Re: Moon over Maple Ridge
Oct 03, 1996 11:25 PM
by Eldon B. Tucker
>One more thought, has anyone seen the programm on PBS regarding the Mandelbrot set?
>I would love to learn more about this new Theory. It had to to with exploring
>the most minute particles which became possible with the computor age.
>What they showed on T.V. was an design like mandalas with little buddhas as the final
>symbol it lokked very mystereous but also very interesting.
>Please coment on this.
I don't have time to write anything new right now, but did post something
on the subject a while back on theos-l. It's been such a long time since
then that I think that many readers haven't seen it, so I'll repost it
in reply to your request.
> Date: Mon, 30 Jan 1995 11:47:54 -0500
> From: Eldon Tucker <firstname.lastname@example.org>
> Subject: Regarding Chaos
The subject of chaos, as a new subject of study, has the
potential of enriching our understanding of live, and the
law of cycles, and how the world works. We can derive many
new keys to unlock the mysteries that stand before us in our
There's a very good book, "Turbulent Mirror," by John Briggs
& F. David Peat, Perennial Library, Harper & Row Publishers,
New York, 1989. This 222 page paperback presents the many
areas of thought related to the study of chaos in both a
mathematical and scientific manner, and in a well-digested,
clearly-presented philosophical presentation. I'd highly
recommend it as an important supplement to theosophical
studies, and would personally place it much higher than "The
Source of Measures."
When we come to a study of chaos, as a modern discipline, we
first need to realize that the term "chaos" was coined.
Nonlinear dynamics and other areas of mathematics and
physics, grouped under the term "chaos," are not extensions
of early religious thought, simply because the same term was
There is not the duality of chaos versus cosmos in the sense
of randomness versus order. We don't have "accidents" at
times and the karmic results of actions, the results of
previous causes, at other times.
This is not to say that everything *appears* to be ordered
and well-behaved. While the mathematics of a living system,
of a system undergoing continual iteration or self-feedback,
is deterministic, ordered, and not random in nature, the
matter of *predictibility* is a different subject.
There are certain basic stages to the manifestation of a
living system. A good graphic analogy, a good metaphysical
symbol, is the bifurcation curve. At a low energy level,
life cannot sustain itself, and death results. At a slightly
higher energy level, life adjusts to its environment and can
exist. At this stage it is stable, balanced, and ordered in
a predictable, near-linear way. At yet a higher energy
level, it undergoes its first bifurcation, where it now has
a dual state, and it goes back and forth. At yet higher
levels, the number of states that it goes through become
more and more varied and unstable, until its state is
totally unpredictable or chaotic.
Again, we don't have a duality of chaos versus cosmos in the
sense of randomness versus order. What we rather have is
predictability versus unpredictability, but order
nevertheless. We can have a system where we can, say, plot
on a x/y graph an ellipse that represents all states of a
system. That system is well-defined, is ordered; its states
only exist on that curve. But the system may be "chaotic" in
the sense that we cannot predict from one moment of time to
the next where on that graph its state will be. The system
is chaotic in the sense we cannot predict a precise future
state, but is ordered. That order, that holds it to the
well-defined set of stages, is called a "strange attractor."
Another example of apparent chaos is in the static on phone
lines, which comes under "intermittency." No matter how
clear we try to make the line, there will be small,
apparently random bursts of noise. When we examine those
bursts of noise, they have the same pattern of small bursts
of noise, at increasing degrees of magnification. We have a
fractal order to the signal on the phone line. The order is
not random, accidental, but described by fractals.
(Fractals represent another area of study, that related to
theosophic thought. We have a type of mathematical object
that has fractional dimension, that has an infinite amount
of detail, that at different levels of magnification shows
the same pattern or richness of detail [the
macrocosm/microcosm idea], and models real-life processes.)
With chaos, we have order in the universe, but sometimes
that order eludes us, sometimes that order is unpredictable
in either time or space. That unpredictability and apparent
disorder arises from living systems being at too high an
energy level, being at too high a level of self-feedback,
and where they have moved from an ordered existence along
the turbulent pathway towards "chaos".
When the apparent order is gone, the higher type of order is
maintained in an almost metaphysical way, in strange
attactors, in unseen forces that maintain order in the
apparent external chaos of external unpredictability.
Consider karma. If life were operating at a slower pace, we
might have a more-immediate sense of cause-and-effect
feedback for our actions and interactions with others. Now,
in the turbulent, tense, difficult Kali Yuga, our karmic web
is in a chaotic stage, where karma acts as a strange
attractor, still guaranteeing that our results come back to
us, but not externally predictably in a linear fashion in
time and space. We know that the fruits of our actions will
return to us, but cannot say when or where.
Is everything karmic? No. There are accidents. Life is
imperfect and all beings, even the highest Dhyani-Chohans,
are subject to error. And there is yet an even more
important ingredient: the free will of others in the
present. Everything that other people do is not simply the
results of *our* past actions. The whole of life is not
merely a puppet show for *us*. Others have their free will
do, and everyone participates in making what will happen.
The interaction between us and others is *negotiated* in the
sense that the person on each side of a relationship has an
influence on what will happen. We have, between ourselves
and others, not so much a give and take of x units of
"karmic currency" as we have a living bond through which we
co-create what happens.
Coming back to chaos, an important idea is the "butterfly
effect," the sensitive dependence on initial conditions.
Certain systems may be living at a point where the slightest
external change, the slightest perturbation, would cause a
radical state change. A pencil balanced on its lead point
would be an example of this. As we increase our energy
levels, and move from the regions of ordered to turbulent
existence, we find such points becoming more frequent.
Taking some of the symbols from chaos, and using them as
theosophical symbols, we could consider three for now. A
*fractal* shows the macrocosm/microcosm relationship, and a
study of how and when fractals occur in nature is rewarding.
The *bifurcation curve* is the best mathematical
illustration of the law of cycles, and should replace the
symbol of the serpent swallowing its tail. And the
*mandelbrot set* (which I haven't discussed in this posting)
is an excellent example of the karmic web, of the law of
A caveat must be given at this point. Mathematics is a tool
to model life, but *is not life itself.* Life has many
options as to how it will manifest itself, and external
forms are patterned after mathematical principles, but the
life itself was not "caused" or controlled by the
mathematics of those forms. The forms and the associated
mathematics were chosen by the life, not the causes of the
A second warning is that when we deal with a new field of
scientific and philosophical thought, we approach it with an
open mind, but not accept everything on face value, and
assume that because many ideas are attractive and ring true,
that we accept everything without due critical thought. The
Wisdom Teachings in Theosophy relate to a far grander type
of learning that we find in popular disciplines, and it's
important to never lose sight of its majestic heights.
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