Imagine being in a relatively small 3-sphere. Since geodesics behave differently from euclidean space, light will follow different trajectories, and I am wondering what the impact would be on our perception of depth.
On the one hand, suppose that an object starts out at your location (let's say at a pole), and then moves away. Initially the solid angle it subtends from your eye will get smaller, though not as fast as in Euclidean space.
Then when it reaches the equator, it will attain a minimum, but then start appearing larger again, until at the antipode it will look as if it is right there at your location, though more fuzzy. In fact, you will see it in any onubstructed direction that you look.
In the image (of a 2-sphere) you can think of a line segment (geodesic if you want) whose ends touch two of the adjacent drawn meridians somewhere close to a pole. When moving that to the equator with one end along a meridian, the other will get ever further from the adjacent one, but afterward it will get closer again, until at some point close to the opposite pole it will touch both meridians again and look just as large, and then grow further.
Being used to Euclidean behavior of space (and the constancy of the size of most objects), we would probably perceive it as leaving at some speed, then slowing down (and eventually coming to a standstill and turning around). In any case, right from the beginning it would look closer to us than it really is.
On the other hand, if we use both eyes, there is a second effect. Since the angles of a geodesic triangle sum to more than $\pi$, the triangle formed by our eyes and a (point) object that is right in front of us (at any distance) will have angles at our eyes that are larger than the angle they would make in Euclidean space, hence the point would seem further than it really is. In fact, when further than a quarter great circle, our eyes would have to bend outward to focus on the point. I guess we would just interpret that as two points.
There is no real contradiction here of course, the light bends how it bends, and if that is at odds with our experience, then so be it.
My questions (not fully mathematical, but since the setting is more math than anything else I think it is still on-topic) How do you think we would actually perceive a solid object moving away at constant speed?