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Feldenkrais Articles:

Feldenkrais & Dynamic Systems Theory - A technical discussion by Mark Reese

A Dynamic Systems View of the Feldenkrais Method

By Mark Reese

Different philosophical approaches have been called upon to explain or emphasize aspects of the Feldenkrais Method; phenomenology and cybernetics are two noteworthy examples. Dynamic Systems Theory, which owes its origin to ideas popularly known as chaos, is another promising avenue of approach.

The term ‘chaos’ refers to behaviors that are highly unpredictable in their fine details, but which exhibit high degrees of regularity when observed at a macro level. Chaos theory draws attention to the self-organizing properties of nature, both animate and inanimate and, indeed, has provided a theoretical language in which to discuss both. Nature’s floating clouds, swirling eddies, spiral galaxies, growing leaves and animals––all are patterns of chaotic complexity. Chaos theory can likewise give us insights about human posture, movement, cognition, emotions, and learning.


There is a historical basis for approaching the Feldenkrais Method from dynamic systems theory. Feldenkrais at times proposed his ideas in similar terms, and one of his closest friends and theoretical collaborators was Aharon Katchalsky Katzir*, one of the world’s leading chaos pioneers until his murder in 1972 by Japanese terrorists. Some of the important sources for chaos theory include, among others, Rene Thom’s "Catastrophe" Theory, and Ilya Prigogine’s theory of "Dissipative Structures." The ideas in this article derive from Hermann Haken’s theory of "Synergetics," as interpreted by scientists Scott Kelso and Esther Thelen. Most of the material in this article originally stemmed from an attempt to explain the Feldenkrais Method to the developmental psychologist, Esther Thelen, after reading her seminal book, A Dynamic Systems Approach to the Development of Cognition and Action.


* * *


It can be demonstrated in numerous instances how Moshe Feldenkrais was ahead of his time in his thinking about cognition and action. Among other forms of therapy or somatic disciplines, Feldenkrais's approach to movement education is unique in its embodiment of dynamics systems concepts. In this article I will present a number of examples.

Conventional exercise and physical education methods involve strictly following position indications for good form or posture, literal movement instructions and imitation of visual models. These methods are consistent with hierarchical motor control theories that invoke "higher centers" or a homunculus to order the body through commands to adopt new postural and movement patterns.

Feldenkrais maintained that these approaches were based upon an incorrect theory of control and that in actual practice, conscious self-direction alone is insufficient for functional learning. Rather, functional learning emerges through pursuing exploratory variations constrained and facilitated by functional demands and the environment. Feldenkrais sometimes likened his movement lessons, which he hated to be called "exercises," because of connotations of mechanical repetition, as scientific experiments, demonstrating how human beings would arrive up similar solutions to motor problems, based upon common features of structure and function, and common environment and task demands.

These emergent solutions to problems of action (to use the phrase of Nicolai Bernstein, Russian physiologist) are reminiscent of "convergent evolution," whereby living things without shared ancestry evolve common characteristics when occupying similar ecological niches. Well known examples of this phenomena include the hydrodynamic shapes of fish and porpoises, and the common appearances of desert plants belonging to different families. In learning and in evolution, common solutions will emerge without plans, instructions, or imitation, despite difference in origins. Thus Esther Thelen has described crawling as an opportunistic solution to an infant’s problem of action, a unique discovery with a unique learning trajectory, not an inevitable result of genetic or neural programming.

In contrast to explaining movement solely in terms of anatomy and kinesiology Feldenkrais lead us to understand movement’s organization, meaning its embodied, intentional, contextual nature, i.e. how one organizes an action in an environment in order to meet our needs for action. Feldenkrais recognized the seamless and coherent integration of physical, biomechanical and energetic factors, together with our goals and environments.

Feldenkrais understood well the nonlinear nature of change. Small differences in any aspect of the task or environment may trigger nonlinear changes in an action. His methods embody a way to discover empirically which control parameters might be efficacious for the learning of more advantageous movement and postural behavior. He believed that sensitivity to the requirements of learning are crucial, and that mechanical repetition, forced stretching or manipulation, cannot be primary agents for changing patterns of action.

In contrast to teaching improved posture by adopting a position specified by a visual reference such as a plumb line or grid, Feldenkrais emphasized that posture was a component of action, and must be learned in the real time situation of meeting task demands. Far from being a position, Feldenkrais's 1940's formulation of "acture" closely resembles chaos models. Posture can be well represented as an attractor* (see definition at end of article), a zone of stable variation including many positions constrained by task demands, balance, biomechanics, support surface and many other factors. The chaotic, yet highly organized movements present even in "static" posture, called "postural sway," demonstrate the impossibility of adopting a truly fixed upright position, whether it is deemed good or bad.

In order to induce the instability necessary for phase shifts in a system from one highly stable attractor to another, Feldenkrais developed many techniques including novel tasks, novel environments, novel spatial orientations and effort substitutions.

Here are a few examples of how Feldenkrais taught improved posture:

a) One series of lessons includes variations on standing and oscillating. Stand and oscillate forwards and backwards, then side to side, first with feet apart, then will feet together, sometimes with eyes open, sometimes with eyes closed, then make circular movements in one direction, then in another. In an other series of variations one leg is placed in front of the other, and in another one stands with the arms in front of behind or out to the sides in various combinations.

Exploring these movement variations destabilizes existing postural attractors and a new attractor emerges defined as a zone of easy movement in all directions further specified by the extra balancing requirements of narrow stance and omitted visual cues.

b) Standing and turning reorganizes posture in a manner compatible with the situation of turning and seeing to the side. Our habitual posture may be disposed toward primarily forward movement or static orientation.

c) In a quadrapedal posture, on hands and feet, one alternately lifts one hand and the other, one foot then the other, right hand and foot together, then left, then right hand with left foot, then the other diagonal, then both hands, both feet, and finally hopping with all four lifted at once. While the initial placements of the arms and legs will vary enormously among individuals, almost everyone will converge towards the same posture. The task demands impose a similar postural solution, despite disparate positions and movement trajectories during the destablized, highly exploratory phases.

In contrast to conventional physical therapy which has emphasized the primarily mechanical factors of muscle strength and flexibility, skeletal alignment and mobility, Feldenkrais saw how postural and movement problems are tied to behavioral habits, including cognitive, motor, environmental and perceptual aspects. In conventional therapies, neurological patients may be given regimes of passive stretching. In Feldenkrais work, however, to use one example, a child with cerebral palsy is never passively stretched. It can be demonstrated that an elbow which will not normally bend, except with force, may bend easily if the child is moved in an exploratory way such that she perceives the value of bending the elbow in order to lean on it while sitting up. Movements and exercises without imbedded functional values are superficial, and may represent little more than noise to a nervous system seeking multi-modal correlation between rich sources of movement and perceptual information related to value laden action trajectories toward desired goals.

Another striking example is Feldenkrais's systemic view of chronic pain. Rather than residing in some literal way "in the body" Feldenkrais understood most musculo-skeletal pain (except the pain of immediate trauma) as expressing a pattern of action, a habit embodying emotional, biomechanical, neuro-chemical and other components. Change the pattern and you can eliminate the pain, despite structural problems. Examples of how this is done include:

a) Let us say a given joint such as the shoulder is painful when raising the arm. Feldenkrais discovered that he could move the proximal side of the joint, that is, move the scapula relative to the humerus, without pain. Thus, due to contextual differences, one may obtain a kinematically isomorphic movement which is categorically not perceived as such by the person. This proximally induced movement is completely painfree to the individual and does not trigger the protective, defensive reactions of the more normal, distally evoked movement. This technique so destabilizes the system, enabling new patterns, that after a few repetitions of the proximal movement, the normal distal movement may be accomplished without pain as well.

b) Often a movement is painful in one orientation but not another. Take, for example, flexing on the back, i.e., lifting the head and bring an elbow forward toward the opposite knee, while lifting the knee toward the elbow. If a similar movement is done in the sitting position, or leaning on one's hands and knees, pain may be absent. When the initial movement is performed again on the back, it can usually be done without pain, and with greater flexibility and coordination. These variations of orientation alter the degree of anti-gravity muscular work, change spatial relations, generate new proprioceptive information and, most importantly, change the category of action, by which the nervous system organizes the motor pattern. By dissociating the movement from its habitual context, the system has an opportunity to recognize that the movement is not necessarily dangerous, and it ceases being painful.

c) In cases of orthopedic or neurological problems, novel movements are often first taught on the "better" side of the body, that is, the side that is uninjured, pain free, less stiff, and under better neuro-motor control. Many movements of the body are reciprocal, e.g., the ability to shorten and lengthen one leg is the same, with respect to the pelvis, as the lengthening and shortening of the opposite leg. It is significant that even though the movements are physically isomorphic, movements performed on the right or left sides of the body are nonetheless perceptually highly distinct. This fact is very useful for learning new patterns.

By manipulating the environment of familiar task demands, it is possible to destabilize attractors and help new ones to emerge:

a) Alteration of spatial orientation. One lesson provides a radical demonstration of the context-based nature of learning, and the importance of spatial orientation as an essential though normally tacit component of action. One is asked to perform a simple series of foot movements, including supination and pronation, dorsi and plantar flexion, and rotation, while one lies on one's stomach, with the knees bent at right angles to the ground. Although most people would have no difficulty in performing these movements in a seated position, in this altered physical position, most people are utterly incapable of doing them. Even when they can be clumsily performed, without visual feedback people are often incapable of discriminating the position of their feet in space and which movements their feet are actually doing! The lesson then proceeds with augmenting the movement by visually tracking the foot. This, interestingly enough, destabilizes the action further, making the person even more confused, disoriented and uncoordinated. This is a good example of Edelman's multi-modal reentrant processing concept* (see definition at end of article): since the person has never correlated their foot movements with visual cues in this position, the visual tracking does not refine the movement as one would expect, but adds another perceptual-action demand to the task space. Soon, however, the visual cues do help people learn the necessary coordination. Even more helpful, however, is that students are asked to perform similar movements in different positions—standing, lying on the back, etc., until they are able to transfer and generalize information to the novel position of lying on the stomach.

b) Alteration of the environment. In Functional Integration, the primarily non verbal, hands-on technique, the student may be placed upon rollers (tubes made of cardboard or plastic material or rolled blankets) of various sizes in various orientations. For example, the student may be asked to lie on a long narrow roller placed lengthwise under the spine. This environment creates novel balancing requirements, because it is easy to fall off the roller. The practitioner moves the student in a variety of ways in order to elicit the emergence of different postural and movement patterns adequate to deal with the roller's pressure and balancing requirements.

Support. One of the most significant alterations of the environment is created by the Feldenkrais practitioner providing conditions of greater support . Just as research (see EstherThelen, A Dynamics Systems Approach…") showed how infant stepping could be re-elicited in the more supportive environment of water, so too are many actions easier to learn, and previously acquired abilities easier to elicit, when greater support is provided. In Awareness through Movement, simply doing movements while lying down enables people to perform various movements they are unable to do while upright, Presumably this is due to lessened anti-gravity muscular effort, the reduction or elimination of balancing requirements, increased proprioception due to a greater surface area when contacting the floor, and heightened kinesthetic sensitivity.

Part of Feldenkrais's rationale for utilizing support was a perceptual argument that a Weber-Fechner phenomenon was at work, enhancing those discriminations needed for learning. Just as smaller changes in illumination are perceivable against lower levels of background illumination, Feldenkrais claimed that smaller changes in muscular efficiency may be registered against a background of reduced effort. For this reason Feldenkrais often advised students to use small, even minuscule, movements in the initial stages of learning. When an action is facilitated through support it reduces muscular effort thereby lowering the threshold at which differences in movement organization can be perceived and acted upon.

