Archive for January, 2011

(Mandelbrot set: by António Miguel de Campos)

I’ve been called upon to reveal some scientific research to support my assertion that human behaviors follow the same fractal patterns that are the building blocks of the natural world around us. The onus is on me to provide some proof that the fractalic axiom “as above, so below” applies not only to the physical world, but also to the intangible world of human emotion and behavior. In other worlds, is there any proof that quitting smoking (ending the conscious pollution of your own body) contributes to the efforts to curb global warming (other than my own intuitive ideology)?

I started by looking into the now quite well known research of Masaru Emoto, the Japanese author and entrepreneur who meditated over different glasses of water using various phrases (“you fool” or “gratitude” and the like), froze the water, and then photographed the crystals that formed. In his findings, the positive thoughts caused the formation of beautiful crystals, where the negative thoughts formed ugly ones. This seemed to me like a natural place to jump off the bridge between physical fractal patterns and human behavior, because human behavior caused the regular or irregular fractal patterns that grew as the water froze.

Unfortunately, I had to give up this line of reasoning because so many well informed folks (this man in particular) felt that Dr. Emoto’s experimental procedures were not designed to eliminate enough possible sources for error (for example, the petri dishes in which the crystals formed were not sealed so contaminants–foreign material or even warmed air from the body of the photographer–could have affected the crystal formation). Also, all the photographs were not published. It is conjectured that that Emoto only released the photos that supported his claims. (This is not to say that I don’t believe in the work that he’s done, just that I decided that this study isn’t the best one to use in the effort to prove my own scantily supported claim.)

I decided next to go back to the man who “discovered” fractals in the first place, Benoit Mandelbrot. (What a great name). I started off at this page called fractal wisdom, which is a beautiful website that illustrates the history, beauty and mathematics behind fractals. I read there that Mandelbrot actually started thinking about fractal patterns when he noticed an unusual pattern in cotton prices. Economists had believed that short-term cotton prices should be random but that long-term data would fit a predictable bell curve average as they reacted to real-time economic forces (technology, weather limitations,etc). Unfortunately, the data wouldn’t cooperate with the neat-and-clean model. Here is a succinct excerpt from Eureka! Scientific Breakthroughs that Changed the World by Leslie Allen Horvitz:

Mandelbrot understood something the economics professor did not. Mandelbrot wasn’t looking at the statistics: he was viewing the diagram in terms of shapes and patterns. It was his conviction that other laws, with different behavior, could govern random phenomena. He began to extend his search and gathered cotton price movements from the Department of Agriculture records dating back [60 years] all the way to 1900. Mandelbrot was conducting his investigation at a time when economists accepted as a matter of faith that small, transient changes in price had nothing in common with large, long-term changes. Mandelbrot took issue with this view. Instead of separating small changes from big ones, his picture of reality bound them together. Rather than seek patterns at one scale or another, he was searching out patterns across every scale.

When he ran the cotton price data through IBM’s computers, Mandelbrot was gratified to find that the results dovetailed with what he had expected. While each particular price change was random and unpredictable, the sequence of changes was independent of scale. To put it another way, the overall pattern of changes was unvarying: curves for daily price price changes and monthly price changes matched perfectly.

Economics are driven by human behaviors. Buying and selling and acting and reacting all fall under the realm of social activity. And there’s more too…Before Mandelbrot got his computer to make the beautiful spacial and dimensional designs that he later termed to be fractals, another man found a similar patterns in the financial market:

Ralph Nelson Elliot  (1871–1948), a professional accountant, discovered the underlying social principles and developed the analytical tools in the 1930s. He proposed that market prices unfold in specific patterns, which practitioners today call Elliott waves, or simply waves. Elliott published his theory of market behavior in the book The Wave Principle in 1938, summarized it in a series of articles in Financial World magazine in 1939, and covered it most comprehensively in his final major work, Nature’s Laws: The Secret of the Universe in 1946. Elliott stated that “because man is subject to rhythmical procedure, calculations having to do with his activities can be projected far into the future with a justification and certainty heretofore unattainable.” The Elliot Wave Principle posits that collective investor psychology, or “crowd psychology,” moves between optimism and pessimism in natural sequences. These mood swings create patterns evidenced in the price movements of markets at every degree of trend or time scale. (from Wikipedia)

This article, written by Robert Prechter, Jr., describes Elliot’s market trend patterns as fractals even though the term wouldn’t be coined until nearly 30 years after Elliot’s death. (As a brief aside, Prechter developed a theory called socionomics, a theory that addresses the fractal patterns of social trends in areas such as finance, economics, politics, fashion, entertainment, and history.)

So. There you have it. Two tested and true scientifical guys who say that human behavior is, indeed, fractal in nature. I’ll end this treatise with an awesome quote I found in the course of this research, written by Peter Bearse (a Harvard graduate with a Ph.D in economics.)

