Archive for the ‘Form from Chaos’ Category

(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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(Roger-Noël-François de La Fresnaye)

I was reading a blog posting this afternoon when I came across this quote:

The greatest threat to science and scientific progress is not religion, ignorance, or superstition, it is the mistaking of a model or paradigm for Reality, or “laws of Nature.” It is the creation of a type of religious fundamentalism around a paradigm – a kind of black and white, authoritarian absolutism about the model.

I couldn’t find the author of the quote, so I googled it. It belongs to Richard Milton, author of a book entitled Alternative Science: Challenging the Myths of the Scientific Establishment. There is a “read inside” option on the Amazon page for this book, and so I did. In the introduction to the book (which is pretty much all I could read for free) I found some very interesting information.

After mentioning a few scientists who were demoted or dismissed because their work showed “repeatable and empirical evidence” of such things as consciousness affecting electric instruments, positive effects of homeopathy, and the discovery of cold fusion (which is cheap and isn’t supposed to work–despite the fact that 92 universities and corporations have recreated cold fusion results), Milton goes on to say that:

The scientific fundamentalism of which these are disturbing signs is found today not merely in provincial pockets of conservatism, but at the very top of the mainstream management of science, on both sides of the Atlantic. In times such as these, some academics appoint themselves vigilantes to guard the gates of science against troublemakers with new ideas and new discoveries.

This all reminds me of the latest chapter I read in The Incarnation of Ahriman by Rudolf Steiner. I go back and forth on some of the things that Steiner said, but , I’ve gotta say, this particular chapter really vibed with me. He basically said that the ancient people knew inherently that spirituality was a part of the world around them. They felt themselves in the stars at night. They believed that the forces that push the water down the river were also inside of them. They knew that if they prayed, the energy from their thoughts would reach the gods of the rain and these gods would bless them. Our newer, more evolved sensibilities have put the kibosh on this type of tomfoolery. We believe that for something to be accepted, it needs to be evidenced in repeatable scientific forms. None of this “it just feels right” nonsense for us…

(This is a bit ironic because we often trust scientists to tell us what our reality is, because we can’t always experience it ourselves. When I teach my middle school class about some historical scientific beliefs, such as “the world is flat” and we all giggle and yammer about how silly that is. The funny part is that I have never experienced first hand the roundness of the Earth. If some highfalutin scientist came on the news and said that they have just proven in Laboratory LMNOP that the Earth is actually shaped like a stiletto high heel, experientially speaking, I would have no evidence to disprove her…We trust scientists to shape our world view for us, because we don’t have rocket ships or billion dollar labs.)

Steiner goes on to say this:

Today, gazing up from earth to the star-world, it appears filled with fixed stars, suns, planets, comets, and so on. But with what means do modern human beings examine all that looks down on them out of cosmic space? They examine it with mathematics, with the science of mechanics. What lies around the earth is robbed of spirit, robbed of soul, even of life. It is a great mechanism. What the ideas of Galileo and Copernicus have brought to mankind is grand and mighty, but not an absolute truth, by no means and absolute truth. It is one aspect of the universe, one particular perspective. For modern education we need these illusions of a mathematical nature about the universe, we must acquire them, but we must know that they are illusions. (emphasis added by me)

It just feels right.


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(Jean-Baptiste Lamarck)

In the last month I have witnessed a lot of death in nature. There was the green snake killed by the scrub jay (an experience on which I wrote a blog entry). Then two weeks ago I saw a little brown bird being pecked to death by a crow. Over the weekend I saw a tiny squirrel baby separated from it’s mom, and very near death. Today I saw a badly injured jay being killed by another jay. That is a lot of nature kill in a very short period of time.

I remember reading the book Animal Wise by Ted Andrews. Andrews says that the world of nature “mirrors the magnificence of our souls.” When animals show up in our lives, they are there as messengers of the divine, to direct us on our spiritual path.

What’s my message after seeing all this killing and death in nature around me? Smite the weak? Root out the timorous and peck it to death? If I were to take Andrews literally at his word, I might  think my spiritual path had taken a decidedly Darwinian turn. That is, if I hadn’t recently read this:

Unfortunately, we conveniently “forgot” about the cooperation necessary for evolution when Charles Darwin emphasized a radically different theory about the emergence of life. He concluded 150 years ago that living organisms are perpetually embroiled in a “struggle for existence.” For Darwin, struggle and violence are not only a part of animal (human) behavior, but the principle “forces” behind evolutionary advancement. Darwin wrote of an inevitable “struggle for life” and that evolution was driven by “the war of nature, from famine and death.” Couple that with Darwin’s notion that evolution is random and you have a world [of] a series of meaningless, bloody battles for survival. (from The Biology of Belief by Bruce Lipton)

Darwin gave us “survival of the fittest.” He told us that if you want to win, you have to beat everybody else. But, as Lipton points out, Darwin may have gotten the scoop on this story, but he wasn’t the first scientist to have a theory on the topic. A French biologist, Jean-Baptiste de Lamarck wrote a book on evolution fifty years prior to Darwin.

