Two Mathematics Concepts You Should be Thinking About

Mathematics is more than numbers on a page

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. 

Common Denominators

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.

Snowmen
In honor of the approaching winter, I give you these snow people. One of them is missing an eye. But still they have more in common than not.
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?

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Author: Angela Noel

Seeker and promoter of awesome people and ideas.

41 thoughts on “Two Mathematics Concepts You Should be Thinking About”

  1. Ha I would never look at you funny! I love these Maths analogies. They remind me of two phrases that I’ve heard in life & have really stuck with me.

    “We have far more in common than that divides us” The MP Jo Cox, that was sadly murdered last year said this.

    And a director that I worked with on a musical that was had a very multi-cultural cast, stood up in front of us before a performance one night and said “We are like a field of sunflowers. Each one of us is different, but at once, we are just the same”. I thought it was a beautiful way to look at it.

    1. I like both quotes. But I think I like the last one best. I agree, It is a beautiful way to look at it! It’s no wonder both of these stuck with you–1) because you are a wonderful person and it doesn’t surprise me much that these insightful thoughts would stick in your mind and 2) because they’re both articulated perfectly.
      Thank you so much for sharing. I am a better human today because you shared these simple, powerful words.

  2. I love how you’ve blended math and philosophy, or possibly psychology or sociology. Interesting concepts when applied to everyday interactions. Your mind is amazing!
    From school, I learned something they don’t exactly teach – social skills are the most important thing. If you’re friendly, but not a pushover, you set yourself up for happiness, and you increase your chance of having successful relationships. Maybe a little Prisoner’s Dilemma is mixed into this, but it works. 🙂

    1. Thank you for the thought! I think you’re right though, being friendly and having good social skills matters so much–but giving in too much is like falling into quicksand. Striking the balance, having boundaries without having impenetrable walls, makes such a difference. Thank you for sharing!

  3. I am impressed with the way you make connections that are obvious only after you point them out! I see the world like that, as a web or net or tapestry, connections joining everything… but some connections aren’t so easy to spot. Thank you 🙂

  4. I love the math analogies, Angela. It is a great reminder that we humans have far more in common than we realize as we struggle to live our lives the best we can. And I relate to the concept of finding more than one path to achieve the same result. My husband will start to drive somewhere and I’ll ask where he’s going. He’ll reply that though he knows this isn’t the route I would take he will get us to the same destination. And he does! And I have to laugh at myself for being so rigid I only saw one way to get there.

    1. That’s a great example! Thank you for sharing it. I think others could relate to your experience with your husband, including me. Kudos to your husband and you both for seeing the laughter in it. Great comment, thank you!

    1. I wish I had paid as much attention in French as I did to other subjects. I heard once that the difference between languages isn’t so much what can be said, but what can be said easily. To me, that’s a way to recognize how different cultures value different things. I don’t have enough knowledge of French (or any other language for that matter) to see what insight there might be there, but I’d sure be interested to know more! Thank you for reading and adding your comment–if you have any thoughts on your remembered French, I’d love to hear.

  5. I love these maths analogies. Honestly, I wasn’t quite expecting the way you’d apply them to daily life, but they make so much sense!

    I love the one on the lowest common denominator. If more people thought this way, I’m sure we could make the world a better place!

    1. I find the common denominator idea so useful. Every time I’m tempted to judge someone else, I try and remember we are much the same–judging him or her is just like judging myself. It doesn’t always work, but it helps a lot! Thank you for sticking with the post and reading all the way through.

  6. Some say the universe is governed by mathematics and its extension in physics. I rather think this post is trending toward proof of point. Often there are many routes to find the same answer. Considering most people I know on here area not interested in differences, but co-join in matters that affect us all and things we all consider to actually be important. Life is too important to let it slip past grumbling and muttering about things. Back to maths; solutions not problems.

