Archimedes. - Eureka man: the life and legacy of Archimedes

Eureka Man

BY THE SAME AUTHOR

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Eureka Man

The Life and Legacy of Archimedes

Alan Hirshfeld

Copyright 2009 by Alan Hirshfeld

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LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA

Hirshfeld, Alan.

Eureka man : the life and legacy of Archimedes /

Alan Hirshfeld.

p. cm.

Includes bibliographical references and index.

eISBN: 978-0-802-71979-9

1. ArchimedesBiography. 2. ScientistsGreeceBiography. I. Title.

Q143.A62H57 2009

509.2dc22

[B]

2009005608

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First U.S. edition 2009

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CONTENTS

There was more imagination in the head of Archimedes than there was in that of Homer.

VOLTAIRE, PHILOSOPHICAL DICTIONARY

T HE CITIZENS OF ancient Syracuse would have recognized the man who is said to have bustled past them naked and dripping and shouting, Eureka! (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.

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 crowns makeup without sampling or defacing it in any way.

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?

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. Eureka! The mundane had become momentous; to find the crowns volume, Archimedes is said to have realized, all he had to do was immerse the crown in a vessel full of water and mea sure 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 Eureka! became the joyous expletive that erupts whenever an experiment yields a sublime result or disparate ideas cohere into a beautiful theory.

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 pi 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 devils darkest imaginationweapons 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.

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 tongue-twister names like truncated cuboctahedron and rhombicosidodecahedron, 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.

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 Eureka! work on buoyancy was unmatched in the ancient world.

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.