Maps : The Mercator projection

paralleloscope

The Living Force

Although The distortions of the Mercator projection was mentioned here, I thought it could have its own thread. The Mercator conformal projection was made to conserve angles (useful for navigational purposes), but does not serve in representing realistic proportions of landmass, such as an equal-area projection might.

On the map / Simon Garfield said:
Well, what is the good of Mercator’s famous world map of 1569? It’s riddled with distortions and full of countries many times larger than they really are. And yet, astonishingly, it’s still essentially the map we use today. Countries have been added of course, and the shapes of coasts and borders have been corrected and politically adjusted, but the map that shaped the end of the Renaissance, saw in the Enlightenment and adorned Victorian classrooms remains the display of choice, right through to the latest Google Maps. It is the definitive icon of our world and to mess with it looks like terrorism. Not that people haven’t tried.

We aren’t looking at one map, of course, but a projection of the world – a template for all maps. Which is perhaps a litttle ironic for Gerardus Mercator, born in Flanders and working at the time in Duisburg, on the Rhine, was not himself a prodigious cartographer. When he laid out his famous world projection in 1569, at the age of fifty-seven, he had produced less than ten maps. But this new one was an undoubted wonder – mathematically meticulous and constructed with startling scale and ambition. It measured roughly 2*1,25 metres over eighteen printed sheets and must have stunned all who saw it.

The things that look wrong to us now – Greenland the size of Australia rather than a third of it, an Antarctic continent that bumps raggedly and indefinetly along the base – were not the strangest things then, for exact proportionate sizes were not yet known and the polar regions were but dismal myth. The strangest thing to his contemporaries was that Mercator, a man who had never been to sea (and would never go), would so effectively help the mariner plot a true course across the oceans after so many centuries of intuitive guesswork.
[...]
Mercator used the blank space on the unexplored interior of North America and his empty oceans to justify his new device to all who might find his projection unfamiliar. He explained that he intended 'to spread on a plane the surface of the sphere in such a way that the positions of places shall correspond on all sides with each other both in so far as true direction and distance are concerned, and as concerns correct longitudes and latitudes.' In so doing, Mercator had created a grid which, in the words of his recent biographer Nicholas Crane, ‘would prove as timeless as the planetary theory of Copernicus. In seeking the essence of spatial truth, he had become the father of modern mapmaking.’

What has happened to Mercators projection since? It has inevitably been modified and improved. This process began almost as soon as his world map was first published (most notably by Edward Wright, Edmund Halley and Johann Heinrich Lambert), and has continued up to Google _ which, extraordinarily, found Mercator’s neat and symmetrical rectangles perfectly suited to the pixelated tiles that make up a digital map. The projections resilience is even mare remarkable when one considers the forces that have raged against it for the last four hundred and fifty years. In 1745 a Frenchman named Cesar-Francois Cassini de Thury suggested using a cylindrical projection, sometimes shown as two hemispheres placed on top of each other with their centres at the poles. This showed a true scale along its central meridian and all places at right angles to it, but a varying level of distortion elsewhere. A more radical transformation was proposed by the Scottish astronomer James Gall at a meeting ln Glasgow ln 1555, Gall highlighted the essential fault with the Mercator projection - the shapes of the land masses were vaguely right, but their sizes were wrong, Applying his new ‘stereographic cylindrical’ theory first to the constellations and then to earth, he found a way of flattening the earth to a more compact scale, while also decreasing some of Mercator’s distortions (although introducing others).

Without due acknowledgement, many of the attributes of Gall’s work were picked up by the German Arno Peters in the mid-1970s and turned into a hot political quarrel that has still not entirely subsided. The argument was relatively simple: because of its high-latitude distortions, the Mercator map over-emphasized the size and significance of the developed world at the expense of the under-developed (which tended to be closer to the Equator), Peters’ cylindrical projection (now generally known as the Gall Peters projection) was therefore put forward as both an anatomically and politically correct alternative, and even though its claims were not novel (and it was often compared to a washing line on which countries had been hung out to dry), its alternative to the ‘cartographic imperialism' and ‘Euro-centric ethnic bias' of Mercator's map took on a voguish momentum.

When I first saw above clip I was dumbfounded, the Mercator image of the worlds geometry/geography relation is etched deeply. I had thought that the spherical peel to a rectangular grid was a pretty accurate representation. I wasn't aware that projections can't be accurate, only estimations with certain trade-offs:

http://www.colorado.edu/geography/gcraft/notes/mapproj/mapproj.html said:
Some distortions of conformality, distance, direction, scale, and area always result from this process. Some projections minimize distortions in some of these properties at the expense of maximizing errors in others. Some projection are attempts to only moderately distort all of these properties.

Conformality
When the scale of a map at any point on the map is the same in any direction, the projection is conformal. Meridians (lines of longitude) and parallels (lines of latitude) intersect at right angles. Shape is preserved locally on conformal maps.
Distance
A map is equidistant when it portrays distances from the center of the projection to any other place on the map.
Direction
A map preserves direction when azimuths (angles from a point on a line to another point) are portrayed correctly in all directions.
Scale
Scale is the relationship between a distance portrayed on a map and the same distance on the Earth.
Area
When a map portrays areas over the entire map so that all mapped areas have the same proportional relationship to the areas on the Earth that they represent, the map is an equal-area map.

projections.jpg

Of course an official change of maps for a Gall-Peters version wouldn't solve any problems of empire in itself (by representing size proportions properly), especially not at this late hour. For me this has been food for thought on how maps (which are not the territory) and information in general is projected through computational matrixes and distorted by the interest point we seek to focus on (subjectivity). And in the case of the Mercator projection just another lopsided prevailing convention which has had an effect on how we see the world, just how much or exactly what is difficult to say.

He had bought a large map representing the sea,
Without the least vestige of land:
And the crew were much please when they found it to be
A map they could all understand.

'What’s the good of Mercator’s North Poles and Equators,
Tropics, Zones, and Meridian Lines?'
So the Bellman would cry; and the crew would reply
'They are merely conventional signs!

‘Other maps are such shapes, with their islands and capes!
Bill we've got our brave Captain to thank:’
(so the crew would protest; ‘that he’s thought us the best -
A perfect and absolute blank!'

Lewis Carroll, The Humming of the Snark
 
parallel said:
When I first saw above clip I was dumbfounded, the Mercator image of the worlds geometry/geography relation is etched deeply. I had thought that the spherical peel to a rectangular grid was a pretty accurate representation. I wasn't aware that projections can't be accurate, only estimations with certain trade-offs:

Interesting, thank you for posting. The video was most illustrative (humorous, too - i.e. but where is France) and i agree with the lady at the end, seeing it upside down was "freaking me out", although, why not.

Of course an official change of maps for a Gall-Peters version wouldn't solve any problems of empire in itself (by representing size proportions properly), especially not at this late hour. For me this has been food for thought on how maps (which are not the territory) and information in general is projected through computational matrixes and distorted by the interest point we seek to focus on (subjectivity). And in the case of the Mercator projection just another lopsided prevailing convention which has had an effect on how we see the world, just how much or exactly what is difficult to say.

Yes, difficult to say.
 
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