Mathematics

I got my Bachelor of Science in mathematics in 2017. It was a practical choice for many reasons. I grew up competing in mathematics competitions and when I got to undergrad I realized that I craved the decisive (and easy, for me) calculation, operation, and algorithm of early college-level mathematics. My first few semesters were wrapped up mostly in "applied" mathematics – calculus, statistics, differential equations – with one notable exception: I took a First Year Seminar titled “The Shape of Space”. In that class, I was first introduced to the idea that geometry can be something outside of the four perpendicular walls of my earth tone apartment, or a black-box theatre. 

 

Advancing through degree requirements led me to taking more theoretical classes and researching number theory with my incredible advisor, Dr. Carrie Finch-Smith. Proofs of seemingly obvious things (the existence of numbers, the absence of patterns to prime numbers) are agonizing or impossible tasks. Some proofs are disproven, reconfigured, simplified as time goes on. 

 

When I was in undergraduate, every time I mentioned to someone that I was a math major and a dance minor, the inevitable response was “How cool! I bet your math informs your dance so much.” I resented the implication that dance could not stand on its own or that somehow I was only able to dance or choreograph because I had a mathematical brain and not that I was good at math because I had a choreographic brain. 

 

Stepping outside of this into a world where I am privileged to be surrounded by artists who understand the value of dance, I have begun to uncover just how my choreographic brain can mobilize mathematical considerations inside of my dance making. 

 

Geometry

You can’t draw a perfect circle. Mathematically, a circle is the complete set of points equidistant from a center. This is an infinite set of points. We can create neither infinities nor equalities by hand. All we get is messy cycles, eccentric circles, repetitive events. 

Try this: Get a sheet of paper. Draw a circle. Is it a perfect circle? Definitely not, but imagine that it is. In 2-dimensions, you have created a circle. Now, pick up the paper, holding it parallel to the plane of your face. Slowly rotate the paper until it is perpendicular to your face, directly in line with your eyes. The two sides of the circle slowly converge until it appears that they merge, or disappear depending on the thickness of your paper and line. The eccentricity of the circle increases, becoming elliptical, and eventually, linear. 

More abstractly, consider a Euclidean (rectangular, like our sheet of paper) geometry. A line is infinitely long, infinitely straight, infinitely infinite. Wrap that rectangular plane around itself. Stretch it and twist it (okay, it’s stretchy paper) into a torus (donut). That line may connect back onto itself, becoming a circle or a spiral. It could not connect, it could be an infinite series of crossings, intersections, never lining up. 

Circles have no beginning, no end. Lines have no beginning, no end. 

Circular, linear. The oppositionality of these two classifications disintegrates with a simple shift in geometry. A shift in perspective. Linear: straight, clear, predictable, forward, clean. Circular: curved, meandering, cyclical, queer, closed. 

These ideas about the shape of space come from The Shape of Space by Jeffrey Weeks. Inside, he tussles with complex mathematical concepts in an attempt to understand the shape of the immeasurable universe. I’m curious how these considerations might be scaled and applied to a universe exactly the size of a performance space, a stage, a rehearsal room.

I investigate how to blur the binary between circular and linear. How can I juxtapose the two in shape or space or pathway or energy. I find myself running in a circle and wonder where the linearity of the movement lies. Is it separate? Are my extremities zig zagging as my torso loops? Can I alter this? Can my arms create circular pathways while my torso does the same? Can I rotate my body in circles tracing circles with my arms, moving circularly through a space? 

Henri Lefebvre speaks of distance in regard to its relativity (Einstein would be proud) in his text The Production of Space. Objects mark distance and seem fixed, but perception is easily shifted to blur distance into proximity, absence, concealment, etc. Each of these states is equally true, but concurrently false. Lefebvre postulates that social relations are not as visible as object relations, but rather are hidden by them (211). I wonder if this is where dance as an embodied form—discounting representational forms—becomes so illegible (and frightening) to many audiences. While theatre is about establishing relationship, is dance? Dance thrives on the multiplicity of meaning that is associated with distance and proximity: a complex writing of the body blurs associations that appear obvious within objects. Is the choreographic partly the sculpting or illuminating of social space?

