Bringing it Down to Earth
a fractal approach

'Clouds are not spheres, mountains are not cones,
coastlines are not circles, and bark is not smooth,
nor does lightning travel in a straight line.'
~ B. Mandelbrot

We want to think about the future - it's our nature. Unlike other creatures, humans possess an acute awareness of time and we often look to the future with a sense of expectancy. Science too is concerned with the future. In fact, all sciences rely on their power to make predictions. Astrology itself has often been called the divine science because it not only permits us insight into the puzzles of order and chaos and gives substance to life, but it also allows us to project a moment into the future, to see what lies ahead in time - a capacity usually reserved for the gods. However, when it comes to making astrological predictions, there seems to be a limit to the accuracy one can expect to achieve. Events seldom turn out precisely as foretold but, on the other hand, they will often come close. It's almost as if the outcome had certain parameters within which it could manifest and then within those parameters, an unlimited set of choices - a controlled randomness. Astrological prediction suggests that there is a subtle, perhaps not so subtle, structure hiding behind the static of outward appearance.

The study of nonlinear dynamics is the study of just this sort of blend of order and chaos and how it manifests in nature. There is a young science which is just beginning to make its impact on many fields, a science which I believe is naturally in tune with many of our astrological precepts and could be a useful tool, or at least offer new insights to anyone prepared to investigate it. Here I intend to introduce the relevant concepts to those who have not yet encountered them. 'Chaos', as this young science is called, deals with predictability in complex systems - systems such as Earth's sometimes turbulent weather patterns - and although it is still a fledgling science, it has already made remarkable headway towards solving some of Nature's most baffling puzzles. Social scientists and economists are employing the basic tenets of Chaos theory in making predictions about society and market trends and biologists are putting it to use in mapping the ebb and flow of populations. In his best-selling book on the subject, James Gleick writes, "...Chaos has become the shorthand name for a fast-growing movement that is reshaping the fabric of the scientific establishment."

It may be said that science deals primarily with making observations of this process we call 'the universe', and science likes to reduce processes to numbers, but those numbers often seem to have a mind of their own. A mathematical model, Chaos theory comes to science out of the use of computers in the modeling of real world systems. Computers allow us to actually view the elegant beauty inherent in mathematics - something which, before now, was exclusively the domain of mathematicians. The Mandelbrot set (so-named after its discoverer, Benoit Mandelbrot), a computer generated visual representation of the geometry of Chaos and a beautifully eerie configuration, is a structure of such rich complexity as to be almost lifelike. Changes in one variable of the set will flutter and reverberate throughout the whole, spinning-off possibilities ad infinitum. It shows us how the dynamics of nature are nonlinear - rarely does she follow a straight line - and how the relatively simple nonlinear equations used to create such images as the Mandelbrot set do mimic nature. In fact, realistic computer-generated landscapes, ("fractal forgeries", as Mandelbrot calls them), are only possible because the mathematics used to generate them imitate natural processes.

If Chaos theory is so important to modeling the behavior of complex systems - that is, the behavior of the natural world, then perhaps it has a similar role in the complex workings of astrology, for astrology also reveals a subtle relationship between simplicity and complexity; it too imitates life. Astrology and Chaos both provide means of plotting the unfoldment of processes in time and they each allow one to get a holistic overall view of nature. So if Chaos provides an increasingly accurate picture of how creation behaves, how might we as astrologers usefully apply this model? Does Chaos provide a workable approach to the astrological? As a metaphor for how randomness and determinism interact, Chaos would appear to be very important to astrology, but in order to see whether it meshes with the astrological design, we must first match-up the gears of this mechanism with those we use in practice everyday.

