Mercator’s projection is based on a cylindrical perception of the earth. Later interpreters used the analogy of the earth as a balloon to explain the method. Put the balloon inside a cylinder with the same diameter as the balloon at the equator. If the balloon is inflated, its curved surface will be pressed and flattened against the cylinder’s walls. The curved meridians are ‘straightened’ as they meet the cylinder, as are the parallels. One consequence of such stretching and flattening is that the North and South poles can never touch the cylinder’s walls, and effectively stretch onwards into infinity. If the cylinder is then unrolled with the imprint of the balloon’s meridians and parallels, the resulting rectangle approximates to the Mercator projection. This description offers one plausible explanation as to how Mercator developed it. Having spent decades on the mathematical and practical creation of terrestrial globes, Mercator was able to conceptualize how to adapt accurately the surface of such globes to represent a flat map. Take a segment, or gore of a globe, which looks rather like a vertical slice of an apple or an orange. Redraw it on a flat piece of paper, but retain the width of each meridian at the equator from top to bottom. Then stretch out the parallels to compensate for the gradual straightening of the meridians (as with the balloon analogy), and you are left with a thin rectangle. If the same method is applied to each globe gore, you have a series of rectangles which, when stitched together, make a flat map.47
The result still caused distortion of land masses at the northern and southern extremities, but if Mercator could accurately calculate how far apart to space his parallels he could achieve something unique: what cartographers call ‘conformality’, defined as the maintenance of accurate angular relations at any point on a map. Notwithstanding the distortion of land mass, navigators could plot a straight line across the map’s surface and, if they maintained a consistent angle of bearing, would still arrive at their projected destination. For Mercator, this meant straightening the meridians and calculating how far apart his parallels should lie if they were to retain a straight line of bearing. So, for example, at the equator the distance between any two meridians is twice the same distance along the parallel running 60° N, due to the convergence of the meridians. On his map Mercator therefore widened the parallel at 60° N to twice its actual length, ensuring that an oblique angle running through it would be straightened.48 All the other parallels were subject to the same calculation, and were lengthened accordingly.
Mercator produced what cartographers today term the first cylindrical conformal projection – it treated the globe like a cylinder, and maintained accurate angles across its surface. Sixteenth-century pilots, of course, could not care less about its title; Mercator’s method simply allowed them to ‘straighten’ the meridians, which no longer curved inwards towards the poles, but instead ran perpendicular to the parallels. They could now plot a rhumb line using Mercator’s projection, but rather than following a spiral and running off course as on earlier charts, a straight rhumb line now retained its accuracy in navigating from one location to another. It was a relatively simple but ingenious solution to the problem of projecting the entire earth onto a plane surface which had preoccupied mapmakers since the time of Ptolemy. Mercator appeared to have finally squared the geographical circle. It was a decisive breakthrough which would change maps for ever, and immortalize Mercator.
However, even a cursory glance at the shape of Mercator’s world reveals some obvious problems inherent in the projection. As the balloon analogy shows, the meridians are never allowed to converge on a single point, so the polar regions stretch into infinity, always already beyond the map’s rectangular frame. This is just one of the reasons that Mercator requires his small inset map to explain the geography of the North Pole. The mathematical stretching that takes places at the poles also affects the relative size of land masses in higher altitudes, which is why in the southern hemisphere Antarctica dwarves every other continent, and Greenland looks the same size as South America, when in terms of surface area it is actually only an eighth as large. In contrast, Europe appears twice the size of South America, when it actually covers just half the surface area. The stretching of the parallels north to south also means that Mercator’s projection distorts distances between locations over long seaborne journeys – though at the time it seemed more important to ensure pilots arrived at their location rather than how long it took them, particularly in an age before the advent of steam.
