The problem is that you cannot unfold a sphere into a flat surface without causing severe distortion complete with pac-man style wormholes. It's easier to see with a cube. I suspect most of us have built a paper cube before. You trace out the 6 faces on a flat surface, cut them out, and fold them into a cube. Unfold it again, and you'll see that many of the faces aren't anywhere near the edge they touched as a cube. Those edges are what I'm calling the pac-man style wormholes... you cross one boundary and appear instantly on another face of the cube. It works when it's assembled as a cube, but when you lay it flat, you need wormholes.

What this means is that the Earth cannot be both a sphere AND a flat surface. It must be one or the other (assuming we aren't going into higher-dimensional math and allowing for wormholes). I hope that's simple enough. It's either a globe or a plane - it can't be said that "either way works".

So if you make a flat map (any map really), we'll want to test the latitude and longitude of any city on your map against empirical observations. (These were outlined by a previous poster.) If the flat map does not match the known latitude and longitude at any point, we either need to prove the accepted latitude and longitude of that city is incorrect, or we must reject the map as inaccurate.

As I've just pointed out, there is no way for both the globe and a flat map to represent the exact same latitudes and longitudes without severe distortion. We also know that the standard globe model DOES accurately represent the latitude and longitude of every city on it. (Please let us know if you'd care to dispute this point.)

So... before making any FE map, you would first want to come up with some justification for why you are going to challenge the latitude and longitude of cities all over the Earth.

The same can be said for distances between these cities. If we can measure (or even estimate) the distance between any 2 points on the Earth, we'll need to make sure your new map reproduces those empirical results correctly. Once again, you'll first need to establish that there are a pair of cities on the globe which are represented inaccurately.

So if you have a specific, testable reason to challenge the latitude and longitude of any city on the Earth, please share that. (My apologies if this has been given before... if so, I have missed it and would appreciate being directed to it... thanks).