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

Smithsonian Magazine | Subscribe

(Continued from page 1)

Another unique text is the "Stomachion," arguably the first treatise on combinatorics, the branch of mathematics concerned with the organization of elements within sets. In this passage, Archimedes describes a puzzle in which a square is cut into 14 irregular pieces. The puzzle's solution lies in determining the number of ways the pieces can be arranged back into a square. It is not known if Archimedes solved the puzzle—those pages have been lost—but modern mathematicians have determined the answer: 17,152.

Noel's Walters art museum team deciphered most of the palimpsest, but couldn't read through the forger's gold-leaf painting. That's where the Stanford Synchrotron Radiation Lab (SSRL) came into the picture. The lab generates X-rays from powerful beams of electrons that race around a 260-foot-diameter ring in the windowless, doughnut-shaped building at nearly the speed of light. A couple of years ago, while working on an unrelated Exploratorium project, I was getting a tour of the SSRL when Uwe Bergmann, a German-born physicist, stopped my group in the curved hallway. He told us he was working on an experiment that involved exposing inked parchment to the SSRL's X-ray beam. Bergmann had read about the palimpsest in a German magazine and had deduced that the SSRL would be able to image iron in the ink underneath the gold paintings. The experiment Bergmann showed me that day had convinced him that his technique could work on parchment—and he was practically jumping up and down in excitement.

To reveal the hidden ink, X-rays that form a beam no thicker than a human hair strike ink on the parchment. Their energy causes certain elements in the ink to fluoresce, or glow. Detectors pick up each element's distinctive wavelength of fluorescence, and a computer converts the data into computer images. "The X-rays just care about the element on the parchment," says Bergmann. "You can observe the iron in the ink no matter what is above or below it."

In the past two years, SSRL's imaging experiments have provided some exciting new results, including the signature of the scribe who first copied the liturgical texts and the date he did it (Ioannes Myronas, on April 29, 1229).

Now we're at the end of the ten-day run. We've been scanning one of the most difficult pages in the book, the introduction to Archimedes' "Method of Mechanical Theorems," which is covered by a gold-leaf forgery of a seated saint. A diagram on the page contains critical information about how Archimedes thought about geometric proofs, information Heiberg ignored. This is the second run of this page; to extract more faint lines from underneath the painting, the detectors have been tuned to image calcium, rather than iron.

We've already had some success. Stanford's Reviel Netz told us earlier in the week that he was able to see clearly for the first time one of the labels for a drawing that accompanies Archimedes' "Method of Mechanical Theorems." The label, Netz says, decided a long-standing dispute among scholars about what they considered an error in the diagram.

After Stanford, the palimpsest will be hand-carried by conservator Abigail Quandt back to the Walters Art Museum in Baltimore, where it will undergo additional imaging work to reveal more of the text from Hyperides, the Athenian orator, which is expected to contain new information about the foundations of Greek democracy, Athenian law and social history. The team expects to wrap up its work sometime in 2008, then the document will go on display for three months at the Walters and later at other museums. Its text will be published for scholars and students to pore over. "What we've been finding with the Archimedes Palimpsest is that this book never ceases to give up its secrets," says Noel. "It's like working with a great mind; you're made to think of things in new ways—from the nuts and bolts of medieval history to the roots of calculus and physics."

Mary K. Miller is a co-author of Watching Weather and a writer and Web producer for the Exploratorium in San Francisco.