Perspectives on the relation between information and ... - Science Direct

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Perspectives on the relation information and dynamics: An epilogue

Peter J. Beek a,b,*, Piet C.W. van Wieringen

a

aFaculty of Human Movement Sciences, Dept. of Psychology, Free University, van der Boechorststraat 9, 1081 BTAmsterdam, The Netherlands b Center for the Ecological Study of Perception and Action, Universi& of Connecticut, Storrs, CT, USA

Abstract In this epilogue to the special issue of Human Mooement Science on the role of information in dynamical accounts of action, three broadly defined approaches are distinguished, namely the ecological approach formulated by Gibson, the perception-action approach formulated by Kugler and Turvey and the dynamical approach formulated by Kelso and Schoner. These three approaches serve as a framework for discussing the various contributions to the special issue, which address current conceptual problems in connecting information and dynamics and propose novel ways to solve them.

1. Introduction One of the greatest contemporary challenges in the field of study concerned with the execution and control of perceptual-motor action is to provide a unified, coherent account of the informational basis of movement. What is the role of perceptual information in the guidance of movement, and conversely, how does movement contribute to the perceptual world? Or, to borrow Turvey’s phrase, “how does light get into muscle and how does mucle get into light?” 1

* Corresponding author. ’ Turvey, personal communication. 0167-9457/94/$07.00 0 1994 Elsevier SSDI 0167.9457(00023-8

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By now, there is wide consensus that the bulk of traditional research on “motor control” has focussed on the motor system per se and that it has neglected the essential role of (perceptual) information in the production of movement, resulting in a limited view of the control of action. Particularly with the advent of the ecological approach to perceiving and acting (e.g., Michaels and Carello, 1981, Turvey et al., 1981, Turvey et al., 1990) and its close companion, the dynamical systems approach to movement coordination (e.g., Beek and Beek, 1988, Haken et al., 1985, Saltzman and Kelso, 1987, Schiiner and Kelso, 1988a, b, c), it has become commonplace to emphasize the intimate connections between perception and movement in the control of action. 2 As a consequence, “perception-action couplings” and “perception-action patterns” have become a primary focus of research. But exactly how should we conceptualize the connections between perception and movement in the pursuit of an empirically progressive programme of research on the control of perceptual-motor actions? And, relatedly, how should we conceptualize (perceptual) information and (movement) dynamics 3 to be able to explain how humans and other animals perform such actions in the environment? Moreover, how can we insure that our conceptualizations allow us to capture the learning, development and evolution of the connections between perception and movement in a meaningful manner? Questions such as these are the concern of the present special issue. Quite deliberately, we have described the topic of the special issue as the dynamics of perception-movement systems with special focus on the role of perceptual information. Although we expected to solicit with the so-described topic articles of sufficiently different theoretical persuasions (which was indeed the case), we attempted at the same time to confine the theme of the issue by explicitly framing the problem of the relationship between perception and movement as the problem of the relationship between information and dynamics. In so doing, we realized that perception and movement, and even more so, information and dynamics are problematic terms that take on a variety of meanings in the study of the control and

’ Contrary to what appears to have become common usage, we prefer to talk about the relationships between perception and movement rather than between perception and action. We view perception and movement as the basic functions that compose actions. ’ Here, we use the terms information and dynamics in a general sense to be able to frame the topic of the special issue without a priori theoretical restrictions. As we go along we will see how these concepts find their expression in the literature, including the articles in this special issue.

