By Angela Noel
October 26, 2017
I have two favorite mathematics concepts. That sounds weird, I know. I’m a communications and writing major, an author and a blogger, but I’m also a collector of mental oddities. I find little scraps of interesting tidbits from all kinds of places and add them to the museum of my mind. The scraps can come from anywhere, a technical specification, high school algebra, Nietzsche, an ad on the radio, or a quote in a magazine. I pull them out to illustrate ideas, as either analogies or examples. Most of the time, they’re useful little tools, bringing context to complexity. Sometimes, they confuse people. I hate it when that happens.
Hopefully, this isn’t one of those times. Because these two concepts form so elegant a metaphor for life and human interactions, I can’t resist sharing them with you.
Mathphobes, please keep reading. I’m not about to amaze you with knowledge of multivariable calculus–mainly because I don’t know the first thing about it. These two little gems I learned in my first fifteen years, and you did too.
I’m guessing though, that many of us left these things buried where we hoped never to see them again: in the textbooks of our youth. But, maybe I can change your mind about their usefulness and application in daily life.
Fractions are a part of our daily lives. You can’t read a recipe without dealing with fractions. Kids learn how to reduce fractions by the fourth grade, but even before then they know how to add and subtract when the denominator is the same. You need the same denominator (the bottom number in a fraction) to be the same in order to add or subtract it. So what makes the common denominator one of my favorite math concepts?
When I think of the world and how separate and distant we all feel sometimes, how people look at differences rather than similarities, I wonder why. Why is it that we don’t see the humanity in the person we’re shouting at? Why is it that it’s so easy to make somebody who looks different than ourselves into the enemy (implicitly or explictly) when really, he or she is more like us than not?
In these moments, the common denominator helps me. Maybe we disagree on politics, religion, music, and art. But what do we have in common? What’s the ONE THING that unites us both? Maybe it’s the smallest of things: we’re both wearing pants today. Or maybe it’s something bigger, like we both love our kids and want the best for them. Whatever it is, by finding it, we can add our two disparate selves together and figure some stuff out. We can make our two fractions into something bigger and better if we find what’s common among us.
Finding the common denominator is a starting point to finding our connection points as human beings. I think we can do this more. I know we can.
The Transitive Property
My second favorite mathematical concept is a bit more advanced. It comes from the world of algebra and logical reasoning. Most of us took algebra in junior high or high school. We learned a group of truths called, “properties.” These properties allowed us to take one value or numerical expression and manipulate it in different ways in order to solve a problem.
My favorite of these is called “the Transitive Property of Equality.” It states that if x=y and y=z then x=z. So if I know the value of x, then I also know the value of y and z, because they’re all the same–they equal each other. The beauty of this property is not only in its simplicity, but in the name itself. It fundamentally tells us that things that don’t necessarily look the same at first glance, can still equal the same result.
Our relationships to each other and our world are similar. Many roads, for example, lead to truth and wisdom. Many of us would say our road is x, and assume that the only way to get there is the way we know best. But that’s simply not true. The way we arrive at joy, peace, and wisdom isn’t nearly as important as the fact that we DO arrive. Looking different, being different, acting different, does not assume that we are, at our core, fundamentally different. As we can see from the finding the common denominator, we are more the same than not. And when we realize all the things we have in common, and see that our pathways toward a meaningful, creative life might be different but lead toward the same thing, we suddenly begin to understand.
The glorious chaos of our universe and the miracle of existence might be explainable in formulas and numbers, but those same insights we name– these mathematical concepts we consider immutable and true–are as likely to describe and unravel truths about ourselves if we only allow them to.
Yes, I do have two favorite mathematical concepts. I use them in general conversation fairly often. Every once in a while people look at me funny. I hope this isn’t one of those times. Remember, you’re more like me than you aren’t. I can do the math to prove it.
Your turn: What things do you remember from your schooling that continue to be useful in your adult life?