Both astrology and Chaos are the study of what physicist David Bohm calls the 'implicate order', the notion of unbroken wholeness. Implicate order is the order of the hologram, in which the whole object is enfolded in each part, and each part contains the image of the whole. Ours is a holographic reality, an undivided universe where everything influences everything else in a cosmos of the ultimate complexity. Wholeness, where even the minutest part plays a crucial role in shaping the total picture. There is also a current trend of thinking in ecology, the Gaia hypothesis, which regards the planet Earth as an undivided conscious whole and where to exist at all is to exist in connection with the planet. Astrology takes this a step further, predicating a universe that is self-aware, interconnected and purposeful - an entirely integrated system. We stand in relation to our surroundings interactively - it feeding into us and we feeding into it. And, as astrologers, we employ our charts as tools for understanding this relationship. Astrology is about making correlations between one part of our system and another, the happenings up there and our lives down here. We use the chart to trace the unfoldment of an idea, a business or a human lifetime, and all of these could be thought of as systems interacting with other systems. Chaos too is involved in the investigation of how systems interact and uses its own symbols and cartography - specifically, nonlinear equations and graphs - in order to do it.

Briggs likens the nonlinear equations of chaos to a 'mathematical twilight zone', but in truth the world they represent is the real word we live in. By putting different values through these equations, scientists plot the effects of feedback - the effects of interaction - on a system. Feedback loops in nature can amplify or stabilize, as when a relatively small perturbation in the atmosphere over an ocean later grows to hurricane proportions (the amplification of subtleties, which has been summed up in the term 'butterfly effect' - the theory that a butterfly flapping its wings in the air over one part of the globe can, in combination with all the billions of other tiny influences, eventually affect the weather over an area thousands of miles distant), or when predators prey too successfully on their prey, thus reducing the available food and causing a reduction in their own numbers - which in turn allows the prey population to increase again. This supports more predators, who in turn reduce the prey population back to normal (stability). But more importantly, feedback and nonlinearity portray essential dynamics of the world we live in. They describe the vital tension of creation. Our world is a double- mirror whose self-organization is continually adjusting. Parts play into parts and feed back into each other to a degree of complexity which is capable of creating an infinite range of unique creatures and situations - a richness out of relative simplicity.

The importance of Chaos theory is derived from its new perspective on the world as dynamic and nonlinear, yet predictable. You can look at nature piece by piece, as in the reductionist method, or you can see it as a dynamic whole, and when scientists think about such things as changing dynamic systems, they plot them out on a multidimensional graph or map in a place called phase space. In their book about chaos, Briggs and Peat tell how scientists who study the complex predator-prey systems at work in nature have shown that these systems exhibit certain behavior in phase space - behavior not noticeable through reductionist techniques. For example, if we examine just the activities of the predator alone, we will see how its survival as an individual depends simply on its ability to hunt and kill its prey. We need to look at the 'whole' - in this case, the entire population of predators and prey - to perceive the effect mentioned above, (the stabilizing effect of over/under predation). Phase space dimensions attempt to represent all the variables of a system, and the resulting shapes on this map, shapes which are called attractors, show how the system changes over time. Even the most complicated systems of nature, when plotted mathematically in phase space and followed over time, stay within a certain measure but, within this measure, the orbits of the system never intersect, indicating that the system never exactly repeats itself, but neither do the orbits wander off in unpredictable ways. In other words, the system is attracted to an inescapable overall behavior and the resulting shape of this creative confinement is quite distinctive. It is the shape of the Strange Attractor.

Edward Lorenz, one of the pioneers of Chaos, describes an attractor as "a limit set that is not contained in any larger limit set and from which no orbits emanate". Which means, in plain English, a simple description of all the conditions that could possibly occur. In the weather machine, for example, we must include all temperatures between about -45° to +45° (Celsius) as being possible across the planet as a whole, all wind speeds from 0 up to about 200 mph, all precipitations from 'none' to 5" hailstones, etc. A Strange Attractor is an attractor with a self-similar or fractal nature. In essence, an attractor is the working out of all the possibilities within a certain frame of reference and the expression of the whole through its self-similar parts. There is likewise a continuum that each astrological symbol represents and a continual process by which the invisible upper levels of the astrological filter down into the realm of eventualities.

The Strange Attractor is a bizarre blend of determinism and chaos. It consists of a number of curves and directions, yet the big picture it gives us is always predictable. Lorenz has compared the earth's climate to a strange attractor, "...the attractor", he states, "is simply the climate, that is, the set of weather patterns that have at least some chance of occasionally occurring." The day to day weather fluctuations we experience make up the background chaos of the earth's climate, which in turn defines the equilibrium level of the system - the attractor - the overall predictable form a system will take. Otherwise stated, the overall global form (the attractor) is predictable - the local details within the overall form are not.