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coordination of perceptual-motor actions. In fact, the diversity of meanings of these essential terms in current approaches and theories in the field of movement control and coordination formed a primary motive to organize and edit this special issue. It appeared to us that the scientists advocating these approaches and theories, whether presented as “ecological” or “dynamical” (or as both or neither), were in fact all dealing with the type of questions mentioned in the opening paragraph without having arrived at an in any sense conclusive account of the connections between perception and movement. What we saw instead was a collection of approaches, conceptualizations and proposals with a strong family resemblance, but with many important meta-theoretical, conceptual and methodological differences as well. The collection of articles in this special issue confirms our impressions in this regard. Our goal in this epilogue is to summarize and to evaluate the contributions in the present special issue with regard to its main theme. In so doing, we hope to identify the critical issues in furthering our understanding of perception-movement patterns. Broadly speaking, we distinguish three perspectives on the relation between perception and movement that we use as a framework for our discussion, namely the ecological approach formulated by Gibson (19791, the perception-action approach formulated by Kugler and Turvey (1987, 1988) and the dynamical approach formulated by Schiiner and Kelso (1988a, b).

2. Action-specific

perceptual variables

In formulating his ecological approach to visual perception, Gibson (1979) made (at least) two important contributions to the understanding of the relationship between perception and movement in the execution of action. Firstly, he conceptualized information as specifying affordances, that is as possibilities for action. What an animal perceives is what the environment affords that animal to do, or, to use the phrase of Michaels and Care110 (19811, “perception is for doing”. Information is specific to action. Secondly, he underscored, and demonstrated experimentally, that information for the control of action is being generated by movement of the actor and/or motion of the environment relative to the actor. Changes in the relationship between actor and environment are always accompanied by perceptual flow fields that provide information effectively specifying these changes. One consequence of Gibson’s ecological approach to movement-induced

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perceptual information has been an increased interest for the role of movement in the exploration and pick-up of information. This theme is addressed in the present special issue by Hughes and Jansson in the context of haptic texture perception. In their extensive survey of the literature they found no clear evidence that active exploration aids texture perception. The authors conclude that it is too early to draw any definite conclusions on the basis of the available evidence and suggest a number of experiments to shed more light on this issue. In our opinion, the review of Hughes and Jansson raises the important theoretical need to demarcate the conditions under which perception benefits from movement and the conditions under which it does not. In this context, it is important to distinguish between the perceptual information that is required for the proper guidance of movement and the perceptual information that is required to make a proper perceptual judgment. In the former case the information in question is by definition actively generated, while in the latter case, which is predominant in the literature reviewed by Hughes and Jansson, it will depend on the nature of the task, i.e. the required judgments, whether the information in question only becomes available when active movements are made. For instance, measuring the temperature of a liquid with one’s finger may be more accurate when keeping it still, while probably the opposite will hold when judging its viscosity. Ideally, one would like to have a hypothesis or model of the informational quantities that are required to make the kind of perceptual judgments used in the reviewed experimental tasks, so that predictions about the efficacy of active movement can be derived from more specific theoretical considerations than is presently the case. A first and important step in this direction has been made by Solomon and Turvey (19881. In fact, Gibson’s ecological approach culminated in a large programme of research aimed at identifying perceptual variables that are specific to the control of particular actions. To date, a fair number of perceptual quantities have been identified that exemplify the fruitfulness of this approach. Undoubtedly, the best known and most studied example of such a quantity is tau (Lee, 1976, 19801, the inverse of the relative rate of dilation of an expanding closed optical contour. It has been suggested that actions as diverse as steering an automobile (Lee, 19761, catching (Savelsbergh et al., 1991) and hitting a ball (Bootsma and Van Wieringen, 1990; Lee et al., 1983) and the regulation of gait in long jumping (Lee et al., 1982) are guided on the basis of tau. In the present special issue the relation between movement and tau is addressed and elaborated by Tresilian and by Schoner.

