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 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:

 
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.

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:

 
Such terror had seized upon the Romans, that, if they did but see a little rope or a piece of wood from the wall, instantly crying out that there it was again, Archimedes was about to let fly some engine at them, they turned their backs and fled.

Plutarch, Life of Marcellus, in Parallel Lives, 17

 
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:

Archimedes . . . was . . . as fate would have it, intent upon working out some problem by a diagram, and having fixed his mind alike and his eyes upon the subject of his speculation, he never noticed the incursion of the Romans, nor that the city was taken. In this transport of study and contemplation, a soldier, unexpectedly coming up to him, commanded him to follow him to Marcellus; which he declining to do before he had worked out his problem to a demonstration, the soldier, enraged, drew his sword and ran him through.

Plutarch, Life of Marcellus, in Parallel Lives, 19

 
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:

 
As Archimedes was carrying to Marcellus mathematical instruments, dials, spheres, and angles, by which the magnitude of the sun might be measured to the sight, some soldiers seeing him, and thinking that he carried gold in a vessel, slew him.

Plutarch, Life of Marcellus, in Parallel Lives, 19

 
Death at the hands of a looting soldier searching for gold would not be a surprising end for a Syracusan captured by the Romans. But what is intriguing is the mention of what Archimedes was actually carrying, which was likely worth more than gold. These strange devices created by Archimedes for predicting the movement of the heavens, or marking time, or estimating location may have been what Marcellus was really after. They were certainly within Archimedes’ scope. We know he wrote a book on the construction of planetaria, although tragically this is lost, and in his long friendship with Eratosthenes he must have spoken of, and had probably seen, the armillary spheres constructed by his friend in the great porticoes of the museum. Furthermore, his creation of mechanical planetaria is hinted at by the Roman statesman Cicero in his Tusculan Disputations(book 1, chapter 25). We also have another tantalizing quote by the fourth-century AD poet Claudian, suggesting that Archimedes took the theoretical models of the universe he had read of in Alexandria and, through his engineering genius, made them into real devices:

Look! By his skill an old man of Syracuse has copied the laws of the heavens. . . . An animate force within attends the different stars and moves along the living mechanism with its regulated motions. A pretend zodiac runs through its own private year and the simulated moon waxes with the new month.

Claudian, Archimedes’ Sphere, in Epigrams

 
But even more extraordinary than this, we may actually have an ancient example of one of Archimedes’ machines. Thanks to a chance discovery in 1900 and the work of another Alexandrian, we might even be able to reconstruct one of these devices, perhaps the most exotic mechanism from the ancient world: not a clock or a planetarium, but a computer.

The story of Archimedes’ computer begins, appropriately enough, in Egypt. Since its invention there sometime in the fourteenth century BC, a device known as the clepsydra, or “water thief ,” had been used for marking out time.

Improved on by the Greeks, it was a simple but very effective timer consisting of a metal sphere with a tube sticking out of the top and small holes drilled in the bottom. The container was filled with water and the tube was stopped up. When you wanted to begin timing something, you’d take the stopper out and let the water slowly drain out of the tiny holes in the bottom. Every time it was filled with the same amount of water it took the same time to empty.

The clepsydra was an ideal timer, often used in courts to time the speeches for the defense and prosecution so lawyers and clients had equal time and didn’t drone on too long. When the bung was taken out, you started pleading your case. When the water ran out, you stopped—time up! The system had an added advantage. Should your great speech be interrupted, you could put the bung back in and put everything on hold. And so in Greek courts began our obsession with, and indeed enslavement to, time. Plato became one of the earliest writers to complain about the relentless pace of life when he said, “Lawyers are driven by the clepsydra—never at leisure” (Plato, Theaetetus, Introduction and Analysis, part 2).

But the problem with this device is that it wasn’t a clock, just a timer. When it was full, water rushed out quickly, slowing as the head pressure reduced. This made it a very uneven way to measure time even if it was refilled as soon at it emptied. The people of Alexandria were used to uneven time. Each day was divided into twelve “hours” not of a fixed length but simply one-twelfth of the time between dawn and dusk. Confusingly, this meant that an hour in summer was a lot longer than an hour in winter.

