+What's a _woman_? An adult human female. (Let's [not play dumb about this](/2018/Apr/reply-to-the-unit-of-caring-on-adult-human-females/) today.) Okay, but then what does _female_ mean? One common and perfectly serviceable definition: of the sex that produces larger gametes—ova, eggs.
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+That's one common and perfectly serviceable definition in the paltry, commonplace _real_ world—but not in _the world of the imagination!_ We could _imagine_ the existence of a creature that looks and acts exactly like an adult human male down to the finest details, _except_ that its (his?) gonads produce eggs, not sperm! So one might argue that this would be a _female_ and presumably a _woman_, according to our definitions, yes?
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+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 male 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?
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+No, because humans whose gametes 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 a lot of information](https://www.lesswrong.com/posts/mB95aqTSJLNR9YyjH/message-length), but what it _means_ for the world to contain information is that some things in the world are more probable than others.
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+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`.
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+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.
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+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.