May 20, 2005  


Archimedes Manuscript Yields Secrets Under X-Ray Gaze

By Heather Rock Woods

For five days in early May, the ancient collided with the ultra-modern at SSRL, bringing brilliant, long-hidden ideas to light with brilliant x-ray light. A synchrotron x-ray beam illuminated the obscured work—erased, written over and even painted over—of ancient mathematical genius Archimedes, born 287 B.C. in Sicily.

Abigail Quandt, head of book and paper conservation at The Walters Art Museum, slides a framed page of the Archimedes parchment into a holder that moves in front of the x-ray beam like a book being read by a stationary eye.
(Photo by Diana Rogers)

Archimedes’ amazingly advanced ideas have been lost and found several times throughout the ages. Now scientists are employing modern technology, including x-ray fluorescence at SSRL, to completely read the Archimedes Palimpsest, the only source for at least two previously unknown treatises thought out by Archimedes in the 3rd century B.C.

“This is for broad public interest, to reveal the mind of the greatest mathematician of antiquity,” said Will Noel, curator of manuscripts and rare books at The Walters Art Museum in Baltimore. “There’s nothing more important and more romantic in the history of ancient science and currently in the history of medieval manuscripts. We’re discovering new readings of Archimedes.”

Archimedes is legendary for sitting down in his bath, sloshing water over the sides, and immediately recognizing this gave him a way to measure the volume of a supposedly all-gold wreath to determine if the craftsman had cheated the King of Sicily by slipping in cheaper silver. As the story goes, he leapt out of his tub and ran naked through the streets shouting ‘Eureka’ (I have found it). He also discovered pi, the mathematical equivalent of inventing the wheel. Archimedes did not just take steps toward calculus, as formerly believed, he actually created and used calculus methods, the basis for modern engineering and science. He is also credited with designing fearsome war weapons, like claws that pulled attacking boats from the water.

The Walters Art Museum is leading a broad public and private effort involving experts from diverse fields to study and conserve the manuscript. The palimpsest is a 1,000-year-old parchment made of goat skin containing Archimedes’ work as laboriously copied down by a 10th century scribe. Two centuries later, with parchment harder to come by, the ink was erased with a weak acid (like lemon juice) and scraped off with a pumice stone, and the parchment was written on again to make a prayer book.

Three pages of the palimpsest recently traveled to Menlo Park because scientist Uwe Bergmann (SSRL) had his own Eureka moment in 2003. From a magazine article, he learned the manuscript ink contained iron pigment.

“I read that and I immediately thought we should be able to read the parchment with x-rays,” Bergmann said. “That’s what we do at SSRL—we measure iron in proteins—extremely small concentrations of iron.”

SSRL and Ametek-Edax in New Jersey—which makes an x-ray system convenient for pages too fragile to travel—are now studying the manuscript with x-ray fluorescence. X-ray light tuned to a specific energy causes the remaining traces of iron ink to fluoresce (see sidebar). A detector catches the fluorescence and renders the 2,000-year-old thoughts of the mathematical genius readable.

Bergmann credits many of SLAC’s staff with helping set up the experiment, especially Martin George (SSRL), who developed custom software to continuously scan the pages one line at a time from top to bottom. The hair-thin x-ray beam could not rest on any one spot of parchment for too many milliseconds for fear of damaging the delicate fibers. Many of the pages are in terrible condition, damaged by mold and fungus. But mold, which scatters visible light, should be transparent to x-rays, allowing a clear view of the ink below.

A photograph of one page of the Archimedes Palimpsest. Visible and UV light cannot see Archimedes' text under the gold painting done by a 20th Century forger. The text is oriented sideways like this when scanned.
(Image provided by Will Noel, The Walters Art Museum)

“The Archimedes ink is only one to two microns thick, there’s hardly anything there,” said Abigail Quandt, head of book and paper conservation at The Walters Art Museum.

