Literature Review

What strategies can be identified in effective Math and Art Trail?

What other approaches are effective for incorporating Math and Art into a creative practice for a specific audience?

“Anthropology has had no lack of interest in the visual; its problem has always been what to do with it.” (MacDougall, 2007. 276)

With the 'Math and Art Trail' participants aim to observe effective application of 'Math and Art' principles as a whole within overlooked aspects of society.

Through the 'Math and Art Trail' process it becomes easier to develop an understanding of the magnitude in which mathematics has been integrated into society, and perhaps more specifically its influence on creativity and intelligent design.

Although somewhat conflicting in nature, the concepts of both 'Math' and 'Art' exhibit strong cohesion when applied to creative practice such as architecture, engineering, or spatial design. However are there more latent applications of 'Math and Art' within our immediate constructs which through the 'Trail' process, we can train an eye for? Can we use the process to develop a firmer understanding of the fundamentals of aesthetics, and what strategies can be identified to nurture this development?

The focus of 'Math and Art Trail' is the search for aesthetic value within areas of life that we may usually disregard. To identify efficient strategies employed in the process it is important to first identify what would make the 'Trail' process successful.

Strategy by definition “refers to a plan of action designed to achieve a particular goal”. (Oxford, Second Ed. 1975)

When undergoing the 'Math and Art Trail' process what particular goals are being striven for? The simple act of following a path without the intention of making progress towards a certain point by a certain time is a forgotten concept within the fast pace of life in the 21^st century. It is that lack of closure that ironically allows participants of the 'Trail' process to open up to the realization and personal growth -which can be identified as one of the main goals of the process. To take full advantage of the 'Trail' one would have to be willing to accept the presence of mathematical concepts within art itself and the artistic medium. In doing so, one is introduced to another key focus of the 'Math and Art Trail', which is training a level of awareness of this presence by learning to enhance one's perception of their immediate surroundings.

”We mark off our journeys by things gathered along the way: notes, rocks, memories, signs and inscriptions. Objects carry with them the scars of their own existence” (Smith, 2008)

Firstly it is easy to gain a feel for how mathematical systems have infiltrated the creative endeavors of humanity. As mentioned earlier it is inevitable to witness mathematical presence through mediums such as architecture and engineering. It is also interesting to note the level at which quantitive or statistical information has been adopted and creatively utilized by print advertising and large scale visible marketing campaigns. What was once the sole territory of creative execs on Madison Avenue, has now been assumed by the general public in a new wave of consumer-consciousness -“newly stimulated by the growing discussion of the economics of imperfect competition.” (Abrams, 1952)

Such displays of human intervention on our environment tend to make one consider how much we have used these very human concepts to shape our ever-changing world. By imbuing the nature of creation with mathematical personality, society has produced feats of engineering -towering skyscrapers and monumental structures; and has analyzed and determined ways of producing reactions in the public's commercial habits. “We look out into our world with wonder and now concern—as we cope with the possibility that the footprint of man has weighed heavily on our environment.” (Smith, 2008) As a result, there is ample demonstration of 'Math and Art' principles within superfluous aspects of construction and societal development -one just has to develop an eye for them.

Stepping away from constructed humanity, it is remarkable to observe mathematical presence in naturally occurring design, and within life itself. Ammunition indeed for the argument of higher 'Intelligent Design', complex mathematical equations and demonstrations of pattern and code can be found in even the humble snowflake. (Roach, 2007)

The occurrence of natural mathematic formation has been widely documented throughout history. By addressing concepts from mathematical text such as 'Euclid's Geometry', and resulting principles such as the 'Golden Ratio', one can learn to relate the dynamics of these concepts to their individual surroundings. As detailed in the article 'Line of Sight' (Smith, 2006) It is imperative to have a sense of spatial awareness and a keen eye for mathematical aesthetics when finding ones own identity through creative practice. Through “the lived experience” (a reference one can directly affiliate with the 'Math and Art Trail') we develop an understanding of these approaches and in doing so make progress within our own creative journey.

Euclid's Elements detailed the Golden Ratio as a specific division of a straight line, which has been attributed to the innate beauty found in naturally occurring phenomena (O,Connor, & Robertson, 2001; Cook, 2010). From the formation of leaf patterns to molecular alignment, the Theories detailed in Euclid's texts have been used as a basis of research into attraction between men and women, specifically if this can be mapped with values concerning geometry and proportion. (Livio, 2002)

“Euclid founded geometry, a concept that is fundamental to getting an understanding of how mathematics works in the world. This is the core of what makes maths beautiful, this conceptual overlay”. (Cook, 2010)

It's relationship with beauty has seen the Golden Section along with Fibbonacci's numerical theories attached to numerous creative endeavors throughout history. From The Parthenon and Greek architecture, to the paintings of Leonardo Da Vinci, even loose affiliations with Mozart's 'Sonata's' and 'Beethoven's Fifth'. (Garland, 1987; Lowman, 1971). Several photography techniques have been based on Euclidian theory, the most widely observed being the 'Rule of Three'- which states that ”the important compositional elements should be placed at the intersections of imaginary lines that divide the image into thirds horizontally and vertically.” (Krages, 2005)

