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Reading Between the Lines

Scientists with high-tech tools are deciphering lost writings of the ancient Greek mathematician Archimedes

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A thin beam of X-rays scans the writings of the legendary Greek scientist and mathematician Archimedes, a hidden text that may be the most important ancient scientific document discovered since the Renaissance. As faint lines emerge on a large computer monitor at Stanford's Synchrotron Radiation Laboratory, I can just barely make out the ghostly image of the Greek letter lambda.

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As a Webcast producer for the Exploratorium science museum in San Francisco, I have been documenting this experimental use of one of the most sophisticated tools of modern science, to decipher a 1,000-year-old book made of goatskin. Known as the Archimedes Palimpsest, dubbed Archie for short, it looks terribly fragile. The edges of most of the book's 174 pages are burned, and tears, holes and spots of purple mold dot their surface. The parchment is smaller than I thought it would be, not much larger than a hardback novel.

I want simply to gawk, but the hum of machinery reminds me that I have work to do. Since I've been spending so much time around Archie, the imaging team has given me the job of shift supervisor this afternoon. I check the intensity of the X-ray scanner, note the time, and record the temperature and humidity from the environmental monitors near the document. In its pages is the only known surviving record of two of Archimedes' works, and the only version of another one in the original Greek. In addition, there are 14 pages of rare commentaries on Aristotle's treatise on the logic of categorization and another 10 pages that record two previously unknown speeches of Hyperides, an Athenian orator and politician from the fourth century b.c. Most of these are invisible to the naked eye—they've been obscured by mold, written over by a medieval priest or almost destroyed by a modern forger who didn't recognize, or care about, their true value.

Archimedes may be best known for rising from his bath and running naked through the streets of Syracuse, a Greek city-state on what is now the island of Sicily, shouting "Eureka." ("I have found it.") According to legend—and it is more likely legend than fact—the third-century b.c. mathematician had just discovered that he could determine the purity of gold in part by measuring the volume of water it displaces. Archimedes was celebrated in his own time, as well as ours, for his practical applications of mathematics and physics. The screw that he invented still moves water uphill, and the catapults and other weapons he designed defended Syracuse from Roman invaders. (Syracuse eventually fell under the Roman siege, and Archimedes was killed by an enemy soldier at the age of 75—supposedly after drawing geometric figures in the sand and snapping: "Don't disturb my circles!") He also estimated the value of pi. "Archimedes was the greatest mathematician in the ancient world," says William Noel, a curator of ancient manuscripts at the Walters Art Museum in Baltimore and the person most responsible for the care and reading of the palimpsest. "He was the first scientist to apply abstract mathematical principles to the world around him."

Archimedes wrote his treatises on papyrus rolls, the originals of which have been lost. But his works were faithfully copied by generations of scribes and made the leap onto bound goatskin parchment by sometime late in the fifth century, probably in Constantinople. That city's great libraries were sacked by Crusaders in 1204, but one parchment, penned in the 900s, somehow survived and was secreted away to a Christian monastery near Bethlehem. In 1229, a Greek priest who needed parchment for a prayer book took apart the Archimedes manuscript, scraped and washed off the pages and copied liturgical text on top of Archimedes' writings in a process known as palimpsesting (from the Greek word palimpsestos, meaning "scraped again"). Horrifying as that seems now, the original text probably would not have survived had the scribe not recycled it and subsequent monks not preserved the prayer book—unaware of what lay beneath the scriptures.

These Archimedes treatises were essentially lost to history until 1906, when a Danish classics scholar, Johan Ludwig Heiberg, discovered the thousand-year-old manuscript in a library in a Greek Orthodox monastery in Constantinople. Heiberg recognized that the faint writings underneath the prayers came from the mind of Archimedes. Heiberg was allowed to photograph many of the pages, and he published scholarly articles on those writings he was able to decipher. But Heiberg couldn't read some pages, and he ignored the diagrams. Then, sometime after World War I, the palimpsest disappeared again, removed from the library under mysterious circumstances—possibly stolen from the monastery—and is believed to have been in the hands of a French family for much of the 20th century. It resurfaced again in 1998, when an anonymous private collector in the United States bought the document at auction for $2 million.

The palimpsest might have remained out of public view—and the hands of scholars—had the Walters Art Museum's Noel not managed to contact the new owner, through the selling agent, and request access to it. To the curator's delighted surprise, the owner (who remains anonymous) personally delivered it to Noel and his colleagues for conservation and study at the Walters.

The palimpsest had deteriorated significantly in the century since Heiberg first examined it in Turkey. Humidity had spurred the growth of mold, and there were even more holes in the pages than before. Worst of all, four of them had been covered with gold-leaf paintings. Apparently, in a misguided attempt to make the book more valuable, a previous owner had used palimpsest pages to forge an illuminated Byzantine manuscript.

Before they could begin deciphering Archie's secrets, the Walters' conservators, led by Abigail Quandt, began the painstaking job of halting the damage. It took four years to take the book apart and clean it. Meanwhile, using ultraviolet light and various techniques to enhance images, scientists from Johns Hopkins University, the Rochester Institute of Technology and other institutions were able to reveal about 80 percent of the manuscript. According to Reviel Netz, a professor of classics at Stanford University, this work added substantially to Heiberg's efforts.

The document's most important treatise is called "The Method of Mechanical Theorems." In it, Archimedes uses the way an object can be balanced to derive its geometrical and physical properties. Even more important is the method's description of infinity, a concept long considered too problematic for ancient Greek mathematicians to grasp. Our modern understanding of it was refined by Issac Newton and Gottfried Wilhelm von Leibniz when they independently invented calculus. From the palimpsest, scholars now know that infinity was understood by Archimedes 20 centuries earlier.

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