relation-to-my-gender-problems/). But since I _do_, somehow, go on living like this—having briefly explained the theory, let's get back to the dreary, how do you say?—_application_.
-Defining sex in terms of gamete size or genitals or chromosomes is like the using the never-flipped first bit in our abstract example about the world of length-20 bitstrings. It's not that people _directly_ care about gametes or chromosomes or even genitals in most everyday situations. (You're probably not trying to mate with most of the people you meet in everyday situations, and sex chromosomes weren't discovered until the _20th_ century.) It's that that these are _discrete_ features that are [causally](https://www.lesswrong.com/posts/vhp2sW6iBhNJwqcwP/blood-is-thicker-than-water) entangled with everything _else_ that differs between females and males—including many [correlated](https://www.lesswrong.com/posts/cu7YY7WdgJBs3DpmJ/the-univariate-fallacy-1) statistical differences of various [effect sizes](/2019/Sep/does-general-intelligence-deflate-standardized-effect-sizes-of-cognitive-sex-differences/), and differences that are harder to articulate or measure, and differences that haven't even been discovered yet (as gametes and chromosomes hadn't respectively been discovered yet in the 16th and 19th centuries) but can be theorized to exist because _sex_ is a very robust abstraction that you need in order to understand the design of evolved biological creatures.
+Defining sex in terms of gamete size or genitals or chromosomes is like the using the never-flipped first bit in our abstract example about the world of length-20 bitstrings. It's not that people directly care about gametes or chromosomes or even genitals in most everyday situations. (You're not trying to mate with most of the people you meet in everyday situations, and sex chromosomes weren't discovered until the _20th_ century.) It's that that these are _discrete_ features that are [causally](https://www.lesswrong.com/posts/vhp2sW6iBhNJwqcwP/blood-is-thicker-than-water) entangled with everything _else_ that differs between females and males—including many [correlated](https://www.lesswrong.com/posts/cu7YY7WdgJBs3DpmJ/the-univariate-fallacy-1) statistical differences of various [effect sizes](/2019/Sep/does-general-intelligence-deflate-standardized-effect-sizes-of-cognitive-sex-differences/), and differences that are harder to articulate or measure, and differences that haven't even been discovered yet (as gametes and chromosomes hadn't respectively been discovered yet in the 16th and 19th centuries) but can be theorized to exist because _sex_ is a very robust abstraction that you need in order to understand the design of biological creatures.
-Discrete features make for better word _definitions_ than high-dimensional statistical regularities, even if most of the everyday inferential utility of _using_ the word comes from the high-dimensional statistical correlates. A dictionary definition is just a helpful pointer to help people pick out "the same" [natural abstraction](https://www.lesswrong.com/posts/cy3BhHrGinZCp3LXE/testing-the-natural-abstraction-hypothesis-project-intro) in their _own_ world-model.
+Discrete features make for better word definitions than high-dimensional statistical regularities, even if most of the everyday inferential utility of using the word comes from the high-dimensional statistical correlates. A dictionary definition is just a helpful pointer to help people pick out "the same" [natural abstraction](https://www.lesswrong.com/posts/cy3BhHrGinZCp3LXE/testing-the-natural-abstraction-hypothesis-project-intro) in their _own_ world-model.
-(Gamete size is a particularly good definition for the natural category of _sex_ because the concept of [anisogamy](https://en.wikipedia.org/wiki/Anisogamy) generalizes across species that have different sex determination systems and sexual anatomy. In birds, [the presence or absence of a _W_ chromosome determines whether an animal is _female_](https://en.wikipedia.org/wiki/ZW_sex-determination_system), in contrast to [the _Y_ chromosome's determination of maleness in mammals](https://en.wikipedia.org/wiki/XY_sex-determination_system), and some reptiles' sex is determined by [the temperature of an lain egg while it develops](https://en.wikipedia.org/wiki/Temperature-dependent_sex_determination) (!). And let's not get started on the [cloaca](https://en.wikipedia.org/wiki/Cloaca).)
+(Gamete size is a particularly good definition for the natural category of _sex_ because the concept of [anisogamy](https://en.wikipedia.org/wiki/Anisogamy) generalizes across species that have different sex determination systems and sexual anatomy. In birds, [the presence or absence of a _W_ chromosome determines whether an animal is female](https://en.wikipedia.org/wiki/ZW_sex-determination_system), in contrast to [the _Y_ chromosome's determination of maleness in mammals](https://en.wikipedia.org/wiki/XY_sex-determination_system), and some reptiles' sex is determined by [the temperature of an lain egg while it develops](https://en.wikipedia.org/wiki/Temperature-dependent_sex_determination). And let's not get started on the [cloaca](https://en.wikipedia.org/wiki/Cloaca).)
