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 That wouldn’t be superseded until Jean Piccard published his new calculations in AD 1671.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:
A gentler old age and no dulling disease quenched thee, and thou didst fall asleep in the slumber to which all must come, O Eratosthenes, after pondering over high matters; nor did Cyrene where thou sawest the light receive thee within the tomb of thy fathers, O son of Aglaus; yet dear even in a foreign land art thou buried here, by the edge of the beach of Proteus.
Dionysius of Cyzicus, “Peace in the End,”
epigram 5, in Palatine Anthology
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
Give me but one firm spot of land on which to stand, and I will move the earth.
Archimedes, quoted in Pappus, Synagoge, book 8
Eratosthenes 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.
It was only when Archimedes finally left Alexandria and returned to Syracuse that he found the opportunity to exploit practically the knowledge he had gained in Egypt. Only back home, in the relative backwater of Sicily, was there time and reason to apply the knowledge he had won to the business of everyday life.
That is not t
o say that Archimedes’ life was “everyday” by the standards of an ordinary citizen of Syracuse. He seems early on to have become a close friend (and may even, according to Plutarch, have been a relation) of Hiero II, a commander in the wars against Carthage who had managed to seize power in Syracuse around 270 BC and whose rule would grant his city one last Indian summer of peace and freedom before it lost its independence forever.
Syracuse was then, for a while, an Alexandria in miniature, where state and philosophers relied upon each other for support and protection. Just as the Ptolemies had their scholars, so Hiero had Archimedes, who through his correspondence with Eratosthenes and Conon remained in touch with the heart of the Hellenistic intellectual world. But Syracuse and Hiero had need of practical things, far removed from the ethereal abstractions of the great library, and it was in his brilliant adaptation of pure theory to practical advantage that Archimedes would now make his name.
Of all the stories told about this greatest of thinkers perhaps the most famous derives from this time, and it is one in which we see both how the state and academia could become co-dependent and how a moment of genius could become enshrined in legend.
The story goes that Hiero invited Archimedes to the palace to present a problem to him. He had decided to order a precious votive crown made for a temple in the city as thanks for his victories in war. He had chosen the maker and sent from the treasury a large quantity of gold with which to manufacture it. In time the beautifully wrought crown had been returned to him and he had dedicated it in the temple. But now a rumor had come to his ears that the maker, for all his craft, was a cheat and had kept some of the gold for himself. Of course the first thing palace officials would have done on receiving the crown was to weigh it to confirm that it weighed the same as the quantity of gold the craftsman had been given. This had indeed been done and the weight was correct, but the rumor suggested he had achieved this by alloying the gold with extra, cheaper silver, something not only offensive to Hiero but no doubt in his mind very offensive to the gods to whom the crown had been dedicated. So the ruler summoned Archimedes, who was asked to discover a solution. He did, and in the process invented the whole field of hydrostatics.
Exactly what provided the inspiration for the solution may never now be known, but the story, and it is a famous one, was already current in the lifetime of the first-century BC Roman architect Vitruvius, who recounts the story:
He by chance went to a bath, and being in the vessel, perceived that, as his body became immersed, the water ran out of the vessel. Whence, catching at the method to be adopted for the solution of the proposition, he immediately followed it up, leapt out of the vessel in joy, and, returning home naked, cried out with a loud voice that he had found that of which he was in search, for he continued exclaiming, in Greek, Eureka! (I have found it out).
Marcus Vitruvius Pollio, Architecture, book 9, chapter 10
The method he had discovered was simple but revolutionary. In the bath he had realized that the volume of water displaced by the immersion of his own body was equal to the volume of his body. So now he filled a bowl to the brim, placed in it a piece of gold that weighed the same as the crown, and noted how much water spilled over the brim. He then repeated the experiment with a piece of silver of the same weight. This time it displaced more water than had the gold—because gold is far more dense, so a piece of any given weight has a much lower volume. Finally he filled the pot once again to the brim and then placed in it the crown itself. This displaced a quantity of water somewhere between the volumes displaced by the lumps of gold and silver. It contained some gold but was not pure. From this Archimedes could then work out exactly how much silver the craftsman had surreptitiously alloyed with the gold as a ratio of the displaced volumes of water. It was a brilliant experiment, using just water and logic to untangle the proportions of two metals bound tightly together in alloy. Hiero was rightly impressed. Although we never hear of him again, the craftsman, we might imagine, was less so.
Of course, the exact details of the story, and in particular the running through the streets naked shouting “Eureka!” are really not provable. Indeed, we know from Plutarch that Archimedes didn’t really like taking baths anyway and that
oftimes Archimedes’ servants got him against his will to the baths, to wash and anoint him, and yet being there, he would ever be drawing out of the geometrical figures, even in the very embers of the chimney. And while they were anointing of him with oils and sweet savours, with his fingers he drew lines upon his naked body, so far was he taken from himself, and brought into ecstasy or trance, with the delight he had in the study of geometry.
