New technology reveals ancient math texts

SiliconValley.com
New technology reveals ancient math texts

By Esther Landhuis, Mercury News

It sounds like the plot of a sci-fi novel: Powerful X-ray beams are used to illuminate the long-lost theorems of ancient Greek mathematician Archimedes, lifting them from faded 10th-century parchments.

In fact, it happened last week at the Stanford Linear Accelerator Center.

Using state-of-the-art circular particle accelerators called synchrotrons, the scientists shone ultra-fine light beams onto three pages of the aged texts. Tuned to a specific energy, the light caused traces of iron in the ink to fluoresce, revealing for the first time the wispy outlines of Archimedes' 2,000-year-old ideas etched onto a goatskin document known as the ``Palimpsest.''

Though much of its text has been deciphered over the years by visible or ultraviolet light, about a quarter of the 174-page document remains unread, said SLAC scientist Uwe Bergmann. Efforts have been hampered by a form of medieval recycling in which parchment pages were erased and written over, allowing the rare material to be reused -- in this case replacing mathematical theorems with prayers.

Odd circumstances brought this ancient book into the realm of modern science and engineering.

While attending a 2003 conference in Germany, Bergmann came across a magazine article that mentioned the Palimpsest and other religious texts whose ink contained iron. ``I immediately thought it would be possible to use our X-rays to image the document,'' said Bergmann, whose own research uses synchrotron X-rays to detect extremely small amounts of iron within proteins.

The intense beams -- generated by accelerating electrons around a circular track at close to the speed of light -- are used to probe the sub-microscopic world in a variety of fields, including materials science, environmental sciences and solid-state physics.

Bergmann contacted the Walters Art Museum in Baltimore, which houses the Palimpsest, and convinced the curators that SLAC's X-ray system could penetrate the document's prayers to reveal Archimedes' hidden thoughts.

The team plans to read the entire text and transcribe it onto a DVD -- a process that will take several years.

``Reading the pages is very, very hard work,'' said Stanford classics and philosophy Professor Reviel Netz, who has begun decoding the Palimpsest pages analyzed at SLAC last week. ``In one of the pages, it's a word a minute, in another page, it's a word an hour.''

It may be slow going, but in a strangely satisfying way, scientists say the project has allowed science to come full circle. Much of Archimedes' ancient work -- including the creation of calculus methods -- underlies present-day science, and now -- 2,000 years later -- physicists are applying some of their most sophisticated tools to get back into the head of this legendary mathematician.

``We're like the great-great-grandchildren of his own mind,'' Bergmann said.

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