Applications of nonlinear dynamic systems theory in developmental psychology: 
Motor and cognitive development
 
Nonlinear Dynamics, Psychology, And Life Sciences, Vol. 1 (1), January 1997, 55-
68

Mary Ann Metzger
University of Maryland UMBC

ABSTRACT
Applications of nonlinear dynamical systems theory to psychology have led to 
recent advances in understanding neuromotor development and advances in theories 
of cognitive development.  This article reviews published findings associated 
with a specific coherent and influential application from which a theory of 
adaptive, self-organized cognition has been derived and related to a theory of 
developmental dynamics of the neuromotor system.  The review focuses on 
implications of two theories for quantifying developmental phenomena, and 
suggests a method for quantifying the cognitive theory.

KEY WORDS:  developmental psychology; nonlinear dynamical systems; motor 
development; cognitive development; multiprocess model.

Developmental psychology addresses the nature of behavioral and psychological 
changes associated with growth in human and animal species. As an infant grows, 
new skills emerge in motor, cognitive, and social behavior. The skills are 
complex and the processes by which they are generated are adaptive. Thus, 
developmental psychology encompasses a natural subject matter for nonlinear 
dynamic systems (NDS) theory. NDS theory has attracted the attention of 
developmental psychologists, who have applied it with some notable success. 
Although NDS theory has had an impact on many developmental psychologists, the 
full variety and extent of the impact is outside the scope of this article: 
Developmental psychology is a large field within general psychology, accounting 
for about 15% of the 17541 psychology journal articles published in 1995 
(PSYCINFO database). Specifically, applications of NDS to social development 
will not be considered here. Instead, the following treatment will be limited to 
the achievements associated with a specific coherent and influential application 
of NDS theory in the field of neuromotor development and to related systematic 
applications in the field of cognitive development.

 In developmental studies of motor skills, three features of NDS repeatedly 
emerge, as can be illustrated by the advanced skill of walking. First, advanced 
skills are stable, easily identified, patterns essentially different from their 
component skills, showing features of complexity: Walking is a coherent pattern 
different from components of leg flexion or body posture. Second, advanced 
skills are not fixed, rigid patterns but fluid, stable states of adaptation to 
environmental constraints, showing self- organization: Walking varies in the 
ways specific muscles are involved in an action, spontaneously adapting to the 
terrain. Third, over a wide variety of starting points and environments, the 
typical infant eventually acquires typical advanced skills, showing nonlinearity 
with a stable attractor: Most children, even those impeded by illness or 
disability, eventually develop a pattern that is recognizable as a walk. Thus 
motor development thus has features of NDS in component processes, complexity in 
stable patterns, and adaptive self-organization.

 The dynamical features of motor development have analogies in cognitive 
development. For example, speaking in sentences is essentially different from 
the component skills of remembering names or vocalizing; sentences are 
characteristically created new, fluidly adapted to constraints of the child's 
native language; and most children eventually acquire the skill of creating 
sentences in their native language. Motor development and cognitive development 
invite treatment by NDS theory.

BACKGROUND

 Throughout the history of developmental psychology the dynamical features of 
motor and cognitive development have been central to research and theory, but 
general appreciation of dynamical approaches to development have previously been 
idiosyncratic, lacking an accessible coherent terminology and shared 
conceptualization of phenomena of NDS and complexity. Piaget's theory of the 
dynamic relation between action and thought, called sensorimotor development, 
were originally published in the 1930s and were influential in the United States 
from the 1950s. Lewin's field theory of social and cognitive development was a 
substantial force well appreciated in the 1940s. Systems concepts can be found 
in the work of Gesell, which dominated motor development since the 1940s. These, 
along with others systems approaches have been reviewed by Thelen and Smith 
(1994, pp. xx-xxii, 312-323). Contributions by the researchers of history are 
enjoying renewed appreciation now that a common approach of NDS has become 
accessible and psychologists inspired by NDS theory have made a series of 
advances in understanding development.

