New Internationalist

The New Flat Earth

Issue 123

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The new flat earth
Traditional world maps have often been gross distortions, showing Europe, North America and parts of Asia as much larger than they really are. Next month, for the first time in English, the New Internationalist will publish the startling ‘Peters projection’ which portrays each country according to its true surface area. Here we explain how this new map came about.

Historian turned map-maker Arno Peters. AT FIRST SIGHT the Peters map of the world (Fig. 8) does look peculiar. A huge Africa dominates the centre with the distended southern part of the continent stretching down like an elephant’s trunk. And across the top the Soviet Union appears to have been sat on by the same animal to make it fit the space.

But where does the distortion lie — in his map or in our expectations?

Arno Peter’s new projection of the world was first published back in 1974 and since then has produced its share of both controversy and converts. Its most attractive aspect is that it presents all countries according to their true surface areas. Most of us assume that this is what all maps do anyway — so we may be surprised to learn that Europe, which on the traditional ‘Mercator projection’ looks larger than South America, is in reality only half its size.

It is the ‘Eurocentric’ character of most previous maps to which German historian Arno Peters most objects — a distortion produced and reinforced, he says, by ‘four centuries of European world domination’.

While he was writing his own history of the world, Peters was surprised to discover that there was no map of the world that he considered fair or even scientific — and came to the conclusion that cartographers had produced a ‘faulty school of thought based on false premises’. Despairing of traditional-minded map-makers coming up with anything better he decided to do the job himself

The cause of all the argument is that the earth is inconveniently round. This makes it easy enough to represent on a schoolroom globe. But a globe is only of limited use: you can’t fold it, put it on a wall or print it in a book.

A sheet of paper is altogether more handy but it’s not possible to show the earth’s features on a flat surface without causing distortion. So if you insist on having the world in this form you must decide what kind of distortion is the most acceptable — or least unacceptable.

A simple representation of the earth can be produced by wrapping a sheet of paper round a globe model of the earth and transferring the detail horizontally onto the resulting cylinder ( Fig. 1.). When the paper is unfurled you can see that the characteristics of the equator will be shown quite accurately but everything else will be 'wrong’. The horizontal circles of latitude, for example, are compressed closer and closer together the nearer you get to either north or south pole and what you finish up with is a map something like Fig. 2.

This kind of map would have been of only limited use to the early navigators of sailing ships. True, it would have shown them which countries lay directly north or south of each other and which were directly east or west. The captain could thus set his compass and sail off with every hope of reaching a destination along any of these directions. But when it came to setting an intermediate course, like north-west, he would have been in trouble. For drawing a line at 45 degrees on this map would not show him which places lay northwest of his starting point; the map did not have what cartographers call 'angular fidelitv'.

In 1569 a cartographer living in Germany called Gerhard Kremer produced a solution — and published it under his Latin name of Mercator. His answer was to move all the places on the map so that their relative positions on the sheet corresponded to compass bearings — without worrying too much about what this did to distances or areas. The countries came out peculiar sizes but the sailors didn’t mind; they were only too happy that they could use Mercator’s projection to choose the correct setting for their compasses and know that, however long it took, they would eventually get to the right place.

The distinctive thing about Mercator’s projection (Fig. 3) is that in order to achieve its ‘fidelity of angle’ for the mariner the lines of latitude have to be placed progressively further apart as they move away from the equator— the precise opposite, in fact, of the cylindrical projection that we started out with.

This has a drArnotic effect on the apparent areas of countries: those furthest from the equator appear much larger that those closer to it Greenland for example appears to be twice the size of China. when it is in fact less than a quarter of the size (Fig. 4.). And you can’t represent the polar regions on this system at all since they would be infinitely large.

Even to fit Greenland into the Mercator projection in a map of this shape you have to move everything down so that the equator finishes up two-thirds of the way down the sheet. And, as a result, Europe is placed in the centre of the world — adding positional prominence to its already inflated size.

Mercator’s map, says Peters, is an expression of the epoch of the Europeanisation of the world, the age in which the white man ruled the world’. And it is certainly true that throughout the colonial era it showed the imperial countries large and central while their colonies appeared relatively small and marginal — though in fairness to Mercator this was not really his intention.

Ships and planes nowadays navigate transcontinental journeys with the use of radio beacons. The main use for Mercator’s world map and its successors is to give anyone from a schoolchild to a transnational businessman a ‘feel’ for place, distance and size. Yet remarkably the projection they have most commonly used is the one designed for sixteenth century sailing ships — with all its bizarre characteristics.

Many attempts have been made to supersede Mercator’s map or at least reduce its worst distortions. Most of these, like the Aitoff projection (Fig. 5) have needed to use a’ rounded grid’ in order to get closer to area fidelity. But in these cases the strict north-south and east-west directions are lost.

The rounded grid also produces another Eurocentric characteristic the maximum distortions occur at the far left and the far right, with Europe in the centre shown relatively correctly. Europeans will appreciate just how unsatisfactory this is if, using the same principle, America is placed at the centre (Fig. 6.). In either case Australia looks odd, though it is quite possible, of course, to produce a map with Australia at the centre if desired.

