Bringing it Down to Earth: A Fractal Approach
© 1995 firstname.lastname@example.org
are not spheres, mountains are not cones,
are not circles, and bark is not smooth,
does lightning travel in a straight line.'
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.
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."
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.
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
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.
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.
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.
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.
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.
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.
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.
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
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.
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
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.
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?
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,
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?
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
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.
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
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.
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
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.
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.
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.
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.
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:
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."
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.
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.
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
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.
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.
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.
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.
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.
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.
author wishes to express her thanks to Michael Jacobs for all his excellent
technical and moral
and to her advisors, Julian Armistead and Ken Negus, for their contributions
to this project.
David (1993). The Undivided Universe: an ontological interpretation
of quantum theory. London : Routledge.
David (1980). Wholeness and the Implicate Order. London : Routledge.
John (1989). Turbulent Mirror: an illustrated guide to chaos theory
and the science of wholeness.
: Harper and Row.
John (1992). Fractals: the patterns of chaos: a new aesthetic of art,
science and nature. New York : Simon and Schuster.
Ali Bulent (1993). Applied Chaos Theory: a paradigm for complexity.
Boston : Academic Press.
Dennis (1983). The Astrologer's Reality. Sebastopol : CRCS Publications.
Dennis (1987). Cosmic Loom: the new science of astrology. London
: Unwin Hyman, Ltd.
James (1988). Chaos: making a new science. New York : Penguin.
Nina (ed) (1992). Exploring Chaos: a guide to the new science of disorder.
New York : W.W. Norton.
Theodor (1995). The Golden Section: a cosmic principle. Considerations,
vol. 10, no.1, Jan-March 1995.
Hendrik A. (1991). Fractals: endlessly repeated geometrical figures.
Princeton, NJ : Princeton University Press.
Edward N. (1993). The Essence of Chaos. University of Washington
J.E. (1979). Gaia : A New Look at Life on Earth. Oxford University
Benoit B. (1988). The Fractal Geometry of Nature. New York : W.H.
Foster (1991). The Art of Modeling Dynamic Systems: forecasting
for chaos, randomness, and determinism.
: J. Wiley.
Heintz-Otto (1992). Chaos and Fractals: new frontiers of science.
New York : Springer-Verlag.
Clifford A. (1990). Computers, Pattern, Chaos, and Beauty: graphics
from an unseen world. New York : St. Martin's Press.
Eliot (1990). Nature's Chaos. New York: Viking.
Suggested Pdf Resources
- Considering Organisation Structure and Design from a Complexity
- principles drawn from the complexity paradigm: 'The Fractal Web', is presented. In A non traditional approach is taken by Pascale, Milleman and Gioja (2000, p. 197).
- Cosmic Symmetry-breaking, Bifurcation, Fractality and - Fractals
- specific nucleic acid sequences, many features of life as we know it on Earth are . the proton and neutron are a composite of up and down flavours uud and udd. ..
- Agile Project Management
- Along with predictability, they inherited a deterministic, reductionist approach . to us – is a force of attraction exerted by a celestial body, such as the earth, guidance – a project plan with fractal tasks – often has tasks at too small a groups and demonstrating that bringing a problem to the group is not a sign of weakness.
- Earth's relief, shape and fractal dimension of coastlines, and number
- irregularity, is the fractal dimension D of the coastline; it is a fraction lying between 1 Earth is roughly spherical overall would only bring insignificant cor- rections. .
- Muscle - National Strength and Conditioning Association (NSCA)
- Bring Your Mind to the Line. By Suzie Tuffey . approach to preparing for his or her race.
Suggested News Resources
- Lalive | Legal Engineering in Comparative Law – An Introduction
- Such reasoning is common to all civil law systems, and to all systems which apply a “top down approach”. Here the law exists ex ante, and its pre-existing conditions are compared to the case.
Suggested Web Resources
- Bringing it Down to Earth - A Fractal Approach
- We want to think about the future - it's our nature.
- Bringing It Down To Earth A Fractal Approach | RM.com ®
- Bringing It Down To Earth A Fractal Approach articles, reference materials. Need more on Bringing It Down To Earth A Fractal Approach?
- EEP Teaching Company Math DVDs
- and often a fresh new approach to mathematical concepts that should help in and geometry, and bring it all back down to Earth -- learn how to play "Let's Make of equations and inequalities; and the future (fractals and captivating chaos).
- Astrofaces: Faces In Astrology - Send Photo Data - www.astrofaces
- Fractal Approach, Bringing it Down to Earth: A Fractal Approach by Michelle Jacobs.
- Munster & Lovink: bringing network down to earth » the Internationale
- Munster & Lovink: bringing network down to earth .
dracaena sanderiana cultivation
taringa state school
chalukya art and literature