Lesson 4: Exploring What’s Between

Lesson About the Simple and Complex 

Is life simple or complex?

Chaos theory says it can be both, and moreover, it can be both at the same time. Chaos reveals that what looks incredibly complicated may have a simple origin, while surface simplicity may conceal something stunningly complex.

We have all experienced occasions when life’s complexity confuses us. Trapped in a maze of alternative possibilities, a direct and simple decision becomes increasingly difficult to take. Yet chaos theory suggests that it is possible to discover a way out by engaging in chaos’s dynamic dance between simplicity and complexity.

The Paradoxical Science

Paradox, a statement that appears simple yet acts to generate complex resonances within the mind, is a good way of thinking about how simplicity and complexity are entwined. The fourteenth-century philosopher Nicholas of Cusa depicted God by means of paradox—“the coincidence of opposites.” Quantum theory, when describing the essence out of which matter and energy arises, refers to “the quantum mechanical ground state,” which is both total emptiness—an absolute vacuum—and a plenum of infinite energy.

Paradox is central to the ways Eastern philosophy attempts to see the truth beyond our restrictive ideas of reality. In a famous passage from the Taoist Chuang Tzu, the master dreams he is a butterfly and then wonders if he is really a butterfly dreaming he’s a man.

Fractals—the geometry of irregular shapes and chaotic systems—are a way of seeing and thinking about the complexity/ simplicity paradox of nature. Trees and rivers, clouds and coastlines can be described by fractal geometry. It comes as a surprise that this inexhaustible complexity was generated when a computer was fed with a very simple mathematical rule that was then applied or iterated again and again.

Mathematical fractals grow through a process of computer recycling, with the output from one cycle becoming the input for the next. At one level, the complexity of the fractal is a curious illusion, because although the figure’s detail may be infinite, the way it grew was simple. This is also true of many of nature’s forms and processes.

Intermittency: The Storm Within the Calm

Whenever interactions, iterations, and feedback are at work, simplicity and complexity constantly transform into one another. The situation becomes particularly striking when the simplicity and complexity alternate in what scientists call ‘intermittency’.

Intermittency raises the interesting question: Does chaos emerge because regular behavior has temporarily broken down? Or is regular order really a breakdown of reality’s underlying chaos? Do riots occur because the good order of society has failed? Or is a stable, calm society intermittency’s manifestation of underlying chaotic complexity?

Many societies give intermittency an explicit role. It usually goes under the name of carnival or fiesta, an outburst of happy, creative chaos, a time for dressing up, eating, dancing, flirting, building bonfires, and general rule-breaking within otherwise ordered social norms. Such bursts of chaos allow the good order of society to continue throughout the rest of the year. Such societies understand a simple but complex truth that underlying the chaos of carnival is the renewal of important feedback loops that hold society together.

Intermittency is like a brief storm on a hot summer’s day—bustle and noise that ends as fast as it began.  The storm brings a few moments of inconvenience, but it also renews the earth.

Sometimes chaos also bursts, uninvited, into our lives and can result in renewal or transformation. Intermittency is the unwelcome guest at a party. An irrational act, striking dream, or unfortunate coincidence challenges the normal order of our lives by asking us to give more attention to its nuances and subtle patterns. An unexpected illness or a child who gets into trouble can have the effect of cementing a family together. Too much stress makes people ill, but researchers have discovered that a little of life’s chaos is necessary for the immune system to function efficiently.

Complexity and Chance as the Gateway to Order

Intermittency is a dark secret of the Universe discovered more than two thousand years ago. The Greek philosopher Pythagoras believed numbers were gifts from the gods, and mathematicians today still repeat the aphorism, “In mathematics the numbers are God’s, all the rest is man’s.”

Numbers are pictured as lying on a line marked off by the milestones of integers 1, 2, 3…. Between these milestones are fitted the rational numbers—numbers made out of ratios of the integers. For example, between 1 and 2 can be fitted numbers such as ½, ¾, 7/8, 31/32, etc. Actually, an infinite number of rational numbers exist between any two integers. Moreover, between any pair of rational numbers, no matter how close they lie, exists an infinite number of other rational numbers. The Pythagoreans felt they knew everything about the numbers. There were no gaps, no holes in which to put anything else.