The discovery that the “geometry of nature” is fractal has radical implications for human beings’ understanding of their society and of their role in things social and political. What does this mean? It means that there is now, for the first time in human history, a firm mathematical and scientific basis for a continuing (r)evolution of society worldwide in ways that focus upon the fulfillment of individual potential as the fundamental aim of human development. Individuals and their actions, however small and localized they may be, can finally be recognized as influences on historical patterns. The “big picture” is a construct of many tiny, interactive patterns. The “Organization Man” is dead or dying in any of his “top down” variations.

Some would say that such a basis was provided over two hundred years ago by the Enlightenment based upon Newtonian physics. Yet, even at the time, the great English artist and poet, William Blake, recognized that this was not so. Subsequent history up to the present time was to prove him right. The Enlightenment was grounded in scientific values, especially relentless testing of theories in light of experimental facts. Mathematical theories provided the basis of Newtonian physics, however, were also employed to rationalize hierarchical systems of power — the dominance of the “little” by the “big,” of the “lower” by the “higher,” etc. Now, such inversions can revert to turn the right side up. The true math-ematical-scientific basis for a continuing American revolution has only recently come into view. And such a view it is! — the potential empowerment of the individual in all spheres depicted by color graphics, creative advertising and fascinating geometrical figures as well as mathematical formulae and scientific studies; enabled by “decentralization,” “devolution,” “flattening of hierarchies,” “reinvention” of selves and organizations, “learning organizations,” “grass roots” individual or community-based initiatives; “think globally; act locally,” and many other ways.

The basis of the fractal revolution is the principle underlying chaos and other natural patterns, that of “self-similarity.” This means that the basic patterns are the same at any scale. They are the same at large “macro” scales as at small “micro” scales. The large is revealed by, and grows out from, the small. Wholes mimic parts (and vice versa); the bigger is revealed in the smaller. (Emphasis in paragraph one added by me. Full article here.)

(Mandelbrot set: by Steffen Rehm)


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(Mandelbrot fractal)

What is a fractal? Why is it important? How can I turn a fractal into a philosophical metaphor that will knock everyone’s socks off? These questions and more have been knockin’ around the old noggin during the last few days…This blog posting will attempt to satisfy each question, and hopefully anyone who may read them.

So, I looked in three different dictionaries and online and found that the definition which made the most sense to me, a physics layperson, on Wikipedia, which is very convenient because I can’t cut and paste from a real dictionary.

fractal is “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. (read more from Wikipedia here.)

The other definitions were pretty hefty, so I won’t reiterate them. What they say, along with the above passage, is that a fractal is a shape that is similar no matter what magnitude you use. Here’s an a good illustration:

(Koch Snowflake graphic by Shibboleth in WikiCommons)

At first it may seem like just a neat shape trick. That is, until you consider that fractals appear all around us. They are inside our bodies (veins, vessels, dendrites, wrinkles, cell makeup) and outside our bodies (trees, mud cracks, crystals, sea shells,  cauliflower, mycelium, stalactites and mites, etc., etc.) Here’s a simplified version of a tree fractal. Notice how each iteration is a smaller copy of it’s parent:

(copied from here.)

Fractals appear to be nature’s favorite building block, withstanding the test of time and constant evolution. Any pattern that appears over and over in nature throughout billions of years must be something very special. One might even call fractals…magic. Here are some really neat examples of fractal images:

(snow crystals magnified using a scanning electron microscope)

(Fern Fiddlehead-photo by Janhatesmarcia)

(Lightning on the Columbia River-photo by Ian Boggs)

So, the only thing left is to leave you with a metaphor that will knock your socks off. There is an ancient Hermetic axiom:

As above, so below.

Things are the same on a tiny (microcosmic) level as they are on the larger (macrocosmic) level. Using one use plastic containers for snacks causes disease and global warming. Arguing with the checkout stand lady contributes to the war in Afghanistan. Being nice to myself gives other people around me the opportunity to learn how to be nice to themselves too. We can save the world by changing our bad habits. Its written into the very fiber of our world…

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(Carl Jung, 1909 in Zurich-photo from the Library of Congress Prints and Photos division)

I’m presently reading a book called The Shadow Effect, written by Deepak Chopra, Debbie Ford, and Marianne Williamson. It is a book all about the dark side of humanity, the dark little secrets about ourselves that we try to banish from our reality. Unfortunately, says The Shadow Effect, banishing “the shadow” only serves to make it stronger in the long run. An excerpt from Deepak Chopra:

The first step in defeating the shadow is to abandon all notions of defeating it. The dark side of human nature thrives on war, struggle, and conflict. As soon as you talk about “winning,” you have lost already. You have been dragged into the duality of good and evil. Once that happens, nothing can end the duality. Good has no power to defeat its opposite once and for all…There’s a shocking conclusion hidden in this: you can’t have a universe if you don’t have darkness contending with the light (The Shadow Effect, p. 14 and 22)

The Shadow is, according to Carl Jung, the part of us (all of us) that causes us to commit unconscious acts of violence or hate against others, ourselves, or the earth. The Shadow doesn’t want you to know it’s there, it wants you to think that it is you, so that it can remain intact. Once you know it’s there, the power of the Shadow immediately decreases. Once you begin to give yourself permission to have darkness in you the darkness looses its iron grip. Here’s another quote from Deepak Chopra:

The shadow, then, is a shared project. Anyone can have a hand in building it. All you need is the ability to remain unconscious. Countless fear-mongers believe they are doing good. Every defender of the homeland expects to be honored and praised. Tribes warring against other tribes deeply believe that they must struggle in order to survive. We resist our shadow and deny its existence because of past indoctrination and the hypothesis of social conditioning. Childhood experiences can cause unending later reminders that “this is good, this is bad; this is divine, this is diabolical.” Such indoctrination is the way all societies are structured. What we over look is that we are creating a shared self at the time. If children were taught to become aware of their shadow, sharing even dark feelings, forgiving themselves for not being “good” all the time, learning how to release shadow impulses through healthy outlets, then there would be much less damage to society and the ecosystem (p 26).

Of course, for children to be taught that the shadow exists and can be tended to in a healthy way, the adults of the world need to first tend their own shadow, which is very hard to do on your own. Chopra gives four steps: 1. Stop projecting 2. Detach and let go 3. Give up self judgement 4. Rebuild your emotional body. It all sounds so easy doesn’t it?

I suggest therapy. Everyone needs a therapist. It’s an interesting phenomenon that so few people use this amazing tool. Many people would rather pop pills (herbal or conventional) to try to feel better, happier, healthier. The only thing that can truly begin to allow you lasting eternal health, is to face your shadow, a shadow that was created in your childhood and has continued to leach your conscious moments more and more assiduously as you let it go unchecked. I love my therapist. Anyway. I end this blog post with a poem.

The Guest House

This being human is a guest house.
Every morning a new arrival.

A joy, a depression, a meanness,
some momentary awareness comes
as an unexpected visitor.

Welcome and entertain them all!
Even if they’re a crowd of sorrows,
who violently sweep your house
empty of its furniture,
still, treat each guest honorably.
He may be clearing you out
for some new delight.

The dark thought, the shame, the malice,
meet them at the door laughing,
and invite them in.

Be grateful for whoever comes,
because each has been sent
as a guide from beyond.


(Click here for the story of this amazing nebula)

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(Robert Kennedy at a CORE rally in 1963-photo from Library of Congress Prints and Photos Division)

My counselor said something very interesting the other day. She said that assertive equals respectful. Usually we think of assertive people as the opposite of respectful. They are more likely described as domineering or powerful or authoritative. They know what they want and they know how to get it and all that.

I had just finished talking about a dynamic between my partner and I, where I feel like my power is being taken away from me and I dig my heels into the ground and refuse to budge. My partner sees this as being assertive. My counselor saw it as being stubborn. Here’s the difference. When I know what I want and can voice it clearly without anger, then I’m being assertive. When I am reacting/defending my (fill in the blank) out of fear that it will be taken away from me, I’m being stubborn. One feels good, helpful, open and loving. The other feels constricting, hateful, small and mean.

I’ve been ruminating on this for a few days now. My New Year’s resolution is to try to stop being so reactive to my partner and everyone else in the world, not because I want them to like me better, or even because I want to be a better person. I’m doing it because it makes me feel better. To hell with altruism! I want to feel great all the time! I want to be relaxed and un-triggered  as much as possible. The other stuff (people liking me better and being a better person) are just welcome side effects.

So anyway, all this got me thinking about being truly assertive and how people think about power. I googled “how to achieve power,” to see what people think about it. (Secretly this is research for a new writing project I’m doing too.) Here are some insane steps that I found on wikihow.com in an article entitled How to Achieve Commanding Success:

  1. Believe in yourself . Otherwise, no one will believe you. However you see yourself, others will see you. Except for possible self-derogatory remarks for the purpose of humor, never demean yourself. Act as if command in social situations has always reverted to you all your life.
  2. Build some folks’ self esteem by complimenting them. People like to be around those who make them see something new or good about themselves. Compliments are doubly effective if you mean them, so whatever good you notice in others, be sure to mention it. If somebody says something good to you about someone else, pass the compliment on.
  3. Wear down some folks’ self-esteem. In his book Impro, the improvisation guru, Keith Richards, says that whenever somebody belittles another’s worth, his own worth rises. You will notice many leaders use this technique, criticizing superfluously. If you notice someone making a mistake or doing something less than good, say, “You’re really bad at handling money.” or “You’re physically clumsy.” However, the point here is not to make him feel worthless; the point is to make him dependent on you and look up to you.

Wow. With advice like this, it’s no wonder so many people are so emotionally twisted up! This is like a recipe for personality disorder! I agree with my counselor. True power comes from a source much deeper than our human intellects can muster. I want to treat the people around me with respect (which doesn’t always mean that I have to agree with them, only that I need to truly listen to them and empathize with their feelings qualitatively), calmly, coolly, and collectedly. Reptile Brain, deactivate! (until a tiger comes anyway…)

(Sojourner Truth-1864-Photo from the Library of Congress Prints and Photos Division)

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