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Virtually none of these changes in the intellectual and political world are immediately discernible when first reading Ptolemy’s Geography. There is scant acknowledgement that the astronomer was writing at the culmination of a thousand-year tradition of Greek mapmaking, and little trace of the impact of Roman geography on his writing, despite the generations of Roman imperial administration of Alexandria since Augustus’ conquest in 30 BC. Nor is there any mention in Ptolemy’s work of the Alexandria library, which by the middle of the second century was a pale shadow of its glory under Eratosthenes, after a fire in 48 BC destroyed many of its books and buildings. Instead, Ptolemy’s work reads like a timeless scientific treatise of high Hellenistic scholarship, serenely indifferent to the changes in the world around it. Ptolemy followed a well-established geographical tradition: establishing his astronomical credentials and then writing a treatise that, just like Strabo’s Geography and Hipparchus’ Against Eratosthenes, spends most of its time explaining itself in opposition to its immediate predecessors.
Ptolemy had already completed a monumental treatise on astronomy, a compilation of mathematical astronomy in thirteen books that became known as the Almagest. It provided the most comprehensive model of a geocentric universe, and would endure for more than 1,500 years before being challenged by Nicolaus Copernicus’s heliocentric thesis, On the Revolutions of the Celestial Spheres (1543). Ptolemy’s cosmology marked a decisive turn away from Plato’s and the idea of divine heavenly bodies. The Almagest expanded the Aristotelian belief in a geocentric cosmology shaped by a mechanical physics of cause and effects. Ptolemy argued that the spherical, stationary earth lies at the centre of a spherical celestial universe, which makes one revolution around the earth every day, revolving from east to west. The sun, moon and planets follow this celestial procession, but they trace different motions from the fixed stars. Ptolemy also listed the planets according to their proximity to the earth, beginning with the moon, followed by Mercury, Venus, the sun, Mars, Jupiter and Saturn. Developing Hipparchus’ astronomical observations and Euclid’s geometrical principles, Ptolemy catalogued 1,022 stars arranged into 48 constellations; he explained how to make a celestial globe; and he used trigonometry (and in particular chords) to understand and accurately predict eclipses, solar declination, and what appeared to be the irregular or retrograde motion of the planets and stars from a geocentric perspective.44
Like Hipparchus and many of his Greek forebears, Ptolemy believed in the ‘affinity of the stars with mankind and that our souls are a part of the heavens’.45 From this spiritual statement emerged a more practical approach to the study of the cosmos: the more accurate the measurement of the movement of the stars the more precise the calculations of the size and shape of the earth. In the second book of the Almagest, while explaining how gathering astronomical data can produce more accurate measurement of terrestrial parallels, Ptolemy admitted:
What is still missing in the preliminaries is to determine the positions of the noteworthy cities in each province in longitude and latitude for the sake of computing the phenomena in those cities. But since the setting out of this information is pertinent to a separate, cartographical project, we will present it by itself following the researches of those who have most fully worked out this subject, recording the number of degrees that each city is distant from the equator along the meridian described through it, and how many degrees this meridian is east or west of the meridian described through Alexandria along the equator, because it was for that meridian that we established the times corresponding to the positions [of the heavenly bodies].46
The Almagest was probably written shortly after AD 147. The need for a ‘separate, cartographical project’ based on the astronomical observations recorded in the Almagest was the spur for Ptolemy’s subsequent text, the Geography: an exposition, in the form of tables supplemental to the larger astronomical work, that would provide coordinates of key cities. After completion of the Almagest, as well as writing treatises on astrology, optics and mechanics, Ptolemy completed the eight books of this second great work.
