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.
Wait what?

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.

Blasphemy.

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?

No.

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 X

^{2}, 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.

Thanks for the extra motivation to math this morning!

ReplyDeleteOf course! Glad I could help your motivation stay high. ^_^

DeleteIs it a bad thing that I'm reading this instead of doing my Trig homework? :P

ReplyDeleteAnyway, nice post. Can't say as my heart agrees with you, even if I know you're right. lol.

But guys. "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."

Algebra will never be the same.

Ever.

Ho-hum Brandon do your Trig homework. :P

DeleteHa, well it's hard to convince the heart and the mind to agree sometimes (well, technically make the emotional centers of the brain agree with the logic centers of the brain, but colloquial language is a thing I guess).

Ah yes, the classic tale. Also, if you get into higher maths, t starts to tag alone more often than z, so there's that odd dynamic.