But because our brains are good at using sex-category words to simultaneously encode predictions about _both_ absolute discrete differences and high-dimensional statistical regularities of various effect sizes, without our being consciously aware of the cognitive work being done, it's easy to get confused by verbal gymnastics if you don't know the theory.
I sometimes regret that so many of my attempts to talk about trans issues end up focusing on psychological sex differences. I guess I'm used to it now, but at first, this was a weird position for me to be in! (For a long time, I [really didn't want to believe in psychological sex differences](/2021/May/sexual-dimorphism-in-the-sequences-in-relation-to-my-gender-problems/#antisexism).) But it keeps happening because it's a natural thing to _disagree_ about: the anatomy of pre-op trans women is not really in dispute, so the sex realist's contextual reply to "Why do you care what genitals someone might or might not have under their clothes?" often ends up appealing to some psychological dimension or another, to which the trans advocate [can counterreply](https://thingofthings.wordpress.com/2018/06/18/man-should-allocate-some-more-categories/), "Oh, you want to define gender based on psychology, then? But then the logic of your position forces you to conclude that butch lesbians aren't women! _Reductio ad absurdum!_"
-This is a severe misreading of the sex-realist position. No one wants to _define_ "gender" based on psychology. Mostly, definitions aren't the kind of thing you should have preferences about: you can't coerce reality into changing by choosing different definitions! Rather, there's _already_ a multivariate distribution of bodies and minds in the world, and good definition choices help us coordinate the concepts in different people's heads into a _shared_ map of that territory.
+This is a severe misreading of the sex-realist position. No one wants to _define_ "gender" based on psychology. Mostly, definitions aren't the kind of thing you should have preferences about: you can't coerce reality into changing by choosing different definitions! Rather, there's _already_ a multivariate distribution of bodies and minds in the world, and good definition choices help us coordinate the concepts in different people's heads into a shared map of that territory.
-_One_ of the _many_ distinctions people sometimes want to make when thinking about the multivariate distribution of bodies and minds in the world, is that between the sexes. But sex is by no means the only way in which people differ! In many situations, you might want to categorize or describe people in many different ways, some more or less discrete _versus_ continuous, or high- _versus_ low-dimensional: age or race or religion or subculture or social class or intelligence or agreeableness.
+_One_ of the many distinctions people sometimes want to make when thinking about the multivariate distribution of bodies and minds in the world, is that between the sexes. But sex is by no means the only way in which people differ! In many situations, you might want to categorize or describe people in many different ways, some more or less discrete _versus_ continuous, or high- _versus_ low-dimensional: age or race or religion or subculture or social class or intelligence or agreeableness.
It's possible that the categories that are salient in a particular culture ought to be revised in order to fit the world better: maybe we _should_ talk about categories like "masculine people" (including both typical men, and butch lesbians) more often! But the typical trans advocate shell game of just replacing "sex" with "gender" and letting people choose their "gender" isn't going to fly, because sex actually exists and we have a need for language to talk about it—or maybe, the fact that we have a need for language to talk about it (the fact that the information we observe admits compression) is what it means for sex to "actually" "exist".
Conversely, another classic gender-critical trope is that sex is _just_ about genitals and chromosomes and gamete size. Any "thicker" concept of what it means to be a woman or man is sexist nonsense. With some trepidation, I also don't think that one's going to fly. It's hard to see why most gender-critical feminists would care so much about maintaining single-sex spaces, if sex were strictly a matter of genitals or (especially) chromosomes or gamete size; it would seem that they too want mere statistical tendencies to be part of the concept.
-This is somewhat ideologically inconvenient for antisexists like I used to be, insofar as it entails biting the bullet on on masculine women and feminine men being less "real" women and men, respectively. Are our very concepts not then reinforcing an oppressive caste system?
+This is somewhat ideologically inconvenient for antisexists like I used to be, insofar as it entails biting the bullet on masculine women and feminine men being in some sense less "real" women and men, respectively. Are our very concepts not then reinforcing an oppressive caste system?
I don't think the situation is quite that bad, as long as the map–territory relationship stays mostly one-directional: the map describing the territory, rather than the territory being bulldozed to suit the map—outliers needing a slightly longer message length to describe, rather than being shot. In my antisexist youth, I don't think I would have wanted to concede even that much, but I couldn't then have explained how that would work mathematically—and I still can't. Let me know if you figure it out.
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