In Functional Integration support may be provided by lying on rollers, pillows and surfaces that lessen muscular effort, and especially through use of the practitioner's hands in ways that support the body of the student in order to relieve postural work that the system is engaged in. In a Gibsonian sense support is understood not in a purely mechanical sense, but in the ecological sense that the surface provided to the student is perceived as affording* (see definition of affordances at end of article) reliable support for action. This enables relief from postural muscular effort, and enlarges the field of action-perception possibilities.

Furthermore, in light of Fogel's concept of co-regulation* (see definition at end of article), providing support can be understood as helping establish communication within the framework of the activity. Relevant information about the activity is conveyed as participants negotiate their relative, cooperative share of the action's effort.

Of particular interest—because of their practical value and theoretical challenge—are highly sophisticated manual procedures often done while the student lies on a treatment table, involving pushing through the feet or lifting the spine or head. If performed accurately, and it takes many years of training to achieve such accuracy, it is possible to support, and therefore convey information about, enormously complex patterns of postural behavior. Feldenkrais went so far as to say that, given ideal support, you could create in the brain a tabula rasa from which to work. Obviously an overstatement, one nevertheless observes an enormous destabilization of attractors. Such an incredible degree of plasticity enables the system to enter many novel attractor states.

Feldenkrais emphasized how any new movement learning always exploits previous learning and the inherent possibilities of the system. For example:

a) In an early approach to self-defense techniques he developed back in Palestine in the twenties, Feldenkrais watched the spontaneous defensive reactions of individuals to a knife attack. He then invented a defense technique that was grafted on to and tuned this already existing pattern.

b) In the teaching of a new behavior, we often tune or refine existing movement patterns, irrespective of ideas about "normalcy" that may constrain rehabilitation therapists. For example, when teaching a person to walk again after a joint injury, we might facilitate the limping pattern that emerged as the person's way of coping with the trauma. Then we may gradually enlarge the repertoire by shifting the environment or altering task demands. If, on the contrary, as some therapists do, one ignores the existing, adaptive pattern, and tries to forcibly move the person through a "normal" range, the person may defensively react––in effect, become more stable in their pain avoidance pattern–– and be unreceptive to new learning. Feldenkrais emphasized that one needs a learning theory, and not just orthopedics, to account for post-trauma, adaptive changes. And the job of rehabilitation is therefore not just mechanical but, rather, systemic. After a serious injury and healing, even under the best circumstances, one does not simply recover function and behave identically to one's previous patterns. Post-traumatic behavior is a creative solution to a unique problem of action. Furthermore, it is possible to learn better function, through new means, than one had before.

c) Intrinsic system dynamics. Feldenkrais invented many lessons that explore and utilize intrinsic system dynamics, similar in some respects to the Kelso experiments (see Kelso references below). Some of these entail oscillatory movements generated through rhythmic ankle flexion, performed while lying on one's back. Because of the pendulum features of these movements, the coordination involves finding how to push off when the kinetic energy of the previous push and return has been dissipated (like pushing a child on a swing). There is no need to specify the frequency nor the force required, because these will emerge from system dynamics. There is a great improvement in ones posture after doing these variations, presumably because one learns to perceive how efficient compression forces can be exerted through the skeleton (without the need of anti-gravity work) in a manner analogous to the upright postural demand of organizing gravitational compression. In another series of lessons, involving lifting and dropping the legs or other parts of the body, one learn inter-limb coordination that do not depend upon neural coordination but rather structural-functional joint and limb properties. As a physicist Feldenkrais greatly appreciated the fact that movement has self-organizing properties. And as a judo teacher he knew what it meant to utilize gravity, momentum and other physical forces.

Implied here is also the idea that actions contain subsidiary coordinations that when learned, may be transferred to other skills. Feldenkrais understood how to construct and deconstruct action components out of and into subsidiary coordinations. Contrast this with reductionist models of action that emphasize local muscular strength elements.