 Explicit acknowledgment of NDS theory is manifest in an influential line of 
research in motor development which has coalesced around the work of Esther 
Thelen, a summary of which has been provided by Thelen and Linda Smith and by 
Savelsbergh books of readings on recent advances (Smith & Thelen, 1993; 
Savelsbergh, 1993). Advances in motor development and in other lines of research 
independently guided by concepts of NDS, have directly influenced the field of 
cognitive development (Howe & Rabinowitz, 1994; Bogartz, 1994; Cooney & Constas, 
1993). Thelen and Smith have also authored a second book (Thelen & Smith, 1994) 
in which they generalize from approaches found fruitful for motor development to 
analogous areas of cognitive development, in the process presenting a new theory 
of cognitive development.

 The application of NDS to developmental psychology has taken place against a 
background of some less obvious, but well-substantiated properties of the 
developing infant. For early neuromotor and cognitive development, the 
background of research has established a few characteristic themes. In the 
neuromotor system, the theme is generation and eradication. Newborn infants have 
changes in structures that are generated within the constraints of their 
environment. During the first year of life changes in the brain include both 
creation and elimination of cells and connections. These changes participate in 
accommodation to physical growth of limbs, a problem of managing limbs for which 
mechanical properties change each day. In processes underlying development of 
neural and limb structures, the activity of each affects the structure of the 
other (Bekoff, 1981; Cowan, Fawcett, O'Leary, & Stanfield, 1984; Nowakowski, 
1987; Provine, 1993). In the cognitive system, the additional theme is 
sophistication. Infants are sophisticated in their perception of properties of 
the world. Infants weeks old can distinguish the sounds of human speech and 
classify certain speech sounds as the same despite variations in the production 
of the sound such as the sex of the speaker. Infants as young as 3-4 months 
distinguish cats from other mammals, excluding horses and tigers from the 
concept. These and other cognitive and perceptual skills of early infancy have 
been reviewed by Eimas (1994) and by Held (1993). A theory of development will 
need to encompass these characteristic themes.

 The perspective of NDS has so far followed different courses in the fields of 
motor and cognitive development. In motor development, application of 
quantitative NDS theory has led to discovery of a result that demonstrated the 
error of a strongly held prior belief. That revelation has generated interest 
and energy sufficient to restructure the field of motor development. The field 
moved from describing developmental stages to dynamical systems theory, a 
progress directly tied to the application of well-known physical laws and 
quantified aspects of motor performance. Although the achievements in motor 
development have stimulated investigators to study cognitive development from 
the perspective of NDS. Models based on complexity and NDS have provided 
inspiration and guidelines but have not yet demonstrated a particular utility or 
dislodged an important prior belief. Analogy, quantification, prior beliefs, and 
discovery have brought these two related fields to dissimilar states with 
respect to using NDS theory. For motor development, the theory is now widely 
accepted and systematically applied. For cognitive development, it is not yet a 
dominant force.

APPLICATIONS IN MOTOR DEVELOPMENT

 Application of NDS theory to motor development followed a path paved by the 
work of Kelso and Turvey and their colleagues. They applied dynamical systems 
analysis to problems of adult perception and action. One common characteristic 
of their approach is the sophisticated application of physical principles of the 
mechanics of motion. When studying the behavior of an actor-environment complex, 
they typically quantify the properties of bodies in motion. Quantification is 
applied to features of the environment, and also, whenever useful and 
appropriate, to the actor or to some part of the actor-environment complex.

 Quantification of features of actions may be illustrated by a result by Kelso 
and his colleagues (Schoener & Kelso, 1988). In this study, investigators gave 
adult subjects instructions to flex and point both index fingers to the beat of 
a metronome, but with opposite phases, having one finger point while the other 
flexed, resulting in a simple rhythmic organization. The organization was easy 
to illustrate by superimposing the sinusoidal graphs of the position of each 
finger over time, showing a constant phase difference of 180 degrees. When the 
rate of the metronome was increased, the simple rhythmic organization was 
disrupted. Finger movements went through a period of disorganization before 
falling under the regime of the stable attractor in which the fingers moved in 
unison. The regime could be managed by variations in the order parameter of the 
frequency of the metronome. The ease of observation of the movements of the 
fingers and the simple regularity of initial and final patterns enabled the 
investigators to produce quantitative descriptions of the features of the 
systems characterizing the nature of the order parameter, transients, and 
attractors.

