Cartograms as Map Projections

Abstract

Since the time of Ptolemy 2000 years ago the objective of map projections has been to produce maps of high metric fidelity, and this is still the prime objective today. Thus the emphasis on direction, distance, and area preservation. These properties are needed in order to serve a variety of purposes. This way of looking at maps considers them as a type of terrestrial graph paper. This is possible because, paraphrasing John Donne, we use "the net of Meridians and Parallels cast over the world". Different kinds of geographic graph papers are used for different kinds of problems. Thus there are the classic conformal, equidistant, and equal area projections. Particular solutions are provided by the conformal projections, such as the Mercator projection, or the stereographic. Other maps such as the azimuthal projections, including the gnomonic projection, show directions. Equal area projections are most often used for larger regions or countries and for the depiction of statistical information. There are also quite a large variety of lesser known properties for which special projections are used. Still other projections serve for general purpose maps. Another type of map is referred to as a cartogram. It is the intent of this note to explain how these relate to convention maps of the two dimensional surface of the earth. But these cartograms are often not considered as belonging to the class of map projections. One difference between these and, say topographic maps, is that the phenomena depicted may change more rapidly in time, possibly often even hourly. This suggests that animation is a proper domain for cartograms. However not all history is quite this rapid and these maps can also be useful even if they are based on census information for which the change may be noted only every decade or so. In another respect cartograms have a property in common with the Mediterranean portolan charts of the thirteen to fifteen hundreds in that they are based on empirical observations rather than strictly spherical or ellipsoidal geometrical considerations. Geographic Graphs: This notion of map projections as graph paper for spheres can be extended to serve additional, non-traditional uses. A considerable number of these are provided by the class of cartograms, taken to be a special type of map projection. These can be classified in at least two ways. One grouping might be by type of problem or purpose. One common use is simply to present a point of view. This can be as simple as the ego-enhancing "Here's a Representation of My Favorite Region"; these are often intended to be humorous and colorful, and sometimes appear on post cards. Many of these can be referred to as 'Fisheye' maps (Rase, 1997). One more serious recoded use is to aid pilots by enlarging the vicinity of an airport, with a kind of local bubble enlargement. Or they can depict the state of the world from an alternate point of view, as in "The Atlas of the Real World" (Figure 1).