Is this how change happens?

The Belousov – Zhabotinsky or B-Z reaction is formed by combining several chemicals including a bromine and an acid in a Petrie dish. The solution is unstable, and in a non-equilibrium state it oscillates. The pattern, shown in this photograph, emerges slowly at first little blue dots in a red-brown solution, but accelerates into spirals and curves.

This reaction was so counter-intuitive that in 1951 when Boris Belousov, who first observed it, tried to publish his findings the journal refused saying he must have got something in the experiment wrong. In 1961 Anatol Zhabotinsky, a grad student was able to reproduce these same effects.

The B-Z reaction has now been recreated many times. B-Z is one of several non-equilibrium chemical reactions. The Briggs-Rauscher reaction where a beaker oscillates from clear to opaque blue or black in a pattern that can be precisely modeled mathematically.

Oscillation

Oscillation is feature of change in a non-equilibrium state and not just in chemicals. We are all familiar with what happens when one places a microphone too close to a speaker:  “Screeeeeeeeeeeeeek” – feedback!  The sound waves coming from the microphone are amplified through the speakers and the sound waves from the speakers are picked up by the microphone and so on, wave oscillation heard as ear splitting sound. Electric guitarists use this same principle, but control the gain to make distortion, the “dirty” or “fuzz box” sound of heavy metal music and Chicago blues.

The first law of thermodynamics is that energy can neither be created nor destroyed, it can only be transferred from one form to another. The second law of thermodynamics is that in any closed or isolated system entropy (inevitable decay and decline) always increases. Based upon external input energy (growth) increases, but if the system then remains isolated decline begins. I am not a physicist, but that sounds like a recipe for oscillation.

It says to me that without some external energy input a system’s energy will decline and that system equilibrium requires input-transference balance to avoid a destructive oscillation.

Is this how things break into chaos and how order emerges from chaos? I think so and I think we know this somehow, maybe deep in our DNA. We have expressions like  “two steps forward- one step back” or the depressing inverse “one step forward-two steps back”. We observe “growth spurts”  and “growing pains” in our children, growing things accelerate and level off.

S-curves and fractals

This growth-leveling function is often depicted in a Sigmoid curve or S-curve. After initial input, e.g. water and fertilizer for a seedling, growth accelerates, then levels off.

In thinking about change -say continuous improvement – we attempt to control the inputs the way a farmer controls the water and fertilizer.  We know improvement may level off and so we conceive another project, another solution to start the improvement again. It is never clear if that will happen and there is a period of uncertainty. Will we create a destructive oscillation or will new growth occur?

The B-Z reaction demonstrates what we thought was disarray and chaos has a pattern to it. In 1975 mathematician Benoit Mandelbrot coined the term fractal from the Latin root fractus meaning broken or partial (fractured, fraction) and the extension to geometric reassembly. A fractal is “self-similar,” a geometric shape, structure, or pattern of growth that exhibits the same structure regardless of scale. Examples in nature include tree branching, snowflake crystals, and fern leafing.

Mandelbrot created a set of numbers that modeled the process of fractal geometry and In 1980 working with the IBM Watson Research Center he created stunning visualizations of fractals and the progression or “ordered chaos that they represented.  

(Note: Still photographs do neither the B-Z reaction nor the Mandelbrot set justice, but video of each is available on YouTube and Wikipedia Commons respectively.)

I think that how elements combine and break apart, how things grow and decay, how organisms and organizations self-organize and dissolve, is old knowledge, pre-historic knowledge. My evidence for this is not scientific but artistic.

What did ancient artists know?

For more than 7000 years artists have been drawing the spirals and wave patterns found in the Belousov ­- Zhabotinsky reaction and the fractal images of the Mandelbrot set.

The images at the left are of artistic work that is between 2500 and 7000 years old. Somehow these artists knew about the patterns of spirals and waves. Somehow they interpreted nature in ways that mirror the self-similar patterns of the advanced mathematics of fractals and the chemical oscillation of combined unlike chemicals.

What truth about change did these artists access? How much did they know about complex systems, non-equilibrium states, and oscillation?

What can we learn from these artists and from the Belousov-Zhabotinsky reaction and the Mandelbrot set to make change in our organizations and ourselves easier?

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