The Europe-centered Character of our Geographical View of the World and its Correction

Scandinavia seems larger than India on Mercator's map although lndia (3.3 million square km) is exactly three times as large as Scandinavia (1.1 million square km) (Map 10). Greenland, with 2.1 million square km, seems to be larger than China which in reality is more than four times as large (9.5 million square km) (Map 11). The equator, as we know, divides the world into two equal halves. On Mercator's map however, the equator is set so 10w that two thirds of it serve to represent the northern hemisphere while the southern hemisphere is left only the bottom third of the area of the map (Map 9).

The map of the world, which Mercator designed himself, devoted 63% of its space to the northern hemisphere and this is the ratio on the new JRO map of the world. On the Philips' map of the world it is as great as 67%; on the Freytag-Berndt-Artaria it is 65%.

In an attempt to save the Mercator map, the equator has been moved to the center. If one then portrays both hemispheres to the 80th Degree of Latitude, the northern tips of Greenland and Spitzbergen are missing as are Grant Land and Franz-Joseph Land.

If one chooses a point in north and south which permits the portrayal of the whole of Greenland however (84th Degree of Latitude), the map attains a quadratic format and Antarctica (admittedly initially only shown in small parts) has become the largest continent of the world. In addition, the specific European-oriented distortion of the world of states remains uncorrected on both of these widely changed adaptations of Mercator's map.

A comparison of individual countries confirms this main fault of Mercator's map; Italy is there shown equal to Somalia (in reality twice her size). (Map 13) Great Britain is shown equal to Madagascar. (also more than twice her size). (Map 12) France appears almost larger than the Niger (actually more than twice France's area). (Map 14) Sweden seem to be twice the size of Egypt where actually the reverse is true - Egypt is more than twice the area of Sweden (Map 15).

It is always the countries of the "Third World", as we say nowadays, the ex-colonial states, the countries of the colored peoples which are disadvantaged on Mercator's map. This map is thus an expression of the epoch of the Europeanisation of the world, the age in which the white man ruled the world, the epoch of the colonial exploitation of the world by a minority of weIlarmed, technically superior, ruthless white master races... This epoch may not however be eternalized by retention of a geographical view of the world created by it and belonging to it as laid down in Mercator's map.

We are not concerned however only with Mercator's map but with all those maps of the world which propagate Mercator's geographical view of the world. This includes, apart from Mercator's map itself, many global maps which reduce only the worst distortions of that map in order to gain their inheritance without changing the basic view of the world which produced them.

Such "Mercator-type" maps (of which the van der Grinten Projection is the currently most well known) I will list here under the title of "Pseudo Mercator". (Maps 16, 17, 18, 19, 20, 21) They can be easily recognized by the fact that on them Greenland appears greater than Arabia, which in reality is one and a half times as large as Greenland.

All "Pseudo Mercators" suffer from the same defects as the Mercator map itself: they no longer fit into our post colonial world, in an epoch of international understanding, universal equality of rights and worldwide communication. In addition to this they represent a worsening of the Mercator map as they sacrifice that map's advantages (angular fidelity and a right-angled grid system) without removing its most damaging error (the Europe-centered distortion).

There is unfortunately no doubt that Mercator and Pseudo Mercator maps still rule our geographical view of the world. The global maps shown here, of German and foreign cartographical houses, prove it (JRO, Bartholomew, FaIk, Freytag-Berndt, Philip, Rand McNally, Ravenstein, Hallwag, Kümmerly & Frey, Stuttgarter Mission Press, Perthes, Mair) (Maps 1, 2, 3, 4, 5, 6, 16, 17, 18, 19, 20, 21).

On 2nd January 1974 the central map office of the Federal German Republic (Geocenter) answered the question as to how far Mercator and Mercator derived maps control the map market with "about 99 per cent". In the great Readers Digest Atlas and in the small pocket atlas of Haack we find the old representation of the world unchanged. (Maps 27, 22) If one studies the map of the news on German television it shows the old map of the world. (Map 24) If one orders a global map stamp from the educational publishers Westermann for use in schools (equatorial scale 1:175,000,000) one automatically receives the Mercator map; (Map 25) and if the Federal German Post Office wishes to instruct one on air mail tariffs they offer one the world in the Mercator projection (Map 26) and when foreign statesmen sign treaties with the Federal German Republic in the great assembly hall of the foreign office in Bonn, over their heads hangs the old map of the world from the colonial era (Map 23).

