Week 4 - Reading Summary and Activity

My reading to summarize this week is a journal article entitled Dylan Thomas: Coast Salish Artist published in the Journal of Mathematics and the Arts in 2011.  The article is authored by Dylan Thomas and Doris Schattschneider.  Thomas is a relatively young (b. 1986) Coast Salish indigenous artist whose art often employs geometric patterns such as tessellations and various types of symmetry.  Schattschneider is an American mathematician who is an expert on the type of mathematics present in Thomas’ art. 

The article begins with some basic background information on Coast Salish history and culture, presumably for readers unfamiliar with indigenous groups of the Pacific Northwest region.  The majority of the article is written in the first person by Thomas, discussing a number of his silkscreen prints which are included in the article.  Along the way he talks about his interest in M.C. Escher as a teenager, other artists that have influenced his style, his mentors and their various teachings, and his interest in geometric patterns and how he combines it with traditional Salish motifs.

Along side Thomas’ description of his art, Schattschneider provides explanations of the mathematical relationships contained in his art.   I have provided one example from the article below:

Thomas: “I grabbed some gridded paper and got to work. This time it only took me 2 days to come up with a tessellation that worked both mathematically and aesthetically with a Salish design of salmon. After I was finished with the design on paper, I moved it onto the computer to continue the tiling.”

Schattschneider: “Each print is based on dividing a square into smaller and smaller squares, each square in turn divided into three isosceles triangles as shown in Figure 13a.  The whole print is created by rotating that square 90^O three times about point C, giving it 4-fold rotation symmetry.”

I found Thomas’ artwork fascinating because not only does it showcase the beauty of our little corner of the world, but there is a creative element as well as a mathematical element to appreciate.

I wanted to see more of Thomas’ creations, and his portfolio can be viewed on his website here: http://dylan-thomas.ca/

STOP#1:  Traditional Knowledge vs. Scientific Knowledge

I’ve always been interested in the wealths of knowledge held by indigenous groups that Western/European culture historically would have deemed “uncivilized” and “primitive”, for example the ability of Polynesian navigators to travel across the open ocean for thousands of kilometers with great precision, or the ability of Amazonian shamans to prepare effective medicines from local plants.  The indigenous groups often have a spiritual/cultural explanation for how these things work, but of course modern science also has an explanation too.  One might be tempted to label these things as binaries or polar opposites with one being right and the other therefore being wrong, but I think examining the two ways of understanding and considering how they evolved and how they complement each other is what is most interesting in my opinion.  I think this article by Thomas and Schattschneider provides another example of this kind of situation.  Both of their contributions show that there isn’t really a dichotomy of math vs. art; seeing both the artistic side and mathematical side of Thomas’ silkscreens provide a richer, multidimensional way of understanding them.

STOP#2:  The Grid

Examining Thomas’ silkscreens reminded me of last week’s main themes, “the grid”. I began to think about how Thomas is taking natural forms such as wild animals and by stylizing them and arranging them symmetrically he is actually in some ways putting them “on the grid”.  I began to think about other artists such as Salvador Dali whose surrealist works like The Persistence of Memory could be thought of as taking depictions of everyday items like clocks “off the grid”.  I felt like part of last week’s readings had a subtle theme of “the grid is problematic and off the grid is better”.  The Doolittle reading I summarized seemed to suggest that Western thought was “on the grid” and indigenous thinking was “off the grid”.  Although in some ways I would agree, overall I think that on vs off the grid is just another unnecessary false dichotomy.

https://www.britannica.com/topic/The-Persistence-of-Memory

 Activity - Bridges Math and Art Conference

I had a lot of fun checking out the Bridges website - there are so many excellent examples of mathematical art!  I will definitely be showing this to my colleagues and my own math classes!  I was drawn to one piece called Runes by Mike Naylor because it reminded me of the spirograph toy I had as a child.

https://www.playmonster.com/product/spirographtravel-spirograph-design-set/

Turns out it is an interactive digital art piece, so I found it embedded on the artist's website here:http://mike-naylor.com/runes/ and started playing around with it.  Essentially it is a visualization of multiplication using a clock-like arrangement of the numbers.  You get to choose how many numbers to be arranged around the "clock face" and then hovering over any of those numbers causes the visualization by creating arcs from one number to another.  For example, if you hover over 2, an arc will be drawn from 1 to 2 (because 1x2=2), a line will be drawn from 2 to 4 (because 2x2=4), a line from 3 to 6 (because 3x2=6), etc.  The result are some really cool patterns!

I chose 60 for my amount of numbers around the outside since it is a highly composite (divisible) number.  I then experimented comparing divisible numbers such as 15 and indivisible numbers such as 31 and 41.

Some interesting asymmetrical patterns also emerged when I selected a value in between the whole numbers, such as between 1 and 2 or between 41 and 42:

I then maxed out the amount of number at 360 and recorded a quick screen capture of it automatically moving from one value to the next:

I spent well over an hour playing around with this interactive art piece, and I will definitely be spending more time looking at some of the other artists' work this weekend as I chip away at my term 2 report cards!