My intuition of this problem is much simpler — assuming there’s some rough hierarchy of concepts, you can guesstimate how many concepts can exist in a 12,000-d space by taking the combinatorial of the number of dimensions. In that world, each concept is mutually orthgonal with every other concept in at least some dimension. While that doesn’t mean their cosine distance is large, it does mean you’re guaranteed a function that can linearly separate the two concepts.
It means you get 12,000! (Factorial) concepts in the limit case, more than enough room to fit a taxonomy
It means you get 12,000! (Factorial) concepts in the limit case, more than enough room to fit a taxonomy