The question must now be asked whether the public clings to this false view of the world because they do not realize that it is a distortion of the truth or because they wish to delude themselves over Europe's loss of a world-dominant position by retaining the vision of an artificially enlarged Europe manipulated into the center point of the world.

An opinion poll carried out in 1968 showed that 94% of those questioned accepted that representation of the globe shown by Mercator and Pseudo Mercator maps as being the actual, undistorted picture of the world. 5% knew that it was impossible to show the surface of the globe on a fiat sheet without distortion, but regarded it as a special cartographical problem and accepted that a true to life picture of the surface of the earth was being offered - with the exception of certain distortions in the polar regions. Only 1% proved to be truly informed as to the disfiguring distortions of the Mercator projection.

This made it clear that it was not ideological intent but lack of information which was the real cause of the continued propagation of our outmoded geographical view of the world. But was there an alternative to those false geographical views of the world given by Mercator and Pseudo Mercator maps?

As I contemplated this question I was busy with preparations for an atlas volume to my "Synchronoptical History of the World". It was clear to me that the only solution was a world map with area fidelity as I did not wish just to reduce the Europe-centered character of our geographical view of the world but to correct it. This debarred map design of a "half-hearted" nature.

In cartographical text books I found an astonishing number of map designs with area fidelity which how ever had only seldom - and then only for special map contents - been included in atlases. They were never offered as individual maps or as wall maps for use in schools.

Area fidelity alone was apparently not the answer. There had to be other properties added if a global map was to find general acceptance; as all cartographical textbooks were agreed that global maps with area fidelity were to be preferred to those without area fidelity.

A survey of all those global maps which have been known in principle for centuries and available in several variations (Sanson, Bonne, Lambert, Hammer, Behrmann, Goode) (Maps 28, 29, 30, 31, 32, 33) showed that in all cases area fidelity had been bought at the cost of other serious defects. Even the external shape of the map was incommunicative; above all, there was no clear map picture; parts o~ the earth were crushed together, north did not lie above south, rounded meridians hindered orientation and on the two designs with a right-angled network of latitude and longitude and area fidelity, Europe was so squashed up that they had to be discarded.

It was thus not only lack of information about the serious mistakes of our conventional global maps that was responsible for their uncriticized perpetuation - there was no genuine alternative to Mercator's projection: a map altogether superior to Mercator's and with area fidelity.

On all existing global maps with area fidelity, a partial superiority (area fidelity) was overcompensated for by serious detects in the map representation. it was thus understandable that so far none of these area-true maps had been able to displace Mercator's projection.

On the other hand this failure was a confirmation of the inability of all these designs to correct the outdated geographical view of the world.

The task thus was to create a map which retained all major advantages for general use of the Mercator map and added other qualities, especially area fidelity.

I began to form a catalogue of these qualities which had to be united in this new map of the world.

1. Fidelity of Area. This alone ensured equality of treatment required in our time by all countries of the earth; it permits them to be portrayed in their true size, readily comparable one with another and shows them in their real geographical significance. Area fidelity is the prerequisite for the application of a global map in thematic cartography which only relinquishes this virtue if climatic or chronological zones are of greater importance than area fidelity.

A map with absolute area fidelity cannot also show true intervening distances but does not necessarily have to abandon this virtue completely.

The concept of 'interval fidelity' includes two cartographical qualities a) fidelity of distance on the meridians; b) reproduction of all those geographical points separated from the equator by an equal distance on one line of latitude parallel to the equator. This last quality is the kernel of interval fidelity for a general global map as it dictates the applicability of a global map for map content with climatic-oriented expression. I have thus included this partial interval fidelity under the title of:

2. Fidelity of Position in the catalogue of essential qualities of a global map but I have not included the accuracy of distances on the meridians. This latter (distance fidelity) seemed expendable as it was a quality which could not be realized all over a global map.