The finished text was substantially more than the promised table of key geographical coordinates. Ptolemy chose not to gather data himself or through agents, but instead collated and compared every text available to him in Alexandria. He stressed the importance of travellers’ tales, but warned about their unreliability. The Geography acknowledged the need ‘to follow in general the latest reports we possess’ from pre-eminent geographers as well as historians. These included etymological and historical sources – Roman authors like Tacitus and his description of northern Europe in the Annals (c. AD 109) and periploi of uncertain origin, such as the anonymous Periplus of the Erythraean Sea (c. first century AD), a merchant’s guide to places in the Red Sea and Indian Ocean. The most important author quoted in the Geography was Marinus of Tyre, whose work has since been lost, but who according to Ptolemy, ‘seems to be the latest [author] in our time to have undertaken this subject’.47 The first book defined the subject of geography and how to draw a map of the inhabited world. Books 2 to 7 presented the promised table of geographical coordinates, but now enlarged to include 8,000 cities and locations, all listed according to their latitude and longitude, beginning in the west with Ireland and Britain, then moving eastwards through Germany, Italy, Greece, North Africa, Asia Minor and Persia, and ending in India. Book 8 suggested how to divide the into twenty-six regional maps: ten of Europe, four of Africa (still called ‘Libya’) and twelve of Asia, a running order that would be reproduced in the earliest Byzantine copies of his book illustrated with maps, and most subsequent world atlases.
The wealth of geographical information contained in Ptolemy’s tables included not only the scholarly tradition of geographical enquiry, but also astronomical calculations and the written testimony of travellers. From the beginning of the Geography, Ptolemy made it very clear that ‘the first step in a proceeding of this kind is systematic research, assembling the maximum of knowledge from the reports of people with scientific training who have toured the individual countries; and that the inquiry and reporting is partly a matter of surveying, and partly of astronomical observation’. Such ‘systematic research’ was only possible thanks to the consultation of the Alexandria library’s Pinakes, or ‘Tables’, the first known library catalogue indexed according to subject, author and title, created by Callimachus of Cyrene, c. 250 BC. The Geography was an immense data bank, compiled by the first acknowledged armchair geographer, a ‘motionless mind’48 operating from a fixed centre, processing diverse geographical data into a vast archive of the world.
For Ptolemy, there was no space for speculative cosmogonies on the origins of the universe, or attempts to establish the indeterminate and shifting geographical and political boundaries of the . The Geography’s opening statement set the tone, with its enduring definition of geography as ‘an imitation through drawing of the entire known part of the world together with the things that are, broadly speaking, connected with it’. Ptolemy regarded geography as a comprehensive graphic representation of the known world (but not, we should note, the whole earth), in contrast to what he called, with a nod towards the Roman preoccupation with land surveying, ‘chorography’, or regional mapping. Whereas chorography requires skill in ‘landscape drawing’, Ptolemy said that global mapping ‘does not require this at all, since it enables one to show the positions and general configurations [of features] purely by means of lines and labels’, a geometrical process in which mathematical method ‘takes absolute precedence’.49 Using a telling corporeal metaphor to contrast the two geographical approaches, Ptolemy believed that chorography provides ‘an impression of a part, as when one makes an image of just an ear or an eye; but the goal of world cartography is a general view, analogous to making a portrait of the whole head’.
