In 1154 a Muslim scholar at the Norman court of Sicily finished a map of the known world for King Roger II. It has south at the top, seven climates running across it like shelves, and some 431 towns I could read and place. I set it beside a modern map to see where it is right, where it bends, and how it compares with the Christian Hereford map drawn about 146 years later.
The map is upside down, at least to us. Al-Idrisi, a scholar born in Ceuta, put south at the top, as many mapmakers in the Islamic world did, so Arabia and Africa sit above the Mediterranean and Europe hangs underneath. He drew it in Palermo for Roger II, the Norman king of Sicily, and wrote a long book to go with it, the Book of Roger, which walks across the known world in seventy sections: seven climates, bands of latitude from the equator northwards, each cut into ten pieces from west to east. Laid side by side, the sections make one great rectangle of the world, from the Atlantic to China.
The original silver map is lost. In 1928 the German scholar Konrad Miller rebuilt it from the manuscripts as one sheet, with every name transcribed. I read 431 of its towns on Miller's reconstruction, 362 clearly and 69 with some doubt, found where each one really is, and measured how the map bends the world. Click a town on either map to see it on the other, or turn the old map north up.
Left: Konrad Miller's 1928 reconstruction of the map (public domain), south at the top as drawn; the Turn north up button rotates it. Dots: the 431 towns I located, coloured by region, or by local error (Map layers). Right: the same towns where they really are. Map layers on the left add the modern grid of latitude and longitude, bent to where the map would put it; on the right, the climate lines of the old map laid on the globe, an arrow from each town to where the old map puts it, and al-Idrisi's own road distances. Sources: Miller (1928); al-Thurayya (CC BY 4.0); Pleiades (CC BY 3.0); Natural Earth.
Al-Idrisi's world is a grid. The red lines that run straight across the map divide it into the seven climates of Greek and Islamic geography, bands of latitude from the equator in the south to the cold north, and each climate is drawn the same height, about 754 pixels on Miller's sheet. The climates work: the median latitude of the towns rises from climate to climate without a break, from 15.6° in the first, with Aden, Sanaa and Aswan, to 48.4° in the sixth, with Paris, London and Constantinople, and 53.2° in the seventh, where only three English towns are legible.
But the shelves are not the same depth in reality. The latitudes that best separate the towns of one climate from the next fall at about 18.0°, 28.6°, 35.8°, 40.4°, 47.3° and 53.2° north. The second climate covers 10.6 degrees of latitude; the middle and northern ones an average of 5.8. So the south is squeezed and the Mediterranean and Europe, where the towns are thick, are spread out. By those boundaries 74% of towns sit in the right climate and every one is within one climate of it.
The real latitude of the towns in each climate
Each dot is a located town, placed at its true latitude (across) in the climate the map puts it in (up). Dashed lines: the latitudes that best separate neighbouring climates. Hover a dot.
Within each climate the map behaves like a rectangular grid of degrees. Fitted as a whole, it draws a degree of longitude 0.93 times as long as a degree of latitude, as if the whole world lay at about 21° north, and the fit puts the median town 239 km from where it is. Longitude is easier to get right than latitude here: the fit explains 0.98 of the spread in longitude and 0.90 in latitude, because the climates squeeze and stretch the north to south direction.
Turned north up, the map points the right way. Across all 92,193 pairs of located towns at least 100 km apart, the median error in direction is 10 degrees and 99% are within 45 degrees. Distances keep their order too: the rank correlation between distance on the map and on the ground is 0.95.
Where it goes wrong is a matter of neighbourhoods. For each town I took its eight nearest real neighbours, fitted the best simple stretch and turn from the map to the ground on them alone, and asked where they put the town. The median miss is 55 km, and 76% are within 100 km. But it varies a great deal. Sicily is the most faithful region on the map, with a median local error of 21 km, followed by Syria and Palestine (26 km), Morocco and Algeria and Iberia. The edges are worst: Arabia (156 km), central and eastern Europe (212 km) and Sind and India (247 km).
