Literature Review

In what ways can creative practice integrate Math and Art?

Lidy van Deursen

Math and Art 175006

AUT Auckland University of Technology

          This literature review aims to compare and contrast the current knowledge on the similarities and differences in the fields of mathematics and the arts. These two fields might initially seem very different but in recent years there has been a lot of debate over whether they are in fact connected; this literature review aims to explore these alleged connections. History suggests that in the past math and art have at times been considered as parts of the same practice and it is interesting to see in modern times their connections being reexamined in the search for greater understanding of both fields as well as the possibility of integrated practice.

           Historically it would seem mathematics and art have previously been considered as parts of the same, whole although they have “been on opposite poles when describing the real world” (Velichová, 2010, p. 677). In ancient Greece mathematics fell under the category of the fine arts and both artists and scientists were grouped together and considered bizarre people interested in the useless, strange and outrageous. The mentality of the time was that “artists belonged together with scientists” (Velichová, 2010). In support of this it is suggested in the paper ‘Fine arts and Geometry’ that man is endowed with a certain ‘geometric instinct’ that enabled him to satisfy his innate need for construction (Ladopoulos, 1970). From this it would be understood that geometry is something that comes naturally to man. The author also claims that the birth of fine art should be attributed to the “internal need” of man to represent and express (Ladopoulos, 1970). This claimed geometric aptitude can be applied to both construction of the artistic and the practical, placing early geometry between what might be considered the early fields of art and science.
             Consistency of proportion has been noted since hundreds of thousands of years before Euclid introduced his famous geometric theories. The human hand has been proven to correspond with the proportions of the golden ratio (the proposed most attractive proportions in nature and design) (Samoila, 2010). Scientists find the study of the human hand accountable for artifacts being produced in this special ratio. This occurred from about the time when primates evolved into humans, long before any education would inform them of the significance of this ratio. “Using the hand for hundred thousand years implied also carefully observing the hand and its inner proportions” (Samoila, 2010, p. 169). The Fibonacci sequence is closely linked to the golden ratio and they have been claimed to “attribute to the contribute to the harmony in nature” (Carafoli, 2009, p. 246).
           Pythagoras is cited by professor and proclaimed ‘mathartist’ Sims as “the first thinker to advocate proofs” and “teach the connections between mathematics, nature and the arts.” (Sims, 2004, p. 52) Pythagoras theorem is a key visual mathematics-teaching tool for Sims.

           Giliola Giurola believes that “the relationship between mathematics and art has always been clear” and that mathematics has many applications when applied to reality. (Guirola, 2010, p. 92) Chakravartty agrees with this adding “in both art and the sciences, successful representation is a matter of fitting or approximating things in the world” (Chakravartty, 2010, p. 40). When asked to think about the combined study of mathematics and the arts the first connections one might guess at is geometry in art and the use of visual diagrams in mathematics to help with the visualisation and understanding of concepts. In ‘Geometric Symphonies’ Paul Cézanne is quoted saying “in nature everything is modeled according to three fundamental modality: the sphere, the cone and the cylinder. You need to learn to paint these very simple figures, then you can make everything you want.” (as cited in Comitá, 2010) From this artists’ statement it is clear that he considers the world to be made up of assignable geometric entities that can be replicated for use in art. Sims is also in agreement, calling the conviction that mathematics and art are opposites a “disabling counter-productive myth” (Sims, 2004, p.53) He instead encourages understanding that both fields are fundamental expressions of our consciousness and are “connected by the voice of nature” (Sims, 2004, p. 53)
          For the combination of mathematics and art, digital technology has now advanced to the point that it is the “the primary choice” of mathematical tool used in the production of art (Schattschneider, 2003) In the same article compasses, rulers, grids and computers are cited as physical tools for the creation of art that rely on the power of mathematical relationships and processes to give them their creative power. (Schattschneider, 2003) Visual art is also beneficial in highlighting mathematical concepts by giving pictorial support with the recognition of mathematical principles.

          Modern day computers have allowed the study of geometry to extend beyond its previously hand drawn past. The Euclidean Geometry which has existed as the basis of taught geometry through the ages “has no way of describing objects in our everyday lives” (Velichová, 2010, p. 681) Euclidean Geometry, being only concerned with perfect abstracts non-existent in nature became inadequate in describing the real world. Bernoit Mandelbrot writes about geometry and its application to the world: “Fractal Geometry is not just a chapter in mathematics, but one that helps Everyman to see the world differently.” (as cited in Velichová, 2010 ) Chaos theory and fractal geometry has allowed computer art to become more realistic and in the opinion of Guirola “fractals are not only mathematic elements” but are also “art objects thanks to their variety and their pleasant graphic aspect.” (Guirola, 2010, p.100) In contrast to this James Elkins presents a strong argument about the way that fractals are used, he believes that by the time fractals are seen by their audience they are being experienced at a “double remove”. Elkins cites the fact that fractal art is presented independent of its mathematical context and with an overlay of unrelated colours that are not determined by the equation itself. (Elkins, 2009, p. 45) Although Elkins claims to see why fractals are considered an important discovery in geometry and that they are so popular in art (because they mimic nature so well) he maintains a level of sobriety when it comes to them being simply imported into art. Fractals are also considered by Elkins to be of limited use to drawing, as their construction is limited to the computer.

