# Gall-Peters projection

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 cylindric 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 longitude given in radians, remove the π/180° factors.

The various specializations of the cylindric 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. There are always two standard parallels on the cylindric equal-area projection, each at the same distance north and south of the equator. The standard parallels of the Gall-Peters are 45° N and 45° S. Several other specializations of the equal-area cylindric have been described, promoted, or otherwise named.[1][2]

Named specializations of the cylindric equal-area projection
Specialization Standard parallels N/S
Lambert cylindric equal-area equator
Behrmann cylindric equal-area 30°
Craster rectangular equal-area 37°04'
Trystran Edwards 37°24'
Hobo-Dyer 37°30'
Gall-Peters (= Gall orthographic = Peters)  45°
Balthasart 50°

## Origins and naming

The Gall-Peters projection was first described in 1855 by clergyman James Gall, who presented it along with two other projections 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), and formally published his work in 1885 in the Scottish Geographical Magazine.[3]

The name "Gall-Peters projection" seems to have been used first by Arthur H. Robinson in a pamphlet put out by the American Cartographic Association in 1986.[4] 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 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

Peters proposed a corrected date line in the Bering Strait, so the complete Russia is displayed on the right side of his map. * The Greenwich great circle is shown in green. The Bering Strait great circle is shown in red, and traverses the city center of Florence. *

Arno Peters, an amateur 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.[5] In any case, the difference is negligible in a world map.

## Controversy

At first, Peters's foray into cartography was largely ignored by the cartographic community. Campaigns 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 another thing, inappropriate use of the Mercator projection 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.[6][7][8][9][10][11][12][13] 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.[9] Cartographers had witnessed a 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.[6] 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 of his predecessors had.[12][13]

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."[14]

All of those claims were erroneous.[15][16] 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.[17] 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. Several scholars have remarked on the irony of the projection's undistorted presentation of the mid latitudes, including Peters's native Germany, at the expense of the low latitudes, which host more of the technologically underdeveloped nations.[18][19] 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.[15][20]

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.[21]

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"[22]—his—and did not acknowledge the prior art of Gall[15] 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.[23]

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 (including Which Map is Best[4]) 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,[24][25] 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 geographic and cartographic communities do not unanimously disparage 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. Some cartographers, including J. Brian Harley, have credited the Peters phenomenon with demonstrating the social implications of map projections, at the very least.[26] Crampton[23] sees the condemnation from the cartographic community as reactionary and perhaps demonstrative of immaturity in the profession, given that all maps are political. Denis Wood sees the map as one of many useful tools.[22] Lastly, Terry Hardaker of Oxford Cartographers Limited, sympathetic to Peters's mission, became the map's official cartographer when Peters, overwhelmed by the technical aspects of cartography, sought to pass on those responsibilities.[22]

## Uses in the media

The Peters projection map was featured in the United States television drama The West Wing (season 2, episode 16), in which the (fictitious) Organization of Cartographers for Social Equality is given access to the White House Press Secretary due to Big Block of Cheese Day. Dr. John Fallow (actor John Billingsley) explains why the President of the United States of America should champion the use of this map in schools, because it correctly represents the size of the countries and therefore gives due prominence to countries in less technologically developed parts of the world that are otherwise underestimated.

The map is also a favorite of military strategist Thomas Barnett, who has included it in his presentations of The Brief, which have aired on C-SPAN in the United States.