Having established his methodology, Ptolemy then proceeds to discuss the size of the earth and its latitudinal and lo
ngitudinal dimensions through a detailed critique of Marinus of Tyre’s methods, before providing his own geographical projections for drawing world maps. One of the most significant aspects of Ptolemy’s calculations involved the size of the whole earth in relation to its inhabited realm, the . Revising the calculations of Eratosthenes and Hipparchus, Ptolemy divided the globe’s circumference into 360° (based on the Babylonian sexagesimal system, in which everything was measured in units of sixty), and estimated the length of each degree as 500 stades. This gave him the same circumference of the earth as Posidonius: 180,000 stades. This was certainly too small, possibly by as much as 10,000 kilometres, or more than 18 per cent of the earth’s actual circumference, depending on the length of stadion used. But if Ptolemy believed the earth was smaller than predecessors like Eratosthenes imagined, he went on to argue that its inhabited dimension was much larger than many believed: his stretched from west to east through an arc of just over 177°, starting from a prime meridian that ran through the Fortunate Isles (the Canary Islands), to Cattigara (believed to be somewhere near modern-day Hanoi in Vietnam), a distance he estimated as 72,000 stades. Its breadth was calculated at just over half the length, covering just under 40,000 stades, running from Thule, situated 63° N, to the region of ‘Agisymba’ (in sub-Saharan Africa), located by Ptolemy at 16° S, a latitudinal range, on his measurements, of just over 79°.50
Such measurements naturally lead to the question of how Ptolemy arrived at his calculations of latitude and longitude. He calculated parallels of latitude according to astronomical observations of the longest day of the year at any given location. Starting at 0° on the equator with a longest day of twelve hours, Ptolemy used quarter-hour increments for each parallel until he reached the parallel representing the longest day as fifteen and a half hours, at which point he switched to increments of half an hour, up to the limit of the , which he estimated as lying along the parallel of Thule, with a longest day of twenty hours. Drawing on this method of measurement, as well as Hipparchus’ calculations based on astronomical observations of the sun’s altitude on the solstice, Ptolemy drew up his tables of latitude, although the relative simplicity of his method of observation meant that many of them were inaccurate (including Alexandria).
The calculation of longitude proved even more difficult. Ptolemy believed that the only way of determining longitude was to measure the distance between meridians west to east according to time, not space, using the sun as a clock: all places on the same meridian will see the noon sun crossing the plane of the meridian at the same time. Ptolemy therefore began his calculation of longitude at his westernmost point, the Fortunate Isles, and drawing each meridian moving east at intervals of 5°, or a third of an equinoctial hour, and encompassing twelve hours, represented as 180°. His measurements may have been inaccurate, but his was the first systematic method to provide consistent data that allowed subsequent mapmakers to project a grid of latitude and longitude over the inhabited earth, a graticule composed of temporal rather than spatial calculations. We tend to think of mapmaking as a science of spatial representation, but Ptolemy was proposing a world measured not according to space, but by time.51
Towards the end of book 1 of the Geography, Ptolemy begins to move away from Marinus to explain his other great geographical innovation: a series of mathematical projections designed to represent the spherical earth upon a plane surface. Although acknowledging that a globe ‘gets directly the likeness of the earth’s shape’, Ptolemy points out that such a globe would need to be extremely large to be of any use in seeing the earth and plotting movements across it with any precision, and it would not in any case allow a view ‘that grasps the whole shape all at once’. Instead, Ptolemy suggests that ‘drawing a map on a plane eliminates these difficulties completely’, by creating the illusion of seeing the entirety of the earth’s surface at a glance. Nevertheless, he admits that it brings its own problems, and ‘does require some method to achieve a resemblance to a picture of a globe, so that on the flattened surface, too, the intervals established on it will be in as good proportion as possible to the true intervals’.52 Ptolemy here encapsulates one of the major challenges which has faced mapmakers ever since.
Marinus had tried to resolve the problem by creating a rectangular or ‘orthogonal’ map projection which, according to Ptolemy, ‘made the lines that represent the parallel and meridian circles all straight lines, and also made the lines for the meridians parallel to one another’. But when a geographer projects a geometrical network of imagined parallels and meridians onto a spherical earth they are in effect circles of varying length. Marinus neglected this fact in favour of prioritizing the measurements made along his prime parallel running through Rhodes at 36° N, and accepting increasing distortion north and south of this line. He accepted a centrifugal representation of terrestrial space, where the accuracy emanates outwards from a definable centre, dissipating the further one moves towards the margins, and finally leading to absolute distortion. Like a good Euclidean, Ptolemy wanted his terrestrial space to be homogenous and directionally uniform, and quickly dismissed Marinus’ projection. But even Ptolemy was unable to square the circle of map projection, and acknowledged that a compromise was required.
Fig. 3 Diagrams of Ptolemy’s first and second projections.
