Each and every map represents a distorted view of reality. Therefore, cartograms are not as unusual as they might appear at a first glance. Map projections are a central aspect of the Worldmapper project because the maps (respectively cartograms) featured on this website are not very different from other re-projections of the world, albeit in a different way than conventional projections used in cartography. Rather than trying to solve the conflicts of distortion when drawing a three dimensional surface on to a two dimensional area (be it a screen or a paper map), Worldmapper cartograms distort our image of the world on purpose and show each country in proportion to a specific set of quantitative data.
A conventional map serves as a reference map to guide through the distortion of a cartogram with a more common image of the world, although in many cases a population cartogram (see related maps above) is the more natural basemap since is helps us understand how other topics are different from the population distribution (rather than distribution of land).