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Archimedes Unbound

William Cannon

One of the great apocryphal stories in the annals of science is how the Greek mathematician Archimedes ran naked through Syracuse shouting, "Eureka!"—fresh from the bath where he figured out that the force of buoyancy was equal to the weight of the liquid displaced.

Less famous, but just as hard to believe, were Archimedes' last words, uttered in the third century to a Roman soldier unimpressed with the finer points of geometry. Archimedes had helped defend Syracuse by designing a network of lenses and cranes. The lenses bounced sunlight into the eyes of attacking Romans on ships. When the half-blind Romans squinted their way close to shore, gigantic cranes would teeter their ships over. Unfortunately those measures turned out to be more annoying than fortifying. Archimedes, supposedly drawing curlicues in the sand when the Romans finally broke through, was killed for admonishing a fumble-footed soldier, "Don't disturb my circles!"

It would not be the final erasure applied to Archimedes' hard work.

Natural image of the <em>Archimedes Palimpsest</em>Click to Enlarge Image

In the 12th century a monk in Constantinople scraped the parchment containing perhaps the only version of Archimedes' "Method of Mechanical Theorems," then overwrote it with healing prayers. The treatise described a calculus-like procedure that anticipated Newton's and, had it been published in the 16th century with the rest of Archimedes' then-known tracts, might have greatly accelerated the progress of mathematics. The parchment also held six other treatises, including the famous "On Floating Bodies," here alone in Archimedes' original Greek.

Ah, but Archimedes—or, more accurately, a 10th-century scribe—had left too strong an impression. The indentations in the goatskin leaves, at a 90-degree angle to the overlying text because the parchment was cut in half and rotated to allow for more pages, survived intact. And soon, with the aid of multispectral lighting and digital imaging, Archimedes' treatises will appear as they were when they were set down, sometime between the years 950 and 975.

"This is the missing link between us and the diagrams that Archimedes drew in the sand," says William Noel, manuscripts curator at the Walters Art Gallery, where the manuscript, the Archimedes Palimpsest—the oldest of only a handful of surviving Archimedes texts—is on public display for the first time. The Walters, in Baltimore, holds one of the largest illuminated manuscript collections in the world. After the palimpsest—a book overwritten by another—was sold at auction last year, Noel tracked down its new owner and procured a loan of the manuscript. Visitors to the gallery this summer will have until September 5 to view it. Then the Walters will embark on an ambitious five-year, high-tech project to recover Archimedes words and diagrams from the impressions under the prayer book.

Unlike Euclid, whose geometry was on the curriculum of the educated cleric and whose works thus survived in abundance, Archimedes was considered theoretical, too technical, too abstract. That and the fact that parchment was hard to come by in the Dark Ages made the manuscript ripe for reclamation. As Noel likes to put it, "The monk's need for a medium on which to put down his religious rites far outweighed his need for mathematical text."

Digitally enhancedClick to Enlarge Image

Noel says no one knows where the Archimedes manuscript originated, but he suspects it was in Constantinople, "probably in a monastery or the imperial palace." He says that fortune favored Archimedes; the manuscript was written in an enlightened cultural center, where the ancients were valued. It was even lucky that an important religious document was copied over it—it acted as a sort of bodyguard. "It meant that throughout the centuries it was looked after in monasteries."

An enduring mystery, Noel says: "How could it have remained unknown for so long?" From the 15th century to the early 19th, the palimpsest found sanctuary in a monastery at Mar Saba, a few miles east of Bethlehem. It somehow migrated back to Constantinople, to a convent where, in 1907, a Dane named Johan Ludvig Heiberg, alerted by a catalogue, "went and saw it and realized what it was," Noel says. "He transcribed what he could of the manuscript using a magnifying glass and natural light."

Heiberg's reading had to suffice for a century. A few years after he examined the palimpsest, during World War I and afterward, a time of French occupation of Turkey, the palimpsest's trail became murky. It surfaced in the 1920s, in a private collection in Paris. It remained in France until last fall, when it went up for auction at Christie's and sold to an anonymous bidder for $2 million.

Noel went to work, connecting with the new owner through a London antiquarian book dealer. The owner, who remains anonymous, agreed to turn the palimpsest over to the Walters to exhibit, clean up and help decipher.

Most antiquarians rank manuscript conditions from fine to fair, the latter describing what most people would consider doorstop material. Noel describes the palimpsest in terms that suggest exponentially worse than fair.

"Before we can do any real work, we have to unbind it and stabilize the leaves." Each page will be photographed under a variety of light spectra to produce digital images that can be computer-manipulated at high resolution to their best advantage. Then the digitized pages will be reassembled in their 10th-century order. Thus, from beneath the pages of the prayer book a second book will emerge—a virtual Archimedes that the gallery will make available to scholars and the public. The original book will be rebound the way it was found, in its prayer-book order.

Considering his limitations, Heiberg did an astounding job back in aught-7, Noel says. "He was a brilliant scholar. But because the manuscript was so difficult to read, he had to make a lot of guesses." Already experts who have viewed the palimpsest have found textual variants from Heiberg's transcriptions. Plus, Heiberg did not take the book apart, so he missed passages and diagrams that would have been obscured by the prayer-book binding. And, of course, Heiberg did not have access to the new technology.

What picture of Archimedes will emerge from the digitally enhanced palimpsest? American Scientist hopes to arrange a critical review of the virtual Archimedes. We trust review copies will be a little easier to come by than they used to be.

(For more on the Archimedes Palimpsest and the Walters Art Gallery events surrounding its exhibition, see—William J. Cannon

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