I recently carried out a survey of the use of blind techniques in different branches of science by analyzing the “Methods” section of papers published in leading journals. In this survey, which I summarized in the Skeptical Inquirer, I found that the use of blind techniques has gone furthest in parapsychology, where 85 percent of published experiments were carried out blind. In medicine and psychology, where everyone pays lip service to the idea of blind techniques, in practice the number of blind or double-blind papers was below 20 percent. In biology, the number of blind papers, out of over 900 reviewed, was less than 1 percent, and in the physical sciences—chemistry and physics—the number of blind studies was zero. We then interviewed top professors in leading departments of physics, chemistry, biology, and molecular biology at Cambridge, Oxford, and other universities. Most people in the physics and chemistry departments there neither use nor teach blind techniques.
The idea that modern science is so objective and unbiased in these areas seems to be based on the notion that, by putting on a white coat, one becomes completely objective, and is not subject to the biases that everybody is. So I suggest checking out blind techniques in the laboratory. Do you get different results in a physics experiment if you do it blind compared with doing it with the usual open conditions, where you know which sample is which?
TM: The New Age could probably profit from this as well. It would probably wipe out most of the things I’m objecting to.
RA: The popularity of double-blind methodology in parapsychology is obviously due to the difficulty researchers have convincing people of the validity of the results. In other words, it’s due to the special weight of skepticism that’s applied to the fringe of speculation. So, somehow, there’s the fundamental dialectic of the evolutionary mind. It has to do with the balance and interplay between speculation and skepticism. These are the two forces at work, and we want them to both be healthy and freely interplay. If a new technique such as double-blind experiment can work, then the interplay of these forces will guarantee that it’s used. To summarize your case against the New Age fuzz, Terence, there seems to be an area in the evolving mind where the speculation is not balanced by an appropriate amount of skepticism. You want to shine a flashlight of skeptical consideration onto that area of unbalanced fuzz. We’re interested in balanced fuzz.
TM: Speculation and skepticism begin to sound like novelty and habit. So maybe these things are just counter-flows in the intellectual life of the culture that redress each other, and though we do have certain long-running forms of fuzz, it does tend to correct itself over time. But in the present historical moment, we are seeing an incredible fragmentation, syncretic theorizing, and a richness of ideological competition due shortly to self-correct.
RS: But what I see on the fringes is a whole lot of small cults and gurus that are all vying for space in Common Ground magazine. It’s a highly competitive market. What’s keeping all of them in check is competition. If one cult does particularly well, it grows. Others fade away if they don’t get enough supporters. There’s a free market with a clamor of competing claims.
That’s on the fringes. But the main ground is occupied by a kind of Stalinist central control of government-funded official science, which marginalizes everything else. A free market approach would allow a more informed debate.
TM: I’m a little surprised, because you seem to be implying that here is yet another area where the solution to all problems is the practice of untrammeled capitalism, and the unleashing of unrestrained market forces. Welcome to the new millennium.
RA: It’s almost the definition of science that it’s to be an alternative to the diversity that has been experienced in world cultural history in the sphere of religion. Very early on people knew that every town had different gods. This multiplicity was acceptable. Even though some people thought their gods were more powerful than the gods of other ones, they agreed that there would be a lot of gods. So everything fit together in a context of diversity.
Science appealed to people who lost faith in religion. In science they hoped that there could be a unique global planetary system of thought. Many people would think it appropriate that there’s a monopolistic control of the funding of scientific research, because each thing is supposedly going to reinforce, validate, and confirm everything else—because this is the idea of scientific truth.
I think the idea of a free market in science would require giving up the idea that there is some kind of absolute scientific truth, and that a given question could be settled either true or false according to this universal canon. I don’t believe in this idea. That’s why a free market in scientific research would be good. Perhaps if science was liberalized in this way, it would become very much like religion, where you would have groups like Baptists, Vendantists and Shiites who would believe in this or that system. You have to wonder if this kind of diversity would be acceptable by our species in the future or not, and what’s the alternative.
Boundaries which are too firm (iron curtains) may be involved in world problems, and could be treated with therapies informed by the new math. Chaos and cosmos must be properly balanced for a healthy social system.
Perhaps, as there’s an increase of complexity in our culture, as we approach the Eschaton, there’s an accompanying decrease as fractality actually vanishes at an alarming rate. This is what’s meant by “the death of nature.”
CHAPTER 9
FRACTALS
Ralph Abraham: This epic in four parts I’ll call “Fractals on My Mind.”
Part one: The sandy beach.
If we look at a map of the Hawaiian Islands, we find a firm curve between Hawaii and the Pacific Ocean. But if we go down to the shore, we find a sandy beach. It is the boundary between land and sea, but it is not a firm curve. There is water in the sand, and sand in the water. The more closely we look at the beach, the more indistinction we see. The transition from land to sea is a fractal. It is spatially chaotic. It is natural. The Milky Way is a sandy beach in the sky. It is natural also. Nature teaches us fractal geometry and chaos theory.
