Quest Magazine

By Theodore St. John

Originally printed in the SEPTEMBER-OCTOBER 2005 issue of Quest magazine. 
Citation: St. John, Theodore. "Timeless Epiphany." Quest  93.5 (SEPTERMBER-OCTOBER 2005):175-179

When we try to pin down the origin of the time-flux in our perceptions we encounter the same tangle of paradox and confusion that greets attempts to understand the self, and it is hard to resist the impression that the two problems are really closely related. I strongly believe that it is the 'whirling vortex of  self-reference' which produces what we call consciousness and self-awareness that drives the psychological time-flux. It is for this reason I maintain that the secret of mind will only be solved when we understand the secret of time.

—Paul Davies, God and the New Physics

Time flows. But if something flows, it changes with respect to time. So time must change with respect to time. But nothing can change with respect to itself. This paradox flows from the basic paradox inherent in the definition of time. Read any general physics textbook and you will find that time is defined by a unit of time: the duration, or amount of time from one cycle to the next, of a time standard. Any phenomenon that repeats itself may be used as a time standard.

Time is not defined as something, but by something because nothing physical can define a unit of time. It has no physical existence, though it can be measured. Time is not material itself, but a concept that allows one to understand change in the material world. The fact that time is not physical doesn't matter to science. As long as it can be measured, it can stand on its own. It is considered real.

Space, in terms of length, is defined in the same way: by the measurement of something that occupies space, like a ruler. But it does not present the same paradox as time; a unit of space is defined by a physical object, which does not appear to change. It is tangible and much easier to grasp because you can literally grasp it in your hands. A student must accept both these definitions as fact in order to learn any of the other relationships in physics, but some of us never get over the gnawing feeling that something is missing in the basic philosophy behind these concepts. And then there are those who have experienced timelessness, a mystical moment of extreme clarity that reveals innate wisdom and leaves one with certainty that there is some kind of ineffable distortion in our everyday perception of reality.

The mystery of time and timelessness is an ancient one that is probably solved in every generation of humankind. You would not think to find it written in science texts because those who understand it do so through direct experience of timeless unity. They generally express their experience artistically in terms of images, allegories, myths, and parables. These expressions automatically take on a religious and even fairy tale appearance, and are thus forbidden to enter the halls of science. However, the question of time and timelessness does appear at the pinnacle of quantum physics, in an equation known as the time-independent Schrödinger equation. This equation is too difficult to explain here, but it is mentioned here to direct the interested reader, who is academically inclined, to learn how timeless reality is understood in modern physics. If you are interested, The Tao of Physics by Fritjof Capra is a great place to start.

Science is based on measurement, and time and space are fundamental units of measurement. I submit that the circular reasoning used to define time and space—two different aspects of the same—is what creates the "whirling vortex of self reference" in ordinary perception. This conceptual vortex locks the metaphorical sword of awareness in the stone of measured reality.

In The Metaphysical Foundations of Modern Science, first published in 1924 and most recently in 2003, Edwin A. Burtt recognized the problem with the idea of absolute time. Burtt explained that the concept of space and time as independent quantities, each with their own fundamental existence, is actually a relatively new idea, which was defined by Isaac Newton in the seventeenth century.

Before Newton, the difference in space and time was certainly recognized. People knew that things moved in space and changed in time, but they were not considered to be fundamentally different phenomena. Instead, they were seen as aspects of motion. The strict definition of time as an absolute was then stated by Newton:

Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without regard to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time; such as an hour, a day, a month, or a year.

This definition was accepted because it was such a useful concept. In order to derive meaning out of reality, Newton separated motion into two aspects and considered time to be the absolute. Motion then was considered to be secondary, the process by which time was measured. He did the same thing with space, saying that absolute space remains always similar and immovable, and then defined absolute motion as a translation from one absolute place to another. We are so used to it that we rarely give it any thought and when we do, it is hard to imagine any other way of looking at it. But back then, the idea of motion as a measure of time was recognized as a philosophical blunder, as expressed by mathematician Isaac Barrow:

Nor let anyone object that time is commonly regarded as a measure of motion, and that consequently differences of motion (swifter, slower, accelerated, retarded) are defined by assuming time as known; and that therefore the quantity of time is not determined by motion but the quantity of motion by time: for nothing prevents time and motion from rendering each other mutual, aid in this respect. Clearly, just as we measure space, first by some magnitude, and learn how much it is, later judging other congruent magnitudes by space; so we first reckon time from some motion and afterwards judge other motions by it; which is plainly nothing else than to compare some motions with others by the mediation of time; just as by the mediation of space we investigate the relations of magnitudes with each other (Burtt 158).