 Astrology also exhibits this type of behavior, and it too has its Strange Attractors. You see, contained within the chart's overall form are the factors of the signs and planets, and each is itself an attractor of sorts. In astrology, Saturn, for example, has often been called the planet of manifestation, but even a term as broad as this leaves out many of the functions and qualities attributed to Saturn. Take a look in any rulership book and you'll find lists of such things as: gravity, solitude, icebergs, and bricks, - things and conditions which do not seem to have the least bit in common yet, for the astrologer, these are considered to be different facets of the same jewel. Astrology says that, at some level, all of this 'Saturn fallout' is self-consistent and connected, that there is a sort of devolution on the part of the cosmos - a path of descent - in which Saturn makes its appearance here at our level in images, events and concrete forms.

Within the overall form we call Saturn sleeps incipient chaos, and in the astrological chart it signifies many different things in an infinite number of situations. Saturn displays itself over and over again in many self-similar forms - multiple variations on the same theme - but Saturn is always Saturn. The essential function of the planet can express itself in a multiplicity of ways, and it is for this very reason that British astrologer Dennis Elwell reminds students to 'stick with the dynamics', the essential function of the planets, when interpreting charts. Each astrological planet is a self-consistent holon, (to borrow Koestler's term), a bundle of meaning which accommodates, in one category, everything the planet represents. Each planetary holon can be explored within itself to reveal hidden symbolic consistencies. For example Elwell calls Saturn the 'agency of incarnation' meaning ' a pinning-down in time and space of what was previously in an unmanifest state'. This is a very broad outlining of the planet and a definition which describes it at the level of function - what the planet is striving to bring about. Here we have gathered together all the various and scattered meanings of Saturn within the overall boundary of a planet's significance - within the planetary attractor.

In his book, The Fractal Geometry of Nature, Mandelbrot encourages readers to see fractal figures and landscapes as natural contours resembling coastlines, rivers and mountain ranges. Indeed, ever since they first spoke of the 'Seahorse Valley' - and probably before - people have been seeing organic shapes and creatures in the M-set. And these comparisons are not just fanciful, for the value of the images lies in their ability to model the complex forms of nature. The term 'fractal' was first coined by Mandelbrot from the Latin fractus (meaning'fractional' or 'fragmented') as a step towards developing a language of understanding the way the universe uses and reuses the same forms redundantly in both living and non-living things. The human vascular system, for example, is a complicated network of self-similar structure very much resembling the branching streams of a watershed, which in turn maintains its self-similarity, its fracticality, down to the tiniest rivulet. Fractals are both functional and descriptive in nature, and the objects and processes they represent are self-similar at many different scales.

This scaling function - this thing called fractal - constitutes a major result of Chaos. In the real world, coastlines and mountain ranges are apparently formed by chance; they are molded through the ages by the multiple influences always at work on them. We can say that the shape of a mountain or coastline is partly determined by its initial state, but the constant and unpredictable forces of erosion - wind and rain - over time shape the details of the rock face or shore and, even at the tiniest scale, these features are self-similar. The closer we examine them, the more self-similar details they reveal. The system's attractor is traced by the point which represents the system and as its movement folds and refolds over itself in phase space, it creates a fractal curve of infinite complexity. But each folding sequence is a mirror image of the entire system; it is self-similar at smaller and smaller scales. In fact, current analysis of the structure of the universe suggests that these fractal dimensions are everywhere.

Fractals can be mathematical objects, such as those we see in the Mandelbrot set, or they can represent processes such as those at work in the formation of clouds over the ocean, or in the growth processes of plants. Even under virtually the same conditions, one cloud will not be formed exactly like another cloud, yet each contains a self-similar structure. Trees are fractal in that a branch looks like the whole tree and even the tree's root system is self-similar in nature, branching out below the ground, but each individual tree is a separate and unique expression of tree-ness. In the lesser plants, heads of broccoli or cauliflower possess a striking fracticality; disassemble one and you'll see what I mean. These fractals are self-similar but not necessarily self-same, and have been envisioned as pictures compressed within pictures, wholes within wholes, or parts of parts of parts...