Then around 270 BC a barber in Alexandria had a simple but brilliant idea that would change time forever. Ctesibius worked in his father’s barbershop but was something of an amateur inventor as well. Visitors to the shop could have seen his ingenuity in the angle-poise mirror he invented to assist his father, but it was when he turned his mind to time measurement that he made his greatest breakthrough. Ctesibius realized that if the clepsydra was always full, then the water pressure would always be the same and the water would flow out at the same speed. So he added another water tank above the clepsydra. This poured water into the top faster than it could flow out the bottom. That meant the clepsydra was always full and any excess water just overflowed. Then he put another tank below the outflow to catch the water coming out of the clepsydra. That tank now filled up at a constant speed, so if a scale was put on the tank and a pointer was floated in it, then he could measure time constantly. Ctesibius’s water clock made him justly famous. In 270 BC he had created not only the first mechanical clock but one so accurate it wouldn’t be bettered for another 1,800 years.

Using the knowledge he had gained from his days of experimenting in his father’s barbershop, Ctesibius was now inventing a whole new subject: hydraulics. He realized that the constant dripping of water could do more than tell the time. Soon Ctesibius’s clocks were smothered in stop-cocks and valves, controlling a host of devices from bells and puppets to mechanical doves that sang to mark the passing of each hour—the very first cuckoo clock! Having mastered the hours, Ctesibius now found time to invent the organ and build singing statues for the Ptolemaic pharaohs.

Mechanical marvels like these must have come to Archimedes’ attention when he first arrived in Alexandria, since they’d first been constructed only twenty years or so before. Indeed, Ctesibius may still have been alive when the young philosopher first stepped ashore at the Great Harbor.

Just where these devices were set up is unclear from what we can recover of the city plan of ancient Alexandria, but across the Mediterranean in Athens a nearly contemporary device does survive which may fill in a missing link in the story of Archimedes’ “spheres.”

If you walk through the Plaka district of Athens that skirts the foot of the Acropolis, you come eventually to the Roman marketplace, or agora. Here amid the ruins a strange little octagonal building, constructed in white Pentelic marble, still stands. Known today as the Tower of the Winds, after the weather-beaten figures of the winds carved onto its faces, it has survived only because it was thought to be the tomb of Socrates and Plato and was later converted into a small Christian church or baptistery. Long before that, however, it was known as the Horologion of Andronicus and was the municipal clock of ancient Athens, built by the astronomer Andronicus of Cyrrhus in the first century BC. On the sides facing the sun were sundials for telling the time on sunny days, while on the top a weather vane indicated the wind direction.

But inside, through one of the two Corinthian doorways, was Ctesibius’s legacy: a mechanical device for telling the time on cloudy days or at night when a sundial wouldn’t work—a mechanical water clock. The sockets and scars that line the walls of this peculiar marble tower can still be made out today. These once held the mechanism for one of the water clocks invented by Ctesibius, and inside the drip, drip, drip of his clepsydra beat out the rhythm of the classical world.

But the Tower of the Winds may have held a device even more extraordinary than a water clock—indeed, Ctesibius’s device may simply have provided the steady power for a yet more groundbreaking ancient discovery, one that contemporary sources hint may have been invented by Archimedes, inspired by the astronomical work of his friend Eratosthenes and the hydraulic genius of Ctesibius. And we can conjecture this because we have one of these machines, thanks to a storm in the Aegean Sea.

 
 
Spring weather on the seas off Greece is notoriously changeable, and it was with some annoyance but little surprise that Captain Dimitrios Kondos and his group of Greek sponge divers found themselves sheltering from a storm, miles off course, by an isolated island known as Antikythera, between Kythera and Crete in the Ionian Sea, just before Easter in AD 1900.

As the weather cleared, the men decided to make the most of their unplanned trip by diving in the deep, clear waters off the island. After all, even the great Greek philosopher Aristotle had said that the best, softest sponges lie in the deepest waters. The first man down was Elias Stadiatos. It was a dangerous dive of some two hundred feet to the seafloor: There was always the chance that the divers might return to the surface with nitrogen narcosis—the notorious “rapture of the deep.”

When Elias broke the surface again that was exactly what his crew-mates thought had happened to him. The man was shouting incoherently. As they dragged him out of the water and unscrewed his heavy helmet, he clutched at Captain Kondos and began jabbering about a pile of dead women on the seafloor—everywhere dead women.

His friends tried to calm him, thinking nitrogen narcosis had driven him mad. But Elias Stadiatos wasn’t mad, and, disturbed but intrigued by his diver’s words, the captain ordered another dive later that day to discover exactly what it was he had seen. Better prepared than his comrade for what lay beneath, this diver returned to the surface with a very different story. There were indeed human bodies littering the seafloor, but they were not corpses—they were ancient statues from a long-lost wreck, surrounded by a treasure the likes of which had never been seen.

