Manifest World Change Through Fractals and Chaos Theory

When we look at the world around us, particularly as portrayed in the media, many of us feel a sense of helplessness at our perceived inability to manifest change. Despite historical evidence to the contrary, of individuals to small groups making significant to profound change (Abraham Lincoln - Abolition of Slavery (America), Continental Congress - Declaration of Independence, William Wilberforce - Abolition of Slavery (Great Britain), Nelson Mandela - Apartheid, Woman's Suffrage, etc.), the common attitude of "What Can I Do?" prevails.

Perhaps there is anecdotal evidence, using rigorously defined mathematical concepts, to build the premise that a single individual can manifest the significant, to even profound, change they desire.

First of all, let us briefly describe the two mathematical concepts I plan to invoke in this discussion. (Note: these are well documented concepts in mathematics that have been well studied and rigorously defined. There are a wealth of papers, books and journal articles documenting these concepts).

In 1961, Edward Lorenz was modeling weather using a numerical computer model and, in the course of setting up another iteration of his model, he input data in which he rounded a numerical value in the sequence from 0.506127 to 0.506, an apparently insignificant truncation. The result, however, was a completely different weather scenario. Lorenz subsequently published the results in a 1963 paper for the New York Academy of Sciences. At the time, he noted that "One meteorologist remarked that if the theory were correct, one flap of a seagull's wings could change the course of weather forever". In later reports, the seagull was changed to a butterfly, resulting in the "Butterfly Effect".

The phrase "Butterfly Effect" refers to the possibility that minor, seemingly insignificant changes (such as a butterfly flapping its wings) might produce large, unforeseen events elsewhere. Hence the title "Does the flap of a butterfly's wings in Brazil set off a tornado in Texas?" for Lorenz's 1972 presentation at the 139th meeting of the American Association for the Advancement of Science.
"The flapping wing represents a small change in the initial condition of the system, which causes a chain of events leading to large-scale alterations of events. Had the butterfly not flapped its wings, the trajectory of the system might have been vastly different. While the butterfly does not "cause" the tornado in the sense of providing the energy for the tornado, it does "cause" it in the sense that the flap of its wings is an essential part of the initial conditions resulting in a tornado, and without that flap that particular tornado would not have existed" (Wikipedia).

Stated another way, the "Butterfly Effect" does not propose that a butterfly flapping its wings causes the change, merely that the flapping results in an imperceptible change in local conditions. Rather than these imperceptible changes being instantaneously lost in the overall environment, they begin to make further changes in the immediately surrounding environment in a cascading effect of causes and effects. With each successive change, the local environment becomes slightly larger and the effects slightly more pronounced. Over a given period of time, the effects become noticeable (although the original source may remain unknown), culminating in an observable "event".

"A fractal is generally "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole", a property called "self-similarity". Because they appear similar at all levels of magnification, fractals are often considered to be infinitely complex (in informal terms)" (Wikipedia).
There is a more precise, and mathematically correct, definition of a fractal (i.e. Wikipedia), however, this less rigorous definition captures the specific concept behind fractal theory that will serve my current purposes:

The specific characteristic of fractals that we will, therefore, consider is that of "Scalable Self-Similarity", meaning that similar features (recognizable shapes that one might incorrectly refer to as "patterns"), are repeatedly evidenced as one moves upward and/or downward in scale (magnification).

Throughout the history of mankind, we have multiple examples of individuals who have desired change, worked toward their desired change and, finally, manifested that change, often despite overwhelming odds. The best known example to Christians would be Jesus Christ. Other examples, in addition to those provided above, would include Mahatma Ghandi (Indian Independence Movement) and Mohammed (Islamic Prophet).

As a very broad generalization, from simple beginnings (i.e. a small audience, the initial almost imperceptible change), an idea (or philosophy, movement or religion) is initially taught. Gradually, the idea or teachings are spread to a progressively larger audience, within which the message gains popularity (the imperceptible change begins to spread outward, beyond its local environment). At some point, a critical mass in popularity is reached and change (the "event") becomes possible but not, necessarily, realized (for example Tiananmen Square, 1989) (please refer to The Tipping Point for an introduction to dramatic change subsequent to achieving "Critical Mass").

As an individual, you may have an idea or ideas to effect change on a local, national or international basis. However, as an individual, how do you manifest this desired change? Simply speaking, exemplify the change, live the change, be the imperceptible change in your local environment that you desire. BE the change you wish to see.



Fractal Example (from The Beauty of Fractals - Peitgen and Richter, 1986 - Springer Verlag)

Thus we come to scalable self-similarity. Most fractal diagrams begin with the large scale image, focus on a recognizable shape, then begin a series of magnified views to chase that shape to deeper and deeper levels (smaller and smaller scale). As one progresses downward, the recognizable fractal shape is evident, singly and as large groups of the same fractal shape repeated throughout the structure of the mathematical equation modeled.

Let us look at it from a different angle, let us work from small magnification (a single fractal shape) and move upward in magnification (i.e. to a larger, more global image). You, as an individual, wish to effect change (the initial fractal shape). By speaking it, living it, exemplifying it, you begin to make your imperceptible change evident to those around you (multiple occurrences of the fractal shape in space and time, but still at small scale, within the local environment). Depending upon how radical your idea is, you may or may not elicit a sympathetic response in those around you (determining the frequency at which the fractal shape appears in the overall image). However, as a generalization, even the most radical ideas have elicited a response in like minded people.

There are many examples of profound ideas, having a considerable effect and change on society, being "discovered" at approximately the same time, by people widely separated in space. The example that comes to mind was the introduction of Calculus, virtually simultaneously by Sir Isaac Newton and Gottfried Wilhelm Leibniz. There are many other examples of such "Synchronicity".

As you embrace your change, picture yourself as the initial shape in a fractal image. As you move through time, making your small imperceptible change on those with whom you interact, other, similar shapes (other individuals) might be expected to "appear" in the overall pattern (adjacent to you or, in the case of synchronicity, quite distinct in space and time within the host fractal image). With more time, self similar shapes can be expected to appear more frequently in the form of groups, movements, beliefs, societies, etc.

Obviously, this is an abstraction of these mathematical concepts. However, many historical examples exist of profound change derived from an individual or even a small group of like minded individuals having the desire and will to pursue the change they desired. Similar change will, no doubt, occur again in the future of mankind. However, there is no guarantee that that change will be the change you exemplify.

However, if you don't make the attempt to manifest the change you desire in the world; by living it, speaking it, exemplifying it (making that initial imperceptible effect), it is guaranteed the "event" will not occur, at least as a result of your efforts (or lack thereof).

Individuals can make change, significant to profound change, by making the decision to ACT.

Many of the classic books in the "Personal Development" genre are available on the Integrated Success Program web-site, with additional material available on the Integrated Success Program Blog.

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