There still remained one crucial problem. Mercator could not offer a reproducible mathematical formula for his projection which would allow mapmakers and pilots to copy his methods. Neither the logarithms nor the integral calculus required to reproduce trigonometric tables delineating the projection’s parallels and meridians were available to him. This made his empirical achievement all the more remarkable (and an enduring mystery), but it still meant pilots found it difficult to use the projection. Writing in 1581, the Elizabethan mathematician William Borough said of Mercator’s explanation of his method, ‘by augmenting his degrees of latitude towards the Poles, the same is more fit for such to behold as study in cosmography by reading authors upon the land, than to be used in navigation at sea’.49 Although Mercator had effectively solved a centuries-old problem of mapmaking for navigators, he appeared surprisingly indifferent to providing an explanation that would ensure its immediate fame and longevity; without further mathematical explanation it remained the preserve of scholarly cosmographers.
Nothing seemed to prepare Mercator for resolving the age-old conundrum of plotting the entire surface of the globe onto a flat map and retaining conformality for navigation. His greatest work up to this point in his career remained the 1541 terrestrial globe. On its spherical surface, Mercator had no difficulties projecting the curvature of the earth, but a method of transferring such an image onto a flat map had eluded him for more than three decades. There is, however, an intriguing possibility: the years spent working on connecting events through time in the Chronologia enabled him to imagine a new way of connecting places in terrestrial space on a flat map. Throughout the 1560s, as he laboured on his chronology, he also compiled the data and invented the projection that would culminate in the 1569 world map. Both publications came out within months of each other. Perhaps, in the same way that Mercator allowed believers to read laterally across time and navigate the different religious temporalities in the Chronologia, his new projection allowed navigators to travel across the space of God’s earth, using a rhumb line to pursue a ‘middle way’ between inaccurate straight-line and impractical great-circle sailing, ‘accurately’ connecting places in space, just as the Chronologia ‘correctly’ located different events in time.50
Unlike any of his earlier geographical efforts, Mercator’s map is noticeably bereft of imperial patronage, religious affiliations or political boundaries. There are no imperial eagles and few far-flung territories claimed on behalf of European rulers expressing their global dominion. It offered a more accurate method of navigating across the earth, but it also offered its Christian readers a vision of spiritual peace and concord that drew on the Stoic principles of Cicero and Macrobius. In the rarely read dedication to the map, Mercator honours his patron Duke Wilhelm, but he takes it as an opportunity to describe the world’s people and countries within a cosmic image of harmony that evokes the classical gods of antiquity, but which subsumes them under the sway of a Christian God who is unconcerned with wars, famine and religious conflict:
Happy countries, happy kingdoms in which Justice, noble progeny of Jupiter, reigns eternal and where Astraea, having regrasped her sceptre, associates herself with divine goodness, raising her eyes straight to the heavens, governs all in accordance with the will of the Supreme monarch and devotes herself to the submission of unfortunate mortals to His sole empery, seeking happiness . . . and though Impiousness, the enemy of virtue, causing Acheron to riot, raises some gloomy disorder, no terror is felt: this allgood Father who, residing on the crest of the world,
orders all things by the nod of His head, will never desert His works or His kingdom. When the citizen is in this wise governed he fears no ambush, he has no dread of horrible wars and mournful famine, all pretences are swept away from the unworthy backbiting of sycophants . . . dishonesty, despised, lies prone, virtuous deeds everywhere call forth friendship and mutual treaties bind men solicitous of serving their King and their God.
A contemplation of the world on his map enables Mercator’s readers to understand that, as long as they are ‘governed’ by a belief in God, regardless of their religious belief, then riot, conflict and the destructive pursuit of earthly glory can be seen as transitory, and insignificant when viewed from a cosmographical perspective.
Such an interpretation of the projection might be appropriately ‘oblique’, rather like a rhumb line. But then again, Mercator had himself withdrawn into a world of coded critique and arcane symbolism following the traumatic events of the 1540s. Today, both supporters and detractors of Mercator’s projection tend to judge it as a disinterested mathematical innovation, and believe its wider theological and cosmographical contexts, as well as Mercator’s own life, to be relatively incidental. But Mercator’s career shows that in the mid-sixteenth century it was impossible to separate science from history, history from geography, geography from cosmography, and cosmography from theology. For Mercator, everything was connected, but also ultimately subsumed under a spiritual authority, a divine architect who oversaw everything including the projection of the world He created.
