Sculpting Mathematics

Last week we saw how beautiful works of art can often be inspired by complex mathematical equations that do not normally exist in nature. One such equation is “Fermat’s Last Theorem,” a theory conjectured by Pierre de Fermat in 1637 that states: “no three positive integers x, y, and z can satisfy the equation xn + yn = zn for any integer value of n greater than two” (323). Visual artist, programmer, and engineer Stewart Dickson was inspired by Fermat’s theorem and its potential solution. He sought to bring its “abstract ideas into the world of physical sculpture” via the assistance of new computational visualization capabilities of the digital age (324). But beyond the artist’s personal exploration, can such highly specialized and academic sculptures reach a mass audience?

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Figure 1. Fermat’s Last Theorem visualized in Mathematica by Stewart Dickson and Andrew J. Hanson 1990.

Top subfigure illustrates the n=3 case (x3+y3=z3).

bottom subfigures illustrate the n=5 case (x5+y5=z5).

In his artist’s statement, titled “Art and Mathematics,” Stewart Dickson articulated the importance of the emergence of computers, stating:

“never before have we had such a tool with which we can test the structure of our understanding of ourselves and our world.”

However, instead of leaving his visualization in the two-dimensional plane, in which he declares as “fundamentally unsatisfying in the lack of tactile presence,” Dickson is most interested in

“bring back artifacts from Cyberspace into the space I physically occupy” (“Artist’s Statement”).

Indeed, Stewart Dickson uses a symbolic mathematics programming language, Mathematica, to digitally visualize mathematically based concepts, and then in turn made sculptures based on the in silico objects, as evident in his n=3 project, where Dickson made “sculpture, of a… superquadric surface parameterized in complex four-space… similar to Fermat’s own proof of the n = 3 special case ”(324).

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Figure 2. Sculpture of Fermat’s Last Theorem by Stewart Dickson and Andrew J. Hanson.

Dickson is not alone in creating art works based on concepts in mathematics, science, or other academics. Others include Charles Perry, Brent Collins, Carlo Sequin, Arthur Silverman, Elizabeth Whiteley, Helaman Ferguson, Stuart Dickson, George Hart, Charles Longhurst, and Simon Thomas (323). Their art works are not only beautiful but also highly cerebral, embedding sophisticated levels of information within them. However, according to Wilson, that also raises a provocative question in that

“typically artists assume that their audiences have a certain cultural background that will enable them to interpret and enjoy artworks. The lack of this background does not deter artists from exploring frontier areas of culture, but it does create obstacles for reaching audiences” (334).

Though the intrinsic meanings of the works might be lost on most people, I don’t believe that one necessary would need to be an expert in those academic fields to benefit from the aesthetics of these works. To many, they may remain as esoteric pieces of art, of which they may wonder through their own ideas and perhaps come upon a serendipitous discovery through them.

References:

Wilson, Stephen. Information arts : intersections of art, science, and technology. Cambridge, Mass: MIT Press, 2002. Print.

Dickson, Stewart. Artist’s Statement: Art and Mathematics. The Art & Frame Shop and The Williams Gallery of Fine Art (http://www.wmgallery.com/dick_395.html). n.d. Web. 20 Feb 2015.

-Yinrou Wang

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