In Chaos theory, when we look at the large picture, apparently random events can be shown to happen within patterns, with the Strange Attractor representing the overall predictable state. And in astrology we can easily see the birthchart as a Strange Attractor: It outlines the pattern of the life and personality, but within that pattern there are infinite variations on the theme. Truly, each sign or planetary principle is in itself a strange attractor. Each contains a full potential of self-similar or fractal expressions, but these expressions never fall outside the attractor. An astrological planet contains all of its possible presentations within the overall predictable form of the planetary symbol.

Time also has its fractal dimensions, and whenever we switch one increment of time for another - as we are in the habit of doing in astrology - we are making practical use of these self-similar fractal-time dimensions. Progressions and directions are not only symbolic, as some astrologers have called them, they are also fractal expressions of the whole and, in regarding the astrological chart as fractal, we begin to see that there are many systems within the system, many wheels within wheels. What are harmonics if not the fractalization of the birthchart?

If the phenomenon called the Strange Attractor in modern non-linear scientific observations describes a tendency for any dynamic system to produce recognizable patterns where only random chance was formerly considered the most reasonable, exactly what does this say about astrology? Why do people and situations tend to develop astrologically characteristic patterns of identity if all of life's influences are purely random? Why, with all the choices before me, am I attracted to being like the patterns in my birth chart? The answer must be that, at some level, all this apparent randomization is attracted to a central point which, at the most comprehensive and generalized level, is predictable.

Consider the polymorphism of astrological symbols, or how in the astrological chart the same dynamics apply to any context. We use the same symbols to describe an infinite number of personalities, situations and eventualities. Astrological influences can only really be described as possibilities, and it is very difficult to anticipate the movement of the events they instigate. In this respect astrology is somewhat like atmospheric physics or a weather report. The meteorologist looks at the general state of the system and then , within that, he looks for clues as to the sorts of events which might present themselves; if there are clouds in the sky, it might likely rain. The same is true of astrology - we know that certain planetary configurations present a certain climate and, within that climate, certain events are likely to occur, but how can astrologers claim to know what they know? How is it that we are able to track the events of a person's life and say that this or that circumstance belongs to this or that planet? Just as life on earth could not exist without a predictable general climate, the astrological chart could not function if there were not generally predictable components. The very fact that we can make predictions - or interpret the chart at all with some degree of success - implies that, at some level, these factors are predictable and reliable. Is it feasible to regard the general factors of astrology as basins of attraction or, even yet, as Strange Attractors whose ultimate natures are fractal?

To understand, we can look at a complex of thought conceived by Dennis Elwell. The process he envisions is one whereby a planet's essential nature steps-down through a series of transforms, into the level of earthly manifestation - the level of our experience. Elwell explains that "events around us have crystallized out of higher levels of significance". In his model the cosmos manifests itself on a number of different levels or dimensions, with the uppermost level being all-inclusive. As he illustrates, "What we [as astrologers] call Saturn or Neptune can express itself in different ways - on different levels, in fact - without losing its essential nature. At each level there is a transformation, but Saturn is always Saturn, and Neptune is always Neptune". He compares this transformational process with the different expressions of water, which can take different forms at different times depending on the prevailing conditions around it. Water can express itself as a liquid, as a vapor when it's heated into steam, or as a solid when frozen into ice, but its essential nature always remains the same - it continues to be H2O. Like the different manifestations of water, each planet can display itself quite differently under different conditions without losing its essential nature. So in this sense, bricks and bones are not merely ruled by Saturn - they are Saturn.

This essential planetary nature, which Elwell calls the planetary 'intent', is the most inclusive and generalized state, and it is also the most deterministic and unchangeable. Every act, every event and its meaning owes its existence to an intent or cause - an initial state - which eventually displays itself as an idea or expression, and in turn materializes in the realm of events. In chaos theory, order and randomness are twin manifestations of an underlying determinism, and in astrology the predetermined unitary principle generates the lower manifold level. But the form this planetary intent will ultimately take is the most unpredictable because, at that level - the level of the actual event - it is the most open to circumstance. In fact, to list all that is compressed in the upper level would be impossible, as it would be to list all of its eventualities.