• • •
Within his lifetime, Mercator’s projection was a qualified failure. Sales were slow, and many like Borough complained that Mercator’s inability to explain his methods made them virtually useless for practical use for seaborne navigation. It took an Englishman, Edward Wright, in a series of mathematical tables in his book Certaine Errors in Navigation (1599), to provide the calculations required to translate the projection for the use of pilots, who slowly began to adopt the method during the course of the seventeenth century.
Mercator himself seemed indifferent to his achievement, and spent the final three decades of his life continuing work on his cosmographic project, of which the Chronologia and his world map represented just two elements. In 1578 he published an edition of Ptolemy’s Geography, which lovingly reproduced the Greek geographer’s maps as historical curiosities, an important but now redundant conception of the earth as it was understood by the Hellenic world. The edition effectively ended the classical geographer’s influence on contemporary mapmaking. From now on, mapmakers trying to map the world would chart their own path rather than revising and updating Ptolemy.
Mercator continued to write theological works with a direct bearing on his cosmography, including a study of the Gospels, Evangelicae historiae, published in 1592. Finally, just a year after his death in 1594, the culmination of his cosmography was finally published. The Atlas sive cosmographicae meditationes de fabrica mundi et fabricate figura (subsequently published in English as ‘Atlas, or Cosmographic Meditations on the Fabric of the World and the Figure of the Fabrick’d’) was the first modern atlas to use the title, with 107 new maps of parts of the world, although it omitted to use the 1569 projection on its world map, another sign of Mercator’s indifference to its scientific innovations. Instead he chose a double hemispherical stereographic projection to depict the world. In the Atlas, Mercator offers an illuminating reflection on the place of his earlier world map within his cosmography. He tells his readers that he has used geographical information from his earlier map of Europe and the world map of 1569, and implores them to turn to cosmography, ‘the light of all history, both ecclesiastical and political, and the idle onlooker will learn more from it than the wayfarer from his lengthy, irksome, and expensive labours (who “often changes skies but not his mind”)’.51 Mercator takes a quote from the Roman poet Horace’s Epistles, which was subsequently used by the Roman Stoic philosopher Seneca, to emphasize the true value of cosmography: to meditate on spiritual conscience rather than terrestrial orientation. Developing this Stoic perspective, Mercator invited his reader to ‘think diligently of the glory of your dwelling-place, which is only temporarily granted to you, along with the poet George Buchanan, who thus compares it to the celestial realm in order to draw forth your souls, immersed in terrestrial and transitory affairs, and show the way to higher and eternal things’.52 Buchanan (1506–82) was an internationally renowned Scottish historian and humanist scholar, a Lutheran sympathizer, tutor to Mary, queen of Scots and her son, the future King James I of England, and a well-known Stoic. It is typical of Mercator that he quotes a poem by Buchanan rather than choosing his own words to summarize his Stoic approach to mapping the earth and the heavens:
May you perceive how small a portion of the universe it is
That we carve out with magnificent words into proud realms:
We divide with the sword, and purchase with spilled blood,
And lead triumphs on account of a little clod of earth.
That strength, seen separately by itself,
Is great indeed, but if you compare it with heaven’s starry roof, it is as
A dot or the seed from which the old Gargettian [Epicurus] created innumerable worlds.
In a final explicit evocation of Macrobius’ ‘Scipio’s Dream’, Buchanan concludes that, because humanity is confined to such a small part of the universe, the pursuit of worldly glory is foolish:
How tiny the part of the universe is where glory raises its head,
Wrath rages, fear sickens, grief burns, want
Compels wealth with the sword, and ambushes with flame and with poison;
And human affairs boil with tremulous uproar!53
Speaking through Horace, Seneca and their neo-Stoic follower Buchanan, Mercator recommended that an individual simultaneously retreat from and transcend the religious and political discord of his generation, and instead pursue spiritual shelter by an acceptance of a larger cosmic harmony. Only cosmography could provide a suitable perspective from which to view the theological conflict of the Reformation, and to offer a way of turning away from its intolerance to embrace a more inclusive perspective of divine harmony.
