Chaos and the Open Mouth Syndrome

When, in the late 1970's, Physicists discovered fractals, they revealed a strange and foggy part of This Magic Sea.

Nature, it turns out, was responsive in a way nobody even imagined. The discovery dismayed and confused many, but delighted and enlightened others.

It was so strange nobody knew what to call the new field of investigation. Eventually it was nicknamed Chaos Theory and popularized by James Glieck.

Now known as complex number theory, the system of mathematics renovated scientific interest in the dynamics of non-linear systems, like clouds, rivers or life.

The alluring patterns were discovered by a weather scientist who, like all meteorologists, knew that although weather had familiar, repeating patterns, you could never predict exactly what it would do next.

Every cloud in the sky is different from every other one. But each sky has a particular pattern. Although clouds are different from each other they are also similar. A thunderhead looks like a thunderhead, a cirrus like a cirrus.

How does Nature do this? What is it that is similar between different clouds?

Formulae

Some natural phenomena can be reduced to a simple mathematical relationship, a formula. Once the formula is known, the scientist can substitute different numbers for the variables and predict how the relationship will develop under different conditions. This works for some formulae, called linear relationships, but not for non-linear relationships.

When scientists add the value into the formula for a non-linear relationship, they can never predict exactly what the outcome will be. Non linear systems can react in more than one way to what seems to be exactly the same set of conditions. Physicists used the word chaotic to describe this very common behavior, because they thought if nature didn't do what their formulae predicted, nature must be random, uncoordinated activity. Webster defines chaos as confusion and disorder.

Chaos

Really, the confusion and disorder was in the minds of the scientists, not in Nature. Maybe we mean random, uncoordinated activity when we use the word chaos today, but chaos comes from a Greek word chaos meaning abyss and derived from a still older word chainein to gape as in a chasm or wide open mouth.

Chaos was the gap between human understanding and the real world; the wide open mouth when scientific predictions failed. With the advent of modern computers and computer hacks who spend all day diddling with them, a whole new world flew into the open mouth of chaos. Solved once, or a few hundred times, the equations describing non-linear behavior yielded meaningless answers. But solved millions of times by high speed computers, the simple non-linear formulas unfolded into fabulous images of reality.

Iterations

The more times the equations were solved, the more detail appeared in the image. There was no end to the detail. Within the general boundaries of the equation the images resolve into an infinity of detail - just like life. There was lots of chaos around the physics labs in the universities when the so-called fractal images started decorating computer screens.

So stunned was the senior physics faculty at one Southern California University they actually forbid the students to continue investigating these aberrations. You just know how that turned out.

Chaos Theory

Chaos Theory describes how orderly patterns of behavior emerge from apparently chaotic surroundings.

The Mandelbrot set, named after the mathematician who discovered fractal designs, results from the iteration in the complex plane of z -> z2 + c. The formula reveals nothing of the beautiful infinity of patterns resulting from its solution. The letters mean nothing by themselves. The first few solutions (iterations) for the formula present only "random" dots on a graph. The formula must be solved many times by a computer before the patterns become evident. The more times the computer solves the equation, the more detailed and beautiful the pattern on the monitor. Within the boundaries of the set, the patterns implode forever.I have included a program on this disk that lets you play with fractals and generate strikingly beautiful patterns. Hyperlink over to read more about fractals.

Fractals and the uncertainty of change

Fractals open the door to understanding nature's responsive behavior. Nobody is sure why, or how, seemingly random events result in structures of such infinitely expanding symmetry. The old systems of thought can't figure out the cause and effect of Chaos. This is because the reductionism view insists on seeing cause preceding effect and working from the small to the large. Chaos demonstrates the reverse is also true.

What has already happened changes the probability of what will happen next.

That's against classical probability theory. According to that, each time a coin is flipped, the chances of it landing on one side or the other is exactly 50:50. Chaos theory shows, in the complexities of real life, the chances are not really equal and the next throw has a different probability than the last. Not only does it have a different probability, the chances are, each new solution of the equation will add to the construction of a beautiful and symmetrical pattern. The world is constructed like that. Nature isn't random. It is responsive.

The Possibility of Life and Evolution

Life is a clear example of the foolishness of Probability Theory.

According to the odds, life is impossible.

Any biologist who has studied behavior knows animals have a habit of doing something different every time the researcher thinks an experiment proves something definitive. This is why scientists, by habit, always qualify their statements with "seems to be" or "apparently" or "probably".

Very few scientists have had the courage to investigate Synchronicity.

Psychologist C.G. Jung coined the word to describe those totally unexplainable coincidences that happen from time to time. Jung and Sigmond Freud were contemporaries.

They were friends, at first, but later Freud shunned Jung. Freud went with the Cartesian world of dualism and reductionism.

Mental disturbances, thought Freud, were caused by individual events that happened in a person's childhood - usually linked with sex. Jung agreed, to a point, but also believed illnesses were also caused by disturbances in a kind of universal unconsciousness. There were, he insisted, ideas everyone held in common, called archetypes. And these controlled how individuals behaved and what happened to them.

Violations or suppressions of archetypes, like sex, Jung said, could lead to mental illness.

Archetypes, Jung said, were the sort of bonds that kept brothers from banging sisters. Jung wondered if maybe Nature's responsiveness could be more than - impersonal. If maybe nature could somehow be responsible for the strange coincidences he named synchronicity.

Maybe?

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