Part two: Two roads diverged in a yellow wood.
Dynamical systems have attractors and basins. Imagine a dynamical system with two attractors, red and green. No matter where you begin, you will be attracted to one attractor or the other. Perform an experiment by choosing a starting position, then following the rules of the system, to find which attractor is your destiny. Color the starting position red or green, depending on the outcome. After a million experiments starting from different positions, the domain is mostly colored red and green. The red region is called the basin of attraction of the red attractor, likewise with the green basin. The domain, colored red and green in this way, is called the basin portrait of the system. Between the red and the green are the basin boundaries, which might be outlined in yellow. The yellow boundaries, in a generic dynamical system, are fractals: a wide, frothy zone, of mixed red and green, like a sandy beach. Or a yellow wood.
Part three: Fractals in my mind.
Both of the two little math lessons I just completed are applicable to psychology. Let’s imagine, as Kurt Lewin might, that a person’s mind has its own space. Lewin was the founder of social psychology, and within that the notion of field theory in psychology. The field operated in a mental space, which he called the life space. The mental process was, to him, a dynamical system (the field) working in the life space. Thus, we may regard the multiple attractors and basins of the psychological field as the stable states of the mind. I am suggesting that in a normal psyche, the basin boundaries are thick fractals, which permit a kind of porosity between these components of the psyche, and thus, integration. But in another mind, the basin boundaries may be like concrete walls or iron curtains. This is a dynamical model for multiple personality syndrome: the sandy beach model. From the perspective of this model, the pathology comes from the poverty of chaos in the basin boundaries, and thus I call it MPD, for multiple personality dischaos. If we were therapists
, we could try to devise a treatment to increase the fractal dimension of basin boundaries, based on chaos theory and fractal geometry, which are new branches of post-Euclidean math.
Part four: Fractals in the collective mind.
Rather than going on with individual psychology here, I want to look at the mind of the whole enchilada from this point of view. The collective conscious and unconscious of our society is a massively complex system, which Kurt Lewin also described in the paradigm of life fields. Chaos theory suggests a sandy beach model for this massive system also. Thus, boundaries which are too firm (iron curtains) may be involved in world problems, and could be treated with therapies informed by the new math. Chaos and cosmos must be properly balanced for a healthy social system.
Rupert Sheldrake: I’d like to try and summarize, Ralph, what you said, and see if I can add to it.
Personalities—and of course social relationships and international relations and the behavior of different groups of pigeons—fall into different basins, and we can visualize this as a landscape containing different valleys. If something’s in a particular region, the ball will roll down in a particular valley.
Each of these basins represents a different kind of subper-sonality. You pointed out that personalities are made up of different sub-personalities, which is currently a very fashionable view. Everyone’s talking about subpersonalities. For example, the Jungian psychologist James Hillman says we need a polytheistic psychology, where all the different gods and goddesses not only represent the archetypes, but they are real in some sense; we’re possessed by different ones at different times. We’re not a single personality with different functions, but a kind of emulsion of a number of different personalities. Everywhere we find these multiple models, of which yours is one. All of them seem to be saying that we must get away from monotheism, which is reflected in psychology by the idea of the central, dominating ego. We’ve got to build more democratic models where you have a kind of grassroots democracy, with all these different personalities.
A second point you seem to be making is that the boundary between these different basins is not a straight line or a rigid wall but rather a fractal boundary, namely one that has many ins and outs and curves and filigrees and patterns. With that kind of boundary, moving from one basin to another is very easy because you never quite know where you are and can cross boundaries without realizing it, whereas a rigid wall makes it difficult to get from one to the other.
I’d like to take up the idea of the plurality of models. Terence’s model is monotheistic, in that he has a single Eschaton, and this takes us immediately to the polytheism versus monotheism argument. My view of polytheism is that in all its actual existing forms, it is not in fact radical polytheism. It involves a plurality with some overarching unity beyond it. My question to you is, are you advocating a radical polytheism, and denying an overarching unity?
RA: No. My main message has to do with the rigidity of boundaries in between things. I think that everybody would agree that there is plurality in religion, in life, in the mind, in the stream, in the sky, and so on. What’s important is the rigidity of the boundaries in between these things. If you worship in the Shiva temple is it okay to go to the Rama temple? Do you have to be faithful to one god and never admit the existence of others? This is a denial of something that’s obvious even to children, and it inevitably brings about a disintegration of the personality.
In this religious or mythological context it’s appropriate to think of Shiva and concepts of that sort as attractors. There are multiple attractors. Considering the population of the planet through all times, there are zillions of attractors, and some people have visited one and other people have visited two or three and so on. An openness to all attractors, I guess I would say, is some kind of prerequisite for the stability and longevity of a culture, or the health of an individual. This idea is based on a cosmology in which the stream has the same morphology as the heavens, which have the same morphology as some abstract mathematical object. Under the ambience of this idea, our experience of nature is that rigid walls are very unstable.