Despite a profusion of more realistic-seeming compromises Mercator’s map has still retained much of its grip over the years. This must be partly because we are accustomed to his view of the world, but also because the shapes and grids of the alternatives all look a bit uneasy and unreliable.

Life would be a lot simpler if we could replace all of these projections with just one— and one which reflected what most people actually want from a world map.

This is what Arno Peters is trying to do. He fixes on two things that a world map must have to be internationally acceptable. The first is ‘fidelity of area’. No country nowadays would accept a new map that showed it smaller than it really was — there is too much national pride at stake.

Secondly the north-south and east-west directions have to be true. This is not just to provide reassurance to the reader who can scan along the grid lines to link one country easily with another; it also allows time zones to be pictured in a straight- forward way and shows which countries are at the same latitude and therefore will have similar climatic conditions.

Beyond these two fixed principles, the compromises have to start. No map of the world will give any country exactly the same shape that it has on the globe. On the simple cylindrical projection it is clear that countries around the equator will come off closer to their appearance on the globe while as you move further north or south the countries are progressively squashed.

Since distortion of shape is inevitable the most sensible thing is that the distortion be evenly distributed. Such distortion is easiest to visualise if you consider you live in a square country. In this case a distortion of 2:1 will change the square into a rectangle with one side twice as long as the next one so your country comes out either tall and thin or low and wide.

On any projection it is possible to have at least some of the square countries come out approximately square. And on our first cylindrical projection this would have been the case for the countries along the equator. On the Peters map the aim has been to keep the maximum distortion below. 2:1 in inhabited areas. He does this by choosing as the undistorted countries not those at the equator but those at the 45 degree lines of latitude which in the northern hemisphere run through Spain and in the southern hemisphere through New Zealand. (See Fig. 8). On the Peters map the maximum distortion then occurs in the polar regions, where countries like Iceland tend to be flattened, and along the equator where Nigeria and India look taller and thinner than we are used to.

The most striking thing about the Peters map to the unaccustomed eye is certainly the distortion at the equator— even though this is at no point greater than 2:1. Yet the Mercator map — the one we usually accept — actually distorts Europe by 4:1. On the Peters map Europe and North America are relatively little distorted since they lie close to the 45th parallel.

But the size and shape of countries are not the only innovations on the Peter’s map. Another is the colouring. One of the most potent symbols of the dissolution of the British Empire, for those old enough to remember it, has been the disappearance of those splashes of red around the world. Indeed since the 1960’s there has been relatively little need for political maps which give the same colour to countries under the same administration — since most are now independent Peters suggests that we start again and, instead of emphasising the difference between countries, we should highlight the growing links between nations in the same region. So he has given each continent its own colour green for America, yellow for Africa, red for Europe, and has distinguished between countries by giving them a different shade of the same basic colour.

This new, harmoniously coloured, equal-area map is the first fruit of what Peters sees as a revolutionary ’new cartography’ and one that will ‘defeat the ideologies that have hitherto stamped all world maps’.

English-speaking readers will probably be most familiar with the Peter’s map from the occasions when we have used it in this magazine in outline — or perhaps from its appearance on the front cover of the Brandt Commission report. The first complete translation of the map into English will not, however, appear until next month when it will be published by New Internationalist.

In fact the June 1983 edition of the New Internationalist magazine will consist entirely of a foldout world map on the Peters projection — so you will be able to come to your own conclusions. You may get rather less to read next month but, as usual, plenty to think about.

Arno Peters’ book, ‘The New Cartography’ is published
by Carinthia University Press, Kiagenfurt, Austria.

FIGURE 1

FIGURE 1
Wrapping a sheet of paper round a globe and transferring the information across to it horizontally gives a ‘cylindrical projection.’

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FIGURE 2

FIGURE 2
This map will portray countries at the equator fairly accurately but seriously distorts those nearer the poles. Lines of latitude are squeezed closer and closer together. North-south and east-west directions are ‘true’ on this map but intermediate directions like north-west cannot be plotted as straight lines.


FIGURE 3

FIGURE 3
Mercator’s projection moves the places on the map so that they fall under correct compass directions. But to achieve this the lines of latitude have to be moved further apart as you near the poles.

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FIGURE 4

FIGURE 4
This makes areas near the poles relatively bigger. So Europe (9.7 million square kilometers) seems larger than South America (17.5 million square kilometers) and the – infinitely large – polar regions cannot be shown at all.


FIGURE 5

FIGURE 5

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FIGURE 6

FIGURE 6

Subsequent attempts to show country sizes more accurately use ‘rounded grid systems like Aitoff’s. These, however, maximise the shape distortion at the edges. The normal ‘Eurocentric’ version (left) distorts America while the American version (right) pushes Europe into a corner. In either case Australia comes off second best.

FIGURE 7

FIGURE 7
Rounded grids also create directional confusion, you must follow the grid lines carefully to see which point lies east or south or another. And on simpler maps of this type the grid lines are often left out.

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FIGURE 8

FIGURE 8
The Peters projection is faithful to both north-south and east-west directions and to the relative areas of countries. Shape distortion is evenly spread; in this case the shapes of countries along the 45 degree latitudes are shown more truly than those along the equator.



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