It's time to resume working on an article I've promised myself for years. Perhaps it could become a book. I've been too busy painting though. But also, the one gallery representing me (Marigold Gallery on Canyon Road in Santa Fe) closed in January so I've been thinking about next steps.
But the main reason I am thinking about this now is that I see some excitement generated in the community to revisit the design techniques that I see as mathematical, involving dynamic symmetry concepts. I could even touch on the deeper mathematics behind the techniques in an appendix. This will fulfill my need to marry my two passions: painting and mathematics.
In any case, two years ago I took a zoom workshop with Michele Byrne (now of Santa Fe) well-known artist specializing in using a palette knife, my favorite painting tool. An added benefit of the workshop was to see how she employs dynamic symmetry in her work:
https://www.oilpaintersofamerica.com/2022/03/dynamic-symmetry-and-how-i-incorporate-it-into-my-plein-air-and-studio-and-practice/
It reminded me of another technique called Informal Subdivision from a book on Design by Andrew Loomis:
And then Kevin MacPherson has been publicizing his technique of the Magic Grid, which uses a construction similar to Loomis':
So, well known artists have been employing mathematics in their painting - consciously. How many of us do this unconsciously?? And can such an article (or book) help all artists?
One more comment here: the brand name I adopted a few years ago, Radical Impressionist, refers to the mathematical concept of 'radical' (another name for 'root' such as the square root or nth root). Search for posts here on mathematical concepts by selecting appropriate labels to the right such as Dynamic Symmetry, Golden Spiral, etc. I've written posts about specific paintings also, paintings that employ these concepts (golden proportions with an intentional golden spiral in the underlying design: can you see it?):
Updates April 21, 2022:
Before leaving this post I would like to add one more reference: Jack Leibowitz's book, Hidden Harmony: The Connected World of Physics and Art. Jack is a physicist (and full disclosure, a friend) who happens to have attended the same undergraduate school I did: New York University. His career included professorship at Catholic University in Washington DC, where he was joint Chair of the Physics and Art departments. Many years ago Jack and I met in a plein air class in Santa Fe and we found that we have a common interest in math and science and their connections to paintings. His book references some advanced mathematics abut harmony; in particular the theorem by the important female mathematician, Emmy Noether, whose theorem, the Noether's Theorem, "states that all continuous transformations correspond to conservations laws" critical to our understanding of harmony in nature. In addition, the law underlies mathematical concepts of groups and symmetry (related to my PhD thesis).
Personal notes:
I first became interested in the connections between mathematics and art while I was a Mathematics Instructor at NYU during my graduate school years. I taught a course on Introduction to Mathematics which had a section on Math and Art. I covered topics such as perspective, dynamic symmetry, non-euclidean geometry and the geodesic dome, topics covered in Morris Kline's tome, Mathematical Thought from Ancient to Modern Times. Kline was a professor at NYU and at one point he asked me to substitute for a couple of his classes. I was barely older than the students and remember the experience vividly. (I still have a hair trinket that Kline gave me as a thank you.). Later I co-taught an interdisciplinary course - "Art in Math" at Cooper Union, for one semester with a professor of Architecture, Arthur Corwin. This course, "co-developed with Professor of Mathematics Paul M. Bailyn, received the first Edwin Sharp Burdell Award for creative synthesis of Science and Art". Arthur's wife of 45 years was a close friend; my son's middle name was her first husband's name, James.
I also taught sections about math and art in a course on a Liberal Arts Approach to Mathematics, a required course for non-math majors at the College of Mount Saint Vincent in Riverdale, NY, where I was a Professor of Mathematics and Computer Science for ten years before I left the academic world. I still recall one student's comments: "more coloring books". I liked to show pictures of tessellations of the plane in color. And I enjoyed teaching "Groups and their Graphs" in the advanced course I taught on Algebra, which has many examples of symmetry groups. The connection between mathematical groups and graphs of the plane is the topic of the book by my PhD Advisor, Wilhelm Magnus. So this is another example of my interest in the topic and its influence perhaps on my decision to become a painter after I left the academic and corporate worlds.
Then in the corporate world at the NYSE, one of our main responsibilities was to provide the traders with a visualization of how stocks are traded and how fast. Our "Display Book" was the center of trading for over twenty years, beginning before I came on board in 1987. I loved working on this product, first writing code and then managing its development. Management involved communicating the design with the customer and illustrating how the design was based on mathematical concepts emphasizing performance with the Black-Scholl in mind. This actually touches on dynamic symmetry and optimization of visualization. Google the
Display Book. It was finally replaced in 2012, ten years after I took early retirement to paint full time.
I am now Facebook friends with an NYSE colleague who was instrumental in designing the "Book" for the traders. He has also retired and is spending time playing the guitar and performing, We keep up with each others' pursuits in the arts.
I also remember a meeting with the NYSE president at the time in which he veered off topic to bring up the internet and playing games that were played at the time on the Atari. This topic was prescient and alluded to how trading would change in the future, using the computer more and more.
So I've come full circle from having an interest in painting and art early on and winning my high school's art award upon graduation to teaching topics on math and art; and then to employing visualization to help others at the NYSE. And finally to developing my paintings using composition design constructs as exhibited in ancient to modern times.
References:
Jack Leibowitz, Hidden Harmony: The Connected Worlds of Physics and Art, The Johns Hopkins University Press, Baltimore, 2008,
Hidden Harmony-AmazonMorris Kline, Mathematical Thought from Ancient to Modern Times, 1972,
Amazon.
Wilhelm Magnus and Israel Grossman, Groups and Their Graphs, Random House, 1964.
Amazon.
Watch this blog for more updates!!
Karen, Mar 29, 2022 (updated Apr 21, 2022)
