The World Map Problem

How It All Went Wrong

Long ago, in 1587, a Flemish geographer and cartographer named Gerardus Mercator created a remarkably accurate nautical map that suspended the major land masses of the earth in their “school-house” positions.

The method he used, quite genius for the time, was to obscure distance near each pole in order to allow for an arced space to be easily represented on a two-dimensional map.

Gerardus Mercator's Pretty darn good map

In 1580, only 7 years before the Mercator projection, the ‘orientation’ of the world map had not yet been established. Many maps were still being published with the world ‘upside down’ from our modern vision. see Nicolas Deslien’s 1566 South-Orientation Map

This method was so popular that it survived as a fundamental cartographic approach moving forward into the modern psyche.

Consider the Mercator method using late-20th century satellite imagery:

Gerardus Mercator's method used on satellite imagery

Revealing the foundation of the approach, representative ‘squares’ of area are increased the closer you get to each pole. Here is the same projection with area marked with filled squares, to show the distortion:

Distortion caused by Gerardus Mercator's method

This causes a serious amount of distortion around the ‘actual’ size of associated land-mass, in that squares are almost not comparable across the map.

For example, an elongated square near the south-pole is only proportional to those a similar distances from the equator near the north pole, not the equatorial regions themselves.

As a more obvious example that should hit home, this is like defining the distance between buildings in New York through a Fish-Eye lens.

Source: http://www.estatevaults.com/

Despite the invention of satellites, the Mercator method is taught in millions of school’s world-wide.

To add the the confusion, satellite imagery has two major limitations:

  1. All of the land masses are not naturally visible by a single observing angle
  2. The visible view is already distorted by the curvature of the earth

So, this infers the problem: there is no natural way to see the entire earth at the same time.

This doesn’t, though, align with our impression of land as we move across it.

The distance it takes us to cross the city is constant, measurable and not in accordance with a visual representation that involves heavy skewing.

How Wrong Is It?

Let’s start with the currently taught “school-house” map of the earth:

Because the distortion approach skews the vertical distances, a comparison shows that the ‘visible’ land-mass can be increased by up to 10%.

Here is an example of land mass differences comparing the Mercator method vs actual square miles:

The information has been normalized around the comparison of the United States and estimated based on visible area of country boundaries.

In fact, the nature of the equatorial distance skew dictates that the inaccuracy is simply a matter of being closer to the poles.

Taking the same world image and applying a motion-blur relative to the visual area inaccuracy, we see the map mis-representative by an overwhelming majority.

The Search for an Accurate Map

In 1855, a clergyman named James Gall noticed this mis-representation and produced the first land-area map of the world.

In this representation, Gall started with a similar approach as Mercator in that the longitudinal and latitudinal griding still shows the curvature offset and area bias.
But, an additional skew was included to offset the area mis-allocation in the final visual land areas.

Gall used an Orthographic projection to map a spherical spatial object into a two-dimensional representation. Very impressive for 1855.

The result is a close to 1/1 ratio between the visual land area space and the actual measured area of each country.

Source: wikipedia

This map suffers from similar distortion points as well and was only accepted in obscure academic circles for almost 100 years.

Finally, around 1957, Arno Peters decided to re-invent the same map with a more reasonable coordinate system (that overcomes the confusion around arc coordinates).

Peters used a Ellipsoid projection to map the earth, not starting from the sphere like Gall. There is controversy that Peters ‘stole’ the Gall foundation by simply remapping the coordinate system.

Peter’s method created a more extensive re-implementation of Gall’s original idea, leading to many more variations on the same approach.

Where We Are Today

The European Space agency uses a variant of the Gall-Peters projection, lacking the equatorial skew necessary to accurately represent visual land mass. This causes a visual ‘squash’ of the equatorial regions:

Source: http://esamultimedia.esa.int/images/EarthObservation/Envisat/tapisserie_100x55_H.jpg

Google Maps uses the Mercator projection (now almost 500 years old and inaccurate visually).

Notice Greenland is as large as Africa and that Antarctica is a behemoth.

Source: https://maps.google.com/

Bing Maps uses the Mercator projection:

Source: http://www.bing.com/maps/?FORM=Z9LH2

Conclusions

Between out-of-age school boards and popular convention, the world hasn’t adopted an accurate view of the world area map.

This results in people having bizarre understandings about the comparative regions of the world beyond their local space. Even further, almost 40 years after the invention of satellite imagery, children are still being taught using a 500 year old method of land representation.

Next time you look at a map, keep in mind how it is skewing your representations of the world you live within.