Goal and non-goal orientation. The use of goals as attractors can be a two-edged sword, and it is important for learning strategies to be flexible in how goals can operate as control parameters. Goal direction enhances learning by providing a better understanding of what is expected and desired, and can help call up memories of how similar problems of action have been solved. However, conscious attempts to achieve a goal that is perceived as impossible, can further deepen existing attractor wells. Individuals may have a long history of learning that they cannot succeed at various tasks dues to pain, poor coordination, lack of strength, etc. Conscious attempts may merely trigger effortful and unsuccessful strategies. This is another reason why Awareness through Movement sequences are as much deconstructive as they are constructive of specific skills. In order to bypass learned inabilities, Feldenkrais ingeniously invented surprise-ending lessons that bypass expectations:

a) Moving the pelvis while sitting in a chair in various ways, triggering standing up efficiently, without the thought of getting up.

b) Lying on the floor, holding one's foot and moving it towards the mouth and other directions, leading to rolling to sit up, without any conscious idea that the lesson is about learning an improved way to sit up. I watched my own son Nathan learn to roll from back to side in precisely this way at the age of three months. Rolling to the side appeared as an accidental consequence of finally putting his big toe in his mouth! This is just one example among hundreds, of how Feldenkrais was a master at utilizing early development movements as a way of furthering coordinative skills for both children and adults. Such lessons also demonstrate that the adult's conception of what the child is learning may not at all be an accurate representation of its developmental trajectories. Many actions are learnt in the course of gaining coordinations needed for satisfying other than obvious goals. This is analogous to Gould's remarks on evolutionary change (see reference below), that organic structures may be exploited for different functions then those they originally served, and so too in learning behaviors.

Due to context sensitivity, environmental familiarity or unfamiliarity is another important variable, acting to trigger or suppress the emergence of previously learned patterns. This can be advantageous or problematic, depending upon whether the patterns are desireble.

Feldenkrais induced through the introduction of novel task demands, the stage of destabilization preceding phase shifts and new learning. One of the most powerful (and quick to produce) examples involves moving the eyes opposite to the direction of the head in order to induce greater flexibility throughout the body while turning and looking to the side. According to Feldenkrais, our inflexibility resides not in our muscles and joints but, rather, in our habits of unnecessary muscular efforts. Due to the importance of vision for the control of many movements, directing one's eyes in nonhabitual deeply destabilizes normal movement patterns, and enables the emergence of more efficient patterns that are suppressed under current circumstances. This approach is incredible effective and easy, in principle, to test experimenally. Such methods stand in sharp contrast to prevalent therapeutic modes that strive to either stretch, relax, or strengthen the neck muscles, none of which addresses the dynamic systems characters of action.

Also effective in increasing the neck's range of motion without stretching, is simply to move one's eyes many times in the same direction as that of the head. Deep changes in muscular tonus are elicited such that one can turn one's head and neck much farther in the direction of one's gaze. Feldenkrais liked to explain such effects by invoking neuro-reflex pathways involving tonic adjustment. Here, a dynamic systems explanation would be that moving the eyes elicits strong attractors reflecting a long history of performing coordinated eye and head movements in visually guided behaviors.

Feldenkrais emphasized how action and perception are inextricably intertwined (see Reed below). The easily misunderstood name for his system of movement education, "Awareness through Movement," reverses the more conventional idea of movement awareness. Feldenkrais movements were intended to further knowledge and perception, and not seen as ends in themselves. Only through movement can one perceive oneself and the world, and perception makes movement possible (as Shakespeare said, "Sure you have sense, else you could not have motion."). Also, Feldenkrais emphasized many linkages between motor and cognitive processes. Some examples include:

a) In the oscillatory movements, mentioned above, one learns from the body's movement. One can neither say that one instructs the body, nor that the body instructs itself.

b) A series of counting lessons shows how in effect one counts one's own patterned eye movements as much as objects in the world. In other words, counting involves multi-modal correspondences and correlations. The learning of speed reading involves learning how to speed up and smooth out eye movements so they don't stop on individual words, as one does when subvocalizing.

c) In lessons involving visualization we learn how eye movements and other specific patterns of muscular contraction are correlated with attention shifts. For example visualizing the right side of one's body entails eye movements to the right. Exploring in one's mind the shape of one's foot elicits coordinations reflecting a history of putting on socks, getting foot massages, and walking on different surfaces. So-called "imaginary movement" draws upon our earlier experiences of movement exploration. The training of visualization, perception and action are all interrelated.

