Lesson about the Fractal Curls of Duration
Time in our modern world has become our captor. The essence of time has been reduced to mere quantity, a numerical measure of seconds, minutes, hours, and years. We never seem to have sufficient time, yet when a little time is given to us, we waste it. Time’s qualities have vanished. For us, time has lost its inner nature.
In other societies, time is an energy of the Universe, a river to be navigated, a bosom on which to find rest. In our postindustrial world, time has become mechanical, impersonal, external, and disconnected from our inner experience.
However, chaos theory shows that it is possible to reconnect ourselves with the living pulse of time. The last lesson of chaos was about living within the new dimension of fractal space. This lesson is about living within the new dimension of fractal time.
We’ll begin with a simple story, one which crops up in different versions in many cultures. One day a monk, returning from the forest where he had been collecting wood, stops to listen to a bird. Its song is particularly beautiful, and the monk is held, entranced, for a few moments before continuing on his way. Arriving back at the monastery, he discovers new faces. While he was listening to the bird, all his friends died and a century passed by. Through entering fully into a single moment of time, the monk touches eternity.
The monk’s story recalls Blake’s assertion that it is possible to experience “the world in a grain of sand and eternity in an hour.” Indeed, it resonates with the way creative people experience a time quite different from that measured by a clock.
Time’s Fractal Nature
As long as we believe time is a straight line, an arrow speeding from past to future, it’s difficult to account for many of our inner temporal experiences. We usually dismiss them as delusions, dissociations, quirks of memory and perception, certainly not anything to do with the essential, physical nature of time.
Chaos theory replaces the line with an endlessly complex figure of fractal dimension. At every scale of magnification, the fractal reveals new patterns and intricacies. Chaos theory argues that there are no simple lines in nature. What may look from a distance to be linear reveals on closer examination the twists and turns and arabesques of infinite fractal detail. Other lines turn out to be not even continuous but composed of clusters of tiny discontinuities, and clusters within these clusters.
So what about time, that line we assume to run from past to future? Why should it be the only one-dimensional line remaining in nature? What if the linear time of our technological world is no more than a convenient delusion of our mechanistic world, concealing a living vibrant time within the interior curling details of a fractal?
This notion, that time has a fractal dimension, accords with our immediate experience. It gives us the door to enter into time’s eddies and currents and to explore its turbulent vortices. In fact, we’ve probably already been there.
In the midst of a life-threatening accident, time can appear to stand still. Events happen in slow motion. We have a strange world of time to decide whether to brake or accelerate out of a potential crash. It is as if each event within the crash panorama is unfolding in its own individual time with its own special rate of being and movement.
This experience of time may not be so much an illusion brought about by a mind overcharged with adrenaline as a momentarily clear vision of just how things really are in the dimensions of time. In moments of crisis we temporarily disconnect from the mechanical time of the clock and enter into fractal time, experiencing its temporal nuance.
Listen to someone humming the first few notes of a familiar tune and the entire music shape seems to be born in our heads. It is something all of a piece. In one moment we have accessed a fullness of time inherent in those first few notes. Now try the experiment of asking someone to hum the same few notes, but this time with a second’s interval between them. Now the notes remain just what they are, single sounds, each isolated in an island of time. The time of the music is no longer present to us; we hear no tune. The notes refuse to combine into any recognizable sonic shape.
When we are willing to enter into a fractal dimension, our experience expands into time. We explore time’s nuances and act according to our own internal rhythms.
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As we explore time’s fractal details, microevents flood in on us full of nuances hardly noticed before, while at the same time we begin to sense the flow of vaster and slower waves of time—the movement of the Sun across the sky, the warming of the Earth, the growth of seeds, the aging of the trees. Those fractal dimensions of time are also curling and breaking inside our bodies. When the society we have created cuts us off from the deeper meaning of time, it robs us of our connection to the rhythms of life itself.
