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“To see all of the globe, you have to rotate it; to see all of our new map, you simply have to flip it over.”

That's a way to see half of the Earth, and then separately see the other half.

Surely the distortion of the perceived distance between areas just north and south of the equator is the same or greater than that between Japan and Hawaii in current maps. In fact it's very difficult to judge the relationship between the north and south in general because they are basically two separate maps.

And while I can see the appeal of centering the maps on the poles, as it is "apolitical" and probably leads to less overall distortion, it prioritises what are, for the vast majority of humans, the least relevant parts of the world, at the expense of all the other parts.

It honestly doesn't strike me as useful at all, though I appreciate that it can be academically interesting to create new map formats that satisfy some manufactured constraints.

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I feel sorry for anybody living close to the equator. At least the Mercator map chops an ocean, not land where people live (but people living on islands close to that line could have something to complain.)
This map has major distortion in political dimension, prioritizing Global North over Global South.

To be honest, I’m not sure we need A map of the world. Several maps centered on different regions would do a better job from educational perspective, showing point of view of people living there.

How many times will we have to discover, again and again, that Mercator projection is really the worst possible map, apart from all the others?
This is cool, but the flipping-over aspect seems a bit annoying, perhaps one could draw lines connecting points of the border of the right side to corresponding points on the left side instead to not require the flipping over.

And make versions that are aligned in other directions rather than the equator perhaps

Coincidentally, yesterday I saw (again) “The West Wing” scenes[1] that express this problem (and the related social issues). It was the first learned about map projections and I think if they aren’t already an explicit topic in school, they ought to be. I find it very interesting.

[1] https://youtu.be/eLqC3FNNOaI