 Quantifying features of the environment may be illustrated by a recent finding 
by Michael Turvey and his colleagues (Turvey & Carello, 1995). Reasoning from a 
theory that perception arises in the course of meaningful action and in turn 
guides further action, these investigators studied the relation of perception 
and action arising from the process of wielding, that is, handling a tool-like 
object. Subjects were handed an object hidden from view by a screen. They were 
constrained to moving the object only by moving the wrist. From this wielding 
experience, they were asked to estimate the length of the object. The relevant 
objects in the test all had identical handles, but otherwise different shapes, 
lengths, and dynamical properties. Dynamics of rotation of objects in relation 
to torque applied can be quantified by the laws of mechanics and the properties 
of matter. The quantities involved in characterizing the motion of a particular 
object are determined by the distribution of its mass around axes in three- 
dimensional space. When the axes have been properly placed in space, this 
distribution can be uniquely given by three numbers, the moments of inertia. The 
moments quantify the motion of the object that can result from the application 
of any torque. Since the action of wielding can be reduced to the application of 
torque through movement of the wrist, there is a natural connection between the 
action of wielding and the moments of inertia of the object. Consequently, for 
an unseen object, judgments of length might be based on the subjects' detection 
of the moments. This, indeed, appeared to be the case: Judgments of length were 
only marginally predictable from the actual length of the object, but precisely 
predictable from a single quantity, which was essentially the ratio of the 
largest to the smallest moment of inertia. Thus, quantifying physical properties 
provided another in a series of examples demonstrating the close connection 
between action capabilities and perception.

 Inspired by work of Kelso and Turvey, Thelen (Thelen & Smith, 1994, p. 75) 
turned her attention to quantifying the dynamics of motion associated with the 
development of walking. An early result of her effort was to overturn a strongly 
held belief about the processes involved in infant motor skills. The general 
concept of the belief involved a process in which new centers in the developing 
brain, cortical centers, would inhibit primitive reflexes eventually permitting 
them to be replaced by similar, but voluntary, actions. The behavior pattern 
under study was the stepping pattern: when held upright supported around chest, 
the newborn infant's legs move in a coordinated stepping pattern. The stepping 
pattern disappears in infants soon after birth and reappears around 10 months of 
age, near the time of the first appearance of independent walking. The generally 
held belief was that the mechanism for the disappearance of the stepping pattern 
was cortical inhibition of the immature reflex and the later reappearance was in 
a more mature form. After the work of Thelen and her colleagues (Thelen and 
Fisher, 1982), summarized by Thelen (1989), it was clear that this belief was 
wrong. In her own words:

 We proposed that the developmental transition from stepping to
 no-stepping was triggered by a simple, nonneural scaling of a
 body composition parameter, the increase of nonmuscular or fat
 tissue, which made the legs comparatively heavy and weak and 
 prevented the infant from lifting the leg upright, but only when
 the infant was in the biomechanically demanding upright posture
 ... My colleagues and I have shown that stepping in young
 infants can be elicited or suppressed by a number of contextual
 manipulations that systematically change the biomechanical
 demands on the legs, including postural changes, submerging in
 water, adding weights, and placing infants on motorized
 treadmills... (Thelen, 1989, p. 92)

 For the stepping pattern, Thelen found there was no motor program to be 
overridden, no reflex pattern to be suppressed or released by higher centers. 
There was only what Thelen and Smith termed the "resonance" of the biomechanical 
properties of the legs moving within the context, thereby assembling into a 
stable self-organized state, stepping or no- stepping according to the 
constraints. The prior belief cortical inhibition of stepping was demonstrably 
in error.

 Since the belief in cortical inhibition had been profoundly held, when it was 
overturned by Thelen's result, much interest was generated. That interest was 
given direction by the groundwork laid by Thelen, Kelso, and Turvey. The NDS 
approach, quantified through laws of physics, was suited to resolving more 
questions of motor development. Motor activity could be measured continuously 
and movement within constraints could be quantified and related to known laws of 
mechanical motion of springs, levers, pendulums, and pulleys. The laws of motion 
of these objects have well-established parameters such as those representing 
inertia and elasticity. These parameters could be used to guide the 
investigation of how important constraints of limb and context change during 
infancy and childhood giving opportunity for the emergence of new stable 
movement patterns such as are illustrated in the study of walking by Clark, 
Truly, and Phillips (1993). New stable patterns of behavior could be self- 
organized requiring no central planning mechanism. Attractive concepts, refined 
methods, demonstrable results, and new understanding all contributed to firmly 
establish the NDS approach as a major force in the modern study of motor 
development. 