Astrology is based on the Hermetic doctrine of correspondence: As above, so below, and we can see how Elwell's thesis forms a triangle of manifestation where the one above becomes many below. In this model the general significance, the intent or direction of a planet, filters down to our level of events, with ever-increasing multiplicity, while the planetary essence remains the same. Here we can see that Elwell's intent level has formed an image of the Strange Attractor, a hyper-dimensional cosmic order wherein a planet's significance is always operating within certain boundaries and possesses an overall predictable form. Yet through the unfolding of what already exists as potential, it can take on many and varied self-similar forms. This model displays the nonlinear dynamical behavior of global determinism and local apparent randomness. This structure also suggests that fractal-scaling is the function by which the higher level of meaning is translated into our level of experience in a process which is perhaps not so much linear as it is permeative - as in the way water permeates a cloth, seeping in here and there depending on conditions.

It is common practice for astrologers to track circumstances up to the level of rulership and function where everything happening at this level is also being stated in a more comprehensive way at the higher level. Astrology is a symbolic language, and symbols are compressed meaning. What appears as disorder on this micro-level is, for the astrologer, a signal of a higher and invisible cosmic order. For astrologers there is the implication of purpose at the back of events and, when they take place, we look to see how the nature of the event is revealed in the planetary configurations of the moment. We demonstrate the presence of the higher levels by taking events and actually tracing the circumstances up through the fractal dimensions of manifestation to this higher level of significance. We raise our perception to the overall predictable Universal level - the level of the strange attractor. But the language of astrology is a relatively 'loose' language. Each factor represents a whole bundle of self-similar issues, any of which have the possibility of making an appearance at a relevant time given the right conditions.

On September 14, 1994, the city of Chicago experienced a series of mishaps, all seemingly unrelated. A power outage shut down the regional air traffic control center and brought O'Hare International Airport to a virtual standstill for one and one half hours. Computer failure at the Chicago Board of Trade, the world's busiest commodities exchange, shut down all activity until noon that day. And MCI (the long distance telephone company) had their service disrupted for about two hours by a problem with a software switch. These problems began in the morning at about 8:45 am. An astrological chart drawn up for Chicago at the time the troubles began shows Mercury rising and forming a T-square with a Moon/Uranus/Neptune conjunction, in turn opposing Mars. By astrological standards this is a tightly dynamic configuration - squares, and hard aspects in general, are considered in astrology to be the enabling irritants for creation - and this T-square was being made especially potent by it's angularity. We can see how Mars, being directly at midheaven, could signify breaks and severences - in opposition to the Uranus/Neptune conjunction: abnormal situations possibly involving electrical lines and computer technology - and this axis in T-square configuration to Mercury, bringing in communication, travel, commodities exchange. Cosmic commands will make themselves known whenever and wherever they can, and here we have an example of how one configuration presented itself in different yet very self-consistent ways. There was an overall direction to the configuration yet it fractalized into a number of situations.

When planets are especially active, as in the case above, things tend to manifest as bunches of odd coincidences. But because they manifest in self-similar ways, and always as one of a whole, we can trace their presence in events up to the higher more comprehensive level. Now, when concrete predictions are attempted, it must be realized that what appears here on our level is the end-product of a fractalization process which begins at a much higher, and more inclusive level. There is a hierarchy of manifestation, from above to below, with the macrocosm generating the process. Each planet is a bundle of meaning - an attractor - which manifests at the lower levels in concrete forms and situations. And this is the challenge, for at the event level we encounter the vast multiplicity where manifestation relies on available conditions and contingency. We can say that the chart configurations represent the climate, but what form the precipitation will take, where it will fall and to what degree - rain, hail storm, or full-blown hurricane - we often cannot tell. The event, the final entity emerging out of the general climate is a special instance and more or less a product of what appears at our level as local randomness.

