It is said that mathematicians study the separatrix and physicists study the attractors, but the overall picture has these complementary things that have to be understood. The separatrix gives more information about short-term behavior, while the attractors determine the long-term behavior. What is most amazing about them is that there aren't very many. And that's kind of surprising because there's so much variety in the world. I would have expected more variety in the mathematical models for the long-run dynamical behavior, but most of them look alike.
RMN: When an attractor disappears due to sudden catastrophic change, the system becomes structureless and experiences a term of "transient chaos" before another attractor is found. How have you applied this idea to cultural transformations?
RALPH: Well, that's actually a commonly expressed idea which might turn out to be unfounded. People--including me--want to use this aspect of dynamical systems theory called bifurcation theory to model bifurcations in history. History is a dynamical process and it has bifurcations. And here we have a mathematical theory of bifurcations, so let's try it. That makes sense. But the bifurcations that are known to the theory, as universal models of sudden change in a process, are not usually characterized by this transformation from one equilibrium stage to another through a period of transient chaos. That's very exceptional in the theory, and I don't know if natural systems show this characteristic either.
Let's say you could collect data about a civil war where you had maybe monarchy before and democracy afterwards, and the monarchy was very steady with institutions that you can depend upon, and so was the democracy, and in the middle you were constantly overrun by the troops of one side or the other, or by guerrillas. If this whole history were reduced to data and then you applied the rigorous criteria of dynamical systems theory to these data, and measured the degree to which it's chaotic, you might find that the monarchy had a chaotic attractor as the model for its data, in the democracy there is also a chaotic attractor of a completely different shape, and in between you don't have chaos at all; the transient is not transient chaos but is transient something else, or it's transient chaos but it's much less chaotic.
You know that heart physiology shows more chaos in the healthy heart and less chaos in the sick heart. I think it's dangerous to take the casual aspects and implications of these ideas of chaotic theory and start wildly trying to fit them into some preconceived perception of external reality. A better idea is to get some data and try to construct a model. There's no lack of numerical data about social and historical process. For example, the total weight of mail sent in mail bags from the American Embassy in Russia to Washington, D.C. is known for over a century. Political scientists have an enormous amount of data. I think the serious applications of mathematical modeling to the political and social process will proceed in the numerical realm. The result might not fit someone's preconception based on an intuitive understanding of these chaos concepts. So I don't know if social change is going to be characterized by chaos or not. I guess it might, according to some measures and observations, and might not, according to others.
DAVID: Do you see the process of evolution as following a chaotic attractor, and if so does that mean there is a hidden order, so to speak, to evolution? May what has appeared to evolutionary biologists as chance and randomness actually be a higher form or order?
RALPH: No. I think that the understanding of dynamical systems theory presented in popular books is extremely limited and a lot of physicists for example have studied attractors exclusively while as I said the mathematicians have been studying the separatrices. Attractors are very important in modeling physical processes in some circumstances, and that is very fine, but when you're speaking about evolution, if you want to make models for an evolutionary process, then probably the best modeling paraphernalia that mathematics has to offer you are the response diagrams of bifurcation theory. Bifurcations have to do with the ways in which attractors appear out of the blue, or disappear, and the way in which one kind of attractor or size of attractor changes into another.
These transformations appear in scientific data and in mathematical models in a much smaller variety of transformation types than you would suspect. And dynamical systems theory, at the moment, is trying to accumulate a complete encyclopedia of these transformation types called bifurcation events. Bifurcation events assembled in some kind of diagram would provide a dynamical model for an evolutionary process. Therefore, the actual attractors involved are almost of no interest. From the bifurcation point of view it doesn't matter if the process is static, periodic or chaotic. What's important is whether the attractor appears or disappears. And here there is plenty of room for chance and randomness.
And so as bifurcation theory becomes better known, I think the style of making models of process will undergo a radical and very exciting revision. The main point of my books, Dynamics: The Geometry of Behaviour, is to present the beginning of the bifurcation encyclopedia as far as it is known to date. There are about twenty-two different events there.
DAVID: Do you think it's possible to form, or have you already formed, a mathematical theory to explain the phenomenon of how consciousness interacts with the material world?
RALPH: No. There are models, specific mathematical models, for different perceptual functions of human mammalian physiology which represent the frontier of neurobiology today. One example is Walter Freeman's model of the olfactory bulb. These models are mathematical objects known as cellular dynamical systems, which include neural-nets and excitable media as special cases. These mathematical models for perception pertain to the question of how consciousness interacts with the natural world. And they comprise a conceptual frontier today. In that context, what would an idea be?
In the context of the olfactory bulb, what is a smell? So it turns out that from the perspective of reductionist science, along with its mathematical models, a smell is a certain space-time pattern on the olfactory cortex, a pattern of excitation. The cortex consists of a sheet of oscillators side by side vibrating. A certain pattern in their frequency, phase relationship, and amplitude, is a smell. There is a certain picture, where inside a region there is a larger oscillation, and outside, a smaller one. This picture is recognized as a smell.
