A 3-Step Guide to Living With Chaos

Mandelbrot_Chaos_Nature

Life can appear like a collection of random, unpredictable events strung together over the course time. These seemingly random events can form incredibly beautiful, complex, and intricate patterns—patterns so miraculous that one might imagine only a divine hand could ordain them.

And yet this chaos-to-order dynamic can be teased out of nearly every facet of life on earth. Our world is chaotic: weather systems, geological formations, immigration patterns, the organization of a zebra’s stripes—yet within that chaos lies and order that may hold the key to resolving our capital-P-Problem with capital-L-Life.

Step 1: Recognize that Chaos is a Real and Unavoidable Reality

Edward Lorenz first came across quantifiable chaos in 1961 while attempting to devise a basic model for predicting weather patterns. In order to save time, Lorenz wanted to review his simulation by starting in the middle, rather then running the whole sequence all over again. It was reasonable to assume that as long as he inputed the exact same calculations that he’d gotten the first time around, he should be able to recreate the same results.

This slight deviation, however, resulted in a drastically different result. It turned out that minute changes had been made to Lorenz’s figures, changes that should have been innocuous. They were not. This observation became known as systemic “dependence on initial conditions,” popularly known as the butterfly effect

image-double-rod

A double rod pendulum animation showing chaotic behavior. Starting the pendulum from a slightly different initial condition results in a uniquely different trajectory.

The term butterfly effect was coined by Lorenz in a paper called “Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?” [1] The idea was to illustrate how seemingly insignificant, harmless events can have drastic consequences on the outcome of sensitive systems.

Take an experiment as simple as flipping a coin. There are two variables in a flipping coin: its velocity through the air and how far it travels. Theoretically, it should be possible to control these variables and accurately predict how the coin will land every time. It turns out that coin flips are impossible to predict over time. Slight variations to even the hundred decimal point caused by a random fluctuation in air pressure can dramatically alter the sequence and disrupt its predictability.

This unpredictability is inherent in nature. Anecdotally speaking, nature seems chaotic.

Step 2: Realize There is a Pattern

A few years later, Benoit Mandelbrot, an employee at IBM began to notice something rather strange. While analyzing the fluctuation of cotton prices over the first half of the 20th century the prices seemed to fluctuate at random, but when scaled over time they followed a discernible pattern. The fluctuation of prices day-to-day matched the fluctuation of prices month-to-month and this pattern had been replicating consistently for over sixty years, through an economic depression and two world wars.[2] 

How could that be possible? How could such a specific pattern be repeating through time? And why?

These kinds patterns are called self-similar. This basically means the picture of the whole is replicated within its parts. The branches of a plant repeat the same structure as they get smaller and smaller, on into the very veins of the leaves themselves.[3] 

image-self-similar-leaf

Self-similarity creates shapes or patterns known as fractals. The Mandelbrot Set, devised by Benoit Mandelbrot, is a basic self-similar equation that graphs a fractal. The animation shown below demonstrates how a self-similar shape replicates itself ad-infinitum as you change scale. Mandelbrot_Set

These types of fractal patterns are all over. The weather works in fractal patterns, coastlines form in fractals, the way trees and lakes branch out are fractals. The universe can be seen as a fractal: compare a diagram of an atom to that of a solar system.

 

SolarSystem_to_Atom

And yet, self-similar systems, remarkable as they are, are still 100% unpredictable.

 

Step 3: Finding Confidence Within The Chaos


It is natural to want control our lives in a way that makes us feel safe and comfortable. Yet, the absolute control we seek is mathematically impossible. No matter how much knowledge we have attained, no matter how great our understanding of our circumstances, there is simply no way to predict what will happen tomorrow. The combination of all possible variables are infinite and unimaginable. Unpredictability is as much a part of life on Earth as carbon and oxygen.

Our struggle to control life, the have it work to our will (and to imagine that is even possible) creates a paradigm that is untenable. Mankind has been involved in a life-long struggle to control and supplant nature, and this struggle has been an absolute failure. We have polluted our bodies, our minds, and our environment with this need to control the uncontrollable. The friction of our lives is the friction of this struggle.

Chaos has an order. Beauty comes from that chaos. Order arises from unpredictability. To live in a chaotic world one must embrace the unpredictability, to relish those glimpses of beauty that flash before us with the stroke of a lightning bolt. And just as we catch a glimpse of that pattern, to bask in the glory of its expression, it dives back into the chaotic soup of unpredictability. Chaos gives life to order and order in turn gives life to chaos.

This natural fluctuation is the rhythm of being. In order to enjoy life, we must learn to dance to the rhythm, not fire the conductor. Embrace it, don’t fight it.

Stay in the now. That is where your life is. That is where the beauty is.

As they say in Louisiana, if you don’t like the weather, don’t move, just wait five minutes. A butterfly might be flapping its wings your way.

Notes:                                                                                                        
Lorenz, E.N. (1972) Predictability; Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas? Available from The American Association for the Advancement of Science (http://eaps4.mit.edu/research/Lorenz/Butterfly_1972.pdf(Back to Post)
Mandelbrot, B. The Variation of Certain Speculative Prices. The Journal of Business, Vol. 36. No. 4 (Oct., 1963) (The University of Chicago Press(Back to Post)
3 Bio-chemically, the cells in a plant’s meristeme(s) are able to respond differentially to the concentration of one (or two) plant hormones in a process called self-affine mapping. For more: Ida, T; Sambonsugi, Y. Self-affine mapping system and its application to object contour extraction. US National Library of Medicine (2000) (The National Society for Biotechnology Information(Back to Post)

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