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The Common Denominator



You know something I hear a lot from people that really grinds my gears?


"I'm the common denominator"

Now, don't get me wrong. It's not the math reference that's upsetting. But it just doesn't make any sense to me from either an accuracy standpoint of the metaphor or an emotional standpoint from how our lives are actually lived. In defense of math, people, and life experiences everywhere, I am here to change your mind about this expression forever and give you a new math metaphor to explore.


Now, if you haven't touched fractions since 5th grade, let me run you through the basics and give you some definitions that might be helpful. The denominator is the bottom number in a fraction and the numerator is the top number:

2 = numerator

4 = denominator


When you are adding or subtracting fractions, you need to find what is called the "common denominator" to make the numbers able to be added/subtracted (or even just more accurately compared).


2 + 2

4 7


What is the sum of these fractions? Which is bigger? Who knows! In order to solve this problem, we need to translate these fractions into the form of a common denominator: a shared bottom number. This is a mathematical process of making two different fractions "match" by changing them for the purposes of comparing/adding/subtracting. The easiest way is to multiply the two denominators by each other to find a number that is divisible by both denominators (4x7=28). For the sake of the problem above, putting those fractions in common denominator form changes the problem to look as such:


2(7) + 2(4) = 14 + 8

4(7) 7(4) = 28 28


By finding the common denominator, we can now accurately compare these fractions for size and add as needed. The common denominator is merely a number used to help compare two different fractions more easily. So on a most basic level, when people say "I am the common denominator" regarding their life experiences, they are using an inaccurate term.


If we could put this into human terms, it would actually be quite useful. Was my 2/4 or their 2/7 the bigger problem? Hard to tell when we're comparing 4ths and 7ths. Finding a common denominator would give me better precision in saying, "ya, all things being comparable, I was 6/28th more responsible for the break up than they were." Buuuuuuut we cant do that with humans in the way we can with neat, understandable, math!


What I understand people to *mean* when they use this expression is "things are going poorly in my life, and I am involved in all of those things therefore I must be the reason everything is shit. I'm the problem."

In what follows, I'll challenge you to consider is that:

1. There is no alternative to being involved in the problem

2. Math may just be able to swoop in and save the day!


Let's get started.




1. There is no alternative to being involved in the problem. The reason this expression/feeling is so commonplace is because unfortunately, we have no choice but to be involved in the situations in our lives. By the very nature of existing and being alive, we are involved in our life and the situations that happen to us.


It is true to say that I have been involved in every failed relationship I've ever had. By the nature of being part of that relationship, I am one of the variables in its success or demise. You know what is ALSO true? Whomever I was partnered with is ALSO involved in every failed relationship THEY have ever had. So literally every person on this planet can say "I was a part of every relationship/job/hobby/whathaveyou that has failed." It would be a strange and very different thing to say I have been involved in the dissolution of every relationship that all other people have had. Or that some stranger has been involved in every one of my failed relationships. See what I mean?


Now, to be even more specific, I also understand people tend to focus on the failure aspect of this story. People don't often say "I am the common denominator of all of my successful relationships, promotions at work, graduations, etc etc". I find that when people are in the space of feeling or saying this, they are looking for a reason that things went wrong. They want to have a clear, concrete, tangible answer as to why suffering is happening and be able to "fix it" so it doesn't happen again. Counterintuitive as it may seem, taking most or full responsibility for why things have gone poorly is actually a very common protective mechanism. If I'm to blame, then I can control whether or not I get hurt in that same specific way again! Makes sense -- except for the bit where that belief leaves us feeling like a garbage human who is incapable of getting things right and who is destined to #DieAlone. But aside from that!.....


So at this point, you may be thinking "well great, Lisa, now you've ruined my go-to, you've given me a math lesson, and now I have no recourse for when things feel like crap in my life." And I hear you...but wait...

Is that a bird? A plane?

Nay...

It's math swooping in to save the day!


As promised:

2. A potentially more *useful* way of working through these experiences where things have gone wrong can be to really look for: The Greatest Common FACTOR


Back to fractions:

2

4


You may be a total Math Wiz and have seen this fraction above and were maybe even a little judgy of me for having picked it. "2/4ths?" you say, "What are you a nube? That's 1/2." and you'd be right, my friend. If you remember your basic math, you probably easily spotted that the fraction 2/4 can in fact be reduced. Reducing fractions is a way of taking a bigger and more cumbersome fraction and finding what is the smallest, most manageable equivalency. This is done by identifying a number that can be divided by both the numerator AND the denominator.


