Week 4 Readings: Mathematics and the Arts

Reference: Dylan Thomas & Doris Schattschneider (2011) Dylan Thomas: Coast Salish artist, Journal of Mathematics and the Arts, 5:4, 199-211, DOI: 10.1080/17513472.2011.625346

Summary: This article resembles an autobiography of the Coast Salish artist Dylan Thomas. In it, he acknowledges his teachers and influences that helped him develop his unique style of combining Coast Salish traditional shapes, mathematics and modern elements. Thomas was inspired by Susan Point's spindle whorl piece (a tool used to spin wool for weaving used by the Coast Salish people) which exhibited rotational symmetry. Another major inspiration was M.C. Escher and his tessellations. Studying these artists, Thomas developed:

• Sacred Cycle - a cyclical piece depicting three salmon exhibiting three-fold rotational symmetry. 
• Salmon Spirits - an extended tiling piece with salmon rotating in four-fold symmetry.
• Ravens Housepost - a flowing vertical pattern of raven heads rotated 180 degrees repeating.
• Eagles Housepost - a repeating vertical pattern of eagle heads rotated 180 degrees from a central face.
• Horizon - a piece depicting a salmon mirrored in the vertical and horizontal plane whose tails overlap such that they create a perfect circle in the centre.
• Mandala - a cyclical piece with concentric circles in which squares have been inscribed with the Coast Salish circles, crescent and trigon motifs, inspired by Hindu and Buddhist traditions, exhibiting four-fold rotational symmetry.
• Infinity - a group of salmon flowing clockwise in an ever shrinking tessellation with each salmon taking up a wavy triangular space, exhibiting four-fold symmetry with each quadrant exhibiting dilation symmetry inspired by M.C. Escher's print Smaller and Smaller. 

Stop 1: "I spent days staring at Escher's symmetry drawings such as his butterfly and lizard tessellations and from these, soon figured out how I could make a tessellation. I began experimenting with different shapes and after about 3 days I found a design that worked" (Thomas & Schattschneider, 2011, p. 202).

This quote from the author demonstrates focus, determination, and perseverance. From my interpretation, Thomas was strongly motivated through his inspiration. We have innate abilities that allow us to figure things out regardless of formal teaching and terminology - this might be a really good example of why teaching outside of student means could work as long as they are hooked! Visual art might be a strong contender for this possibility of over-reaching to inspire because students would have something study, all the steps can be figured out in a two dimensional plane without needing to imagine any hidden critical pieces. 

I would love to see what his work looked like as he progressed through the days sketching. The process of creation is something I'm fascinated with.

Stop 2: "It is interesting to note that Dylan's path to making his first tessellation parallels that of Escher. Escher, too, had no mathematical background for this task, and figured it out by studying several geometric tessellations by majolica tiles in the Alhambra. Later he studied a display of tilings in an article by mathematician George Polya, and from one of these, Escher produced his first tiling by lizards with 4-fold symmetry" (Thomas & Schattschneider, 2011, p. 203).

Similarly to stop 1, it's interesting to hear that M.C. Escher too had a similar experience of not being introduced to tessellations and tilings through mathematics, but just figured it out by personal intrigue and fortitude. Do all students have this kind of experience of perseverance in their lives? 

Stop 3: "Although I derive much of my inspiration from outside First Nations art, Mandala was my first truly cross-cultural piece of art. I enjoy doing cross-cultural art because art itself is one of the only practices that can be found in all cultures. Art is one of the things that makes us human, and bridging different cultural art forms helps me to feel the unity of humankind" (Thomas & Schattschneider, 2011, pp. 208-209)

This idea of art being a practice found in all cultures is something else I'm interested in as it is not part of Bishop's (1990) six mathematical activities found in all cultures (below), but I argue that it should be! There are so many mathematical decisions that go into creating artwork that perhaps it might actually be a culmination of several of these individual math activities rolled into one. 

Wonders: 

• Does art work for every type of mathematical concept? 
• Can I isolate the concept of fractions, for example, and develop art from it? 
• Could I isolate the concept of logarithms and develop art from it?

Reference: 
Bishop, A. J. (1990). Western mathematics: The secret weapon of cultural imperialism. Race & Class, 32(2), 51–65. https://doi.org/10.1177/030639689003200204