Meditation on a Summer Afternoon

It’s a beautiful day. Low 20’s and a stiff breeze. The maples, aspen, and elm that line the back of our property are swaying and swooshing in the wind. It’s a comforting sound—one that reminds me of the waves of Lake Huron against the shore, all night—all day—long.  Which reminds me of the fog horns of the lakers as they passed Sarnia in the night. My childhood memories do not go back to the time when my parents and I actually lived in Sarnia, though I must have spent at least the first six months of my life there. But, visiting a favourite aunt and uncle in the house that my grandfather built on Cromwell Street, always brought that mournful sound in the night, triggering some ancient primitive memories. It makes me want to cry, though I have no idea why.

My office window is next to a maple that is probably about forty feet tall—and I’m about twenty-five feet up so that I am looking directly into the middling branches. Have you realized that there is a mathematical pattern in the branches of a tree? In my maple, wherever a branch begins, another begins at roughly the same place on the other side of the limb. In other words, as it grows, each branch splits into three parts with the central part continuing on and the pair of side branches going off in new directions. Sometimes they split into three, and so on and on. Such self-replicating patterns are called fractals. If you search hard enough and with an open imagination you can find fractal relationships in all living things, from the shape of a snail’s shell to the pattern of seeds in a sunflower, to the pattern found in the branchings of your blood vessels.

I don’t find it amazing that nature mimics mathematics. What else should it be based on? I know many dismiss or belittle evolution as “random” events; in fact, they often say the same thing about our universe. But, nothing could be further from the truth. If our universe was the result of purely random events then we would be living in a state of chaos. Actually, we wouldn’t be living at all because chaos and life cannot exist together. On the other hand, when confronted with the overwhelming beauty and complexity of life, the universe, and everything some insist that there must be an intelligent creative force behind it all. Why? That raises more questions than it answers. Where, for example, can this intelligent force reside if it is outside of our universe (which it must be, if it created it)? And, of course, what came before this “force” or being?

There are many, many things that you and I do not understand when we look around us. How, for example, did my maple “know” that splitting branch growth into three parts would give its leaves the maximum amount of surface area for collecting sunlight? It didn’t “know”—and that’s the beauty of it. Over millions of years trees that depend on manufacturing chlorophyll from sunlight have always “maximized” the surface area of their leaves (some, like cacti, minimize their surface area in other to preserve water.) One way works; others don’t work so well and so such trees do not flourish.  In plants that must preserve water, a tubular shape gives the least amount of surface area. Look at a cactus; look at a tree; different mathematics for difference purposes.

There are valid reasons found in chemistry and physics for the patterns that living things follow. The Fibonacci sequence (0, 1, 1, 2, 3, 5, 8, etc.) when followed by a plant—for example in the organization of leaves in a single cabbage plant—expend the least amount of energy for the layers of growth (cut a cabbage in half along its “equator” to check it out).  Or is it the other way around? A plant “prefers” the least expenditure of energy as it grows and so “created” the first Fibonacci sequence. Life is not modeled on math, but mathematics is derived from observing life.

My trees are still bending and bowing in the wind. It looks like chaos from my perspective, but that is perspective only. If I look down on the forest as the wind blows through it, I would see patterns in the way the trees bend—the same kind of patterns in the waves on the sea. If I looked from even further away I would see the immense patterns of weather across the planet with all its local subsets. And, of course, as we retreat further and further into space we see the patterns in the orbits of the planets; and, further yet, in the orbits of the stars around the centre of our galaxy. And, even further, the beautiful and mysterious patterns (that look amazingly like fractals) in the long filament-like arrangements of the galaxies themselves. If you want to see what it looks like here is a piece of it: http://www.windows2universe.org/the_universe/Cosmology.html.