RS: They’re not that unstable. Our own skin, for example, has pores in it and is not absolutely smooth. Nevertheless, it forms a clear functional boundary, and everywhere you look in biology you find functional boundaries. There’s a cell membrane around each cell. It’s not an infinitely permeable boundary.
RA: It has little holes in it with pumps that are designed for particular things in the environment. The permeability is, as it were, part of a structure that’s rigidly connected with that species. If these holes were plugged up then of course the cell would instantly die.
RS: Of course, you’re not denying the importance of boundaries. Your whole model is based on boundaries, isn’t it?
RA: That’s right. It has to do with their crookedness.
RS: Their crookedness is the mathematical model for their permeability.
RA: Yes.
Terence McKenna: It seems extraordinarily arcane. Nature is fractal. This is a new discovery, and it’s a very powerful insight, but it doesn’t wipe out some of our previous accomplishments; I’m thinking of all the work that was done to show that these systems are also hierarchical. Without tossing the baby out with the bath water, it might be better to say it’s fractal and hierarchical. We’re back to Whitehead’s notion of certain stubborn facts that are, I suppose, like raisins of resistance embedded in this fractal ocean of infinite permeability. I think above all these psychoboundaries and membranes there is ultimately a frame that is all-inclusive and defined. The form of monotheism I’ve probably fallen under the sway of, is some kind of neoplatonic pyramid of ever-ascending abstract hypostases that leads into the One. If what we mean by the Eschaton is the absence of boundaries, then what we’re saying is that the fractalization of reality occurs ultimately on such fine scales that from the point of view of the perceiver, the boundaries have dissolved completely. Or the boundary and the thing bound have become so homogenized that it no longer makes sense to speak of boundary and medium. I picture it as a kind of extremely marbleized liquid or surface where every domain can be found to be lying next to a mutually exclusive other domain, rather like the kinds of diagrams you get when you carry out four-color mapping problems to fourth and fifth stages of resolution. You have these extraordinarily complicated structures where every point lies next to the boundary that separates it from points that have been somehow defined as other. I’m not sure that we have any disagreement here.
RA: What we’ve got here in your description is a speculation built upon a speculation built upon a speculation and coming eventually from some kind of absolute and pure faith. The One, to Plotinus, was something that you could explore toward, but not actually arrive at. We have to understand, on the testimony of these early experts, that The One is an article of faith, and even the best traveling shaman has only been so far. The assumption of the existence of The One, beyond this, is monotheism at its best. God is called “The One” to make sure that you don’t think perhaps it’s Two. I agree with your idea that cosmos is hierarchical. I don’t even care if it has a finite number of layers or an infinite number. However, the wildest shaman has traveled and seen only another image, maybe more complex, of what we see in ordinary reality and nature. There are multiple basins, there are fractal boundaries, there are many possibilities, different regions, complexity, where harmony is hierarchically organized, and we’ve never gotten to the top. Therefore, to say it’s one or two or three can only be an article of faith, not an extrapolation from observation, normal or arcane. We’re talking about pure faith. When you get to the top frame, I don’t see any reason why it shouldn’t have two basins, separated by a fractal.
TM: My understanding of fractals is that they are a kind of homogenization of levels not present, domains distant, and that the idea is if you have a sufficient sample of the fractal, not very large, you can in fact extrapolate the contours of the entire system. Therefore it isn’t nece
ssary to send the shaman or mathematician for a total overview. The cosmological principle can be extrapolated from local measurement and local physics.
RA: Without an article of faith, you can’t get a cosmological principle. We don’t have any evidence from the boundaries of space.
TM: Isn’t the idea that fractals are a kind of holographic plan that recurs on many levels, always following the same pattern? If you have ten levels and you know the pattern on 2 through 7, you also know the pattern on 1, 8, 9 and 10.
RA: Few fractals in nature have that property, which is a special property of self-similar fractals that are like integers within the field of all real numbers. They are exceptional. Mostly it just means you have two basins, red and green, and their boundary is kind of stirred up so wherever you are you’re within one millimeter of each side, or even a tenth of a millimeter of each side.
TM: Well, I’ve limited my model building to the use of self-similar fractals. My model of the Eschaton, at least on a mathematical level, is self-similar.
RA: If you have three basins fractally entwined, then wherever you are in the sandy beach, you’re not only within one millimeter of the red and green, but the yellow one is there also. That means, if you travel as a shaman and you see this pattern at the end of time, and there’s any blur in your vision, anything slightly human remaining in your travel, you might see it as one, even though it isn’t. You would mistakenly see it as a blur of the three colors into a kind of gray Eschaton.
The Evolutionary Mind Page 16