Motion is the fundamental reality, not time or space. As the Greek philosopher, Heraclitus said, "The only constant is change." Motion is change; time and space are only measures of motion, conceptual tools that we use to "compare some motions with others by mediation." We need something constant for our minds to hold onto, so we artificially separate change (motion) and defined relatively constant units called space and time. A spatial measurement does not actually measure space, it measures a change in space. In order to measure something in space, there has to be a difference between one end and the other of the thing being measured, and there must be a way to identify the ends, such as the physical ends of the ruler or tick marks on a line. The same is true for a time measurement—it is a measure of change from a point in one cycle, to the same point in the next.

A spatial standard does not require any sort of pattern, although a regular pattern in space can certainly be used as a standard since a beginning and an end can be perceived. But a time standard must repeat at regular intervals because the regularity of the interval is what allows one to pin it down, that is, to mentally convert change into an apparent constant.

Something that can be perceived as changing repeatedly by the same amount in both space and time, such as the wave pattern shown in figure 1, can be used to define both space and time. This is the key: you can measure change in two different ways, spatial and temporal, so it appears that the measurements are two fundamentally different phenomena. But it is the measurement that makes them appear to be different, not the phenomena themselves. Space and time are two different ways of measuring change. The only difference between the two measurements is the frame of reference. If the observer is in the same frame as the wave, there is no relative motion between the observer and the wave, so the only change that can be measured is the change in space, for example, from the beginning to the end of the wave. In this case, the wave cannot be used to measure time. A second frame of reference, one that moves relative to the first, is required for the wave to change in time.

To illustrate this, look at the wave pattern in figure 1. It is stationary in your frame of reference, so there is no way to use it as a time standard. It can be used to measure a unit of space because you can see where the wave crosses the grid lines. I could now define one unit of space as the distance between one cross-point and the next. Distance is, of course, an amount of space, and defining space as a measure of space is circular reasoning. But that circularity can be avoided by saying that a unit of space is the difference or change between one cross-point and the next.

Now, if you could not sense anything else in the universe, you would not experience the "psychological time-flux." If you forget about everything else that tells you that time is passing, such as clocks, schedules, aging bodies, increasing entropy, and so on, and focus only on the wave, it would just be as it is—timeless. In order to use the wave to create the feeling or impression that time is passing, you would need a moving reference frame.

Imagine that there is a rectangular slot on this page and the wave is a track cut in a different piece of material moving from left to right behind this page. Now imagine that a pin is placed in the slot as shown in figure 2, and the pin is allowed to ride in the wave-shaped track.

The pin will move up the slot until the wave reaches the peak and then down to the bottom of the slot. The instant it started moving, you would sense time, and one unit of time could then be defined as the change that occurs, for example between one peak and the next. Notice I didn't say a unit of time could be defined as the time between one peak and the next, again because that would be circular reasoning.

The fact that we can measure the exact same change in two different ways, just by using two different reference frames that move relative to each other, is the secret of time. We perceive that reality is made up of "things" that "change" in time. That perception creates the separation of "change" into space and time. Taken together the change in space and time make up space-time—a state of energy. The things that we think of as being "things" are not permanent things, they are patterns of energy. A pattern of energy is a unit of space-time in a particular state—it exists in a unique state of space and time. When an object moves, it changes to a new state of space-time—a new "location" in space and time. If an object is on earth, it is always moving because the earth is always moving.

Space-time is energy and energy is a process; energy is change. The statement that "the only constant is change" is not just a catchy phrase; it is the law of conservation of energy. The only constant is change because change is energy, and energy is change. Energy can neither be created nor destroyed it can only be changed in form. In other words, energy is timeless, eternal. Eternal does not mean for a very long time, it means no time. It is our perception of energy that creates the psychological time flux. Thus time as an independent, fundamental quantity does not exist. The only reality is now—the energy that exists right this moment. If you consider the past and future to be real, then the current moment cannot exist because it would simply be the interface between past and future. But past and future are not real; they are mental constructs created by the concept of time, which is a tool that allows one to understand the process of energy interacting with energy.

Does this mean that physics is wrong to define space and time as it does? No. The definitions of space and time are simply names assigned to measurable unknowns. On the contrary, both classical physics and modern physics are increasingly reliable, verifiable, and undeniable. But they are simply tools that are used to mathematically (symbolically) express measured reality. Because they subsist entirely on relationships—differences—real as well as perceived differences, they are limited to the world of opposites. Symbols used in physics are expressed in the form of an equation, which is itself a duality; there are always two sides of an equation separated by the equals sign. Therefore, although a complete theory can be derived for measured reality, physics cannot express undifferentiated awareness, but only provide an intellectual platform from which awareness can grow.

