Gall-Peters projection
Encyclopedia
The Gall–Peters projection, named after James Gall
and Arno Peters
, 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.
where λ is the longitude from the central meridian in degrees, φ 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
/180° factors.
where λ is the longitude from the central meridian (in radians), φ is the latitude, and R is the radius of the globe used as the model of the earth for projection. Hence the sphere is mapped onto the vertical cylinder, and the cylinder is stretched to double its length. The stretch factor, 2 in this case, is what distinguishes the variations of cylindric equal-area projection.
, 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.
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. 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.
In 1967 Arno Peters
, a filmmaker and historian, devised a map projection identical to Gall's orthographic projection 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, including Oxfam, National Council of Churches, New Internationalist magazine, and the Mennonite Central Committee.
Peters's original description of the projection for his map contained a geometric error that, taken literally, implies 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.
Beyond the lack of novelty in the projection itself, the claims Peters made about the projection were also familiar to cartographers. Just as in the case of Peters, earlier projections generally were promoted as alternatives to the Mercator. 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. As early as 1943, Stewart notes this phenomenon and compares the quest for the perfect projection to "squaring the circle or making pi come out even" because the mathematics that governs map projections just does not permit development of a map projection that is objectively significantly better than the hundreds already devised. 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 long despaired over publishers' inapt use of the Mercator. As a 1943 New York Times editorial states, "…The time has come to discard [the Mercator] for something that represents the continents and directions less deceptively… Although its usage… has diminished… it is still highly popular as a wall map apparently in part because, as a rectangular map, it fills a rectangular wall space with more map, and clearly because its familiarity breeds more popularity." Presumably wall map publishers liked the projection because it sold. Because of the lack of novelty both in the projection Peters devised or in the rhetoric surrounding its promotion, the cartographic community had no reason to think Peters would succeed any more than Edwards or his predecessors had.
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. Suggesting cartographic imperialism, Peters found ready audiences. The campaign was bolstered by the claim 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. Peters's chosen projection suffers extreme distortion in the polar regions, as any cylindrical 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. 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,
This attack did not endear him to 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 (including Which Map is Best) 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:
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. Crampton 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. 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.
(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.
James Gall
James Gall was a Scottish clergyman who founded the Carrubbers Close Mission. As well as writing on religious matters, often from a rather unorthodox standpoint, he had an interest in astronomy...
and Arno Peters
Arno Peters
Arno Peters developed the Peters world map, based on the Gall–Peters projection.Born in Berlin, Germany, he began his career as a filmmaker who studied American techniques of filmmaking during the late 1930s, and helped to revolutionize film production in Germany at the time...
, is one specialization of a configurable equal-area map projection
Map projection
A map projection is any method of representing the surface of a sphere or other three-dimensional body on a plane. Map projections are necessary for creating maps. All map projections distort the surface in some fashion...
known as the equal-area cylindric or cylindrical equal-area
Cylindrical equal-area projection
In cartography, the cylindrical equal-area projection is a family of cylindrical, equal area map projections.-Cylindrical projections:The term "normal cylindrical projection" is used to refer to any projection in which meridians are mapped to equally spaced vertical lines and circles of latitude ...
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.
Formulae
The projection is conventionally defined as:where λ is the longitude from the central meridian in degrees, φ 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
/180° factors.Simplified formula
Stripping out unit conversion and uniform scaling, the formulae may be written:where λ is the longitude from the central meridian (in radians), φ is the latitude, and R is the radius of the globe used as the model of the earth for projection. Hence the sphere is mapped onto the vertical cylinder, and the cylinder is stretched to double its length. The stretch factor, 2 in this case, is what distinguishes the variations of cylindric equal-area projection.
Discussion
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.| Specialization | Standard parallels N/S |
|---|---|
| Lambert cylindric equal-area Lambert cylindrical equal-area projection In cartography, the Lambert cylindrical equal-area projection, or Lambert cylindrical projection, is acylindrical, equal area map projection... |
Equator |
| Behrmann cylindric equal-area Behrmann projection The Behrmann projection is a cylindrical map projection. This is an orthographic projection onto a cylinder secant at the 30° parallels. It is equal-area, but distortion of shape increases with distance from the standard parallels. Scale is true along the standard parallels and constant between two... |
30° |
| Smyth equal-surface (= Craster rectangular) | 37°04′ |
| Trystan 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 GallJames Gall
James Gall was a Scottish clergyman who founded the Carrubbers Close Mission. As well as writing on religious matters, often from a rather unorthodox standpoint, he had an interest in astronomy...
, who presented it along with two other projections at the Glasgow meeting of the British Association for the Advancement of Science
British Association for the Advancement of Science
frame|right|"The BA" logoThe British Association for the Advancement of Science or the British Science Association, formerly known as the BA, is a learned society with the object of promoting science, directing general attention to scientific matters, and facilitating interaction between...
(the BA). He gave it the name "orthographic" (no relation to the Orthographic projection
Orthographic projection (cartography)
An orthographic projection is a map projection of cartography. Like the stereographic projection and gnomonic projection, orthographic projection is a perspective projection, in which the sphere is projected onto a tangent plane or secant plane. The point of perspective for the orthographic...
), and formally published his work in 1885 in the Scottish Geographical Magazine.
The name "Gall–Peters projection" seems to have been used first by Arthur H. Robinson
Arthur H. Robinson
Arthur H. Robinson was an American geographer and cartographer, who was professor in the Geography Department at the University of Wisconsin in Madison from 1947 until he retired in 1980...
in a pamphlet put out by the American Cartographic Association in 1986. 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
Arno Peters
Arno Peters developed the Peters world map, based on the Gall–Peters projection.Born in Berlin, Germany, he began his career as a filmmaker who studied American techniques of filmmaking during the late 1930s, and helped to revolutionize film production in Germany at the time...
