Chaos and Coordination: The Alexander Technique and the New Science of Complexity

By David M. Mills, Ph.D.

“…the law is simple only for those who acquire a new conception of simplicity.”
Ian Stewart

“I would not give a fig for the simplicity on this side of complexity, but I would give my life for the simplicity on the other side.”
Oliver Wendel Holmes

There are two distinct ways in which Alexander’s work can be thought of as ‘scientific.’ One is the essential scientific quality of the method he used to make discoveries about himself as he evolved his technique. The other refers to the scientific ‘verifiability’ of what he discovered. There have been many efforts to demonstrate either the nature or the effectiveness of Alexander’s principles and methods in ‘scientific terms.’ Most research has been of the ‘effectiveness’ type, showing that Alexander lessons do indeed improve some specified physiological function (in other words, that it ‘really works’). Much of the ‘nature’ type has attempted to attribute that effectiveness to, for example, some particular key reflex mechanism or other. Much of this work has been of great interest and value. Nevertheless, from a broadly scientific point of view, it has not been really ‘satisfying’–not from any inadequacy on the part of the researchers, but due to an historical limitation in the available science itself. Research up to this point has been trapped, as it were, within a certain ‘linear’ science. This linear view–which, to grossly simplify, seeks to analyze the world in terms of proportionalities and linear (i.e. solvable) mathematical relationships–leads us to view the functioning of human individuals as a sum of the functioning of their ‘parts.’ As an example, consider the efforts of Frank Pierce Jones to demonstrate the effects of Alexander lessons on untrained individuals. In order to produce clear, measurable effects, Jones defined a number of head positions relating to the subjects’ ‘normal,’ ‘best’ and ‘guided’ ways of sitting or standing. We know, of course, that Alexander’s work was not about ‘head positions’ and that therefore such measurements as such must entirely miss the point of the work–and so did Jones. But in a sense the need to produce unambiguous data forced him to describe the effects in such terms nevertheless. What other choice did he have? He could either be clear and unambiguous about a part of the matter, or speak only of the whole in ways which would be, from a scientific point of view, rather vague. Jones, appropriately, chose the former. Others have followed Jones’s lead, using ever more sophisticated devices and methods of measurement and analysis. A broad underlying assumption of all such work is that, just as a complex mathematical relationship can be viewed as the sum of simpler linear relationships, we can seek a precise understanding of various systems within ourselves and then eventually ‘add them up’ into an understanding of our whole selves. I want to make very clear that I am not criticizing those who have followed this course. Indeed, it is the essence of good, classical science. Despite the undeniable benefits of this kind of science, however, it cannot–in relation to Alexander’s work–tell us ‘what we really want to know, that is, what is primary control and how does it ‘control’ the coordination of the individual?

Alexander’s work is not about the functioning of the parts of the individual, but about the control of the individual as a whole. What our science has lacked in the past was a sufficient vocabulary of wholeness to enable us to be as clear and rigorous in our quest for understanding whole human actions as we have been in studying the physiology of our sub-systems. As I said, this substitution of studies of parts for a study Of the whole is not a failure on the part of the researchers involved. Historically, it has been the way of science to precisely answer questions that could be answered rather than speculate vaguely about the questions that really fascinate us but which we lack the resources to answer. So it is that from Alexander himself, through Jones to the present physiological researchers, we have been bound by a certain Cartesian legacy. Even when we have insight into the wholeness of the functioning of the human individual, we lack a framework for describing it fully. The vocabulary, methods, even the concepts with which to think about the questions have been about parts. However, over the last decade and a half a new scientific perspective has emerged which can provide, among other things, just such a vocabulary. This ‘new science’ has several names, but is most commonly known as Chaos Theory.

paddle ballIn the original Congress presentation, the basic concepts of Chaos Theory were presented visually by demonstration. Here I can only give my readers instructions for carrying out a few demonstrations of their own of the basic concepts. First find, make, or imagine a ‘paddle ball’ (a small rubber ball attached to a wooden paddle by a long, thin elastic cord). First simply let the ball hang at the end of the cord. Pull it or push it in any way you like. Various things will happen in the short run (physicists call this ‘transient behavior’) but in the long run the result is always the same. The ball ends up at rest at the end of the cord. Call this situation 1.

