The special rel just-so story I had got was night people and day people, and the night people had set true N to the north star, while the day people used the midpoint of sunrise and sunset for true N, so all their cardinal directions were rotated relative to each other.

They were then confused why their measurements of distances always agreed but of position always differed, until someone came up with the rotation equations that allowed one to map day to night and night to day.

Change normal trigonometric rotation to hyperbolic, and you've got most of special rel.