Where is the edge of this space? Is it as finite as it appears? We believe that the universe is finite, but we can’t see it’s finiteness. A stage is simply finite, even measurable, but it is similarly amorphous. The walls that we construct between “on” and “offstage” are cardboard at best. How does this extend to our everyday lives? Goffman’s seminal text, The Presentation of Self in Everyday Life, is a (problematic and dated) step in the direction of understanding this (a precursor to the field of performance studies). 

Number Theory

0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1

Binary. Bullshit. 0. 1. The number 1 is phallic. The number zero (or the absence of number) is vaginal. There is a priority of 1 over 0. Something over nothing. Whole over empty. Lines over circles. The infinitely many numbers between 0 and 1 don’t matter unless you’re getting a percentage grade or calculating interest or paying at a gas station. 

Binary is just counting in a different modulus (modulo 2). What if the issue isn’t the binary itself, but the assumption that the binary is the only way of seeing things. 

When people think of mathematics and choreography, most moderately educated people immediately think of the Fibonacci sequence. It’s not hard to see why. The Golden Ratio, Fibonacci spirals, the “natural” occurrence of the two in organisms is fascinating. It’s inspired countless choreographers, visual artists, photographers (Anne Teresa de Keersmaeker tapes a Fibonacci spiral onto the floor of several of her works including Vortex Temporum c.2016, BAM). 

For me, I’m more interested in the recursiveness of the Fibonnaci sequence.

0 1 1 2 3 5 8 13 21 34 55 89

Each previous number informs and effects its successor. 

If Butler is to be believed in her “Performative Acts and Gender Constitution: A phenomenological approach” , then gender is a “stylized repetition of acts.” 

These acts are not identical. They are informed and influenced, shifting consistently with each new enactment of the act. They are repetitive, but functionally different. These acts are also interactions. These cycles of performativity, direct or indirect, conscious or unconscious. They are intersections, less invasive, they can be tangents, less still, they can be complete misses. Each connection informs the next, each interaction spurs another, reforms a behavior, cements it, unseats it. The repetition of an act influences the next performance of the act. 

In my opinion, the real weight in Butler’s work is in the conclusion that “gender reality...is real to the extent that it is performed.” This claim has weight in several dimensions. First, it creates a space for dissenting performances of gender as “real.” For myself and other non-binary individuals, this is crucial to our identity. There is a claim perpetrated that the gender binary is a matter of fact, and that performances of other genders, or indeed transgender performances, are simply acts. However, Butler’s writing would serve to illustrate that these acts are critically embodied in order to self-actualize. Secondly, the claim presents the possibility that gender could be unperformed. Butler states explicitly, “The prescription is invariably more difficult, if only because we need to think a world in which acts gestures, the visual body, the clothed body, the various, physical attributes usually associated with gender express nothing.” (530)

 

This theoretical consideration carries the implication that by doing, we can undo. Working in the exact mechanisms that are oppressive or proscriptive creates space for dissenting performances. The imperfection of repetition redefines the formalist structure being created. I rely on this fact every time I slide eyeliner across my lids, shimmy into a dress, or paint dye into my hair. My externalized presentation affirms an internal sense of self and unsettles outside readings of my body. 

Number theory is incredibly choreographic. Modular arithmetic is a scalar approach to a broad system. Sequences and series operate like scores for generating new information in a criterion. Numeric coverings are like puzzles constructing time (numerals) and space (frequency) both imploding expansive infinities and allowing minor conclusions to operate in infinitely small and large scales. 

And of course, even on a rhythmic, somatic level, these arithmetical operations function to proscribe and facilitate movement, patterns, spatial pathways. 

So yes, I suppose you could say that my mathematics does inform my dance. Or you could, as I do, say that the relationship is recursive, reflexive, reiterative.

Works Cited

Butler, Judith. “Performative Acts and Gender Constitution: An Essay in Phenomenology and Feminist Theory.” Theatre Journal, vol. 40, no. 4, 1988, p. 519., doi:10.2307/3207893.

Goffman, Erving. The Presentation of Self in Everyday Life. Doubleday, 1990.

Lefebvre, Henri, and Donald Nicholson-Smith. The Production of Space. Blackwell Publishing, 2016.

Weeks, Jeffrey R. The Shape of Space. Marcel Dekker, 2002.

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