Sunday, December 25, 2011

A Tale of Math Treasure

An exhibition traces the reconstruction of a long-missing collection of writings by Archimedes

There is much cheesy lore about the ancient Greek mathematician Archimedes of Syracuse: that he popularized the word “eureka”; that he used mirrors to set Roman ships on fire; that a Roman soldier killed him in 212 B.C. while he was tracing diagrams in the sand. Not only is the lore probably untrue, historians say, but it also fails to capture the true significance of his achievements, which spanned mathematics, science and engineering and inspired the likes of Leonardo da Vinci, Galileo and Isaac Newton. Some credit him with having essentially invented the basic ideas of calculus. An exhibit opening in October at the Walters Art Museum in Baltimore will showcase a decade-long effort to restore some of his longlost texts and unearth some of his previously unknown contributions. “Lost and Found: The Secrets of Archimedes” focuses on a parchment book known as the Archimedes Palimpsest.

At one point in history, all of Archimedes’ works that survived through the Dark Ages were contained in just three tomes made by 10th-century copyists in Constantinople. One, called Codex C, disappeared some time after Western European armies sacked the Byzantine capital in 1204. Then, in 1906, Danish philologist Johan Ludvig Heiberg found a book of prayers at a monastery in the city and noticed that it was a palimpsest—meaning that the parchment had been recycled by cutting up the pages of older books and scraping them clean. Among those older books, Heiberg realized, was Codex C. Armed with a magnifying lens, Heiberg painstakingly transcribed what he could read of the older text, including parts of two treatises that no other eyes had seen in modern times. One was the “Method of Mechanical

Theorems,” which describes the law of the lever and a technique to calculate a body’s center of gravity—essentially the one still used today. Another, called the “Stomachion,” appeared to be about a tangramlike game. Soon, the book disappeared again before resurfacing in 1998 at an auction in New York City. There an anonymous collector bought it for $2 million and lent it to the Walters museum. When the palimpsest reemerged, says Will Noel, who is its curator, “it was in appalling condition.” As the exhibition will display on panels and videos, imaging experts were able to map much of the hidden text using high-tech tools—including x-rays from a particle accelerator— and to make it available to scholars. Reviel Netz, a historian of mathematics at Stanford University, discovered by reading the “Method of Mechanical Theorems” that Archimedes treated infinity as a number, which constituted something of a philosophical leap. Netz was also the first scholar to do a thorough study of the diagrams, which he says are likely to be faithful reproductions of the author’s original drawings and give crucial insights into his thinking. These will be on display, but the studies go on. Netz is now transcribing the texts contained in the palimpsest, which he estimates at about 50,000 words, most written in a shorthand typical of medieval copyists. He plans to publish a critical edition in the original Greek. “It will take probably several decades to translate it into English,” he says.

Source of Information : Scientific American Magazine

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