Overnight the wreck became one of the most celebrated finds from ancient history, and when Captain Kondos returned the following year, this time with Greek archaeologists, it was to salvage Elias’s “dead women” from the greatest ancient treasure ship ever found. Over the summer of 1901 thousands of priceless items were winched from the Antikythera wreck. Huge boulders scattered across the site proved to be rare bronze statues, covered with two thousand years of encrustation. Marble statues also reappeared, along with coins, beautifully decorated Greek vases, jewelry, and lavish tableware. Everything fine and rare from the ancient world seemed to be there.

But there was something else besides the obvious treasure. Divers that summer had recovered a lump of thick bronze corrosion with traces of wooden panels clinging to the outside. It certainly wasn’t a bronze statue, so no one took much interest. But it would prove to be the most extraordinary object to have survived from the ancient world. By 1902 this corroded lump had still not been properly examined, but a lot more was known about the Antikythera wreck. Pottery on board had been identified and dated. The wreck was of a merchant ship that had sailed sometime in the first century BC from the Greek islands of Rhodes and Cos to Rome with a priceless cargo of Greek art no doubt destined for the home of a wealthy Roman.

Like the sponge divers some two thousand years later, this ship too seems to have been caught out by a storm and driven toward the remote little island of Antikythera. But its captain hadn’t been as lucky as Captain Kondos. The wealthy buyer who sat in Rome all those centuries ago waited in vain for his shipment of Greek wonders, as the ship carrying them had disappeared beneath the waves.

It was sometime in 1902 that an archaeologist at the National Museum of Greece, Valerios Staïs, decided to have another look at the mysterious lump. When he looked carefully he saw there was something among all the corrosion—metal plates covered with writing. He got a specialist in Greek inscriptions to check it out, and sure enough it was ancient writing—from the first century BC. All the words on it that were legible also seemed to refer to astronomical or zodiacal terms.

But there was more to come. Since its removal from the water the wooden panels that had encased the object had begun to dry and crumble away. As Staïs gently removed them he made another discovery—layers of carefully interlaced cogs and wheels. Whatever was in this lump was some kind of ancient machine.

Initially there were two schools of thought. One said that it was clearly too complicated to be ancient and must have been dropped overboard onto the wreck centuries later. The other said it was just an astrolabe, a type of navigational device known from the seventh century BC onward. But it was in fact neither. The writing on the plates was clearly ancient Greek of the same period as the wreck, so it had to be contemporary, and it was obviously much more complicated than any ancient astrolabe. It would take more than another fifty years for the answer to be found, and then not by an archaeologist but by an English physicist.

Derek de Solla Price was in a unique position to tackle the problem of what was by then known as the “Antikythera mechanism.” Holding PhDs in both experimental physics and the history of science, he had been trying to understand the mechanism since the early 1950s, when the first X-ray images of the still only partially inspected device had been taken. In 1959 he published his initial findings in Scientific American, suggesting that the device was far more complex than previously thought, but this paper was met with disbelief by classicists, who considered such a thing impossible for the date.

It was only in the early 1970s that gamma ray images of the machine, taken by the Greek atomic energy authority, came into his hands and he could finally announce to the world what lay behind the corrosion and concretions: a computer.

Price’s meticulous study of the cogs, gear ratios, and inscriptions enabled him to put together a model of how the Antikythera mechanism worked and what it did. The mechanism was a hugely sophisticated analog computer for calculating the movements of the planets, the rising and setting times of stars and constellations, and the phases and movements of the moon—a complete mechanical calendar and model solar system in a box. By turning a crank handle that would have been on the outside of the wooden box it was possible to calculate the time, day, month, season, and year. It even corrected for errors in the old Egyptian calendar, which, without leap years, lost a quarter of a day each year. The Antikythera mechanism had a special “slip dial” that could be adjusted for that. By looking at how this dial was set, modern computers have calculated when the mechanism was last set and hence the date of the wreck: 80 BC.

So sometime in 80 BC the proud owners must have set the correction dial on this incredible device for the last time. Perhaps they had just sold it to a wealthy Roman and were shipping it off, along with numerous other Greek treasures, from Rhodes or Cos. The new owner must have been looking forward to its arrival—perhaps more so than all the other treasures on board. With this machine he could calculate exact dates and times, make corrections for the notoriously inaccurate official calendars—in short, be master of time itself.

