It’s the first in a series of three that I can very highly recommend.
> there's no way that there's a 1-to-1 correspondence between concepts and dimensions.
I don’t know about that! Once you go very high dimensional, there is a lot of direction vectors that are almost perfectly perpendicular to each other (meaning they can cleanly encode a trait). Maybe they don’t even need to be perfectly perpendicular, the dot product just needs to be very close to zero.
It’s the first in a series of three that I can very highly recommend.
> there's no way that there's a 1-to-1 correspondence between concepts and dimensions.
I don’t know about that! Once you go very high dimensional, there is a lot of direction vectors that are almost perfectly perpendicular to each other (meaning they can cleanly encode a trait). Maybe they don’t even need to be perfectly perpendicular, the dot product just needs to be very close to zero.