Absolute angular fidelity, still a necessary cartographical property for marine navigation, can more easily be dispensed with in a general global map if the east-west axis remains as in reality by means of positional fidelity. Angular fidelity includes yet another property the omission of which devalues even a general global map: the true to life representation of the northsouth axis. Our geographical consciousness demands that in every map north is to be at the top of the sheet and vertically above south. Maps with rounded meridians are not popular because they complicate northsouth orientation.

Naturally it is possible to trace the north-south axis on a globally rounded meridian network if the meridians are extended, but this mental conversion, vital for such "rounded" maps, impedes direct access to the contents of the map.

Apart from this, the rounded meridian networks lead to distortion of the land masses whose shapes are made unfamiliar. For these reasons

3. Fidelity of Axis is vital to a map of the world. Together with positional fidelity this ensures angular fidelity to the main points of the compass (north-south and east-west) and a direct orientation results. By adding axial fidelity and positional fidelity to area fidelity we have defined a map which is suitable in practically all properties for thematic cartography. Through these three qualities the desired map is extensively mathematically defined.

There are however, three other aesthetic, practical requirements of content which are not necessarily connected with these qualities and they must also be included in the catalogue.

In accordance with the current level of knowledge, a world map must show the entire globe. In Mercator's time, when Australia and Antarctica were undiscovered and Greenland, Canada and northern Siberia were still unexplored, a map of the world which was incapable by the nature of its constructional principles of showing the globe to the full extent of its poles may have been acceptable. Today however, the completeness of the representation of the whole surface of the globe.

4. The Totality, has become an essential requirements for a modern map of the world.

This requirement means that repetitions of individual parts of the world on the map are also unacceptable. it is no less important that the external appearance of the required maps should be in accord with our sense of beauty. The dimensions of this map, rectangular by definition of its mathematical limits, must approach the proportions of the Golden Section and also the associated DIN format.

5. This Proportionality is of an aesthetic and practical significance not to be underestimated. Finally the uniqueness of a global map is important to the success and survival.

6. This Originality is characterized by the fact that its constructional principles permit only the production of a single map of the world.

The Mercator Projection owes its supreme position to this uniqueness. If one had been able to reduce its over-emphasized zones, or expand the relatively miniaturized equatorial areas without offending the principle of its construction it would have been done and then there would not have been several standard maps of the world but none at all.

It is still desirable today that only one map of the world should dominate the geographical view of the world.

The opinion of cartographical teaching, that each of the qualities to be shown on a map requires its own favorable projection, is valid for maps of the world only so long as those properties demanded by thematic cartography are not united in one map. For in truth every map of the world is a part of thematic cartography, even the political and physical maps of the world.

The existence of various projections is a fault which should not be retained unnecessarily.

The required global map has been largely defined by the three mathematical and three practical qualities. Apart from this there are general criteria which have their own values and influence the applicability of a map of the world.

The ability on a map to terminate whole sections of the earth at the left hand edge and easily to reorientate oneself on the right hand edge (and vice-versa) is considerably important.

7. This is Restorability of Map Content. Only by virtue of this property is it possible to remove Europe and Africa from the center of the map to the sides and to put other continents in the middle and this appears legitimate and even desirable. it is possible today to find various maps of the world in USA with America as the central feature while in Japan and Australia, Europe and Africa often appear on the left side of the map and America on the right. This restorability as desired is of value even if only used as a theoretical model to illustrate the fact that the placing of our continent in the center of the map is not dictated by nature. The overpowering size of the Pacific Ocean (bisected on our conventional maps, with half on the left and half on the right) can only be truly expressed on a map in which America or Asia form the central point. Map grids with rounded meridians which only permit such variations of representation by redrawing (such as Mollweide and Aitoff) (Maps 34, 35, 36, 37) reinforce the false Impression of the compactness of the conventional map's picture.

