I realize that my audience is mostly writers. I also realize that math can be a sensitive subject for writers. However, I’m going to tread through the landmines and attempt to talk about it anyway. LIAA today is going to take a different turn than usual.
I’m gonna get persuasive on you.
Sorry about that.
In short, I’m here to convince you that math is actually an art.
Goodness did I already lose? Or can I try anyway?
The Purpose of Math
Everyone reading this can probably do math. If you know how to read, you also know how to math because basically zero school teach only reading and no math. Even if you can only add simple sums or do basic multiplication, you can math. Or maybe you went all the way through algebra and geometry. If you’re an overachiever, you took pre-calculus or trigonometry in highschool. Good for you.
In short, educational institutions ensure your basic understanding of math. Some of you can do more than others. You smart people, you.
Myself, I’m currently taking Differential Equations, which is basically Calculus 2.5 (because for some reason, they decided that you take it before Calculus 3, but it’s not Calculus 3… I don’t totally understand it either, it’s okay). Recently, I had to write a rather short (1,400 word) paper on the following prompt:
“Can differential equations be used to predict the future?”
I don’t have time to go in-depth into what differential equations are and what they do, nor is this blog the place for me to give you a 1,400-word essay that answers the question, so let me sum up: differential equations are models that involve rates. Acceleration is a rate, for instance, as is velocity (speed). Population growth, flow of chemicals into a vat, airflow around the wings of an airplane, pollution change, climate change, weather patterns, and many more physical phenomena can be “modeled” by these equations, and they’re often quite complicated.
Because they model rates with respect to time, many of these equations can predict values for future times. When you watch the weather, what you’re really watching is a visual representation of a differential equation which is a mathematical representation of change air pressure and moisture movement.
Did I lose you yet? Did you fall asleep? (It’s okay if you did… I’ve almost fallen asleep during my class… whoops.) I mean… what is the point?
It might be obvious that people like me (engineers, mathematicians, scientists, etc.) need to know math, but what about the normal people, the people who don’t have to spend their days modeling weather patterns or stress balances on bridges? Few writers need to know how to derive acceleration from velocity and use it to determine the impact experienced by a skydiver given the size of a parachute and the skydiver’s weight. We writers don’t need to know calculus to write books.
Let’s not even go all the way to calculus, let’s stop at algebra and geometry.
X and Y. Proofs. Sine and Cosine and Tangent and those other three we don’t talk about, and the six hyperbolic functions no one really knows about. What is the point of these stupid things? I mean, who cares if the triangles are congruent by the Side-Angle-Side theorem and that the two angles are congruent by virtue of their being exterior alternate angles of two parallel lines cut by a transversal?
I’m not even sure what half those words mean, so what good are they? I mean, we can just as easily take a rule out and measure the sides of the triangles to show that they’re the same, if eyeballing isn’t enough.
Not to mention X and Y. They’re like a pair of long-separate lovers, always trying to find one another and the solution to one is always related to the other. Turns out algebra is basically just a sappy love story about two characters who struggle with their identity and somehow end up together by the end. If we’re lucky, there’s an occasional love triangle happening with Z. Yay.
I don’t know about you, but my daily life rarely consists of comparing triangle sizes and finding X and Y. I dunno, maybe your day does. If so, great, good for you. The rest of us, however, may not see a point in these maths. Are they made for their own sake?
To tell you truthfully, there are three basic sets of math: foundational math, cornerstone maths, and application maths. Everyone takes foundational math. If you’re in school for more than a year, you take foundational math. Elementary math. Your basic sum and difference and multiplication and division, with fractions and decimals on the side. Geometry and Algebra and pre-Calculus are all cornerstone maths. They are based on the foundations (and without the foundations, you’d fail at all of these), and provide a strong support for the real maths.
What are these real maths I speak of?
See, most people stop there. When they go to college, they’ll take college algebra or pre-Calculus or “Math for the Liberal Arts” or maybe an intro to statistics. Except… the point of math is missed.
To truly understand and realize math’s potential, you can’t stop two-thirds of the way through. You can’t lay a foundation and slap a cornerstone at each corner and call it a house. If that’s all you do, you’ll complain when the rain gets you wet. Don’t blame the math you’ve taken; they’re doing their best.
So what are the application maths?
You’re not gonna like it, but they’re the hard ones. Calculus (all of them), Statistics (like actual applied statistics, not just learning how to push buttons on a calculator and copy the solution), Stewardship/Accounting maths, and the maths beyond constitute the application maths.
Here we find the true reason why people hate math: they stop too soon. When you stop before you finish the house, you’ll be unsatisfied with the results.
The purpose of math is to build an array of tools until you finally have enough to tackle the complexities of life.
Art in Math
Good art tells a story. I once gave a persuasive speech on art, and how all true art tells a story. Again, it’s essentially a 1,400 word essay I don’t have time to share. Let’s just assume that I’m right (I realize that this is a huge assumption, but bear with me), that art tells a story. I also claimed above that math is an art.
Well, based on the idea that art tells a story, is there art in math?
I say yes.
All story-problems aside, where is the story in math?
Consider the following equation:
(note: all equations written in Mathcad Prime 3.1)
This is a simple equation. It may look complicated, but when you solve it (thanks, calculus 1), you find a simple numerical answer: 2.773.
Where did I get that answer? What does it mean? Why does it matter? How is this art? How does this tell a story?
One of the points I made in my speech “what is art” was this: sometimes the story is behind the art, instead of the art itself.
Let’s consider another equation:
Can I solve this one?
There is no answer. Or perhaps there is every answer.
Now there’s an interesting story. Because if you were to replace X in the denominator with X2, you’d find that the equation is equal to 1. One.
Where is the art? Enough of these weird examples, where is the art? Sure, we can admit math has purpose, but art?
I find the art of math in the stories you can tell with numbers. The stories are abstract, they’re hidden beneath weird squiggly lines and Xs and “dx” and that scary infinity. The story of math isn’t a traditional story. It comes from the beauty in natural patterns. You find the art of math in the way it flows through every part of our lives without our conscious awareness. It’s in the subtly that math possesses when it interacts with you.
Let’s conclude by going back to differential equations. This interesting (and slightly tedious) section of math is all around you, all the time. It’s manifested in the way you breathe, in the way your heart beats and the way your muscles and tendons and bones react to impact. The neurons firing in your brain that enable you to read and comprehend (at least somewhat) this sentence flit through the realm of math.
You are surrounded and engulfed in math, even if you don’t know it.