planisphaerium

The word planisphere derives from the Medieval Latin planisphaerium, a compound of planus, meaning flat or level, and sphaera, meaning sphere — itself borrowed from the Greek sphaira (σφαῖρα). A planisphere is, literally, a flat sphere: a two-dimensional representation of a three-dimensional spherical surface. The term was used first in astronomical contexts, describing the projection of the celestial sphere onto a flat surface — a disk that showed the positions of stars as they would appear from earth over the course of a year. The oldest known planispheres are astronomical: the earliest surviving example is attributed to Ptolemy's Planisphaerium, though this text may actually represent a later Arabic tradition translated under his name. Astronomical planispheres, still sold today as adjustable circular star charts, allow the user to set a dial to the current date and time and read which constellations are visible above the horizon.

The extension of the term to geography — the flat representation of the terrestrial globe — followed naturally. By the sixteenth century, planisphere referred to any map projection that attempted to render the spherical earth on a flat surface. The cartographic challenge is fundamental and inescapable: a sphere cannot be unrolled onto a plane without distortion. Every map projection preserves some properties at the expense of others. An equal-area projection preserves the relative sizes of landmasses but distorts their shapes. A conformal projection preserves local angles and shapes but distorts areas. The Mercator projection, conformal and invaluable for navigation, makes Greenland appear as large as Africa. No flat representation of a sphere can be simultaneously accurate in area, shape, distance, and direction. The planisphere is always a compromise, always an argument about which distortions matter least.

The history of map projections is a history of mathematical ingenuity applied to the insoluble problem that the planisphere embodies. Ptolemy described several projections in his Geography. Mercator's 1569 projection solved the rhumb-line problem. The sinusoidal projection, developed in the sixteenth century, preserved areas. The stereographic projection, known to antiquity, preserved angles and circles. Johann Heinrich Lambert in 1772 produced a series of projections of remarkable mathematical elegance. In the twentieth century, Arthur Robinson developed a projection specifically designed to look aesthetically balanced rather than to satisfy any single mathematical criterion. The Peters (or Gall-Peters) projection, which became politically contentious in the 1970s and 1980s, restored accurate relative areas to world maps, making Africa appear as large as it actually is rather than as small as the Mercator projection renders it.

Today, the word planisphere is used most commonly in astronomy, for the rotating star-chart disks sold in planetarium shops and used by amateur observers. In cartographic contexts, 'map projection' has largely replaced planisphere as the technical term. But the concept remains central: every digital map you view on a screen is a planisphere, a solution to the ancient problem of how to show a curved world on a flat surface. The software calculates a projection, and the projection makes choices. The flat sphere is always, in some sense, wrong — and always, in some other sense, the best we can do.