Paarth Madan

A medium to iterate on my own thoughts.

Basis Vectors

Posted at — Jun 16, 2020

A vector is a concept I’ve come across in mathematics, physics and computer science.

It also has parallels in biology, business, literature, and further – a list that’s certainly non-exhaustive.

In any case, one of the beauties of a vector, at least in the contexts I’ve explored it in, is it’s ability to be represented by this duality between the basis vectors.

A vector is an element that’s part a space. Think a point in a coordinate system, or an arrow in a plane.

In any space, a set of basis vectors can be defined, such than any other vector can be represented as a combination of those vectors.

I find the concept is really beautiful. It appeals to nature as I know it, and aligns well with the universe.

I like to think of these bases possessing that innate yin and yang quality.

A balance.

A relationship.

Basis vectors are a set of vectors that are not parallel. Usually, they’re orthogonal or perpendicular, but what’s extremely comforting is that they don’t need to be.

So long as they’re not parallel with one another, they can take on any relative angle, and all vectors can still be represented by a little bit of each vector.

I think there’s a strong parallel between vectors, and us, as people.

We all possess certain personalities and characteristics, and that too, varying amounts of them. Think of these characteristics as your basis. They don’t need to be in complete alignment for you to take on any value in the space we call the universe.

In a trivial example, if every person was composed of a “physical” vector, “mental” vector, “personality” vector, “knowledge” vector and “experience” vector, and your life was the vector that was the combination of these bases in the space of life, then I propose you can land anywhere in that universe.

You just need to tweak how the basis vectors are scaled. There’s comfort in knowing that there certainly exists a combination of the bases to get where you want.

It’s easy to limit yourself based on your traits, or seemingly unchangeable circumstances. Vectors teach us that so long as you have a diverse set of bases, regardless of how small or large, you can scale it to get to the desired outcome.

What these basis vectors are for us, is an infinite set of characteristics that make you, you, and me, me.

It’s not helpful to think about the actual vectors, rather internalize the notion that regardless of what they are, there is a way to navigate the space.

A personal (and trivial) example, is my tendency to think I lost in the genetic lottery, because of my weak, small, wrists and limbs. I can’t lift as heavy, as the bottle neck to most of my lifts is my wrists. My chest can handle more weight, but my wrists can’t. If we think of wrist strength, and chest strength as two vectors, and how much I can bench as the final outcome, regardless of what values those basis vectors take on, there is a way to represent the desired outcome.

Of course, that example has limitations, but the general idea is to adopt a growth mindset. To better understand that your basis vectors aren’t a limitation. What’s far more significant is the way you apply your scalars.

I think, what comes with this analysis, is a sense of liberation.

It’s a freeing to think there’s an innate quality in mathematics, that is conducive of so much flexibility.

Mathematics is often viewed as rigid, but most of the founding principles suggest it’s the opposite.

Extremely fluid and flexible, just like our lives.

It’s up to you, now, to determine where you want to end up in this space of life. Choose that final vector, and the scalars will figure themselves out.

I think this post is far more beneficial, for those who have an existing understanding of vectors. I’m no professor, so I wouldn’t (or haven’t) done the subject matter any justice.

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