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Breaking the Scientific Line of Time
European peasants of the Middle Ages had no need for clocks. They read the changing patterns of stars in the night sky and knew the time to plant and harvest. They heard the cock crow in the morning and watched the first rays of the sun turning the sky pink. They worked until the hot Sun became too high in the sky for them to stay in the fields. They felt the cooler period of the afternoon and returned to work until the setting Sun brought them home again. They heard the cuckoo in spring and the distant sounds of the monastery bell announcing the offices of the day.
Gradually, this medieval consciousness of time began to shift. The church had once taught that time belongs to God, and so usury—lending money against time—was therefore a sin. But early in the fourteenth century, the first mechanical clocks began to appear on public buildings and time was well on the way to being secularized. The rise of banking, with its practice of loans and promissory notes, demanded a time in which the future could be anticipated and economically controlled.
Time became abstracted from immediate human experience and reduced to a number, something to be manipulated by an equation. How much profit will I make if my interest is compounded over twenty years? How long will it take me to pay off the principal of a debt? If I make 100 percent profit on a ship sailing to the East, is it worth locking up my capital for a whole year?
The only way this was going to work was if that symbol “t” for time was well behaved, or what mathematicians call “single valued.” You can’t balance the books if time is fractal or multidimensional. Time for an accountant can’t keep folding back on itself, it can’t be rich in its texture, it can’t be layered.
The extent to which time was transformed into a commodity can be seen in the colloquial phrases of the English language: “Time is something we spend or save, put aside or waste, and generally don’t have enough of.” This new vision of time ultimately made capitalism and the rise of international corporations possible. Time had become money and money was numbers.
Abstract, numerical time lends itself very well to physics. Here, equations only work when time is a number on a line. In physics, there’s no room for bits or lumps of time; no grain of sand can be allowed to foul the watchmaker’s universe. The time of science and commerce began to dominate consciousness. So bit by bit time became mechanical and monolithic.
Time today is much like a journey between two railway stations. We’ve left the station of our birth and are on the way to our final destination. We think of our life and living as whatever length remains of the track of time before we arrive at the last station. Instead of time being our companion and friend, it is what is being eaten up fast, just as the train eats up the track ahead of it. We desperately try to fill in the time remaining. We divide our journey on the track of time into months, days, weeks, hours, minutes, seconds, and, if we’re working on a computer, microseconds. We always have to get a certain amount done within a given period of time.
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Fractals are self-similar, and so it is with fractal time. In a satisfying work of art, each portion of a painting metaphorically reflects the movement going on in the whole of the painting. In a great piece of music, such as a Beethoven string quartet, a fractal self-similar time is unleashed. Time expresses itself in the subtly changing tempos that are like water moving in a rock-littered mountain stream: time curls, spills, separates, flows around obstacles, merges, pools quietly, slips forward, flashes with light and darkness. Music invites us to be with each moment as it flows into new directions and detail. Yet always the paradox: Each moment of musical time is freshly yet subtly echoing the moments past and to come.
Psychiatrists say a dream unfolds in the brain in only seconds, yet those seconds may contain a long and complex story. A dream is a microcosm of the dreamer’s life because it can be read as a reenactment of existential issues, or what one dream researcher called the individual’s “survival strategies.”
According to neurophysiologists, our brains never remember an event in exactly the same way twice. Each memory is subject to the transformations constantly going on in the brain. Each event in our remembering is both a new event and the same event we’ve remembered before. Each remembrance of an event connects to the whole structure of our consciousness.
As Proust said in his famous meditation on time: “When from a long-distant past nothing subsists, after the people are dead, after the things are broken and scattered, still, alone, more fragile, but with more vitality, more unsubstantial, more persistent, more faithful, the smell and taste of things remain poised a long time, like souls, ready to remind us, waiting and hoping for their moment, amid the ruins of all the rest; and bear unfaltering, in the tiny and almost impalpable drop of their essence, the vast structure of recollection.”
