Life and Math: A Dynamical Perspective!

Intro:

Math has bled into my life so much that over time my perspective has been increasingly shaped by that in some pretty entertaining ways, and also some crucial ones. Ha, changes in a system over time, if that isn't the essence of dynamics then I don't know what is!

Part I:

This universe is a system. The world is a system. Life on this planet is a system. Humanity is a system. You're a system. I'm a system. We're all systems. We’re all part of bigger system.This is where dynamics kicks in.

I am impacted by this person, that person, this event, that event, so many variables, so many factors. The matrix that is life gets huge, and is tough to solve. I don't think anyone knows how to solve their own system let alone the infinitely many other systems out there. That’s okay though. The journey of trying to figure that all out is important and amazing, albeit stressful at times. That too is okay.

Part II:

In math there are the concepts of eigenvalues and eigenvectors and for a time they actually confused sometimes. Even now, I have to constantly remind myself what they actually are. I have to dig deep each time.

I can use them, I can tell you some things about them, that was always the case. I think knowing what eigen means helps me to remember things. That kind of reminds me of the crucial elements of what an eigenvalue or eigenvalue is, ha in some cases eigenspaces.

We take eigen to mean proper or characteristic. And an eigenvalue would be a proper value, or characteristic value, with the latter nomenclature being more prevalent these days. In german eigen means own or self, very appropriate, no? The thing is eigenvalues and eigenvectors are very important to dynamical systems, specifically continuous ones. Alas, I digress.

Part III:

The magic of dynamical systems is that we don't need to know the solution to a system to say something about it. We can find ways to observe behavior, and make predictions, usually accurate ones without having to actually solve the system. We can talk about the solution and how the system behaves, again, without knowing how to solve the system.

How do we usually start to approach dynamical systems, well we usually are finding eigenvalues to say something about the system. Isn't that great? How fitting is that to life? To figure out a system, we needn't solve it, we needn't know the answers so to speak. No we can say something about the system, our system, by figuring out our self value(s).

There are layers to this. In life, at best we get a typical continuous system and we can understand it reasonably, despite some hardship. At worst, we have stochastic systems, totally random, based on probability, but yet we can still say something.

More realistically, I feel like most systems are chaotic ones. They are dynamical, we can draw conclusions and usually solid ones. But the systems are subject to small disturbances that can change how they behave drastically. Things can change in an instant. Yet we can still reasonably adjust and still make predictions, we can adapt, we can at least see some way to change.

Conclusion:

Math is beautiful to me. It is the language that we speak about the universe in. People always say it's about numbers. That is true to an extent, but those numbers mean something. They have symbols, they convey a message, they are representations of things that exist in the real world, a way to describe things. We can say something about the past, the present, and the future with them.

Math is about language, communication, representation, systems, relationships. Math is about everything, a different way to look at the universe. I want to change the narrative about math over time. I have been doing a lot with that, and I am proud of the results so far.

With that, I leave my ad for dynamical systems!

https://www.youtube.com/watch?v=tu2HkdAElGg