While I like to see this movement, I wanted to develope it into a modern view.

Not only this, but how perception is dependant when seeing tessellations. Sort of like using a line of a shadow or light, depending on your point of view to support the line?:)

What mathematics would describe this?

It would be fun to use a modular form to make an Escher-like repeating conformal map of the earth in the hyperbolic plane. Escher himself veered towards similar possibilities. In addition to the famous hyperbolic tiling, Circle Limit IV or “Angels and Devils”, he used the same angels and devils to tile the sphere, as a wood carving. The real starting point is a smaller sphere tiled by one angel and one devil, with both of the Escher works as branched conformal lifts. (Indeed if you look carefully, the angels and devils are both just decorated triangles, rendering angels and devils equivalent to each other by reflection. So you could start with a disk with three marked points for the two wingtips and the joined feet of either creature.)

But he definitely is an amazing philosopher. There’s a scholarly site for papers on him that has many of his main papers.

-cvj

My personal preference is not for strict equal-area projections, since they distort shapes so badly. Better to compromise between shape/size issues, as Peirce’s map does pretty well.

As Wolfgang points out, putting the South Pole at the top makes an interesting political statement. Although you still have to defend your equatorial-centrism.

Cheers,

-cvj

To do better, you have to abandon flatland and go to Google Earth.

The Mercator projection, which makes Greenland bigger than Africa, was Peters’ great strawman, and at the time, it really was used occasionally for wall world maps in education, though it was already fading from fashion. The Mercator is terrible for that purpose. But there are lots of projections that are better for world maps than the Mercator. For that matter, Peirce’s quincuncial projection doesn’t distort relative sizes that much, though it’s not equal-area.

And now for some cranky unsupported speculation of my own: I think the Peters map’s sales pitch works in part because we are social bipeds, and associate *height* with “bigness”. While it represents areas accurately, the Gall-Peters makes tropical countries look relatively bigger even than they are, by stretching them vertically so they look tall. That gives a sort of shock of the new: look how huge Africa is! But if you turn the map sideways, suddenly Eurasia looks huge again.

This and many other interesting things are in Louis Menand’s book The Metaphysical Club. I recommend it highly.

CSP got into lots of trouble for being more into free love than was standard for the time (I think cohabiting without marriage?)

Now if we can only find a way to get the majority of kids (and some adults, too) in the USA to find their country on *some* world map.

This is slightly off topic, but I can’t resist bringing it up. I grew up in a S.Asian nation and came here as an undergrad. I have gotten the following questions/ comments from people I’ve met in the USA:

* “I didn’t know there were pianos in that part of the world” (after hearing me play a Mozart sonata). This was from a Physics instructor.

* “Are there brown skinned Christians?”

* “Are there eggs in your country?”