How faithfully each region is drawn
Median local error: how far each town is from where its eight nearest neighbours on the map say it should be. Regions with at least five located towns. Hover a bar; click to see the region on both maps.
Northern Europe sits in between, at 71 km. That fits the way al-Idrisi says, in his preface, that the work was done: by gathering the reports of travellers who came to Roger's court. The coasts that ships from Palermo sailed were described by many of them; the far east and the far north by few.
The located towns, region by region
Number of towns, median local error, median error in direction between pairs of towns in the region, and the scale at which the region is drawn relative to the map as a whole (1 = average). Click a row to see the region on both maps.
Sicily is not only the best drawn region. It is also the biggest. Measured the same way as in my study of the Hereford map, comparing distances between pairs of towns on the map and on the ground against the map's average, Sicily is drawn at 1.42 times the average scale, more than any other region: Greece and the Balkans 1.38, Italy and England 1.25, Syria and Palestine 1.25, and at the other end Morocco and Algeria 0.68 and Arabia 0.59. The rectangular grid alone would leave Sicily at 0.99, so the enlargement is the mapmaker's choice. I read 20 towns on it, from Palermo, Messina and Syracuse to Butera and Caronia, more than on all of England and central Europe together.
Its one fault is a turn. The best local fit rotates Sicily by about 31 degrees anticlockwise, so its pairs of towns are off in direction by a median 28 degrees, one of the larger figures on the map, while their spacing is the most accurate. Al-Idrisi had the island's shape right and set it slightly askew.
At the top of the map, beyond the equator, are the Mountains of the Moon, and below them the lakes from which the Nile flows north across the whole height of the map to the delta. The text is precise. The source of the Nile, it says, is in the Mountains of the Moon, "whose beginning is sixteen degrees beyond the equinoctial line", from which ten springs feed two lakes, whose rivers join in a third, very great lake. It also quotes Qudama that the Nile runs 5,654 miles from source to sea.
The map does not show sixteen degrees. Miller's reconstruction puts the mountains only about 130 pixels beyond the equator line, a sixth of the height of a climate. And 5,654 miles, at about 2 km to the Arab mile, is some 10,900 to 11,300 km, against about 6,650 km for the real river. Where the Nile runs through towns, though, the map is good. Fitted on the whole map, Aswan comes out at 23.3° (really 24.1°), Alexandria at 32.5° (really 31.2°), and Egypt spans 13.7 degrees of latitude on the map against 13.2 in reality.
England, "the island of Inkiltara", sits in the far north west of the map, astride the boundary between the sixth and seventh climates: London, Dover and Hastings in the sixth, Lincoln, Grimsby and Salisbury in the seventh. I could read 8 English towns, too few for firm figures, but they tell a clear story. North to south, England is in the right place: on the map as a whole its towns come out, at the median, within a tenth of a degree of their true latitude. East to west it is pushed 2.3 degrees too far east, and the island is turned: the best local fit rotates it about 37 degrees clockwise, so that Paris, really 148 degrees from London, is drawn at 191 degrees, nearly due south.
Measured from Jerusalem, as in the Hereford study, the English towns point the right way to within a median 12 degrees on al-Idrisi's map, against 8 for the British towns on the Hereford map, which was made in England. Hereford gives Britain 8.1% of its names and draws it at 1.5 times its average scale; al-Idrisi draws England at 1.25 times, more than France (1.18) but less than Sicily.
The Book of Roger is full of distances: so many miles from one town to the next, so many days' march. Dozy and de Goeje's 1866 edition of its chapters on North Africa and Spain gives the text in Arabic and French. I took 63 distances between towns I could identify, 37 in miles and 30 in day stages, and checked each against the scan line by line.