What we perceive in the form of differences is the process of transforming chaotic energy into awareness. The world of opposites is merely the surface of the expanding universe, that is, expanding universal awareness. It is impossible to perceive the expansion because everything expands together and every observation collapses the space-time state function into the present moment. Every observation expands awareness. The information that resides outside of you is becoming part of you. It enters you via the wave front known as your body. Thus the inner realm is where the awareness resides. An ancient prophet once said, "God is an intelligible sphere who's center is everywhere and circumference, nowhere." Another prophet said, "The kingdom of God is within you."

Measured reality is where the quest begins. It gives us a sense of certainty—something we can grasp, something we can put our hands on and understand. We can understand it because we can perceive it with our physical senses. But just as a computer requires ones and zeros to process information, we need the opposites—the difference in light and dark, left and right, up and down, you and me, and so on—to create awareness. Ironically, the very thing that allows us to perceive is what forces us to focus on the surface of measured reality, where the transformation occurs, and ignore the inner dimension, where the individual differences reunite with the universal consciousness in timeless reality.

Measured reality is the reality that exists in time. That is, measured reality is temporal. And everything that is temporal is temporary. That pattern of energy in your brain and throughout your body is your mind, your ego, which you use to run your life. But that pattern is temporary. It changes as you live and it will change forms when you die. Your mind exists in space and time and does not recognize any other reality. It says, "I think, therefore I am," but it does not realize that the truth is, "I think, therefore I am temporary."

Your mind was created by opposites and is itself made up of opposites. That pattern of thoughts and memories that you have created out of information is what you identify with, what you call your self. Thinking is a temporal process, it exists in time and so it is temporary. If you identify your self with your thoughts, you too will be temporary. The thinking part of you is the mortal part of you.

Your mind looks only at the past and hopes for the future. It rarely focuses on the present, because everything it knows is in the past. It is made out of the past. That is how you know it is not the real you, because the past is not real. Remember that past and future are those concepts that we use as tools to understand measured reality, and the present is all that is real. Nothing exists except the moment now. As Eckhart Tolle explains so beautifully in The Power of Now, the true self is not the thinking self, it is the knowing self—Joseph Campbell's hero with a thousand faces. The thinking self says "I think, therefore I am" but the knowing self is timeless and says, "I am that I am" (Exodus 3:14).

References Burtt, E. A. The Metaphysical Foundations of Modern Science. New York: Dover Publications, 2003. Capra, Fritof. The Tao of Physics. Boston, MA: Shambala, 2000. Tolle, Eckhart. The Power of Now. Novato, CA: New World, 2004.

Theodore St. John is Lieutenant Commander in the medical Services Corps for the U.S. Navy. Presently, he is head of the Research and Science Department at the Naval Dosimetry Center in Bethesda, Maryland.

By Patricia Monaghan

Originally printed in the SEPTEMBER-OCTOBER 2005 issue of Quest magazine. 
Citation: Monaghan, Patricia. "The Spirit of Chaos and the Chaos of Spirit." Quest  93.5 (SEPTERMBER-OCTOBER 2005):166-173

One day, chaos grabbed me.

I had actually studied chaos, scientifically. I had been a science writer for years, first specializing in geophysics and later in alternative energy. But science remained a fairly intellectual enterprise, especially when I was working on my doctorate in science and literature, examining connections between early quantum theory and post-modern literary theory. Then suddenly, my husband was diagnosed with cancer and was up against chaos in the non-technical sense.

I already knew something about chaos, because I had grown up in chaotic family environment. My father was a highly decorated, but deeply damaged, Korean War veteran. He brought war home in his psyche, in a way that will become familiar to so many thousands of other families in the next decade and beyond. And we his children, growing up with violence, suffered from secondary post-traumatic stress syndrome. One of its manifestations is that the psyche can adapt to erratic behavior by investing heavily in attempts to control the environment. I was one of those people who had to have everything "just right" in order to feel safe enough to function.

Nothing is "just right" when someone you love is terminally ill. I was blessed with having a strong, unconflicted relationship with my husband, the novelist Robert Shea. Bob accepted cancer as a spiritual challenge. He once told me that the secret of happiness is to live like you have cancer, but not actually have cancer. It was a great spiritual challenge for me as well. Having life spiral out of control was more terrifying than anything I had ever previously experienced, and I experienced a spiritual void such as I had never known. And so, I began to study the science of chaos.