This kind of modeling does provide the possibility of making a simple model for the natural world, a simple model for consciousness, and a simple model for the interaction between the two. The interaction model, in this cellular dynamics context, is based on resonance. A lot of my work has to do with vibration and resonance phenomena in this context and has provided a specific mechanism for the transfer of a space-time pattern from one such medium to another. However, these mechanical models may be too simple to provide intuition as to such things as how your mythology, your perceptual filter, function so as to limit your perception of the natural world to a certain paradigm in your consciousness? Such models, which I think is the essence of your question, would have to do with a more linguistic or symbolic approach rather than at the mechanical model level.
DAVID: Could you define beauty in a mathematical way?
RALPH: People do say mathematics is beautiful, and some mathematical objects are certainly beautiful. Whatever beauty is, if you could define it in some way, it would include mathematics within it somehow. If you define it, for example, in terms of cognitive resonance, then mathematics provides the ultimate opportunity for cognitive resonance because the bare bones of cognition itself are represented by these mathematical objects. The strongest resonance of forms takes place in certain special areas, precious little rings of human experience. One is mathematics, another is music, and then of course, mysticism--the three M's, three crown jewels of beauty. But I wouldn't know what the experience of beauty really is, and J certainly wouldn't think a mathematical definition would be appropriate.
DAVID: From chaos theory we know that small errors in calculation can grow exponentially in time, making long-term prediction difficult. With this in mind do you think
it's possible to foresee what life for humanity will be like in the twenty-first century?
RALPH: This idea of the exponential divergence, the so-called sensitive dependence on initial conditions, is very much misunderstood. When a process follows a trajectory on a chaotic attractor, and you start two armchair experiments, two processes, from fairly close initial conditions, then indeed they diverge for a while. But as a matter of fact what is happening is that both of the trajectories go round and round. You can think of yarn being wound on a skein. So they diverge for a while, but pretty soon they reach the edge of the skein, and then they fold into the middle again. They always come back close together again.
They have a certain maximum separation-it might be four inches or something and that's it. That's not very scary. They do not diverge indefinitely and go off into infinity. That's exactly what doesn't happen with chaotic attractors and that's why chaotic attractors might be very reassuring to people who would otherwise have anxiety about chaos. Because the chaos in a chaotic attractor is very bounded and the degree to which things go haywire is extremely limited. So that's the good news, and after you know the process for a while, you know it forever. Chaos is very much the same as the steady state; it's not scary at all.
Now if our evolutionary track, this species on planet Earth going into the twenty-first century, for example, were modeled by a chaotic attractor, then we can answer the question where will we be in the twenty-first century. Because it would be pretty much the same mess as now. But it's not modeled very well by a chaotic attractor. A better kind of mathematical object for modeling an evolutionary process is a bifurcation diagram. In this context, a chaotic attractor is changing in time. There may be bifurcations, for example, a catastrophe, a comet or something. Who knows? And it may be that some bifurcations occur under the action of parameters controlled by us, such as how much energy we use, how much waste we make. And that's why bifurcation diagrams are more interesting than chaotic attractors for modeling our own process. Under this more general kind of model we cannot say where we will be in the twenty-first century. Or if we'll be.
RMN: Why do you think that the understanding of chaos theory is vital to our future?
RALPH: This fantasy of the importance of mathematics has to do with the idea that we might have a future, that we might have something to do with it, and that conscious interaction with our evolutionary process is possible and desirable. And in this case, things will go better if we understand our process better.
The importance of chaos theory to our future is that it provides us with a better understanding of such processes, the behavior of complex systems such as the one we live in. This is due to the fact that chaotic behavior is characteristic of complex systems. The more complex the system, the more chaotic its behavior. And if we don't understand chaotic behavior, then we can't understand the complex system that we live in well enough to give it guidance, make informed decisions, and participate in the creation of our future.
DAVID: Would you tell us about any current research projects that you're working on?
RALPH: I have an ongoing project with visual music which is just one of a family of related projects having to do with chaotic resonance in cellular dynamical systems. If you had a cellular dynamical system such as a two dimensional spatial array of three-dimensional dynamical systems, and the state of each of the dynamical systems in the two-dimensional array were visible as a color, then you'd see the simultaneous state of this complex system as a colored picture, and the evolution of this system as a movie of colored pictures. This is experimental dynamics and graphic art, all at once.
Complex dynamical systems have very high dimension, they are really hard to see. The conventional methods of scientific visualization, an important field in computer research today, only work for low dimensional systems, for simple systems. But we want to understand very complex systems. So we have to develop a technology to visualize complex systems. And I believe that this kind of development will take place not only in the physical sciences, but more in the biological sciences, even more in the social sciences, and much more in the domain of the visual arts. So my current research is on the frontier of cellular dynamical systems, chaotic resonance, and the visual arts.