 One of many examples of application of dynamical systems principles to another 
area of motor development is study of development of the motor skill of hopping 
on one foot (Roberton, 1993). Roberton and her colleagues characterized the 
process of skilled hopping as a coordination of the support leg, the swing leg, 
arms, and posture. Over the period from early childhood to adolescence, various 
patterns of coordination appear and disappear from the action, with both smooth 
and abrupt changes. Roberton found that the components of action of the support 
leg could be quantified as a spring with force proportional to displacement. The 
ratio of these two quantities, a measure of the stiffness of the spring, could 
be measured directly from the motion of the child when analyzed by the equation 
of motion of a spring. The degree of stiffness governs the amount of jolt 
delivered to the body at each landing. Since children often have different 
levels of skill depending on which leg is the support leg, Roberton was able to 
analyze whether stiffness was determined by general features of body size and 
proportion. She found that skill in hopping was attributable to stiffness of the 
support leg and that the degree of stiffness was not due to general growth or 
body size factors. The parameter of stiffness is the control parameter managed 
by the coordinated system of skilled hopping.

 A second example is application of dynamical systems methods to the motor skill 
of reaching for an object, widely studied, but particularly well described by 
Savelsbergh and van der Kamp (1993, p. 296). They describe the sequence of 
stable patterns:

 ... newborns display reaching without grasping. Around 2
months of age ... there is a decline in reaching attempts, which
are characterized by jerky movements with closed hands -
heralding a change to more coordinated movements - open hand
contacts object - occurring after 3 month. At the time infants
start developing more coordinated reaching and grasping
movements for stationary objects (16-20 weeks), they will also
successfully reach for moving ones... 

 Savelsbergh and van der Kamp proposed that reaching from a supine position 
(zero degrees) would be more constrained by gravity than would be reaching from 
an inclined (60 degrees) or upright (90 degrees) seated posture. When they 
tested infants in these positions, they found that for younger (under 20 weeks), 
but not for older infants, the gravitational constraint determined whether or 
not the infant would attempt to reach the object.

 In the usual course of development of visual-motor coordination, there is a 
change around 4 months from a visually elicited ballistic style of reaching to a 
visually guided reaching with mid-course corrections of trajectory. In grasping, 
infants show that of many possibilities for grasp configuration only a few can 
be considered stable attractors, and over the course of the first year infants 
begin to coordinate grasping style with features of the object, appropriately 
adjusting the orientation and size of the opening of the hand. In one sense, the 
finding by Savelsbergh and van der Kamp is an analogue of Thelen's finding of 
the role of physical constraints in stepping, but there is a difference. Unlike 
stepping, reaching for and grasping objects implies a capability of visual-motor 
coordination, since the eyes guide the hand to the object, and motive to explore 
objects in the environment. This introduces a link to cognitive development. 
Visual-motor coordination provides an example of two separate systems working 
simultaneously in cooperation to produce an action. The concept of simultaneous 
operation of two or more neural systems is the foundation of Thelen and Smith's 
NDS theory of cognitive development.

 The application of dynamical systems methods to the study of the development of 
visual-motor coordination is particularly instructive because reaching for an 
object is clearly an exploratory action and is clearly related to the perception 
of that object, but for researchers in the field of visual-motor development, 
the relationship is even closer than it might appear. Savelsbergh and van der 
Kamp began their study with the assumption of "the inseparability of perception 
and action", relying on the results of many experiments with infant animals that 
demonstrate that it is possible to delay or preclude the later development of 
specific perceptions by preventing the infant from performing specific actions. 
In other words, perceptions are products of action and only perceptions so 
acquired through action can serve as guides to future action. The 
"inseparability" of the two processes forms a bridge between motor systems and 
cognitive systems and serves as the basis for moving from the clearly quantified 
phenomena and explicit theories and phenomena of motor development to the 
analogous phenomena and theories of cognitive development.

