Oh Nothing, Just Teaching Myself Group Theory…
As the title of my post suggests, I delved into group theory this week. Group theory is the branch of mathematics that deals with symmetry.
Up until this point, I was reading Mario Livio’s “The Equation That Couldn’t Be Solved,” a pop-science book about symmetry and the way mathematicians learned to describe it. This book was actually the reason I chose to focus on symmetry in the first place. Unfortunately, it got really boring a few chapters in—the author spent way too much time on background knowledge that I did not need.
I returned from a trip to Bobst Library with four books of relevant material, two of which were pretty serious math texts: David Joyner’s “Adventures in Group Theory” and Cyril F. Gardiner’s “First Course in Group Theory.” I started working through the symmetry section of Joyner’s book, and spent half of my time just reviewing linear algebra. I gained some valuable insights, but translating matrix math into visuals is a bit hard to imagine.
Gardiner’s book turned out to be a much better choice. It begins the explanation of groups with a geometric example—an equilateral triangle. Basically, groups are a way of describing the symmetry of something. With the triangle, the group is defined as the series of motions you can enact on it to make it look like it hasn’t moved at all. The two primary motions are rotating it and flipping it horizontally. All of the rest of the motions are combinations of those two. I’m not going to go into too many more details regarding the definition of a group, but I am most likely going to use those rules as the basis for my project. The definition is fascinating because it translates a concept that we innately understand into words and symbols. I want to translate those words and symbols into a new visual concept—a process akin to entering a phrase in Google Translate, and then retranslating the resulting phrase back into its original language. The end result is usually not quite what you started with, and you learn a little something about the language and its idioms by doing it.