Not only did Lamarck present his theory fifty years before Darwin, he offered a much less harsh theory of the mechanisms of evolution. Lamarck’s theory suggested that evolution was based on an “instructive” cooperative interaction among organisms and their environment that enables life forms to survive and evolve in a dynamic world. (Biology of Belief)

Lamarck’s theory was shot down by scientists of the day and by the church, both of which adhered strongly to creationism. However, modern scientists are beginning to come back around to this theory, noting the many instances of symbiotic relationships in nature.

We need to move beyond Darwinian theory, which stresses the importance of individuals, to one that stresses the importance of the community. British scientist Timothy Lenton provides evidence that evolution is more dependent on the interaction among species than it is on the interaction of individuals within a species. Evolution becomes a matter of the survival of the fittest groups rather than the survival of the fittest individuals. (Biology of Belief)

Darwin’s theory gave rise to the ideals of modern capitalism. Get rich. It doesn’t matter who or what you destroy on the way, because they are weaker than you if they can’t beat you. Only the strong can survive and the weak don’t matter.  The oil spill isn’t really Darwin’s fault, but the way that he presented the world, as a war of individuals, certainly encourages the ideology that created it. But Lamarck knew that that which appears to be weak is a part of the strong, and by destroying it, the whole is compromised.

The green snake, the brown bird, the baby squirrel, and the jay are a part of me. The message is (right now anyway) that things (ideas, experiences, thought patterns) can be broken down and taken apart and let to leave my present existence, but through my good intents and practices, their gifts will not be forgotten or capitalized upon inappropriately. I didn’t cause the pain, but I am witness to it, and I honor the power behind it. As in nature, balance is key.

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I just got back from spending a night with twenty-one 5th graders and eight parents. We had really good food, thanks to the selfless devotion of one Jason B., who held a “food prep night” before we left. Fresh greens, garlic bread with real garlic, tomato sauce with fresh oregano. And real meatballs. Then liege waffles for breakfast. And quiche. With bacon. The kicker? He made home-made marshmallows. Seriously! I thought that only machines and chemicals could make marshmallows! But no. And boy howdy, do they ever make good ‘smores.

The trip was well organized, thanks to the help of Luminara S. We did a plant and animal scavenger hunt (organized by Pat B.) in the woods, an intuition game  (you get blindfolded and have to walk through the group of classmates who stand like trees), built tree limb shelters and we did a talent show. We found a dying baby squirrel who was parted from his mamma. We walked under two waterfalls. We got dumped on and checked into the lodge an hour early. We sang Israel Kamakawiwo’ole’s Somewhere Over the Rainbow around the campfire. It was great.

The lack of cynicism was amazing. They sang along with that ukelele like nobody was watching. They walked toe-heel through the forest, quiet like foxes, as the Whole Earth Nature School instructor had  shown them. They wiped the spit off the spit bug to see what he looked like under there (the spit comes out of his butt!). They assiduously stuffed the chinks in their dead wood shelters with moss, then tore it all down without complaint when we were done.

One of my favorite teachers, a man named Dennis Klocek, said that children are able to rest through appropriate play. I don’t think I fully understood that until this weekend. They are resting from the pulling of the world, from media telling them who they are supposed to be, and from the feeling that they just aren’t measuring up to that invisible standard. In play, they are able to let their imaginations and curiosity take over for a moment, without feeling like it’s wrong or stupid. They can relax within themselves.

As always, this weekend my students taught me more than I could ever hope to give to them. I am very blessed.

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I’ve been tired. I believe, if I’ve counted properly, that I have 14 1/2 days of school left. (I mentioned this fact on Thursday and one of my students said that he didn’t know that teachers counted down too. Ah youthful naivety).

I thought I was going to talk about John Dee in this blog. I’m going to start it off different, and see if I cant’ squeeze him in there.

