<br><h3> Chapter One </h3> THE ESSENTIAL ARCHIMEDES <p> <p> <i>There was more imagination in the head of Archimedes than there was in that of Homer.</i> —Voltaire, <i>Philosophical Dictionary</i> <p> <p> The citizens of ancient Syracuse would have recognized the man who is said to have bustled past them naked and dripping and shouting, <i>"Eureka!"</i> (I have found it!). It was Archimedes, the celebrated mathematician, scientist, inventor, and confidant of the king. That Archimedes seemed oblivious to his own nakedness and to onlookers' bemused stares was perhaps only mildly scandalous, given his reputation for eccentricity. To residents of this long-ago Sicilian city-state, Archimedes had always occupied an enchanted middle ground: one foot planted squarely in the world of men, the other dancing to some private muse of nature. <p> Archimedes was naked and wet because, only moments earlier, he had purportedly jumped from his bath, elated at his flash of insight into a problem he had been puzzling over. The Syracusan king, Hieron II, had given the royal metalsmith a specific weight of gold to be fashioned into a splendid wreathlike crown. Now the king suspected that the completed crown, destined to adorn the statue of a deity, had been cut with less valuable silver and that the smith had pocketed the unused gold. Hieron directed Archimedes to establish the crown's makeup without sampling or defacing it in any way. <p> Archimedes knew that gold is more dense than silver. So if a certain weight of silver had been substituted for the same weight of gold, the crown would occupy a larger space than an identical one of pure gold. But how does one measure the volume of an irregular crown? <p> Stepping into his brimful bath, as legend tells it, Archimedes noticed water splashing over the rim. The more of him that was immersed, the more water overflowed. <i>Eureka!</i> The mundane had become momentous; to find the crown's volume, Archimedes is said to have realized, all he had to do was immerse the crown in a vessel full of water and measure the spillage. Doing so later, he informed Hieron that the crown was indeed too large for the original weight of gold. The smith was guilty. Primitive scientific deduction and measurement had one of its earliest successes. The true "gold," however, lay in Archimedes' broader conclusions; he established the key principles of buoyancy that govern the flotation of hot-air balloons, ships, and denizens of the sea. And his <i>Eureka!</i> became the joyous expletive that erupts whenever an experiment yields a sublime result or disparate ideas cohere into a beautiful theory. <p> This homely incident and its technical spinoff are the merest glimmer of the manifold genius of Archimedes and the profound impact he had on the development of mathematics and science. Archimedes' interests ranged widely: from square roots to irrigation devices; planetariums to the stability of ships; polyhedra to pulleys; number systems to levers; the value of the mathematical constant ITLπITL to the size of the universe. Yet this same cerebral man, when called upon by his king, developed machines of war so fearsome, they might have sprung from a devil's darkest imagination—weapons that held at bay the greatest army of antiquity. Ironically, it was for his feats of engineering, not for his beloved mathematics and science, that Archimedes' reputation swelled to mythic proportions in the ancient world. The Roman statesman-philosopher Cicero claimed that Archimedes possessed a genius greater than one would imagine possible for a human being. <p> Archimedes is universally acknowledged to have been the most proficient mathematician of antiquity and among the top mathematicians of all time, on par with the likes of Isaac Newton and Carl Friedrich Gauss. Archimedes derived the mathematical properties of parabolas, spirals, and polyhedra. He conjured geometric solids with t ongue-twister names like <i>truncated cuboctahedron</i> and <i>rhombicosidodecahedron</i>, the latter an implausible sixty-two-sided conflation of abutting triangles, squares, and pentagons. He developed new ways to compute square roots, lengths of arcs, and volumes of spheres, cylinders, and cones. For the last, he used an elementary form of calculus almost two millennia before its full introduction by Newton and Leibniz. No wonder Galileo called him superhuman. <p> Although pure mathematics was his greatest joy, Archimedes also made seminal contributions to science. His center-of-gravity concept, now a staple of freshman physics, was among the earliest abstractions of physical objects for the purpose of analyzing nature. He solved previously intractable problems in mechanics by mathematically collapsing real objects into imaginary points of mass. Indeed, Archimedes pioneered the union of mathematics and physics that was to become a hallmark of modern scientific analysis. He is also reported to have studied optics and written a treatise on mirror reflection (now lost). And, of course, his <i>Eureka!