[TeMPOraL]

I think GP is saying that GGP assumes "tone" is one direction, in the sense there exists a vector V representing "tone direction", and you can scale "tone" independently by multiplying that vector with a scalar - hence, 1 dimension.

I'd say this assumption is both right and wrong. Wrong, because it's unlikely there's a direction in embedding space corresponding to a platonic ideal of "tone". Right, because I suspect that, for sufficiently large embedding space (on the order of what goes into current LLMs), any continuous concept we can articulate will have a corresponding direction in the embedding space, that's roughly as sharp as our ability to precisely define the concept.