-Title: Subspatial Distribution Overlap and Cancellable Stereotypes; Or, Gender Identity as Cognitive Illusion
+Title: Subspatial Distribution Overlap and Cancellable Stereotypes
Date: 2021-06-01 05:00
Category: commentary
Tags: categorization, epistemology
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](TODO: linky and accents) 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`**. _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](TODO: linky) 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 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`).
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`.
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 stuff. A dictionary definition is just a helpful pointer to help people pick out "the same" concept in their _own_ world-model: in teaching a young child about sex (or "gender"), you only have to say "boys and men are the ones with a penis, examples include your Dad and Uncle Frank, non-examples include your Mom and Grandma Mary" and the child's brain's pattern-matching faculties will soak up the rest, [...]
-(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 or configurations of sexual anatomy. In birds, the presence or absence of a _Z_ chromosome determines whether an animal is _female_, in contrast the _Y_ chromosome's determination of maleness in mammals, and reptiles' sex is determined by the temperature of an lain egg while it develops (!). And let's not get started on the cloaca. [TODO: verify all])
+(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 or configurations of 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 [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).)
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projects / Ultimately_Untrue_Thought.git / blobdiff