# Gall–Peters projection

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Gall-Peters projection of the Earth

The Gall-Peters projection is one specialization of a configurable equal-area map projection known as the equal-area cylindric or cylindrical equal-area projection. The Gall-Peters achieved considerable notoriety in the late 20th century as the centerpiece of a controversy surrounding the political implications of map design. Maps based on the projection continue to see use in some circles and are readily available, though few major map publishers produce them.

## Description

The projection is defined as:

$x = \frac{R\pi\lambda}{180^\circ\sqrt{2}}$; that is, $x = \frac{R\pi\lambda\cos 45^\circ}{180^\circ}$
$y = R \sqrt{2} \sin \phi$; that is, $y = \frac{R\sin \phi}{\cos 45^\circ}$

where $\,\lambda$ is the longitude from the central meridian in degrees, $\,\phi$ is the latitude, and $R$ is the radius of the globe used as the model of the earth for projection. For lambda given in radians, remove the $\pi$/180° factors.

The various specializations of the cylindrical equal-area projection differ only in the ratio of the vertical to horizontal axis. This ratio determines the standard parallel of the projection, which is the parallel at which there is no distortion and along which distances match the stated scale. The standard parallels of the Gall-Peters are 45°N and 45°S. Other named specializations of the equal-area cylindric are Lambert Cylindrical Equal Area (standard parallel at the equator), Behrmann Cylindrical Equal Area (30° N/S), Craster Rectangular Equal Area (37°04' N/S), Trystran Edwards (37°24' N/S), Hobo-Dyer (37°30'), and Balthasart (50° N/S).

## Origins and naming

The Gall-Peters projection was described formally in 1885 by clergyman James Gall in the Scottish Geographical Magazine. He had presented it along with two other projections thirty years earlier at the Glasgow meeting of the British Association for the Advancement of Science (the BA). He gave it the name "orthographic" (no relation to the Orthographic projection).

The name "Gall-Peters projection" seems to have been used first by Arthur H. Robinson in his 1985 response to Arno Peters's 1983 book, The New Cartography. Prior to 1973 it had been known, when referred to at all, as the "Gall orthographic" or "Gall's orthographic." Most Peters supporters refer to it only as the "Peters projection." During the years of controversy (see below) the cartographic literature tended to mention both attributions, settling on one or the other for the purposes of the article. In recent years "Gall-Peters" seems to dominate.

## Peters World Map

Arno Peters, a historian, devised a map based on Gall's orthographic projection in 1967 and presented it in 1973 as a "new invention." He promoted it as a superior alternative to the Mercator projection, which was suited to navigation but also used commonly in world maps. The Mercator projection increasingly inflates the sizes of regions according to their distance from the equator. This inflation results, for example, in a representation of Greenland that is larger than Africa, whereas in reality Africa is 14 times as large. Since much of the technologically underdeveloped world lies near the equator, these countries appear smaller on a Mercator, and therefore, according to Peters, seem less significant. On Peters's projection, by contrast, areas of equal size on the globe are also equally sized on the map. By using his "new" projection, poorer, less powerful nations could be restored to their rightful proportions. This reasoning has been picked up by many educational and religious bodies, leading to adoption of the Gall-Peters projection among some socially concerned groups.

Peters's original description of the projection for his map contained a geometric error that, taken literally, imply standard parallels of 46°02'N/S. However the text accompanying the description made it clear that he had intended the standard parallels to be 45° N/S, making his projection identical to Gall's orthographic. In any case, the difference is negligible in a world map.

Arno Peters was the son of social activists and probably gained his lifelong concern about equality from his parents, Lucy and Bruno Peters. In 1929, when Peters was 13, the famous African American activist and NAACP field secretary William Pickens visited the family and left a signed copy of his book Bursting Bonds. During the Second World War, Peters' father was imprisoned by the Nazis for refusing to obey the totalitarian regime.

## Controversy

At first, Peters's foray into cartography was largely ignored by the cartographic community. Crusaders for new projections spring up now and then, rarely making much of an impression. For one thing, the mathematics that governs map projections does not permit development of a world map that is significantly better in any objective sense than the hundreds of map projections already devised. Peters's map was no exception in that regard, and in fact Peters had (probably unwittingly) based it on a projection which was already over a century old. That projection - Gall's orthographic - passed unnoticed when it was announced in 1855 for the simple fact that it lacked any remarkable properties. Peters's co-option of it did nothing to change that. For another thing, Mercator's inappropriate use in world maps and the size disparities figuring prominently in Peters's arguments against the Mercator projection had been remarked upon for centuries and quite commonly in the 20th century. Even Peters's politicized interpretation of the common use of Mercator was nothing new, with mention of a similar controversy in Kelloway's 1946 text. Cartographers had witnessed an eerily similar campaign twenty years prior to Peters's efforts when Trystan Edwards described and promoted his own eponymous projection, disparaging the Mercator, and recommending his projection as the solution. Peters's map differed from Edwards's only in height-to-width ratio. Cartographers, who had long despaired over publishers' stubborn use of the Mercator, had no reason to think Peters would succeed any more than Edwards had, or, for that matter, any more than any other of the long line of (perhaps) well-intentioned, zealous, but poorly informed predecessors had.