They are consistent. The stated miles and the straight line distances rise together (rank correlation 0.89), at a median of 1.42 km of straight line per stated mile, with half the routes between 1.23 and 1.58. The Arab mile is usually put at about 2 km, so either the roads ran between a third and two fifths longer than the straight line, or the mile in these itineraries was shorter. A day stage is a median 36 km in a straight line, and in all 4 routes that give both, a day is about 25 miles.
Al-Idrisi's road distances against the straight line
Each dot is a distance stated in the text between two towns (across, in Arab miles) against the great circle distance between them today (up). Both scales logarithmic. Hover a dot.
The map seems to follow the book. For the 18 routes in miles whose two ends I located on the map, distance on the map tracks the stated miles (rank correlation 0.74) more closely than it tracks the real distance (0.48). It is a small sample, but it is what you would expect of a map put together from itineraries.
About 146 years after al-Idrisi, a clergyman in Hereford drew the largest medieval map of the world that survives, with east at the top and Jerusalem at its centre. I measured it the same way in an earlier study. Measured from Jerusalem, with the best rotation and scaling, al-Idrisi's map explains 0.94 of the spread of real positions, against 0.84 for Hereford; the median town lands 330 km from where it is, against 516 km. Directions from Jerusalem are right to a median 13 degrees (19 on Hereford), with 99% within 45 degrees (81%).
The same tests on both maps
Similarity fit about Jerusalem, as in the Hereford study: share of the spread of real positions explained, median distance of a town from where the fitted map puts it, median error in direction from Jerusalem, and share within 45 degrees. Al-Idrisi: 430 towns; Hereford: 140.
The comparison is not quite like for like. The Hereford sample is smaller and full of classical names copied from Roman books; al-Idrisi's is larger and mostly towns of his own century, many of them on trade routes. But the difference in purpose shows. Hereford is a picture of history and Scripture that spends its space on the Holy Land, drawn 4.5 times its average scale. Al-Idrisi's map is a geographer's: Syria and Palestine get 1.25 times, Mecca sits close to the middle of the map, in the second climate, while Arabia is drawn at the smallest scale of any region (0.59), and the extra space goes to the island where the map was made. Both maps spend most on home.
The map. Konrad Miller's 1928 reconstruction, from Wikimedia Commons (public domain), 12,999 by 5,958 pixels. It is a modern redrawing from the manuscripts, not the original, and Miller added the transcriptions, so every position here is a position on Miller's sheet. I read 431 town labels by eye, 362 clearly and 69 with some doubt, and recorded the pixel of each town's symbol. Miller drew towns as small brown discs; I found 5,329 of them automatically and snapped 386 of my readings (90%) to the nearest disc, a median 1.9 pixels away. The others I checked by eye.
Real places. I gave each town a modern position and checked it against three gazetteers: al-Thurayya, which maps the towns and roads of the early Islamic world, Pleiades for ancient places, and Natural Earth for modern towns. 365 of the 431 (85%) match a gazetteer entry of the same name, a median 0.7 km from my position; the rest are small towns the gazetteers do not list. I left out names I could not identify with confidence.
Measures. All measurements are made with the map turned north up. The global fit is the best affine map from map position to longitude and latitude. Local error, direction between pairs and scale by region are defined in the paper; each region needs five located towns to be scored. The climate boundaries are the latitudes that best separate the towns of neighbouring climates. The Hereford comparison repeats exactly the similarity fit and Jerusalem bearings of that study. The distances come from Dozy and de Goeje (1866), read in the Internet Archive's text and checked against the line they come from.
What this is not. A sample of legible towns, not the whole map: rivers, mountains and peoples are left out, and coverage is thin where labels are few or unreadable, in India and central Asia, eastern Europe and Africa south of the Sahara (9, 10 and 1 towns). The reconstruction is Miller's: where his redrawing differs from the manuscripts, so does my measurement. With clear readings only (362 towns) the median local error is 52 km and the median global miss 235 km, close to the figures for all towns.