Theater of the World

by Thomas Reinertsen Berg

  But how long was the stadion used by Eratosthenes? If he used the Egyptian stadion, equivalent to 157.5 metres, he calculated the Earth’s circumference at 39,960 kilometres, which is only 1.6 per cent from the actual length of 40,075 kilometres. If he used the Athenian stadion of 185 metres, however, he calculated the Earth’s circumference as 46,620 kilometres–16.3 per cent from the correct answer. Eratosthenes also based his calculation on misconceptions–in Syene, the Sun is not at its zenith at the summer solstice; nor is the city situated on exactly the same longitude as Alexandria.

  Ultimately, however, the question of the stadion’s length and these geographical blunders are insignificant. Eratosthenes knew that the calculated distance between Alexandria and Syene was approximate–it was based on the time it took to travel between the two cities by camel. The important thing was that he had something he could use as a unit of measure.

  With knowledge of the Earth’s circumference, Eratosthenes was able to find out just how much of the Earth was covered by the oikoumene. In his Geographika, he described the relationship between the size of the Earth and that of the oikoumene, illustrating it on the first map we know of to feature lines of latitude and longitude.

  Eratosthenes probably used eight circles of latitude. The northernmost was situated at Thule, the second at the mouth of the Dnieper River in Russia, the third at the city of Trake in northern Greece, the fourth–the major circle of latitude–at Athens and Rhodes, the fifth at Alexandria, the sixth at Syene, the seventh at the city of Meroë in modern Sudan, and the southernmost at Sri Lanka and the Land of the Kinnamomom (cinnamon) Bearers, which the Greeks thought lay somewhere south of Khartoum.

  Eratosthenes’ main line of longitude stretched from Ethiopia in the south to Thule in the north, and passed through Meroë, Aswan, Alexandria, Rhodes and the mouth of the Dnieper River. East of this he placed three lines of longitude that passed through the Euphrates, the Caspian Gates and the Indus River, respectively. To the west, one line of longitude passed through Rome and Carthage, another through the Pillars of Hercules and a third through the west coast of Portugal.

  Lines of longitude can be placed anywhere one pleases–unlike north and south, which start and end at the poles, east and west don’t begin or end anywhere. The placement of 0 degrees east and west–the prime meridian–is therefore a matter of taste, and over the years cartographers have located this at Jerusalem, Alexandria, Rome, Paris, Copenhagen, Kongsvinger, Trondheim, Bergen, Kristiansand and Oslo. Highly political negotiations resulted in the official prime meridian being located at Greenwich in 1884–France was particularly dissatisfied at this, and continued to use the country’s own Paris meridian long afterwards. But the prime meridian is simply a point from which we start counting, and while the distance between the degrees of latitude is determined by the height of the Sun in the sky, we count degrees of longitude using time. The Earth rotates once–360 degrees–every twenty-four hours, and 360 divided by twenty-four is fifteen. The Earth therefore rotates 15 degrees of longitude in an hour.

  Two pages from Jacopo d’Angelo’s translation of Ptolemy into Latin. To the left is Ptolemy’s first projection, which he was least satisfied with, while to the right is his second–which was more accurate, but also more complex. Printed by Nicolaus Germanus in Ulm in 1482. See here for more information about d’Angelo’s translation.

  Eratosthenes placed his 7 degrees of longitude where he saw fit–the distances between them varied, and it would be fair to say that they were little more than a system of artificial lines that helped him to place the various cities on his map. They were based on assumptions, wild guesswork, and some surviving solar observations and documents from Alexander the Great’s military campaign.

  Eratosthenes’ oikoumene was 78,000 stadions from west to east and 38,000 stadions from north to south, and therefore took up around a quarter of the Earth. Eratosthenes believed there was a good chance that three other continents also existed, and that they too were inhabited. Using mathematics, he confirmed the Greeks’ suspicion that they were aware of only a small part of the world.