Might it be that each “event,” or even each moment, in our life is a fractal microcosm of our entire life?
Nature’s Multiple Elastic Clocks
Everything from atom to cell, from tree to cosmos, carries its own internal clock that measures its individual passage of time, which is to say, the amount of process it has experienced. Chaos theory tells us that systems tend to self-organize, preserving their internal equilibrium while retaining a measure of openness to the external world. Something similar happens with time. Each element of a system possesses its own clock, its unique measure of the amount of internal process that is taking place with respect to the outer environment. In the self-organization of a larger system, the internal “clocks” of the smaller systems couple together.
Time’s rhythms range from the fast ticking of the atom to the expansion of the entire cosmos. Time unfolds within the geological processes of Earth, the changes of the seasons, the life of a fly. Each system contains its own measure of time and, as systems connect into environments, time becomes ever richer and multi-dimensioned.
Every one of us is a multiplicity of internal clocks. Our cells have their own individual timekeepers that switch on and off various biochemical processes. Cells organize into individual organs whose internal clocks instruct them to secrete hormones and chemicals. These chemical messengers cause the time rhythms of various organs to couple together in the larger, self-organized system of the body. Some of the subsystem clocks operate on limit-cycle repetitions, the female menstrual cycle, for example, and high and low metabolism during the day, sleep and wake cycles. Other of our internal clocks—such as the many rhythms of the consciousness—are more open to environmental influence.
When the brain perceives something as a threat, a variety of signals override the normal cycles of the various organs. Adrenaline is secreted, which interrupts the regular heartbeat, speeding it up. Other secretions cause blood vessels to contract and move the major blood supply to the inner organs, reducing the effects, say, of a surface wound. Under immediate threat, the whole nature of our internal time changes so that the leap of an aggressive animal or oncoming car is reduced to slow motion.
The electrochemical activities of the brain are a measure of living time, a time that maintains a healthy balance between restrictive order and excessive chaos.
Researchers have classified our various states of awareness—active thinking, dreaming, deep sleep, anesthesia, and even coma—in terms of the fractal dimension of the brain’s electrical activity. All this suggests that the actuality of time, the time of perceiving and thinking, is quite complex and multidimensional.
As we have already seen, self-organizing systems sacrifice some of the individuality inherent in their components in order to give birth to the collective. Yet these hidden degrees of freedom are always present to animate the system. The brain operates with a multiplicity of internal clocks. We are conscious of some of these when we think out a problem in chess or try to explain why the economy isn’t going to pick up. But others, such as the control of respiration, body temperature, orientation, and remembering, function unconsciously. In short, our bodily experience of time is a very rich one.
One of our many internal clocks literally ticks out its rhythm—the beating of our heart. These rhythms are in turn evoked in the drumming and dancing of people all over the world, from rituals in an African village to a rave in a London warehouse. But as we’ve discussed, this measure of process, this natural clock, has an inner fractal nature. The stamping feet of traditional dancers, the drumming of a jazz musician, and the beat given by an orchestra conductor, are never totally exact and mechanically metronomic. Computer analysis shows that, like healthy heartbeats, the rhythmic intervals in such music are always slightly irregular. It is this fractal fluctuation within regularity that brings the music alive. The heart that has locked itself into a limit cycle is on its way to heart failure, but the heart that is open and fluctuating with fractal variance is vibrant.
Seeing time as a measure of process in touch with its environment accords more directly with our experience than seeing time as the equal interval ticking of a mechanical clock. We begin to get a feel for the different “times” of process when looking at time-altered photography. In a slow-motion portrait of an athlete running, we see the fractal movements occurring throughout the runner’s body. In a several-day time-lapse sequence of clouds over a landscape and plants growing, we glimpse some of the hidden, long-range pulses going on in the area.