The detector signals create a real, readable image from x-ray light, rather than visible light. The x-rays pass right through the parchment, simultaneously registering iron from the Archimedes and religious texts on both sides of the parchment. The four layers of text are already helping Stanford University historian of ancient mathematics Reviel Netz to decode the text.

“We get incredible resolution; you need it when you’re reading erased and overwritten ancient Greek cursive,” Noel said.

While much of the manuscript can be, and has been, read by visible or ultraviolet light during the past six years of painstaking analysis and restoration, “now we’re concentrating on the really difficult bits,” Noel said. The main tools are x-ray fluorescence, optical character recognition (teaching a computer to recognize fragments of ancient Greek symbols) and multi-spectral imaging (using light of different wavelengths).

One of the most intractable problems was seeing the original ink on four pages that had been painted over with Byzantine religious images, which turned out to be 20th Century forgeries intended to increase the value of the prayer book.

The Edax x-ray system recently showed it was possible to penetrate the paintings. At SSRL, the assembled team practically jumped with excitement as the original writing beneath one painting was unveiled on the computer screens. Archimedes’ hidden text deals with floating bodies and the equilibrium of planes.

Another page studied at SSRL contains an introduction to the only copy of Archimedes’ Method of Mechanical Theorems, where Archimedes showed how he arrived at his theorems. As faint ancient Greek symbols—mingled with the religious text—appeared on screen, Netz began identifying the characters and letters by comparing the layers of text from the synchrotron images and from the multi-spectral images.

X-ray fluorescence imaging at SSRL revealed the hidden text. This x-ray image shows the lower left corner of the page.
(Image provided by Will Noel, The Walters Art Museum)

“I don’t think x-rays will make invisible material simply visible,” Netz said. “It will add a layer of information combined with others that will enable me to read the text.”

The anonymous private collector who bought the palimpsest for $2 million at auction in 1998 has loaned the manuscript to The Walters and is funding the studies. The studies have revealed surprising finds, including that Archimedes was the first Greek to use infinity and to set rules for infinity. Scholars have also advanced the reading and allowed the first interpretation of the Stomachion, which solely survives on one page of the palimpsest. This treatise deals with combinatorics—the number of ways a problem can be solved—which is used in modern computation.

Researchers come from RB Toth Associates, Rochester Institute of Technology, Johns Hopkins University, ConocoPhillips and Rutgers University. The team plans to decipher the entire text, catalog and transcribe it digitally, and create an interactive DVD. They will then exhibit a few pages in 2008 before returning the irreplaceable parchment to its owner.

“There are so many things we want to see with x-rays. This is sensational. We’ll be back,” Noel said.

For more information, see:

How X-Rays Read Medieval Ink

By Heather Rock Woods

Synchrotron radiation is a powerful tool to study the Archimedes Palimpsest. In contrast to an x-ray tube, the synchrotron beam is more intense, is collimated (parallel), does not need to be focused, can be polarized and is very easy to tune.

Iron has 26 electrons in different orbits around the nucleus. An x-ray tuned to an energy of 7.1 kilo-electron volts (keV) can knock out an electron from the innermost orbit of an iron atom.

Missing an electron, the unstable atom immediately fills the hole by grabbing an electron from a farther out orbit. Since the replacement electron has less energy (it was less tightly bound to the nucleus), as it falls into its new place it emits x-ray fluorescence, a photon with 6.4 keV, exactly the difference between the two electrons.

This creates a fluorescent signal at an energy specific to iron. The detector window is set to 6.4 keV to capture the iron signals. Like an old dot matrix printer, the detector builds an image dot by dot, mapping out each spec of iron-containing ink.

Extra ink in one spot causes a more intense signal. Generally, the ink from the Archimedes text is no more than a faint stain in the fibers of the parchment, while the thicker, un-erased ink of religious text sits on its surface. Where the two overlap (the texts are written perpendicular to each other) the iron signal is stronger, which may allow researchers to separate the two texts.


The Stanford Linear Accelerator Center is managed by Stanford University for the US Department of Energy

Last update Tuesday May 24, 2005 by Topher White