The Rise and Fall of Alexandria (21 page)

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 to 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:

 
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

 
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:

 
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.

What we know of Archimedes’ last days are sketchy but indicative of how one worldview was replacing another. Plutarch tells us it all began when Archimedes developed the compound pulley, not for practical purposes but as a way of explaining a mathematical problem to his king. He then demonstrated its efficacy by pulling a laden ship from its dock single-handed, using a complex series of ropes and pulleys.

As the Roman siege tightened, it was these mechanical skills that Hiero called on Archimedes to use against his enemy. Plutarch tells us that Archimedes turned his mind to creating wonderful siege engines which employed the mathematics he so loved to perform similar apparently superhuman acts. Great catapults were designed to rain stones upon the legions who foolishly believed themselves to be out of range. When Roman ships approached the harbor walls, cranes were swung out which either dropped huge rocks on their ships to sink them or hooked them out of the water, dumping their crews in the sea before overturning them and consigning them to the depths. Plutarch provides a vivid description of the result on the Roman soldiers’ psyches:

 
Of course, these tales had probably been greatly embellished over the centuries between the siege of Syracuse and Plutarch’s day, but they contain at least an echo of what was clearly a gargantuan struggle and a glimpse into the difference in mind-set between Greeks and Romans. Romans could terrify Greeks with numbers and brutality—their strength was their army; Greeks, however, could panic Romans with their minds. Their strength was in books—their arsenal, a library in Alexandria.

In the end, however, the relentless might of the Roman army triumphed, and thought gave way to force. As the Roman army flooded into the town, the Roman general Marcellus sent out orders to fetch Archimedes for him. But somehow things went wrong and Archimedes was killed. But Plutarch cannot leave it so baldly writ and gives us instead one last glimpse of the great man, still the disconnected theoretician, still more in love with ethereal mathematical ideas than reality, still more concerned with universal constants than the value of his own life:

 
This is probably Plutarch’s own romantic notion of the great man’s death. He also records two other versions, the last of which may perhaps hold more of a glimmer of the truth: