All learning centers on one simple question; "How do I know if this is true?" Extending this into the classroom, we might also say, all learning centers on knowing if kids are interested. This week, in our ongoing series on education and learning, we're going explore how teachers might use the only legitimate small group truth test; "fractals," to better gauge their students' interest. We'll do this by exploring an actual fractal from Emergence Personality Theory, the "Face Fractal."
Chapter Twenty Six
Fractals! No, Not That Again! Do We Have To?
Okay. I know. I've repeatedly used a rather esoteric term; "fractals." Scientific types might even accuse me of misusing this word. Or at the very least, casually tossing it around like a layman pretending to be a scientist.
In truth, I use this word a lot. Why? Because I have come to love fractals. And because I have come to love what they can do for me. For instance, with fractals, I can often discern the nature of things within small groups. At times, from a single example. For instance, using fractals, I can discern the essential nature of the way a single child learns. Often, by observing nothing more than this one, single child.
Of course, in order to do this, I must be able to see the fractal patterns which underlie this child's nature.
This said, I would still, at this point, guess that for most folks reading this column, the word "fractal" remains a vague and mysterious term. An obscure geometry of dubious value. If this is how you feel, please don't worry. Moreover, if you have, at all, felt like I've been throwing this word around like a braggart tosses bigness, then please, do not trouble yourself one bit. You see, I quite understand.
The problem is, if I cannot get across to you what the word "fractal" means, then you will be unable to see the truth in most of what I've been saying. This is especially true since much of what I've written contradicts accepted beliefs with seemingly counter intuitive statements. Things like that the problems in education lie in what you cannot see (e.g. the fractals) rather than in what you can see (e.g. the statistics).
In addition, you have heard me openly disdain the use of research statistics for exploring the nature of things in small groups (e.g. the grades of a single child, the reason a teacher is boring). Thus, since research statistics are the currently worshipped god of educational truth, in all likelihood, the only way you'll be able to believe what I'm saying will be to learn to see the nature of my research tool; fractals.
For instance, I've told you that blankness is a state of learning (Dead Stops). And that kids drop out of school because schools make information more important than people (Outer Layers vs. Inner Layers). Are these ideas true? In order to know, you'll have to be able to picture these things as visual relationships. Fractal relationships. Not statistical relationships.
I've also claimed that a ten minute test which results in five pieces of information holds the power to significantly raise the overall level of our kids' educations, nationally, in one year (The Emergence Personality Fractal). And that we can consciously improve our kids' chances for learning if we concentrate on how they do and do not connect to their teachers (Layers 9 and 10).
Are these things true? Here again, if you cannot see the fractal relationships behind these ideas, you cannot know.
What, then, can I do to help you to know if these things are true? To be honest, I know of only one thing. I need to take another crack at teaching you to see the nature of fractals. Not just the nature of oak leaves and cumulus clouds, mind you. Rather, I need to teach you the very nature of fractals themselves. A nature so obvious and simple that even the most well meaning complexity scientists have so far missed it. And yes, I know what this statement makes me sound like.
And if you still don't understand what fractals are?
Then I'm afraid you'll have to delve deeper into what prevents you from connecting to me. You see, no connection, no learning. At least, no real learning. And lest you think what I'm saying here is mere hype, consider this. One of the most respected men in educational research, a Harvard man, recently rejected me. And my work. Why? Because he didn't like a word I had used in my e-mail address. An old e-mail address, no less. The word? "Mystical."
Imagine. A world famous educator and researcher with whom thousands of teachers study dismissed my entire life's work because of a word in my e-mail address. Sight unseen. So what does this say about his scientific methods? More important, would you want this man to be your child's teacher? Talk about killing the love of learning.
Fortunately, even if you have these prejudices, if I can get you to understand fractals, you'll have a way to see past them.
This said, now let's take yet one more look at what underlies, and proves, most of what I've been presenting here; fractals. Hopefully, I'll at least spark enough interest in you to permanently arouse your curiosity.
To this end, I'll offer you a useful example, an easy to learn fractal tool which could help you to better understand your students during class work. And most everyone else in your life as well. How? By teaching you to read certain movements within peoples' faces. Mostly, within their eyes.
Are you at least a little curious? Or skeptical, perhaps. Then let's begin.
What Is A "Fractal?"
So what is a "fractal" again? Begin by knowing that a fractal is one of the two kinds of geometry present in our world. And yes, no matter what people say, in our world, there are only two major categories of geometry. Fractal. And other than fractal. Which, to simplify the process, we'll refer to as fractal (non linear) and classical (linear).
Now before proceeding, let's first define the word, "geometry." What is "geometry?"
Geometry is the measurement of visual shapes and patterns. Spaces, originally. Moreover, you can know this for yourself by dissembling the word. The "metr" part of the word comes from an old english word which meant "limits" or "boundaries." Thus the "metr" part tells us what we do with geometry; we measure the limits of something. As in meters, and metrics, and metronomes.
The "geo" part then comes from a word referring to the space in which we live; Earth. Thus, the "geo" part tells us what we're measuring; we're measuring the visual patterns of the spaces in our world, as in, "geography" (measures of the visual patterns of earth spaces) and "geology" (logical words about the visual patterns of earth spaces.)
Expanding on these ideas a bit, it might be helpful to know that in ancient Greece, measuring the visual patterns of spaces (geometry) was considered sacred knowledge. A science which the ancient Greeks believed allowed them to peer into the very nature of the spiritual world. Or at least, a way in which they could know there was a spiritual world. And in truth, I'm saying very similar things here about fractal geometry. Specifically, that it has sacred qualities, one of them being, that it reveals the underlying structure of natural objects. Or the true visual essence of natural relationships, if this is easier for you to grasp.
As for what makes these two geometries different, know I have spent several decades looking for a way to define fractals. To my surprise, I discovered that we can completely define the essence of these two things using only three qualities. Moreover, two of these qualities are the same for both geometries, while the third is what makes them different. Let's start with the two qualities which are the same.
The first quality. Both classical geometry and fractal geometry refer to recognizable shapes. This is the first quality. In order for it to be geometry, we humans must be able to recognize these shapes. At least, in theory. And while it might take a bit of work to learn how to do this, this quality must always be present. No recognizable shape. No geometry.
The next quality? Both classical geometry and fractal geometry must refer to recognizable shapes which always repeat. This is the second quality. In theory, all classically geometric shapes can manifest in an infinite amount of ways. So too naturally occurring fractal shapes, which can also manifest in an indefinite variety of ways.
The thing to know here is that when I say, "always repeat," I'm basically referring to that geometric shapes can manifest over and over and over and still not exhaust the possibilities. This potential for repetition is what this second quality refers to. Moreover, it also refers to that in geometry, these repetitions are ongoing. Squares to circles. Waves to water erosion. Cubes to trapezoids. Pendulum swings to mood swings. All these geometric repetitions recreate themselves in endless ways.
Note that it is this second quality which disqualifies as fractal most man made objects, such as couch covers and wall paper. At some point, the detail within these things ends. Whereas, with the nature of something like stock market sales, while humans do initiate these transactions, the resultant cost variations are indeed fractal. Why? Because there is an infinitely detailed nature hidden within these variations, a natural complexity which defies linear analysis. As well as that there are endlessly recurring, recognizable patterns within what appears to be an infinite quantity of detail.
So "always repeat" is the second quality. Then there is the third quality, the one which makes these two geometries differ. What makes these two geometries different?
Classical Geometry refers to "recognizable shapes which always repeat identically," while Fractal Geometry refers to "recognizable shapes which always repeat differently." This is the entirety of geometric definition. Simple, really. However, like E=MC2, this very simplicity is what makes it so hard to grasp.
All this said, what exactly makes these two geometries so important to education? Sacred, even?
Their importance lies in that they are the only two ways in which we can truly learn to know and recognize things. Moreover, in order for us to know the nature of anything in our world, we must be able to recognize the visual patterns of relationships present within these things. No visual recognition. No real understanding.
In essence then, both geometries hold the potential to be our teachers. They are, in fact, the essence of being a teacher, regardless of what subject is being taught.
Why this need to be able to visualize a thing's nature in order to learn what it is? Because all things within our world are made of light. And while much of this light falls outside the range of our natural eye sight, with analog aids (like televisions and radar), we can see all of these visual patterns. Which is why we Emergence Practitioners define "human consciousness" as "the skill of picturing movement."
Here, "picturing movement" is just a way to refer to that we know things only by measuring light. No coincidence, "picturing movement" is yet one more way to refer to what happens in fractal geometry.
Some would now ask, but what if an oak leaf (which is fractal) were perfectly still. Would this mean it was no longer fractal?
My answer? No. The leaf would still be fractal. Why? Because the thing which enables us to see this leaf is that something in this measurement process must be moving; either us, or the leaf, or both.
What I'm saying here is, the movement I've been referring to here is "relative" movement. The very word which defined Einstein's genius, in fact. This means, whenever we look at a thing, the quality which enables us to see this thing is "movement."
What I'm saying is, either us, or the thing we are looking at, or both, must be moving. No movement. No access to the nature of the thing.
