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.
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
“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.
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.
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
(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
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
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
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.
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