Mathematics is a Tool For Storytelling

Mathematics is a tool for storytelling. To see this, consider my brother. He is an applied mathematician. One of his current areas of study is groundwater. He tries to understand, and help other people understand, what happens to water that is deep within the ground. He collects data about the water’s behavior at different locations within the ground and then uses mathematics to stitch that data together into a story about what the water is doing. He’s a story teller.

This says, in a short and succinct way, what I have been trying to express to myself for 10 years but only now fully realized. I grew up thinking math was about calculating. In graduate school, I was introduced to the idea that math was all about problem solving. Now I realize its neither of these things, ultimately. In the end, mathematics is about story telling. Let’s explore how with an example.

Here is a video of a hole puncher being squeezed.

It is a simple story that is told using the medium of film. Translating it into verbal language, we have:

The handle is pressed and the hole punching cylinder moves down. Then pressure on the handle is released and the hole punching cylinder moves back up.

In verbal language, the basic units are words, and those words are formed into stories through the use of sentences.

In mathematical language, the basic units are quantities, and those quantities are formed into stories through the use of functions.

Let’s translate the verbal story into mathematics piece by piece. “The handle is pressed”, in this case, describes a rotation of the hole puncher’s handle around its pivot point as a function of time. The two quantities are time, in seconds, and angle of rotation of the hole puncher handle, in degrees. They are formed into a story by the function:

$f(x)=45x$

where $x$ is time and $f(x)$ is the angle. By representing the time with a slider and the handle with a line segment, this piece of the story can be visualized using GeoGebra like this:

“…and the hole punching cylinder goes down” describes the vertical position of the cylinder relative to its starting position, in inches, which we’ll call $g(x)$ , over time, which is still $x$ . These quantities are formed into a story by the function:

$g(x)=-0.3x$

Using a vertical line segment in GeoGebra to represent the hole-punching cylinder, the simulation now looks like this:

And finally, the rest of the story:

…Then pressure on the handle is released and the hole punching cylinder moves back up.

This requires changing the original functions into piecewise ones, describing the handle and cylinder as they travel down, pause briefly, and then travel back up to their starting positions:

Adding this to the simulation completes the story:

This example illustrates the fact that mathematics is a tool for telling stories. Modern simulation software like GeoGebra allows people to perceive these stories in ways that were impossible a short time ago. Thinking of mathematics primarily as a story telling tool will drastically reshape the way I instruct and develop learning materials for my students moving forward.