Like most of us in western society today, my philosophy had been unconsciously influenced by dualism. Much of that unconscious orientation was derived from the African philosopher Augustine of Hippo, who changed little of his philosophy when he changed his allegiance from Persian Manichaeism to Christianity in the early fourth century. Following "Saint" Augustine's lead, our culture describes opposition while other cultures see polarity. In Japanese Shinto, for example, good and evil are not opposites; evil, represented by the storm god Susano-o, is whatever is out of place, out of balance, rather than something permanently opposed to goodness. In Shinto, something can be good in one context and bad in another, depending on where it occurs and when it occurs.

Our own language harbors a similar spiritual truth: our word "evil" derives from the word "full," thus what is "e full" is excessive, beyond natural boundaries. The word is not related etymologically to the word "good," which derives its roots from that which means "to gather" or "to bond together." So even in our own language we have a different vision than the one that says that good and evil are opposite forces that can never interact.

Augustine and his lot argued the soul and the body are separate, that they were at war. This persistent misapprehension was accompanied by other dualities: women as opposite to men, the head as opposite to heart, light opposite dark, and so on. Such visions encourage dualism and separation, rather than bonding and holism. They affect us, whether we will it or not.

Today, I'd like to talk about the order verses chaos duality. Its history begins with Plato, whose ideal world of abstract perfection leaves out most everything in our real world, which looks tattered and imperfect by comparison. In science, the Platonic tradition includes Euclid and Pythagoras, who imagined a world of perfect unalterable forms of triangles, circles, and squares, predictable and clear.

But life is not that way. Life is messy, erratic, and unpredictable. Is life itself, nature herself, therefore deficient? The philosophy with which I grew up with encouraged me to think so. And so, confronted by the erratic, messy, chaotic process of cancer, I had no philosophy to fall back upon for understanding.

Chaos came to the rescue.

There are two theories vital to understanding chaos. These are "sensitive dependence upon initial conditions," also known as "the butterfly effect," and the self-similarity of fractal geometry. To illustrate these concepts, let me share with you poems that resulted from my many years of struggle to understand the chaos of my own life, poems published in my book, Dancing with Chaos.

Stepping aside from the science of chaos to reflect on its literary heritage, we can find descriptions of chaos in literature in such early writers as the Greek Hesiod's Theogony and epics such as the Sumerian Epic of Gilgamesh. To ancient writers, chaos was the great formless sea from which form emerged. Dancing with Chaos begins with my translation of one of my favorite classical writers Ovid, whose Metamorphosis is a series of tales of transformation:

In The Beginning

Before land, sea, sky, before all that:
nature was chaos; our cosmos, all chaos;
all the same enormity, all in one;
there was no form, no moon to walk
the night, no earth to dance with air,
no ocean touching shimmeringly
the fractal reefs and particulate sand;
life and lifelessness the same,
roughness, smoothness the same,
heat falling into cold, cold into heat,
dampness falling into drought,
heaviness falling into weightlessness,
yieldingness falling into adamant.

Now let me tell you how things change,
new rising endlessly out of old,
everything altering, form unto form,
let me be the voice of mutability,
the only constant in this world.

Mutability, change, chaos—it is the only unchanging aspect of life on this plane, "the only constant in this world." But it is not, as you might imagine, utter disorder. Chaos has its own rules, which science has been unfolding for us.

The first principle of chaos—sensitive dependence upon initial conditions, or the butterfly effect are the subject of this somewhat whimsical poem I wrote:

The Butterfly Tattoo Effect

Does the flap of a butterfly's wings in Brazil set off a tornado in Texas?

—Edward Lorenz

Charlene was fifty when she got it:
one small butterfly, perched on
her right shoulder, bright blue
with stipples of pink. Everything
in her life seemed safe by then:
husband, children, house and dog.
She wanted to be a little dangerous.

When she left the Jade Dragon
she called her oldest friend, Joanne,
in Florida, with the news. A tattooed
gal at fifty, she bragged. I ain't done yet.

Joanne laughed that throaty laugh of hers.
An hour later on her way to work,
she stopped on a whim and bought
a gallon of red paint for her door.
That night, she didn't drive straight
Home, but stopped for a drink at an old
haunt from her more dangerous years.
No one she knew was there, so she talked
awhile to Flo, the bartender, told her about
feng shui and red doors, and oh yes, she
mentioned the tattoo just before she left.

It rested in Flo's mind all night as she
She was warmer than usual, sassy and loud.
Things got wild. There was dancing.
A new woman stopped in and picked up
one of the regulars. Washing up past midnight,
Flo thought of her old friend Paula, who
lived in California. It was still early there.

