The Möbius Band in Art


Artists, along with mathematicians, have been fascinated with the Möbius band. Because of its visually perplexing one-sidedness, its association with infinity, and its symbolic power, artists have been interested in depicting the möbius band since its discovery in 1958.

Symbolism

The fascinating properties of the möbius band - its one-sidedness and one-edgedness - have unsurprisingly resulted in association of the shape with symbolic meaning. Most prominently, the möbius band is often associated with the concept of infinity, because of the infinite uninterrupted paths one can trace along its single surface. The band is also associated with unity and non-duality, due to the fact that two sides and two edges are joined and become one side and one edge in the construction of a möbius strip. Because of its symbolism for infinity and unity, some couples opt for möbius band-shaped wedding rings. On a similar note, some consider the Möbius band to be a fitting symbol for the relationship of space and time in the universe - they appear to be separate, like the two sides of the möbius strip, but there actually is no separation; space and time are not distinct and together form our universe.

Max Bill

http://www.bluffton.edu/%5C~sullivanm/baltimore/billwhole1.jpg
Max Bill (1908 - 1994) was a Swiss architect and artist. Bill was one of the first artists to explore the Möbius strip. Beginning in 1935, Bill created a series of Endless Ribbon sculptures, which were essentially larger-scale Möbius bands rendered in paper, granite or metal. When Bill created the first sculpture in 1935, he thought he had discovered a previously unknown shape (Maor, 140). Bill seems to have been highly disappointed to find that the shape has been discovered some 70 years previously. In his initial disappointment, he abandoned the idea of further working with the shape and worked on unrelated projects (Ibid). However, the intrigue of the Möbius band must have been too great because he returned to working with the band. He stated  "What I could not find in Möbius' explanation [of the band] is of primary importance to me: the philosophical aspects of these surfaces as symbols of infinity." (Maor, 141). 

Bill's explorations of the band as a sculptural object representative of infinity resulted in some striking and intellectually stimulating works. His renderings of wide möbius bands emphasize the illusion of of the object having two sides. But if one traces along the side, we find that the object is, in fact, a single-sided möbius band. From any angle, part of the object is always hidden from the viewer, imbuing the object with an appropriate sense of mystery. The scale and apparent weight of the objects also lend them a sense of permanence, drawing a connection between infinity and time, suggesting the concept of eternity.

M. C. Escher

Perhaps the artist who best exposed the general public to the intriguing Möbius band, M. C. Escher created a number of prints and lithographs exploring the perplexing band. Mauritus Cornelis Escher, born in the Netherlands in 1898, was a dutch artist best-known for his mathematically significant works involving tessellations, impossible buildings and depictions of infinity. 

Escher seems to have been drawn to the Möbius band because of its connection with the infinite. Escher was introduced to the möbius strip by an unnamed English mathematician (Maor, 141). Escher was inspired to create 3 works based on the perplexing and fascinating object: Mobius Strip I (1961), Mobius Strip II - Red Ants (1963), and Horsemen (1946). As Eli Maor states, "Escher, a genius in portraying the ambiguities and ironies of life, found in the möbius strip a fertile ground for his creative talents." (Maor, 148)

Like Max Bill's sculptures, Escher's works are intellectually stimulating and visually perplexing. Further, we can see the band's symbolism of infinity, unity and non-duality explored in Escher's works. In Möbius Strip II, pictured at left, ants crawl on a Möbius strip ladder.  The image portrays ants on an endless mission to climb the ladder, but they will never reach any other destination, they are doomed to crawl around the ladder for all of eternity. The ladder is suggestively arranged in the shape of the infinity symbol, emphasizing this concept of infinite motion. 

In Möbius Strip I, pictured at right, three creatures seem to chase one another endlessly. Closer inspection reveals that the three creatures are actually all unified as one, joined in an endless ribbon. The shape also resembles a knot, emphasizing the concept of unity.

In Horsemen, below, we see a combination of Escher's tessellations with the concept of the möbius band. This rendering does not portray a true möbius band, rather the shape obtained by cutting a möbius band in half lengthwise. Because the two strips are joined in the center, we can move from one side of the object to the other without crossing any boundaries, just as on the true möbius strip. The two teams of horsemen march around the strips endlessly,
yet they merge into one another in the center of the object. With their inverted colors and merging forms, the two teams seem to become one, suggesting non-duality.





Keizo Ushio

Keizo Ushio (1951 - present) is a Japanese stone sculptor whose works are fascinating from an aesthetic as well as mathematical point of view. Ushio creates his works by first carving a torus (a doughnut shape) from stone or granite. He then splits the torus by drilling holes through the object (Friedman et al, 2). In some cases, the result is two interlocked rings, whereas in other cases (more relevant to our purposes), a Möbius band-shaped cut creates a torus that appears to be made from two separate pieces whereas in reality it is composed of only one piece. Ushio then textures the outside and/or cut portions of the object, to emphasize the curious shape of the cut or to emphasize the illusion of there being multiple pieces. 

In Ushio's work Dream Lens, pictured at right, we appear to have a torus made up of 3 separate pieces - one shiny, one smooth and matte, and one roughly textured. However, this work was created by splitting a torus with a three-twist möbius band shaped cut. This means that the torus is thus composed of one unified piece! The three different textures are obtained by covertly transitioning from one texture to the next as the surface passes through the center of the torus (Friedman et al, 6)




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