Artist Tony Robbin Explores Geometry and the Fourth Dimension in New AAAS Show

Tony Robbin, an acclaimed artist and a geometry enthusiast, says that the culture of art and the culture of math are one and the same. "Everyone is working on the same problem," he explains. "Everyone is trying to understand space in the same way." After all, he has been studying geometry and working on the depiction of space in the fourth-dimension in his paintings and sculptures for more than 30 years.

Robbin's latest work is related to four-dimensional topology, which examines how two-dimensional surfaces move in four-dimensional space to become knotted. On a canvas, Robbin demonstrates this in the interweaving fields of various geometric shapes—cube octahedra, dodecahedra, and quasicrystal tessellations—in bold, vibrant colors. For the viewer, this creates the experience of seeing multiple objects in the same place at the same time.

From 4 April to 16 June, Robbin, will display his latest work in a public exhibit in the AAAS gallery at 12th and H Streets, NW, in Washington, D.C. This show, which comprises seven paintings, five digital prints, and five instructional posters that show how art is related to mathematics, is Robbin's first solo exhibition since 1992. The gallery is open Monday through Friday, 9 a.m. to 5 p.m.

At the 5 April exhibit opening reception at AAAS, from 5-7 p.m., Robbin will also be signing copies of his new book, Shadows of Reality, The Fourth Dimension in Relativity, Cubism, and Modern Thought , which investigates different models of the fourth dimension and how these were applied in art and physics.

Topology, in general, is the study of the properties of geometric figures that are not changed by stretching or bending. The fourth dimension is all the space that one can get to by traveling in a direction perpendicular to three-dimensional space.

"We've had exhibits here showing the intersection of art with chemistry, physics and paleontology," said Virginia Stern, director of the AAAS Art of Science and Technology Program, who organized this exhibit with AAAS curator Shirley Koller. "We're thrilled to have Tony Robbin back here to show us his representation of higher-dimensional geometry in his beautiful paintings, full of interesting detail." Robbin had a solo exhibition at AAAS in 1992.

As a 13-year-old visiting Paris, Robbin was inspired by the Impressionist paintings he saw and decided wholeheartedly that painting was his calling. He painted portraits and landscapes and "regular stuff," he says, through his childhood and undergraduate education at Columbia University, where he majored in English, since a bachelor's in fine arts wasn't offered.

Having already created an impressive body of work as an amateur, Robbin was accepted into the Master of Fine Arts program at Yale University in 1965. Upon graduating from Yale, he held several teaching jobs in the state system of New Jersey and in 1974 landed a solo exhibit at the renowned Whitney Museum of American Art, where a curator pointed out that his work looked four-dimensional, thus beginning his life-long fascination with higher-dimensional geometry.

Shortly after the Whitney exhibit, Robbin met a retiring professor who bequeathed him an entire library, including two very influential books of the early- and mid-20th century: Henry Parker Manning's Geometry of Four Dimensions, and William Ivins Jr.'s Art and Geometry: A Study in Space Intuitions. For Robbin, these books solidified the intersection of art and geometry and clarified his newfound fascination with this symbiosis. The application of geometry in art was first widely explored in the art world in the 14th and 15th centuries by artists—and mathematicians—such as Filippo Brunelleschi, who is credited with the discovery of linear perspective, Leon Battista Alberti, and Piero della Francesca.

"The Ivins book proved that there was a deep structure in geometry and a deep structure in the artistic understanding of space, and that these two were intimately connected to one another," Robbin explained in an interview.

Robbin delved into the subject by auditing courses in relativity at the New York University and hiring graduate students to tutor him in space-time and Einstein's general theory of relativity. A transforming experience for Robbin was a 1978 Ph.D. thesis by art historian Linda Dalrymple Henderson, who wrote about the use of four-dimensional geometry by modern artists at the turn of the 20th century.

"This book proved that four-dimensional geometry was not some idiosyncrasy on my part, but a basis for the whole of modern art" Robbin said. Widely accepted in academe, but not by professional artists, Henderson's argument provided strong encouragement for Robbin's research and work.

In Shadows of Reality, published last month by Yale University Press, Robbin has a chapter furthering Henderson's argument. One of the exhibit posters, taken from this chapter, demonstrates that the Cubists were influenced by four-dimensional geometry by showing a Picasso portrait from 1910 alongside drawings from a 1903 geometry textbook by Esprit Pascal Jouffret, who was also one of Marcel Duchamp's most important mathematical sources.

Around 1979, Robbin became interested in digital art after visiting a Brown University mathematician, Thomas F. Banchoff, who had created computer-generated images of hypercubes. "I couldn't believe I was seeing this," Robbin said. "I had been dreaming about this." At this time there were no hypercube programs commercially available, so Robbin decided to go back to school to become a computer programmer. Within 15 weeks of studying programming at Pratt Institute, and with the help of the world-renowned geometer H.S.M. Coxeter, who was at the time in his 90s and a professor emeritus at the University of Toronto, he was able to create some of the most sophisticated programs visualizing four dimensions. Such computer visualizations of higher dimensional figures have enhanced the conceptual capabilities of mathematicians and physicists.

All of Robbin's creations have been influenced by his discovery of and work with the digital hypercubes in the 1980s. He received a patent for the application of quasicrystal geometry to architecture. Quasicrystals are non-repeating patterns in three dimensional space. He got the idea of making architectural structures using quasi-lattices because of the interesting shadows these structures create.

Robbin suggested that if one were to stand beneath one of these structures, the casting of shadows would change patterns from moment to moment like a kaleidoscope. "Quasi lattices are triangles at 10 in the morning. At noon, they're five-pointed stars and dexagons. And at two in the afternoon, they're squares," Robbin said. He implemented this geometry for a large-scale architectural sculpture at the Danish Technical University in Lyngby, Denmark, and one for the city of Jacksonville, Fla.

Lonnie Shekhtman

5 April 2006