Turning Leaves, Mathematics, and God

As leaves turn colors the human eye appreciates the change, human heart absorbs the season. The leaves will soon fall to earth by gravity, a force no one can explain – except to say it exists. One is put in mind of the Creator, a God at once intelligent, creative, caring, mystical, and infinite.

Infinite, you might ask?  Intelligent, you might challenge? Creative, caring, and mystical you might concede, or not. Of course, no short article will convince you of what you may not believe. Still, there is a lot to these observations, more than meets the eye, worth a moment of reflection.

Leaves, like tree branches, rivers and streams, snowflakes, clouds and hurricanes, nebulae, and spiral galaxies, are “fractals,” repeating patterns, infinitely similar despite changes in size. They are everywhere geometric, often pleasing to the human eye, and necessarily mathematical.

To be specific, nature’s unending, infinitely complex patterns are defined by an equation, Z equals Z squared plus C. The value (Z) times itself plus some constant (C) produces a new value Z, which – when plugged back into the equation – gives a repeating pattern, a Mandelbrot set.

Mandelbrot, somewhat surprisingly – and proving we are all still learning – is a modern mathematician, Polish American, who died in 2010. He discovered that equation, invented the word “fractal” in the 1970s, started people thinking deeper about patterns.

His observations followed inquiries. Perhaps the world was not smooth but rough, yet sensible. Have you ever noticed that giant galactic gas clouds called nebulae are strangely similar to our clouds? Or that the human mind sees math in nature, reproduces it in art and architecture, that we love symmetry – and asymmetry?

Wrote Mandelbrot: “Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.” These facts fascinated him, and should cause pause.

What fractals are is math, which was not – could never have been, with its complexity – a work of man. Math predates man, is both infinite and intelligent, suggesting an origin that is also both.

If the world could as easily be disordered, but is not, rather is highly complex and ordered, one is forced to ask why, or from what source does that extraordinary, infinite order flow?

There is more for inquiring minds. Another mystery, like the prevalence of “fractals” in our universe, is the “golden ratio.” It shows up everywhere. Two quantities fit it if their ratio is “the same as the ratio of their sum to the larger of the two.” The number is 1.618. Greeks called “phi.”

Recall, that the Greeks also discovered “pi,” or 3.14159, the ratio of a circle’s circumference to its diameter, the way around to the way across. Those Greeks obviously had time on their hands. The bigger point is that certain constants are strangely defining of our universe.

Thus, phi – or the golden ratio – shows up all throughout the human body, and in nature more broadly. Distances of dozens of human anatomical elements – and nature – fit phi. Why?

There is no clear answer, nothing that makes it necessary, or puts phi in the category of random, or of similarity to other numbers. The human body, and much of nature, was designed around phi. That is the obvious conclusion since that is the fact. But why?

Galileo, who lived from 1564 to 1642, was Catholic. His answer was simple: “The universe is written in the language of mathematics.” Not to question Galileo, but the question within that answer is: If written in the language of mathematics, who wrote it? Man did not, so who did?

Some will punt, adopt the modern notion that Nature is responsible for itself, pantheism, or God is just the sum total of what is in the universe. But that begs the big question: If the universe is designed with order, written in math, who wrote the math, who distilled the order from chaos?

On beautiful fall days, when politics leaves me wishing for something better, when the fretting, fuming, and preoccupation with nonsense produces a long walk, I wonder: Is there more to all this, to the veins in a leaf, to a branching tree, to a stream’s efficiency, than meets the eye? For me, I think we know; for me, I think so.

Robert Charles is a former Assistant Secretary of State under Colin Powell, former Reagan and Bush 41 White House staffer, attorney, and naval intelligence officer (USNR). He wrote “Narcotics and Terrorism” (2003), “Eagles and Evergreens” (2018), and is National Spokesman for AMAC. Robert Charles has also just released an uplifting new book, “Cherish America: Stories of Courage, Character, and Kindness” (Tower Publishing, 2024).