More on Archimedes' Palimpsest

"Reading Between the Lines"

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

by

Mary K. Miller

March 2007

Smithsonian Magazine

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.

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.

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."

An earlier entry...

Archimedes' Palimpsest

Archimedes' Palimpsest

"Finding Archimedes in the Shadows"

by

Edward Rothstein

October 16th, 2011

The New York Times

“The Archimedes Palimpsest” could well be the title of a Robert Ludlum thriller, though its plot’s esoteric arcana might also be useful for Dan Brown in his next variation on “The Da Vinci Code.” It features a third-century B.C. Greek mathematician (Archimedes) known for his playful brilliance; his lost writings, discovered more than a hundred years ago in an Istanbul convent; and various episodes involving plunder, pilferage and puzzling forgeries. The saga includes a monastery in the Judaean desert, a Jewish book dealer trying to flee Paris as the Nazis closed in, a French freedom fighter and an anonymous billionaire collector.

At the center is an ancient volume, its parchment recycled into a 13th-century prayer book. And at the climax we see those old folios, charred at the edges and scarred by dripping wax from the candles of devout monks, being meticulously studied for 12 years by an international team using the most advanced imaging technologies of the 21st century. And what is found is more revelatory than had ever been expected.

The Archimedes Palimpsest has precisely this history. It really does begin with a 10th-century copy of Archimedes’ third-century B.C. writings. Three centuries later they were scraped off the parchment, which was reused — creating a “palimpsest.” And while there aren’t enough dead bodies or secret cabals to support a full-fledged thriller, there really is a sense of excitement in the account of the book’s history, restoration and meanings, at an exhibition at the Walters Art Museum here: “Lost and Found: The Secrets of Archimedes.”

Almost nothing about the tale is banal or ordinary. In a companion book, “The Archimedes Codex” (Da Capo), William Noel, the museum’s curator of manuscripts, describes how the saga was brought to its conclusion. In 1998, after reading about the Palimpsest’s sale at a Christie’s auction to an anonymous purchaser for $2 million, the museum’s director, Gary Vikan, suggested to Mr. Noel that he discover who bought it and whether it might be exhibited at the Walters.

The purchaser not only deposited the book with Mr. Noel but also provided funds for the project, as scientists and other experts took it apart for restoration and research. The owner, who remains anonymous, also stipulated that all the findings and images be made available to the public. (Next month Cambridge University Press is publishing a two-volume account of the team’s discoveries.)

It may be difficult, at first, to understand the fuss. At the exhibition’s start you come face to face with two leaves from the Palimpsest; all you see is a fragment of a ruined manuscript, charred, stained and inscribed with prayers. But lines of reddish text, scarcely visible, run perpendicular to those prayers. And you can also make out the ghost of a diagram, a spiral. Above these leaves a series of slides shows the same pages under colored lights, revealing various details.

The juxtaposition neatly demonstrates the challenge posed by the Palimpsest and the technology used to explore it. The effort is made more complicated by the Palimpsest’s nature. After being erased, each leaf was rotated 90 degrees and folded in half, one Archimedes page yielding two of the prayer book’s.

That book was apparently in use for centuries at the Monastery of St. Sabbas in the Judaean Desert. Its towers peek out of the rocks in one of David Roberts’s otherworldly Holy Land illustrations from 1842, shown here. But by then the book was gone. In 1844 a biblical scholar happened upon it at the Metochion of the Holy Sepulcher in Istanbul and saw the curious mathematics underneath; a leaf from the book was found in his estate and deposited at Cambridge University Library.

Then, in 1906, the Danish Archimedes scholar Johan Ludvig Heiberg saw the book in Istanbul and recognized seven treatises by Archimedes behind the prayers, making it the oldest source for his writings in existence and the sole source for two unknown works, “Method” and “Stomachion.” Heiberg deciphered much of the text and took photographs that he worked on in Copenhagen.

It was assumed that Heiberg discovered all there was to find out, which may be one reason that, when the battered volume was put on sale almost a century later, few buyers were panting after its riches.

What became startling to the Walters, though, was the extent of the restoration required. Through much of the 20th century the Palimpsest had disappeared. Heiberg’s photographs juxtaposed with leaves of the book show how ruinous that century was for its condition. Some leaves disappeared. Illustrations of Evangelists, forged to look medieval, were inexplicably painted on some pages.

As part of the restoration the book’s history was examined and is surveyed here. There was the devastating impact of World War I on Istanbul’s Greek communities, which affected a large number of artifacts. Some damage may have happened at the Metochion. Similar stains appear in another Metochion book at the Walters.

The exhibition also notes that in 1932 the Palimpsest had been offered for sale by a Jewish dealer in Paris, Salomon Guerson, who recognized its importance. But no purchasers were found. The suggestion is made that Guerson may have ultimately been responsible for the forged illustrations, seeking to raise money to escape Nazi-occupied Paris by creating a more attractive volume. (A green pigment used in the paintings was only available after 1938.) Later the Palimpsest came into the possession of Guerson’s friend Marie Louis Sirieix, a Resistance fighter whose daughter Ann married Guerson’s son; Ann put the manuscript up for sale in 1998.

The exhibition also explores the heroic restoration guided by Abigail Quandt, the museum’s senior conservator of manuscripts, as she attempted to dissolve mid-20th-century glues, examine fragments and remove debris, until contemporary technologies could reveal what the naked eye could not.

Some revelations have become public, including the discovery of two speeches from the great fourth-century B.C. orator Hyperides. In addition one of Archimedes’ works, “Stomachion,” was uncovered in enough detail to be interpreted by Reviel Netz, a classicist at Stanford University and co-author of the companion book: it was an attempt to examine how many ways a set of pieces can be arranged in the form of a square. Visitors are challenged to move colored pieces of felt to explore that question, a style of inquiry, Mr. Netz suggests, that had not been associated with Greek mathematics. As for the title “Stomachion,” the exhibition tells us: “In the ancient world, if you had a puzzle, you didn’t have a brain-teaser — you had stomach trouble.”

The show’s final gallery, which turns to the documents’ substance, is almost too cursory. Instead of the museum including a gallery detailing other restoration projects, it would have been far more illuminating to extend this mathematical section further.

Turn instead to the companion book and read about Archimedes’ geometric proofs. Mr. Netz argues that this manuscript’s diagrams may be closest to the ones Archimedes drew. They were not meant to be pictorial, he says. In fact, if they seemed to illustrate the conclusion too closely, they would appear more like examples than proofs.

So we see straight lines deliberately shown as curves; points placed off kilter; and here at the show, an unusual example in a discussion of floating bodies (the subject that led to the story of Archimedes leaping out of the bath in the ecstasy of insight and running naked outside shouting “Eureka!”). The diagram shows an inverted semicircle sitting inside an incomplete liquid sphere.

Archimedes, the exhibition suggests, created a “radical idealization of real-world phenomena.” But it may also be that he knew that the ideal world of straight lines and regular objects was only an approximation of the real world’s curves and complexities. Such approximations and calculations were among his preoccupations. Mr. Netz sees anticipations of 17th-century calculus and of other aspects of modern mathematics.

And we see, throughout, hints of someone standing triumphant at the borders of the ancient world, peering at us through accumulated catastrophes and layers of destruction, and surviving — just like the hero of any good thriller.


EUREKA! or "Archimedes and the Golden Crown"