Flo picked up the phone, right then,
and called. Somehow the subject of Charlene's
tattoo came up. Paula had been thinking
of getting one too. Why not? Life marks us all,
why can't we chose our scars just once?
They talked till late. The next day Paula
walked into a dealership and bought
the reddest car she saw. By nightfall she was
driving fast, towards the sea. And the next morning

the world awoke to news of seismic convulsions
on every continent brought on by
the simultaneous shifting into high gear
of millions of women in sleek red cars.

To understand sensitive dependence upon initial conditions—the butterfly effect—we must hark back to the simpler days when Newton's physics gave us the perhaps overwhelming confidence that if we knew the original position of any moving object, and the force and angle from which it was hit, we could trace its trajectory and find out where it would land. The formula was great for baseball and for Newton's apple, so it seemed to scientists in the pre-chaos days that, if given enough information of where very sub-atomic particles were at the moment of the big bang, we would know the future. Simply do the math!

Then, Edward Lorenz came to the forefront. But in order to explain Lorenz's discovery of the butterfly effect, I need to go back to the turn of the twentieth century. Physicists at that time—just a few years before Einstein broke the news of relativity—thought they had pretty much got their field under total control. The prominent scientist Lord Kelvin even told a class of graduating physicists that they would have boring careers because pretty much everything was already known. Among the few problems still unsolved, Lord Kelvin admitted, was something called the "Three Body Problem." Let me describe it in a poem that begins with an epigram from the man who finally solved it:

The Three Body Problem

These things are so strange
I cannot bear to contemplate them.
—Henri Poincare

It was easy to figure out when there
were just two: me, you. Easy, remember?
The route between us, always starting
here, ending there. Me to you. Never
the other way: starting there, ending here.
Pattern set, route established. We knew
what to expect, how to act. We thought
we about the future.

Ah, the future. It would be the same; route
set, pattern established. We knew how
everything moved, me to you, one of us
a satellite and one a sun, one peripheral
to the other's center, me drawing the same
circles around you, over and over. Easy.

But then suddenly, as we were looping
our usual loop, me to you, me to you—
suddenly, there was the other. A new body.
A third. Me, you, the other. What would we
do now? Where were the centers, how could
the circles be drawn, who was to move how?

Two bodies, then a third.

This could have been many stories,
even one as simple as two friends,
having coffee one morning, who
make space for someone to join them,
after which their conversation falters.
Each of us has many such stories.

Two bodies, then a third.
And everything is different after that.

This is one of those stories. This is
the story in which the third body
is one with arms that reach and hold,
eyes that gleam and smile, a body with
all the parts a body needs to come
between other bodies. That story.

No one can predict what will happen
when a third body joins a two-body
system. Linear equations are useless.
One thing is certain: things will change.
We could not go on as before, just another
loop added, once an opening had been made

for chaos—

When three bodies interact, everything
becomes important. Huge changes are caused
by the tiniest gestures: a glance, a whisper,
the touch of fingertips on the inside of a wrist.

Two bodies, then a third.
And everything is different after that.

Everything was different after Poincaré. He pointed out that linear equations cannot solve the three-body problem. Only non-linear equations could do the job. If you think algebra was hard, don't go anywhere near non-linear equations. In fact, when Poincaré lived, nobody could solve a non-linear equation: even a lifetime was not enough time to "do the math."

The computer, however, brought us enough computational power to solve relatively simple non-linear equations (some are still too long to figure out). In 1960, when Edward Lorenz was a meteorologist at MIT, he was running some atmospheric models on a big mainframe computer. He faced the following problem: every time he plugged in data, the same answer kept coming out. Why then was weather so unpredictable if a model of weather was so predictable?

One day, Lorenz arrived to find out that the computer had malfunctioned in the middle of a run. So he started it over. But he rounded off the point at which the program had ceased, by merely a fraction. When he returned, the results were entirely different. All from a few decimal points! What Lorenz had discovered is that calculation must be based upon precise data. But the most minute change in the input can completely change the outcome. If an action is iterated and reiterated through a system, each action can create more than its equal and opposite reaction. Even a tiny action can cause a major upheaval. This poem addresses that significant realization:

The Poised Edge of Chaos

Sand sifts down, one grain at a time,
forming a small hill. When it grows high
enough, a tiny avalanche begins. Let
sand continue to sift down, and avalanches
will occur irregularly, in no predictable order,
until there is a tiny mountain range of sand.
Peaks will appear, and valleys, and as
sand continues to descend, the relentless
sand, piling up and slipping down, piling
up and slipping down, piling up—eventually
a single grain will cause a catastrophe, all
the hills and valleys erased, the whole face
of the landscape changed in an instant.