The movement variability in all Feldenkrais lessons embodies an important principle from evolutionary and ecological biology— that variation is a key to the potential required for learning and adapting to novel conditions. A well-learned skill embodies sufficient variability to meet the demands of changing environments and tasks.

Feldenkrais invented thousands of manual and active techniques in order to facilitate the unique solutions that are required by unique persons who face unique problems. He eschewed routines and mechanical exercises, and promoted an exploratory journey that can enhance the coordination and abilities fitting the goals of the individual. Implicit in this work is an attention to micro differences in learning, micro differences in muscular patterns, joint movements, postural dispositions. Many therapies ignore, trivialize or try to wipe out these differences, based upon a Platonic ideal of healthy movement or posture, technologically implemented through machine-like movements often involving the literal coupling of humans and machines. Feldenkrais was a refugee from more than one totalitarian regime and put a high value on human freedom and individual differences.

New research methods and theoretical ideas seem to support much more attention to these individual differences and provide the scientific means to learn more about such differences. It is heartening to see, perhaps for the first time, scientific interest being paid to such a "close-up" view of action and learning.


Edelman, Gerald M. (1989). The Remembered Present: A Biological Theory of Consciousness. New York: Basic Books.

Edelman, Gerald M. (1992). Bright Air, Brilliant Fire: On the Matter of the Mind. New York: BasicBooks.

Feldenkrais, Moshe. (1981). The Elusive Obvious. Capitola, CA: Meta Publications.

Fogel, A. (1993). Developing Through Relationships: Origins of Communication, Self and Culture. Chicago: University of Chicago Press.

Glick, J. (1988). Chaos: Making a New Science. New York: Viking Penguin.

Gould, Stephen Jay. (1980). The Panda's Thumb: More Reflections in Natural History. New York: W.W. Norton & Company.

Katchalsky, A.K., Rowland, V., & Blumenthal, R. (1974). Dynamic patterns of brain cell assemblies. Neuroscience Research Program Bulletin, 12.

Kelso, J.A. Scott. (1995). Dynamic Patterns: The Self-Organization of Brain and Behavior. Cambridge, MA: MIT Press.

Kelso, J.A. Scott. (1982). Human Motor Behavior. Hillsdale, NJ: Lawrence Erlbaum Associates. Chapters 10, 11, and 12. M.T. Turvey, Hollis L. Fitch and Betty Tuller (Authors).

Chap. 10: "The Bernstein Perspective: 1. The Problems of Degrees of Freedom and Context-Conditioned Variability."

Chap. 11: "The Bernstein Perspective: 11. The Concept of Muscle Linkage or Coordinative Structure."

Chap. 12: "The Bernstein Perspective: 111. Tuning of Coordinative Structures with Specail Reference to Perception."

Reed, E.S. (1989). Changing Theories of Postural Development (pp. 3-24). In: Woollacoot, M.H., & Shumway-Cook, A. (Eds). Development of Posture and Gait Across the Life Span. Columbia, SC: University of South Carolina.

Reed, E.S. (1988). James J. Gibson and the Psychology of Perception. New Haven, CT: Yale University Press. (page 231)

Thelen, E. & Smith, L. B. (1994). A Dynamic Systems Approach to the Development of Cognition and Action. Cambridge, MA: MIT Press. (pp. 56-61)

Thelen, E. (1995). Motor Development: A New Synthesis. American Psychologist, 50 (2), 79-95.

Thelen, E., Ulrich, B.D., & Jensen, J.L. (1989). The Developmental Origins of Locomotion (pp. 25-47). In: Woollacoot, M.H., & Shumway-Cook, A. (Eds). Development of Posture and Gait Across the Life Span. Columbia, SC: University of South Carolina.



