Great work, guys. You successfully demonstrated exactly what I said. Sort of, actually. Existoid read without comprehension, so that's at least more than was apparent before.

Every coordinate in 3D space is directly mapped from a single point on the globe to a single point on troolon's FE. It's a globe. Anyone standing on the surface of the Earth would perceive it to be a globe, which has converging lines of longitude at both poles.

But by all means, continue attacking this representation of the globe, expressed in a scary foreign coordinate system.

Let me summarize troolon's point as I understand it, and as I understand you to be restating:

Troolon makes no claims as to which version of earth is a reality (globe or flat). However, whichever earth is "reality" - globe or flat - we can use a coordinate system to create a map projection to look like the other shape. In other words, if we assume the earth is a globe, we can use a 3D coordinate system to create an accurate map that looks like an monopole, it's just an AE projection of a spherical reality. Or, if we assume the earth is flat, we can use a 3D coordinate system to create a 3D model of a globe, but it's just a spherical projection of the flat reality. Of course you can use a 3D coordinate system to make any map projection, regardless of what the underlying reality is.

I'm not disputing that. You seem to think I am. I'm making a different argument:

If we assume that,

*in reality, * the earth is a globe, and we map that globe using an accurate 3D coordinate system onto an AE projection (with the north pole at the center), and our AE projection is accurate to the globe reality, then regardless of unit of measure

*the absolute distances between each line of longitude at the circumference of the map is zero*. That's because on an actual globe, such lines would converge at the south pole (which is represented as a big circle on this AE projection). The projection makes the lines of longitude

*appear* to diverge, but if they diverged

*in reality* then the distance between each could not possibly be zero. Two lines that are spaced apart can't have a distance of zero between them, can they?

Look at this image:

https://www.dropbox.com/s/ungp3c57f3ulcks/Monopole%20map%20with%20longitudes%20at%20the%20circumference%20highlighted.png?dl=0Each red line would have a distance of zero between each other (no matter what units of measure you choose to use), if the world, in reality, were a globe, and this map was merely a projection of that real globe onto a flat surface.

By contrast, if we assume that,

*in reality, * the earth is flat, with the north pole at the center, and we map that flat world using an accurate 3D coordinate system onto a spherical projection, with the outer circumference of the world condensed into a point at the "bottom" of the sphere, then regardless of unit of measure

*the absolute distances between each line of longitude which converge to a point at that "bottom" of the sphere cannot be zero but a positive number!*.

Remember, in this latter example we are assuming that the earth, in reality, is flat and so those red lines in my attached image are some measurable distance apart. Say, roughly 10,000 miles apart along the curve of the circumference. And that 10,000 miles of real ice between each is "projected" to a single point.

That's why I put an emphasis on this particular quote from troolon, which I repeat here without emphasis:

"Taking an orthogonal ruler, to a flat-earth coordinate system produces invalid results. Just like taking my bend ruler to your globe would completely invalidate it."

In other words, when you put actual, measurable numbers of distances between each line of longitude, the same coordinate system will produce invalid results depending on whether

*the real shape of the object measured *is a flat monopole world or a globe. [EDIT: and thus my WW2 plotting chart evidence. The planes flying over the ocean had to have precisely measured distances between each stated coordinate - each line of longitude - on their charts, or else they would virtually always crash into the ocean and die. They couldn't just fly between unknown distances along each latitude until the next longitude without knowing the number of km they were traveling!].

I'll restate my final statement from my previous post a little differently given the fuller explanation above:

'The lines of longitude cannot both converge AND diverge in reality, because the absolute, measurable distance between converging lines and diverging lines cannot be the same. That's impossible. So, either longitude, in reality, converges (as in RET), but the AE projection using a 3D coordinate system merely appears like they are diverging when they're not.

**Or**, lines of longitude, in reality, diverge further south (as in FET), but global representation merely make them appear like they are converging when they're not.

In reality, the same lines of longitude cannot both converge and diverge. They must be actually doing one or the other. Yes, the projection can make it look however you want.