Walking yesterday, my heels crushed chamomile
and released intoxicating memories of home.
Earlier this week, I wrote an old love, flooded
with need and desire. Last month I planted
new flowers in an old garden bed—

one grain at a time, a pattern is formed,
one grain at a time, a pattern is destroyed,
and there is no way to know which grain
will build the tiny mountain higher, which
grain will tilt the mountain into avalanche,
whether the avalanche will be small or
catastrophic, enormous or inconsequential.

We are always dancing with chaos, even when
we think we move too gracefully to disrupt
anything in the careful order of our lives,
even when we deny the choreography of passion,
hoping to avoid earthquakes and avalanches,
turbulence and elemental violence and pain.
We are always dancing with chaos, for the grains
sift down upon the landscape of our lives, one,
then another, one, then another, one then another.

Today I rose early and walked by the sea,
watching the changing patterns of the light
and the otters rising and the gulls descending,
and the boats steaming off into the dawn,
and the smoke drifting up into the sky,
and the waves drumming on the dock,

and I sang. An old song came upon me,
one with no harbor nor dawn nor dock,
no woman walking in the mist, no gulls,
no boats departing for the salmon shoals.

I sang, but not to make order of the sea
nor of the dawn, nor of my life. Not to make
order at all. Only to sing, clear notes over sand.
Only to walk, footsteps in sand. Only to live.

Sensitive dependence upon initial condition did not displace Newtonian physics; it extended it. But it also complicated it. Chaos theory tells us we can calculate the trajectory of any baseball's arc through the air, so long as we know the exact location and angle from where it was thrown. But "exact" turns out to be an extremely hard thing to determine. Even the slightest difference between the angle of a pitcher's arm between one pitch and another makes all the difference in the world of where the ball lands. Life is not wildly unpredictable. It is just very, very, very hard to measure.

The second important part of chaos theory I want to discuss is fractal geometry. Again, I want to use a poem as illustration. When I began working on Dancing with Chaos as a book rather than a "pile of poems," I looked for a narrative to help the reader understand process of chaos: rigid stasis, catastrophic dissolution, then re-emergent order. This is the process of life and other turbulent systems: nothing stays the same.

Chaos science is based on the examining turbulence, which you can easily observe by watching a river. Just before its rapids, a river looks very sleek. This shiny spot is called "laminar flow," and I think of it as being like those points in life where everything is peculiarly calm—the proverbial "calm before the storm."

Laminar Flow

A: A violent order is disorder, and
B: A great disorder is an order.
These two things are one.

—Wallace Stevens

We were driving. You were silent.
I had given up speaking and sat watching
out the window as the hedgerows flew by.
You wanted to drive to the top of a hill
to see a chapel. Or perhaps it was I who
wanted that. We were driving, in any case.
In my memory, we are often that way:
driving. Not speaking, just driving.

That time I was remembering a farmer
who had loved me. Loved me and sent me
away, back to you. I missed his nakedness.
You were never naked with me. Your eyes
were always cloaked, your heart shrouded.

There was some confusion, I remember.
Something about a wrong turn along the way,
at the bottom of the hill. Finally we found
the chapel, a charming place beside a pleasant
overlook above a river. Children ran laughing
along the paths. There was nothing wrong.
There was absolutely nothing wrong.

Understanding turbulence means getting rid of that ideal world of Plato, Augustine, and his friends. It means getting our feet wet in the real world. One of the great innovations of chaos science has been the articulation of a new geometry that describes this bumpy, inexact world in which we live much better than the old geometry did. The old geometry which consisted of what we learned in high school—finding the area of parallelograms, squares, rectangles, and triangles—this was Euclid's geometry, used for over twenty-five hundred years. Nobody really questioned it, because it worked. But it excluded some important aspects of our world.

In the 1950s, about the time Lorenz was messing around with his computer simulations of weather, a brilliant mathematician named Benoit Mandelbrot set his mind to whether Euclid's geometry was correct. For first time in two and half millennia, someone looked at the world afresh. Mandelbrot realized that our world is not composed of parallelograms, squares, and triangles. Nothing is quite as regular as that. The sun is a sphere only if viewed from a long distance; closer up, all sorts of bumpy things jut out of it. Everything in the natural world is this way, fractured and fractioned. So Mandelbrot coined the word "fractal" to describe the real geometry of our world.