APPLICATIONS IN COGNITIVE DEVELOPMENT

 Although it is not crucial that such a theory require every aspect of 
development be self-organized, Thelen and Smith strive to explain all products 
of human cognitive development as emergent stable states self- organized in the 
natural movements of the physical system acting within the constraints of the 
context. Their theory characterizes cognition as dynamic and self-organizing. In 
the case of perceptual-motor development of infants, dynamic cognition theory 
has a foundation in numerous results, not the least of which are those detailed 
observations by Piaget of the cognitive content of motor behavior during early 
infancy, which he called the sensorimotor period. According dynamic cognition 
theory, the infant grows in cognitive skills through processes of exploration 
based on perception and action. Actions of the infant are seen to emerge self- 
organized in each instance from the operation of motor and neural subsystems 
under constraints of the context, arriving at a stable state of coordination to 
meet the demands o view, action is inseparably tied to perception and the 
perception-action complex is the embodied basis of natural categories from 
which, arguably, all cognitive skills may be derived.

 In dynamic cognition theory, when going from perception to cognition it is 
necessary to have a theoretical account for self-organization of the capacity to 
form categories in order to treat nonidentical objects as equivalent, for 
example, perceiving a cup as unchanged when seen from different perspectives. 
According to their theory the mechanism for creation of categories self-
organizes from the simultaneity of a perception and its associated action. As an 
example using adult categorization, consider the letter a as it might appear in 
many handwritten variations. How is it that many physically dissimilar variants 
are classified as instances of the same category and many physically similar 
patterns, such as o, are excluded? The mechanism proposed by Thelen and Smith is 
that the sequential neural pattern associated with perception of the handwritten 
letter is coupled in a synchronous manner with the neural pattern of the action 
of writing, each dynamic pattern mapping onto the other. For the person viewing 
the handwritten letter a, by virtue of previous experience, the dynamic neural 
pattern of the perception is connected to and activates some aspect of the 
dynamic neural pattern of the action. In theory, the mapping of these 
perceptual-motor patterns can create expectations for variations in the 
appearance of the handwritten letter associated with variations in constraints 
and parameters of motor control, thereby identifying the object as an instance 
of the handwritten letter a. Thelen and Smith cite several results demonstrating 
aspects of simultaneous activation resulting in coordination of the senses in 
infancy, but so far no direct evidence that infants create categories per se 
through this process of expectations derived from the parameters of simultaneity 
of perception and action.

 Dynamic cognition theory finds both supporting and challenging research 
results. The theory is supported by a variety of findings showing cognitive 
skills arise after the relevant motor skills have been established. For 
instance, infants show sensitivity to 3-dimensional depth only at a time after 
having acquired control of head motion (Thelen & Smith, 1994, p. 199-200). The 
theory is challenged by the sophistication of the newborn infant in forming 
categories. Examples of such very early categorization skills are plentiful 
(Meltzoff & Moore, 1983; Meltzoff, 1993). In studies subsequently replicated by 
others, Meltzoff and his colleagues have demonstrated that in the hours 
immediately after birth infants spontaneously imitate adult's simple facial 
expressions and hand gestures. This finding seems to require a degree of 
cognitive skill. For example, classifying the adult human in the same category 
as the infant, and categorizing faces and hands into different categories. These 
skills might f there has been some opportunity for development of actions 
related to the apparently requisite cognitive skills, but they appear very 
early, thus presenting a challenge to a theory that holds that self-organizing 
features of action serve as the sole basis of cognition.

 Theoretically, during the process of self-organization that results in the 
creation of a category there forms an expectation based upon the perception-
action complex (Thelen & Smith, pp. 229-233). This might seem to introduce the 
circularity of having a cognitive state (expectation) precede the self-
organization of the necessary basis of cognition (categories), but the 
circularity is only apparent. The circularity is only apparent, since the theory 
derives the expectation from the dynamics of the neural patterns (attractors) 
created by the perception-action system and activated by the task. Since it is 
in the nature of attractors to govern what will happen next, the activity of the 
system in the regime of the attractor is itself the expectation. Expectation has 
no separate status as a cognitive entity. This type of expectation is invoked by 
Thelen and Smith to explain infants' demonstrable surprise when certain types of 
novel events are depicted (p. 225). The novel event serves as a perturbation of 
the ongoing processes disturbing the ongoing perception-action attractor and 
thereby permitting activation of competing action-perception systems. The 
perturbation would be reflected in behavior showing surprise, the competing 
systems would be in the generation of new concepts following the perturbation. 
One feature pervading the discussion of the relation between cognition and 
perception-action attractors is that the attractors of interest govern 
unobservable or inaccessible processes, the forms of which are not known, so 
that only approximate models of the attractors and their processes are available 
for testing the theory.

