Matt McIrvin, on a quest to figure out when the USA was displaced from the center of the world (at least where map-makers are concerned), points to a fascinating map projection site put together by Carlos Furuti. It goes through all the different ways people have thought of to project a spherical Earth onto a flat map, doing their darndest to preserve nice features like shapes and sizes. Only after looking at all these different attempts does it really hit you how distorting most world maps are, if only because the nice features of one will draw attention to the glaring shortcomings of some other one. Round spheres are really quite geometrically different from flat planes -- who knew? My favorite projection is the Quincuncial Projection shown below. It is "conformal" (angle-preserving) almost everywhere, except at the four points where the Equator takes a dramatic right turn. These are also where the size distortions are the most dramatic; fortunately, we can stick these points in the middle of various oceans, where nobody is the wiser. The other obvious problem is that Antarctica is sliced into four little bits. But Antarcticans aren't a crucial constituency, so we can learn to live with it.
The reason this is my favorite, besides the fact that it's both fairly accurate and intrinsically cool, is that this projection was invented by Charles Sanders Peirce, someone known much more for his philosophy than for his cartographical skillz. (And "Peirce" is pronounced like "purse," just so you don't come off as a poseur when you drop his name in conversation.) Peirce was the orginator of pragmatism as well as semiotics, and was labelled by Bertrand Russell as "certainly the greatest American thinker ever." His manuscripts, if Wikipedia is to be believed (hey, why doesn't Wikipedia support trackbacks?), run to over 10,000 pages. And here he is inventing new ways to map the world. All of which is simply to say: if Charles Sanders Peirce were alive today, he would definitely have a blog.