Let's show what I mean on an example.
Flying towards a VOR (not knowing the distance), HSI course pointer pointing
towards the VOR. Let's say the plane is really far from the VOR and we turn the course pointer 5 degrees (no matter what way) CDI will move to one side (far because of the distance). If the plane was close to the VOR and we turned the course pointer 5 degrees CDI would not move as much (or should not because the deviation is really small).
based on this example CDI needs to know distance from VOR to work properly, yet it works without knowing the distance. How?
(If I'm wrong about something, quickly correct me)