Math and Spirituality: Connections History and Lessons Learned
Chapter Three
The Chokwe Creation Myth
At one time the Sun went to pay his respects to God. He walked and walked until he found the path which led to God. He presented himself to God, who gave him a cock and said to him: "See me in the morning before you leave."
In the morning the cock crowed and woke up the Sun, who then went to see God. God said: "I heard the cock crow, the one I gave you for supper. You may keep him, but you must return every morning." This is why the Sun encircles the earth and appears every morning.
The Moon also went to visit God, was given a cock, who also woke him up in the morning ... So God said: "I see that you also did not eat the cock I gave you for supper. That is all right. But come back to see me every twenty-eight days."
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And man in turn went to see God, and was given a cock. But he was very hungry after his long voyage and ate part of the cock for supper and kept the rest for his return trip. The next morning the Sun was already high in the sky when our man awoke. He quickly ate the remains of the cock and hurried to his divine host.
God said to him with a smile: "What about the cock I gave you yesterday? I did not hear him crow this morning." The man became fearful. "I was very hungry and ate him." ... "That is all right," said God,"but listen: you know that Sun and Moon have been here, but neither of them killed the cock I gave them.
That is why they themselves will never die. But you killed yours, and so you must die as he did. But at your death you must return here."
“The topfigure is God, the bottom is man, on the left is the Sun and on the right is the Moon. The path is the path that leads to God.”
Telling the Tale
The telling of the Chokwe creation myth begins with the drawing of the figure, say with a stick in the sand. As the stick moves through the sand, starting up top at God, the creation myth is told. I imagine the a captive audience of children looking and listening intently.
The story-teller continues to tell the tale as they draw the figure, never lifting their stick up from the sand. If you would like to take a moment to imagine this process, take a look at the image, starting at the uppermost line that is beneath the little image representing god.
If you start following that line to your left, you start with god and move towards the sun. With your mouse, your finger or your mind you can trace the entire figure all in one go. Really take a moment and try. It is a process you that you might find pleasurable!
If you did not enjoy tracing the figure, that is okay too. We live in a world that is so incredibly good at grabbing our attention that a simple tracing exercise may not be very appealing. But if you could imagine being a child 400 years ago. Hearing this story and seeing this drawn out in front of you, I believe you would be filled with a sense of wonder.
Wonder
It is a great tragedy of our time that we do not associate mathematics with aesthetic pleasure and our sense of wonder. The vast majority of modern humans associate mathematics with childhood trauma and hardship. But it was certainly not always this way.
Mathematics has been inspiring wonder in people since before recorded history. It is no coincidence that geometric designs are found in religious traditions, iconography and architecture all over the world. From Buddhism to Christianity, Islam, to Hinduism and Chinese Folk Traditions and literally everywhere else.
And the appreciation of mathematical aesthetics is not limited to the spiritual realm. The joy we feel from visual art and from music can be attributed to mathematical properties. And there is a sense of wonder and joy that comes with the practice of math itself.
Earlier I defined mathematical properties as “the most fundamental truths of our universe”. So the practice of learning math is actually the practice of coming into knowing a new fundamental truth of the world. And when viewed in this lens I think it is easy to see why that might be an awe-inspiring, wonder-inducing experience.
18th century swiss mathematician Leonhard Euler (pronounced Oy-ler) proved an equality (known as Euler’s identity) between a bunch of irrational fundamental numbers. Give it a google if you feel so inclined.
Every single time I see what Euler proved I cannot believe it is true. One of the numbers included in that identity, ∏ has inspired people for thousands of years. We know people have been approximating the value of ∏ (an irrational number that continues on forever after its decimal point) since around 2,000 B.C.
And since then humans have come up with more and more ingenious ways to more accurately find its value. First with geometric constructions, then with advanced calculus and now with modern supercomputers we have been able to accurately calculate ∏ to one hundred trillion digits. The lengths people will go to discover the digits of ∏ is not fueled by anything practical. Their curiosity and sense of wonder is what drives them.
