A brief look at map projections

Each and every map represents a distorted view of reality. Therefore, cartograms are not as unusual as they might appear at a first glance. Map projections are a central aspect of the Worldmapper project because the maps (respectively cartograms) featured in the project are basically not different from some sort of re-projection of the world, albeit in a different way than conventional projections used in cartography. Rather than trying to solve the conflicts of distortion when drawing a three dimensional surface on to a two dimensional area (be it a screen or a paper map), the worldmapper cartograms distort our image of the world on purpose and show each country in proportion to a specific topic. This is reason enough to reflect a little bit on what map projections are and in what way they create a distorted view of the world.

Worldmapper map using different projections

For the unfamiliar eye, Worldmapper maps may appear quite unusual and for some are difficult to read in the first place. It helps to have a reference map for a better orientation. The Worldmapper website has a land area map to enable viewers getting a real orientation in relation to the country’s real size:

Worldmapper map using the Peters projection
(click for larger view)

This map is based on the Peters map (or, to be more specific, the Gall-Peters projection) is a cylindric equal-area projection that squeezes the regions closer to the poles in order to preserve the country’s real size. The worldmapper version of this also shows the distinctive colour scheme which is used throughout all worldmapper maps: The colours used on the maps group the territories into 12 geographical regions, and allow for an easier visual comparison between the maps than would otherwise be possible. The shading of each territory within a region is consistent throughout all of the maps.
The Gall-Peters projection is just one of the many ways to create a cylindric equal-area projection. There are many ways to perform this transformation, such as the following which is based on the ideas of Lambert:

Worldmapper map using the Lambert projection
(click for larger view)

But some people find these kind of maps almost as unusual as the worldmapper cartograms. The Gall-Peters projection is included as the main reference map on worldmapper, as it allows the best comparison with the real size of countries. Many people are nevertheless much more familiar with the Mercator projection which distorts the land area considerably the closer one gets to the Polar regions. The countries in the higher latitudes are thus much oversized and create the shape which makes the landmasses of the northern hemisphere dominate. The projection preserves angles and is thus an aid for navigation, although certainly less useful for a good impression of land area. This is how the worldmapper map looks like using the Mercator projection:

Worldmapper map using the Mercator projection
(click for larger view)

These maps have one thing in common: They are preserving one kind or another of a metric property, be it conformal, equidistant, or some other property as e.g. in the Gnomonic projection or many others.
Other cartographers were not satisfied with these sometimes extreme distortions and tried to find some compromises that do not have a consistent transformation just preserving one sort of property. The Robinson projection is one of these, making a compromise between the above shown equal-area and conformal projections and still showing the whole world at once, coming much closer to many people’s imagination of the world while not exaggeration the higher latitudes as much as Mercator’s projection. This is the worldmapper view of the Robinson projection:

Worldmapper map using the Robinson projection
(click for larger view)

Another perhaps more unique compromise projection is the Dymaxion projection, widely known as Fuller map. Its quite charming character comes from the idea of putting the worldmap on the surface of a polyhedron, which makes it appear like a paper pattern (and could indeed used as one – but print it out before you start torturing your screen with scissors). The main idea is to show the whole globe on this pattern, expanding from one central point. It can be rendered from any central point of the planet, and allows to show landmasses in one contiguous stretch (but cut also allow to cut the continents on the edged). This is one way of showing the Fuller projection in the worldmapper style:

Worldmapper map using the Fuller projection
(click for larger view)

This gives a brief overview of projections and how they relate to the worldmapper style maps. However, the more true reference map for worldmapper is the population cartogram. Almost all worldmapper topics refer one way or another to the world’s population, and thus show the real shape of the countries in terms of humanity. Maps of death, disease, but also wealth or sports, should all look like the population map if the world was an equal and fair planet. The population is the reference to the number of people being born, living and dying, and each map that uses some sort of human-related topic and that looks different than the world population map shows an imbalance and shows that there must be something wrong about this. So beyond Gall-Peters, or Mercator, or all the others, this map is as much a basemap for worldmapper:

Worldmapper population cartogram
(click for larger view)

Quite interesting to see that this puts the northern hemisphere once more in the spotlight (note the wiggly line that draws along the Equator), but unlike at Mercator’s map, Russia becomes very small and East/South Asia enormously big. And even if it adds little sense to it, this map can be reprojected as well, such as onto a Robinson projection:

Worldmapper population cartogram in the Robinson projection
(click for larger view)

Lastly, to go one step further to a real re-projection of the world using the social space as the property to be preserved, the following population cartogram is the redrawn picture of the original worldmapper population map. The only difference is the underlying data on which this based on: It uses an equally distributed grid for the transformation (rather than countries, as the original worldmapper maps do it). This results in a different appearance: The size of the countries remains the same as in the previous map, but the shape is very different. The grid allows for an accurate re-transformation according to where people really live, thus this map is a huge step that brings the original cartograms closer to a real projection that preserves not a metric, but a social property on an unprecedented precision. At the same time, this map preserves its geographical reference with the grid (faded out in this version, but shown on this map), so that it can be interpreted in a much more advanced way than the original map. This map shows e.g. the Himalayan region disappearing for China as it is sparsely populated, the same with Alaska for the United States or the central region of Australia. Also, the population distribution on the Indonesian islands is more detailed, with Borneo now becoming quite small compared to the densely populated island of Java. These are all details that can not be seen on the original population cartogram, but now emerge using the new projection:

Worldmapper map using the gridded population projection
(click for larger view)

Rediscovering the WorldMore gridded population maps are shown on the website http://www.worldpopulationatlas.org/. And many more ideas of how much more can be done with this new projection are shown on this website: http://www.viewsoftheworld.net/?tag=gridded-cartogram
Update: You can also read more about map projections, density-equalising cartograms and gridded cartograms in my book on Map Transformations of Human and Physical Space published in 2013.
Read more details about it and see where you can buy it here.

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