In Chaos theory, a structure of global determinism and local apparent randomness creates a stable arrangement that is self-similar at many scales; fracticality. Fractals are both order and chaos - they produce a configuration which is at one level predictable, and at another level unpredictable. Astrology, like Chaos, is connected with the notion of sensitive dependence on initial conditions of the system and each has its strange attractors - the definitors of equilibrium within the system. But as the system develops predictability breaks down - the one above is pushed into bifurcation, multiplicity and infinite complexity. As a system evolves over time, small changes amplify through feedback with the environment; there is an exponential progression of complexity and this imposes strict limitations on predictability. The quantity of data becomes unmanageable and the quality of the data deteriorates rapidly. We can certainly say that all happenings have astrologically appropriate moments, but not everything contained in those moments will be able to manifest at that time. Nor can we yet calculate all the permutations of a planet and its combinations for a given time period.

The eclipse of April 15, 1995 brought with it a number of disasters, not the least of which were deadly gas attacks by a terrorist cult on commuters in a Japanese subway, and the bombing of the federal office building in Oklahoma City by right-wing militia members. Now according to astrological theory, eclipses are 'seed times' or moments when the higher dominions make a fresh impress on the lower. Eclipses have an orb of influence, often showing effect beforehand when events are seemingly drawn toward a basin of attraction, and then leave residual traces in their wake. In the eclipse chart of April 15 we find the Sun conjunct Mercury in Aries opposite Moon in Libra and all three in T-square to the Uranus-Neptune conjunction in Capricorn/Aquarius, which also fell on the detrimental Saturn-Pluto midpoint. Among the other notable aspects for the eclipse was a Venus-Saturn conjunction which fell midpoint the Moon, and Mars in Leo, and a waxing sextile between Uranus and Pluto, which might have played a more minor role were it not for these two planets also being in antiscion.

Dennis Elwell was so convinced that a potentially dangerous situation was building (and it was!) that he went public with a prediction saying there would be a crop of maritime disasters surrounding that eclipse. His confidence was boosted by the realization that the eclipse fell on the anniversary of the sinking of the Titanic with the Sun, Mercury and Jupiter returning to their places held previously at the time the mighty ship went down. Uranus was to become stationary that month, and at the precise degree of Aquarius that was rising at the time of the sinking. There was indeed a slight up-surgence of emergencies at sea in the months preceding the eclipse, including the loss of the Achille Lauro, but nothing of the sort near the magnitude prophesied.

As it happened, I have maintained a correspondence with Dennis for some years and I wrote to him on the day of the eclipse about the non-occurrence of the predicted disaster. I wanted to make the point that 'disasters' had happened elsewhere which could clearly be linked to the eclipse. This is the relevant paragraph:

"I've noticed that the April 15 eclipse also has a lot to say about the subway gassing in Japan. According to 'Bills', the nation of Japan is ruled by Libra - and this eclipse, as you know, takes place across Aries-Libra with the Sun conj Mercury - transport. Sun/Merc opp moon are T-square Neptune. Neptune not only rules ships and the sea, but 'gasses' as well. Neptune in mutual reception with Saturn (in draconic-Leo) - a cold-hearted religious fanatic espousing an apocalyptic doctrine? - Neptune is still conj Uranus - the 'out-of-the-blue' gas attack - and they are both draconic-Gemini - transport again."

About 10 days later a sceptical friend of mine reading that paragraph pointed out that he was mildly impressed by the links to the Japan gas attack, but not overwhelmed as it was, after all a retrospective view. But, he pointed out, what was much more impressive was that with hardly any 'tweaking' at all, the same paragraph could be read as a graphic prediction of what took place just 3 days later - the horrific bombing in Oklahoma City. And, of course, he was right. Without intending to, by describing the Japanese events I was also unwittingly predicting the Oklahoma bomb.

