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 ProblemThese things are so strange
I cannot bear to contemplate them.
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
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 PoincarÃ©. 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 PoincarÃ© 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."
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,
are not circles and bark is not smooth, nor does lightning
travel in a straight line.—Benoit Mandelbrot
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—
The smallest gesture
is the same as the largest:
when you placed your hand
on mine in that cafÃ©, 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.
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.
Describe disruption of laminar flow.
Is uncertainty random?
Are unpredictable instabilities chaotic?
Distinguish between noise and chaos.
Is chance further reducible?
Are all attractors strange?
- vDraw a basin of attraction.
Name a useful dissipative system.
Can a stable equilibrium last?
How turbulent is the heart?
In the wilderness
between center and edge
the vortex is born.
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.
Wait. Long. Enough.
A: Distantly I hear
of the theory:
which "does not
get us any closer."
Two gold pins.
flying far away.
My hands tracing
the hollow of your throat.
Abandoned to the dance.
never the same thing exactly,
never exactly the same,
but repeating the same thing,
never exactly the same thing,
but repeating, recurring, repeating.
As any instrument
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.