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It's easy to think that "to look is to see". That to open one's eyes, and take in the universe, be it unsuspecting or otherwise, is simple. That to hear, and listen, and "sense" it, is to have sense about it.
Humans have long recognized that there was something weird about their world, and this impression persists. Elders, around long enough to see and believe, relayed this info to their progeny. They wrote it out on cave walls, and built grand structures to show the world and whomever it may concern that, yes, they too thought there was more there than was meeting their eye.
In school, you can study "science", and practice its "method" to better understand what it really is you are seeing and experiencing. You can learn about the fabulously consequential achievements of some of your ancestors who were particularly attentive observers. Soon, you too will begin to notice that, whatever and wherever it is we are living, it's a real, real complicated thing, and that's for sure.
We are now realizing that the great discoveries of Einstein, Newton, and all the other "Plancks" they stood on, were parts of a paradigm that was, in fact, all of these things together, connected in a vastly complex "multi-level universe". The name of the model is "Chaos Theory".
That term, Chaos, means to say this: that in all systems, no matter how chaotic and random things appear to be, there is always organization to be found. Always. Everywhere. Period. That, according to "Chaos", there is no such thing as chaos. Perhaps you need to look harder, but somehow or another it all makes sense.
Born late in the last century, from the observations and evaluations of a diverse group (sociologists, climatologists, biologists, economists, mathematicians), it is a concept known by another name, as "Complexity Theory", which made the cover of TIME around 1992. Though not technically synonymous, "Complexity Theory" and "Chaos Theory" are talking about this same broad paradigm, or explanation, for what it is we are living and awake to. It is widely considered among the great discoveries of that 100 years of human advancement.
Hence, to be hip to it all, the older term has been preferred by many, such that when waxing philosophical one alludes to it as, simply, "Chaos".
Critical to the development of this model are the mathematicians. It is their formulas and number magic, especially when coupled with the amazing speed of modern computers, that have opened our eyes to how so much of the previously unexplainable can, well, be explained. Alas, we've seen already as students of physics and chemistry that "it always comes down to math" on the most basic levels. Now we're wanting to say the same is true of chaos. Er, Chaos.
This matters to humans. Their instincts as survivor freaks mandate that they learn and know as much as they possibly can. So we start this venture, of trying to understand these "folks", humans, here at the beginning, in Chapter One, by trying to understand what is "going on" in the universe in the first place. This thing called livin', a happening we call "Chaos".
Very basically, it is "the fractal" that is the focus of the Chaos Theory Model. A fractal can be considered to represent any "thing" that has mass and therefore form. That is, every "thing". So, trees and people and everyday objects, as well as "things" like cultures and cities, countries, worlds. Teams. Bands. Armies. In the sea and in the atmosphere, groups of gases and water that collectively act as a "thing" show us again how "things" want to aggregate somehow and form, together, a "thing". We call these units-of-anything "fractals", and the anything they are or become a component of, it's "a fractal" too.
Since all things are so positively unique, we use this term that means "unique geometrical object", or "fractal". That term, fractal, was coined by a German scientist by the name of Mandelbrot, who was making them by plugging mathematical equations into his computer. He showed that if you print this on an X/Y graph, the screen soon would "paint" out some very familiar objects we see in everyday life. He called them "fractals". They are actually sets of numbers, generated by this equation, and are also referred to as Mandelbrot Sets.
So why? How can a mathematical equation be connected to something so abstract as living and non-living objects? Is our existence, and the existence of any fractal, somehow driven and locomoted by a kind of mathematical engine?
In this universe that so baffles us, we should try to look at it and see fractals, and employ all our smarts and insights to explore the deep complexities in even the simplest of "things".
Do The Math
When we studied The Calculus in college my teacher, a lefty, said on the first day of class that people have told him often that the course changed their life in some way. It's true of major math. There's a certain messing with the mind that goes on, an enlightened perspective somehow. It lets you notice it's a pretty nutty universe out there. Or out here, rather.
OK. Let's say I throw my pen at the wall. Now, I can always calculate the thing a certain distance from that wall. It gets half-way there, then half of that, and half of that, and so on, and I can always make that number smaller. So, theoretically, the thing never gets there, but I see it smack the wall, so something's wrong with my theory.
We see that, at the extremes of things, simple laws of math and physics seem to "break down", and no longer apply to the situation. Such "never really get there" asymptotes keep wanting to occur at these extremes. What are they approaching?
