At first glance, Timea Tihanyi and Jayadev Athreya make strange bedfellows.
Tihanyi is an interdisciplinary visual artist who teaches in the University of Washington’s School of Art and has spent more than two decades working in ceramics. Athreya is an associate professor in the UW’s Department of Mathematics and director of the Washington Experimental Mathematics lab.
But despite our stereotypes of math and art, Tihanyi and Athreya say they are much more similar than we often think.
That’s why they are collaborating on Axiomatic, a project that seeks to create real-world representations of complex theoretical mathematics, with the goal of highlighting the similarities between the two fields. The first public exhibition of their work kicks off this weekend, at Seattle’s 9e2, an event showcasing collaborations between STEM fields and the arts.
Athreya and Tihanyi describe their studies as “what if” disciplines — disciplines searching for new ideas and new ways of looking at things. In Axiomatic, the pair takes a literal approach to the idea of looking at knowledge in different ways.
Their 9e2 exhibit tracks Tihanyi’s process in creating a porcelain sculpture of a 5-cell, a basic object in 4-dimensional geometry.
Yup, you read that right — this is a sculpture of an object that has 4 dimensions. So how does one go about sculpting something that is in 4D?
Athreya says the process begins with complex computer modeling, to come up with various possibilities for the sculpture. Their work here is based on a collaboration with mathematician Henry Segerman, Assistant Professor, Oklahoma State University, whose book Visualizing Mathematics with 3D Printing first explored visualizing the 5-cell.
The pair has also begun work on sculpting 2-dimensional patterns in 3D, which takes a slightly different approach, but rendering 4D objects in 3D is actually simpler than it seems.
“We represent 3-dimensional objects in 2-dimensional space all the time,” Athreya explained. Think of a flat map of the world, he says. That map is a projection of the globe — a 3D object — onto a piece of paper — a 2D plane.
“The 5-cell is actually the projection of a 4-dimensional object into 3-dimensional space,” he explained. “Think of it as a solid shadow.”
Tihanyi says the process is like holding a lightbulb over an object, and examining the shadow it casts on the floor.
“If you take the lightbulb further away from the object, or put it closer,” the shadow’s size, thickness, and even the shape we perceive changes, she said.
At its core, this is the same process that makes shadows very long in the evening, and very short at noon. The object itself remains the same, but its shadow “is so completely and shockingly different,” Tihanyi said.
Once the computer has generated several possibilities for the “solid shadow,” the pair use a 3D printer to create mini models of some of the variations that strike them. It’s then up to Tihanyi to experiment with rendering those models as sculptures.
Tihanyi said the process of creating a sculpture of the 5-cell was particularly challenging.
“There is a feasibility in the 3-dimensional world. So I couldn’t have two thin parts and two thick parts because it would never hold up in ceramics,” she said.
“As a visual form, it was very interesting to me because of these opposites,” but the things she found attractive were also what made the shape difficult to work with.
After some initial trials, several of which collapsed during the kilning process, Tihanyi eventually created the sculpture being showcased in the 9e2 exhibit. The exhibit also includes one early attempt that collapsed.
This exhibit is still the early stages of the Axiomatic project, and will be on display at 9e2 from October 21 to October 29. Some of Tihanyi and Athreya’s future work will be exhibited at Tihanyi’s individual show in January, and an exhibition showcasing the entire project will open next summer.
In the meantime, the UW is hosting a father-and-son duo who also work in art and math this November, and many other collaborations between artists and those in STEM will be on display at 9e2 in Seattle.