A Case for a Tri-Globe Projection

Flattened spheres, more or less distorted, more or less stretched… Some of these maps are called conformal because they “preserve” shapes — actually angles — which makes them very useful for navigation, especially when the path is loxodromic. This is the case, for instance, with the Mercator projection, a nautical world map from the Age of Exploration: at a constant heading, you draw a straight line.

Paradoxically, it is not necessarily the shortest route.

But these maps mostly suffer from not being proportional: Greenland can appear to rival Africa in surface area, even though Africa is fifteen times larger…

Other maps are called equal-area because they preserve areas. This is the case with the emblematic Peters projection, which aimed, at the turn of the 1970s, to restore a certain equity between the North and the South — earning it selection for the French edition cover of the Brandt Commission report in 1980.

In these cases, angles become distorted and shapes are strained. A third category of maps exists that are neither conformal nor equal-area, belonging to no “tribe,” in a word: aphylactic. These world maps attempt to compromise between preserving areas and angles — doing as well as possible, or as little harm as possible. Their structure is often complex; here are three examples:

All in all, the perfect map is only a dream. These geographical biases are fairly well known, but if I mention the aporia of world-map geometry, it is first to acknowledge it, and then, if possible, to overcome it — or more precisely, to “work around” it.

My proposal, already old since it dates back to 2009, is quite simple: if we cannot represent the entire surface of the globe on a flat sheet without distorting it, then let us represent the Earth as it appears, but from multiple viewpoints, so that all places can be seen. The choice of using globes is compelling for several reasons:

• The image of the globe corresponds to the phenomenological perception of world space that has been developing over the past few decades. Even if earlier representations exist — such as the frontispiece of Man and the Earth by Élisée Reclus, drawn by František Kupka — space exploration made it possible, through photography, to show the Earth “for real.” In 1968, the Apollo 8 mission produced the first visual embodiment of this idea: an “Earthrise,” the blue-and-white marbled planet appearing on the horizon of the lunar surface — barren, grey, cratered — all against the immense black of interstellar space. In 1972, during the Apollo 17 mission, another unprecedented photograph was taken: the Earth fully lit and visible in its entirety, like a blue marble — “a blue marble,” as the astronauts put it. The image truly became iconic, not merely of global consciousness, but of planetary consciousness. Since then, the image of the terrestrial globe has become omnipresent.

• Finally, representing the Earth in perspective requires drawing several globes — at least two, one for each hemisphere. But which ones? The northern and southern hemispheres? Magellan had such a map when he attempted to sail south around the new continent that blocked the western route for Spanish merchants. Only one half remains, preserved at the Topkapi Palace Library in Istanbul; it has been attributed to Pedro Reinel and would probably date from 1519.

The azimuthal equidistant polar projection, known as “Postel’s,” had the notable advantage of showing the global ocean. It appears in Le grand Insulaire et pilotage by André Thévet in 1586.

Western Hemisphere and Eastern Hemisphere? This became the choice of many world maps from the late 17^th century onward, in which the Old and New Worlds were drawn as two distinct hemispheres, such as Pierre Moullart-Sanson’s double orthographic projection in 1697, or Guillaume Delisle’s double stereographic projection in 1720.

Terrestrial Hemisphere and Oceanic Hemisphere? In 1753, Nicolas-Antoine Boulanger designed a “New world map dedicated to the progress of our knowledge.” The Earth is tilted at 45°, enabling two opposing hemispheres: a maritime hemisphere and a terrestrial hemisphere.

A century later, a similar cartographic approach appears in Élisée Reclus’s work in 1868.

Showing the world through a composition of multiple globes allows for a plurality of viewpoints. It makes possible a relative decentering, or at least a form of polycentrism, at a time when the world has become increasingly multipolar. The publication of The Atlas of Atlases by the weekly Courrier international in 2005 revealed a social need to see the World differently.

But the great moment of global cartography is earlier. During the Second World War, in the United States, many atlases and maps were published to allow the public to follow the course of the war. In this context, the most interesting cartographer was likely Richard E. Harrison, who offered multiple viewpoints on the conflict.

At this point, several questions arise. I asked myself what the most relevant choice was, and it seemed to me that the orthographic projection was the best suited:

One could opt for a subjective or “realistic” perspective: looking at the Earth from a viewpoint arbitrarily placed at a certain altitude — here, for example, at 10,000 km. Compared with an orthographic projection, the distortion is greater and the mapped surface smaller.

Conversely, one could choose a projection that creates no illusion, such as Delisle’s stereographic projection, or an equal-area azimuthal projection truncated at a single hemisphere. The advantages would be twofold: the preservation of surface areas and the representation of the entire hemispheric space.

But this is not really a globe. The orthographic projection appears as a kind of compromise. Distortion remains limited and is easily compensated for by the brain because it is somehow “natural,” unlike mathematical projections. To enable such compensation, it makes sense to use appropriate graphic design — for instance, shading that plays on light and shadow to signify global curvature. However, because a single globe represents less than 50% of the Earth’s surface, it becomes necessary to map not two globes but three, even at the risk of duplicating some areas — which, in practice, turns out to be more an advantage than a drawback.

Il reste alors à déterminer les points sur lesquels centrer ces projections. Deux structures majeures dans la configuration générale du globe ont conduit à un choix qui n’a rien d’absolu. La plus grande partie des terres émergées et habitées se situe dans l’hémisphère Nord, ce qui justifierait un certain angle pour permettre de mieux appréhender cette partie de la planète, au détriment de l’Antarctique. Trois axes Nord-Sud ont été mis en évidence par les géographes :

The empirical solution I settled on is a composition of three globes centered on:

Here are several maps made with a tri-globe projection.

The earliest ones are taken from a series of maps produced in 2009 as part of my high-school teaching.

Others, more recent, were used to illustrate the article “La ligne Nord-Sud, permanence d’un clivage ancien et durable” published in January 2024 on the Géoconfluences website:

The two maps drawn by Alexandre Nicolas come from a project for an Atlas of Global History, still unfinished, to be published by Autrement.

The global-history approach, which has developed over the past twenty-five years, is characterized both by a global vision, stricto sensu — that is, of the globe become World — and by a decentering of perspective, a “step aside,” as Sanjay Subrahmanyam would say. No equivalent exists in geography — a true global geography — even though the foundations were likely laid as early as the 1940s, if not earlier, in Élisée Reclus’s work in the 19^th century.

The tri-globe projection proposed here is only a tool to see and display world space, in its entirety but with “relative polycentrism.” It is not the perfect map — which can never exist — but a projection meant to be rotated.