  Shortly after this, Crates of Mallus created a globe based on Eratosthenes’ calculations of the size of the Earth and oikoumene–the first globe that we know of with any certainty. It was huge, with a diameter of around three metres, and showed the part of the world known to the Greeks together with three other, unknown parts. Directly south of the equator is antoikoi (‘those who live on the other side’), on the other side of the northern hemisphere perioikoi (‘those who live nearby’) and south of this the antipodes (‘those with their feet the other way’). The continents were thought to be islands without any contact with each another.

  Not everyone accepted Eratosthenes’ calculations. Hipparchus of Nicaea (190–126 BC) wrote a treatise in three books titled Against the Geography of Eratosthenes, in which he criticised his predecessor’s lack of astronomical observations when drawing maps. ‘Hipparchus,’ Strabo wrote, ‘shows that it is impossible for any man, whether layman or scholar, to attain to the requisite knowledge of geography without a determination of the heavenly bodies and of the eclipses which have been observed.’ Hipparchus, the Greek who knew most about Babylonian mathematics, developed the modern system that uses 360 degrees of longitude and 180 degrees of latitude, and showed how eclipses of the Sun and Moon help us to determine the degrees of longitude. His major work was a catalogue of the exact positions of 850 stars.

  THE STARS | In the library in Alexandria, Claudius Ptolemy can find no better geographical calculations based on astronomical observations than those performed by Hipparchus. He is ‘the only one,’ Ptolemy writes, to have given us accurate coordinates–despite the fact that Hipparchus’ text was 300 years old at the time of his reading it. Ptolemy was first and foremost an astronomer, and therefore shared Hipparchus and Strabo’s view that astronomical observations were the key to geographical knowledge, while reconnaissance at sea and on foot provided inadequate results. Unfortunately, he was far too ahead of his time to be able to follow this principle–simply too few observations had been recorded. ‘If the people who visited the individual countries had happened to make use of some [astronomical] observations, it would have been possible to make the map of the oikoumene with absolutely no error,’ Ptolemy laments.

  Ptolemy was well aware that he had insufficient knowledge to create a complete world map–just as ‘all subjects that have not reached a state of complete knowledge, whether because they are too vast, or because they do not always remain the same, the passage of time always makes far more accurate research possible; and such is the case with world cartography too,’ he writes. ‘For the consensus of the very reports that have been made at various times is that many parts of our oikoumene have not reached our knowledge because its size has made them inaccessible, while other [parts] are themselves different now from what they were before because features have ceased to exist or have changed.’

  This is why Ptolemy highlighted the necessity of using the latest available surveys, claiming that he had little to offer in terms of new knowledge of the world. As he described it, his work was to use the latest information to update and correct the work others had done before him–first and foremost that of Marinus, a geographer from Tyre in modern Lebanon, who probably died around the time Ptolemy was born. We know of him from no source other than Ptolemy’s Geography. ‘Marinus of Tyre seems to be the latest [author] in our time to have undertaken this subject, and he has done it with absolute diligence,’ Ptolemy writes, never attempting to conceal the fact that the geographical data in his Geography is for the most part taken from his predecessor.

  But Ptolemy’s work on how to best reproduce a spherical globe on a flat sheet of paper was pioneering. This challenge–which continues to tax us today–was first taken up by Democritus 450 years earlier, when he drew the land mass as oval-shaped instead of circular, and later by Eratosthenes with his artificial lines. Others must also have tried to find solutions
to this issue, as Ptolemy writes that Marinus of Tyre had criticised ‘absolutely all’ previous attempts to create flat maps, but information about these has not survived.

  Ptolemy proposes two different map projections, and common to both is that they bend in different ways to simulate the curvature of the Earth.

  The first projection has completely straight lines of longitude that meet at an imaginary point beyond the North Pole. Across these, Ptolemy arranges curved lines of latitude, which get longer the closer they get to the equator. The ratio between the equator and the northernmost line of latitude, which passes through Thule at 63 degrees north, is correct, and at the centre is a line of latitude that passes through Rhodes. ‘Above all, the semblance of the spherical surface will be retained,’ Ptolemy wrote of this projection, but was still somewhat dissatisfied as it has an inherent error. In reality, the lines of latitude become shorter the further north or south of the equator they are–but here, they get longer south of the equator. To resolve this, Ptolemy makes the southernmost line of latitude, 16 degrees south of the equator, the same length as the equivalent line of latitude in the north, causing the lines of longitude to buckle. He regards this as a minor error, however, since his map doesn’t extend so far south, but it would result in greater problems as areas of the world further south were discovered. The projection does not lend itself particularly well to expansion.

