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Nov 12, 1994 07:20 PM

by Jerry Schueler

John <Not to be too technical, but there are a number of different formulations of exactly what "Complexity Theory" really is. I have come at it from economics, and among those I discourse with, complexity theory would probably be described simply as the study of complex systems moving in multidimensional, multiscalar spaces.> Agreed. I have absolutely no background in economics, and will assume you are correct in those areas. John <Some of these systems seem to cycle back and forth between states of (relative) order and chaos, others seem to remain perched on the "edge of chaos" (as Stuart Kaufmann so poetically put it). Chaos theory, then, is the study of one aspect (a "subset") of a complex system...the behaviour of the system in its chaotic phases.> I believe the term for the first type is intermittency - one of the three "routes to chaos" (the other two being crisis and period-doubling). There is certainly a lot of ongoing work looking at systems in their chaotic phases, but how systems evolve to chaos is also an area of concern. To some extent, there is even disagreement about when full chaos is reached. Different systems tend to display chaos differently. John <The Santa Fe people are perhaps the best known, but are certainly not the only ones studying complexity.> Agreed. One of the strongest voices against AI is probably Roger Penrose. I just bought his latest book about this, but haven't had time to read it yet. John <The Institute itself was begun by a few people who had studied chaos theory, and a good number who had not. In fact, I believe the original impulse came from (if I remeber correctly) an initial conference composed of a group of economists and a group of physicists who had sat down to discover whether there were points of possible conversation between their very different disciplines. Many of them had never worked with chaos theory.> True. I was being overly simplistic. John <I'd like to talk with you more about complexity/chaos' application to not only psychology but to the "spiritual" realm in general.> Wow! I am not sure what you mean here? We will have to define terms. I view "spiritual" as that which lies above the Abyss, which is to say above the Ring-Pass-Not of the human mind. Chaos begins in the Abyss, and is reflected 'downward' into matter throughout the 'lower' planes (I am here using the Gupta Vidya Model supplied by HPB in the SD Vol I; the Abyss is just above Globes A and G, and separates the 7 lower Globes from the 5 upper Globes according to the 12-Globe model presented by G de Purucker. The Abyss, the real source of all chaos, is equivalent to the 11th Sephiroth, Daath, in the Qabala). John <Let me ask you if you've integrated scaling into your ideas...in your information "equations". Information certainly is delivered to the human awareness at many different (one might almost say `discrete') scales.> According to Claude Shannon, the founder of information theory, information refers simply to the number of possibilities, Z. So that information, I, can be expressed as: I = log to the base 2 of Z Shannon used the logarithm to the base 2 because modern communication works with binary numbers or bits. The human mind probably does not work in binary. However, the idea still holds that Z will be large, so therefore I will be large. Shannon also developed the equation for what is called the Shannon uncertainty, Shannon entropy, or simply information entropy. It consists of a negative constant times the integral of the probability of information times the log of that probability. However, Shannon information does not concern itself with meaning, and it only applies to closed systems. Of course, like you suggested, a lot of information comes to us without meaning - such as the background 'noise' of our environment. I doubt that equations will apply to the brain's ability to receive information like electronic equipment does. However, a lot is being done in research today, such as looking at the brain as a complex of parallel circuits. And several brain models are being discussed, but again, even the most simple ones are skimpy with equations. I agree with you that incoming data must be scaled. The idea that I am currently working on is that our brain, as a complex system, undergoes bifurcations. I am not so sure about period- doubling, because there are simply too many variables. But as the brain approaches a bifurcation point, only a tiny outside influence is needed to cause drastic changes. In some cases, its rather like the straw breaking the camel's back. I read all sorts of horror stories in the newspapers and on TV news, such as a kid who shoots his parents because they won't but him a radio, or a 'good' student pulling out a gun and shooting everyone on campus because he only got a B in some class, and so on. While these are dramatic, we all go through bifercations at various points in our lives, many for the best (they are nothing more than instances in time where choices must be made; where our lives go down one particular road rather than another). Often these critical points can be detected via 'nuances' and taken advantage of. But I am not so sure that we can actually develop mathematical equations for this kind of thing for individual people (although statistically we may, as people tend to follow the Poisson distribution in their collective actions). I guess one of the things that I am trying to say here, is that you can't always tell what the scale should be, because the psyche gives events 'meaning' in a very individual manner, as per Jung's synchronicity. Jerry S.

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