Mathematics lives largely in an unseen world. Mathematicians see the relationships of such entities without physical interaction. In his book, The Math Gene, Keith Devlin writes:
“The difference is that, in mathematics, the off-line thought is focused on objects that are themselves pure abstractions, whereas in everyday life our thoughts generally focus on real objects or fictional versions of real objects…”
Devlin argues that mathematicians see math as stories in which the characters (mathematical entities) interact through mathematical operations or relationships.
Now, we turn to the words of a master of mime. Marcel Marceau would often say, when not onstage, of course:
“Mime makes the invisible visible.”
Such a simple concept serves as a guiding principle of pantomime which lives in imaginary worlds created by movement artists. Audiences, in their genius as he talked about it, could enter and see great truths about themselves and humanity.
Leaning again on Devlin’s words but this time from The Language of Mathematics, we read:
“Mathematics is the science of patterns, and those patterns can be found anywhere you care to look for them, in the physical universe, in the living world, or even in our own minds…mathematics serves us by making the invisible visible.”
Devlin’s text echos Marcel Marceau’s spoken words regarding the power of mime to make the invisible visible. Mime leans heavily on people’s abilities to visualize the invisible. In this way, mime can contextualize mathematical ideas and enable an audience to place an abstract concept into a story.
For example, numbers are inherently an invisible entity. We enumerate by creating a one-to-one correspondence between objects and numbers; yet a number itself remains invisible. A simple operation that can act on a group of objects is division. To place this concept into a story, we perform a sketch which ponders the question “What is it like to be the remainder?” In the sketch, Tim plays a clown who, almost compulsively, divides objects into two groups as they emerge from a suitcase. Repeatedly, one object is left–the remainder of the division. The pantomime touches on a universal human experience — aloneness. In fact, the dramatic line of the piece relies heavily on a tension between togetherness and separateness. Primary school audiences are often heard counting in order to determine the cardinality of a set of objects in order to anticipate if such aloneness will result. After seeing this sketch in a performance, a child from a third and fourth grade classroom wrote,
“Thank you for coming to my class to teach and show us some pantomime….I especially loved the remainder act because it made me laugh. I DID see the remainder.”
The popularity of this sketch and frequency of comments like that above underscores the ability of a performing art to place mathematical ideas into a story in a way that physicalizes the abstract. Watch the sketch below to see this invisible concept yourself.
The Plunger
“In our show, we go beyond performing mime to introduce mathematical ideas, we also teach mime that have elements of math intertwined. Audiences enjoy learning mime illusions like touching an invisible wall or catching a mime ball. Both illusions lead to discussions of mathematical concepts. Let’s illustrate with the illusion of the mime ball. To begin, the audience learns to hold a mime ball that is essentially the weight of an orange. After practicing to toss and catch the mime ball several times, we remind the audience that the ball is created with mime. As such, we can pick another mime ball out of the air, smash it together with the first and reform the resulting mass into a mime ball with twice the weight as the original. We approximate the expected weight by tossing the newly formed ball into the air and catching it. Putting this ball aside, we snatch five mime balls from the air, mash them together and estimate their weight by again tossing them into the air. Soon, we smash 100 mime balls into one; the ball has grown so heavy that we cannot lift it. So, we reverse the process and divide the ball in half and reform the hemisphere into a mime ball. Children in an audience often rush to note that the resulting ball is 50 times heavier than the original ball or half as heavy as the preceding ball. Such a concept enages children and can easily be used by teachers to underscore lessons in the classroom. To see Tim present this in video, watch below.”
The Ball
“Our mime also introduces ideas outside the elementary and secondary curriculum. In a duet sketch, Tanya’s character interacts with a huge tube seen to the right. After the sketch, the audience is introduced to the mathematical field of topology. Given the rules that one object is equivalent to another as long as there is no breaking or connecting of pieces, the audience is asked what letters of the alphabet the huge tube could make if it started as the letter “S”. Note the answer depends in part on the style of font that one imagines. You can see the sketch, as well as the verbal component that asks topological questions in this video.”
The Tube
“Our mime also introduces ideas outside the elementary and secondary curriculum. In a duet sketch, Tanya’s character interacts with a huge tube seen to the right. After the sketch, the audience is introduced to the mathematical field of topology. Given the rules that one object is equivalent to another as long as there is no breaking or connecting of pieces, the audience is asked what letters of the alphabet the huge tube could make if it started as the letter “S”. Note the answer depends in part on the style of font that one imagines. You can see the sketch, as well as the verbal component that asks topological questions in this video.”
Read about Tim and Tanya’s Math and Mime in the New York Times, 2015.
About Tanya and Tim Chartier:
Dr. Tim Chartier is a professor of mathematics at Davidson College, North Carolina. Professionally, he’s won awards for both his teaching and research. In K-12 education, he’s actively helping develop a sports analytics program for secondary schools. He also served as chair of the Advisory Council for the Museum of Mathematics in New York City, which delights young and old. Tim enjoys running, biking but mainly, spending time with his family. Tim’s inside the silver dryer vent in the picture. See if you can figure out how he is gets into that pose.
Tanya Chartier has taught multi-age classes from K-5, theater at the middle school level, and is currently a Reading Specialist for the Davidson Center for Learning in the town of Davidson. She has taught in both the Education Department and Theater Departments at Davidson College. Between her undergraduate studies in English Literature at Denison University and graduate studies in the Teaching of Reading at Western Michigan University, Tanya studied literacy in Japan as a Fulbright Fellow. Tanya enjoys hiking and camping, especially with family.