Cover Story - October 4, 2006

Cover story: X-rays at SLAC expose theorems of Archimedes under medieval prayers

by Marion Softky

A modern marriage of ancient wisdom with space-age technology at the Stanford Linear Accelerator Center (SLAC) is producing new insights into the mind and work of one of the greatest mathematical thinkers of antiquity.

Just this year, scientists have aimed powerful X-ray beams at faded pages of a scruffy medieval prayer book and come up with long-buried writings of Archimedes that shed new light on his discoveries about floating objects, mechanical theorems, and even a mathematical game.

Greek copies of Archimedes' original works were recycled by a medieval monk in Constantinople, who wrote a prayer book on top of the parchment after scraping and washing it to erase the old writing.

"The Archimedes Palimpsest" (a palimpsest is a document that has been erased and written over) is now on loan to the Walters Art Museum of Baltimore. It is being studied by scientists and scholars from all over the country to tease out the messages under the Latin prayers and later forged pictures of gilded saints.

Just this summer, the news media watched as a beam of high-powered X-rays from the Stanford Synchrotron Radiation Laboratory (SSRL) at SLAC zapped the most difficult pages that had resisted gentler techniques. The hair-sized beam — brighter than a million suns — penetrated dirt, mold, gilt paint, and medieval ink to reveal Greek writing and diagrams from Archimedes' treatise, "The Method of Mechanical Theorems."

"We're getting a vastly better understanding of one of the greatest minds of all time," says Uwe Bergman of Menlo Park, the SLAC physicist who first realized that X-rays from the SSRL could excite the iron in the original ink and make it glow. "We're also showing it is possible to read completely hidden texts in ancient documents without harming them."

Twisty tale

Dr. Bergmann, an enthusiastic scientist from the Black Forest in Germany, relishes the twisty tale of how Archimedes' work filtered from Syracuse in Sicily, where Archimedes was born in 287 B.C., to SLAC in California in 2006.

Archimedes, of course, may be most famous from the legend that gave us the expression "eureka." As he was sitting in his bath, the story goes, he figured out how to measure the volume of a solid — and then ran naked through the streets of Syracuse shouting "Eureka" ("I have found it!").

Archimedes' works covered an extraordinary range, from calculating pi and discovering the laws governing levers, to inventing pulleys, catapults and devices that crashed or clawed Roman ships. He invented a pump that worked like a screw and is still used today.

"He was a genius," says Dr. Bergmann. "He was dealing with infinity and calculus almost 2,000 years before Newton and Leibniz."

Archimedes was a towering figure in his time. His works were transcribed onto papyrus. As the papyrus failed, his works were copied onto parchment made from animal skins. The copy that became the palimpsest was made in the ninth century. "It may have been a copy of a copy of a copy. No one knows," Dr. Bergmann says.

In 1229, a monk needed some parchment for a prayer book, so he raided the library and collected several old documents. It was probably too expensive for the monastery to make its own parchment, Dr. Bergmann notes. "It takes a flock of sheep to make a prayer book. This was medieval recycling."

In making the prayer book, the monk first scraped the pages and washed the Archimedes script with a mild acid like lemon juice. Then he cut the pages in half, and rotated them 90 degrees, so that his writing was horizontal while the old writing was vertical. "That's nice," Dr. Bergmann says. "We can see both inks and separate the texts."

The palimpsest surfaced publicly on July 7, 1907. The front page of the New York Times proclaimed: "Big Literary Find in Constantinople." A Danish scholar had recognized it and bought it. Later he translated it to the best of his ability.

A forger got hold of the palimpsest after 1939, and painted over four pages with gilt pictures of the four evangelists.

The palimpsest surfaced again in 1998, when an anonymous American bought it for $2 million at Christie's. He loaned it to the Walters Art Museum in Baltimore, and supported extensive research to find and interpret the Archimedes text.

Actually, the 174-page palimpsest is not made up just of Archimedes documents, it contains four other ancient books, Dr. Bergmann notes.


Dr. Bergmann never heard of the palimpsest until 2003. He had earned a Ph.D. from the State University of New York at Stoneybrook, writing his thesis at Brookhaven National laboratory using X-rays "I develop novel X-ray techniques to study all sorts of problems," he says.

By 2003, he was working at the SSRL and living in Menlo Park with his wife, Elisabetta, and their daughter Sofia, a third-grader at Oak Knoll School.

Dr. Bergmann credits his discovery of the palimpsest to his mother. He was visiting his family in the Black Forest while attending a conference on photosynthesis. At the time he was studying spinach, using X-rays to excite manganese and iron.

His eureka moment came one evening when he was reading a pile of clippings put out for him by his mother. An article on the palimpsest mentioned that the ink contained a lot of iron.

Wow! "I thought, if we can study iron in spinach, we should be able to detect it in ink," he recalls. "I was 100 percent convinced. That was my eureka moment."

Dr. Bergmann contacted the Walters Art Museum, attended a workshop, and did tests to prove the X-rays would not harm the fragile manuscript. In May 2005, the first pages came to SLAC; they included one of the forged pages with the gold paint, which are the hardest to read. "We didn't image anything important, but we showed we could do it," he says.

To scan one page takes 12 hours. The X-ray beam, the size of a human hair, pulses back and forth across the page; it shuts off at the end of each line to protect the paper. The beam is tuned to a frequency that makes iron, or sometimes other elements, fluoresce. For one page, it makes 15 million measurements.


Results started to pour out when several pages including those covered with evangelists Mark and Luke came back to SLAC in March 2006.

The beam focused on the first page of a book called Folio 1. Dr. Bergmann exults, "Not only could we read the whole Archimedes text, we could read the name of the culprit." Johannes Myronas dedicated his prayer book with a flourish on April 13, 1229.

The scientists and scholars who interpret what they find, were excited to be able to read major sections of Archimedes' famous treatise "On Floating Bodies." "One page was never read before," says Dr. Bergmann.

These pages, which had been copied in Greek, differed in some respects from Latin translations that have been available to scholars, Dr. Bergmann notes. "We were the first in modern times to read the treatise in its original Greek," he says. "There are differences."

In August, the SLAC team scanned more pages, including those under evangelists Matthew and John. These contained Archimedes' most important work, "The Method of Mechanical Theorems." This appears nowhere else, and includes diagrams, says Dr. Bergmann.

The Web site,, notes that two treatises: The Method of Mechanical Theorems" and the "Stomachion," are found only in the palimpsest.

Dr. Bergmann hesitates to interpret much of the material the team has unearthed, because it needs extensive further analysis. "The scholars have a lot of work over the next two years," he says.

So far SLAC has scanned 14 of the 174 pages of the palimpsest, including images overlapping on both sides of each page. Dr. Bergmann and the palimpsest team are busy planning for a return visit for more pages early next year.

Dr. Bergmann hopes they will pursue the Stomachion. This is a game like Tangrams, only it has 20 shapes that can be assembled into a rectangle in 14,000 ways. "Archimedes wrote a treatise about that."


Posted by someone, a resident of Atherton: other
on May 24, 2012 at 8:47 am


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