Ahead of a talk in Dublin, geometrist Tom Banchoff talks to TARA BRADYabout working with the fourth dimension and his collaborations with Salvador Dalí
THERE’S A PASSAGE in Edwin Abbott’s classic Victorian novella Flatland: A Romance of Many Dimensions, wherein the hero, a humble Square, encounters the self-absorbed monarch of Lineland. The latter, having no concept of any space beyond his own, quickly becomes incensed by this visiting tetragon, with his outrageous suggestion of a second dimension. The Square, in turn, meets a Sphere, a strange round being who carefully explains and physically demonstrates the existence of a third dimension.
It’s just too much knowledge for the poor old Square, who winds up languishing in prison for attempting to explain this third dimension to his fellow flat shapes.
If only he could have called on Tom Banchoff. A geometrist and professor at Rhode Island’s prestigious Brown University, Dr Banchoff is a preeminent authority in differential geometry. A long-time explorer of higher dimensions, the mathematician first came to public attention back in the late 1960s. His pioneering work in computer graphics allowed much lesser intellects to see amazing four-dimensional shapes of a kind previously only known to, well, other differential geometrists.
“Back in the late 1960s when I came to Brown I met a young computer scientist – Charles Strauss – who had just finished his PhD in computer graphics,” says Banchoff. “He was trying to help engineers and architects take complicated plans and show them what they’d look like if they built them. He was ahead of his time. I had a problem in that I had plans for some objects I couldn’t build without a four-dimensional space. But using the computer we could build it and take a picture of it and move it around and make new a whole new set of conjectures. It was a very slow process, like animating a cartoon. But it was a tremendous thing. When the pictures came back from the lab they were like nothing I’ve ever seen in my life. They were beautiful, entrancing images.”
Others thought so too. The Washington Post promptly dispatched a reporter to capture these revolutionary new images. “The next day there was a front-page article in the style section,” recalls Banchoff. “It was pictures of our work; of me holding models; of the computer graphics and also, in the background, a painting by Salvador Dalí.”
The iconic Iberian artist had been interested in painting in the fourth dimension since the 1950s. It did not take long for Dalí to pick up on the story.
“He was fascinated by the idea of using a computer,” recalls Banchoff. “He asked us to come down to New York and meet him. We didn’t know what to expect. But he was very well versed in the science of making these images. He had very specific questions about making the stereographic images and how we went about rotating them in space. He was very excited because, of course, he had been trying to do that in his own work.”
Dalí and Banchoff continued to correspond and consult for the remainder of Dalí’s life. “I would visit with him every year and show him what I was working on and he would show me what he was working on. It is strange to think of the Dalí paintings I’ve seen half done.”
Banchoff promises there will be no unwieldy mathematical terms when he appears at Dublin’s Science Gallery later this month to talk us through Dalí’s use of geometry. Math-phobes should be advised, however, not to ask for too many quotes from the late painter.
“The people around him didn’t know anything about mathematics,” recalls Banchoff. “So they never understood the subjects we were discussing even though he was very well versed in them. One of the last times I saw him in Spain he got very excited about one of the 4D films I was showing him. He started talking about Hyperbolic Umbilic Diffraction patterns and how amazing it was to see Hyperbolic Umbilic Catastrophe theory in a formula he’d never come across before. Well, the people around him were frantic. They thought he was babbling or hallucinating or something.”
Tom Banchoff presents The Many Minds and Dimensions of Salvador Dalí at the Science Gallery, Dublin 2 on March 31st