+"I know that I'm a girl because girls like specific things like rainbows and I like rainbows so I'm a girl."
+
+"Is that how you knew in the first place?"
+
+"Yeah."
+
+"You know there are a lot of boys who like rainbows."
+
+"I don't think boys like rainbows so well—oh hey! Here this ball is!"
+
+(When recounting this conversation, the parent helpfully adds that rainbows hadn't come up before, and that the child was looking at a rainbow-patterned item at the time of answering.)
+
+It would seem that the intepretation of this kind of evidence depends on one's prior convictions. If you think that transition is a radical intervention that might pass a cost–benefit analysis for treating rare cases of intractable sex dysphoria, nonsense answers like "because girls like specific things like rainbows" are disqualifying. (A fourteen-year-old who could read an informed-consent form would be able to give a more compelling explanation than that, but a three-year-old just isn't ready to make this kind of decision.) Whereas if you think that some children have a gender that doesn't match their assigned sex at birth, you might expect them to express that affinity at age three, without yet having the cognitive or verbal abilities to explain it. Teasing apart where these two views make different predictions seems like it should be possible, but might be beside the point, if the real crux is over [what categories are made for](/2018/Feb/the-categories-were-made-for-man-to-make-predictions/).
+
+Anyway, that's just a hypothesis that occurred to me in early 2020, about something that _could_ happen in the culture of the current year, hypothetically, as far as I know. I'm not a parent and I'm not an expert on child development. And even if the "Clever Hans" etiological pathway I conjectured is real, the extent to which it might apply to any particular case is complex; you could imagine a kid who _was_ "actually trans" whose social transition merely happened earlier than it otherwise would have due to these dynamics.
+
+For some reason, it seemed important that I draft a Document about it with lots of citations to send to a few friends. I thought about cleaning it up and publishing it as a public blog post (working title: "Trans Kids on the Margin; and, Harms from Misleading Training Data"), but for some reason, that didn't seem as pressing.
+
+I put an epigraph at the top:
+
+> If you love someone, tell them the truth.
+>
+> —Anonymous
+
+Given that I spent so many hours on this little research and writing project in May–July 2020, I think it makes sense for me to mention it at this point in my memoir, where it fits in chronologically. I have an inalienable right to talk about my own research interests, and talking about my research interests obviously doesn't violate any norm against leaking private information about someone else's family, or criticizing someone else's parenting decisions.
+
+(Only—[you two have such beautiful children](/2023/Dec/hrunkner-unnerby-and-the-shallowness-of-progress/)!)
+
+### The _New York Times_ Pounces (June 2020)
+
+On 1 June 2020, I received a Twitter DM from _New York Times_ reporter Cade Metz, who said he was "exploring a story about the intersection of the rationality community and Silicon Valley." I sent him an email saying that I would be happy to talk but that had been pretty disappointed with the community lately: I was worried that the social pressures of trying to _be_ a "community" and protect the group's status (_e.g._, from _New York Times_ reporters who might portray us in an unflattering light?) might incentivize people to compromise on the ideals of systematically correct reasoning that made the community valuable in the first place.
+
+He never got back to me. Three weeks later, all existing _Slate Star Codex_ posts were taken down. A [lone post on the main page](https://slatestarcodex.com/2020/06/22/nyt-is-threatening-my-safety-by-revealing-my-real-name-so-i-am-deleting-the-blog/) explained that the _New York Times_ piece was going to reveal Alexander's real last name and he was taking his posts down as a defensive measure. (No blog, no story?) I [wrote a script](/source?p=Ultimately_Untrue_Thought.git;a=commitdiff;h=21731ba6f1191) (`slate_starchive.py`) to replace the _Slate Star Codex_ links on this blog with links to the most recent Internet Archive copy.
+
+### Philosophy Blogging Interlude 3! (mid-2020)
+
+I continued my philosophy of language work, looking into the academic literature on formal models of communication and deception and writing a [couple](https://www.lesswrong.com/posts/4hLcbXaqudM9wSeor/philosophy-in-the-darkest-timeline-basics-of-the-evolution) [posts](https://www.lesswrong.com/posts/YptSN8riyXJjJ8Qp8/maybe-lying-can-t-exist) encapsulating what I learned from that—and I continued work on my "advanced" philosophy of categorization thesis, the sequel to ["Where to Draw the Boundaries?"](https://www.lesswrong.com/posts/esRZaPXSHgWzyB2NL/where-to-draw-the-boundaries)
+
+The disclaimer note that Scott Alexander had appended to "... Not Man for the Categories" after our Christmas 2019 discussion had said:
+
+> I had hoped that the Israel/Palestine example above made it clear that you have to deal with the consequences of your definitions, which can include confusion, muddling communication, and leaving openings for deceptive rhetorical strategies.
