SON. Whispers hover in a windowless room in the basement of the math department. It is the final exam session. The university hired me along with other experienced math students to help junior ones in preparing for exams. A group of novice mathematicians raise their hands and ask me, "How can we solve this problem?" I look over the exercise and tell them, "Listen to the algebra, and it will lead you to the solution." Then I walk away.

Many years later, I was a confused rookie in a beginner salsa dancing class. Was it a right foot and left hand or a left hand and right foot? I approached the professor, who looked over and told me, "Listen to the music, and feel the rhythm." Then, the instructor walked away.  I became upset then, but I also grew upset with Patricio from many years ago because we were both ignoring the silence others may be immersed in. And while it is true that listening to the tunes within dancing and math-ing is fundamental for understanding.  We should not suppose that all can hear such beats.

BRIDGE.  Now, still a beginner dancer, I keep wondering how an expert can listen to the silence and how a beginner can listen to the rhythm. So, I started thinking about the interplay between a beginner and an advanced partner in math or dancing. Several threads tie mathematics, dancing, and partner work together. Music and math have a rhythm—a structured flow of ideas or sounds—within themselves, and such structure guides the algebra and the dance steps. Additionally, most of us learn these disciplines with others by either solving dances or dancing problems together. Both activities are deeply social—we go out dancing and math-ing to share music and ideas with others.

I must remind the reader that salsa and bachata dancing are partner dances, and I am the lead of the dance due to gender-assigned roles. My job is listening to the music and deciding the dance steps. My dance partner is called the follow, and she interprets the leads given to her. For me, to lose the rhythm while dancing is always a bit terrifying, akin to how a beginner mathematician might feel in an exam because so much depends on it—the dance moves, the algebraic steps to be performed. Without listening to the music, how can one decide what will happen next?

"There is this guy who is super nice, but it is such a chore dancing with him" is a confession you will hear from follows after a tequila or two :P And of the many sins a lead can have on the dance floor, to be disconnected from the music is a particularly egregious one.

MONTUNO.  I am a sinner lead. I am guilty but not malicious. For some of us, the rhythm in salsa is hard to grasp because it has several layers of instruments. The cowbell, the congas, the piano, and everything else are all playing at complementary beats. Even bachata, whose beat is more straightforward than salsa's, can get tricky on a rainy day :(  Among percussion instruments, the cowbell is friendly to beginners because it produces a loud sound at the odd beats, precisely when you are supposed to move your feet. Other instruments, such as the conga and the clave, have a more complex or subtle presence in the song. The sum of all those instruments creates a rhythm that the lead aims to express through a follow. But if a lead fails to dance on time,  the couple "gets dragged around by a chicken with its head cut off." 

So, here is my central question. What can we do when the follow recognizes the rhythm better than the lead? In such cases, I wholeheartedly value dancers who embrace the rhythm as something sacred much more important than the lead, the gender role, and the dance itself. 

MAMBO.  I am a beginner lead in dancing, and I have the privilege of dancing with advanced dancers. By contrast, in math, I am an advanced follow. The math apprentices are the leads because they must solve the problem by selecting the appropriate moves and executing them on time.  

Whenever math beginners ask me a question, I do not answer it. I start asking them to explain the problem to me so I understand how much of the mathematical beat they hear. Then I ask them to lead a first step, which prompts the answer, "We do not know what to do." I smile, look at them, and always answer, "I will not give you any clue. Please make a guess, and we will start from there." After receiving an answer, I signal the errors, if any, and ask for another guess. In dancing, the above situation is akin to a follower refusing a lead, strongly signaling her disagreement, or breaking the connection. Math-ing and dancing then become awkward and frustrating. Every leader knows of a follow who evoked such feelings on the dance floor.

Yet, we want redemption from our sins, not just damnation.

To avoid such an unproductive inferno, I create successive versions of the math problem for the beginner that highlight the missing steps while silencing everything else. Thus, I become a math cowbell that pierces the silence in which the beginner is immersed. In dancing, some dancers start with versions of the dance that are simpler than their potential and more reflective of the timing in the music. They may put in place a version of the footwork that highlights the essential beats while being quieter about other ones. They may alternate the tension in their frame to stress the timing.

These dancers are now the cowbells. They become music themselves.

OUTRO.  To become a cowbell, one must listen to the others' silence and how the sound leaks into it. "I must f*ck*ing love you for dancing like that. Your confusion is not my problem. You should go and figure out by yourself!" a friend told me while smiling, leaning over, and waving the tequila in her hand. I agree with her wholeheartedly because learning and listening are personal responsibilities. We should not outsource them by default. Plus, even the best of us have long days where mojitos are the only accepted philosophy.

Still, a small miracle is at the end of the above effort—a follow who approaches the silence and becomes rhythm—one who brings the lead to its full potential without solving the math problem or back-leading the dance. And for me, getting music—or math—into silence is a gift comparable to the Promethean feat of stealing fire and bringing it to us—the ones living in the darkness.