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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 (ie. 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.
In 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 spiralling 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 pmctice 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 file 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 (eg 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 Cautesian 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 'psyche-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 refered 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 possiblities. 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 analyse 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.
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