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 they're 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. Each such sequence is individually less probable than all Heads, but there are vastly more of them.
-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 which set the coin came from, but if we look at the aggregation of many flips, we can get _godlike_ confidence as to which collection we're looking at.
+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 which set the 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.
A single-variable measurement like height is like a single coin: unless the coin is _very_ biased, one flip doesn't tell you much. But there are lots of things about people for which it's not that they can't be measured, but that the measurements require _more than one number_.
projects / Ultimately_Untrue_Thought.git / blobdiff