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The contribution of Tresilian focuses on the explanatory status of tau with regard to the timing of interceptive actions. He argues that the (often high) correlations between tau and movement kinematics that are reported in the literature in themselves provide no proof that tau was actually used in the control of movement and regrets the paucity of experiments in which properties of tau are manipulated and tested vis-a-vis alternative candidate variables for time-to-contact. He argues further that tau might be combined with other sources of perceptual information, such as vergence or distance, in estimating time-to-contact. The subsequent discussion focuses on the results of Lee et al.‘s (1983) experiment in which a falling ball had to be punched. Whereas Lee et al. interpreted their data in terms of a continuous guidance by tau of the coiling movement preceding the punch, Tresilian shows that the data can also fit a model in which movements are assumed to be pre-programmed on the basis of time-to-contact information derived from the height from which the ball is dropped. Whatever the relative merits of both models, one drawback of Tresilian’s model relative to Lee’s model is that time-to-contact (TTC) is no longer specified optically, but has to be derived from the initial height of the ball and the gravitational force, or when updated, by a combination of these two variables and ball velocity (because along the ball trajectory Mactual) = u(actual)TTC + 0.5g(TTC12). So even when one would agree that the ballistic model is much simpler than that of Lee et al., it has the drawback that, whereas the optical specification of TTC by the tau-margin seems straightforward, the advantage of (“direct”) specification of TTC is lost. An attractive feature of Tresilian’s alternative model is that it attempts to account for the relationship between time-to-contact information and the organization of movement in terms of movement kinematics and muscular forces. Although radically different theoretically, this attempt is akin to the concern of post-Gibsonian workers in the ecological approach, such as Kugler, Turvey and Warren, to connect information (in the specificational sense of the word) with the kinetics of movement.

3. The “perception-action

cycle”: Information

and forces

The notion of a perception-action cycle was first introduced by Kugler and Turvey (1987, 1988) and meant to capture the “circular causality” (1987, p. 87) between (perceptual) information and (muscular) forces. On this perspective, actions are conceptualized as the product of force fields

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which lawfully give rise to flow fields, which are picked up by the perceptual systems to adequately control the force output of the action system. The force fields are high in energy and momentum content and low in information content, whereas the opposite is true for the flow fields. The relevant descriptors of the force fields are kinetic and the relevant descriptors of the flow fields are kinematic. 4 According to Kugler and Turvey (1987, 1988) the cycle is closed in that forces and flows are complementary, but open in terms of the properties that constitute the descriptors of the flows, i.e., the informational (intentional) constraints. Thus, the perception-action cycle may be viewed mathematically as a set of reciprocally closed transactions that map kinetic (force) descriptors onto kinematic (informational) descriptors. This does not imply that the resulting behaviour is completely deterministic. A particular perception-action cycle always assumes a particular intention (or action goal) on the part of the actor. The intention acts as an extraordinary boundary condition that harnesses the laws. By changing the intention the specific properties and lawful regularities of a perception-action cycle alter. It only makes sense to talk about a specific perception-action cycle if the intention underlying it is made explicit. The notion of a “perception-action cycle” is at the heart of a research programme aimed at identifying information-force transactions. Ideally, these transactions are cast into mathematical models that precisely describe how flow fields and force fields relate to one another and, thus, that allow for quantitative predictions. Such mathematical models entail two types of terms, viz., terms relating to the active and passive forces governing the movements of limbs, and terms relating to the various perceptual flow fields guiding these movements. The basic picture is provided by Fig. (I), which summarizes the theoretical arguments advanced by Warren (1988). He conceptualized, for a moving actor in a stationary environment, the “perception-action cycle” in terms of four laws: Motion

= f( Force)

Flow =f(Force)

= f( F,,, + FCX,) Law of Physics

=f( Fi”t + F,,,)

Law of Ecological

(1) Optics

(2)

that is “related to the causes of ‘In this context, the term “dynamical” would mean “kinetic”, motion”, i.e., forces and moments. As pointed out by Kelso in the present special issue it is important from the meaning it has in the dynamical systems to distinguish this use of the term “dynamical” approach.

