# Is that painting real? Ask a mathematician.

## Engineers use a mathematical process dubbed 'stylometry' to set apart real Van Gogh paintings from forgeries.

After Japanese insurance kingpin Yasuo Goto won a high-stakes bidding war by offering \$39.9 million for a painting at a 1987 auction, an unforeseen controversy erupted: Was the painting, Vincent van Gogh's "Still Life: Vase With Fifteen Sunflowers," truly the work of the Dutch master, or a clever fake?

Some art dealers and historians thought the character of the brushstrokes differed from other Van Goghs; others disagreed. The stalemate was never resolved. But after 20 years, help is finally arriving from an unlikely quarter. Computer scientist Richard Johnson of Cornell University in Ithaca, N.Y., is embarking on an international project to define Van Gogh's unique style in mathematical terms, with the intent of shining a focused beam of objectivity on the traditionally muddled question of attribution.

On May 14, teams of engineers that Mr. Johnson recruited will meet with art students and curators at the Van Gogh Museum in Amsterdam to announce what they think sets real Van Gogh paintings apart from forgeries. By analyzing a database of 101 paintings by the artist and his known imitators, the scientists have arrived at what they say are key elements of Van Gogh's "visual signature," which can be distilled into numbers. This, they say, will give art experts an important new tool to assess works like "Vase With Fifteen Sunflowers." They can compare how closely a disputed painting's visual signature matches the baseline "signature" derived from the database.

"We want to get a dialogue going between computer scientists and art historians," Johnson says. "There's a lot of potential in this kind of cross-pollination."

The approach Johnson's teams are using, dubbed "stylometry," isn't limited to visual art. Scientists are also using statistical formulas to determine the authorship of letters, literary texts, and even musical compositions.

"There are techniques that allow you to turn an artwork into a point in some geometric space and ask, 'Is there a neighborhood of work of a particular artist?' " says Daniel Rockmore, a computer scientist at Dartmouth College who has published several papers on the topic.

While the specifics of stylometric analysis differ depending on the medium being examined, the basic strategy is similar across the board. First, the work of art in question is divided into components, which can be words, high and low tones, or different visual frequencies (the frequency of a still pond in a painting is distinct from that of a busy flower garden, for example). Next, each component is subjected to statistical tests that measure how they compare to components of authentic works created by the same artist. Mathematicians can plot the point that represents how the work performs on these tests in n-dimensional space, with n being the number of tests used. In his attempts to differentiate genuine Brueghel sketches from fakes, for instance, Mr. Rockmore measured 72 statistical features of each disputed sketch, such as the percentage of light and dark portions in a given visual frequency.

"We took the entire body of known Brueghels and said, 'Do we believe this picture's distance from the known Brueghels is significant?' " he says. The real Brueg­­­hels were statistically uniform, clustering on a geometric plot, while imitations ranged all over the map.

Statistician Jose Binongo of Emory University in Atlanta used a related strategy when he set out to determine who wrote "The Royal Book of Oz," published under L. Frank Baum's name in 1921. Many Oz fans insist the book is Baum's last hurrah, but others contend his collaborator, Ruth Plumly Thompson, wrote it.

To resolve the debate, Mr. Binongo split samples of known writings by Baum and Thompson into 5,000-word segments, then isolated the 50 most commonly used words in each segment. Counting how frequently each of these 50 words was used yielded a sequence of 50 numbers that specified a point in 50-dimensional space. Baum's and Thompson's excerpts occupied distinctly different zones in this space. And when Binongo performed the same analysis on chunks from "The Royal Book of Oz," the points generated all clustered in Thompson's zone, persuading many historians that she is the true author.

Even as historians and academics acknowledge stylometry's validity, they sometimes express an almost visceral aversion to it. "Is it true that every artist has one clearly identifiable, characteristic style that can be picked up by this technology?" wonders Ellen Handy, an art historian at the City College of New York. "Can artists really be resolved to a single pattern?"

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