The Rise and Fall of Alexandria (20 page)

The angle of the shadow in Alexandria had been 7 degrees, so Eratosthenes calculated that the distance between Syene and his point must be 7/360th of the circumference of the earth. As he knew that distance was 4,900 stadia, he calculated that 1 degree was 700 stadia and hence that the circumference of the world was 700 ✕ 360, or 252,000 stadia. Sadly we do not now know exactly which measurement of a stadion he used (there were several), but the “walking” stadion which we might imagine a royal pacer to use was about 516.8 feet. This would give a circumference for the earth of 24,662 miles. The circumference around the poles is now known to be 40,008 kilometers (24,860 miles). Using just a stick, a well, and a royal pacer, he had proved the earth was a globe and measured its circumference to within 318 kilometers (198 miles) of its true diameter while never leaving Egypt.

But Eratosthenes had only just started. Having noted that the sun reached the zenith at Syene on the summer solstice but on no other day, he calculated that the earth’s axis must be tilted toward the sun. This would explain how at different times of year the sun rose to a different height above the horizon. To measure this he also created another first in the history of science, the armillary sphere—a model of the celestial globe constructed from a skeleton of graduated metal rings (or
armillae
), linking the poles and representing the equator, ecliptic, meridians, and parallels, with a ball representing the earth at its center. So pleased was he with this device that he was said to have set one up in “that place which is called the square porch” (quoted in Charles Kingsley,
Alexandria and Her Schools,
lecture 1), almost certainly the portico of the museum, and it was here that he then used it to calculate the angle of the earth’s tilt at 23 degrees 51 minutes. Its true value is 23 degrees 46 minutes. He was just a twelfth of a degree off. His proof provided the first scientific explanation of a phenomenon that every Greek and Egyptian experienced: the seasons. When the Northern Hemisphere is tilted away from the sun, it is winter there; when it is tilted toward the sun, it is summer.

Emboldened by the success of these measurements, he now went on to attempt to span truly astronomical distances. Using the same lunar eclipses which had first hinted at the shape of the earth, he first calculated the distance between the earth and the moon and then the distance now known as the astronomical unit, between the earth and the sun. Sadly, due to mistakes in his understanding of how large the sun and moon were relative to the earth—something even Aristarchus had had trouble calculating—these figures were somewhat less accurate. His distance from the earth to the moon came out at 122,300 kilometers (76,437.5 miles), as opposed to the real figure of approximately 384,600 kilometers (240,375 miles), and his calculation of the astronomical unit was, somewhat more accurately, 125.5 million kilometers (78,437,500 miles) as opposed to the true figure of about 150 million kilometers (93,750,000 miles).

Inspired by his new understanding of the shape of the world on which he lived, Eratosthenes now turned his attention to mapping it, creating a detailed drawing of Egypt as far south as Khartoum and correctly hypothesizing that the annual Nile flood was caused by rains in unknown hills far to the south where the Nile had its source. Previously it had been believed that the flood was caused by the Etesian winds blowing water up the delta and preventing the Nile from draining into the Mediterranean. Eratosthenes’ correct hypothesis would not finally be proved until the eighteenth and nineteenth centuries AD, when the sources of the Blue and White Nile were finally discovered by Speke, Burton, and Bruce.

But for a man who had measured the world, mapping Egypt alone would never be enough, so he set out, with his usual breathtaking self-confidence, to draw up something even more impressive. He had measured the world; now he intended to map it. This lost masterpiece was a landmark in both mapmaking and geography. Covering the world from Iceland and the British Isles to Sri Lanka and from the Caspian Sea to Ethiopia, it was built around a daring new concept of prime meridians and their offsets, or what we would call longitude and latitude. For his prime line of longitude he chose his own city, drawing the north-south line from the mouth of the Borysthenes (Dnieper River) south through the Euxine (Black) Sea, through Rhodes and Alexandria, down to Syene. Had his map and his prime meridian survived, perhaps we would today use Alexandrian mean time rather than Greenwich mean time as the world’s chronological baseline.

For his prime meridian of latitude, Strabo tells us, Eratosthenes takes the world and

 
And he had a new word for this new work, a new description of what it was to understand the nature of the world and where things are placed upon it. This idea he called “geography”—the first time the term had ever been used.

While his own maps would later be surpassed by those of Hipparchus, Strabo, and Ptolemy, his understanding of the nature and measurements of the earth as recorded in his
Geographica
would remain unrivaled in the ancient world. Following the destruction of the library where it was stored, this knowledge would lie in abeyance for 1,700 years. Only in AD 1491 would Martin Behaim dare to commission a terrestrial globe, and twenty-three years more would pass before Copernicus reinstated the heliocentric solar system. Eratosthenes was the first to assert that it would be possible to reach India by sailing west from Spain—something that Christopher Columbus had difficulty persuading the Spanish monarch of 1,800 years later. He also maintained that Africa could be circumnavigated, something not proven until Bartholomeu Dias’s voyage of 1488. As for the measurement of the circumference of the earth? That wouldn’t be superseded until Jean Piccard published his new calculations in AD 1671.