2/2 = 1

4/2 2


The common factor of 2 only works because BOTH numbers are divisible by 2. Which means BOTH numbers share something in common that allows things to be reduced to a lower form. If we blow this up into a more complex less recognizable fraction, you'll see it starts to get more complicated:


45

324

If you wanted to identify the factors of this fraction aka the numbers that can be divided out of the numerator and denominator, you would identify the versions of "what x what = the number". This helps you find the individual factors.


45 = 3x15, 5x9

324 = 2x162, 3x108, 4x81, 6x54, 9x36, 12x27, 18x18


For each number, there are several options for divisible factors. BUT the fraction can only be reduced by common or shared factors.

45 = 3, 5, 9, 15

324 = 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162


The common factors for this fraction are 3 and 9 and while 3 can be useful, it leaves you needing to reduce multiple times:


45/3 = 15/3 = 5

324/3 = 108/3 = 36


The most expedient way to reduce this fraction is to use the Greatest Common Factor aka the largest number that can be divided out of the both numerator and denominator.


45/9 = 5

324/9 = 36


Got it? Phew. At this point you might rightly be wondering what any of this has to do with where we started and if I'm ever going to just get to the point. And yes, yes I am. Here we go.

Let's say I am a 24. And my last several relationships that ended were as follows:

12 8 16

24 24 24

Following my previous logic of "I'm the common denominator", this is a pretty bleak outlook.

"I can't change that I'm a 24! I can pretend, fake it, repress, or try to hide but through and through I am a 24. It's me, it's my fault, I'm just defective, it doesn't matter who I date, everything I touch turns to s***."


But if you've followed me this far, you know better. And you might be asking a fundamentally different and more interesting question:


"What is the greatest common factor in my unsuccessful relationships?"

12 = 1, 2, 3, 4, 6, 12

24 = 1, 2, 3, 4, 6, 8, 12, 24

8 = 1, 2, 4, 8

24 = 1, 2, 3, 4, 6, 8, 12, 24


16 = 1, 2, 4, 8, 16

24 = 1, 2, 3, 4, 6, 8, 12, 24


Each relationship is unique and has several common factors to that relationship but if you'll notice there are some variables that run all the way through but there is only one greatest common factor: 4.


So if I'm a 24, and keep dating 12s and 8s and 16s, that's a far more interesting puzzle and one that might actually lead to something useful for me. Given that I'm a 24, what draws me so strongly to people who are also divisible by 4? Put in non math terms: if I skew avoidant on the attachment spectrum and I CONSISTENTLY end up dating anxiously attached folks, the far more interesting and meaningful thing to explore is why on earth am I so drawn toward the *kind of person* who is going to divide along the same place as me.


Is it at least possible, that rather than:

"No matter who I date, it's all the same. I date different people but they always end. I'm just a garbage human and everything I involve myself in turns to shit"


that what you could be experiencing is


"I notice that "4" is a common thread in my diverse relationships/experiences. While I find myself being really initially attracted to people who have "4" trait, no matter how many other wonderful qualities we might have as individuals and what parts of the relationship are actually quite good, that "4" is often a relationship ending variable. Why am I not more attracted to people with a "5" trait?"

Can you hear how different that line of questioning, exploration, and resolution is?

I understand falling into the trap of old common denominator thinking and language. It's in the culture, it's easy, it tells a simple story and when we're hurt or grieving, we like simple. When I hear people saying "I'm the common denominator", what I actually hear is "I feel lonely, hurt, confused, and want to prevent myself from being hurt again by avoiding intimacy altogether by making myself the whole problem." And I get that. You may need to spend some time here in your recovery process. But whenever possible, see if you can make the shift to a more accurate and useful frame:


"I want to understand more about this common pattern I find myself in so that I can determine the factors, find the common factors, adjust, tweak, try, and learn how to avoid existing in an avoidable pattern in my life".


Fortunately, you don't need to go to a mathematician to work on this. Unfortunately, this work isn't as clear, clean, and neat as the math version. I wish everything about our brain and emotions could be laid out neatly on graph paper or a spreadsheet to be analyzed and reworked and rewritten without having to live it. But if you'll refer back to point number

1. We have no alternative to being involved in the situations in our lives.


This whole "life" thing is messy. To live it is to struggle, explore, try, fail, try again, get hopeful, feel defeated, get lost, find clarity, rinse, repeat, over and over. But when you are open to looking for and identifying the greatest common factors to your dissatisfaction and unhappiness, things can get significantly easier.





Thanks, y'all!




Lisa






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