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Firing the Cosmic Trigger
with Robert Anton Wilson
RobertAnton Wilson earned his doctorate in psychology from Hawthorn University. From 1966-1971 he was Associate Editor of Playboy, and since then he has written over 26 popular books. He is perhaps best known for Illuminatus! a classic science fiction trilogy which he co-authored with Robert Shea. His Schroedinger's Cat trilogy was called "the most scientific of all science-fiction novels " by New Scientist, and has been reprinted in many languages. In the area of social philosophy Bob wrote such books as Cosmic Trigger, Prometheus Rising, and The New Inquisition He also wrote the introduction to my first book Brainchild. Bob has appeared as a stand-up comic at many clubs around the world, and regularly teaches seminars at New Age centers such as the Esalen Institute. Bob 's poetry has been widely published and in 1 986 he was a guest of the Norwegian government at the Oslo International Poetry Festival.
Bob has also starred in collaboration with the Golden Horde on a Punk Rock record entitled The Chocolate Biscuit Conspiracy, and a comedy record called Secrets of Power. Bob's play Wilhelm Reich in Hell was performed at the Edmund Burke Theatre in Dublin in 1986, and many other theatres. H epresently lives in Santa Cruz, where he continues to write, and co-edit the futurist journal Trajectories with his wife Arlen. We interviewed Bob on the evening of June 18th, 1989, at his previous home in West Los Angeles. A sharp-witted imp with a Brooklyn accent and a twinkle in his eye, Bob never fails to have a joke up his sleeve. He is a jolly prankster with an alchemical talent for blending cultural mythos. Bob spoke with us about the Illuminati conspiracy, brain machines, synchronicity, mysticism and science, nanotechnology, ecology, extraterrestrials, and the mysterious mythic connection between Satan and Santa Claus.
DJB
RMN: What was it that first sparked your interest in consciousness enhancement?
ROBERT: Korzybski's Science and Sanity. I was in engineering school and I picked up the book in the Brooklyn Public Library. He talked about different levels of organization in the brain-animal circuits, human circuits and so on. And he talked a lot about getting back to the non-verbal level and being able to perceive without talking to yourself while you're perceiving.
It was 1957. I was very interested in jazz at that time, and I told a black friend about some of Korzybski's exercises to get to the non-verbal level, and he said, "Oh, I do that every time I smoke pot." I got interested. I said, "Could I buy one of these marijuana cigarettes from you?" He said, "Oh hell, I'11 give it to you free." And so I smoked it.
I found myself looking at a quarter I found in my pocket and realizing I hadn't looked at a quarter in twenty years or so, the way a child looks at a quarter. So I decided marijuana was doing pretty much the same thing Korzybski was trying to do with his training devices. Then shortly after that I heard a lecture by Alan Watts, and I realized that Zen, marijuana and Korzybski were all relating the same transformations of consciousness. That was the beginning.
DJB: Many of your books deal with a secret society called the Illuminati. How did your fascination with this organization begin?
ROBERT: It was Greg Hill and Kerry Thornley who founded the Discordian Society, which is based on the worship of Eris, the Goddess of Chaos, discord, confusion, bureaucracy and international relations. They have no dogmas, but one catma. The catma is that everything in the universe relates to the number 5, one way or another, given enough ingenuity on the part of the interpreter. I found the Discordian Society to be the most satisfactory religion I had ever encountered up until that point, so I became a Discordian Pope. This is done by excommunicating all the Discordian Popes you can find
and setting up your own Discordian Church. This is based on Greg's teaching that we Discordians must stick apart.
Anyway, in 1968 Jim Garrison, the D.A. of New Orleans--the jolly green Frankenstein monster, as Kerry later called him--accused Kerry at a press conference of being one of the conspirators in the Kennedy assassination. Garrison never indicted him--he didn't have enough evidence for an indictment-so Kerry never stood trial, but he brooded over it for years. Then he entered an altered state of consciousness. I'm trying to be objective about this. Kerry, who served in the same platoon as Oswald, became convinced that he was involved in the assassination and that when he was in the Marine Corps, Naval Intelligence had brainwashed him.
Kerry decided Naval Intelligence had also brainwashed Oswald and several others, and had been manipulating them for years, like the Manchurian Candidate. He couldn't remember what had happened, but he had a lot of suspicions. Then he became convinced that I was a CIA baby-sitter and we sort of lost touch with each other. It's hard to communicate with somebody when he thinks you're a diabolical mind-control agent and you're convinced that he's a little bit paranoid.
Mavericks of the Mind: Conversations with Terence McKenna, Allen Ginsberg, Timothy Leary, John Lilly, Carolyn Mary Kleefeld, Laura Huxley, Robert Anton Wilson, and others… Page 17