    Wonderful post Angela

    1. Thank you Gary! Knowing your science background, your comment means a lot! One of the thing you made me think of is how scientists engage in discovery. It’s not a race to be “right” so much as it’s a race to learn what helps explain the complexities of the world. I love how when a new insight is found, the rest of the scientific community says, “Hm. Interesting, I want to learn more and see if I can see what you’re seeing.” That to me, is a true model for living.

      1. Agreed and there are many ways to lead lives too. I just get frustrated when I look around and see how many people are blinkered, believe everything they read in papers or see on tv. It’s so unmindful, science relies on critical appraisal, challenge and progress. People need to apply the sane ethos to self improvement. We might have a chance then of sensible democracy, stopping the bubble attitude and making some way forward into tackling issues that affect climate and trash. All these things go into that true model of living.

  7. You should be a homeschool teacher, Angela 😉 And, this is what kids crave, whether they go to a public school or are homeschooled. They look for how ideas pertain to real life. Once they see this, they retain their knowledge. This is what I strive for now in our homeschooling journey – meaningful connections. I have to admit, I remembered both math concepts after reading your post, but I haven’t thought of them between learning them in school and now. However, I do believe they will safely be retained now that I have read your post. Thanks for more beautiful thoughts and words, and for teaching me a little something. 🙂

    1. What a lovely comment! I think you’re right, there isn’t a lot of room in a typical school environment to make these kinds of connections. It’s in all of us to see these things, I believe, we just need something to fan the flame–just like you’re doing with your kids. The meaningful connections make such a difference to living a wholehearted life. I love your approach of continuous exploration and connection.
      One of my favorite is still the cross-country trip when you guys went digging for diamonds (if I remember correctly)! I wanted to include that in one of my “Awesome Nuggets” round ups, but I didn’t know you yet, and Jake wasn’t around so I could ask him if he minded if I mentioned the adventure–so I left it out. But I still loved the story and it was definitely an “awesome nugget.” 🙂

      1. Well, if you ever feel the inkling again, please feel free to use our digging for diamonds adventure as an “awesome nugget”. It was quite the experience – and the history behind that park is just as amazing.

  8. And, yet another example of why I love your writing! You do have a beautiful knack for making patterns out of chaos….

    1. Thanks, April. I don’t know if all this stuff is taught in every curriculum, but I know I learned it again in college when I took Logic (in order to get out of the formal math requirement.) It’s funny to me that I shy away from mathematics, but still love the concepts and how they apply in different ways.

        1. Well, I must say she stinks. I’m sorry to say that about anyone, but a teacher that tells a student she’s useless should rethink her calling. I’m glad you believed in yourself and did it anyway! I can tell from your writing and all the research you do, you are not one to give up easily!

          1. I certainly wanted to show her that she was wrong, so I did work very hard and I did well in my O’ Level exam. I don’t see the beauty in maths that other members of my family do, but I’m not frightened of numbers or fractions and I know what to do with them.

  9. Absolutely loved your post. Great concepts and how they come to life, isn’t it? If we all can think of a common denominator, the world would be a peaceful place. <3

  10. Okay, I was really scared because, well, math was my least favourite subject. But I read through and have got to say, even with a subject as feared for me as math, I found a common thread of life. Thanks 🙂

    1. Hi Jen! Thank you for stopping by and taking the time to read it. I wonder why so many of us didn’t love math (or maths for my UK friends)? How it’s taught today is so different than when I was in school. I hope the next generation can find these kinds of connections more easily. Maybe, just maybe, if my teachers had helped me connect principles more directly to life I wouldn’t have been so intimidated by the numbers and formulas themselves. Thanks again!

  11. I really enjoyed this post. I’m still a “numberphobe” (can’t even touch-type numbers on the keyboard). Whatever prejudices or judgments we have of others can be overcome simply by knowing, talking with, and looking into the their eyes. We prejudge what we do not know. So, let’s get out there and share a smile with strangers. It’s wonderful how most will smile back. It’s a common denominator.

I love hearing from you! Please share your thoughts.