I think you are right on the source of confusion, I have tried to explain the relation between hyperbolic space and Lorentz transformations in my latest answer.

I think you are right on the source of confusion, I have tried to explain the relation between hyperbolic space and Lorentz transformations in my latest answer. See here: https://news.ycombinator.com/item?id=23549361 https://news.ycombinator.com/item?id=23549361