Next, strike the ball with the paddle using repeated rhythmic hits. (This may take some practice). You will notice that the ball now has a regularly repeating long term motion, the size and frequency of which is determined by that of your paddle strokes. Call this situation 2.

Now continue striking the ball while yourself turning or walking in a circle. (This will take practice). Observe that the ball now has a more complex but still regular long term motion. Call this situation 3.

Our task is now to find a simple way to describe the pattern of motion as a whole in each case. One way is to draw a ‘picture’ of the motion on a graph that includes both the position and velocity of the ball in the same space (what physicists call ‘phase space’). Situation 1 is easy. Since the ball ends up not moving and always in the same place, our picture is a single point. if we look for a moment at the short term effects of how we got the ball moving, that point seems to be drawing the motion of the ball toward itself. It thus goes by the technical name ‘point attractor.’ Situation 2 is a little more complicated. The ball is continually changing the speed and direction of its motion as well as its position. But it goes through a repeating series of these states as it bounces down, slows at the end of the stretch, comes back up etc. Our ‘phase space’ picture will now be, not a point, but a closed loop (called a ‘limit cycle’). It is now this paddle driven loop which attracts the motion of the ball. Situation 3 is tricky (not yet chaotic, but hang on-we’re getting there). Since the motion of the ball is the combination of the paddle-ball cycle plus the walking around cycle, we need to find something that is the combination of two loops. To see the picture, find something ‘donut shaped’ (technically, a ‘torus’)–a donut, bagel, inner tube etc. The paddle-ball cycle is like going around the donut down through the whole and around the outside; the walking around cycle is like going around the circumference of the hole. The combined motion is a spiral through and around the hole. Attach a piece of string to the donut and try spiraling it around to see how this works. If we very carefully arranged things so that when the spiral got back to where it began, it matched precisely, it would follow the same path over again. But suppose it didn’t quite match. Then the spiral would go round and round, never matching, until it had covered the entire surface of the donut. (Physicists couldn’t quite bring themselves to call this a ‘donut attractor’ so they call it ‘toroidal’). The important thing to notice for our purpose is that all of these increasingly complex situations are, mathematically speaking, linear. It is possible to write down equations for the atu;lctors, solve them and thus predict the motion of the ball for any time we like. This might not be an easy task, perhaps, but we could do it.

Now we step nimbly into the realm of Chaos. There is a bit of a cheat built into the entire paddle ball example and it has to do with why you need to practice to get the motion continuous and regular. Observe carefully and you will find yourself making all sorts of subtle adjustments to the angle and power of your strokes-and probably doing other subtle things when the ball is at the extreme of its stretch. In other words there is a good deal of ‘feedback’ in the system of you-plus-the-paddle-ball. It takes practice hiding this feedback so we can pretend the motion only depends on the stretch and the paddle. (If you are feeling particularly ambitious, try the whole thing again with cords of different ‘stretchiness’). To see what this all does to our picture of the motion, imagine that the surface of your donut or bagel begins to crinkle, then to be stretched and folded like filo dough until you have a cross between a donut and baklava. Imagine such a shape in which if you examine any layer you find it made of thinner layers and so on to the infinitely thin and you have what is called a ‘strange attractor’-the portrait of chaos. The shape is definite, but infinitely complex–just as the motion it portrays is determined but unpredictable. We could still write down equations (non-linear equations), but we couldn’t solve them (nor could anyone else). Contrary to our old Cartesian expectations, there is no way to think of them as a combination of pieces. The motion is not predictable because only the ‘whole of it makes any sense.’ This kind of attractor has a peculiar geometric property–it is ‘fractal.’ That means that rather than being a 2 or 3 dimensional figure, it is somewhere in between (e.g. 2.6 dimensional–of course they seem strange). They are ‘self-similar’ meaning that they look about the same at all levels of magnification. Big clouds far off look the same as small clouds close up. The basic shape of a coastline is similar to the basic shape of the kind of rock it is made of–indeed because of this the very idea of the ‘length’ of a coastline depends on what scale you use to measure it. Many seemingly random time sequences are in fact fractal (and thus reveal chaotic, rather than random, behavior), for example the distribution of earthquakes over time, brainwave patterns etc.

