I’ve been describing my love of tap dancing. I told you about how Donald O’Connor is a bit of a idol to me. I also talked a little about how tap rhythms can be viewed a modular arithmetic.

There is a lot of belief (mainly held by tap teachers) that students who take tap classes tend to do better in their math classes. In fact, there are whole websites dedicated to the Math in Your Feet! Amazing! But now, I want to take a small step (see what I did there?) away from tap dancing and towards climate change. This is a necessary step to understand why the games I played in tap class are similar to those in my dissertation research in applied mathematics.

Just like music is (usually) counted in eights for a dance class, there are intrinsic rhythms to our solar system. The most obvious example is that Earth moves around our Sun every 365 days. There are 4 seasons in a year, so each year we work through the seasons three months at a time until we get to 365 days. These rhythms are important and definitely affect the climate. However, these are not the celestial rhythms I studied for my dissertation. I looked at the Earth’s climate over millions of years. A year didn’t amount to much on those scales. On these time scales there are 2 main rhythms.

The first main rhythm is because of Eccentricity. Eccentricity is how round or oblate the Earth’s orbit is around the sun. Eccentricity oscillates every 100,000 years. So, if we treat eccentricity like it was a perfect Cosine curve with the period of 100,000 years then it would look like this:

The second main rhythm for the Earth’s climate on these time scales is Obliquity. Obliquity has to do with how tipped the Earth’s access is as compared to the plane of the ecliptic. The oscillations of Earth’s axis happen on a time scale of (approximately) 40,000 years. So, if both are happening at the same time, we see Obliquity start at the same time as Eccentricity, then it gets off-beat. But by the time Eccentricity has had 2 complete cycles, Obliquity has had 5. This looks something like this:

This is very similar to the tap dance game I used to play. We start the two rhythms in sync, then they slowly get out-of-sync and eventually match back up! Regardless of if we are looking at doing a 3 count paddle & roll tap step to 8 count music or if we are looking at 40,000 year obliquity oscillations to a 100,000 eccentricity rhythm, the main goal is understanding how the rhythms line up.

However, as a mathematician, I have to point out that the game I described in the last post is more complicated than the rhythms above. In the tap example, my rhythms were relatively prime (8 and 3). In this case, the rhythms are not relatively prime (100,000 and 40,000 have many factors in common). This means the climate example was simpler than the tap game. But, in many ways, my dissertation was much more complex. This is because there aren’t only two rhythms in our solar system. There are many other rhythms to consider. But, by analyzing how different celestial rhythms could resonate with each other, I came to some very interesting conclusions about the nature of our planet’s climate.

You see, if two rhythms in a real life system are close matching up, but not quite, then they still may nudge each other just enough to make them resonate. Have you ever tried to clap out a steady beat with a crowd? While everyone starts with a different pace, quickly everyone claps at the same pace. This is the basic idea of resonance. In my dissertation, I worked to show which resonances were possible for a model of our climate system. And which were not possible.

Basically, I was trying to show which rhythms sound cool together. I worked to answer a numbers of questions including:

- Which rhythms don’t sound/look good right now, but if you wait till the next count of 100,000 years, they will conclude in a very satisfying way?
- Which rhythms will never go well together?

And, so it was to this conclusion that I had my epiphany: Tap dancing is not so different from mathematics which is really pretty similar to climate change. There are rhythms in all of these systems that have resonance and, possibly, syncopation. And if you think about it hard enough, then you can define which rhythms work together and which ones don’t!