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of physics )=\awe

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of control

laws of specification Fig. 1. Schematic representation according to Warren (1988).

of the

lawful

relations

between

forces,

motion

and

information

Force = Fint + Fext = g (Flow)

Law of Specification

(3)

AFin, = g( AFlow)

Law of Control

(4)

Eq. (1) captures the fact that, by the laws of Newtonian mechanics, the sum total of the internal forces applied by the actor (Fi,,> and the external forces exerted upon the actor by the environment (FeXt), such as friction, gravity, impulses from collisions, and crosswinds, will cause a unique motion of his or her body relative to a stationary environment. The resulting motion, in turn, uniquely determines according to the laws of ecological optics, the pattern, direction, and magnitude of perceptual flow at the point of observation occupied by the actor - Eq. (2). The inverse of this lawful function expressed in Eq. (3) captures the fact that the net force acting on the actor at any one time is specified lawfully by the prevailing flow patterns. Eqs. (2) and (3) are at the heart of Gibson’s ecological theory of visual perception. To explain how an actor can control his or her action on the basis of optical flow, Warren (1988) points out that the actor must be able to differentiate between Fint and F,,,; when the flow patterns (suddenly) change due to changes in Fext, the actor has to know how much force to apply to restore the original flow pattern. Eq. (4) provides an answer to this problem: the change in perceptual flow specifies the changes needed in Fint 5 to restore the original flow pattern. One reading of Kugler and Turvey’s notion of a “perception-action cycle”, as well as Warren’s (1988) formalisms, is that the relationship between perception and movement is best characterized as a missing dimension problem (Bingham, 1987; Runeson and Frykholm, 1983; Warren

5 Because, as Warren (1988) fails to mention, also the inverse of this relationship is true, the actor is able to control the forces he or she generates on the basis of information provided by the flow changes induced. This is captured by (5) Aflow = f(AF,,,). (4) and (5) are the control laws of action.

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and Shaw, 1985). After all, force fields are conceptualized in the dimensions of Mass, Length and Time and flow fields are conceptualized only in the dimensions of Length and Time. So one might well ask: Where does the missing Mass dimension come from in the inverse mapping from kinematics to kinetics (dynamics)? How does one know how much force to exert solely on the basis of the kinematic properties of the perceptual flow fields? For Warren’s laws to be cast in a single set of (differential or difference) equations, the description of the force fields should be commensurate with the description of the flow fields, that is to say, all terms in the equations should have the same dimension. This problem has not been resolved yet. In principle, however, there are two ways to achieve dimensional homogeneity, viz. (i) by eliminating the unit of mass from the kinetic force terms (i.e., by normalizing for mass) or, (ii) by expressing the kinematic flow terms as kinetic force terms (that is, by expressing the effects of the various perceptual flow fields on movement as forces). The relationship between information (feedback) and the production of force is examined in the present special issue by Newell and McDonald in the context of maintaining various grip force levels using a variable number of fingers. The degree to which performance benefitted from information feedback depended on the specific task goal (required force level), the degrees of freedom (number of available digits) and the precision of feedback (low, intermediate and high resolution). Interestingly, interaction effects were found between task goal and available degrees of freedom and between available degrees of freedom and precision of feedback. Although the interaction between all three variables fell short of significance, the authors suspect that this was due to range effects and conclude, therefore, that information is action-specific. The exact nature of the information specifying the production of force, however, remains unaddressed in this study. Following an earlier suggestion by Fowler and Turvey (1978) in their theoretical re-examination of the Krinskiy and Shik task, it might have been the case that higher order properties of the optical stimulation afforded by the feedback signal relative to the target line (such as its velocity and acceleration and the ratio of its velocity and position) have governed performance. In fact, there are very few concrete examples in the literature of models that show how informational variables map into kinetic variables. A notable exception is the model proposed by Warren et al. (1986) on tau-based control of the vertical impulse in running over irregular terrain. Models such as this go beyond the correlational studies criticized by Tresilian in

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that they explicitly describe how perceptual and kinetic variables relate lawfully. Laws of this type, however, have an incidental character in that they are not embedded in, or derivable from, a more elaborate and formalized theory (which may explain why they are so scarce>. The meaning of this statement will become apparent in the next section when we discuss dynamical - in the sense of dynamical systems theory - accounts of perception-movement patterns.