Plutarch, Life of Marcellus, in Parallel Lives, 17
This glimpse of a disconnected genius, churlish and difficult with his servants, reluctant to engage in the everyday world but retaining an almost childlike delight in the purity of geometry and mathematics, the perfection of shapes and form, is perhaps a truer view of the man. But for all his delight in the abstract, the practical world was catching up with the great thinkers of the third century BC, and what Archimedes was developing in Syracuse would soon come back to haunt both his physical home there and his intellectual home across the Mediterranean in Alexandria.
Contemporary heads of state were especially keen to make practical use of his discoveries. This was not of course a new idea; the foundation of the library had been part of Ptolemy I’s plan to secure his hard-won empire, an empire where his patronage of academia gave him not simply kudos but real power. It was to this end that his grandson Ptolemy III had begun his somewhat unscrupulous and manic collection policy, which included seizing all books arriving in the port of Alexandria for compulsory copying. Usual policy was to return the copy and keep the original—in case anything had been missed. These originals were then marked “from the ships” and placed in the library. For those attempting to remove books from the city, harsh penalties existed. All ships leaving the two harbors were searched, and any books found on board which had not been surrendered for copying were confiscated. Nobody removed information from Alexandria.
Foreign libraries were treated with the same acquisitive contempt. Ptolemy III had, according to Galen (17.1, in Kühn, pp. 601ff ), set out his desire to copy every book in the known world in a letter entitled “To All the World’s Sovereigns.” However, these rulers’ libraries proved reluctant to lend their precious volumes, no doubt aware of the fate of the books “from the ships.” The libraries in Athens were no exception. Indeed, it was only after years of pressure and the payment of a hefty deposit of fifteen talents (enough to pay an Alexandrian workman’s salary for over 120 years) that the Athenians finally relented and released their manuscripts of the complete works of Aeschylus, Euripides, and Sophocles for copying. They never received their copies or saw the originals again. When they protested, Ptolemy told them they could keep the fifteen talents. In his view he had a bargain.
But a new force was rising in the Mediterranean. The Roman Republic also knew all about power, including that held in books, but it took a more selective and practical approach to collecting knowledge. The Romans would use the tools of Hellenistic thought not to delight in geometry or astronomy but to conquer the world, and in the process Archimedes, the Ptolemies, and many Alexandrians would lose their lives.
By the time Archimedes heard that a Roman army was marching on his home city he’d already had plenty of exposure to their methods; indeed, he may already have been partly responsible for them. One of the devices described by Vitruvius is the innocuous-sounding “odometer,” a machine for measuring large distances—in principle like that on an automobile. It was based on a wooden cart with a series of gears connecting the axle to a hopper of pebbles, one of which dropped into a collecting bowl with each full turn of the gears. As the distance it took for the gears to make one full turn could easily be measured, by counting the pebbles in the bowl at the end of a journey and multiplying that number by the basic unit of distance, the total length
of the journey could be calculated. If, as some modern commentators have suggested, this was invented by Archimedes, he would soon have reason to regret their practical applications of his theoretical knowledge. Archimedes himself typically didn’t consider such trifles of any real importance, as Plutarch once again tells us:
Archimedes possessed so high a spirit, so profound a soul, and such treasures of scientific knowledge, that though these inventions had now obtained him the renown of more than human sagacity, he yet would not deign to leave behind him any commentary or writing on such subjects; but, repudiating as sordid and ignoble the whole trade of engineering, and every sort of art that lends itself to mere use and profit, he placed his whole affection and ambition in those purer speculations where there can be no reference to the vulgar needs of life.
Plutarch, Life of Marcellus, in Parallel Lives, 17
The Roman army did not share his noble sentiments. For them the odometer wasn’t a vulgar toy but a device for laying out Roman mile-stones, which meant they knew how far one place was from another, which in turn meant they knew how long it would take to get an army from one place to another. This enabled them to plan military campaigns over wide areas with great precision, and they were planning one right now—against Syracuse and Archimedes’ old friend Hiero.
The Roman army was marching toward Archimedes and Syracuse for a very good reason. The politics of the Mediterranean had swung around again, and Hiero’s former enemies, the Carthaginians, were now his friends. Syracuse was offering help to this great trading nation, and that in turn antagonized the Romans. They, under the guise of improving the security of both themselves and their allies, had decided to confront the competition. But Sicily stood between the two powers and would now feel the force of their first great clash in what became known as the Punic Wars. This was all about the practical politics of power. The Romans weren’t particularly interested in philosophy or geometry unless it gave them an advantage in trade and war, two areas of life quickly merging in the Roman mind.
The Rise and Fall of Alexandria Page 16