When I was young one of the most powerful memories I have of being a child is on a morning like today. The sun is shining brightly, the air has a note of winter still clinging to it, but as the dew lifts it is clear this is only a whisper and the warmth of spring is moving it aside quickly. As is often the case for a kid (at least in my generation) I found myself with nothing to do, so I lay down in the grass. We use all five of our senses to embed a memory, and this one comes packaged with the scent of fescue grass, a few birds chattering, the solidness of the ground beneath me at the same time warm and solid, but still a hint chilly. The grass is decidedly cool on my neck and the sun deliciously warm on my face. The sky is the kind of blue that makes me wonder how blue something has to be before we start describing it as purple. It is a rich blue without clouds, darker with distance from the horizon. The air smells new, as if it had been recently unpacked direct from the factory for this day.
At this moment in time, as a young boy, everything seemed on the upslope – the rest of the day is going to be great. Summer is coming and that means swimming and no school. Bugs aren’t here yet, so I can stay here in the grass all day if I want. It was a hopeful moment. Things around me were literally bright, as were prospects for the rest of the day, and my life. The light was as crisp as the air and it meant, somehow, good things were going to happen.
I still, in my goofily optimistic way, believe that good things are going to happen but it is harder to convince myself of that now. I know it is not smart to watch the news and expect to come away with a bounce in my step about the wonderful world around us, but I still watch it nevertheless. What I found yesterday was this: More people killing innocents in a misguided “defense” of a world that no longer exists. Cruelty disguised as “protection” for people in terms of a law that validates treating different people as somehow lesser than “us”. Politicians talking about “watching” people in our communities who have a different faith, because despite the fact that they have lived as one of us for generations, and serve in our armed forces, as teachers, police officers, fire fighters and parents. More concern about the ability of our fragile planet to survive what we are imposing upon it with every passing day. It is very hard to be hopeful in the face of all this.
So I went outside. And what I found was a dramatic validation of hope all around me. Everything about spring is a testimony to the faith of every living thing out there that tomorrow will come, it will be warmer and we will have babies and produce seeds and before you know it, the time to fly south or bed down for the winter again will be here and we will do so in full confidence that all this will crank up again about this time next year. The very idea of seasons is hopeful.
Looking closely at things around me, they all start out small. We do not experience, nor do we expect a fully-grown tree to burst out of the soil in one, momentous blurp and rise up to its mature height, shaking its leaves loose of soil as it settles in. Trees start as little versions of their mature selves – a few tiny leaves on a skinny little upright twig, and over time the metabolism of the plant keeps producing more and more tiny leaves and sturdier stems and in a few short moments (in geologic time, of course), voila! A tree. Try thinking of the end of a branch of a mature tree, and imagine it clipped off and planted in the ground on its own. It is a small twig of a massive tree, and yet that small part, when looked at on its own (particularly now when its leaves are quite small), resembles a seedling of the same tree. Similarly pay attention the next time you break off a piece of broccoli, and before you pop it in your mouth consider how much it resembles a miniature version of the entire head. You have discovered fractal geometry and the startling proliferation of this form in the natural world…a thing made up of tinier and tinier versions of itself.
Mathematician Benoit Mandelbrot first used the term in the 1970’s, and to be clear, there is no accepted definition of what a fractal is. The best way to describe a fractal relationship is that it is a rule for growing. Apply the rule again and again and an object grows in a pattern that replicates itself, bigger and bigger. Artists have embraced the concept and have created remarkable imagery that is very “organic” in appearance by using mathematical formulae. The “mountains” you see in digital landscapes in movies are fractals, not photos. The dendritic pattern of tree branches, watercourses, the human bloodstream are all fractal patterns. Coastlines, clouds and mountains represent fractal rules for the interaction of water and sand, water and air, rock, water and wind. Scientists are using the math associated with this concept to try to better understand how we are built as humans as well as how the world around us is constructed. Our lungs grow in a fractal pattern. It is possible that weather, the cosmos, all of it responds to these simple rules of replication and growth. You can see Mandelbrot himself discussing this in a TED talk filmed in February 2010, the year he died: http://www.ted.com/talks/benoit_mandelbrot_fractals_the_art_of_roughness
We can go down this rabbit-hole a long way but I will resist that and bring us back to the simple things outside my back door. Today I became fascinated with the unfurling of leaves. Tiny, delicate images of leaves that will be emerge from buds on the branches, and slowly expand, eventually filling the tree with fully formed leaves. They look remarkably vulnerable when they first emerge, but keep on growing and expanding, undaunted, until cooling weather and shortening days in the fall cue their release from the branch and their transformation from leaf to mulch. Now, I can imagine a leaf might emerge like a groundhog, take a quick look around perhaps on an icy day in late spring and retreat – better luck next year - but once begun, this process is ever hopeful. It WILL get warmer, the sun will come out, more leaves will follow, it will rain and the tree will live and grow another year, deposit its spent leaves into the soil below and go back to sleep only to begin again when the seasons cycle.
These rules for growth that seem so universal also seem so inevitable. Once started spring continues, things grow. The rules are unchanged by our behavior, by the variety of the weather or the actions of people with bombs on subways. Nature has a way of reminding us that there are structures greater and at the same time much simpler than our complex laws and rules of human behavior that govern the world around us, creating beauty in an ever-optimistic, methodical way. There is not much we can do about this – thank God.
It is a worthy effort to get outside at this time of year and look at small things following their fractal rules of growth diligently working to become bigger things. We don’t really know why these rules are embedded in the DNA of plants and people, or how they evolved, again – thank God. It is comforting to know that there are still things we don’t know. But for me the inevitability of growth in the face of disruption is a hopeful thing. The constant building of beauty and newness in the springtime distracts me at least a little from all the things around me that seem broken, and reminds me that for all we might fret, summer is coming, and then fall, and then winter, and it will be spring again next year.
1/31/2020 10:29:30 am
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Daniel Howe lives in Raleigh, NC. He's interested in a lot of things so this blog is all over the place.