To Contact Derek

Parrottracks
P.O. Box 371
Anahola, HI 96703
parrott@
whidbey.com
(808) 634-5585
 

Fractals
Excerpts from "Fractals - The Patterns of Chaos"
by John Briggs

DISCOVERING A NEW (AND OLD) AESTHETIC

Chaos theory and fractal geometry extend science’s ability to do what it has always done: find order beneath confusion. However, the order of chaos imposes a definite limit on our ability. With the use of computers, scientists can see chaos, can understand its laws, but ultimately can’t predict or exert control over it. The uncertainty built into chaos theory and fractal geometry echoes two earlier scientific discoveries of this century: the fundamental uncertainty that Godel’s theorem found skulking inside mathematics and the array of essential atomic uncertainties and paradoxes unearthed by quantum mechanics. Science, in this century, seems destined to learn about nature’s intention to remain behind a veil, always slipping just beyond our understanding, imposing a subtle order.

Artists have always exploited and valued what might be called "the order that lies in uncertainty." The British Romantic poet John Keats admired what he called "Negative Capability," the ability to be "in uncertainties, mysteries, doubts." He claimed that this capacity was key to the artist’s creative power. Leonardo da Vinci insisted that "that painter who has no doubts will achieve little," and he advised fellow artists to seek out inspirations for their paintings in the stains on walls. Artists have perennially discovered in the doubt, uncertainty, and haphazard of life a harmony that goes straight to the essence of being. Whatever it is that the painter, poet, or musician depicts – whether abstract or realistic – the artist’s final product implies worlds within worlds. Within art there is always something more there than meets the eye, the mind, or the ear. Because of this ability to intimate worlds within worlds, art has always been fractal. The science of chaos is helping to newly define an aesthetic that has always lain beneath the changing artistic ideas of different periods, cultures, and schools.

The spiral of life, as this pattern might be called, appears on Stone Age structures around the world. This carving is from Sligo, Ireland, dated at about 2500 b.c. By intuition or some ancient religion-science, the inscribers of these marks seem to have grasped that the spiral pattern symbolizes activity in the life-giving boundary between order and chaos. Anthropologists say the spiral is the ancient symbol for the labyrinth, the twisted pathway for a journey to the core of being.

Artists understand the ideas of fractals and chaos intuitively, and in their aesthetic response to the new science may lie its true importance. Whatever the study of fractals and chaos may bring in terms of practical applications, the deepest gift may be the opportunity these ideas offer for radically changing the way we look at nature. Fractals have the power to help us change our values in areas that may ultimately involve our survival on the planet. Aesthetics, which is about our sense of harmony in nature, has become a deadly serious activity.

The question is, shall we inhabit a world shaped (as we have long believed) by lifeless mechanically interacting fragments driven by mechanical laws and awaiting our reassembly and control? Or shall we inhabit a world – the one suggested by fractals and chaos – that is alive, creative, and diversified because its parts are unified, inseparable, and born of an unpredictability ultimately beyond our control?

The difference between these two world-views could not be more stark. As one commentator puts it, the thrall of the old mechanistic aesthetic has today led to a growing suspicion that order, at least as practiced by humankind, actually leads to disorder. From politics to science, humankind seems to be its own greatest threat. Every solution seems to generate its own problem. Planting orderly, genetically tailored trees to replace forests clear-cut by lumber companies leads to devastation of the new growth by pests and disease and the extinction of species. Damming up the Nile River to control floods and provide electric power depletes the soil downstream and increases water salinity. Jungian psychoanalyst John R. Van Eenwyk says, "So where chaos was once seen to undermine order, now order itself is also the culprit. Has science somehow slipped through the looking glass?"

Many scientists are immensely attracted to the new (and perhaps primordial) aesthetic described in this book. Art critic Klaus Ottmann speculates that the attraction results from the fact that scientists have long been starved of the joy that comes with focusing in an unfettered way on the visual dimensions of their work with nature. All of the scientists whose images are displayed here have clearly discovered that joy in their research with chaos and fractals. Several scientists, like neuroscientist Paul Rapp and Gottfried Mayer-Kress, have even been inspired to engage in collaborations with artists as a result of their research. In 1990 Mandelbrot teamed up with Pulitzer Prize-winning composer Charles Wuorinen to create a multimedia performance at New York’s Lincoln Center.

In his book The Reenchantment of the World, Morris Berman calls for an aesthetic that could turn our science (our knowledge of the world) into art. The aesthetic of fractals and chaos holds out that promise. But taking on such a challenge requires a sense of adventure and a certain courage. It means giving up absolute faith in our ability to control our environment ("science will save us"), and instead making our life out of unpredictability’s shapes. It means attaining a certain humility about our place in the cosmos.

But there is also a serious danger that the concept of fractals and chaos will be transformed into a more sophisticated – even more totalitarian – version of our old mechanical view of life. Chaologists’ ability to use simple formulas to generate complexity on the computer may soon convince them that humankind can in fact control complexity and master the dynamical forces of nature. In the past it was just this hubris that led us to a 500-year orgy of cutting nature down to fit our preconceived ideas – virtually simplifying our world out of existence. Social anthropologists say that in an earlier shift from oral to written cultures we learned to simplify reality in order to record it. Now, with the rise of the computer, we have an instrument (ironically, the very instrument that discovered fractals and chaos) that can digest such immense complexity we may be deluded into thinking we have recorded in its circuits the keys to creation.

This danger is real. In an October 1991 Science Times article describing an experiment that demonstrated that ecosystems are naturally subject to chaos, one researcher noted that the discovery of chaos upset the old idea that nature is "balanced." He concluded, "It really cuts the legs out from underneath this position that all we really have to do is leave these [ecological] systems alone and everything’s going to be ducky. What we have to do is understand how these systems behave and then we as people can decide what we want, how to manage them appropriately" (emphasis added). At a vital level this scientist seems to have missed the point about chaos – at least the philosophical point. Fractals and chaos tell us about the inherent value of living in a world that springs beyond our control. Such a world enriches and invigorates our curiosity and awe, and that is why artists have responded intuitively to these ideas.

Perhaps at some level we will all need to become artists and chaologists in order to save it.