This, then, was the successor to the spheres and planetaria that we know Archimedes wrote about theoretically and that Plutarch places in his arms at the moment of his death. But where had this device come from? And who built it? The answer perhaps lies in the one surviving book by a Greek called Geminus. In this almost unknown work he describes a mechanism he says was built in 87 BC. There are three extraordinary things about this description. First, he appears to be describing a machine like the Antikythera mechanism. Second, the wording he uses is repeated almost exactly on the inscribed plates of the mechanism itself. Finally, Geminus was from Rhodes, where another great philosopher, possibly even his tutor, lived; Poseidonius, who according to Cicero, had made a “sphere . . . the regular revolutions of which show the course of the sun, moon, and five wandering stars, as it is every day and night performed” (Cicero, On the Nature of the Gods, book 2, chapter 34). Rhodes was also of course probably the starting point of the mechanism’s fateful last journey, some five years after Geminus had written.

Some have suggested that the mechanism was Geminus’s very own. Certainly the discovery in the cold waters off Antikythera proved he was not just being fanciful in his description. Others have even claimed the mechanism may have been built by the great Archimedes himself, who is recorded in antiquity as having built a model for “imitating the motions of the heavenly bodies.”

One final suggestion takes us back to Athens and the Tower of the Winds. No crank handle was ever found with the Antikythera mechanism, and Derek de Solla Price suggested it may have even been automatic rather than hand turned. If so, it is not taking a great step to imagine Ctesibius’s water clock dripping away at the top of this tower providing the constant power to turn the mysterious, miraculous wheels of the Antikythera mechanism, whirring quietly away below, beautifully mimicking the movements of the heavens so Athenians could tell the time, and know the date and the positions of all the heavenly bodies at that moment.

 
 
But if such a miraculous device did grace the Tower of the Winds, it was marking out the last days of its inventor’s world. In Alexandria the political climate was changing, and a series of immature and ineffectual royal Ptolemies would prove unable to protect themselves, their city, their country, or the scholars who succeeded Archimedes and Ctesibius. The life of Archimedes epitomizes the dichotomy of academic life in the Hellenistic world. Under the patronage of Hiero, king of Syracuse, Archimedes found the time and money to turn his supremely brilliant mathematical mind to questions of pure theory, but only in between solving the more practical problems of his employer. The emergent world order—that of the Romans—had even less time for theory. They had demonstrated this fatally when they encountered the engrossed theorist Archimedes somewhere in a street in Syracuse in 212. There Rome triumphed, and Archimedes’ last problem was solved not with mathematics but with the point of a sword.

Archimedes’ last wish was upheld by the Romans, however, and he was buried in his home city in a tomb bearing the epitaph he had himself chosen. It was not the list of conquests favored by Roman generals, nor the hereditary titles on the graves of kings. Instead, Archimedes chose a diagram of a cylinder circumscribing a sphere with a note describing how the sphere would be exactly two-thirds of the circumscribing cylinder in both area and volume. It was a proof Archimedes had discovered himself and, in his view, vastly more important than odometers, siege engines, and even mechanical computers. It was what his life work had been for—a very Alexandrian epitaph. To the Romans, and indeed even the Romanized Greeks of Syracuse of later years, however, it must have seemed strangely irrelevant. Their age was one of practical action, in which the theories devised in the library of Alexandria had little place. Even Archimedes’ tomb was left to fall into ruins and become overgrown and forgotten, along with his name. In fact it would only be the idle curiosity of the Roman orator Cicero that would eventually bring it back to light, as Cicero himself describes. He tells us that while he was quaestor of Syracuse in 75 BC (some 137 years after the philosopher’s death) he sought out the tomb of an “obscure little man” called Archimedes, but the native population, either still terrified of their Roman masters or simply forgetful, knew nothing about it. Eventually he found his way to an old cemetery by one of the city gates, choked with brambles and thorns, where he remembered

 
having heard of some simple lines of verse which had been inscribed on his tomb, referring to a sphere and cylinder modelled in stone on top of the grave. And so I took a good look round all the numerous tombs that stand beside the Agrigentine Gate. Finally I noted a little column just visible above the scrub: it was surmounted by a sphere and a cylinder. I immediately said to the Syracusans, some of whose leading citizens were with me at the time, that I believed this was the very object I had been looking for. Men were sent in with sickles to clear the site, and when a path to the monument had been opened we walked right up to it. And the verses were still visible, though approximately the second half of each line had been worn away.

Cicero, Tusculan Disputations, book 5, chapter 23

 
So one of the most famous cities in the Greek world, and in former days a great center of learning as well, would have remained in total ignorance of the tomb of its most brilliant citizen, had a man from Arpinum not come and pointed it out. Roman rule had changed Syracuse and its people, and that process of change was now rippling across the Mediterranean.

If even the great Archimedes could be all but forgotten in just over a century in his physical home, what of the fate of his fellow philosophers at his spiritual home, the great library? Dangerous times were coming to Alexandria, and neither books nor their authors would be spared.

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