Now, focusing astrologically for a moment on the two aforementioned calamities, we can see how the aspects of the eclipse chart have a lot to say about both. According to Bills, the nation of Japan is ruled by Libra, and this was of course the axis across which the eclipse took place. Aries-Libra is also descriptive of remonstrance in both cases. The Sun fell conjunct Mercury - transport, as in commuters, or office workers and vehicles, such as vans - in T-square to Neptune-Uranus in Capricorn - the 'out-of- the-blue gas attack by the followers of a religious fanatic espousing an apocalyptic doctrine'. But Neptune not only rules gasses, it also rules chemical fertilizer and gasoline, the components of the bomb used in Oklahoma City. The eclipse of April 15 fell across the horizon at sunrise in Oklahoma City, in T-square to a 10th house Uranus-Neptune conjunction, with Mars (aggression, injury, bombings, fire) in the 5th house (children) by the Koch and Placidus systems. Bills gives rulership of Oklahoma City to Leo, and it is worth noting too that Mars in Leo was exactly at nadir for the moment of the blast. Venus-Saturn conjunct and midpoint Moon-Mars - cold-hearted attacks by right-wing militants on the populace. Saturn-Venus - the federal building, government real estate. Uranus-Pluto - radical upheaval - and, in both of these cases, the surprising abruptness of terrorist activities. Pluto, of course, is both the 'underground' and the carnage as well. These events were all astrologically linked to the eclipse that April - in fact, the day of the Oklahoma City bombing there was a second gassing in a Japanese subway.

This example highlights both the strengths and weaknesses of the Astrological paradigm. Yes - the planets do 'predict'. But exactly how and where their predictions will manifest is itself 'unpredictable'! Even if anyone had 'risked' predicting a bombing, (consciously as opposed to unconsciously like I appear to have done) how on earth would they have guessed 'where' that bombing would happen? After the event, we can look at the eclipse chart for Oklahoma and see remarkable pointers but before the event we wouldn't even have known where to begin looking.

Why are specific predictions so difficult? The problem is not that events are random but that the factors which influence them are so numerous and sometimes so obscure that we haven't got any means of making sensible allowances for them in our equations. This is what justifies astrological method, in which, following on fractal logic specifically, we make the assumption that although we can't see all the necessary detail, it is reasonable (on the basis of historical empirical data) to assume that there will be a fractal similarity between events occurring under similar overall astrological conditions. So what appears to us as local randomness is not really that at all. It is locally 'insufficient data'. The obvious consequence arising from this is that as our data improves so will our accuracy of prediction. So even if we have to limit ourselves to very general predictions at the moment, it need not always be so. In a sense, this problem is not really a limitation of astrology, it is a limitation of our understanding of causation generally.

Climates vary and, within them, oscillations are the norm. A dynamical system, by non-technical definition, is one whose state, at any given time, determines its state projected a short time into the future - and in this respect, it is deterministic, but there are rules for passing from one state to another. To make precise predictions would depend on being able to make an equally precise analog computation. The mechanism may be there in our brains, although in the presence of so much noise it's doubtful that in the human mind this could be done effectively. At this point in our development we are not as yet capable of grasping the incredible complexity of the events around us with their finely interconnected nuances fluttering this way and that, emerging as catastrophe on one part of the globe and fizzling-out completely on another. The law of apparent randomness is that arbitrarily small changes do matter; many futures are possible, but only one can become an actuality, and this is contingent upon every factor involved, no matter how small. The flap of a butterfly's wing may or may not develop into a storm - anyway, the butterfly has long since died once she becomes a hurricane. By linking-back a moment to a self-similar moment, by drawing on analogues, can we possibly see around the corner into future behavior? In principle it would seem possible to predict infinitely into the future - astronomers use mathematical models to predict the orbits of the planets years from now. However, a dynamical system can have more than one attractor and so the features will keep adjusting. Apparent randomness.

But if things were purely random there would be no such thing as statistical regularities, no averages, and no correlations. If determinism didn't exist we couldn't average it. Yet we do; it's there. This averaging of the large-scale features of the planets and their functions is analogous to the sort of fudging meteorologists do in making weather predictions, which leads to a cleaner understanding of the lower features through a process called 'parameterization'. In working at the large-scale - the level of planetary function - we smooth out the fluctuations by not including the smaller-scale features - the minutia of detail - and thereby build a more reliable structure. As people who work extensively with the public will tell you, the masses generally display day-to-day, or even hour-to-hour fluctuations in temperament. The transiting Moon, as it moves through its aspects and signs, reflects a changing public mood, or I should say that the general emotional state of the populace reflects the changing state of the Moon, which rules the public in general. Things will tend to get a little aggressive in a Moon-Mars phase, a little serious in a Moon-Saturn phase, etc., but I would not venture this same prediction on the individual. Parameterization is a theory of general features, and such a theory sees the astrological chart as an interplay of the dynamics of the planets and signs, the functions - what the planets do, not what they might become, and certainly not the eventual undigestible mass of particles. We can reduce the butterfly effect as much as possible by focussing on the pure dynamics of the factors of the chart. The large-scale function is taken to be indicative of the smaller-scale structures and we can estimate at each point the most probable effect, this giving us some idea of the confidence we can put into our forecast. We can realistically formulate our expectations of the large model but a clear understanding of this shorthand involves an extensive knowledge of the language. Astrology is an expert language, the essential dynamics of which must be mastered in order for us to see the quality of the moment in question.

