i think you're still misunderstanding what i'm trying to say. i agree that all of these objects are in 3d, euclidean space. the path light takes between the sun and the moon is a straight line. i'm talking about the way this straight line path
appears to us based on our perspective.
it's like watching an airplane fly into and out of view. from our perspective on the ground, it comes into view at the horizon, makes an arced path across the sky, and then goes out of view at another bit of horizon. the airplane flies a straight line path in 3d, euclidean space, but we see that path as an arc with each endpoint on the horizon.
now imagine that the straight line path of the airplane is a beam of light. the path of the light beam is straight, but to us it looks curved. it's just perspective.
A planetarium is just a movie on a curved screen. When we look up at the universe we are not looking at a movie on a screen. Can't you see that there is a difference?
why a curved screen, though? why not a cube-shaped room, or a pyramid-shaped room, or a hexagon, or any other shape? why do they all choose a spherical shape?
No, you cannot tell how far away they are.
precisely. the night sky doesn't
appear to us to have any depth. it looks like a surface. so all the 3d stuff way out in 3d outer space looks to us like it's on a 2d surface. that's why the moon looks like a circle and not like a sphere.
you say i'm giving you no explanations, but i'm really just asking you to rely on some very basic observations about how things appear to us. does the sky look 3d to you, or 2d? if it looks 2d, but it's actually a 3d space, then do you think this might affect how things way out in space
appear to you?
ultimately, your argument implicitly assumes that all straight lines always appear straight to us. that no straight line path can ever appear curved. you only have to look around your room to see that this isn't the case. or read section 3 of the paper. or both, i guess. i mean you're probably gonna have to look around your room at some point anyway. might as well get two birds stoned at once.
also the more i think about it, i'm not sure the twine thing will work. but i can't tell if that's just because i'm picturing sun-moon orientations that aren't real. i'll get some twine and try it the next time i see the moon out at dusk.