Despite these achievements Eratosthenes was not destined for the universal fame that he deserved. To his fellow philosophers in Alexandria he was known as
beta
or
pentathlos.
Yet to him, and indeed any librarian in Alexandria, this was, in its way, the greatest of compliments. By “beta” his contemporaries weren’t accusing him of being second best but saying that, behind the specialists, he was the finest mind in each subject. Likewise to call him “pentathlos,” the pentathlete, was to imply that while there were specialists who might outclass him within a field, Eratosthenes knew all the fields and was almost as good as the best in each of them. He was a jack-of-all-trades, but he was also a master of all of them—one of the greatest polymaths of all time.

With what many modern scientists would consider a lifetime of achievement already behind him, Eratosthenes returned to his duties at the library. He reorganized the entire institution’s five hundred thousand volumes before adding further to that tally by writing yet more on geography, mathematics, grammar, and literary criticism, and even penning a history of philosophy. None of these has survived complete and many are known only by their name or vague references in later works by other authors. Bearing in mind what these casual asides tell us of the man, we can only guess at what we have lost.

The end of Eratosthenes was as tragic as the loss of his books, though in his mind at least, it was perhaps fitting and right. Having discovered in 194 BC that he was beginning to lose his sight, this visionary thinker realized that he would soon no longer be able to read the collections in the library he had tended and enriched. Without this there was nothing. Unable to continue his work, he chose to starve himself to death. He was around eighty-one years old. He was buried in his adopted home of Alexandria, and his epitaph, written by Dionysius of Cyzicus, states simply:

 
It is doubtful that Eratosthenes himself would have worried overly much about being buried far from home in the sands of Alexandria, or as Dionysius more poetically puts it, “by the edge of the beach of Proteus”—Proteus being a mythical king of Egypt. He had compassed the world, had been the first to really see and describe the globe we all now know we live on. This was his idea, and therefore anywhere on its surface could be said to be his home.

CHAPTER NINE

THE “EUREKA” FACTOR

Archimedes, quoted in Pappus,
Synagoge,
book 8

 
 
E
ratosthenes lived at the high noon of the Ptolemaic Empire, at a moment when the academic star of the Hellenes shone at its brightest, and this star attracted still greater minds from across the Mediterranean. Of those other students in Alexandria, one brilliant light eclipsed all others, a man whom Eratosthenes had met when he was young, who would become perhaps his closest friend and correspondent, and whose life would mark a profound turning point in the fortunes of the philosophers of Alexander’s city.

Archimedes, son of Phidias the astronomer, was born around 287 BC in the city of Syracuse in Sicily. At the time the island was not yet a part of the ever-expanding Roman world but was still made up of Greek city-states whose independence had fluctuated, depending on the degree of intervention from the great trading nation of Carthage across the sea in North Africa and the power and stability of the greatest state among them, Syracuse itself. Since its foundation by Corinthian colonists around 734 BC, the city’s fortunes had risen and fallen many times over, and they had sunk rather low by the time of Archimedes’ childhood, the city having been sacked by the Carthaginians and then having suffered under a series of ineffectual tyrants. This does not of course mean that it was not still a very civilized place to grow up, connected as it was to the international Hellenistic world and peopled with Greek descendants who kept in close contact with developments in the mainland Greek states and Alexandria.

And it was to Alexandria that the young Archimedes was drawn, to the Pharos shining out across the water and to the museum and library where the ideas planted in his Sicilian childhood could flower. We do not know the exact date when Archimedes came to Alexandria; indeed, we have no formal proof that he came here at all, other than his lifelong friendships with men like Eratosthenes and the astronomer Conon, which can have developed only through meeting them in person. That, and one mechanical legacy that remains in use to this day.

Archimedes was an engineer and an inventor, though he would not have thanked any of his contemporaries for saying so. In his mind all that mattered was the beauty of mathematics and the exploration of pure thought. To him the mechanical marvels for which he is still famous were just toys, demonstrations of principles. To us today they seem almost miraculous, the first real applications of the discoveries made in the library at Alexandria to the world outside its porticoes.

One of the most famous of these can still be seen in Egyptian fields in the delta today. The “Archimedean screw” consists of a spiral inside a hollow pipe, the bottom end of which lies in an irrigation ditch by the edge of the fields, and the top of which is over the field. When the screw is turned it captures a puddle of water in the bottom end of the tube and, as it spins, carries it up the length of the tube, ejecting it at the top, in effect making a smooth, perpetual pump. Had this been Euclid studying spirals, the Archimedean screw would have remained a geometrical idea; thanks to Archimedes it became a practical tool that has survived over two thousand years intact. But that same genius that turned abstract thought into practical devices would prove to be a double-edged sword.

It is unlikely, however, that at the time Archimedes was walking in the gardens of the museum with Eratosthenes and Conon, he was discussing engineering problems. His surviving works, of which thankfully there are many, show a mind electrified by the abstractions of mathematics, and particularly geometry: how to calculate the volume of a sphere, how to estimate the number of grains of sand in the universe, how to construct a regular heptagon, the operation of mirrors and levers. It was the source of this pure theory at Alexandria that must have attracted Archimedes here in the first place, where he first held and read the original works of Euclid and Aristarchus, which in later life he would recall, not always favorably, in his own books. Indeed, without his fame and the survival of so many of his works, there are many names from Alexandria and many wonderful books that we might not know of at all.