Life is like a sine curve . . . or maybe a fractal

Guest post from my friend Denise. She is a mathematician and I am proud to call her friend.

Nerd alert. . . nerd alert. . .

Most of you should skip this post. You will probably think I am nuts (which I kind of am). In fact, I probably won’t even publish it. But what can I say. I am a mathematician. And a Mormon.

Several years ago, I was multitasking, or trying to, with a toddler clinging to my leg and whining. And as usually happens, absolutely everything that could go wrong right at that moment, did. I can’t even remember what all was happening, mostly because this exact same scenario has played again and again in my life. And as I thought to myself, what the heck!? Why is everything here happening at once?? I had a sudden realization: life is like a sine curve! Or more specifically, my life is like 6 sine curves, all colliding at once!

A sine curve looks like this

You will notice that it repeats, over and over. It never goes higher than 1, and it never goes lower than -1. It is rhythmic.

So my life, or more particularly, the circumstances in which I find myself, tend to be somewhat sinusoidal. I know; it’s not rocket science. Life is full of bumps, ups, and downs. But why, might you ask, does it have to go down? Why can’t we all be up all of the time? Because we’d be bored! Really! We are eternal beings, and we tend to be happiest when things are improving. We are designed to progress; Heavenly Father created us that way. And hopefully in our own lives, we are progressing. But the circumstances in which we find ourselves are finite. We live in imperfect circumstances. It is like viewing a graph on a graphing calculator. The world itself is not improving. The range (low to high) is only -1 to 1. That’s all there is. So in order for us to be happy, the situations we deal with have to vary a little bit. Sometimes things seem to improve, and then suddenly someone throws up at 2 am (no, I’m not paranoid. . .) But that low point enables us to later on climb to a high point, and that’s the fun of it!

So the thing about sine curves is that when you take several (particularly if they are on a different cycle, or period) and add them together, you get an interesting effect. You get a curve that seems kind of random, although eventually it will repeat itself. And it cycles lower and higher than the usual sine curve — and with seemingly less regularity:

The green curve you see is the addition of the red and the blue one. You can see how it changes a bit. I call this having a family. Taking two (or more!) different sine curves (lives!)and adding them together, you get the potential for both greater highs, lower lows, and a more unpredictable and interesting curve (so that’s more joy, more heartache, and a crazy but much more wonderful life!)

So you can see where I’m going here. Sometimes, when you have 6 different sine curves, all with different cycles, and you add them all together, sometimes everything possible will happen to frustrate and annoy you. . . and then other times, everything will be amazing! But without the lows. . . we’d never reach the highs!

Well, tonight I was watching a Nova about fractals. And I have to add to this little comparison that our own individual actions are more like fractals than sine curves. What are fractals, you ask? Let me show you:

This is a Koch Snowflake. You make it by starting with a triangle, erasing 1/3 of each side, and drawing a new triangle in it’s place. Two important things to understand are iteration and self-similarity. You repeat the same action over and over to create the shape; those are called “iterations”. And the final shape is self-similar. It looks roughly the same on any magnification. If you zoom in on any small part of it, it looks pretty much the same as the whole shape. Got it?

Here’s another one that looks a little more beautiful.

So fractals occur everywhere in nature. Broccoli. . . coastlines. . . blood vessels. . . mountains. . . clouds. . . it’s endless. They are particularly interesting because they give mathematicians a way to model, or describe, behavior that previously seemed to be random. Organic things can now be described by mathematical equations, and that is really cool!

As I think about my life and the patterns that I form through my behaviors, I am led again to think about fractals. Sometimes it seems that my life is somewhat chaotic in nature. Day in, day out, circumstances and reactions vary wildly. Sometimes I go to bed on time. Sometimes (usually!) I don’t. Sometimes I manage to keep the house pretty clean. More often, it’s pretty lived-in. Sometimes I feel in control. Sometimes. . . well, you get the picture. But for me, it is useful to understand the daily fluctuations and patterns of my life in terms of a fractal. If I step back, I can see that the basic shape of my life is pretty much the same. It repeats, over and over again. Things that I think are random and really repeating. And through my small choices, I am slowly determining the pattern that the entire shape will take.

This is important to me because of two major things. First, it helps me to understand the nature of the pattern that I’m in the middle of. It’s ok that some days are crazy and others are quiet if I understand that there is an overall pattern here. What’s the difference? Understanding life’s ebbs and flows changes the way that I swim. I used to like to go in the wave pool at Raging Waters, but trying to swim straight across the huge waves is really hard. It’s much easier to “go with the flow” — jump with the waves and let them carry you.

Secondly, and perhaps more importantly, I can change the shape of the overall pattern by changing the shape of each small iteration. That’s why the scriptures tell us that out of small things proceed that which is great. I have a quote on my fridge right now that says “Enjoy this moment, for this moment is your life.” This is a true statement! The moments define the life. The pattern that we see on a small scale repeats on a large one.

For me at the moment this gives me comfort. As an eternal being, I cannot control the circumstances in which I find myself (i.e. the viewing window of my 6 sine curves). But what I can do is improve myself. I can change the patterns of my life on a small scale, and as I repeat them over and over, I will see a greater shape emerge. I control the final shape that I get, not through any great act, but by the small and simple things. What a concept to understand!

I believe Einstein said that mathematics is the language with which God wrote the universe. I guess this is what is amazing to me — that it doesn’t seem to matter what I am looking at, math underlies it all. Yeah, I’m a math nerd. But if math can help me understand the things I see and experience every day, then I will continue to use it as a tool.

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