Einstein showed it was true of Newtonian Physics. For example, according to the math of relativity, we know we can't speed up a particle too much because, at the speed of light, theoretically, it would weigh an infinite amount. Modern scientists have managed to prove through grand experimentation that the math is for real, that length contracts and time dilates, just as Einstein said. And those particles, barreling down those accelerators, really do get heavier.
We see the oddities of math in numbers like primes, in how they are somehow the building blocks of numbers, even though integers seem so countable as to be accountable. Yet we keep seeing indications that all numbers are not created equal. Can this be?
We've seen a handful of constants that are associated with so many basic things. Pi, Fibonacci's number, Planck's constant, the Ideal Gas Law constant. Bernoulli"s constant. What do they mean? Where are they coming from? What about Mandelbrot Sets, and the constant that is in that equation? Are they these numbers?
And consider "1". The "unit circle", with a radius of one, generates the fancy math of trigonometry, based on all that "1" is, and isn't. Waves and circles and cycles, all somewhere in that vast ever and neverland, between zero and "1". When it comes to math, there is no number so significant as "1". (And don't forget that zero, itself, had to be discovered, by the ancient Greeks.)
A fractal is "1" thing, and therefore we must wonder if everything that applies to 1 can somehow apply to the this unit, the fractal. Halved and subdivided in potentially infinite varieties, and yet still "a" single thing.
And what of 2? Pairs, mates, a duplicate. We see things multiplying themselves by themselves, as "squares", a form of 2. A number of great significance, is 2.
Heat energy decreases by the square of the distance from the source, as does magnetism. And the mysterious nuclear force decreases by the cube of the distance, introducing 3. Why is it, the role of such simple numbers?
So, in Chaos, there is much math. It becomes important to know and understand math, because so much we see displays it. Fractals, and the forces that affect them, reek of math, and demand curiosity regarding the connection.
Levels Of Organization
Interaction of objects (i.e., fractals) of similar size identify a scale of activity referred to as a "level of organization". Individual, discrete, similar size-and-form fractals are thusly subdivided at levels from sub-microscopic to galactic scale and beyond. As if to zoom a lens, we can see our transition from level to level, and note the different forces and time-sequences at work in these different levels of organization.
Consider for a moment, the human. As people, we notice we have a certain "personality", evidence of a specific conscious being. We interact within something called a "society", which has its own "personality" and plight, and issues that identify it.
We may choose to hang with a group, a unit contained of individuals with a common enough thread to weave them, however loosely. This unit will take on a "mentality", or identity, as a fractal of folks prone and disposed to whatever, good, bad and everything in between. Simple parties are an example of this.
Occasionally, eventfully, a "gang" of humans will pull an act of "mob mentality", or "mass hysteria", dropping the jaws of observers from without. Together, somehow, they all became "a thing", i.e., a fractal, which acted and "did" what it did. It was created, existed for a time, peaked somewhere, and vanished. Like a cloud, or a storm, or a school or a swarm, or gaggle, units, and therefore fractal. During the time they were together as this unit, stuff happened that wouldn't have had they not so assembled.
We mix societies in a global village, and this same "pattern" becomes apparent. Through war, patriation, and immigration, as well as environmental forces, countries and cultures themselves go through such birth, maturation, and decline. The forces at work at the personal level, the family and friend level, and the local, national, and now "global" levels are all different, and specific to that level of organization of the human fractal.
And the same is happening in the ecosystem that supports them. Plants and animals are being born, maturing, fruiting, and moving on, in the same game as the fancier species that might be chopping or chomping them, as a major force affecting their general fractalling, at this same level of organization. This level, you might say, is the one defined by anything visible to the naked eye and ear, of all that listens and sees.
Let's go to a new level of organization. Earth, itself, is organized somehow into a solar "system", with a center unit that is profoundly large and emits huge amounts of energy, with a number of objects that seem to relate to this "middle". Later we learn that the galaxy is composed of exactly these subunits, solar system fractals you could call them. Like people in a city, or animals in a herd, or air droplets in a cloud, this galaxy, then, a solitary thing, i.e., a fractal.
And apparently even galaxies organize themselves into clusters, and yank and pull on each other as yet another level of organization. We look at gravity as the key force at work in this scale of immense size, and find we know little about most of it.
Now put away the telescope, and get out the microscope. We look inside this "unit", the human, and soon find new levels of organization. We see the individual organs contorted and juxtaposed, and note that while they all are living as one, that they, too, exhibit a certain "personality", showing things they, particularly, like and don't like. For example one may be struck with a certain disease or injury, and may fail before the others.
