All maps are a distortion in one way or another. It just isn’t possible to present the surface of a sphere onto a flat surface without introducing some sort of inaccuracy. The conventional Mercator’s projection — the one we’re all used to from our school atlases — offers a map on which straight lines are lines of constant compass bearing. Dead useful for navigation, but by preserving the shapes of the nations as they appear on the globe, the map introduces a distortion in the relative sizes of the nations. The Peter’s Projection, on the other hand, deliberately presents relative land areas accurately but distorts the shapes of the land masses.
Now there’s a new way of looking at the world: Worldmapper produces maps on which territories are re-sized according to a subject of interest. Absolutely fascinating.