A few key points need to be emphasized. One is that in the ‘old linear world’ motion is usually viewed as either regular or nearly regular or ‘too complicated’ (i.e. random). The degree to which we have been trapped within this view is that the only word we have for equations and phenomena beyond the linear is ‘non-linear.’ (Note that we face a similar Cartesian difficulty in that our only term for the unity that lies behind the split between the psychological and physical dimensions of ourselves seems to be ‘psycho-physical’). A second point is that, as stated above, ‘chaotic’ does not mean random. Indeed, as our example shows, chaotic systems are those in which feedback within the system makes them highly sensitive to the conditions present. What is emerging from the growing familiarity with systems showing chaotic behavior is that the non-linear is the more general case and that the linear cases are special cases in which it is the very insensitivity to specific conditions that makes them regular and predictable. (Compare this property to what we know about habits). It is in giving up the possibility of prediction that scientists are able to describe the complex behavior of systems in terms of the properties of the system as a whole. (The quantities associated with these properties, which determine the nature of the attractor, are sometimes referred to as ‘order’ or ‘control’ parameters).

What does all this have to do with Alexander? As he said in Constructive Conscious Control of the Individual, we are complex in our multiplicity of parts and relationships but “one and simple” in our functioning as a whole. We are only complicated when we are “out of order.” In effect, our habitual reactions, and the assumptions about our own functioning built into them, constitute a restricted linear model of ourselves which limits our possibilities. Many people, by their habitual way of behaving, reveal a basically ‘pre-Newtonian’ model of themselves in which nothing at all can happen unless they ‘do’ it; many have a Newtonian view of themselves as an implicitly linear combination of functions–i.e. as the sum of their parts. Consider however, that although it is possible to analyze a single joint in isolation and that two joints can be considered as the sum of each in isolation, a system of as few as three joints requires a set of non-linear equations which are unsolvable. Ultimately, even in the simplest mechanical terms, the human individual must be considered as a complex whole. Muscular activity seems to exhibit fractal characteristics. Indeed, it may be possible to give a quantitative definition to what we refer to as ‘quality of movement’ in terms of the fractal dimension of the associated attractor.

In the new terms, we are chaotic systems. One final demonstration: extend both index fingers, side by side and parallel with your palms down, as if pointing to someone across the room with both hands. Now slowly move your fingers from side to side, still parallel, as if pointing at two people in turn. Continue this alternating movement and gradually increase the speed.

What did you observe? First, the same kind of motion only faster, then a moment of very complex movement, and eventually your fingers switch spontaneously to moving opposite each other rather than parallel. This represents two distinct modes of coordination of the finger movement, and the order parameter which determines which one occurs is the frequency of the movement. This may well be a model for the coordination of the individual as a whole. From the perspective of chaos theory, human coordination may be seen as a ‘self-organized’ phenomenon in which the organization lies in the relationships among the parts themselves rather than in the functioning of a central controlling mechanism. So rather than thinking of a central center (the brain) sending a vast variety of individual messages to all the parts of the organism, it may be more useful to imagine each such part as possessing something like a ‘code book.’ Now the center only has to send a simple message identifying the conception of the act being performed (in the role of an order parameter) and then each part finds its own specific contribution to the act in its own code book. In essence, I am arguing–and suggest for future research–that the ‘new science’ will provide a general framework within which primary control can be viewed as the organizing principle of the coordination of the action of the whole individual rather than a controlling mechanism), and that, within that framework, Alexander’s concept of ‘all together one after the other’ can lead to a new paradigm of human coordination.

First presented at Engleburg Congress of Teachers of the Alexander Technique, August, 1991

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