With oak leaves then, if an oak leaf were ever to be perfectly still, and if we could ever keep our eyes perfectly still as well, we would quickly lose our ability to see this leaf. Why? Again, no movement, no vision. No vision, no consciousness. This, in fact, is the nature of the screen of the mind going blank.
In real life, though, everything is always moving in relation to something else, molecules to solar systems. Thus, this stillness never actually occurs. Except in our minds, of course. Moreover, because it doesn't, it never occurs to us what we would happen if it did occur. Invisibility, to be exact. Again, the blank screen of the mind.
Finally, there is one very important idea you must know in order to access the power of fractal geometry. This idea? That in order to see the truth within things, you must, in some way, shape, or form, be able to picture the visual pattern of movement underlying this thing; peoples' faces to academic grades; personal psychology to astrophysics. No moving picture. No understanding. Period. No exceptions.
So what about logical understandings? Can't we logically understand things? Good question. To see the answer, imagine you are visiting a world famous art museum, and as you stand in front of what should be the Mona Lisa, you see only an empty frame with a descriptive plaque beneath it. Now add to this that you are one of the few civilized human beings whom has never seen a visual representation of the Mona Lisa. And that you have been asked to visually describe the Mona Lisa. How well do you think you'd do?
The truth is, even if you were to have learned every logical truth about this painting, and about the painter, and about his times, you still would fail miserably. Why? Because even with the myriad of logically true things you could say, given the rest of eternity, you could not know the visual essence of this painting. Why not? Because human consciousness relies entirely on how our minds fill in that frame. Moreover, in order to know the nature of any naturally occurring thing, we must be able to fill in our minds with recognizable patterns of movement.
What I'm saying here is, the most beautiful logic in the world is still mere captions to these pictures. Why? Because the very nature of beauty itself is rooted in recognizable visual movements. Including in the Mona Lisa herself. As well as in the nature of each and every human virtue, including the nature of truth.
Now let's explore the movement in an actual fractal pattern; the fractal pattern of human eyes.
the Emergence Face Fractal
You can start by taking a look at this week's diagram; the Emergence Face Fractal. What the heck does this diagram represent?
Very simply, it represents the ways human eyes physically move. The basic observable visual patterns human eyes make. Moreover, since this diagram represents a "recognizable visual pattern which always repeats differently," what is in this diagram is fractal geometry. Literally.
What can we learn from this fractal? To see, begin by locating the vertical line which runs smack down the center of the drawing. This axis of movement is our Current Information Line. Specifically, it shows us the kind of information we are currently seeking. And exploring.
As for the movements which occur on this line, "looking up" movements mean we are looking for our thoughts. Our current "mental" information. And "looking down" movements mean we are searching for our feelings, meaning, our current "emotional" information. "Looking straight ahead" then means we are looking to know both. The whole enchilada. The real deal.
Now to see how powerful this line really is, try looking up while trying to sense your feelings. Makes sure you are only looking up with your eyes and not with your whole head. Now try to sense what you are feeling. Did you feel any urges to sense these feelings by looking down?
Now try looking down with your eyes this time, again, not with your whole head. At the same time, try to sense your thoughts. Interestingly enough, you won't be able to do this without feeling urges to look up. At least, with your eyes.
Of course, if you push yourself hard enough, you'll eventually be able to override these urges. Even so, the point is, seeing someone else make these eye movements will unconsciously communicate to you the very thing I've been describing; the true nature of the kind of information the person is currently seeking. Mental. Or emotional. Or both.
A thing to note here is, this line of eye movement, the Information line, is the only one which does not vary with handedness, meaning, with right handedness and left handedness. More important, in this particular diagram, every other line represents eye movement norms for right handed people only. Left handed folks will feel urges to move in the opposite directions. More on what makes this important in a moment.
Now locate the horizontal movement line which goes right through the center of the drawing. This line is the Current Revelation Line. Movements on this axis tell us about our urges to reveal or withhold what we are sensing. Of course, in its extreme form, this revealing dictates whether we will "tell the truth" or "withhold the truth" (lies by omission). However, the important thing to see here is mainly how these eye movements predict our internal urges. In reality, we often choose to override these internal urges.
Okay. So now try this. Ask someone to look you in the eye. Then ask them to look to the right while telling you something. Anything at all. The weather. Their name. Their date of birth. What you'll find is that you'll unconsciously sense they are telling you the truth. Moreover, if you now have them tell you these very same things while moving their eyes to the left, you'll find, you'll feel urges to question what they're saying.