Fundamental Human Questions
One could argue that the human sense of wonder, our sense of curiosity, began when we looked up at the sky. Why does the sun rise every morning? Why does the moon show its full self to us every month or so? We may take these questions for granted with the access to information we have in modern times. But can you imagine living in our world and not knowing? You would go insane carrying on every day without having an explanation for the big bright circles in the sky.
Now let’s return back to the mind of a child. Hearing the story and watching the shape being drawn in the sand. It must be a great relief to hear this story and know why the sun and the moon behave the way that they do. The Chokwe creation myth addresses other fundamental questions about being human, including ones we grapple with more actively in our modern lives.
Why do I have to get up early in the morning? Why do I hunger? Why do I get tired? I can see that sun and the moon are eternal. But me. Why do I have to die?
These questions transcend culture and era. To be human is to demand answers to these questions. Earlier in this chapter I have described the practice of doing math as learning fundamental truths of the universe. So it should come as no surprise that the majority of mathematicians throughout history also contributed to the fields of astronomy and religious philosophy
Our mathematician du-jour Leonhard Euler (again, pronounced Oy-ler) was no exception. Euler was a devout Christian who believed that the study of mathematics supported the existence of god. The practice of math was a means for him to address fundamental questions, such as the nature of death and mortality.
Euler also used math to answer questions about the sky above him. By Euler’s time heliocentrism was widely accepted so he had information available regarding the behavior of the sun and moon. He took interest instead with the nature of comets. And he was able to determine their orbits with great accuracy.
Graph Theory
But these pursuits are all minor footnotes to the legendary intellectual contributions of Leonhard Euler. He is perhaps most famous for creating a field known as Graph Theory. Euler is known for creating this field of study by exploring a civic problem known as the “Seven Bridges of Königsberg”.
This is a problem anyone can look up and try to solve regardless of their mathematical background and education. Graph Theory looks at distinct objects, represented as points in space, and defines them based on their relations to one another, represented by lines. These series of points and lines are known as graphs or networks.
In this field of study Any Diagram that has a series of objects represented as points and tries to show their connections to one another via lines is called a graph.
Graph theory introduced a new paradigm. A whole new way of thinking. And this way of thinking that Euler developed is ever-present now in our daily lives. Graph Theory is used to model biological processes. It is used to understand the behavior of molecules. It is the foundation for how we understand networks. The “Six Degrees of Kevin Bacon” phenomenon is an expression of the properties of graph theory. Computer science, social networks, linguistical models, neurology all rely on graph theory as a way of problem solving. And the list goes on.
If you were to start taking lessons in the field of Graph Theory. On day 1 or 2 you would learn about a special, important type of graph. These special graphs are categorized as traversable. And the way we can tell if a graph exhibits traversability is by seeing if we can trace the entire graph without lifting our pen up from the page.
Or our stick up from the sand.
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Weaving it all Together
This mathematical property traversability is simple to understand. Yet it is a core mathematical property that is critical to a number of academic fields. And the Chokwe people chose to make their creation myth a graph that exhibits this property! And they did this at least a century before Euler even invented the field of study!
But the Chowke people did not choose to make their creation myth a traversable graph because they saw practical value in this mathematical property. To them, there was a simple aesthetic pleasure in drawing the picture without lifting their stick up off the ground. I also believe that the choice to make the creation myth a traversable graph was intentional. Even though the term traversable graph was not yet coined. They did it to teach a spiritual lesson.
It is a profound notion and one that we see across many faiths. It is hinted at in the very last line of the myth.
“The top figure is God, the bottom is man, on the left is the Sun and on the right is the Moon. The path is the path that leads to God.”
We might think that the connections between us and everyone else in the world are a tangled mess. Though in actuality all of these connections can be drawn as one single smooth line.
Whatever force or being that you believe is out there drawing the schematics of our universe. They never have a hiccup or make a mistake. As they draw our reality they do so uninterrupted. They never have to lift their pencil up from the page.
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A revelation that pushes science and technology forward.
An expressive activity done for pleasure.
A means to express spiritual truths about the universe.
A single piece of math is all of these things.
Next Time:
Grappling with the Infinite, Regular Polygons, Math Cults and Murder: The History of the Pentagram