</i> work on buoyancy was unmatched in the ancient world. <p> When pressed, Archimedes could be remarkably adept at invention. The hand-cranked irrigation device, commonly known as the Archimedes screw, may have been developed by him in his youth while studying at Alexandria in Egypt. There are also tantalizing reports that he built a working mechanical model of the solar system, one of the first planetariums, and designed both a steam-powered cannon and a compressed-air organ. He was also a genius in the use of levers and pulleys, boasting to King Hieron, "Give me a place to stand, and I will move the Earth." As proof of his assertion, Archimedes contrived to launch, single-handedly, a fully laden ship using what may have been a compound system of ropes and pulleys. Astounded, King Hieron proclaimed to the Syracusan citizenry, "From this day forth Archimedes is to be believed in everything he may say." <p> The king's declaration proved to be a harbinger of what was to come. Archimedes' treatises, rediscovered after a thousand years of collective amnesia in Eusope, helped guide nascent thinkers out of the Dark Ages and into the Renaissance. Indeed, Archimedes' cumulative record of achievement—both in breadth and s ophistication—places him among the exalted ranks of Aristotle, Newton, and Einstein. When contemporaries searched for a suitable honorific for the fifteenth-century architect Filippo Brunelleschi, they identified him not with his architectural forefather Vitruvius but with Archimedes. Galileo invokes Archimedes' name over a hundred times in his works. The seventeenth-century polymath Robert Hooke dubbed his innovative telescope the Archimedean Engine. And, like a highbrow graffiti artist, the teenage Isaac Newton scratched Archimedes' geometric diagrams on the wall of his school. <p> The name Archimedes graces computer programs, Web sites, a screw-shaped marine fossil (as well as the corkscrew in my kitchen), a short story by Aldous Huxley, an essay by Mark Twain, and, in a double dose of wisdom-by-association, Merlyn's pet owl in T. H. White's Arthurian tale <i>The Sword in the Stone</i>. Archimedes' profile is seen on the Fields Medal, the "Nobel Prize" of mathematics. And the ancient sage's tendency to become lost in cogitation may be the cultural root of characters such as Jerry Lewis's "Absent-Minded Professor" and Hubert Farnsworth in the animated television series <i>Futurama</i>. <p> Today there are Eureka vacuum cleaners, camping tents, and (naturally) bathtub curtains. California's motto is <i>Eureka</i>, as is the name of a prose poem by Edgar Allan Poe. Over the ages, Archimedes' vaunted lever has been exerted in the name of philosophy (Rene Descartes), patriotism (Thomas Paine), international relations (Thomas Jefferson), history (Honore de Balzac), human fallibility (Franz Kafka), revolution (Leon Trotsky), political theory (Hannah Arendt), media influence (Marshall McLuhan), world peace (John F. Kennedy), and racial justice (Robert Kennedy). The Archimedean lever has likewise infiltrated literary works, such as <i>Don Juan, The Three Musketeers, Dracula</i>, and Shelley's philosophical poem "Queen Mab." <p> Archimedes floats through our collective consciousness: a forebear of modern ideas, a symbol of the intellectual heights to which the human species can rise. His ingenuity has inspired generations of thinkers in his own time, during the Renaissance, and up through the present day. He comes to us not merely as a name but as a flesh-and-blood character, swayed by the passions and perplexities of genius. His is a larger-than-life story, no doubt burnished by mythmakers who sought to elevate him beyond his manifold accomplishments. <p> Who, then, was Archimedes? If the barriers of time, language, and culture were magically breached, would Archimedes be the sprightly, avuncular intellectual—like a favorite teacher, perhaps—eager to involve us in his latest mathematical escapade? Or would he be withdrawn and cerebral, occupying some elevated plane of existence, friend only to his invisible muse? Was he roused by life's joys and tribulations or ever lost in blissful cogitation? Where does Archimedes-the-man end and Archimedes-the-myth begin? All that we have to paint the portrait of the true Archimedes are secondhand or thirdhand accounts, set down decades or centuries after his death. And, for additional clues about his personality, we have his own writings—or, at least, imperfect copies of copies of copies of his original writings. Surely, the temptation to bathe an overachiever like Archimedes in a heroic light proved irresistible to those charged with transcribing the great man's words and writing his biography. <p> Ancient historians are notoriously unreliable, both as reporters of events and as portrayers of character. No one can say for sure whether Archimedes truly hopped from his bath and shouted <i>Eureka!</i>—much less whether he preferred solitude over society, was an early riser, or had a predilection for oysters. Most ancient biographers embellished freely, amplifying in equal measure the affirmative aspects of those they admired and the villainous aspects of those they despised. The lives of noteworthy people were more than mere strings of occurrences; they were archetypes to be emulated or avoided. The first-century Greek biographer Plutarch, for example, cast his retrospective eye on a wide array of historical figures. His ranging account of the Roman general Marcus Claudius Marcellus indirectly illuminates Archimedes; this is how we know of Archimedes' supposed "high spirit," his fantastic war machines, his favor of abstract mathematics over "sordid and ignoble" engineering, and the purported circumstances of his death. But Plutarch was not a biographer in the modern sense as much as a moral essayist. His writings are biographical analyses of character: how events shape character, how character shapes events. To his credit, Plutarch quotes liberally from lost works of his predecessors, providing a multidimensional perspective (still woefully incomplete) on his biographical subjects. <p> Virtually nothing is known about Archimedes' formative years. Even the name Archimedes—literally, "Master of Thought"—may be a pseudonym bestowed upon the man by an admirer. Eutocius, who wrote about mathematics and astronomy