Then Pythagoras discovered his famous theorem about the square of the hypotenuse of a right triangle. He used it to calculate the longest side of a right triangle in which the two other sides are one foot long. To his horror, the result—the square root of 2—turned out to be a number never before seen in mathematics. It is an irrational number, one that cannot be expressed as a ratio of two other numbers. If we try to write down an irrational number, we never come to the end of it. Rational numbers, no matter how complicated they may be, are always finite or, like 1/3, repeat in a perfectly regular way (0.33333…). But an irrational number is infinite; it has no internal order to indicate what the next digit will be. In a line that was previously filled with numbers, the irrational number creates its own gap and fits itself in.

The result was so scandalous that for a time it was suppressed by the Pythagorean brotherhood. In fact, it now turns out that the deeply significant numbers of the natural world, like the number pi, which relates the diameter to the circumference of a circle, are irrational. Irrationality is a form of intermittency within the regular number line. Irrational numbers are bursts of infinite complexity, of total randomness inside an otherwise regular system. Irrationality, therefore, lies at the very heart of both logic and the cosmos. Irrationality also exposes something quite curious about complexity.

We can begin with a simple system and allow it to develop in ever more complex ways so that its internal order becomes richer and richer, yet in the limit, when this complexity becomes infinite, it ends up looking exactly like chance and randomness—the opposite of any order. Push complexity too far and it becomes pure chance. Compress the simple and out bursts complexity.

Mathematics exposes one side of the paradox, psychology another. No matter how chaotic and random life seems at the moment, we also sense that it contains some underlying order. People engaged in creative pursuits use chance—the odd spill of paint, an overheard fragment of conversation, the sight of a road sign—as germs and pathways to new forms. Chance events can offer a clue to some deeper pattern in our lives. The Swiss psychologist Carl Jung called apparently disconnected but highly meaningful coincidences “synchronicities” and suggested we should be willing to read these hidden patterns.

Synchronicities sometimes happen when we face an important decision or are in such a desperate situation that we’re willing to stake everything on a last throw of the dice. Maybe synchronicities are always around us. It’s just that in extreme situations we’re more open to letting chance reveal patterns about hidden aspects of our lives. Pure randomness is the same as infinite information, but sometimes that infinite complexity of chaos divulges a clear and simple message.

Catching Ourselves in the Act of Simplification and Complexification

Chaos theory tells us that when life seems to be the most complicated, a simple order may be just around the corner. And when things appear simple, we should be on the lookout for the hidden nuance and subtlety. If the complicated turns out to be simple, and vice versa, does this mean there is no objective assessment of complexity? Are complexity and simplicity totally subjective ideas?

Chaos theory’s answer is that complexity and simplicity aren’t so much inherent in objects themselves, but in the way things interact with each other, and we, in turn, interact with them.
The British painter Patrick Heron writes, “The actual ‘objective’ appearance of things is something that does not exist—or rather, it exists as data that is literally infinite in its complexity
and subtlety. What assuredly floods in upon the retina is an amorphous chaos of visual stimuli into which the human eye learns to inject a favored order of some sort or other.

To fully know oneself would require, in effect, understanding the whole Universe. Meanwhile, the literature of self-help and popular psychology takes a simplistic approach. It is generally based on the premise that an independent “self” exists that can be identified, analyzed, reprogrammed, and improved. Yet if we really look for this self, what happens? The more we try to pin it down, the more we encounter our complex nonlinear interconnections to what is “outside” the self. The Buddha asks whether our ego exists in our sensations, in the forms of our bodies and brains, or somewhere in a chain of causes and effects, action and reaction. The more you seek this ego, this simple, essential self, the more it vanishes as an independent entity and becomes only a mirror that reflects the world.

What is true of the self is true of “the other.” With careless ease we simplify and stereotype individuals who are members of different groups. A stereotype—whether it’s a positive or a negative one—is a cartoon exaggeration of traits or behavior that are assumed to be a characteristic of everyone in the group. In a stereotype, subtlety and individuality are lost. 