"The environment of an observer consists of the affordances of objects, places, and events for that observer...Affordances are the functional properties of objects as, for example, the affordance of a heavy stick or rock for pounding. Any particular object will probably have many affordances. An apple may be eaten, thrown, juiced, or baked, to name but a few of its affordances. Yet a given object will also lack many affordances. An apple is of no use for a brick or as kindling."

from: Reed, E.S. (1988). James J. Gibson and the Psychology of Perception. New Haven, CT: Yale University Press. (page 231)


"When systems self-organize under the influence of an order parameter, they 'settle into' one or a few modes of behavior (which themselves may be quite complex) that the system prefers over all the possible modes. In dynamic terminology, this behavioral mode is an attractor state, as the system--under certain conditions--has an affinity for that state...Attractors may have varying degrees of stability and instability...While some attractor states are so unstable as to almost never be observed, other attractor states are so stable that they look like they are inevitable...but they are dynamic and changeable nonetheless."

adapted from: Thelen, E. & Smith, L. B. (1994). A Dynamic Systems Approach to the Development of Cognition and Action. Cambridge, MA: MIT Press. (pp. 56-61)

Co-regulation :

"Co-regulation occurs whenever individuals' joint actions blend together to achieve a unique and mutually created set of social actions. Co-regulation arises as part of a continuous process of communication, not as the result of an exchange of messages borne by discrete communication signals. Co-regulation is recognized by its spontaneity and creativity and is thus the fundamental source of developmental change. Co-regulation, in social and mental life, allows the individual to participate in the discovery of the unknown and the invention of possibilities."

from: Fogel, A. (1993). Developing Through Relationships: Origins of Communication, Self and Culture. Chicago: University of Chicago Press. (p. 6)


Phase Transitions:

"In physics, different aggregate states of matter--solid, liquid, gaseous--are called phases, and the transitions between them are called phase transitions. When vapor changes from liquid and eventually to ice, this is an example of progressive change from disorder to order." (p. 5)

"...pattern formation and change in the human brain [takes] the form of a dynamic instability. This suggests a new mechanism--phase transitions--for the collective action of neurons in the human cerebral cortex." (p. 260)

"A crucial aspect of pattern-forming dynamics in both brain behavior and overt behavior pertains to critical instabilities. Like many complex, nonequilibrium systems in nature, at critical values of a control parameter, the brain undergoes spontaneous changes in spatiotemporal patterns...The discovery of critical instabilities in the brain highlights the importance of fluctuations--whether of stochastic or deterministic origin--in probing the stability of coherent patterns and creating new patterns when the environmental, task, or internal conditions demand it. Not only do nonequilibrium phase transitions offer a new mechanism for the collective action of neurons, they provide the brain with a switching mechanism, essential for rapidly entering and exiting various coherent states. Thus, phase transitions confer on the brain the hallmark of flexibility." (p. 284)

from: Kelso, J.A. Scott. (1995). Dynamic Patterns: The Self-Organization of Brain and Behavior. Cambridge, MA: MIT Press.

Phase Shift:

"[The] Belousov-Zhabotinskii reaction...takes place at room temperature. Imagine, however, that we assemble our components q in a very cold chamber, the temperature being a parameter in the equation. As we slowly warm the chamber, we pump thermal energy into the dish of chemicals in a continuous manner proportional to the temperature of the room. For a long time, nothing happens; q remains in one attractor in the state space (a point attractor). Then, at a critical temperature, the reaction begins and the spontaneous patterns rotate and change; q jumps to a new region of the space and into a more complex attractor regime.

The temperature changes were continuous, but the behavior of the system was dramatically discontinuous. These nonlinearities, or phase shifts or phase transitions, are highly characteristic of nonequilibrium systems, and are... the very source of new forms. The parameter change, temperature in this case, was entirely nonspecific to q. The temperature had no information whatsoever prescribing the nature of the chemical reaction...The pattern emerged strictly as a function of...the nonlinear dynamics of the system.

