<a id="literary-initials"></a>Or how, at University, I tried to go by my [first-and-middle-initials](https://en.wikipedia.org/wiki/List_of_literary_initials) because I wanted a gender-neutral [byline](https://en.wikipedia.org/wiki/Byline), and I wanted what people called me in real life to be the same as my byline—even if, obviously, I didn't expect people to not-notice which sex I am in real life because _that would be crazy_.
-(This attempted nickname change actually turned out to be a terrible idea that ended up causing me a huge amount of pointless identity-crisis psychological pain—my particular pair of real-life initials never really "felt like a name" even to me (as contrasted to something like "C.J." or "J.T.", which feel like a name on account of having a _J_ in it); I turned out to be incredibly uncomfortable with different people knowing me by different names, and didn't have the guts to nag everyone in my life to switch for something that didn't feel like a name even to me; _and_ the "gender-neutral byline" rationale almost certainly never held up in practice because my real-life first initial is a [high-Scrabble-score letter](https://en.wikipedia.org/wiki/Scrabble_letter_distributions#English) that begins one popular boy name and zero popular girl names. But it was the _principle!_)
+(This attempted nickname change actually turned out to be a terrible idea that ended up causing me a huge amount of pointless identity-crisis psychological pain—my particular pair of real-life initials never really "felt like a name" even to me (as contrasted to something like "C.J." or "J.T.", which [feel like a name on account of having a _J_ in them](https://astralcodexten.substack.com/p/initial-conditions)); I turned out to be incredibly uncomfortable with different people knowing me by different names, and didn't have the guts to nag everyone in my life to switch for something that didn't feel like a name even to me; _and_ the "gender-neutral byline" rationale almost certainly never held up in practice because my real-life first initial is a [high-Scrabble-score letter](https://en.wikipedia.org/wiki/Scrabble_letter_distributions#English) that begins one popular boy name and zero popular girl names. But it was the _principle!_)
Or how I stopped getting haircuts and grew my beautiful–beautiful ponytail. (This turned out to be a great idea and I wish I had thought of it sooner.)
You might think this is "unfair": some women—about 7 per 1000—are 5′11″, and we don't want to say they're somehow _less female_ on that account, so why can't I keep my height? The problem is that if we refuse to adjust for every trait for which the female and male distributions overlap (on the grounds that _some_ women have the same trait value as my male self), we don't end up with a result from the female distribution.
-The typical point in a high-dimensional distribution is _not_ typical along each dimension individually. [In 100 flips of a biased coin](http://zackmdavis.net/blog/2019/05/the-typical-set/) that lands Heads 0.6 of the time, the _single_ most likely sequence is 100 Heads, but there's only one of those and you're _vanishingly_ unlikely to actually see it. The [sequences you'll actually observe will have close to 60 Heads](https://en.wikipedia.org/wiki/Asymptotic_equipartition_property). Each such sequence is individually less probable than the all-Heads sequence, but there are vastly more of them. Similarly, [most of the probability-mass of a high-dimensional multivariate normal distribution is concentrated in a thin "shell" some distance away from the mode](https://www.johndcook.com/blog/2011/09/01/multivariate-normal-shell/), for the same reason. (The _same_ reason: the binomial distribution converges to the normal in the limit of large _n_.)
+<a id="typical-point"></a>The typical point in a high-dimensional distribution is _not_ typical along each dimension individually. [In 100 flips of a biased coin](http://zackmdavis.net/blog/2019/05/the-typical-set/) that lands Heads 0.6 of the time, the _single_ most likely sequence is 100 Heads, but there's only one of those and you're _vanishingly_ unlikely to actually see it. The [sequences you'll actually observe will have close to 60 Heads](https://en.wikipedia.org/wiki/Asymptotic_equipartition_property). Each such sequence is individually less probable than the all-Heads sequence, but there are vastly more of them. Similarly, [most of the probability-mass of a high-dimensional multivariate normal distribution is concentrated in a thin "shell" some distance away from the mode](https://www.johndcook.com/blog/2011/09/01/multivariate-normal-shell/), for the same reason. (The _same_ reason: the binomial distribution converges to the normal in the limit of large _n_.)
Statistical sex differences are like flipping two different collections of coins with different biases, where the coins represent various traits. Learning the outcome of any individual flip, doesn't tell you which set that coin came from, but [if we look at the aggregation of many flips, we can get _godlike_ confidence](https://www.lesswrong.com/posts/cu7YY7WdgJBs3DpmJ/the-univariate-fallacy-1) as to which collection we're looking at.
projects / Ultimately_Untrue_Thought.git / blobdiff