Their comparison with another type of representation, necessarily seen as strange, distorts one's view of the homogeneality of the curvature of the earth and also the fortuitousness of our own map style.

Transparency is the great and justified requirement of our time. That which happens should be able to be seen. This means that a map of the world must have -

8. Clarity of Projection. This requirement is met by making absolute one of the two irreconcilable basic qualities. The absolute angular fidelity of Mercator's map of the world, for the achievement of which he accepted great disadvantages, represents a value which was at once clear to everyone in that Age of Discovery so dependent upon nautical travel. Today, in the scientific era, the objective character of an equalized view of the world based on proportionality is decisive. The fact that this character is based on absolute fidelity of area can be made generally clear.

9. The Obligatory Nature of the Scale.

This quality 15 desirable for the entire surface of a map, even of a map of the world. The quoting of a scale (such as by HaI Iwag - 1:33 million or by Kümmerly and Frey - 1:32 million) is confusing as it engenders the impression of a firm relationship between distances on the map and distances on the ground. There can be no such general relationship because fidelity of distance (like fidelity of shape) belongs to those properties which cannot be incorporated into a map of the world. The erroneous impression given on some other maps of the world that conversion of distance can be achieved is scarcely reduced by the notation "Equatorial Scale" or by the inclusion of complicated conversion diagrams (which can only be used in those rare special cases of a purely horizontal distance measurement on a given polar height).

As scales of distances on global maps cannot be applicable to the whole map they should be avoided. On the other hand there is the desire by the user of such a map to be able to make comparisons between the sizes of different countries of continents and to relate them to the size of the world. This need can be met by the inclusion of an area scale because fidelity of area - in contrast to fidelity of distance - is a cartographical quality which can be realized over the whole map.

The inclusion of a valid area scale indicates to the map user that a direct comparison of area is possible all over the map.

Our catalogue now includes 9 qualities which one must demand of a global map of our day. They are all compatible one with another, their complete realization is thus possible.

The utility value of a global map is however also dependent upon the degree to which three other qualities can be achieved, which, in contrast to the first 9 qualities, can only gradually be realized.

10. Uniformity of Error Distribution.

As in a convoy the speed is not determined by the average speed of all the ships but by that of the slowest ship, so the utility value of a global map is dependent less on the average degree of distortion than on the coarsest distortion which appears.

In order to keep this 10w, the inevitable mistakes which occur on a global map are to be distributed as evenly as possible over the whole surface of the earth. The distortion of inhabited areas should nowhere exceed 100%.

Unfortunately even the best solution to this problem does not relieve us of the need to select those zones of the earth which are to be reproduced most perfectly. The requirement for -

11. The Suitability of Presentation is most sensibly achieved when those areas of the earth where the most people live - the largest portrayed zones - are reproduced most faithfully and with the minimum of errors. The old geographical rule that a distortion of the least populous parts of the earth's surface (such as the Polar regions) is most readily acceptable has thus been complied with; this also meets the present day anthropogeographical and sociogeographical requirements.

As the last but by no means least important quality.

12. The Clarity of the Map is demanded.

This is achieved if the shape of no country of the world and no continent is rendered unrecognizable by extreme compression or distortion.

Distortion of form should be Iimited to vertical and horizontal axes only as the clarity of the map suffers less than with distortion in diagonal directions. The general superiority of the right angle map grid finds its expression in a clear map presentation.

The formulation of these 12 requirements is easier than their combination in one map.

I examined various global maps available to me in the light of my catalogue - and the result was that no map contained more than 8 of the 12 qualities (Map 66). This obviated the possibility of improving the grids of any one of these available maps by the inclusion of all twelve of what I consider to be vital and mutually compatible qualities.

In addition it was clear that some of these qualities - while basically capable of being combined - could not be realized alone but only in conjunction with and in balance with one another.

At the same time, after careful study of several textbooks on general cartography, I was not able to solve the problem which I had set myself by the reduction of these 12 requirements to their basic principles and their unification in a common formula. After several unsuccessful attempts I found myself at a loss for an answer.