, a filmmaker and historian, devised a map projection identical to Gall's orthographic projection and presented it in 1973 as a "new invention." He promoted it as a superior alternative to the Mercator projection
Mercator projection
The Mercator projection is a cylindrical map projection presented by the Belgian geographer and cartographer Gerardus Mercator, in 1569. It became the standard map projection for nautical purposes because of its ability to represent lines of constant course, known as rhumb lines or loxodromes, as...
, 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
Greenland
Greenland is an autonomous country within the Kingdom of Denmark, located between the Arctic and Atlantic Oceans, east of the Canadian Arctic Archipelago. Though physiographically a part of the continent of North America, Greenland has been politically and culturally associated with Europe for...
that is larger than Africa
Africa
Africa is the world's second largest and second most populous continent, after Asia. At about 30.2 million km² including adjacent islands, it covers 6% of the Earth's total surface area and 20.4% of the total land area...
, 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, including Oxfam, National Council of Churches, New Internationalist magazine, and the Mennonite Central Committee.
Peters's original description of the projection for his map contained a geometric error that, taken literally, implies 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.
Controversy
At first the cartographic community largely ignored Peters's foray into cartogrophy. The preceding century had already witnessed many campaigns for new projections with little visible result. Just twenty years earlier, for example, Trystan Edwards described and promoted his own eponymous projection, disparaging the Mercator, and recommending his projection as "the" solution. Peters's projection differed from Edwards's only in height-to-width ratio. More problematic, Peters's projection was identical to one that was already over a century old, though he probably did not realize it. That projection—Gall's orthographic—passed unnoticed when it was announced in 1855.Beyond the lack of novelty in the projection itself, the claims Peters made about the projection were also familiar to cartographers. Just as in the case of Peters, earlier projections generally were promoted as alternatives to the Mercator. 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. As early as 1943, Stewart notes this phenomenon and compares the quest for the perfect projection to "squaring the circle or making pi come out even" because the mathematics that governs map projections just does not permit development of a map projection that is objectively significantly better than the hundreds already devised. 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 long despaired over publishers' inapt use of the Mercator. As a 1943 New York Times editorial states, "…The time has come to discard [the Mercator] for something that represents the continents and directions less deceptively… Although its usage… has diminished… it is still highly popular as a wall map apparently in part because, as a rectangular map, it fills a rectangular wall space with more map, and clearly because its familiarity breeds more popularity." Presumably wall map publishers liked the projection because it sold. Because of the lack of novelty both in the projection Peters devised or in the rhetoric surrounding its promotion, the cartographic community had no reason to think Peters would succeed any more than Edwards or his predecessors had.
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. Suggesting cartographic imperialism, Peters found ready audiences. The campaign was bolstered by the claim 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
Sinusoidal projection
The sinusoidal projection is a pseudocylindrical equal-area map projection, sometimes called the Sanson–Flamsteed or the Mercator equal-area projection. Jean Cossin of Dieppe was one of the first mapmakers to use the sinusoidal, appearing in a world map of 1570...
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. Peters's chosen projection suffers extreme distortion in the polar regions, as any cylindrical 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. 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,
This attack did not endear him to 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 (including Which Map is Best) 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:
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
NACIS
NACIS is a US-based cartographic society founded in 1980. Originally founded by and for academics interested in cartography NACIS (North American Cartographic Information Society) is a US-based cartographic society founded in 1980. Originally founded by and for academics interested in cartography...
), declined to endorse the 1989 resolution, though no reasons were given. Some cartographers, including J. Brian Harley
John Brian Harley
Brian Harley was a geographer, cartographer, and map historian at the universities of Birmingham, Liverpool, Exeter and Wisconsin–Milwaukee. He is the founding co-editor of...
, have credited the Peters phenomenon with demonstrating the social implications of map projections, at the very least. Crampton 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
Denis Wood
Denis Wood is an artist, author, cartographer and a former professor of Design at North Carolina State University. Born in 1945, Wood grew up in Cleveland, Ohio, receiving a BA in English from then Western Reserve University . He received an MA and a PhD in geography from Clark University, in...
sees the map as one of many useful tools. 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.
Uses in the media
The Peters projection map was featured in the United States television drama The West WingThe West Wing (TV series)
The West Wing is an American television serial drama created by Aaron Sorkin that was originally broadcast on NBC from September 22, 1999 to May 14, 2006...
(season 2, episode 16
Somebody's Going to Emergency, Somebody's Going to Jail
"Somebody's Going to Emergency, Somebody's Going to Jail" is the 38th episode of The West Wing.The title is a lyric from the Don Henley song "New York Minute," from the album The End of the Innocence...
), in which the (fictitious) Organization of Cartographers for Social Equality is given access to the White House Press Secretary
White House Press Secretary
The White House Press Secretary is a senior White House official whose primary responsibility is to act as spokesperson for the government administration....
due to Big Block of Cheese Day. Dr. John Fallow (actor John Billingsley
John Billingsley
John Billingsley is an American actor, known for his role as Doctor Phlox on the television series Star Trek: Enterprise.-Career:...
) 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
C-SPAN
C-SPAN , an acronym for Cable-Satellite Public Affairs Network, is an American cable television network that offers coverage of federal government proceedings and other public affairs programming via its three television channels , one radio station and a group of websites that provide streaming...
in the United States.
External links
- The Size of the Matter—An article in the Times of India on why the Gall–Peters projection should be more widely used.
- Peters Projection vs. Mercator Projection—A critique of the importance of the Gall–Peters projection.
- An interactive Java Applet to study the metric deformations of the Gall Projection.
- Daily Mail, UK: Ten of the greatest maps that changed the world