Banchoff on Dali, the Fourth Dimension

Alex Howard, News Editor

In his lecture “The 4th Dimension and Salvador Dalí” on Monday night, Thomas Banchoff, professor of mathematics at Brown University, shared his experiences exploring the fourth dimension through the hypercube and how this led him to become great friends with artist Salvador Dalí.

“The fourth dimension is my favorite mathematical, geometric subject. Salvador Dalí is the most unusual person I’ve ever met,” said Banchoff to open his lecture.

Banchoff has been a professor at Brown for 25 years, and he specializes in differential geometry and topology of the third and fourth dimensions. Banchoff has taught a course every few years since he started teaching at Brown called “Exploring the Fourth Dimension.”

Banchoff told the audience that he became interested in the fourth dimension when he was 10 years old through a Captain Marvel comic book. He said that he decided to explore the fourth dimension until he grew tired of it, which led him to build a career and a social life around this exploration.

“I am going to try to explain to you why it is that a mathematical idea, if you really get caught up in one and really stay with it, really will lead you to meet some of the most interesting people you’re ever going to run into,” said Banchoff.

Banchoff brought in a paper model to demonstrate the conventional building of a three-dimensional box involving a square surrounded by squares. He then brought out another model which was a cube surrounded by seven other cubes, representing the adding of a dimension and thus creating the fourth. This model is a hypercube and it is what led Banchoff to meet Salvador Dalí.

Banchoff says that in the beginning of his career, he was struck by the hypercube structure of the four-dimensional cross appearing in Salvador Dalí’s 1954 painting “Corpus Hypercubus.” In a newspaper article in 1975, Banchoff was photographed holding the hypercube model he built in front of Dalí’s painting, which he says he knew was a copyright issue, but was told not to worry about it. A couple of weeks later, Banchoff received a note in his mailbox asking him to call Salvador Dalí’s representative.

“I asked my computer graphics colleague, ‘What do you think?’ and he said, ‘well, it’s either a hoax or a lawsuit’,” said Banchoff. “A woman answered and said, ‘Oh, Professor Banchoff, Señor Dalí is in New York, and he wants to meet you.’”

Banchoff said that he met Dalí in the bar at the St. Regis Hotel where Dalí had rented two suites, one for him and his wife Gala, and one to use as a studio.

“Talking with him, we found out the answers to some of the questions that had been on my mind ever since I’d seen the painting and realized it was connected with this concept of the fourth dimension, unfolding the fourth dimension,” said Banchoff.

Banchoff and Dalí saw each other several more times after their initial meeting and corresponded often. During his lecture, Banchoff played an excerpt from the 2004 documentary The Dalí Dimension that provided more insight into the dynamic between Banchoff and Dalí.

“I had the feeling Dalí wanted to know what my mindset was as I was looking at the same objects he was looking at, what kind of questions was I asking, how was I using it. We always spoke pretty much as equals,” said Banchoff in the film.

A quote from Dalí in the film provided reasoning from his perspective as to why he held his friendship with Banchoff and other mathematicians and scientists as so crucial: “Scientists give me everything, even the immortality of the soul.”

Banchoff ended his lecture with pictures of himself in front of the hypercube exhibit at the Salvador Dalí Museum in Fugueres, Spain. When Banchoff first showed Dalí the hypercube he had constructed, he said that Dali played with it for a while and then said — not asked — “I may have this,” because he had just started the museum where the model now stands.

College sophomore and Math and Art History major Kate Greenberg said that she found this lecture particularly relevant to her studies here at Oberlin.

“As a Math and Art History major, I am constantly noticing parallels between my classes,” said Greenberg. “I was really fascinated that this conversation between your left and right brain can also take a very literal form, specifically with Dalí’s incorporation of the four-dimensional cross and manipulation of perspective.”

Greenberg says that the creativity necessary for art is also extremely necessary for math, be it through approaching a proof in an unconventional manner or visualizing geometric objects mentally and then having to translate the rotations and changes in perspective of these objects on paper. Banchoff stressed this interaction between the two disciplines throughout his lecture and asserted that “mathematicians can help understand what is behind the mind of the artist.”