Coincidence came to my rescue. I was then occupied with the problem as to why, in this decimal age, the world is not divided into 100 degrees but into 360 and why the Zero Meridian has to run through England. My suspicion was confirmed, that there was a connection between these features and the fact that at the time that they were established, England ruled a quarter of the globe and was thus in a certain manner the center of a world oriented towards colonial conquest.

I then considered whether this arbitrary transfer of the Zero Meridian from the Canary Island of Ferro to the London suburb of Greenwich should not be examined in the light of the desired correction of European centralization. it was of course important to establish if there was a suitable natural line for the Zero Meridian or if one whim were to be replaced by another. As is so often the case, the inclusion of "or" in the question was wrong: there was no naturally dictated position for the Zero Meridian (such as the poles and the equator) but there was a place where it could be located decidedly better than in Greenwich: the Dateline. Unfortunately this now consists of a north-south axis with several deviations which is relatively unsuited to the task of dividing the world and was only placed in its present position because it was on the 180th line of longitude when measured from Greenwich. If however the Zero Meridian were to be moved from Greenwich (as the observatory there was after the Second World War), then the dateline could be relocated on the best line of longitude for its purpose - to that place already hinted at by many corrections - in the middle of the Bering Straits where it will divide practically no inhabited areas and this is relevant to a date line. This line could then also serve as the Zero Meridian from which point the earth could be divided into 100 degrees. If one complements this decimal vertical division with a decimal horizontal division by dividing the distance from north pole to south pole into 100 equal parts, then we would have a decimal division of the earth's surface into 10,000 rectangles. As the distance from pole to pole is only half as great as the earth's circumference, the spherical rectangles along the equator would be twice as broad as they would be high.

l drew the new grid and numbered the resulting rectangles around the world from the Bering Straits to the Bering Straits and from pole to pole from 1 to 100. This obviated the tiresome double nomination according to north-south latitude and east-west longitude and man was given an opportunity to develop an impressive relationship between his new latitude and longitude fields (as I called them in contrast to the existing degrees of latitude and longitude) and his own geographical position in order to achieve a visible relationship to the positions of foreign countries and cities. Although the increasing significance of this new decimal grid to our surveyors encouraged me to publicize it, I laid it to one side unpublished because I doubted that I had the strength to complete the conversion of all Greenwich data.

When I came across the new grid a few weeks later, I carried Gut an experiment which was something new after the dozens of past experiments aimed at achieving the ideal map grid. I intentionally distorted the equatorial zone to the same degree that central Europe was distorted on Mercator's map; that is by the ratio 1:2 or by 100%.

This occurred in the simplest and in the most self-evident manner in that I squared the grid rectangles on the equator. Over these I then constructed the following squares (with area fidelity) in that I divided the area content by the base. So, with the help of chance, I achieved that which I could not have achieved by systematic search - a view of the earth that fulfilled all 12 of my requirements: (Maps 38, 39) it had absolute fidelity of area; position and axis, it showed the whole earth, its proportions lay between Golden Section and DIN-format, the projection was unmistakable in its principle of construction, the map content could easily be restored beyond its limits, the projection was clearly defined by its characteristics, the area scale was applicable to the whole area of the map, the inevitable distortion was evenly distributed over the tour global zones and was nowhere more than 100% between equator and polar circle, the expanded zones were reproduced practically true to form and the overall map picture was of great clarity.

As I now contemplated my new map, the face of our world seemed decidedly strange. (Map 42) A comparison with convention maps showed that it had no similarity with any of its predecessors. The three which most closely resembled it were the Mercator map, because of its harmonious format and clear picture; (Map 40) the new map of the world developed by Agostini in the Goldmann Atlas, because of the shape of the continents; (Map 43) and the square Platt .map due to the even distribution of distortion. (Map 41) But all these maps lacked the most important virtue of my map: area fidelity. So I added that map of the world with the best area fidelity - Behrmann's Truncated Cylindrical Projection. (Map 44) Because the earth's shape an this map bore no similarity with that on my map. I experimented producing cylindrical projections which resembled my map.