 Even with the impediments of unobservability and inaccessibility of the true 
underlying processes, the approach to cognitive development advocated by Thelen 
and Smith has support stemming from results in other areas of psychology and 
related fields. One important requirement for their theory is that a discrepancy 
between expectation and observation results in a perturbation of the system. It 
has long been known from studies of both human and animal behavior that within a 
given context several types of objective environmental change (discrepancies) 
result in creation of nonspecific energy, which is then self-organized in the 
sense of increasing the likelihood of occurrence of the predominant behaviors 
(Amsel & Roussel, 1952) or change the organization of behavior (Trabasso & 
Bower, 1968; Berlyne, 1966; Krechevsky, 1932). Therefore the source and 
nonspecificity of energy for perturbation of the system by novelty has a strong 
basis in previous results. Another important requirement concerns the process by 
which energy is generated by discrepancy process must not depend on any internal 
representation, icon, or judge. That such a process can exist has been 
demonstrated for simple artificial neural networks (Carpenter, Grossberg, & 
Reynolds, 1991; Lewenstein & Nowak, 1989). From just these few observations, it 
can be concluded that there is a substantial factual basis supporting the effort 
of deriving phenomena of cognitive development from perception-action systems. 

QUANTIFYING COGNITIVE DEVELOPMENT

 Specific applications of the theory proposed by Thelen and Smith rely on 
details of interplay of unobservable attractors. It might seem that the 
situation would be completely unsuited to quantification, but that is not the 
case. It is possible to describe the interplay of such approximately-known 
competing processes at least in the sense of judging the extent to which one 
process or another is a more credible source of an observed behavior. A method 
for such quantification has been described for approximate models of for the 
dynamics of attractors (Metzger, 1993, 1995) For this method, models of 
competing attractors can be expressed in any form, including the form of an 
approximate landscape of neural activation. The3 major requirement is each model 
for a process must have, at each instant, some way of forming an explicit 
expectation for what will happen next (must generate a short-term forecast). To 
apply the method there must also be some way of observing what does happen next. 
The method, called multiprocess modeling (West & Harrison, 1989, Metzger, 1995), 
evaluates the credibility models of the process according to their respective 
forecasting errors. Over a number of consecutive forecasts and observations, 
models that make large forecasting errors are given less credit for being 
credible representations of the true process, while models that make smaller 
errors become more credible approximations of the true process.

 Multiprocess modeling has crucial features corresponding to features attributed 
by dynamic cognition theory to perceptual and motor attractors. When the 
cognitive system is in the regime of a given attractor, that fact is represented 
in the multiprocess model by the relative credibility of a model of that 
attractor, compared to competing models. In dynamic cognition, attractors of the 
theory generate expectancies for what will happen next for a particular 
individual in a particular context. Similarly, each model of a multiprocess 
model generates a forecast for what will happen next. In dynamic cognition, when 
some event discrepant from the expectancy of the current attractor occurs, the 
unexpected event generates surprise which can lead the system toward some new 
organization; if surprise can be thought of as a perturbation, the error in 
expectation provides the energy to escape a particular attractor and perhaps 
fall into the regime of a different attractor. Similarly, the credibility of 
each model of a multiprocess model can be affected for each event according to 
the error of its forecast for that event: Models that forecast something closer 
to the actual event gain in credibility, at the expense of the credibility of 
alternative models. In dynamic cognition, the perception-action complex creates 
an evolving context, within the particularities of which cognition is newly 
assembled at each instant. Similarly, by keeping track of the respective 
credibilities of several models of an ongoing the process, each according to its 
consistency with details of an ongoing behavior-environment complex, a 
multiprocess models can carry along an evolving context, which provides an 
interpretation of each behavior of each individual. Importantly, models of a 
multiprocess model can be consistently and informatively applied to approximate 
models, determining their respective credibilities with respect to the true 
process, even though each of which contains processes that are believed to 
correspond only partially and inexactly to true processes.

