Chaotic Dancing – a mathematical choreography
For the Virtual HLF, which took place September 21-25, 2020 in an online format due to the pandemic, a Virtual Reality environment was created for the participants. In this environment, they could create their own avatar and use it to interact with other participants. Naturally, such an interaction can end up being quite stiff since many non-verbal cues people use to communicate like gestures, smiles, etc, cannot easily be incorporated digitally. To prevent awkward conversation from happening some interactive icebreakers were included, like laughing, waving and dancing. The latter turned out to be quite interesting, since it led to an post-conference dancing session at the virtual harbor, the design of which was inspired by the Blohm & Voss shipbuilding company at the Port of Hamburg. Here a look at the chaotic dancing:
But what is the chaotic dancing? Contrary to what the name suggests, it is a very well-defined dance choreography originally created for pedagogical purposes. In this context, it was one of the suggested activities on the International Day of Mathematics 2020 (see here)
It is an outdoor activity that is particularly effective with groups of 15-20 people or more. The participants spread out in the courtyard, park or other area and everyone has to choose two other participants at random and keep this to him or herself. As soon as the music is on, everyone has the task of dancing in a direction so that, viewed from above, they form an equilateral triangle with the two chosen participants. It quickly becomes clear that this is not as easy as it first seems to be. Each movement changes the position of those who have chosen one as a triangular partner, which ultimately triggers a chain reaction. It ends up being chaotic. There is a cheerful atmosphere produced by the desperation about not being able to solve such a simple task.
After the dance, there is a discussion in which different topics can be addressed depending on the course/group. On the one hand, choreography can be used to introduce concepts like algorithms, approximations and the like. After all, choreography can be understood as a simulation of an algorithm. Since this is a deterministic system, which means that once the choreography starts all variables are defined and no movement is caused by a random decision, this is also an example of deterministic chaos. This is what gave the activity its name. Heuristic methods can also be discussed in an advanced course. On the other hand, the dance also reflects something omnipresent in mathematics. Because it shows how one can discover structure and mathematics through arbitrary, carefree playing around. I myself did not even develop the activity (i.e. triangle-forming without the dance), but came across it in a seminar on teaching methods for adult education. There it was only intended as an element to shake up course participants a bit and thus get their brains going. There was no association with mathematics at that time except for the equilateral triangles. Back then I noticed the sensitivity of the choreography to small changes in the starting positions, which is how mathematicians define deterministic chaos, in order to visualize why mathematicians sometimes play around carelessly without having a clear goal in mind: you always find structure and mathematics where you don’t expect it. Analyzing these kinds of ideas always leads to new knowledge.
The exercise can also be used to talk about teamwork. After all, with prior agreement, there are simple ways to solve the task of triangulating quickly and without chaos. The way our actions influence our surroundings can also be a subject of discussion. Another thing that might be addressed with this choreography is the feeling of shame. Many students are not aware of how common it is in science to make mistakes. Errors are a fundamental tool for arriving at a certain point of knowledge. So to be wrong or failing to achieve a goal shouldn’t cause feelings of shame. In fact, making a fool of yourself is necessary to achieve something new. That’s why I encourage the students to dance as wildly and crazy as possible before the dance. Here, too, the foolish behavior without shame has positive consequences because it makes the task much more fun for everyone.
During the Virtual HLF however, these were not the main reasons why the chaotic dancing was performed. In the middle of a pandemic that brought so much anxiety, sorrow and concern to all of us, and which did not allow us to meet in person, it was a way of connecting with people all around the world, spending some quality time together and finding joy in something as simple as dancing. It was a way of traversing separation.