One of Mandelbrot's foundation principles is self-similarity. To understand this, imagine two trees of different species standing side by side. Look at one tree and you will notice that a certain angle is repeated throughout the tree. The large branches come out at an angle, the smaller branches come out at the same angle; if you pick up a leaf, you will notice it also contains the same angle in the smaller veins emerging from the central vein. Look at the tree next to it and you can observe a completely different angle, repeated over and over again, down from the overall shape to the veins in the leaves. This is called iteration, rather than repetition, because forms are not repeated precisely, but with subtle variations. Mandelbrot, dubbing this iteration of patterns at various scales "self-similarity," found that the same pattern system appears in both organic and inorganic life: in glaciers as well as in trees, the striated forms of limestone as well as the spiraling petals of the rose.

Because I had decided that the theme of Dancing with Chaos would be love, the most chaotic of emotions, I wrote the following poem to exemplify Mandelbrot's theories:

The Fractal Geometry of Love

Clouds are not spheres, mountains are not cones,
     coastlines
are not circles and bark is not smooth, nor does lightning
     travel in a straight line.

—Benoit Mandelbrot

1.

Iteration

There is a kind of hunger
that satisfaction intensifies:

I touch you, I touch you again,
and again, and again, and again,

and with each touch I want
to touch you more, I am caught

in this feedback loop of touching and
touching and touching and touching—

2. Self-Similarity

The smallest gesture
is the same as the largest:

when you placed your hand
on mine in that café, it was

the same as when you place
your hand on mine in bed

and when you look into my eyes
for a flashing instant, it is the same

as when you hold them until
we both burst into flame.

3. Measurement

The eye is not a sphere.
My breasts are not cones.

Your nipples are not circles.
Your face is not smooth, and nothing between us
travels in a straight line.

If I were to attempt to
outline your sweet body,
I would be unable to do so:

if I touch it closely enough, so
closely that I trace each cell,
each cell's boundary, each
cell's connection to other
cells, I would be measuring

your outline until the end
of time. And that is what
I am doing, lying here,
next to you in the sun,

trying to move beyond time,
beginning my journey
to the infinite, my hand
slowly, slowly, slowly, tracing
the vast outline of your body.

Building on the work of Lorenz and Mandlebrot, chaos theory has yielded insights in fields as diverse as the stock market analysis and arrhythmia of the heart. It also offers us a new vocabulary for spiritual insight. For, to return to my own story, I had to face the major philosophical questions when I was widowed. The "mind-body problem" I had struggled with as an undergraduate was suddenly no longer an abstraction. And what was I to make of a life—my own—that had become so unruly, so chaotic? Chaos theory came to my rescue by teaching me that we do not live in some abstract perfection, but in a pulsing changeful world. Chaos offered me a vocabulary in a conceptual framework for exploring ways to interpret life that flies in the face of Platonic-Manichean-Augustinian dualism, that message from the past that kept me for so many years from truly embracing the flow of life. The spiritual message of chaos is so well-expressed by that ancient pagan sage, Ovid: that change is the only constant in our world, the one thing we can be certain of.

I would like to end with two paired poems. The first is a poem, I composed from actual questions from physics tests. The second is my own answers to the questions.

Examination

1. Describe disruption of laminar flow.

2. Is uncertainty random?

3. Are unpredictable instabilities chaotic?

4. Distinguish between noise and chaos.

5. Is chance further reducible?

6. Are all attractors strange?

7. vDraw a basin of attraction.

8. Name a useful dissipative system.

9. Can a stable equilibrium last?

10. How turbulent is the heart?

ANSWER SHEET

1. In the wilderness
   between center and edge
   the vortex is born.

2. Distinguish between
   not knowing
   and not knowing:
   one at the root of all,
   one an order
   so immense we
   have to stand
   in another universe
   to glimpse its outline.
   
   

3. Wait. Long. Enough.

4. A: Distantly I hear
   water dropping
   onto porcelain.
   B: Inside
   explosions
   are instants
   of silence.
   
   

5. The weakness
   of the theory:
   the constancy
   of "chance,"
   Einstein said,
   which "does not
   get us any closer."

6. A boulder.
   Two gold pins.
   Three feathers.
   And then:
   an owl,
   flying,
   flying away,
   flying far away.

7. My hands tracing
   the hollow of your throat.

8. Abandoned to the dance.

9. Instead, recurrence:
   never the same thing exactly,
   never exactly the same,
   but repeating the same thing,
   never exactly the same thing,
   but repeating, recurring, repeating.
   