With Euclid clearly still in his mind, he turned to geometry and astronomy for a solution. Imagine, wrote Ptolemy, looking at the centre of the earth from space and envisaging geometrical parallels and meridians drawn upon its surface. The meridians, he argued, ‘can give an illusion of straight lines when, by revolving [the globe or the eye] from side to side, each meridian stands directly opposite [the eye], and its plane falls through the apex of the sight’. In contrast, the parallels ‘clearly give an appearance of circular segments bulging to the south’. Based on this observation, Ptolemy proposed what is known as his first projection. The meridians were drawn as straight lines converging at an imaginary point beyond the North Pole, but the parallels were depicted as curved arcs of different lengths, centred on the same point. Ptolemy could now maintain a more accurate estimate of the lengths of the parallels, as well as their relative ratios, focusing on the parallels running along the equator and Thule. The method could not excise all proportional distortions along every single parallel, but it provided a better model of conformation that retained consistent angular relations at most points on the map than any previous projection.
It was the most influential and enduring attempt yet devised to project the earth onto a plane surface. This was the first example of a simple conical map projection, as its shape suggests, although Ptolemy’s cone also resembles another, more familiar shape: that of the Macedonian chlamys, the iconic image that shaped the foundations of Ptolemaic Alexandria and inspired Eratosthenes’ map of the . Ptolemy’s projection also provided a simple but ingenious method of how to draw a world map and then incorporate geographical data into it. Using straightforward geometry, he describes how to ‘fashion a planar surface in the shape of a rectangular parallelogram’, within which a series of points, lines and arcs are marked using a swinging ruler. Having established the basic geometrical outline, the mapmaker then takes the ruler measuring the radius of a circle centred at an imaginary point beyond the North Pole. The ruler is then marked with gradations in latitude from the equator to the parallel of Thule. Attaching the ruler to the imaginary point so that it can swing free along an equatorial line divided into 180° of hour-long intervals, it would be possible to locate and mark any location on a blank map by referring to Ptolemy’s tables of latitudinal and longitudinal coordinates. The ruler was simply swung to the required longitude listed along the equatorial line, and, according to Ptolemy, ‘using the divisions on the ruler, we arrive at the indicated position in latitude as required in each instance’.53 The geographical outlines on such a map were relatively insignificant: what characterized it were not contours but a series of points, established by his coordinates of
latitude and longitude. A point is of course the first defining principle of Euclidean geometry: it is ‘that which has no part’; it is indivisible, with no length or breadth. To create an accurate map projection, Ptolemy went right back to the basics of Euclidean geometry.
This first projection still had its drawbacks: on a globe, parallel lines diminish south of the equator, but if drawn on Ptolemy’s projection they actually increase in length. Ptolemy effectively went against the consistency of his own projection by solving this problem with meridians forming acute angles at the equator. This gave the projection the appearance of a chlamys, but it was hardly ideal. Ptolemy regarded this as only a minor drawback, as his only extended 16° S of the equator, but it would cause serious problems in later centuries when travellers began to circumnavigate Africa. Nevertheless, the first projection still projected straight meridians, which, as Ptolemy acknowledged from the outset, only corresponded to a partial perspective on the globe from space; like the parallels, meridians trace a circular arc around the globe, and their geometrical reality should retain such a curvature on a plane map. He therefore proposed a second projection. ‘We could’, he wrote, ‘make a map of the on the planar surface still more similar and similarly proportioned [to the globe] if we took the meridian lines, too, in the likeness of the meridian lines on the globe.’54 This projection, he said, was ‘superior to the former’, because parallels and meridians were represented as curved arcs, and because virtually all of its parallels retained their correct ratios (unlike the first projection, where this was only achieved for the parallels running through the equator and Thule). The trigonometry involved was more complicated than the first projection, and Ptolemy still had problems retaining uniform proportionality along his central meridian. He also acknowledged that it was far more difficult to construct a map based on the second projection, as the curved meridians could not be drawn with the aid of a swinging ruler.
A History of the World in 12 Maps Page 7
