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`**. _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 . 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 a very efficient encoding.
-To _be_ efficient, you'd want to reserve the shortest words for the most common case: 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`).
+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`).
Suppose that, even among the very few exceptions that aren't all-zeros or all-ones, the first bit is _always_ in the majority and is never "flipped": you can have exceptions that "look like" `00000100000000000000` or `11011111111101111011`, but never `10000000000000000000` or `01111111111111111111`.
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—I wish I lived in a world where I could do math blogging for the greater glory of our collective understanding of greater reality. ("Gender?" I would say, confused, "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 [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 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 [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 gentials in most everyday situations. (You're probably not directly 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.
If trans advocates go astray in trying to destroy the concept of sex, their gender-critical foes often
+ * trans advocates say: there are exceptions, therefore
The typical gender-critical critique of trans ideology
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