Every map of the world misrepresents it, and the misrepresentation is not a deficiency of craftsmanship but a mathematical necessity. A sphere cannot be flattened without distortion of some kind. Peel an orange and press the skin flat on a table: it splits at the edges, or it must be stretched until the splits close, and no amount of care will make it lie flat and whole at once. A sheet of paper has the same trouble with the earth. The cartographer's decision is therefore never whether to introduce error but which error to accept, and each of the standard projections gives a different answer.
One family of maps, the conformal projections, preserves angles. Any small shape on the globe keeps its shape on the sheet -- precisely what a navigator requires: a fixed compass bearing appears as a straight line, and the course can be laid off with a ruler. The cost is that areas swell as one moves away from the equator, and near the poles the swelling is wild. Greenland, on the most familiar map of this kind, looks about the size of Africa, although Africa is fourteen times the larger.
A second family, the equal-area projections, makes the opposite bargain. Every region is drawn in its true share of the earth's surface, so a comparison of magnitudes is dependable. Shapes, however, are pulled out of true, and the pulling is worst at the edges of the sheet. A navigator cannot use such a map; a demographer comparing the populations of continents can use nothing else.
The question is therefore not which projection is accurate. Each is exactly accurate in the one property it preserves and unavoidably inaccurate in the others, and a projection selected without reference to the purpose is a projection selected badly. A classroom that wants to demonstrate the relative size of land masses and a classroom concerned with how ships were once navigated do not need the same sheet on the wall, and neither sheet is a lie. The complaint that a map lies is therefore almost always a complaint that it was drawn for somebody else's purpose. The persistent public argument about whether a particular world map is misleading proceeds as though one of the alternatives were simply correct, and no alternative is.
What can reasonably be asked of a map is disclosure. A projection named on the sheet permits a reader to discount appropriately; a projection left unnamed invites the reader to take the proportions on trust, and most readers do. The obligation of the cartographer is not to eliminate distortion, since that is beyond anyone's power, but to identify which distortion has been chosen and to make the choice plain to the person holding the map.