In order to limit the scope of the task, I advanced in stages of five steps each from Behrmann's longitudinally accurate parallel circuit, 3Oth latitude, and drew the map with parallels (true to form) on the 35th, 40th, 45th, 50th and 55th latitude (Maps 45,46,47,48,49).

The first test showed that the 35th degree and 55th degree maps could be discarded because of their unfortunate format. I now drew maps for the individual degrees between the 40th and 45th circles of latitude and it transpired that the overall quality of the map increased with the increasing polar height of the longitudinally faithful parallel circle. (Maps 50, 51, 52, 53, 54, 55) I then created the relevant maps for the individual degrees between the 45th and 50th circles of latitude - and it transpired that the overall quality of the map decreased with increasing polar height. (Maps 56, 57, 58, 59, 60, 61) The global map with the longitudinally faithful circle of latitude on the 45th degree was found to be the best truncated cylindrical projection for area fidelity.

A comparison with my original global map - developed from the decimal grid - showed that, although derived from totally different methods, it was almost identical with that drawn from the truncated cylindrical projection using the 45th circle of latitude. (Maps 42, 55, 56) I considered for a moment whether I should not publish it using the newly-won principle of construction - which was familiar to cartographers - instead of complicating it with the burden of a new grid system.

It was not only the fact that I had already publicized my new "Decimal Map" (as I call it to differentiate it from the best of my previously mentioned cylindrical projections) in 1967 in a lecture to the historical and geographical class of the Hungarian Academy of Sciences which stopped me from doing this. I thought of the endless cartographical argument over the question of whether the map with the longitudinally faithful parallel on the 43rd degree (with its better presentation of central Africa) is to be preferred to that with the longitudinally faithful parallel on the 46th degree (with its favorable presentation of Scandinavia).

As the polar circle practically forms the limit of permanent habitation on the earth, and as on my map the stated degree of distortion of 1:2 at the equator is only reached again at the polar circle (there of course in the horizontal, not in the vertical), an almost ideal distribution of the unavoidable distortion is achieved by my Decimal Map and by the cylindrical projection with the longitudinally-faithful parallel on the 45th degree, which equates to my Decimal Map.

Any movement of the longitudinally-faithful circle of latitude from the 45th degree either towards equator or pole can only result in distortions in Ecuador, Columbia, Brasil, Gabon, Congo, Zaire, Uganda, Kenya, Somalia and Indonesia greater than 1: 2 or Alaska, Canada, Greenland, Iceland, Norway, Sweden, FinIand and Siberia. The practical chances of a new, standard global map could be so easily squandered.

Apart from this, the method of construction of my Decimal Map is simpler than producing it in the form of a cylindrical projection with the longitudinally-faithful parallel on the 45th circle of latitude (with area fidelity). In spite of this, I have no objections if you prefer the latter method of producing my map of the world either from practical considerations or because this construction is familiar to you. The deviations from the original are within the limits of drawing accuracy.

You would then have the possibility of producing the individual maps as will be shown in the atlas I shall prepare, using the same principle and methods of construction, which recommend themselves for general use.

lnstead of the method of construction developed by me on the basis of the decimal grid System, you just set that circle of latitude as longitudinally faithful parallel of the right angled partial map, which you determine by halving the longest meridian of your map section. You then draw right angled verticals at the junction points of the meridians and construct, upwards and downwards, the rectangles with area fidelity as with the global map.

If the extract of the map crosses the equator, the smaller part on the other side of the equator is initially ignored; it will be added later by the mirror image of the constructed grid (in process of which a second, longitudinally-faithful analogue parallel is formed if the length of the meridians on that side of the equator is more than half the length of those in the larger half of the map).

Viewed in this light, the map of the world becomes a special case of the described general new principles of construction for production of maps with fidelity of area, position and axis and could perhaps be called a radial projection.

The outstanding fidelity of form shown by maps of countries and continents drawn on this basis prove that this radial projection is principally suited to reproduce faithfully rounded areas of the earth's surface.