Tom,

The fundamental issue that you seem to not understand, is Euclidean geometry doesn't have anything to do with perspective. Euclidean geometry describes where something is. We can use that geometry along with a location to even determine where and when things will happen according to perspective and the angular limit of the eye. As I showed you in the other thread. But what perspective doesn't do is change the physical angle of objects.

And where is the evidence that the perspective lines will approach each other forever and never touch, as hypothesized by Euclid?

This is a strawman. Euclidean geometry says nothing of the sort. It says parallel lines will never meet. Which they won't, or they wouldn't be parallel. It doesn't deal with your 'perspective lines' at all. It describes the location of something relative to another thing, and it's testably accurate at ANY distance you care to name that is physically measurable.

If they do touch at some distance, then your diagram will look a whole lot different.

Your parallel lines will never touch though. They will

*seem* to touch because of the angular limit of the eye, and we can predict accurately where this occurs as I showed you. But once again, Euclidean geometry is dealing with the physical location of something, and there it is correct that two

*parallel* lines will never meet. There is nothing here about 'perspective lines' as you keep saying.

The fundamental premise of this continuous universe model needs empirical evidence behind it -- things to suggest that is how it is in the real world.

What continuous universe? What are you even talking about, as it has nothing to do with the subject of simple geometry. For the third time I say it, in the hopes that repetition will somehow help you get it. Euclidean geometry in and of itself doesn't deal with where things

*appear* to be. It deals with where they physically are. We can use it's properties and the properties of the eye to accurately predict where, say two railroad tracks will no longer be distinguishable as two separate objects, but that's not part of what it tells us on it's own.

Once again, if you wish to say the sun appears to be at 0 degrees, when the math says it's at 20 degrees then you must present one of the following:

A) Proof that the math no longer works accurately beyond 'X' Miles/KM.

B) Proof that the math doesn't work in the real world, contrary to the proofs done upon it since Euclids time.

C) Evidence that the sun is somehow 'special' and immune to this mathematical law.

I think the burden of proof is on you, good sir. You are claiming that they will eventually touch. Have you ever seen this or have evidence.

Railroad tracks will seem to touch at the horizon, and the fact that things are able touch the horizon at all demonstrates that the perspective lines appear to merge. Under the Elucid model it should be impossible for any body to ever get to the horizon.

Empirical observation vs. ancient mathematical hypothesis. You need to show that it is all an illusion. Go.

BTW, this is another strawman, just in case you didn't get that above. Perspective lines have no part in Euclidean geometry. Parallel lines will never meet. They will appear to 'meet' at the point which our eyes can no longer distinguish the angular distance between them. Roughly 0.02 degrees. Now clearly things can get in the way, but you need to explain how a sun that should still be 20 degrees above the horizon, is appearing at 0 degrees.