Is the following true? If space were truly Euclidean then distant objects would NOT look smaller than closer objects. They would retain their absolute size regardless of their distance from the observer, only the sharpness of the image would decrease. Since we see objects get smaller as the distance between us grows, and since we see parallel lines intersect "at infinity", we may infer from that alone that our space is curved and, therefore, non-Euclidean.
This would occur only if space were bent along a tangent away from your center of vision in every direction, so that at infinite distance along the z-axis the object assumed infinite length in the x and y axis. Space is pretty much Euclidean in most places which is precisely the reason why we percieve depth in the way we do
No, that is incorrect, CTEBO. Our space is approximately Euclidean; the amount by which it differs from flat, if at all, is tiny. The effect you're talking about is a simple matter of perspective. The apparent size of an object depends on the size of the angle subtended by the object at your eyes - that's all. Curvature of space is irrelevant.
When you say, "This would occur . . ." What does "this" refer to? In my original post I made two assertions: A) that a truly Euclidean space would yield parallel lines that do NOT meet at infinity along the z axis, and B) that our mode of depth perception (far=small, near=big) is a consequence of curved space. Does your "this" refer to claim A or claim B? P.S. I'm not trying to dispute you
I meant 'this' as in parallel lines meeting at infinity along the z-axis. But forget what i said before, we already percieve it as a tanget towards our centre of vision, what i should of said was that if space were bent in a sine curve away from our centre of vision then we would see planes as remaining a constant length in the x and y axis regardless of distance, hence no convergence. Space is as i said pretty much Euclidean in most places.
