This is an article about the only thing I learned in Calculus 3.
(Don’t worry, it has nothing to do with math.)
Imagine that it’s a Monday. (Unless you’re reading this on a Monday. Then save your imagination for later.) Imagine that you’re sitting in a cramped desk-chair deathtrap in a stuffy room in a college engineering building. There are no windows. There is no music. There is no hope. (Remember, it’s a Monday.)
Now imagine that you are supposed to be learning Calculus. Triple integrals and spherical coordinates cover the board. Chalk dust hovers above the ground, shrouding your feet from sight. You are lost in a mystical forest of confusion.
Then, in a moment of inspiration, your guide turns around and senses the fear and confusion in your heart. In all of your hearts. He knows the questions you are asking. (And they have nothing to do with spherical coordinates.)
What wrong turn have we made to end up in this haunted forest? Are we going to die here? Is there a way out? This is hopeless. This is pointless. Can I give up?
The professor begins a conversation.
“Why are you taking this class?” the professor asks,
You think, “That’s rhetorical, right? Because I’m supposed to take this class. Because I need it to graduate. Because it is a requirement for my major. Just, because.”
He presses into the confusion. “Why is Calc 3 a requirement for your major?”
Ah, now you sense his argument. “Because I need to know Calculus to know Physics. I need to know Physics to know P-Chem. I need to know P-Chem so that I can go to medical school. I need to go to medical school to cure cancer. I’m talking Calc 3 so that I can cure cancer.”
“Assuming you don’t go to grad school for math, will you ever use Calculus again?”
“Sure. Yeah. This can’t be a waste of time, right? We’re doing this because adults do Calculus all the time.” Right? No, that can’t be right. Where is our crazy guide leading us?
“No. You’re not taking this class because it is practical. You’re taking it because it is hard. For you, this class is required to graduate because it sets you apart. If you can understand this, you can understand almost anything. You’re taking this class to prove to yourself and the university that you are able to do hard things, practical or not. This class is a workshop for people who want to do hard things, not math.”
Oh snap. This mystical forest just got real.
Hard Things Are Worth Doing
Aside from the aforementioned P-Chem, Calculus 3 was the hardest class I took in college. I invested an absurd amount of mental energy to understand concepts that I have never used. Concepts that have long been forgotten. Most would see this as an exercise in futility. A waste of time. Impractical. Pointless.
What I learned in Calculus is that hard things give me confidence to do more hard things. Not every hard thing—like Calculus— has been that rewarding. Most hard things are actually kind of pointless. But some are life-changing.
While Calculus did not change my life, it gave me the courage to do hard things that have changed my life. Practically, Calculus is “pointless.” But knowing that I am capable of understanding this pointless discipline has allowed me to learn complicated things that have a point.
(This isn’t a defense of Calculus, by the way. You shouldn’t take it; it’s terrible. Please pursue challenges that might give you a little bit of satisfaction.)
But the point is that unavoidable and pointless challenges—like Calculus—shape how we approach the challenges that are meaningful. How we respond to the impractical challenges of life colors how we respond to the practical ones. How we deal with conflict in the workplace influences how we deal with marital conflict. How we view our work colors how we view our friends. How we research for our History of Jazz paper alters the research methods for our honors thesis.
But I can already hear you arguing that we each have a limited pool of time and willpower. True. In an ideal world we would be able to give the appropriate amount of effort to the appropriate challenges in life. Our best efforts would be directed toward the hard things that have the biggest payoff. The ideal is to take intelligent risk without wasting any time. To not waste our time on things like Calculus.
While that sounds like a good idea, it has the unfortunate consequence of altering the way we view challenge, in general. As we make exceptions and caveats and distinctions between worthwhile hard things and pointless hard things, we develop an allergy to challenge. As we do fewer hard things, we grow worse at approximating the cost-benefit ratio of hard things. So we stop doing hard things completely. What started off as an aversion to pointless hard things turned into an aversion to any type of challenge.
Inadvertently, slacking-off in Calc 3, clarinet practice, Sunday School, pre-marital counseling, and gym class resulted in a life marked by slacking-off (which is is not what we wanted). We wanted to be intelligent about where we invested your time. We wanted to take calculated risks. We wanted to save our energy for the challenges with big payoffs.
But “big payoff” challenges do not present themselves to the picky. They present themselves to the doers-of-hard-things. The ones who keep running when the gym teacher turns his back. The ones who actually learn Calculus. The ones who study, write, and create because it is a privilege, not a duty.
Pointless hard things may not have a clear payoff, but they are worthwhile because they sharpen our attitude toward all challenge.
You Don’t Know What You Need To Know
The tension in modern education is between a vocational model and a liberal education model. The vocational student says, “Teach me what I need to know to do my job.” The student pursuing a liberal education says, “Teach me what I need to know to be a good citizen.” Both models are necessary and serve a purpose.
But for either of these models to work, a student must be willing to admit that he does not know what he needs to know. He cannot be the one that determines the course of his education, whether vocational, liberal, or a mix.
This is one of the major problems with higher education. Students have become consumers at the buffet line of knowledge. They have taken the duty of deciding what knowledge is worth their time. They have taken “self-directed learning” in the worst possible direction.
So now, the cry is not, “Teach me what I need to know,” but, “What do I need to do to get a degree?” Colleges—rather than directing the course of learning and exposing students to hard things—have answered with, “I don’t know. You tell us what you need to know.” Hence, we have degrees comprised mostly of electives.
I say this to highlight that we live in a culture with an allergy to doing and learning hard things. We are not comfortable with the idea of not knowing what we need to know. We are frustrated by requirements and obligations that are not immediately beneficial. Our ideal lifestyle is not a strenuous one, but an easy one. An uninitiated one. An automated one.
But the best lives are filled with challenge. The best minds learn because they don’t know what they need to know. Some are thankful they took Calc 3, even though they can’t remember any Calculus.
So I encourage you to challenge yourself. To do hard things. To learn something that seems pointless or impractical right now. To shape your attitude toward challenge by seeing the value in pointless hard things. You don’t know what you need to know. You don’t know which challenges will have the big payoffs.
Pointless or not, hard things are still worth doing.
What pointless, hard things have made you into a better person? Is there a seemingly pointless thing you’re avoiding to your own detriment? Share your experience in the comments!