If you have some static scene in Euclidean geometry, you can possibly also have a static scene in hyperbolic geometry which looks the same*. But the parallax effects when you move would be different, and also that hyperbolic scene likely would not be natural for hyperbolic geometry (as you say, you would have to make the distant objects larger; if you approach them, you learn that they are in fact large, while the objects close to your original POV are tiny).* depending on what you mean by "looks the same". How do you perceive depth? In a natural model of depth perception based on binocular vision or parallax, the hyperbolic space looks like a bounded ellipsoid (more precisely, stretched Beltrami-Klein model), so it could not look like an infinite Euclidean scene.
No comments yet.