Vectors

Vectors

I got thinking about how people often refer to their significant other as their other half, or sometimes their better half. It is kinda cute, I’ll admit, but for me, I just don’t like how it implies that we are all incomplete halves until we find the other half to complete us. I do believe that the right people can complete a part of you, but just something doesn’t sit right with me about the idea of being incomplete without another person. I like the way it’s phrased in the song “By Chance (You and I)” by J.R. Aquino with the lyric below:

“Could you be the other one so we’d equal two?”

Here, it implies that both parties are complete on their own, but together they become something more. I personally find that approach more meaningful, that we’re all whole, but we can add another person and become more than what we began with. That brings me to vectors.

To any readers who have not learned about vectors in a maths class or have forgotten about them, I’ll try my best to explain. Vectors are quantities that have both direction and magnitude. Basically, they can be visualized as arrows in space. When you add two vectors together, it’s like putting the start of the second arrow onto the end of the first arrow and then drawing a new arrow from the start of the first arrow to the end of the second arrow. When both vectors are facing the same direction, the magnitudes add up like scalar values in normal maths (1+1=2), but in most cases, the magnitudes won’t add up that neatly. In fact, if say both vectors have a magnitude of 1 but point in opposite directions, they add up to 0.

I like to imagine relationships between people, whether romantic or otherwise, as vector addition. With the right people, you’ll both or all face the same direction and add up to something bigger. Each person is a complete and whole value, but together, they add up to something greater, maybe not always 1+1, but they still add up. However, sometimes you’ll meet someone who will subtract from you, a vector pointed in the opposite direction. Maybe they won’t be pointing in the exact opposite direction and make you zero, but you still subtract together. What then? I think that’s where we symbolize the relationships that don’t work out, like an old friend from high school pursuing their dream in an opposing direction to yours or your significant other becoming more of a negative impact on your life or a family member going down a path you can’t follow, etc. In life, we’ll find people who will point us in the right or the wrong direction, and it’s up to us to choose whom to add or subtract from our lives.

So then, as some math nerds reading this might thing, what of the vectors that don’t necessarily add or subtract but instead come out with a magnitude still close to 1? This is where I think the analogy starts to get interesting beyond love and romance. The way I see it, I find these vectors to have the most significant effect on our lives because they can turn you towards a different direction without taking away from your magnitude or adding to it much. These are the people in life you may encounter with whom you have little interaction but these interactions can lead you to where you need to go. Still following? Because the analogy is starting to break down and become more abstract, but I’ll try to keep it together.

In my own life, I can likely name a few people who pointed me in a different direction without knowing it. Some of you reading this, especially the ones who were sent the link to this blog early on, might even be those people. In time, I would find my arrow aligning more towards those people, though turning away from those I haven’t seen in a while. These are the people that made me think more positively, opposite to how I was years ago when I was just a total bummer to everyone around me. I am infinitely thankful for the people who set me on the right path, and perhaps someday, I may find the other one who will add me up to two 🙂

There’s a lot more to this analogy I could add, but at that point, I’ll be talking about higher dimensional geometry and a bunch of other nerdy stuff that I don’t wanna bore you to death with, so I’ll end it here. Stay safe and happy, and I hope you too can find completeness!