  Ptolemy therefore created another projection that he was more satisfied with. Here, the lines of both latitude and longitude are curved, and almost all the lines of latitude are in the correct ratio. ‘It is immediately obvious how such a map is more like the shape on the globe than the former map,’ he writes, but admits that it is much more difficult to draw than his first model. He concludes that there is a need for both a simple and a more accurate projection.

  For decades, cartographic historians have discussed whether Ptolemy drew the map that was included in the first edition of the Geography, or whether this was drawn by someone else. Nowhere in any of his works does Ptolemy ever refer to any included maps. It is also likely that there was no practical need for a world map in the year AD 150–the Romans were more interested in maps they could use in military campaigns and colonisation. Many therefore believe that the maps included in the Byzantine copies of the Geography from the 1300s are the first to be drawn based on Ptolemy’s meticulous records. Others argue it is unlikely that Ptolemy could have possessed so much geographical information and prepared such advanced projections without ever drawing a map himself.

  THE SCANDIAN ISLANDS | To look at maps drawn in accordance with Ptolemy’s instructions is to look at maps we can understand. North is at the top, and the Mediterranean, Europe, north Africa, the Middle East and parts of Asia are recognisable. America and Oceania, southern Africa and eastern Asia–of which Ptolemy knew nothing–are not included. The same goes for the Pacific Ocean and most of the Atlantic. The Indian Ocean is an enormous lake, because southern Africa extends far west, to link up with the Malay Peninsula.

  Ptolemy’s oikoumene extends across a far greater part of the world than it should because he underestimated the Earth’s size. He chose to use the calculations performed by the Syrian mathematician Posidonius (135–50 BC), which claimed that the Earth had a circumference of 180,000 stadions, instead of Eratosthenes’ more correct estimate of 252,000 stadions. This meant that the eastern part of China, which led into terra incognita, was located just 40 degrees of latitude from what we now know as the west coast of America; and here, perhaps, is the seed of Columbus’s voyage west: Columbus also believed the Earth to be smaller than it is. Supported by a 1487 edition of Ptolemy’s work, Columbus believed it was just 2,400 nautical miles from Portugal to China. Had he known that in reality this distance is 10,000 nautical miles–ignoring the fact that America is in the way–he might never have set out on his journey.

  Petrus Bertius’s map of the Nordic region, included in his 1618 edition of Ptolemy’s Geography. There are islands correctly located to the east of Cimbrica (Jutland), if one too many, but southern Sweden and Scandinavia in general have been demoted to the island of Scandia. A striking feature of Bertius’s version is how far north Albionis (Britain) stretches.

  The Sun sets over the sea and the Libyan desert. At the museum in Alexandria, supper is served to the lodging scholars. Ptolemy rolls up Pliny’s encyclopedia and walks back along the colonnade. In the evening he sits in the flickering candlelight of his room and writes down several more place names and coordinates:

  East of the Cimbrian peninsula there are four islands called the Scandian islands, three of them smaller, of which the one in the middle has the following position:

  41°30 E 58°00 N

  But one of them very large and the most eastwards at the mouth of the river Vistula; its ends are located

  to the west 43°00 E 58°00 N

  to the east 46°00 E 58°00 N

  to the north 44°30 E 58°30 N

  to the south 45°00 E 57°40 N

  It is properly called Scandia itself; and its western region is inhabited by the Chaedini, its eastern region by the Favonae and the Firaesi, its northern region by the Finni, its southern region by the Gutae (Gautae) and the Dauciones, and its central region by the Levoni.