'Rule of Thirds' figure. http://www.silverlight.co.uk/tutorials/compose_expose/thirds.html

However, as detailed in the 'New Scientist article 'Truth Plus Beauty' -”Just as an ordinary photograph is a snapshot of natural beauty, an equation is a snapshot of mathematical beauty”. (Mullins,1999)

Perhaps the most overlooked but fundamental demonstration of 'Math and Art' principle is the idea of finding aesthetic value in mathematics itself. The nature of quantifying and explaining the unknown, is a notion that has unceasingly romanced humanity, with the allure of using logic and reason to solve the mysteries of the universe. It is easy to see how mathematic principle can in some ways be deemed an art-form in itself. This idea was well summarized by Smith when he stated that Mathematics -the language of science and knowledge contained “beauty that resides in the experience of understanding equations, a beauty rarely recognized beyond the confines of academia, and it is never celebrated.” (Smith,)

The artist Justin Mullins' work was entirely based on this idea, which he represented by visually reproducing and displaying equations. With an understanding of mathematical philosophy, these paintings reveal hidden contextual meaning.

The Art of Justin Mullins. www.justinmullins.com

By attentively experiencing a 'Math and Art Trail' participants learn to identify the ways in which these mathematical and artistic ideologies affect the world around us. By doing so one will ideally learn to implement this heightened level of awareness permanently into the growing mind-set, and therefore develop a firmer understanding of the way the world operates, and the relationship humanity has with it. As creative individuals, improving our perception of reality in order to augment our findings, is the most efficient way to invest in and improve upon the quality of our creative output.

This is important in cultivating a healthy individual creative practice. Although the approaches of creativity rely heavily on innovation and imagination, it is vital that it be grounded in reality. It would be relatively safe to say in fact that without reality laying the foundations for creative practice, our work as creative individuals loses its relevance and application to the intended audience. This is the nature of augmented reality, and the cornerstone of 'Creative Technologies'.

“When old age shall this generation waste,

Thou shalt remain, in midst of other woe

Then ours, a friend to man, to whom thou say'st,

“Beauty is truth, truth beauty,” -that is all

Ye know on earth, and all ye need to know.”

(Keats, 1820)

The 'Trail' process offers exposure to these elements of aesthetics in a raw and exciting manner. It affords participants the opportunity to adapt their individual perception of reality in a comfortable environment. But what can we as creative individuals take away from the experience, and what approaches can be adopted when applying strategies learned from the 'Trail' process to a specific audience.

“This “real-world experience” shapes an artist’s capture of three-dimensional space either in paint, digitally or on film, in an essentially two-dimensional plane.” (Smith, 2006)

By witnessing these principles in subliminal action we can integrate them into our creative practice. We can learn from the success of existing beauty, be it the fundamental naturally occurring phenomenon detailed by Euclid's geometry, or the practices of existing artists who have adopted these approaches as their own. Once attained, this knowledge of aesthetics will allow us to build a bond and a commonality with our audience, transcending medium through our shared understanding of the most truly beautiful aspects of reality.

References

Abrams, M. (1952). The Sources and Nature of Statistical Information in Specialised Fields of Statistics. Journal of the Royal Statistical Society. Series A (General), 258.

Banks, M. & Morphy, M. (1999). Rethinking Visual Anthropology. Yale University Press, 306.

Cook, H. (2010). The Art of Mathematics. The Melbourne Weekly [Electronic Edition 3.3].

Garland, T. (1987). Fascinating Fibonacci's. Dale Seymour Publications [Electronic Edition]

Keats, J. (1820). Ode on a Grecian Urn. Lines 46-50.

Krages, B.P. (2005). Photography: The Art of Composition. Allworth Press, 9.

Livio, M. (2002). The Golden Ratio and Aesthetics. Plus Magazine [Electronic Edition 22].

Lowman, E.L. (1971). An Example of Fibonacci Numbers Used to Generate Rhythmic Values in Modern Music. Fibonacci Quarterly, Vol 9.

MacDougal, D. (1997). Rethinking Visual Anthropology. Banks, M, 26.

Mullins, J. (1999). Truth Plus Beauty. New Scientist [Electronic Edition 24].

Roach, J. (2007). “No Two Snowflakes the Same”, Likely True, Research Reveals. National Geographic News.

http://news.nationalgeographic.com/news/2007/02/070213-snowflake.html.

Smith, P.J. (2006). Line of Sight, presented at the conference Art and Authenticity. Australian National University, Canberra.

Smith, P.J. (2007). Rediscovering Lines of Longitude -signs of 'New Capture' for art practice at postmodernism's demise, book chapter, Visual Animals (ed.I North), Contemporary Art Centre of South Australia.

Smith, P.J. (2008). When I Consider How My Light is Spent. Catalogue Essay. Truth + Beauty, Gippsland Art Gallery, Victoria, Australia.

O'Connor, J.J. & Robertson, E.F. (2001) The Golden Ratio. Number Theory. JOC/EFR.http://www-history.mcs.st-andrews.ac.uk/HistTopics/Golden_ratio.html.