## Notes

1. ^ Snyder, John P. (1989). An Album of Map Projections p. 19. Washington, D.C.: U.S. Geological Survey Professional Paper 1453. (Mathematical properties of the Gall-Peters and related projections.)
2. ^ Monmonier, Mark (2004). Rhumb Lines and Map Wars: A Social History of the Mercator Projection p. 152. Chicago: The University of Chicago Press. (Thorough treatment of the social history of the Mercator projection and Gall-Peters projections.)
3. ^ Gall, James (1885). "Use of cylindrical projections for geographical, astronomical, and scientific purposes". Scottish Geographical Magazine 1(4): 119–123.
4. ^ a b American Cartographic Association's Committee on Map Projections, 1986. Which Map is Best p. 12. Falls Church: American Congress on Surveying and Mapping.
5. ^ Maling, D.H. (1993). Coordinate Systems and Map Projections, second edition, second printing, p. 431. Oxford: Pergamon Press. ISBN 0-08-037234-1.
6. ^ a b Edwards, Trystan (1953). A New Map of the World. London: B.T. Batsford LTD.
7. ^ Hinks, Arthur R. (1912). Map Projections p. 29. London: Cambridge University Press.
8. ^ Steers, J.A. (1927). An Introduction to the Study of Map Projections 9th ed. p. 154. London: The University of London Press.
9. ^ a b Kellaway, G.P. (1946). Map Projections p. 37–38. London: Methuen & Co. LTD. (Mentions allegations of an "imperialistic motive".)
10. ^ Abelson, C.E. (1954). Common Map Projections p. 4. Sevenoaks: W.H. Smith & Sons.
11. ^ Chamberlin, Wellman (1947). The Round Earth on Flat Paper p. 99. Washington, D.C.: The National Geographic Society.
12. ^ a b Stewart, John Q. (1943). "The Use and Abuse of Map Projections." Geographical Review 33 (4): 590. (Noting quixotic promotions of new projections.)
13. ^ a b Fisher, Irving (1943). "A World Map on a Regular Icosahedron by Gnomonic Projection." Geographical Review 33 (4): 605. (A jab at Mercator and proposal for a replacement.)
14. ^ (1977) The Bulletin 25 (17) pp. 126–127. Bonn: Federal Republic of Germany Press and Information Office.
15. ^ a b c Snyder, John P. (1993). Flattening the Earth: Two Thousand Years of Map Projections p. 165. Chicago and London: The University of Chicago Press. ISBN 0-226-76746-9. (Summary of the Peters controversy.)
16. ^ Euler, Leonhard (1777). "De projectione geographica de Lisliana in mappa generali Imperii Russici usitata". Acta Academia Scientiarum Imperialis Petropolitanae 1:143–153. St. Petersburg. (A proof that no flat map of a sphere can be "totally distance-factual.")
17. ^ Bowyer, T.D.; German, G.A. (1959). A Guide to Map Projections p. 16. London: John Murray. (By 1959, long before Peters's campaign, Bowyer et al. were able to write, "The Mercator was used quite often until recently for world maps but in a modern atlas you may have difficulty in finding more than a single example.")
18. ^ Snyder, J.P. (1988). "Social Consciousness and World Maps". Christian Century 105: 190–192.
19. ^ Robinson, Arthur H. (1985). "Arno Peters and His New Cartography," American Geographer 12(2): 103–111.
20. ^ Canters, Frank; Decleir, Hugo (1989). The World in Perspective: A Directory of World Map Projections, p. 36. Chichester: John Wiley & Sons LTD. ISBN 0-471-92147-5. (Distortion of distance in world maps. Gall-Peters is structurally very similar to Behrmann.)
21. ^ Peters, Arno (1983). Die Neue Kartographie/The New Cartography (in German and English). Klagenfurt, Austria: Carinthia University; New York: Friendship Press.
22. ^ a b c Arno Peters: Radical Map, Remarkable Man. (A DVD documentary.) 2008.
23. ^ a b Crampton, Jeremy (1994). "Cartography's defining moment: The Peters projection controversy, 1974–1990." Cartographica 31 (4): 16–32.
24. ^ American Cartographer. 1989. 16(3): 222–223.
25. ^ Robinson, Arthur (1990). "Rectangular World Maps—No!" Professional Geographer 42 (1): 101–104.
26. ^ Harley, J.B. (1991). "Can There Be a Cartographic Ethics?" Cartographic Perspectives 10:9–16.