Many artists want nothing to do with math or the sciences, and many mathematicians would hesitate to venture outside the realm of graphs when it comes to drawing. But Leonardo da Vinci left a legacy of cross-disciplinary work in both art and mathematics, opening the door for future generations to explore the parallels and overlaps between the creative processes of the disciplines. In the spirit of this great artist, mathematician, inventor and scientist, Saturday’s symposium at the Williams College Museum of Art (WCMA), titled “Reclaiming da Vinci,” explored the interplay between the two fields.
The second lecture of the day followed Edward Burger, professor of mathematics, as he spoke on the fourth dimension, most often considered time, and its implications in art. Burger is a recipient of numerous mathematics and teaching awards, including being named “America’s best math teacher” in a Reader’s Digest special on the “100 Best Things in America.” He opened his lecture by engaging the audience with an interactive discussion of the fourth dimension’s representation and definition.
Defining dimension, Burger first offered an artistic but vague statement: “If you feel very free, you’re in a high dimension,” he said. He then honed in on a more mathematical stance by looking at smaller dimensions and their relationships. “How many pieces of information do I need to locate you?” he asked. If the answer is zero, you are in the zero dimension, represented by a dot. If the answer is one, the representation of dimension must be a line, since one can locate any point on a line with one piece of information. The second dimension is a square, and the third, a cube. To help the audience visualize this progression, Burger used an art metaphor: take the first dimension line, for example, and “ink it up,” or pretend there is ink along the entire line, “and drag it.” The dragged line forms a square, the second dimension. This concept can be applied to any sequence of dimensions, with one building on to the next.
Burger emphasized that art is essential in representing the dimensions; while dots, lines and squares can be drawn, a cube must be sculpted. However, a line drawing can provide a two-dimensional artist’s representation of a three-dimensional cube. We recognize the intersecting lines of such a drawing as a cube because our eyes have been trained to recognize perspective as a two-dimensional representation of the third dimension. It is possible, therefore, to apply this concept to the intangible fourth dimension by making a three dimensional artist’s representation of a four dimensional figure.
Thus the first connection between art and math is art’s potential to explain and conceptualize a mathematical concept. Burger furthered this idea, explaining that the relationship is reciprocal. The concept of the fourth dimension in art can symbolize an idea, as Burger illustrated with three examples of well-known pieces. Take Salvador Dali’s “The Crucifixion, Corpus Hyercubicus” for example: the cross of the crucifixion is actually the “folded-out” representation of a fourth-dimension structure. Just as one can draw a cube in the form of an unassembled box, Burger demonstrated, one can also make each square of this “unassembled box” a cube, thus representing the next level of dimension. Symbolically, the cross in Dali’s painting represents the idea that Christ rose into another dimension unconceivable to man. “There’s a message here that would have been missed if we didn’t understand the math,” Burger said.
Burger’s parallels between math and art emphasized that as he drew out lines, squares, cubes and other artistic representations of dimension, he was “creating art.” He prefaced his lecture with a statement that tied into the overarching theme of the symposium, saying, “I see what I do as exactly the same as what artists do – just on a different canvas.” His creative approach to problem solving is evident – he even taught a class called “Exploring Creativity” last semester that aimed to consider and experience the creative process across disciplines. Like an artist, Burger sees experimentation and even failure as crucial, saying at one point, “So we failed. Great! Happens 99 percent of the time.”
Burger’s lecture was followed by a presentation by Brooklyn artist Alyson Shotz, described in her introduction as “wonderfully medium-less.” Speaking about her work and her journey through different mediums and phases, Shotz said, “I noticed there was a similar process going on between science – or math – and art.” Her work is very experiential; she explained that she is inspired by the way in which her art interacts with its environment and with its audience. Her most famous piece, exhibited at the Guggenheim, uses lenses stapled together in a tall, curved wall structure. Pictures taken at a distance resemble a large mirror-like sculpture, but a closer look reveals the vibrant colors and patterns reflected in the lenses by both the outside world and the passing viewers. A common theme throughout Shotz’s work is her use of simple geometric shapes and unusual mediums to create original pieces that use their environment to add an element of complexity.
Shotz, whose sculpture relies on geometric shapes, sees first the artistic value of these patterns but appreciates their inherent mathematical value. Burger, on the other hand, sees first the mathematical concepts and then recognizes the value and significance of their place in art. Seeing both perspectives offered a well-rounded view of the interaction and collaboration between art and mathematics, making the WCMA symposium a truly interdisciplinary event.