 The strongest points of dynamic cognition theory remain close to the quantified 
region, namely development during the sensorimotor p As an enrichment of the 
field, the theory offers guidance that might alter practices of research into 
cognitive development. For example, Thelen and Smith (p. 341) point out that the 
NDS approach provides a perspective from which researchers can abandon old 
dualisms such as "structure vs. function, nature vs. nurture, brain vs. 
behavior, perception vs. cognition, mind vs. body, competence vs. performance, 
learning vs. development". They urge researchers to abandon the common approach 
of minimizing variability in order to study differences among groups, asking 
them to study, in detail, variability within an individual, with particular 
attention of the role of variability in the emergence of new organization.

 The strongest points of dynamic cognition theory remain close to the quantified 
region, namely development during the sensorimotor period. As an enrichment of 
the field, the theory offers guidance that might alter practices of research 
into cognitive development. For example, Thelen and Smith (1994, p.341) point 
out that the NDS approach provides a perspective from which researchers can 
abandon old dualisms such as "structure vs. function, nature vs. nurture, brain 
vs. behavior, perception vs. cognition, mind vs. body, competence vs. 
performance, learning vs. development." They urge researchers to abandon the 
common approach of minimizing variability in order to study differences among 
groups, asking them to study, in detail, variability within an individual, with 
particular attention to the role of variability in the emergence of new 
organization.

SUMMARY

 The achievements of developmental psychology within the field of motor 
development have been strengthened by quantitative analyses derived from 
physical laws, giving strong guidance to researchers. Without these quantitative 
strengths, the companion theory of dynamic cognition relies on analogy. The 
fundamental ideas of the theory of dynamic cognition are well grounded in a 
variety of previous results of psychological research. Although it gives less 
guidance for quantification, it suggests there are many possible paths for 
future research. As it stands now, it remains primarily a system inspiring new 
ides, questioning old biases, and generating new interpretations, but not yet 
producing an upheaval in the filed of cognitive development. The achievements of 
the filed of developmental psychology itself can be seen as emerging from the 
coordination of separately developing systems, energized by the surprise of 
Thelen's result, given form, support, and structure by the common language of 
complexity, and settling into a new coordinated structure. Having arisen in a 
place fittingly far from the center of the arena of developmental psychology, 
the reorganization that began in the field of motor development has had 
repercussions that are still taking shape in the filed of cognitive development.

ACKNOWLEDGEMENTS
This research was supported in part by NSF grant BNS-9020357 and Fulbright 
Research Fellowship 1994-95.


REFERENCES


Amsel, A. & Roussel, J. (1952) Motivational properties of frustration. Journal 
of Experimental Psychology, 43, 363-368. 

Bekoff, A. (1981) Embryonic development of the neural circuitry underlying motor 
coordination. In M. Cowan (Ed.) Studies in developmental neurobiology. New York: 
Oxford University Press. 134-170. 

Berlyne, D.E. (1966) Curiosity and exploration. Science, 153, 25-33. 

Bogartz, R. S. (1994) The future of dynamic systems models in psychology in the 
light of the past. Journal of Experimental Child Psychology, 58, 289-314

 Carpenter, G. A., Grossberg, S., and Reynolds, J. H. (1991) ARTMAP: Supervised 
real-time learning and classification of nonstationary data by a self-organizing 
system. Neural Networks, 4, 565-588.

Clark, J. E., Truly, T. L., & Phillips, S. J. (1993) On the development of 
walking as a limit-cycle system. In L. Smith & E. Thelen (Eds.) A dynamic 
systems approach to development: Applications. Cambridge: MIT Press. 71-93.

Cooney, J. B., & Constas, M.A. (1993) On determining the dimension of 
discontinuities in human learning and development. In M. L. Howe & R. Pasnak 
(Eds.) Emerging themes in cognitive development: Foundations. New York: 
Springer-Verlag. 154-191.

Cowan, W. M., Fawcett, J. W., O'Leary, D. D., & Stanfield, B. B. (1984) 
Regressive events in neurogenesis. Science, 225, 1258- 1265. 

Eimas. P. D. (1994) Categorization in early infancy and the continuity of 
development. Cognition, 50, 83-93. 

Held, R. (1993) What can rates of development tell us about underlying 
mechanisms? In C. Granud (Ed.) Visual perception and cognition in infancy. 
Hillsdale, NJ: Lawrence Erlbaum Associates. 75-89. 

Howe, M. L., & Rabinowitz, F. M. (1994) Dynamic modeling, chaos, and cognitive 
development. Journal of Experimental Child Psychology, 58, 184-199. 

