The challenge of creating a world map begins with the fundamental difference between the Earth and the paper it is printed on. Cartography must deal with the incompatibility of a three-dimensional, curved object—our planet—and a flat, two-dimensional surface. The problem caused by maps being two-dimensional is that any attempt to translate the globe to a plane results in an unavoidable transformation called projection. This process mathematically converts spherical coordinates into planar coordinates, introducing systematic errors that distort the true nature of the world.
The Geometric Challenge of Projecting a Sphere
The Earth is not a perfect sphere, but a slightly flattened spheroid. Mathematically, it is impossible to transfer its curved surface onto a flat plane without stretching or tearing it. This geometric impossibility ensures that every two-dimensional map is, by necessity, inaccurate to some degree. Think of trying to flatten the peel of an orange without ripping or compressing the material; the curved surface contains a geometry that flat space does not possess. The moment a cartographer chooses a projection, they are deciding how to distribute the inevitable distortion across the map.
The Three Primary Distortions of 2D Maps
The act of flattening the globe invariably distorts four spatial properties: shape, area, distance, and direction. The distortion of Area, or size, is perhaps the most famous problem, often seen in the widely used Mercator projection. On a Mercator map, landmasses closer to the poles are dramatically exaggerated in size relative to areas near the equator. For example, Greenland appears visually comparable to Africa, even though Africa’s actual area is about fourteen times larger.
The distortion of Shape means that the true geometric outline of a landmass is altered, becoming stretched or compressed. While some projections, known as conformal projections, preserve the accurate shape for small areas, they severely distort the size of larger regions.
The third significant distortion is that of Distance, where the scale of the map is not consistent across all points. On most world maps, a straight line between two points does not represent the shortest or true distance. Only a specialized equidistant projection can accurately show distance from a single central point or along a few specific lines, meaning all other distances on that map are incorrect.
Why Map Projections Require Trade-Offs
Because a flat map cannot preserve all geometric properties simultaneously, projections are designed around purposeful trade-offs based on the map’s function. Cartographers select a projection that prioritizes the property most relevant to the intended use, accepting the distortion of others. For instance, a map intended for navigation, such as the classic Mercator projection, is a conformal map. This means it preserves the angle and shape of small features, allowing a navigator to draw a straight line that represents a true compass bearing.
Conversely, a map designed for statistical analysis, like comparing population densities, must be an equal-area projection. These projections, such as the Gall-Peters or Mollweide, ensure that the relative sizes of all landmasses are accurate, preventing misleading visual comparisons. They achieve area accuracy by significantly distorting the shapes of continents, particularly near the poles, causing them to appear squashed or elongated.