during the sixth century A.D., refers to an Archimedean biography by one Heracleides, but that account is nowhere to be found. The twelfth-century Byzantine historian Joannes Tzetzes tells us, without evidence, that Archimedes was seventy-five years old when he died at the hands of the Romans during the siege of Syracuse in 212 B.C. That puts Archimedes' birth close to 287 B.C. Archimedes himself mentions his father, Phidias, within the text of <i>The Sand-Reckoner</i>, an expansive thought experiment on the size of the universe. Of Phidias, an astronomer, we know only that he estimated the relative sizes of the Sun and the Moon. <p> Whether Archimedes was raised in modest or privileged circumstances is uncertain. His father's name, Phidias, derives from that of the great sculptor of the Parthenon and was common among the artisan class. Certainly no elite family would have named a child Phidias. Cicero, a century and a half after Archimedes' death, describes his Greek predecessor as <i>humilem homunculum</i>—a humble little man—which could just as well refer to Archimedes' personal style or oratory talents as to his economic status. The first-century Roman poet Silius Italicus reports in his epic chronicle of the Second Punic War that Archimedes was <i>nudus opum</i>—destitute of means. Given Archimedes' professed devotion to his studies, mathematical accomplishment might have been all the remuneration he sought. Pursuit of the lavish life, were it even an option, would have diminished the productivity that is evident in the historical record. Presumably, Archimedes subsisted on some form of patronage, perhaps a royal retainer, in exchange for his unique civic services to Syracuse. <p> Plutarch intimates that Archimedes was a close friend, if not kin, of the Syracusan King Hieron II, who himself was a nobleman's s on—albeit an illegitimate one. Perhaps the protomathematician and protowarrior-monarch knew each other in their youth and maintained the bond through their respective ascendancies. Or maybe their lives converged only during adulthood, in a long-running give-and-take of mutual self-preservation: Hieron's political wiles kept Syracuse at peace, while Archimedes' military inventions strengthened the city's defenses against onslaught. <p> A historical reference that Archimedes studied under Plato is patently false; although Plato did visit Syracuse a number of times, he died sixty years before Archimedes was born. And, no, Archimedes was not the son of the great mathematician Pythagoras, as one bygone commentator claimed; the pair were centuries and oceans apart. But there is no doubt that the young Archimedes did study mathematics with the successors of Euclid at Alexandria, in northern Egypt. (Assuming the standard chronology is reliable, Archimedes was a young man when Euclid died, but there is no mention anywhere of the two having met.) <p> Alexandria was founded in 332 B.C. by Alexander the Great in the wake of his campaign of conquest. By Archimedes' time, it had already grown to become the intellectual and commercial center of the Hellenistic world: a grand galaxy of buildings, monuments, wide ways, and human strivings. Along the boulevard-like Canopic Way, stretching between the Gate of the Sun and the Gate of the Moon, Alexandria's civic vigor manifested itself in spectacular Dionysian processions, one of which "included a hundred-and-eighty-foot golden phallus, two thousand golden-horned bulls, a gold statue of Alexander carried aloft by elephants, and an eighteen-foot statue of Dionysus, wearing a purple cloak and a golden crown of ivy and grapevines." <p> It was here, after the young Macedonian king's death, that his general, Ptolemy I Soter, established the Temple to the Muses—the Museum—and its extraordinary Library with as many as half a million documents and scrolls. (By comparison, the largest medieval European library, the Sorbonne, had less than two thousand volumes by the fourteenth century A.D.) A later regent, Ptolemy III, was an even more ardent collector. He decreed that all visitors were to relinquish any documents of literary or scientific value, which were then added to the Library's collection; in return, the visitors got cheap papyrus copies of their "donated" works. He also paid a hefty deposit to the Athenian library to borrow the state copies of works by Aeschylus, Sophocles, and Euripides, on the premise of transcribing them; the originals never made it back to Athens. The carefully prepared Alexandrian editions of works became the exemplars whose progeny spread throughout the Hellenistic world and, eventually, to the libraries of medieval Europe. <p> Alexandria was a magnet to the Mediterranean region's most able intellects, including Archimedes. In addition to its rich Library, the Alexandrian Museum had research rooms, an observatory, a zoo displaying exotic species, living quarters, and a dining hall where scholars gathered to dine and debate. Here was an ancient think tank devoted to the arts and sciences, a precursor Institute for Advanced Study, whose collective scholarship became its legacy to future generations—and whose eventual decline under Christian authority in the fourth century A.D. and destruction in A.D. 642 at the hands of Islamic invaders mark one of civilization's greatest losses. <p> <i>(Continues...)</i> <p> <p> <!-- copyright notice --> <br></pre> <blockquote><hr noshade size='1'><font size='-2'> Excerpted from <b>Eureka Man</b> by <b>Alan Hirshfeld</b> Copyright © 2009 by Alan Hirshfeld. Excerpted by permission of Walker & Company. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.<br>Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.