If we could ever include in our model the many smaller-scale structures, all the individual variables, this parameterization would no longer be necessary - the error-growth would be nearly imperceptible. But since, in reality, up to the point of manifestation we must contend with the incipient complexity of the astrological factors, our cartographic work really boils down to being able to anticipate a direction for events and then being able to spot the configurations which would likely indicate increased activity at our level. The higher does have absolute dominion over the lower, but now we can see that the Universal level paints a rather foggy picture - an impressionistic portraiture in which the details are not filled in until it becomes fully manifest at this level. But it effectively demonstrates both the self-similar nature of events and the hidden power of astrology to someday predict such events. This would seem to mean that our predictions, if we are to make them, must be kept very general. The examples above seem to point to this being the case. It is possible to describe trends fairly well - the general shape of things - but the problem in translation - and in describing exactly - is the tremendous complexity of the chart. Regardless of how much we describe of a trend, because of the fractal nature of the transmission, there will always be characteristics left out. Perhaps all we can do for the time being is block in the larger shapes and leave the filling-out of the finer strokes to the boundless possibilities of circumstance.

The holistic patterns of astrology actually have real relevance. If there is a causal chain, with fractal links, going back to the big bang, then astrologers are almost certainly best placed to interpret the significance of the parallel pattern formed by the planets and how these are mirrored in events at the ground level. Essentially this means that we can one day realistically hope to make more impressively accurate predictions, but for the time being the practical difference between randomness and merely untrackable data is nil. The problem for astrologers, and for all analysts, is that we often see the start of a sequence and then its outcome. The connecting steps are so numerous and some so apparently trivial that we may never be able to track them. I think that we will achieve a higher level of prediction only by incorporating more data and different views, i.e. incorporating the other forecasting and analytical disciplines. The logical next step for astrology is to combine astrological analysis with all the other methods of analysis and thus limit the range of options when faced with making a prediction. Step one, if you like, is the astrological observation that a particularly significant configuration is due to start influencing events at a certain time and date. Together with a list of general areas where effects might, on past experience, be expected to manifest themselves. Step two is to pass that general observation to analysts in other disciplines and ask them what they are aware of within their fields that might resonate to these general influences. The challenge will be in persuading them that they have as much to gain as we do.

The planets and our destiny are linked by a common cause - the planets represent the closest and largest usable cosmological fractal-fragment of the original pattern, and we can study this in detail primarily in order to perceive the patterns being woven here at the micro-level. Apparent randomness is a fractal result of the original cause, and that primal cause is deterministic. The program itself was set in motion countless eons ago, from then on it's all inevitable - just a matter of whether you know about it or not. As astrologers, if we can track each development closely enough (even if initially only in retrospect) to be able - come something like an eclipse - to recognize this is at least one of the potential catastrophe points, then the rest is a matter of being able to estimate the presence or absence of significant small-scale structures and their probable manifestation within the attractor for the moment in question. But is absolute certainty impossible? The M-set appears to be infinite, and the event level seems to include facts which, on the scale at which astrology operates, is incredible in its detail, but the Universal level does not appear to include randomness - disorder. It's all organized and completely deterministic. Perhaps it's only our own inability to see this order within the fractalization of events that makes it appear to us as random. Unpredictability? No - trickier geometry, that's all.

 copyleft 1995, Michelle Jacobs


The author wishes to express her thanks to Michael Jacobs for all his excellent technical and moral
support, and to her advisors, Julian Armistead and Ken Negus, for their contributions to this project.

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