Lasers find new sums in very old math

It has been around the world, battered and burned, then left to grow damp and moldy. Yet within its parchment pages lie the secrets of Archimedes' mind.

It looks like an ancient prayer book. But look closer and you'll see something written beneath the text. The document is a palimpsest - a twice-used manuscript - and the underlying words are seven treatises of Archimedes, the ancient Greek mathematician who pioneered the notion of combining abstract concepts with concrete math.

The theorems are barely visible to the naked eye, however, and because the parchment is in such poor shape, deciphering the influential mathematician's ideas will take more than your run-of-the-mill decoder ring.

Currently, two teams of scientists are working to uncover Archimedes' musings.

First completed around AD 1000 by a scribe in Constantinople, the Greek manuscript was likely a copy of a copy of a copy of the original papyrus scroll. Two hundred years after its creation, however, the document was given a facelift. Sometime during the Crusades, a local scribe scrubbed off the ink, cut the book's leaves in half, and rotated the pages 90 degrees. Then he wrote on the parchment again.

The prayer book then disappeared until 1907, when it was translated by a classics scholar. It didn't resurface again until 1998, when it was sold at a Christie's auction to an anonymous collector who placed the document in the care of the Walters Museum in Baltimore.

Over the centuries, the parchment had been severely damaged by water, fire, even forgery. In a recent attempt to increase the value of the prayer book, someone painted miniature evangelical portraits in gold leaf on four pages.

Today, the parchment is covered in purple specks and eaten through in places, says William Noel, an associate curator at Walters. He describes it as "the ugliest manuscript I've ever seen - the color of really bad, mottled, rotting flesh." Which is exactly what it is, of course.

Two teams of scientists are competing to make this manuscript speak - an imaging team at Johns Hopkins University in Baltimore, and a group of scientists at the Rochester Institute of Technology (RIT) in Rochester, N.Y. The Walters Museum will ask the team with the most promising results to examine all of the manuscript's 174 pages.

"It's sort of a 'history of mathematics' genome project," says Bill Christens-Barry, a physicist at Johns Hopkins and a member of the imaging team. "We're trying to look at the foundation of elements of the whole field by stitching together very small fragments of information to understand the whole."

Both teams are using "multispectral imaging" to take pictures of the palimpsest - the same technique the RIT team used in 1996 to read pieces of the Dead Sea Scrolls. The human eye can see light with wavelengths from 400 to 700 nanometers, or billionths of a meter. But a digital camera can measure from 250 nanometers (infrared) to 1050 nanometers (ultraviolet). By photographing the document under UV, IR, and visible light with different filters, scientists can restrict the wavelengths the camera perceives. The filters divide the spectrum into 40 different regions. The researchers then take pictures of each region, ending up with about 40 different pictures of the same page. They load the images into a computer and analyze them statistically to determine which wavelength of light best contrasts the Archimedes text against the parchment.

The RIT team is using remote-sensing software to analyze the images. The program, known as ENVI (the Environment for Visualizing Images), is typically used for geographical mapping, but, in this instance, it contrasts the images in great detail.

Another technique RIT is trying is magnetic imaging, because 10th-century scribes wrote with iron gall ink, which has magnetic properties. Roger Easton, an associate professor at RIT's Center for Imaging Science, notes that magnetic imaging may allow them to see through the evangelical portraits to the underlying text. Since gold is not magnetic, the team hopes that if the ink has any residual magnetism, they might be able to use a magnetic scanner to detect the treatises beneath the portraits.

Dr. Christens-Barry's team is experimenting with confocal microscopy. More commonly used in biomedical research to look at cellular structures, it employs a scanning laser to look below the surface of the parchment. By taking the document and moving it up and down in the microscope as a laser scans each page, the scientists can create layer upon layer of two-dimensional pictures, to try to determine the order brushstrokes were made.

Both teams have just begun their work, but already they are recreating Archimedes. Reveil Netz, a science historian and a classics professor at Stanford University in Stanford, Calif., notes that the palimpsest is changing Archimedes' math from the heterogeneous 1907 translation to something playful and creative. And, he says, it can provide a glimpse into the head of someone who stands at the foundation of modern science.

(c) Copyright 2000. The Christian Science Publishing Society

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