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. It 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 are promoted by UNESCO, and they are also widely used by
British schools.
Description 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, 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.
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. He gave it
the name "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 in a pamphlet put out by the American Cartographic
Association in 1986. Before 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
In 1967 Arno Peters, a German filmmaker, 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.
Controversy At first, the cartographic community largely
ignored Peters's foray into cartography. 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." 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 from that of Edwards. 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, 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,
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 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 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 people's 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, 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,
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. In popular culture
A Gall–Peters projection as well as a south-up Peters map were featured in the American television
show The West Wing, in which the 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 explains why the President of the United States 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 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. See also
List of map projections Gall stereographic projection: Another of
Gall's projections. References
Notes
Further reading Snyder, John P., Map Projections—A Working
Manual: U.S. Geological Survey Professional Paper 1395, Washington: Government Printing
Office. http:pubs.er.usgs.govpp1395 . 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