By the end of the sixteenth century, much of Mercator’s innovative work was either being more efficiently marketed by lesser geographers, or was starting to look intellectually outdated. His Chronologia quickly became obsolete with the publication in 1583 of Scaliger’s more comprehensive De emendatione temporum (‘Study on the Improvement of Time’). His younger disciple Abraham Ortelius had already published an atlas of the world in Antwerp in 1570, although it did not use the term, choosing instead the title Theatrum orbis terrarum (‘Theatre of the World’). As a member of the dissenting religious group, the Family of Love, with its connections to the Protestant Anabaptist sect, Ortelius was freer than Mercator to use his Theatrum to embrace an explicitly Stoic attitude towards the description of the world (just six years before the forces of Philip II of Spain brutally sacked Antwerp in November 1576, killing an estimated 7,000 people). The descriptive cartouches on Ortelius’s world map offer a more explicit version of Mercator’s cosmographical philosophy of peace, concord and indifference to worldly glory. They included quotes from Seneca, asking ‘Is this that pinpoint which is divided by sword and fire among so many nations? How ridiculous are the boundaries of mortals’, and Cicero’s rhetorical question, ‘what can seem of moment in human occurrences to a man who keeps all eternity before his eyes and knows the vastness of the universe?’54
Mercator’s Atlas still deserves its description as the first modern atlas (it was far more innovative than Ortelius’s limited but shrewdly packaged publication), and it established the layout and running order for most subsequent atlases. It sold well and the name ultimately stuck, but Mercator had missed his moment. The earth was moving under his feet (quite literally, according to Copernicus’s new theories of a heliocen
tric universe) and his cosmography represented the discipline’s zenith. It finally displaced Ptolemy’s Geography, but whereas the Greek’s influence lasted for more than a millennium, Mercator’s cosmographical publications barely reached into the following century before, like Ptolemy, they became another historical curiosity. Instead, it was his 1569 world map that would endure.
The pace of political, intellectual, theological and geographical change was simply too fast for any one scholarly individual to explain, and led to what has been called the crisis of cosmography, in which the polarized religious atmosphere would no longer tolerate the pride of the cosmographer’s god-like perspective. The sheer complexity of representing the natural world meant that no single figure could any longer provide a convincingly synthetic and comprehensive vision of everything. Collections of travellers’ reports and voyages compiled by more modest intellects such as Giovanni Battista Ramusio, Richard Hakluyt and Théodore de Bry began to supplant the singular perspective of cosmographers like Mercator. Subsequent geographers like Jodocus Hondius and Willem Blaeu in the Low Countries and the Cassinis in France turned into dynasties, drawing on generations to work on globes and atlases using state finance and employing vast teams of scholars, surveyors and printers. Cosmography fragmented into a series of discrete practices, and its theological and moral power gave way to that of mathematics and mechanics.55
If this fragmentation was seen by some as progress, it also reduced mapmaking’s ability to transcend worldly conflict and intolerant attitudes in favour of a larger understanding of secular and sacred space. As David Harvey has ruefully pointed out, ‘the Renaissance tradition of geography as everything understood in terms of space, of Cosmos, got squeezed out’. As cosmography withered away, geography ‘was forced to buckle down, administer empire, map and plan land uses and territorial rights, and gather and analyse useful data for purposes of business and state administration’.56 But though Mercator’s cosmography quickly became an irrelevance, his map projection, inspired by cosmographical concerns, became central to this new geography. Its mathematical principles were appropriated for measuring nation states and Europe’s growing colonial possessions. The projection was adopted by the English Ordnance Survey, the British Navy’s Admiralty charts, and in a suitably cosmographical twist, by the NASA space agency to map various parts of the solar system. The great cosmographer would undoubtedly have approved.
A History of the World in 12 Maps Page 32