In my tiredness of late, I’ve found myself wanting to watch movies. I’ve watched a bunch this week. A scratchy copy of Shrek pt 1 (which went from two hours down to 45 minutes with all the skipping. Ugh for skippy movies. I hate that moment when the machine makes that stupid noise and you know its going to skip and all you can do is boil on the inside as the words “skipping over damaged area” pop onto the screen), a humdrum thriller entitled Duplicity, an artsy queer movie called Do I Love You? (which I had to turn off do to a high level of failure to be a good movie), and The Proposal, starring America’s Favorite Sweetheart, Sandra Bullock.

Watching all these movies did not rejuvenate me. In fact, I think it made the tiredness worse. I watched the movie so that my brain could rest, but I think it just drugged my brain into dumbness.

Thinking about this reminded me of the Ekhart Tolle book, A New Earth. Tolle would say that my consciousness slipped below my thoughts. He also says that true peace will only come from lifting my consciousness above my thoughts. Wow, that sounds like hard work. Although I suppose that consciousness can’t really weigh that much. Why is it so hard to get it up there then?

Perhaps when I let my consciousness grovel around down there under my pesky thoughts, it gets a little heavy. Out of shape, if you will. And dirty. There’s a lot of dust bunnies down there.

When I lift it up, above my thoughts, that consciousness gets into shape. All that pullin’ an’ squeezin’ makes a consciousness firm and taut. No dust bunnies.

The paradox is that when I do the work to get quiet and lift myself above my thoughts, my brain can rest. When I get lazy and let myself slip into unconsciousness, my brain can’t really rest. It just gets lethargic.

But to be fair, I bet even Jesus would watch a good BBC movie. Or a little Discovery channel. Lethargy in moderation?

Next up: John Dee (couldn’t squeeze him in).

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My next door neighbor invited me to come over and watch his dog (and his cable) last friday night. I was watching an episode of the Ghost Whisperer (starring Jennifer Love Hewitt, who I last saw in that one show from the nineties…I keep thinking it was called Eight is Enough but that isn’t right…you know, the one where the parents die and the kids have to fend for themselves in a cold, hard world, even though they are all so painfully attractive that you sort of feel sorry for them? Anyway.) About halfway through, I saw an aspirin commercial. In the commercial, they showed a person’s skeleton (in electric blue, with pulsing red spots of pain, of course) inside her body as she walked along with her grandchild and her golden retriever.

The lady’s bones looked so clacky and awkward in there, like she was really a robot, or a marionette. Ever since I saw the commercial, I keep picturing what I would look like if I was just bones. (I usually picture white ones, rather than electric blue with pulsing red spots. White is more dramatic for bones.)

Sitting on the couch, legs crossed, reading a book, I’m a skeleton. Standing in front of my 5th graders, writing fractions on the board, I’m a skeleton. Lunchtime, chewing my food, inflexible white jawbone on a rubber band, up and down, up and down it goes, mechanically mashing my taco–which crumbles and falls out the sides, with no cheeks to hold it in–I’m a skeleton.

Imagine if all the flesh in the world disappeared for a day (without us dying of course, which would be impossible, as you know), and we saw what our bodies look like underneath all that fat and blood and glandage. For a little while we would be scared, because we aren’t used to our bones being visible. They move funny. Bones are what mummies are made of and mummies kill you.

Here’s an interesting excerpt from The Tibetan Book of Meditation by Lama Christie McNally:

Stop now and feel the bones beneath your skin. Think of the flesh now covering them—even now it is already in the process of rotting away, getting older by the minute. Picture how it will be in the future—see your flesh fall off and return to the earth, leaving only the pristine white of this pile of bones behind.

Oh yeah! You’re bones are under there! You are a mummy, waiting to happen. Right now, there is a skeleton encased in fat, skin, hair, glands and oily secretions, sitting on your chair scrolling through this blog entry. Gross. (But cool!)

The Bone Poem

Tell me again about the slick bones
of the skull: occipital,frontal, temporal, parietal,

and the forgiving groove of fontanels
stone-hard and stubborn. Tell me about

cervical and thoracic vertebrae rising
from the lover’s lumbar curve, about

and sternum, and floating ribs falling south.
Tell me about humerus, twisting dance of radius

and ulna, how all twenty-eight phalanges
swing open on the hand’s silent hinges.

Tell me about cane-shaped femurs, the fluted
pipe of tibia, and slender, clasping fibula,

tarsals wide and sure, and calcaneum, the calculus
of our unending path. Tell me about the smooth bowl

of the pelvis with its high and wide iliac crests,
the sacrifice of sacrum, and coccyx, memory of tail.

Tell me again about the bony tools of the ear,
how hammer, stirrup, and anvil return to us

the sounds of our small, miraculous lives.

Heather Davis

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