Finding Yoga in Chaos and Order
Expanding Paradigms - January 2010

In Hindu mythology, Shiva is commonly associated with destruction. However, there are other interpretations for this Hindu God, of which I prefer the idea of ‘transformation’. Destruction is a subjective label that we choose to give to transformation.

Growing up, I saw that my parents modeled two opposite views of life. My Mother spent much of her time living in the past, and my father in the future. Watching the bull dozers working on his newly acquired land in East Texas, my father looked into the future and saw the creation of a beautiful new lake. Had my mother witnessed the same scene, she would have witnessed the destruction of a beautiful wooded draw with spring fed streams. That is why my father had the lake put in before my mother had a chance to see what would be lost in the process. Having never seen the beautiful draw that was carved up and turned under the blades of five Caterpillar bull dozers, my mother was free to enjoy the beauty of the resulting lake.

Whether we perceive periods of transformation as creation or destruction is merely a result of whether we look to the future or the past. The past is destroyed in the process of creating a new future.

Balancing the energy of transformation is the quality of stability, represented in the Hindu pantheon by Vishnu, often associated with preservation. Life exists in the space between Vishnu and Shiva, preservation and transformation, order and chaos. Too much transformation leads to chaos, like the boiling plasma of the sun. Too much order is suffocating, like the tightly bound lattice of a crystal where every atom’s position is locked in and accounted for. Life cannot exist at either extreme. It is in the boundary between order and chaos that complexity arises and in which life flourishes.

The fields of Chaos theory, Complexity Theory and Systems Theory are all providing insights into the infinitely complicated relationship between order and chaos. The Mandelbrot set is the best known fractal image that captures this relationship (Fractals are complex geometric patterns that exhibit self-similarity - small details of structure viewed at any scale repeat elements of the overall pattern).

The Mandelbrot set is best understood by diving deep into its heart. This is a similar experience to looking through a camera with an infinitely powerful lens. First you see the distant mountain, then as you begin to zoom in closer and closer you see your friend climbing the mountain. Then you zoom in until all you can see is their face, then the tip of their nose, then a single pore on the tip of their nose. As you continue to zoom in you see the individual cells that make up the pore, then the internal organelles of a single cell and then the molecules that make up the organelle, until you reach a point where light can take you no further. Zooming into the Mandelbrot set is a similar experience. However, because it is a mathematical equation not limited by physics, we do not encounter the same physical limitations imposed by the wave length of light, thus we can continue to dive deeper and deeper into this equation, exploring it’s amazing beauty and mysterious nature through infinite scales.

If you zoom into the center of the dark area of the Mandelbrot set, you will only find more darkness. If you zoom into the outermost areas further away from the Mandelbrot set (in the image above colored red) you will only find more red. In either case, under higher and higher magnification nothing changes, and the observer quickly loses interest. However, if you investigate the boundary between order and chaos, or the boundary between numbers located inside the Mandelbrot set and those located outside the set, you will discover a wonderful world of infinite complexity.

Take two minutes to explore a shallow dive into the Mandelbrot set. This dive is a good introduction to the equation as it stays on the symmetrical center line of the graph, which empasizes the fractal property of self similarity across varying scales, and by diving in and then pulling back out, it emphasizes the property of scaling.

What is staggering is that such complexity can emerge from such a simple mathematical equation! As Nobel laureate Murray Gell-Mann phrased it: “Surface complexity arising out of deep simplicity.” 

If you are interested in the mathematics behind the Mandelbrot set it is surprisingly simple… The Mandelbrot set is generated by taking a simple equation, zn+1 = zn2 + c, plugging complex numbers into c, and then iterating the sequence (taking the result and plugging it back into the equation, and then taking that result and plugging it back into the equation…). For some values of c, after repeated iterations, the result zooms off to infinity. For other values of c, the equation remains bounded and behaves. In the diagram below, the values of c that ‘behave’ are plotted in black and those that ‘misbehave’ are plotted in white.

Complexity arises somewhere between totally ordered and totally random systems.  Complexity occurs not just in mathematical equations, but in Astronomy, geology, biology… and even in sociology. One of the reasons that America flourished for so many years, leading the world in innovation, was the wonderful balance between liberty vs. government (chaos and order), that our founding followers envisioned. In the space between these two extremes, the arts and sciences all took root and flourished.

As we move forward, post 911, we see on the one hand, those that put their faith in government and the establishment of ever increasing layers of control, which if left unchecked will eventually suffocate us, and those that put their faith in anarchy and chaos, which threatens to tear apart our culture. To say that either approach is valid, or that its opposite is invalid is naïve. It is only in finding the right balance between these opposites that we can thrive. It is the age old struggle between Shiva and Vishnu, order and chaos. Yoga helps us navigate between these extremes, finding balance in this infinitely complex fractal that we call life. Through our attitudes and actions, individually and collectively, may we find the strength, courage and above all, the wisdom to seek the middle path that Buddha advocated. ~ Namaste'

Just in case you would like to see more of the mandelbrot set, here are two more, progressively deeper dives into the heart of chaos! Notice that by straying off the center line and zooming into different parts of the Mandelbrot set, the results are staggeringly different!

This final journey ends at a magnification level of 10 raised to the 345th power!