I am always on the lookout for connections and commonalities between mathematics and the arts, dance in particular. In my on-going survey of math/movement/dance approaches out there, most of what I've found seems focused on numeracy and procedural concerns; these are not necessarily wasted efforts, but why stop there? There is also a lot of illustration of math concepts using dance, but the two subjects stay on parallel tracks with no real connections between the two. Overall, approaches like these never get to the deeper commonalities between math and dance because they are often more focused on memorization or performance of prescribed movements than understanding and application.
The main focus of Math in Your Feet is a thorough exploration of patterns. Since my dance form is based in making foot-based dance patterns, it is a natural and meaningful connection, especially if the goal is to develop mathematical thinking and not simply working to improve skills or memorization of procedures or formulas. After patterns, another commonality between math and dance is certain habits of mind and flexibility of spirit in the process of finding solutions. With that in mind, I submit to you two diagrams, one from a math point of view, the other from an arts perspective.
When I look at this diagram from the blog Keeping Mathematics Simple each one of the intersecting circles could describe what I do as a dancer including, I think, even the theoretical.
Coming from the other perspective, when I look at the next diagram, from the article
Defining Arts Integration, I think about how mathematicians go about posing and solving problems and definitely see connections to this arts-based diagram of the creative process. The creative process is a hallmark of artistic activity and, I'll argue, a hallmark of mathematical thinking as well, just not labeled as such.
Be you mather or dancer, what say ye? (Alternative and/or opposing viewpoints welcome!)
As an old charter/diagramer for people, both are acceptable except for the fact that one diagram is a staid, standard image of overlapping/interaction that does not show movement or involvement. While the other shows the active/dynamic action of involvement (the use of arrows is always a sign of movement, hence, change/development.) The first is the overused, traditional imagery while the second is the dynamic, inter-involvement imagery that, in my mind, leads me to seek involvement with the subject.
ReplyDeleteSpoken like a true graphic designer and former educational materials specialist! I'll be calling on your expertise in the near future since I have a diagram of my own in the works. I think I was looking for feedback on the content not the design, but your comments are interesting anyhow! And, I mathematicians do use arrows in their work to denote movement(vectors?) so there's a connection anyhow! :)
ReplyDeleteI am a girl who wanted blinking, colorful lights on my Christmas tree, so can math be colorful AND have arrows? ;-)
ReplyDeleteChristine
Hi Christine! We'd have to ask the math folks, but my thought is why not?! And there might be an interesting math problem in there related to blinking lights...
ReplyDeleteThe circle diagram is confusing; different sizes of overlaps, some areas do not represent anything, no connections, colors seem arbitrary and the words are ideas without context. As a diagram it has no clear information, and why five circles? This says nothing about mathematics or the process. I suppose “keeping math simple” is meant to be the conceptual context. Diagrams are always complex because they eliminate the simplicity and directness and understanding that can only come with the experience of doing.
ReplyDeleteThere is at least some symmetry in the second diagram. I do not know how to make sense of these words or the symbol arrangements; they have no value as I reflect on my experience and attempt to share my understanding.
Both art and math leave me without explanation to the creative process, but clearly this process is the same for both and far more comprehensive than either. Where in these diagrams do they reference the heart, mind and the spirit? Where is the truth, the beauty and the goodness, the joy of human expression and sharing through interactions that I observed in your classes?
I suppose the "Mathematics is..." diagram would have been just as effective presented as a list. However, my interest is in the information those two diagrams are trying to communicate. I guess 'trying' is the operative word here, since folks seem to be focusing on the images.
ReplyDeleteWhat is so interesting to me here is that the comments on this post have veered toward an evaluation/critique of the delivery of the ideas rather than the ideas themselves. From what I know about the three of you, you're all (loosely speaking) visual artists, or work in a medium that uses a visual language. So, my take is that you were all hypersensitive to the medium of the message -- the images spoke louder than the words. I'll try better next time! ;)
No matter, I still need to say, at the risk of being repetative, that the map (diagram) is not the territory (experience). I may not have communicated my point very well, but I was hoping to spark some discussion or observations about whether or not the information in the Math diagram could be applied to a description of the arts, and whether or not the information in the creative process diagram matches the process of mathematical problem solving.
Brad, you said: "Where in these diagrams do they reference the heart, mind and the spirit? Where is the truth, the beauty and the goodness, the joy of human expression and sharing through interactions that I observed in your classes?" The truth is that I don't think those things are represented. How could they be? (But thanks for your nice words. I'm glad you were able to come observe.)
Certainly math and art are quite similar. I was a math minor and have always thought of math as an activity that requires equal amounts of right and left-brain thinking - if not more right-brain. Now if all one if doing is plugging numbers into a formula, then there isn't much creating happening, but...when you get to abstraction then the left-brain, engineer types get lost because it requires a high amount of creative thinking to get ones mind around an abstract concept. I will argue that mathematicians are generally quite intuitive problem solvers, even if they don't know it. And what is intuition? Listening to the creative voice inside.
ReplyDeleteYou were clear, "the map (diagram) is not the territory (experience.)" Yes, all diagrams are visual language, even as a list key from specific experience to generalized concepts. If I were to follow the integration of these ideas the result would not be particularly interesting, nor graceful. There is no formula in math or art to the creative process. We have identified generalizations that can be helpful to develop skill and even proficiency, but eventually must give way to the act of expression.
ReplyDeleteLet's make another list for the creative process and see what we can come up with:
1.Curiosity; demanding effortless attention.
2.Intuition; inner response to outer conditions.
3.Courage to explore and give expression to what is unknown.
4.Reflection with care towards understanding.
5.Contribution to general body of knowledge.
6.Joy and delight in giving expression to what is felt in the heart.
7.Spirit simulation and moral guidance towards revealing harmonies and expressing order in an apparent discordant world.
These are a few qualities we could use to discuss math, the arts and other human activities that creatively lead to progressive and meaningful expressions presently called the "creative process." If there is inspiration the mechanics of expression will eventually become apparent.
Yay! This whole series of comments/conversations is getting me closer to where I want to be in my understanding, so thanks to everyone for your thoughtfulness.
ReplyDeleteThat is a wonderful list Brad -- it is both beautiful in and of itself and useful to me. One of the things I love about your work is that you are in both math and the arts in equal measure. I, on the other had, still have a way to go on the math side, so you are the perfect interpreter of both worlds. Thank you for your thoughts. The thinking here may show up again in a future post.