Mainly what I have been saying over the last ten years is that the perspective lines are finite rather than infinite. There will be a point at the distance where they merge together.
Things which happen where the Ancient Greek model say should happen at infinity will occur a finite distance away.
- The Ancient Greek model says that it would take infinity for the sun to get to the horizon.
- The Ancient Greek model says that a body directly above your head that recedes into the distance would have to increase its altitude by infinity to stop rotating to perspective.
- The Ancient Greek model says that an overhead receding body would have to increase its altitude by infinity to become perfectly constant in its pace across the sky.
All of the above predictions are predicated upon a continuous universe model where parallel perspective lines would only merge at an infinite distance away (read: never).
Merging perspective lines can be backed up empirically -- The horizon is certainly not an infinite distance away. We do witness lines merging in the distance (even if you want to call it limits of optics, they still merge regardless, and perhaps that limit is part of how we experience the world and should not be discounted as an effect separate from perspective).
In contradiction, continuous perspective lines cannot be observed empirically. Rather than something that is seen as in the above examples, they must be imagined to exist.
The phenomenon known as perspective arises from the fact that light generally travels in straight lines. Everything else we know about perspective can all be derived straight from that. To make any of Tom's ideas work, we need light to bend. Tom is simply arguing that light bends.
Let's consider these points one at a time:
"- The Ancient Greek model says that it would take infinity for the sun to get to the horizon."
I think we can all agree, to get the FE model to work with a sunset, we need a substantial amount of light bending.
We can also agree, that the RE model acknowledges a much smaller amount of bending via refraction near the horizon.
"- The Ancient Greek model says that a body directly above your head that recedes into the distance would have to increase its altitude by infinity to stop rotating to perspective."
I frankly don't understand what is meant by "rotating to perspective." I googled that and got no hits. Are we trying to explain why we all see the same face of the Sun no matter where we are on Earth? Again, the FE model is going to need some bendy light to pull that off.
Maybe Tom can explain this one.
"- The Ancient Greek model says that an overhead receding body would have to increase its altitude by infinity to become perfectly constant in its pace across the sky."
Agreed. I can only surmise we're talking about the sun again. The Sun can be observed moving at a constant angular rate across the sky. According to the FE model, we're going to need some serious light bending to make it happen.
So if we start from a flat Earth with a close (3000 miles above) Sun, we cannot make observations match without bendy light. Got it. Agreed. This leaves us with 2 possibilities:
a) The Earth is not flat
b) Light bends
Can we prove that light doesn't bend? At close distances we certainly can. If we avoid refraction, light can be shown to be straight as far out as your experiment can reach (100s of feet?). Earlier I showed how crepuscular rays show light to move in straight lines out as far as the distant clouds (10s of miles?). But what do we know about how light moves out farther than that?
Some have suggested that a great dome in the sky causes dramatic refraction as the Sun's light passes through it, and that is beyond the reach of our crepuscular rays.
Others (Tom) have suggested that there is a natural property of light that makes it bend as it travels really long distances.
These things are hard to test empirically. However, we have more information here. We've acknowledged that we need light to bend to make this work, but we can actually say how much we need the light to bend and in what way.
To make the Sun cross below the horizon from anywhere on the FE, what kind of bending does that take? For simplicity, I'll take the AE map, and let's just sit on the equator on the equinox. At noon, the Sun is 3000 miles straight up. At sunset, the sun is 3000 miles up, 6000 miles to the West and 6000 miles North. We need that Sun to appear to be directly West and right on the horizon. This tells us that light has bent 45 degrees counter-clockwise and around 20 degrees upward on its journey to us.
What do you say Tom? Is this basically what we're talking about here? I know you don't like the AE map, should we use the dual-pole map instead?
Let me summarize:
a) We cannot do empirical measurements to prove the straightness of light out to the 1000s of miles we need to reach the FE sun.
b) We need light to bend to make any of the FE models match observations
c) We CAN work backwards from the observations to see what sort of bending the FE model requires.