The old Chinese proverb states that a butterfly's gently flapping wings in China has the power to dramatically affect weather on the other side of the world. How can that be? - I wondered cynically. Clearly, the Chinese weren't privy to classical modern physics. What were they thinking? My reality and what I considered true couldn't open any more... the belief system was closed.
Then I was reminded by an inner voice. We accept approximation for that is the only way we can define and predict. We round off because it's "close enough." Therefore, we dance from one island of "certainty" to another without consideration of what lies between. But it's all in between. The islands of certainty we cling to are, in fact, infinitesimal points. Don't shut out the possibility to explore in between. Here is where you will find the truth.
Okay, I said. Let's try to get to the "truth." Part of the truth appears to me in the strange world of chaos and fractals. Lately, I've taken an interest in Chaos Theory. I don't understand all its nuances - only enough really to appreciate the mystery that surrounds us... that which is inexplicable. Chaos Theory hints at this mystery as it reveals order out of turbulence, self-organization through some universal guidance that lies beyond my ability to comprehend. Even a brief and limited exposure reinforces the feeling that there is so much more than the "certainty" of what we know.
Chaos Theory speaks of formulas and equations that fold back into themselves, like a baker kneading dough... equations that repeat or iterate endlessly. The result of the previous becomes the input for the next and so on. They feed into themselves, always linked, both as individual pieces and, simultaneously, connected with the whole. As computers graphically plot these iterations, the fascinatingly beautiful world of fractals originates. Here we can see the mysterious order from chaos.
Mathematicians, using modern computers, are able to do some pretty interesting stuff playing with all these fancy iterating equations. They work with numbers and decimals going out 16 places and more. You would think that we're talking really accurate and sophisticated science here.
But something doesn't make sense. And here's where the mystery deepens and creeps further in to my unbelieving mind. It's the butterfly effect.
If these mathematicians round off their initial input to, say, 15 places instead of 16, strange things happen. After only a relatively few repetitions with this rounded input, the results of each succeeding equations begin to shift and wander dramatically. Soon the results no longer resemble what was obtained with a 16-place round off. A whole new picture emerges; the whole changes dramatically by the smallest of inputs.
And here is that mystery, that seems to contradict what the logical mind assumes to be "true." As the input is folded back into itself, back into the whole that defines it, there is an illogical, unpredictable outcome - chaotic, if you will. But the chaos isn't really chaos... there's a pattern. Like the computer-generated fractals, an order emerges from turbulence. To me, that's a mystery.
Can life be likened to those esoteric equations, iterating in the world of mathematics? Does life fold back into itself, recreating and reemerging in a turbulent, chaotic manner? Or is there a divine order, deep and mysterious, beyond our ability to grasp and understand... or is it both? Can infinitely small results be fed back into life with surprising results? Can the smallest contribution, a kind smile for example, produce a sense of joy on the other side of the world?
What if it could?
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