Krechevsky, I. (1932) "Hypotheses" in rats. Psychological Review, 39, 516-532. 

Lewenstein, M. & Nowak, A. (1989) Fully connected neural networks with self-
control of noise levels. in Physics Review Letters, 62 (200), 225-228. 

Meltzoff A. N. (1993) The centrality of motor coordination and proprioception in 
social and cognitive development: From shared actions to shared minds. In G. J. 
P. Savelsbergh (Ed.) The development of coordination in infancy. The 
Netherlands: Elsevier Science Publishers B. V. 463-496. 

Meltzoff, A. N., & Moore, M. K. (1983) Newborn infants imitate adult facial 
gestures. Child Development, 54, 702-709. 

Metzger, M. A. (1993) A step in the right direction. Journal of Mathematical 
Psychology, 37, 477-485. 

Metzger, M. A. (1995) Multiprocess models applied to cognitive and behavioral 
dynamics. In R. E. Port & T. van Gelder (Eds.) Mind as motion. Cambridge: MIT 
Press. 491-526. 

Newell, K. M. & McDonald P.V. (1993) The eveolving perceptual-motor workspace in 
infancy: Reactions to Zanone, Kelso, Jeka, & Schmuckler. In G. J. P. Savelsbergh 
(Ed.) The development of coordination in infancy. The Netherlands: Elsevier 
Science Publishers B. V. 175-199. 

Nowakowski, R. S. (1987) Basic concepts of CNS development. Child Development, 
58, 568-595. 

Provine, R. R. (1993) Prenatal behavior development: Ontogenetic adaptations and 
nonlinear processes. In G. J. P. Savelsbergh (Ed.) The development of 
coordination in infancy. The Netherlands: Elsevier Science Publishers B. V. 203-
236. 

Roberton, M. A. (1993) New ways to think about old questions. In L. Smith & E. 
Thelen (Eds.) A dynamic systems approach to development: Applications. 
Cambridge: MIT Press. 95-117. 

Sameroff, A. J. (1989) Commentary: General systems and the regulation of 
development. In M. R. Gunnar & E. Thelen (Eds.) Systems and development: The 
Minnesota symposia on child psychology. Hillsdale, NJ: Lawrence Erlbaum 
Associates Publishers. 219-235. 

Savelsbergh, G. J. P. (1993) Perspectives on the development of movement 
coordination in infancy. In G. J. P. Savelsbergh (Ed.) The development of 
coordination in infancy. The Netherlands: Elsevier Science Publishers B. V. 1-9 
& 519-524. 

Savelsbergh, G. J. P., & van der Kamp, J. (1993) The coordination of infant's 
reaching, grasping, catching and posture: A natural physical approach. In G. J. 
P. Savelsbergh (Ed.) The development of coordination in infancy. The 
Netherlands: Elsevier Science Publishers B. V. 289-358. 

Schoener, G., & Kelso, J. (1988) Dynamic pattern generation in behavioral and 
neural systems. Science, 39, 1513-1520. 

Smith, L. & Thelen, E. (Eds.) (1993) A dynamic systems approach to development: 
Applications. Cambridge: MIT Press. 

Thelen, E. (1995) Time scale dynamics and the development of embodied cognition. 
In R. E. Port & T. van Gelder (Eds.) Mind as motion. Cambridge: MIT Press. 69-
100. 

Thelen, E. (1989) Self-organization in developmental processes: Can systems 
approaches work. In M. R. Gunnar & E. Thelen (Eds.) Systems and development: The 
Minnesota symposia on child psychology. Hillsdale, NJ: Lawrence Erlbaum 
Associates Publishers. 77-117. 

Thelen, E., & Fisher, D. M. (1982) Newborn stepping: An explanation for a 
"disappearing reflex". Developmental Psychology, 18, 760- 775. 

Thelen, E. & Smith, L. (1994) A dynamic systems approach to the development of 
cognition and action. Cambridge: MIT Press.

Trabasso, T.R. & Bower, G.H. (1968) Attention in learning. New York: Wiley. 

Turvey, M. T. & Carello, C. (1995) In R. E. Port & T. van Gelder (Eds.) Mind as 
motion. Cambridge: MIT Press. Some dynamical themes in perception and action. 
373-401.