What does this imply? A whole lot, actually. Beginning with that in medicine, O.S. means the left eye. Do you know what this "S" represents? It comes from a Latin word which means, "on the left." The word? Sinister. Now think about what this tells us about why we have historically treated left handed individuals with less respect.
Studies show that human babies learn to recognize facial expressions before they speak words. And as most folks in our world are right handed, AND as no one teaches us to see this fractal, many of us feel internal guidance which makes us misinterpret the eye movements of left handed people.
You see, their horizontal facial fractals are the reverse of right handed folks. No surprise here. However, because this occurs witout us ever noticing it, when they look to the left, it means they feel urges to reveal the truth. And when they look to the right, they feel urges to withhold the truth. Moreover, since this visual pattern is the reverse of what most of us internalize as babies, we can easily mistake the motives of left handed people. Which, in all likelihood, has been happening to us for as long as there have been left handed people.
Are you beginning to see how valuable this fractal pattern could become?
Now let's look at what is written in the diagonals between these two crossed lines. The four quadrants formed by the intersection of Current Information Line and the Current Revelation Line.
In the upper right quadrant (which is to your left as you face this diagram), you'll see I've written the combined meaning from these two lines; urges to reveal my true thoughts. Here, true thoughts is indicated by right eye movements on the horizontal line, and urges to reveal these thoughts are indicated by upward movements on the vertical line.
And in the left quadrant? Urges to withhold my true thoughts, as implied by right eye movements on the horizontal line and upward eye movements on the vertical line.
Looking at the bottom quadrants now, you'll see that in the lower right quadrant, I've written urges to reveal my true (right on the horizontal line) feelings (down on the vertical line). And in the lower left, urges to withhold my true (left on the horizontal line) feelings (down on the vertical line).
Please note, these eye movements can be accompanied by head movements as well. Thus, what follows is more focused on head movements than on eye movements. Obviously, both can be in play.
Thus, if you now look at the end points of the two crossed lines (Information and Revelation), starting with the "up" end, you'll see the implied meanings of this head movement. Here, I've written, "I trust my mind." And down? "I trust my heart." To the left? "I want to lie" (or at least, withhold the truth). And to the right? "I want to tell the truth."Now notice the bi directional movement lines just inside of these four head movement end points.
The upper lines represent head movements which vary right to left and back. These particular head movements represent intellectual indecision.
And the lines just above the lower end point? Emotional indecision.
What about the lines just inside of to the person's right end point? The truth be told.
And to the inside of the left end? A person is telling a lie while saying that what he or she is saying is true.
Finally, notice the yellow oval in the middle of the drawing. This oval represents the eye movement zone within which we can visually picture on the screen of the mind. Thus, if you try to look all the way up with your eyes while holding your head level and straight ahead, you'll find it tough to picture anything. Think? Yes. But the screen of your mind will tend to empty.
Conversely, if you try to look all the way down with your eyes while at the same time, holding your head level and straight ahead, you'll again find it tough to picture anything. Feel? Yes. But again, the screen of your mind will tend to empty.
Interestingly enough, most folks find it easy to picture while looking to the left or right while holding your head straight ahead and level. This is why I call this oval of movement, the "awareness zone." Perhaps, this is also the origin of the cliche, "being on the level."
Finally, if you notice the orange circle in the very center of the drawing, you'll see I've labeled it, the "zone of consciousness." Here, it seems, in order to be fully conscious, we need to be looking straight ahead and level.
Perhaps this is the origin of the cliche, "being straight with me."
So what does all this prove? It proves that whether we consciously recognize fractals or not, we still respond to them. At least, unconsciously. Moreover, these unconscious urges deeply affect our judgments as to what people are saying to us. As well as other's judgments of what we are saying. Can you imagine how this affects our ability to trust a teacher? Or believe a student?
What good then would learning to recognize this fractal do us? For one thing, making any fractal pattern conscious means we get to have a say in what we think and feel about people. Including about ourselves. We literally become more conscious.
We also get the inside scoop on how our head and eye movements may be affecting others. Including whether they find us believable or not. Or even worth trying to connect to. Most significant still, by learning to recognize this fractal, we get to witness a real world example of the power of fractal geometry. Not simply as some on paper, technical, cold scientist's data, but rather as a warm, flesh and blood, human pattern of eye movement. "A recognizable visual pattern which always repeats differently."
Are you beginning to see what makes me so love fractals? Can you imagine how much power they hold to change our kids educations?
Know this is only the briefest look at this potential power. In fact, next week, I intend to reveal to you the four most basic fractals in all of human nature. The four visual patterns beneath all of human personality. All of it. Every last thing.
Are you at all curious? Until next week. I hope you are all well.