Film Bridges Artistic and Mathematical Intuitions

December 17, 2007

Canadian filmmaker Jean Bergeron in Minneapolis, at the U.S. premiere of his film Achieving the Unachievable. Photo by Donald Kahn.

On Thursday evening, November 1, 2007, the Institute for Mathematics and its Applications at the University of Minnesota hosted the U.S. premiere of the film Achieving the Unachievable by the Canadian filmmaker Jean Bergeron. The film---which runs a little under an hour---is devoted to the work of the well-known Dutch artist Maurits Cornelis Escher (1898–1972), in particular his unfinished work "Print Gallery." The art world has long been puzzled by the blurry white circular patch in the center of this lithograph. There has been considerable speculation about why the artist left his masterpiece unfinished in this way and whether it could be completed.

About five years ago, a team assembled by Hendrik Lenstra, a mathematician at the University of Leiden in the Netherlands, discovered that an infinite sequence of ever-decreasing copies of the outer portions of the painting, subject to a subtle transformation, which they deduced, fits perfectly in the blank disc. (See "M.C. Escher: More Mathematics Than Meets the Eye," by Sara Robinson; Interviews with Lenstra shown in the film suggest a fantastic bridge that grew between the intuitions of the artist and the mathematician. The film also contains interesting interviews with other artists and mathematicians, including Douglas Hofstadter of the University of Indiana (author of Gödel, Escher, Bach), who had conjectured that the completion of "Print Gallery" ultimately obtained by Lenstra would be impossible.

The film illustrates many of the mathematical structures that enter into Escher's work, including Möbius transformations---which, as described in the accompanying article, have also been a recent interest of IMA director Doug Arnold. He and Jonathan Rogness, an assistant professor of mathematics at the University of Minnesota, developed animations of Möbius transformations that not only won a prize in this year's Science visualization contest but were also incorporated into Bergeron's film. The film was received enthusiastically by the audience of around seven hundred people, including many high school students as well as members of the university and surrounding community. Jean Bergeron, who wrote and directed the film, attended the premiere, after which he took questions from the audience.---Donald Kahn, University of Minnesota.

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