After this essay, you’ll hopefully know what a fractal is. We’ll use this whole fractal thing as a metaphor to understand how we can thrive in complexity.
I left us hanging in the last essay with an introduction to the fractal yin-yang. This is a model I created many years ago, and I think it’s a helpful way to understand what’s going on in our world.
Any duality generates conflict, and interdependent polarities usually create really sticky situations. While that may seem like an oversimplification, almost every conflict is a tension between freedom and limits, self and other, or us and them. Two sides of a conflict are united in a system generated by a question, problem, or decision that needs answering.
In the famous yin-yang symbol, there aren’t just two sides: It also has a curvy line in the middle with dots on either side. The symbol reminds us that nothing is simple or purely one thing or the other, and there’s always a larger perspective at play. In conflict resolution, we call this taking the third perspective.
While the yin-yang is one of my favorite symbols, its simplicity doesn’t do justice to the complexity of what we’re facing. The yin-yang makes sit really easy to imagine we’re in a battle of good versus evil or right verus wrong.
The truth is, this is much more nuanced and complex. The decisions of every individual create our political conflict, so it’s a complex system. This is known as an agent-based system in complex systems theory.
Quick shout-out to Steve McIntosh
Steve McIntosh wrote a book called A Presence of The Infinite, and he’s also a political philosopher. He’s also the author of Developmental Politics, which I highly recommend. Steve recognized that the fractal yin-yang is an excellent way of explaining aspects of our society and human experience.
Thank you, Steve, for the inspiration. Steve and I have talked about this before, and we’ve been bitten by the same muse. But even this fractal yin-yang doesn’t quite capture what I’m thinking about. We need a more detailed and nuanced perspective.
This is a small part of the most famous fractal, the Mandelbrot set. This complexity looks wild, but it is not random: It’s the computation of a very simple algorithm.
Let’s talk fractals
So, fractals were invented by Benoit Mandelbrot in 1975 while he was working at IBM. Fractals are an amazing mathematical discovery, but they also help us understand features throughout the natural world. Fractals reveal that some things we thought were wild and weird are created through a straightforward, replicable system. This understanding is tremendously helpful.
Before discovering fractals, Mandelbrot was interested in how long the coastline of England is. It turns out that this is a tricky mathematical problem. If we used a mile-long or kilometer-long measuring stick to measure a coastline, we would lose a lot of detail. Still, it’d be a lot quicker, and we’d get a sense of the length of the coast.
If we went with a yardstick or a meter-long stick, we would get a much more detailed understanding of the coastline length. If we went with so much detail that we were actually looking at every grain of sand, it would begin to look infinitely long.
This feature is an essential part of what makes a fractal a fractal. This is roughness, and Mandelbrot has a great video that I encourage you to check out. Roughness is a fascinating concept The world is wiggly, rough, and textured, and now we have a way of explaining it mathematically.
I’m going to use a three-part definition of fractals to explain this fantastic discovery.
1. Fractals are self-similar at all scales
Look at the collage of these blood vessels, lightning, river system, and the tree. Each of them looks similar to the other, and any of the little small branching parts look similar to the larger part and the whole thing. That is what we mean when we say something is self-similar at all scales.
This is true with conflict: Conflict between a few people looks similar to conflict with many people, and it also looks similar to conflict on a much larger scale.
Another excellent example is romanesco broccoli, a hybrid of broccoli and cauliflower. It’s even known as fractal broccoli. With the romanesco, you can see that each of the little spiral nodules looks like the whole thing, and it’s made up of baby spiral nodules that look like the bigger ones.
2. A fractal comes from the repetition of a recursive algorithm
Here’s the recursive algorithm for the Mandelbrot set. If you have some mathematical trauma, don’t worry; I can explain it.
The only thing you need to understand about this formula or algorithm that you’re looking at here is that it’s pretty simple: There aren’t a lot of variables.
Just like E = mc2 is amazing in its simplicity, the Mandelbrot algorithm is really simple, too.
An algorithm is basically a problem-solving process. You put an input into the algorithm to create an output. A recursive algorithm means the output becomes the new input, and this process can repeat over and over.
For this metaphor of conflict as a fractal, I think about culture as being our algorithm. We have the input of an experience, and we use our cultural value system to realize how we’re supposed to respond. Our response creates an output, but that simply becomes the new moment we’re in. So that becomes our new input, and we’ll respond to that, and the world will react to us, and so forth.
This is where this tension between self and other, combined with culture, creates our living algorithm. We’re constantly running our value system, taking a new input, and creating a new output over and over. Within our culture, people around us are usually doing something similar to us, so it’s a relatively coherent process.
3. A fractal is infinitely complex
The third part of the definition of a fractal is that it is infinitely complex. Many people follow similar cultural algorithms worldwide, but doing this repeatedly leads to infinite complexity.
This is why I’m modeling the fractal yin-yang with the Mandelbrot set algorithm, as the yin-yang is just a little too simple.
In tomorrow’s essay, we’ll look at the set in detail and focus on the super cool video my fractal friend, Mitch Goldberg, created. I’ll also explain how this ties into our current wicked problems and why the fractal yin-yang is so special. Stay tuned.
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