          Some common arguments cited for the synthesis of art and mathematics include beauty, proportions (including the golden ratio and Pythagoras theorem) and the search for truth and the understanding of nature being a common goal of the two practices.
           Firstly Beauty is an interesting argument as a shared goal between the two practices, Elkins believes that beauty is no longer relevant to modern art, he writes that it is rare to hear an artist describe his work as beautiful and that words of a similar nature would sound “insufficient, in an art critic’s mouth”(Elkins, 2009, p. 37). The word beauty is too unfocused and well intentioned for Elkins to consider it a “workable bridge” between the two practices. Carafoli in his article talks about both mathematics and art having two goals that must be fulfilled, both aim at beauty but they must also search for truth, and in science’s case the truth must also be testable (Carafoli, 2009). Carafoli does however bring up a pivotal question on how one might decide upon beauty? He suggests that for the most part our conception of beauty is superficial, and wonders if there are a tangible set of values that might be more precise in assigning beauty fairly. (Carafoli, 2009). One suggested method is that of George David Berchoff who presented his equation in 1928 that claimed to be able to judge the aesthetic ‘value’ of an object by dividing the amount of order of an object by the level of complexity it possesses (Routio, 2007).
          Proportion is another subject that is commonly broached in the art and mathematics debate. Pythagoras theorem, the golden ratio and the closely related Fibonacci sequence have all been suggested to be superior ratios and potentially the most appealing ratios to the human eyes. A study conducted by Georg. Th. Fechner studied the aesthetic preferences of people that were untrained in the aesthetics field and interestingly concluded that none of the proposed superior proportions (notably including the golden ratio and Pythagoras) were consider more beautiful than the others (as cited in Routio, 2007). This is contradictory to the opinions voiced in the other articles that I have read. Another study by Dio, Macaluso & Rizolatti concluded that when brain activity was monitored and participants were presented with a series of sculptures, “the registered activity in the brain clearly favoured the sculptures in which the proportions were those of the golden ratio.” (as cited in Carafoli, 2009). The documentary ‘The Human Face’ would agree with the later. Experiments were shown where a mask was made to conform to the golden ratio and was then fitted to photographs of a selection of people who were ranked by attractiveness, the fit of the mask on the face was proportional to the perceived attractiveness of the individual with the most highly ranked fitting the mask the best (George & Rossiter, 2001).
          Something that has been pondered by most authors in this study has been when art and math combine are they art or are they math, are they both or are they neither. “Some kinds of art can be called ‘art and mathematics’ and they have an obvious but superficial meaning” (Giurola, 2010, p. 98) Giurola goes on to point out that there are two ways to use art and math together, one is to use mathematics as a tool of art and the other is to paint a mathematical topic which he believes is the more effective path. Elkins doesn’t believe in effective combination of art and science, he points out that what little science there is in art it is altered to serve artistic purpose and therefore ruins the scientific content, he goes as far as to say that “science per se will not appear in art, because without art it would only be science.” (Elkins, 2009, p. 39) Another article confirms that math can only exist in a visual artwork if “appeals to mathematicians” and “encodes a mathematical structure”(Velichová, 2010).

In conclusion there is a long history of mathematics and art proving to be a useful combination and the modern re examination of this combination opens the doors to more collaboration in future ventures. As discussed earlier in the review there are two proposed ways to use mathematics and art together. The first is to use the useful parts of one topic to benefit the end purpose of a particular project or subject, this is commonly seen as every piece of art that uses geometry could be said to be borrowing from the field of math. The Second way that Giurola suggests is that the two might be integrated is to make an artistic work about a mathematical concept. This is again a problematic suggestion as this might then defeat the purpose of art.
          The current research on mathematics and art is largely united in exploring the potential the two topics have together but seeming divided in their opinions to if a work can be both simultaneously mathematics and artistic. Luckily though we have been presented with the question about in what ways can creative practice integrate math and art and the evidence seems overwhelmingly in favour of there being many instances of overlaps and cases where one practice has solved the other’s problem.

References:


Carafoli, E. (2009). Scientific and Artistic Creativity: In Search of Unifying Analogies. The Two Cultures: Shared Problems. Milano, Springer Milan: 239-264.

Chakravartty, A. (2010). "Truth and Representation in Science: Two Inspirations from Art." Beyond Mimesis and Convention 262.

Comitá, A. (2010). Geometric Symphonies. Aplimat 2010. S. U. o. T. i. Bratislava. Slovak University of Technology in Bratislava, Aplimat: 29 - 36.

Elkins, J. (2009). Aesthetics and the Two Cultures: Why Art and Science Should Be Allowed to Go Their Separate Ways. Rediscovering aesthetics: transdisciplinary voices from art history, philosophy, and art practice. Stanford, California, Stanford University Press.

Giurgola, G. (2010). Creative Mathematics and Rational Art in Virtual World. Aplimat 2010. S. U. o. T. i. Bratislava. Slovak University of Technology in Bratislava, Aplimat: 91 - 102

George, S. and N. Rossiter (2001). Survival of the Prettiest: The Human Face. Retrieved August 18, 2010, from http://www.youtube.com/watch?v=1AZe9g2Huz0

Ladopoulos, P. D. (1970). "Fine Arts and Geometry." The Journal of Aesthetics and Art Criticism 28(4): 535-540.

Routio, P. (2007) "Beauty of a Product: Arteology, the science of products and professionals." Retrieved August 20, 2010, from http://www2.uiah.fi/projects/metodi/155.htm

Samoila, G. S. (2010). The Harmonic Geomerty of Art. Aplimay 2010. S. U. o. T. i. Bratislava. Slovak University of Technology in Bratislava, Aplimat: 165 - 174.

Schattschneider, D. (2003) "Mathematics and Art -- So Many Connections." Math Awareness Month - April 2003 Mathematics and Art. Retrieved August 20, 2010, from http://www.mathaware.org/mam/03/essay3.html

Sims, J. (2004). "Notes on a mathartist." The International Review of African American Art 19(3): 52-55.

Velichova, D. (2010). Chaos in Math and Art. Aplimat 2010 S. U. o. T. i. Bratislava. Slovak University of Technology in Bratislava, Aplimat: 677 - 686.