  Over the coming centuries, all the Ptolemaic splendour will fall to ruin, drowning in the Mediterranean at Alexandria’s port. Even in Claudius Ptolemy’s time, the city is not what it once was. Two hundred years earlier, Caesar had set fire to the ships in the harbour while battling Ptolemy XIII; the fire spread, destroying a great number of the library’s books. Caesar’s adopted heir Augustus took control of Egypt after the death of Cleopatra in the year 30 BC, and Alexandria was demoted from the capital of Egypt to a provincial Roman town. The library slipped into a state of gradual decline.

  Ptolemy belongs to the region’s last golden age. His books are among those that survived and were passed on–but only thanks to the random copies and translations created over the centuries, as it seems the Geography was largely forgotten after Ptolemy’s death. Quotations from it occasionally pop up in Latin texts, and the Arabs translated parts of it and improved some of the coordinates, but in Constantinople (Istanbul) around the year AD 1300, Maximus Planudes wrote that he ‘discovered through many toils the Geographia of Ptolemy, which had disappeared for many years.’

  In the year AD 1323, as Ptolemy is being rediscovered and gradually attaining his rightful place in cartographic history, an earthquake destroys all that is left of the great lighthouse that cast its light over Alexandria’s glory days. But Ptolemy’s Geography travels onwards with an Italian monk who, after visiting Constantinople to learn Greek in AD 1395, takes a copy of the book home to Florence, and ten years later publishes the work in its first Latin translation–giving the Europeans an alternative to the view of the world they have held over the more than 1,000 years since the Geography was first published.

  WESTWARDS | Greek natural philosophy built upon Sumerian and Babylonian astronomy and mathematics–these ideas travelled west to Miletus, where new thoughts about the Earth’s place in the universe took shape and resulted in both airy philosophising and concrete maps. Scholars also began to use astronomical observations to cast a net of latitudes and longitudes across the world, making it easier to say exactly where a given place was located. Around the year AD 150, Claudius Ptolemy began to compile all available Greek knowledge of the world, combining it with information provided by travellers to Alexandria to publish his Geography, antiquity’s greatest work about oikoumene–the inhabited world. The work looks back in time, to the knowledge of all Ptolemy’s predecessors, but also forwards–towards a time in which the Europeans would forget much of the Greek geography.

  ‘Ptolemeo de gli Astronomi prencipe’–‘Ptolemy, prince of astronomy, who diligently and accurately observed the heavenly bodies’ in Giacomo Gastaldi’s edition of the Geography from 1548. This was the first edition to be published in Italian, as well as the first editio
n of Ptolemy in handy pocket format. It was also the first edition of the Geography to feature engraved maps of the American continent.

  A medieval map included in a prayer book from around the year 1250, with the east at the top. London is marked in gold leaf, since this is where the book was created, but the religious emphasis on the east means that Europe occupies a humble location down in the bottom left. Norwegia is a peninsula connected to Saxonia.

  HOLY GEOGRAPHY

  Reykholt, Iceland

  64° 39′ 54″ N

  21° 17′ 32″ W

  Snorri Sturluson paces back and forth across the dirt floor of the farmhouse at Reykholt as he speaks. A scribe, perhaps his friend Styrme, is sitting at a nearby table, taking notes on calfskin using a goosefeather quill. Snorri is writing a book about Norse mythology and minstrelsy, and like any good medieval Christian he starts his work with an account of God’s creation. After describing Adam and Eve, the Great Flood and the glory of God, he describes the world:

  The world was divided into three parts. From south to west up to the Mediterranean was the part known as Africa, and the southern portion of this is so hot that everything there is burned by the sun. The second part, running from west to north up to the ocean, is called Europe or Énéa, and the northern half of this is so cold that no grass grows there and it is uninhabited. From north to east and down to the south is Asia, and these regions of the world have great beauty and magnificence; the earth yields special products like gold and precious stones. The centre of the world is there also […].

  At around the same time that Snorri is writing his book, the Edda, an artist in London is drawing a map in a prayer book. Here, Christ is shown lifting his right hand to bless the Earth below him; in his left he holds a globe to demonstrate his dominion over the world. He is standing in the east, as this is the holy cardinal point and the part of the world in which Christianity originated, while two dragons mark the entrance to hell down in the west. The world is divided into three parts–Africa, Europe and Asia–and at its centre is Jerusalem.