Microscopically, we see that these organ systems are themselves subdividable as functional units that anatomists refer to as "lobules", where a certain repeating, totipotent group of cells additively perform the function of the whole (fractal) organ. The kidney, for example, has a lobule that is composed of the "nephron", with components such as the glomerulus (the filter), the tubules (for reabsorption of serum contents), and the collecting system, where urine is concentrated. Millions of these make up a kidney. Such lobular basics is true in all our organs.
And lobules, these discrete units, are grouped as "cells", themselves individual units, bound by their cell membrane. Some are round, some are flat, some are real long and skinny. But they are individual, and like the lobule, the organ, and the human itself, they have a personality and a life span that is finite. Some live hours, others for decades. All, fractals within a fractal.
And these cell units, they are composed of "molecules", where a fantastically diverse set of "really small things" inter-play, and combine and separate as "chemical reactions". They are the "cast" of "characters", indeed fractals, at this submicroscopic level of organization.
Molecules, of course, are themselves composed of subunits referred to as atoms, a word that means "cannot be cut". This old term, of course, has proved incorrect, since we can now identify several sub-atomic "things" we call "particles", themselves discrete entities. We know a unique force is at work here. We see it all as yet another level of organization.
So, from subatomic, to molecular, to microscopic, to gross human size, to regional and global and galactic, these are all, separate "playing fields" for existence, and we call them levels of organization.
Forces and Fractals
It should be increasingly obvious that different sets of "rules" or "laws" seem to apply at different levels of organization. Where gravity will toss us hard off a ladder, gravity is a meaningless force at the cellular level, and likewise means little in our interaction within and among societies. And as another example, a tissue's requirements for temperature are much more critical at that level of organization, whereas we can simply put on a coat if we need to.
We know that atoms "react" with each other, and recognize that there is a force they play with called "electronegativity". This force is a measure of the relative attractiveness an atom has for its outer shell of electrons. Weaker elements tend to give up these electrons to elements with a stronger electronegativity, as they combine in a chemical reaction.
At the sub-atomic level, we know that another entirely different "force" is running things, and they call it "nuclear" force. Here, protons and neutrons are magically held together by this very powerful attraction (theoretically, such like-charged entities should repel). And we do know that you can create quite a POP! at our level of organization by cutting some of it loose (nuclear bombs).
Societies recognize forces at work on their individual fractals, the humans themselves, and how the plight of their existence is shaped by them. The role of the family and parenting. Economics. Of media and educational systems. Of proximity in cities. Of birds of a feather, flocking together.
The global villages have still different "forces" at work on them. For example, pro-society forces ("good") have always been noted to be in a chronic titanic struggle with a certain dark force ("evil", or anti-social), and humans have even crafted religious philosophies to guide its members for as far back and as far in the future as anyone can see. Mysterious forces, these. But forces acting on our fractals, for sure.
We wonder what the force is at work in crazy places like solar systems and galaxies, and black holes. Is it simply a gravity thing, or is it a force we can't know how to measure? We wonder, what might make whole galaxies "cluster". Presumably, different forces, for different levels of organization.
The Pervasiveness of Rhythm
Paramount in importance regarding the unfolding of events, and the events that are caused by the forces acting at these levels of organization, is the absolute pervasiveness of rhythm. The simple tendency of all things to begin, accelerate, reach a peak, and then undergo a decline and ultimate demise, or "return" to some baseline, should be considered a huge observation. It is true of nights and days, and light itself is a wave. It's true of sound, and of noise even. It true of wake and sleep. And of seasons, and of epidemics and bug and bird populations. It's true of people, as individuals, and of all things living and having lived. Of stones and mountains and ecosystems, and of cities and countries. And "fads". And worlds and suns and galaxies. We note that, among other things, they have in common this "finite-ness".
Balance sought, perhaps?
We have learned from science of the conservation of matter, and of energy. And of angular momentum (spinning skaters). We know of gas laws and pressure physics, and of social phenomena, and of all things describable by Le Chatelier (dynamic exchange balance in a system). And the bell curve of Gauss. Chaos, in its observations and musings of the fractal experience, notes these cycles, rhythms, dichotomies, and begs to understand this equalizing rule. We see these systems bob and weave and bounce and curl in various manifestations of the inevitabilities of balance, and of "conservation" of everything, and can't help but presume this common thread has this simple implication: balance, sought.
Excerpted from Understanding Humans by Daniel A. Shields Copyright © 2005 by Daniel A. Shields, MD.. Excerpted by permission.
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