Nor was the concept that an equal area projection was preferable to the Mercator projection at all new to USA school textbooks. Before the First World War the noted cartographer John Paul Goode had spoken and written many times against "the evil Mercator" projection, and at the time of his death in 1932, Goode's School Atlas was the leading atlas used in US public schools (the 2004 edition, which is in print as of June 2006, has the slightly revised title of Goode's World Atlas 21st Edition ISBN 0-528-85339-2). Goode's phrase "evil Mercator" still appears in the section on map projections in the 1939 edition, and the Goode homolosine projection that Goode invented is emphasized.

Peters, however, launched his campaign in a different world than Edwards had. He announced his map at a time when themes of social justice resonated strongly in academia and politics. Insinuating cartographic imperialism, Peters found ready audiences. The campaign was bolstered by the innuendo that the Peters projection was the only "area-correct" map. Other claims included "absolute angle conformality," "no extreme distortions of form," and "totally distance-factual."

All of those claims were erroneous. Some of the oldest projections are equal-area (the sinusoidal projection is also known as the "Mercator equal-area projection"), and hundreds have been described, refuting any implication that Peters's map is special in that regard. In any case, Mercator was not the pervasive projection Peters made it out to be: a wide variety of projections has always been used in world maps. Hence, it could be argued that Peters had simply set up a straw man to knock down. Peters's chosen projection suffers extreme distortion in the polar regions, as any cylindric projection must, and its distortion along the equator is considerable. Indeed, most ironically, the only region lacking distortion happens to be along a latitude just south of Arno Peters's native Germany (and the opposite latitude in the southern hemisphere), not anywhere in the technologically underdeveloped world. The claim of distance fidelity is particularly problematic: Peters's map lacks distance fidelity everywhere except along the 45th parallels north and south, and then only in the direction of those parallels. No world projection is good at preserving distances everywhere; Peters's and all other cylindric projections are especially bad in that regard because east-west distances inevitably balloon toward the poles.

The cartographic community met Peters's 1973 press conference with amusement and mild exasperation, but little activity beyond a few articles commenting on the technical aspects of Peters's claims. In the ensuing years, however, it became clear that Peters and his map were no flash in the pan. By 1980 many cartographers had turned overtly hostile to his claims. In particular, Peters writes in The New Cartography,

Philosophers, astronomers, historians, popes and mathematicians have all drawn global maps long before cartographers as such existed. Cartographers appeared in the "Age of Discovery", which developed into the Age of European Conquest and Exploitation and took over the task of making maps.

By the authority of their profession they have hindered its development. Since Mercator produced his global map over four hundred years ago for the age of Europeans world domination, cartographers have clung to it despite its having been long outdated by events. They have sought to render it topical by cosmetic corrections.

...The European world concept, as the last expression of a subjective global view of primitive peoples, must give way to an objective global concept.

The cartographic profession is, by its retention of old precepts based on the Eurocentric global concept, incapable of developing this egalitarian world map which alone can demonstrate the parity of all peoples of the earth.

This incendiary attack did not endear cartographers, who themselves had long been frustrated by the favoritism publishers showed for Mercator's projection.

The two camps never made any real attempts toward reconciliation. The Peters camp largely ignored the protests of the cartographers. Peters maintained there should be "one map for one world"—his—and did not acknowledge the prior art of Gall until the controversy had largely run its course, late in his life. While Peters likely reinvented the projection independently, the unscholarly conduct and refusal to engage the cartographic community undoubtedly contributed to the polarization and impasse.

Frustrated by some very visible successes and mounting publicity stirred up by the industry that had sprung up around the Peters map, the cartographic community began to plan more coordinated efforts to restore balance, as they saw it. The 1980s saw a flurry of literature directed against the Peters phenomenon. Though Peters's map was not singled out, the controversy motivated the American Cartographic Association (now Cartography and Geographic Information Society) to produce a series of booklets designed to educate the public about map projections and distortion in maps. In 1989 and 1990, after some internal debate, seven North American geographic organizations adopted the following resolution, which rejected all rectangular world maps, a category that includes both the Mercator and the Gall-Peters projections:

WHEREAS, the earth is round with a coordinate system composed entirely of circles, and

WHEREAS, flat world maps are more useful than globe maps, but flattening the globe surface necessarily greatly changes the appearance of Earth's features and coordinate systems, and

WHEREAS, world maps have a powerful and lasting effect on peoples' impressions of the shapes and sizes of lands and seas, their arrangement, and the nature of the coordinate system, and

WHEREAS, frequently seeing a greatly distorted map tends to make it "look right,"

THEREFORE, we strongly urge book and map publishers, the media and government agencies to cease using rectangular world maps for general purposes or artistic displays. Such maps promote serious, erroneous conceptions by severely distorting large sections of the world, by showing the round Earth as having straight edges and sharp corners, by representing most distances and direct routes incorrectly, and by portraying the circular coordinate system as a squared grid. The most widely displayed rectangular world map is the Mercator (in fact a navigational diagram devised for nautical charts), but other rectangular world maps proposed as replacements for the Mercator also display a greatly distorted image of the spherical Earth.

The geography and cartography community is not united unanimously against the Peters World Map. For example, one map society, the North American Cartographic Information Society (NACIS), declined to endorse the 1989 resolution, though no reasons were given. Second, there is a small number of cartographers, including Brian Harley, who have credited the Peters phenomenon with demonstrating the social implications of map projections, at the very least. Within geography more generally, some commentators see the cartographic controversy over the Peters world map as a sign of immaturity in the cartographic profession, given that all maps are political.