   

10. As any instrument
    that translates
    noise, chaos
    into
    music, order.

Patricia Monaghan's essay, "Physics and Grief, " won a 2004 Pushcart Prize for Literature; it appears in Best American Spiritual Writing 2004. Her book Dancing with Chaos(Clare, Ireland: Salmon Publishing, 2002) was nominated for the Library of Congress poetry prize. Monaghan teaches science and literature at DePaul University in Chicago. This article is a part of a transcribed lecture "The Spirit of Physics: The Physics of Spirit" given at the 2004 Summer School at Olcott.

VOLUME 93, NUMBER 5

Contents

What Is Truth?
By Betty Bland

A Brief Overview of Sacred Time and Space
By Fred Alan Wolf

An Ethics Nightmare?
By Philip Harris

The Spirit of Chaos and the Chaos of Spirit
By Patricia Monaghan

The Three Objects: From Questions to Commitments
Dr. Gabriele Strohschen

Timeless Epiphany
By Theodore St. John

Originally printed in the September - October 2003 issue of Quest magazine.
Citation:Burnier, Radha. "Walking Without Crutches." Quest  91.5 (SEPTEMBER - OCTOBER 2003):186-187.

by Radha Burnier

According to the Theosophical philosophy, humanity in the course of its progress, will have to develop enough intuition to understand not only the structure and forces of the physical universe, but also its purpose and place in the totality of existence which includes, besides the physical, many subtler dimensions. We must learn to understand what Nature intends for humanity and where, in her own time, she will take it. Our role is to become a cooperator and a helper in carrying out Nature's Plan for the unfoldment of faculties that lie latent and unrecognized at present within the depths of the human being.

Mighty Teachers who have proceeded on the Path ahead of most of humankind—the Buddhas and other awakened individuals—have consistently refused to provide crutches for people who want to follow the spiritual path, but do not wish to be self-reliant. Gautama Buddha famously said "Be a lamp unto yourself." In "Adyar pamphlets, New Series No. 3" of the same title, the learned author has indicated how the same advice has come from Hindu, Christian, Jaina, and other sources, providing an example of the truth in the ancient view that all wise ones speak of the same verities. They all want human beings to realize for themselves the Plan of Manifestation emanating from the Divine Mind, by exercising their own budding faculties. They do not want to provide ready-made instructions to obey. On the other hand all their guidance is directed to "awakening intelligence."

In the first letter that Mr. A. O. Hume received from K. H., the latter wrote:

To "guide" you we will not consent. However much we may be able to do, yet we can promise only to give you the full measure of your deserts. Deserve much, and we will prove honest debtors; little and you need only expect a compensating return. This is not a mere text taken from a schoolboy's copybook, though it sounds so, but only the clumsy statement of the law of our order and we cannot transcend it.

A similar message was give to C. W. Leadbeater. The teacher was not willing to relieve the disciple of his duty to think things out for himself and learn from his own experiences. In regard to the founders of the Theosophical Society, H. P. B. and H. S. O. also, they remarked: "We leave them to their own devices."

Not understanding this, some people hope to be favored with instructions and orders, while there are other cases of people who believe they are being constantly instructed and guided by highly evolved beings. They receive messages galore. They are elated by the belief that they are the chosen channels for communications from higher levels. Such beliefs could be the result of persistent wishful thinking: what is imagined as desirable becomes perceived reality. A strong desire to be close to a Master creates a strong thought-form—perhaps of oneself being instructed by the Master or great being—and continually feeds that thought-form by mental repetition of the wished-for happening. It ends in seeing one's own thought-form as an independent entity. Thus a devotee of Rama or Krishna sees their favored deity, and a devotee of Kwan Yin or the Lady Mary sees the form created by his or her own mind. Others see or hear various Masters.

In such cases the question why oneself should become the preferred focus of a Master's or deity's constant attention, guidance, blessing, and so forth does not arise. The delusion is so satisfying to the mind and emotions and so skillfully boosts the ego, that questions are not wanted. The crucial fact that one must merit what one gets by a life of selflessness and service, and compensations which are due will come by themselves, is thrown to the wind.

These are the subtle temptations which the serious aspirant must guard against. Universal laws are not broken by even the highest Masters with great powers and the law is, as K. H. wrote to Hume, that one must deserve what is sought, not for oneself, but because it is good. Therefore all that one must do is to "live the life" and be utterly vigilant in observing the egoistic self surfacing in subtle and delectable forms.

Radha Burnier is the international President of the Theosophical Society as well s the head of three international centers: in Ojai, California; Sydney, Australia; and Naarden, the Netherlands. She is the editor of The Theosophist and author of several books, including Human Regeneration, No Other Path to Go, and Truth, Beauty, and Goodness. This article is adapted from The Theosophist 124 (June 2003): 325-6.