an introduction to fractal-scaling in astrology
This article was, to my
knowledge, the very first attempt at redefining the theoretical ground
of astrology in terms of chaos theory. It was written in 1993 and published
in the NCGR Journal, Spring/Summer 1999.
The patterns of the sky have always been a source of wonder. And in response to life's mysteries we have searched for answers in those ever-changing patterns. Even the seemingly insubstantial clouds, wisping and gliding their way across our vision, are heavy-laden with secrets - secrets that are revealed to us when we are ready to see them. In our modern society however, the most obvious features of our world tend to be taken for granted or entirely overlooked as we go about the daily business that is life. We are accustomed to things here on Earth because, after all, this is where we live. But these obvious features contain truths as profound as any occult wisdom. In recent years some bright minds have taken a fresh approach to the old problems of science - problems such as prediction - and started a revolution. Their discovery of the processes that govern nature's design in such everyday forms as the curl of smoke from a chimney or the shape of a leaf, has been called one of the most important realizations of this century. For some of us, it comes like a memory already known.
Astrology is the most comprehensive of subjects, and I try to keep abreast of developments that could impact me as an astrologer. So it immediately caught my eye when I came across a book about a 'new science' - a discipline being born out of the study of complex dynamical systems. The proponents of this new science confine their efforts to describing the behavior of complex systems, but as I read it dawned on me that they are also describing that ancient modeling system called astrology.
This emerging science, chaos theory, is not just a theory, but a whole way of perceiving reality. In short, we now know that simple, predetermined laws can have vastly complex effects. Complexity in nature is the result of holism and huge numbers of principle factors interacting. In nature the same basic shapes are repeated everywhere: the veins in a leaf resemble the branches of a tree, and the branches resemble the whole tree. Turbulance follows the same simple rules. When a dynamical system such as a mountain stream flows, branches and bifurcates, its growth is governed by mathematical workings - eddies form within eddies and swirls form within swirls to an infinite degree. The complex forms arising out of the system are the result of 'iteration' or feedback of the system into itself. This process of iteration in nature creates beautifully complex forms that are strangely redundant in that they possess 'self-similarity' - they appear the same at different scales.
The word being used to describe this multidimensional self-similarity is 'fractal'. The term was coined from the latin 'fractus' meaning fractional, or fragmented. Fractal images, those endlessly repeating, incredibly detailed shapes of haunting beauty generated from relatively simple mathematical formulas, are only mathematical abstractions. But fractals are representative of real-world processes. And the concept of 'self-similarity at many scales' is emerging as the new paradigm for complexity in nature. When you deal with fractals, you are dealing with parts of parts of parts, and these parts feed into each other to create a complex multiplicity ranging from the infinitely big to the infinitely small. Ever notice how a moss-covered rock looks like an aerial view of a landscape? This is a direct result of fracticality. Take a few pieces from a head of cauliflower or broccoli and pull them apart. Notice as you do so how they produce smaller and smaller self-similar shapes, each in itself a tiny replica of the whole.
With the advent of fractal geometry and the concept of self-similar dimensions, we have gained a theoretical model for 'astrological correspondence' and the acausal principle of 'synchronicity' (meaningful coincidence) - both concepts being outgrowths of holism. Astrology is a cosmology of unity; unity of cosmos and self, self and circumstance. And whenever we draw a correlation between the celestial and the terrestrial, or between coincidences, it is simply an expression of this wholeness.
There are many ways in which the astrological model reveals its self-similarity:
No matter how you slice it, the shape of the whole comes through.
Jung called number the 'archetype of order' and in systems such as astrology order takes the form of an unfolding. Harmonic charts are created by dividing the signs into miniature zodiacs - and then tinier zodiacs within these zodiacs. The Zodiac itself represents a dynamic continuum - the cycle of life - wherein each sign can be seen as a stage in a complex developmental process. The Zodiac is a fractally symbolic representation of the perpetual Cycle of the Seasons - starting with the initial 'push' of Aries, and on through the the signs, finally reaching maximum entropy in Pisces, only to begin the cycle again - the ever-iterating universe.
The current model being used to describe the generally predictable form of a system is the 'attractor'. For example, a mountain stream is generally predictable in that water will flow by taking the course of least resistance. But the paths of the individual water molecules within the stream are unpredictable. The attractor (the generally predictable form) is made up of smaller-scale, self-similar yet unpredictable features. Similarly in astrology, each planet, sign and house contains within itself a multiplicity of self-same components. The planets, signs and houses are 'archetypal attractors' - generally predictable forms wherein we find the fluctuating chaos of unpredictable details. They may take forms as seemingly diverse as Neptune's rulership of both 'ships' and 'wine', but astrologers recognize both as different facets of the same jewel - they are self-similar manifestations of the same deterministic 'whole'.
Likewise, the birth chart is an attractor set by the state of the planetary configurations at birth. But as these patterns unfold over time they are subjected to the chaotic feedback of the environment. Even identical twins sharing the same DNA will often turn out quite differently because the DNA molecule will take a slightly different course in the development of each child. There is always enough background chaos and feedback to ensure that 'identical' twins are never perfectly identical. The same is true of so-called 'astrological twins'. There is always enough of a difference in environment to ensure that they develop their own identities within the large-scale determinism of their birth patterns.
In nature, order coexists with randomness. Astrology, like chaos theory, is deterministic and it is not. Both of these systems are operational ways of reconciling the perennial antipodes of fate and free will. We are born at a certain point in space-time, and being self-same with that moment in time and space, carry its qualities with us through life. But what we do with those qualities is up to us. We are given the rules by which the game is played; the strategy is our own.
With this in mind, it is easy to see the predicament astrologers find themselves in when they demand precise answers from a birth chart. One is able to predict with certainty the large-scale features of an upcoming Neptune transit -.eg. that it will serve to dissolve existing structures and attitudes. But exactly what (smaller-scale) form this dissolution will take is open to the individual and the details of circumstance.
Once we become aware of the self-similar processes at work in the universe, our overall perception of the world changes. And this allows us to look at some of our tired old problems from a whole new perspective. The arguments over the house systems, for example, could be resolved by acknowledging that each is simply a different perspective - like taking a photograph from first one angle and then another. The various house systems in use are just different ways of looking at the same structure. As with the Mandelbrot set, we select and then zoom-in on a portion of it, revealing ever more intricacies and nuances. There are many ways to divide the fractal sky, and each division contributes to our understanding of the whole.
As modern science evolves its frame of reference in an effort to unify its theories, we find it becoming less mechanistic and more holistic. And to this end science will slowly and surely come to embrace the very principles that have always informed astrology. Like the systems they study, scientists are being thrown back on themselves. They are discovering that the universe is, as the word denotes, a Unity.
Mandelbrot, Benoit B.
Von Franz, Marie-Louise