In dynamic terminology, temperature is the control parameter, the parameter to which the collective behavior of the system is sensitive and that moves the system through different collective states...In biological systems, any number of organismic variables or relevant external boundary conditions can act as control parameters...Energy level is a common control parameter...[An] example is the gait of horses. As the horse continuously increases its speed, its gait shifts discontinuously from a walk to a trot to a gallop with no stable intermediate pattern. The particular pattern of footfalls acts as a dynamic attractor within a speed range. The preferred gait at any speed level is also the energetically most efficient...Because the gaits are so stable at particular speed ranges, it is tempting to view them as "hard-wired." The neural connections are essential, but the gait patterns are as much a product of the energy and information flowing through the system as of the "hardware" itself...Pattern can be generated by a system seeking cooperative stability. Order is not "in there," but is created in the process of action.

Stability is what defines the collective states of the system and it can be assessed by understanding the dynamics of transitions or phase shifts, when systems lose stability. Fluctuations around the stable states are the inevitable accompaniment of complex systems. It is these fluctuations that are the source of new forms in behavior and development and that account for the nonlinearity of much of the natural world.

Not all changes in systems are phase shifts. Many phenomena are parametric, that is, variables increase or decrease in a continuous manner. It is common to see systems act parametrically within certain ranges of a control parameter and nonlinearly when certain threshould values are reached. Dynamic theory has specific predictions for the behavior of systems close to true transition points. These predictions are based on the assumption of inherent fluctuations which are the result of the coupled component subsystems. These fluctuations act like continuous perturbations in the form of noise on the collective behavior of the system. Within ranges of the control parameter, the system maintains its preferred behavioral pattern depite the noise. However, at critical points, the system loses its ability to maintain these patterns and the fluctuations become enhanced. At these points, the system is dominated by these fluctuations and may display transient behavior where no stable pattern can be discerned. As the control parameter is continuously scaled, the system then exhibits a new or differnent pattern with new values of the collective variable. At this point, the fluctuations are again reduced, as the system evolves into a new attractor state."

adapted from:

Thelen, Esther & Smith, Linda B. (1994). A Dynamic Systems Approach to the Development of Cognition and Action. Cambridge, MA: MIT Press. (pp. 62-63)

"Dynamic systems accounts for the appearance of new forms during development as a series of phase shifts engendered by the loss of stability of current forms. These new forms are autonomous solutions to instability in that the system does not know the solutions a priori, but discovers them through the exploration of the space--exploration which is possible, in turn, because the cooperative assembly of components is not rigidly fixed."


Thelen, Esther & Smith, Linda B. (1994). A Dynamic Systems Approach to the Development of Cognition and Action. Cambridge, MA: MIT Press. (p. 86)



"Re-entry is a process of temporally ongoing parallel signaling between separate maps along ordered anatomical connections. Reentrant signaling can take place via reciprocal connections between maps (as seen in corticocortical, corticothalamic, and thalamocortical radiations); it can also occur via more complex arrangements such as connections among cortex, basal ganglia, and cerebellum."

from: Edelman, Gerald M. (1989). The Remembered Present: A Biological Theory of Consciousness. New York: Basic Books. (p. 49)

Brain maps interact by a process called reentry. These maps are connected by massively parallel and reciprocal connections. Reentrant signaling occurs along these connections. As groups of neurons are selected in a map, other groups in reentrantly connected but different maps may also be selected at the same time. Correlation and coordination of such selection events are achieved by reentrant signaling and by the strengthening of interconnections between the maps within a segment of time. The selective coordination of the complex patterns of interconnection between neuronal groups by reentry is the basis of behavior. Indeed, reentry (combined with memory) is the main basis for the bridge between physiology and psychology.

adapted from:

from: Edelman, Gerald M. (1989). The Remembered Present: A Biological Theory of Consciousness. New York: Basic Books. (p. 49)

Edelman, Gerald M. (1992). Bright Air, Brilliant Fire: On the Matter of the Mind. New York: BasicBooks. (p. 85)

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