The point being is that two different maps can function in completely different ways or topologies and still yeild the same accuracy in results. This illustrates one of the many flaws in the line of logic you've been trying to use here.

No, that was a separate point. What we were discussing was how to "disprove a map". You agree that a map's accuracy can be disproved, yet insist that maps can't be disproved. Let's back up and try again: Using the method I described,

*disprove the accuracy of the results of a RE map* (these are your words; you said this is possible to do). Can you do it? Here is the method again:

Indicate points A and B on a map. Go to the location the map represents at A. Travel in the direction of B the proper distance according to the map's scale (this is where you get to use your math skills!). Demonstrate that the location you stop at is different from the location represented at B.

The possible of existence of functionally different yet equally accurate maps make the whole point moot though.

If you are referring to different projections, you are wrong and once again demonstrating your mathematical illiteracy. They all equally map a globe.

They don't "equal" a globe. I was not, in particular, referring to different projects. I am certainly not mathematically illiterate.

This answer provides no information. My response was predicated on "if you are referring to different projections". You say that is not "in particular" what you refer to. Okay -- so what

*do* you refer to? And yes, they all map a globe equally. All you need to do is reverse the transformation formula to work back to globular coordinates, and the result is the same regardless of projection. The fact that different projections can be successfully used does not in any way prove that maps are inaccurate.

East-West distances are predicted accurately within the model

Demonstrate this. Your "model" is nothing but two circles without any actual mapping involved, so without further information from you I can only assume that it's merely a duplicate of the classic northern azimuthal, which switches to a southern azimuthal when you reach the edge. As we all know, these only address north-south distances.