+
+This is certainly an improvement over the original text without the note, but I took the use of the national borders metaphor to mean that Scott still hadn't gotten my point about there being laws of thought underlying categorization: mathematical principles governing _how_ choices of definition can muddle communication or be deceptive. (But that wasn't surprising; [by Scott's own admission](https://slatestarcodex.com/2013/06/30/the-lottery-of-fascinations/), [he's not a math guy](https://slatestarcodex.com/2015/01/31/the-parable-of-the-talents/).)
+
+Category "boundaries" are a useful visual metaphor for explaining the cognitive function of categorization: you imagine a "boundary" in configuration space containing all the things that belong to the category.
+
+If you have the visual metaphor, but you don't have the math, you might think that there's nothing intrinsically wrong with squiggly or discontinuous category "boundaries", just as there's nothing intrinsically wrong with Alaska not being part of the contiguous United States. It may be inconvenient that you can't drive from Alaska to Washington without going through Canada, but it's not wrong that the borders are drawn that way: Alaska really is governed by the United States.
+
+But if you do have the math, a moment of introspection will convince you that the analogy between category "boundaries" and national borders is shallow.
+
+A two-dimensional political map tells you which areas of the Earth's surface are under the jurisdiction of which government. In contrast, category "boundaries" tell you which regions of very high-dimensional configuration space correspond to a word/concept, which is useful _because_ that structure can be used to make probabilistic inferences. You can use your observations of some aspects of an entity (some of the coordinates of a point in configuration space) to infer category-membership, and then use category membership to make predictions about aspects that you haven't yet observed.
+
+But the trick only works to the extent that the category is a regular, non-squiggly region of configuration space: if you know that egg-shaped objects tend to be blue, and you see a black-and-white photo of an egg-shaped object, you can get close to picking out its color on a color wheel. But if egg-shaped objects tend to blue _or_ green _or_ red _or_ gray, you wouldn't know where to point to on the color wheel.
+
+The analogous algorithm applied to national borders on a political map would be to observe the longitude of a place, use that to guess what country the place is in, and then use the country to guess the latitude—which isn't typically what people do with maps. Category "boundaries" and national borders might both be illustrated similarly in a two-dimensional diagram, but philosophically, they're different entities. The fact that Scott Alexander was appealing to national borders to defend gerrymandered categories, suggested that he didn't understand this.
+
+I still had some deeper philosophical problems to resolve, though. If squiggly categories were less useful for inference, why would someone want a squiggly category boundary? Someone who said, "Ah, but I assign higher utility to doing it this way" had to be messing with you. Squiggly boundaries were less useful for inference; the only reason you would realistically want to use them would be to commit fraud, to pass off pyrite as gold by redefining the word "gold".
+
+That was my intuition. To formalize it, I wanted some sensible numerical quantity that would be maximized by using "nice" categories and get trashed by gerrymandering. [Mutual information](https://en.wikipedia.org/wiki/Mutual_information) was the obvious first guess, but that wasn't it, because mutual information lacks a "topology", a notion of "closeness" that would make some false predictions better than others by virtue of being "close".
+
+Suppose the outcome space of _X_ is `{H, T}` and the outcome space of _Y_ is `{1, 2, 3, 4, 5, 6, 7, 8}`. I wanted to say that if observing _X_=`H` concentrates _Y_'s probability mass on `{1, 2, 3}`, that's more useful than if it concentrates _Y_ on `{1, 5, 8}`. But that would require the numerals in _Y_ to be numbers rather than opaque labels; as far as elementary information theory was concerned, mapping eight states to three states reduced the entropy from log<sub>2</sub> 8 = 3 to log<sub>2</sub> 3 ≈ 1.58 no matter which three states they were.
+
+How could I make this rigorous? Did I want to be talking about the variance of my features conditional on category membership? Was "connectedness" what I wanted, or was it only important because it cut down the number of possibilities? (There are 8!/(6!2!) = 28 ways to choose two elements from `{1..8}`, but only 7 ways to choose two contiguous elements.) I thought connectedness was intrinsically important, because we didn't just want _few_ things, we wanted things that are similar enough to make similar decisions about.