Seduced by our own simple abstractions, we can quickly come to see the world through categories that blind us to the subtleties and the richness of the small things that bring alive the individuality of each encounter and the freshness of each day.

But the obverse is also true. We can be so overwhelmed by detail and complexity that we become unable to abstract the underlying meaning of a situation.

As we have seen, simplicity and complexity are not so much inherent in objects as a function of the way things interact. In both cases, we should be asking ourselves if the apparent complexity or simplicity is inherent in the particular issue we are facing or if it is largely something we are projecting onto the situation. In fact, the act of asking this question may stimulate our creativity in quite unexpected ways.

It’s also important to distinguish between confusion and complexity. Complexity is telling us something essential about our interactions with the world. Confusion is quite different. It is a warning system that informs us we are failing to see the essential simple within the complex or we are overlooking the ripples of nuances within the simple.

One of our most persistent sources of confusion arises from our insistence on parceling the world into dualities. Expecting things to be either simple or complex is one example. Chaos theory points us beyond simplicity and complexity, objectivity and subjectivity, my view versus your view, order and randomness, stability versus hypersensitivity, naked power versus subtle influence, control versus uncertainty. It transcends these and other dualities that underlie our thinking and pump energy into our stereotypes and projections. Chaos theory shows us that it is an illusion to separate the self from the other, and that it can be equally illusory to imagine a false or inauthentic merging of the self with the other.

From earliest recorded times, we have tried to divide the world in a bifurcated way in the hope of discovering a fundamental basis for knowledge and belief. For some philosophers, the Universe was a plenum. For others, it was a vacuum. For some, reality was an eternal flux of endless transformation; for others, indestructible, indivisible atoms. We are told we must choose between free will and determinism, mind and body, continuous creation and a single big bang, order and chaos.

What if each pole already contains the other? How many people in fanatical pursuit of the good have ended up doing harm? The whole story of humankind’s fall in Genesis turns on a duality: Satan’s offer of knowledge to discern the difference between good and evil—and we’ve been struggling with this ever since. The problem is that our fixation on dualities causes us to obscure what is really going on. For example, is the evil, wrongdoing, and unfairness in society the result of individual evildoers and conspiracies of evildoers, as duality tells us? Or do these ills at least sometimes arise out of the activities of ordinary men and women who accept the stereotypes, slogans, and other simplicities of society while at the same time complaining that “it’s all too complex”?

We want to escape the tensions of ambiguity and uncertainty, but the more energy we put into one pole of a duality, the more it takes the charge of its opposite. So what are we to do?

How can we be free of the grip of such dualities? Chaos suggests that irony, metaphor, and humor help to move us beyond duality into a new clarity of vision. Art, music, theater, and sacred ritual all employ rich, ambiguous forms to escape from the trap of duality, as do the disciplines of many of the world’s wisdom traditions. For example, the Sufis, or Moslem mystics, often employ a subtle form of humor to foster insight, as in this story: “A man once asked a camel whether he preferred going uphill or downhill. The camel said, ‘What is important to me is not the uphill or downhill—it is the load!’

Chaos theory, with its simultaneous acceptance of simplicity and complexity, order and chaos, ‘one‘ and ‘many‘, ‘self‘ and ‘other‘, comes closest to the world’s traditional wisdom as suggested by the Sufi story. Chaos invites us to adopt new strategies of life, to walk the tightrope between oversimplifying choices by ignoring subtlety and overcomplicating direct action and clear decisions. 

The brain has a nasty habit of clinging to its simplified way of framing something so that after a time the frame becomes the reality. But we shouldn’t despair over our faulty projections, stereotypes, and habitual prejudices. Chaos theory tells us we were also born with the power to overcome them. At every turn, we meet our natural ability to detect the movement of small sensations beyond dualities. For example, the language we speak is perfectly adapted to encompassing that vast range of orders from simplicity to unlimited complexity. We can formulate explicit instructions for making a meal or write poetry filled with ambiguity, metaphor, and paradox. By applying the “art” of the simplicity and complexity paradox, we can touch the force of life that flows into and beyond our abstractions.