Sensitivity to Initial Conditions (Butterfly Effect)
Demonstrated on a Lorenz Attractor

Excerpt from Piloting Through Chaos—The Explorer’s Mind

© Copyright, Julian Gresser, June 2013, All rights reserved

Butterfly Rescue

I came upon a related series of inventions which are embedded in this book in a curious way.

I like to keep a watchful eye each day for its special points of beauty, which themselves become koans (subjects for meditative reflection). I will go back in time eight months ago. I am meandering around my garden and I look up and there is a stunning gossamer maze, glisten­ing in the sunlight. It is a gigantic spider web. The designer is not home. Transfixed I ask, “How can spiders possibly contrive a web between two trees at a distance of eight feet?” After all, I presume, spi­ders do not fly. It seems miraculous. In the Age of the Internet, we have a university library at our finger tips, and so I look for the answers. I now understand how spiders can vault across improbable spider distances. The koan points the way to deeper questions. For example, how can a human mind learn to vault across vast mind distances?

Some months later in the late afternoon, I see a Monarch, royally basking against the yellow patina on the eaves, as if it has a world of time. I have always had a special feeling for butterflies. I recall the famous passage by the Chinese philosopher, Chuang-Tzu (pin­yin, Zhuangzi), which presents the wonderful challenge of ambi­guity to the Explorer’s Mind. Chuang-Tzu asks that we step into different orders of reality.105

One day about sunset Chuang-Tzu dozes off and dreams that he has turned into a butterfly.

He flaps his wings and sure enough he is a butterfly! He completely forgets that he is Chuang-Tzu.

But then he awakens and realizes to his dismay that after all he is only Chuang-Tzu.

But wait! Is he really Chuang-Tzu dreaming he has trans­formed into a butterfly, or is he in reality a butterfly dreaming he is Chuang-Tzu?

Meditating on the Monarch, the thought appears: How long do butterflies live? I learn that Monarchs are especially long-lived, because of their long-range migrations to wintering roosts in south-central Mexico, a uniquely environmentally favored location. Dur­ing these hibernations, they are able to suppress the synthesis of juvenile hormone, which inhibits aging.106

Another late sunny afternoon in my garden. My wife calls out, “Hurry, a butterfly is caught in a huge spider’s web. It’s probably already dead.” I rush to see what’s happening, and there the poor thing is trapped in the branches of a tree about ten feet from the house. It weakly flaps its wings. Obviously it is exhausted. It waits for the return of the spider and its fate, to be eaten.

I find a ladder and my wife suggests I go up with a mop and knock at the web. The butterfly tumbles down on top of the mop, stunned. I cup it in my hands. It rests for a precarious moment, hovering between life and death, and then, just as in the fairy tales, it flutters its wings and, with a swoop, soars triumphantly over the treetops.

I suggest to Angela, “Why don’t we establish a local club, The Butterfly Rescue, with the goal of helping children and others in desperate need? And Angela tells me about these little boys, ages eight and nine, whose parents were killed only a week before in a head-on collision with an SUV, leaving them paralyzed below the waist, and their kid sister, age six, also seriously injured. When this chapter was written, they had succeeded in raising only $200,000 in oil-rich Texas.107 Perhaps we are all, in our brief lives, deep-down, butterflies—vulnerable, beautiful and ephemeral. I pledged at that moment to do what I can to assist in such calamities, and Book II, Chapter IV, takes the first step in outlining a practical strategy.

I go back to the Internet and I start researching Butterfly Effect and I am told that in chaos theory, the butterfly effect is the sensitive dependence on initial conditions, where a small change at one place in a non-linear system can result in large differences to a later state. The effect derives its name from the theoretical example of a hurricane’s formation being contingent on whether or not a distant butterfly has flapped its wings several weeks before.

       And then the idea comes to me, The Butterfly Network and its Butterfly Effect Experiment. The elements:

  • Enter by clicking the Butterfly Icon, which is an icon empowered by SmartCodeFx Solutions.
  • This takes you to a menu of options, and by one click you can direct funds to a cause of your choice. A prominent example is See Your Impact. There are thousands of other noble causes.
  • There is also a daily series of graphics, organized as a social networked game, displaying the ripples of The Butterfly Effect around the world, with lights flickering on a rotating globe, indicating how near we are to a global tipping point.