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Oct 03, 1996 11:25 PM

by Eldon B. Tucker

Brigitte: >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. -- Eldon > Date: Mon, 30 Jan 1995 11:47:54 -0500 > From: Eldon Tucker <eldon@netcom.com> > 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 theosophical studies. 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 used. 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 living relationships. 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 life. 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. -- Eldon

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