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The more we try to couple our internal flexibility to the external beat of a mechanical time (such as the processing speed of a computer), the more our internal fractal self-organization is threatened. In each of its lessons, chaos theory suggests that we connect, live within the center of complexity, and enrich our feedback loops with the world. Here, it suggests that we restore our bond with the rich time of nature and our own internal clocks.
Time drags its feet when we’re bored, but a whole afternoon can flash by when we’re engaged in something. In which situation do we have “more time”? The conventional mechanical model suggests that both times have equal duration. Yet when the afternoon flies by, we feel we don’t have enough time. Trying to measure inner time using a clock creates confusion about how much time we have in any given situation.
The fractal perspective, however, allows us to ask a different question. Which time has significance for us? Our boredom left one time empty; our passion and enthusiasm make another time rich and multifaceted. And so we don’t need “more time,” but ‘time that is fuller’—fuller not in the sense of getting a lot of things done, but in the sense of engaging the processes taking place.
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Creative Time
Being in the moment means putting yourself at the swirling wall of the vortex where the movement between ‘you‘ and the ‘not you‘ is taking place. Creative people think of these rich times as “moments of truth” times when they experience what it is to be authentic.
When our sole measure of time is mechanical, we experience time as a shopping basket that has to be filled to be brim. We have a number of tasks to do over the weekend and we know that we won’t find time to do them all. So we push ourselves, rush things and lose the flavor of life. An executive’s day may begin with a working breakfast, a rushed lunch, and a business dinner in which problems of negotiation destroy any pleasure in the food.
Others work exceptionally hard yet always seem to find time for a leisurely dinner. They are connected to the food and careful about the time devoted to it. Dinner each evening is not something bolted down in front of the television set, but an act of renewal for the whole family. Each dish has its own time associated with it; the food is there to be savored, and part of its enjoyment consists in the expansive time of talking and arguing with friends over the dinner table.
Dwelling in time in this way allows us to discover the individual rhythms of the day. We enter into the time necessary for each task and therefore experience a multiplicity of times simultaneously. Our individual creativity demands that each activity flower in its own time. The Zen artist may spend hours, days, or even months meditating in front of a blank piece of paper and then finally render a butterfly alighting on a stalk of bamboo in a crescendo of gestures.
We can ask, “How much time did the artist really spend making that drawing? A second? Perhaps months? Perhaps years? Perhaps a whole lifetime was needed before the gesture could be made.”
Creative people, and we are all creative, need a great deal of time (as measured on the clock) in which they are simply “doing nothing.” To the outside world, they appear to be daydreaming or simply fooling around. But inside, they are connecting to the time of the work, to its subtle rhythms and fractal structures. Actress Glenda Jackson referred to the time needed for a character to grow during rehearsals as “putting the bread in the oven.” Her remark evokes the idea of matter sealed in the alchemical vessel and placed within the hot internal darkness of the furnace.
A significant feature of alchemy, which many psychologists take as a metaphor for human internal development, is the necessary time taken for each of its various stages. The “Work,” as the alchemic project is called, cannot be hurried, nor can it be slowed down. Just as with our own life experience, each stage demands its own time.
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So it is not so much that creative people work faster or harder than anyone else, or that they are able to cram a larger number of different activities into a single day. Rather, their many tasks are taking place simultaneously, each within its own time, and these times are coupled together, receiving energy one from the other. If we were to add up the totality of time that seems to be involved in a creative day onto a linear timetable, it would probably exceed a day’s twenty-four hours. But creators make an alliance with the fractal dimensions of time, and time, in turn, gives them the time they need.
This same rich and expansive time is available to all of us, but our industrial society has conditioned us not to experience time in this way. If we do attempt several tasks or engage in a number of interests, we are accused of being a dilettante, unfocused, scattered, and flitting from one thing to another.
And so many of us seem able to do only one thing and arrive back home from that exhausted. If we do want to paint or write our memoirs, it’s something we’ll leave for a weekend or for our retirement, when we hope to have more time. But the truth is this: The time that we really want is the fractal time we have right now.
