Math in Wonderland
Students participating in Southwestern’s London Semester program this fall will visit many of the city’s famous tourist attractions such as the British Museum, the Victoria and Albert Museum, the National Gallery, the Tate Modern and Kew Gardens.
But at these places, they will looking at objects in a much different light than most tourists.
That’s because their guide will be Fumiko Futamura, a math professor at Southwestern who sees the math in art.
So at Kew Gardens, for example, Futamura will show students how to find fractals in nature such as ferns and trees.
At the British Museum, they will look at the symmetry of designs found in textiles and woodwork made by people of various cultures.
At the Victoria and Albert Museum, they will see a machine that was designed to help artists paint things in perspective and see some of Eadweard Muybridge’s famous time-lapse photography of people and animals in motion.
At the Tate Modern, they’ll study a replica of Marcel Duchamp’s famous four-dimensional piece known as The Large Glass, as well as works by optical artist Bridget Riley and Barbara Hepworth, a sculptor who was influenced by mathematical models.
At the National Gallery, they will see how Hans Hobein incorporated an anamorphism in his painting known as “The Ambassadors” and how Jan Van Eyck used five-point perspective in his Arnolfini Wedding Portrait.
Futamura is teaching three classes in London this semester, two of which she developed specially for the program. One class focuses on the mathematical influences on art in general and the other focuses specifically on the math behind the books such as Alice’s Adventures in Wonderland by Lewis Carroll and Flatland by Edwin Abbott.
“Only recently have scholars begun to speculate that Lewis Carroll, who taught math at Christ Church College in Oxford, subtly infused his Wonderland stories with math” Futamura said. “Although the math is very explicit in Flatland, it is much more subtle in Alice’s Adventures in Wonderland.”
Futamura says Carroll may have done this in response to “new” forms of mathematics that were emerging at the time, such as quaternions, projective geometry and symbolic algebra. Carroll, who was very traditional, did not favor these new developments and some believe that he satirized them in his story.
Futamura began teaching at Southwestern in 2007 after earning her master’s degree and doctorate from Vanderbilt University. At first, she taught standard math courses such as calculus and linear algebra. Last fall, she tried her hand at combining art and mathematics in a First-Year Seminar class titled “Hidden Perspectives: Math in Art and Art in Mathematics.” Students in the class were introduced to the mathematical concerts in art forms such as origami.
Futamura said she jumped at the opportunity to participate in the London Semester program this fall so she could introduce students to the culture of London and present math in a new light. “There are so many great museums there and a lot of math was developed there,” she said.
In addition to visiting museums in London, Futamura also plans to take her students to Oxford, Stonehenge, Bath and 2 Willow Road, a modernist house designed in the 1930s.
At Stonehenge, they will look at the mathematics that can be found in the famous circle of 56 holes known as the Aubrey holes.
At 2 Willow Road, they will see another Bridget Riley painting as well as a Henry Moore sculpture.
Their trip to Oxford will include a visit to the Oxford Museum, which Lewis Carroll frequented; a stop at the Alice in Wonderland Shop; and the Alice in Wonderland Cruise, which follows the same route taken by Lewis Carroll (whose real name was Charles Lutwidge Dodgson) almost 150 years ago, when he rowed in a boat up the River Thames with three young girls who asked him to make up a story for them.
The courses will include plenty of hands-on work as well. “To understand how artists use math, the students really have to do it themselves,” Futamura said.
The “Wonderland” class will include a Sept. 26 guest lecture by Melanie Bayley, the doctoral student who first speculated about the math behind particular scenes in Alice’s Adventures in Wonderland, including the Mad Tea-Party and the scene with the Duchess and the baby. For their final project in this class, students will have to research a particular aspect of how math or science influenced Victorian culture.
Futamura said she was introduced to art as a young child by her mother and grandmother. Her grandmother enjoyed the fine arts and her mother did arts and crafts. When she moved to Kentucky from Japan at the age of five, she did not speak English well, but discovered that math was a universal language she could communicate in. At first, math was just a talent versus a passion – her real passion was for art. As an undergraduate at the University of Louisville, she was trying to decide between majoring in art or math when a math professor named Steven Seif pointed out to her that math could be seen as art. After that, she switched her major to math, although to this day she continues to enjoy painting as a hobby.
Futamura said she contemplated working as an animator at Pixar or being an architect, but what she really wanted was to teach math in a creative way. Once she completed her Ph.D., she jumped at the chance to teach at Southwestern.
“My husband and I looked at a map and made a list of the top places where we wanted to live. Austin came up at the top of the list,” Futamura said. “I really wanted to teach at a liberal arts college, preferably a small one. If I were at a research institution, I probably wouldn’t have been able to do as much with math and art. Working here has been like a dream come true.
Futamura’s husband, Patrick Jones, who is one of the most popular math tutors on YouTube, will be joining her for the semester in London.
Although her research interest initially focused on an area of mathematics known as frame theory, lately it has shifted to projective geometry, which allows her to better combine her interest in math and art. Projective geometry is used to analyze what properties of an object are preserved when you draw or take pictures of it from various angles. It is used in creating virtual 3D models for movie special effects, video games and augmented reality.
Futamura is currently writing a textbook that focuses on projective geometry and its connection to perspective drawing. She is working on the book with two co-authors, Annalisa Crannell from Franklin and Marshall College and Marc Frantz from Indiana University Bloomington, who she met at a mini-course they offered in 2009. Futamura has already been published in numerous scholarly journals, but this will be her first textbook. She is taking sabbatical leave in the spring 2012 semester to work on the book.
Futamura also is using her knowledge of mathematics and art to assist Theatre Professor Sergio Costola with a play he is producing titled Hypatia of Alexandria: A Singspell in Three Acts. Hypatia is the first known woman mathematician. Futamura will be serving as a resource for mathematics knowledge and a visual artist for the play. She said she plans to focus on this when she returns from London.
−Ellen Davis and Kristen McLaughlin