4. Dynamical

systems accounts

of perception-movement

systems

The dynamical systems approach to movement coordination is concerned with the application of the formal and analytical tools of nonlinear dynamics to the functional and spatiotemporal patterns of movement organization. The goal of the approach is to construct formal models or “analogies” (dynamical equations of motion) of coordination phenomena that capture the stability and loss of stability of performance as well as changes therein due to learning and development. Instrumental in the “first round” of applications of these tools were instances of abrupt transitions between coordination modes. As these instances of spontaneous pattern formation are accompanied by loss of stability of a coordination mode and the appearance of a new stable mode, they form the king’s road to an identification of a system’s intrinsic dynamics, i.e. the dynamics that arise due to changes in a nonspecific control parameter. To account for changes in the intrinsic dynamics due to informational influences, Schoner and Kelso (1988a, b) introduced the concept of behavioural information and defined it most generally as a required behavioural pattern, be it specified by perceptual information, memory or intention. They endowed behavioural information with dynamics (i.e., they conceptualized it as a perturbation of the intrinsic dynamics), so that the resulting overall pattern dynamics included both the intrinsic dynamics and the dynamics specified by the behavioural information. According to SchSner and Kelso, behavioural information is by definition meaningful and specific to biological functions or to tasks, and, as such, it is reminiscent of Gibson’s (1979) notion of information as specification. The difference between “behavioural information” and the ecological concept of (perceptual flow field) information is that the former finds its expression in the same formal mode in which the coordination dynamics are cast, while, so far, the proponents of the Gibsonian approach have not examined how

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action-specific perceptual variables (such as tau) map into the coordination dynamics of the act. In the present special issue Kelso discusses the nature of coordination dynamics and its relation to behavioural information. The gist of Kelso’s position is that coordination dynamics is not “ordinary physics”, but provides an abstract description of the functional design of biological movement and its stability properties. Kelso “turns the information-dynamics distinction on its head”. Rather than starting with some kind of duality between information and dynamics that needs to be reconciled, he defends the view that the self-organized coordination dynamics that have been identified in the context of movement coordination are already informational in character. In other words, if we fully appreciate the informational character of self-organized coordination dynamics, there would be, by definition, no need to worry about the connection between information and dynamics. Dynamics is wholly commensurate with behavioural information. Even with complete commensurability, however, the problem remains to identify for specific actions (i.e., perception-movement linkages) the intrinsic dynamics of movement coordination and the perceptual information that “informs” this dynamics so that the resulting pattern dynamics corresponds to the observed behaviour. An example of such a concrete model is provided by Schiiner in the present special issue. Schoner distinguishes between control-theoretic and specificational accounts of the linkages between perception and movement, and seeks to unify these within a dynamical approach. The crux of his argument is that action-specific perceptual variables (such as tau) couple continuously into the dynamics of movement and that the resulting coupling is sufficient to account for the observed dependencies between action-specific variables and movement variables. It is shown how, in the case of time-to-contact studies, it is unnecessary to assume that specific levels of expansion rate (e.g., a critical tau-margin) are detected. Thus, the timing of tracking movements and the timing of interceptive movements can be understood in a single conceptual framework. Importantly, the model proposed by Schiiner illustrates how the gap between the Gibsonian approach to (visual) perception and the dynamical approach to movement coordination, which is perceived at least by some workers in the field (e.g., von Hofsten, 1989, see Beek and Bingham, 1991, for a commentary), might be bridged. Prerequisite for such a bridge is that the definition of information is not strictly limited to its effects on the dynamics of movement, but that it is also defined independently of the observed behaviour in terms of

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the properties of the various perceptual flow fields. This also undercuts the danger that the explanatory status of (behavioural) information in accounts of movement coordination becomes circular. That the further unpacking of the concepts of intrinsic dynamics, control parameters and behavioural information is essential for the understanding of perception-action patterns from a dynamical perspective, is apparent from the contributions of Wagenaar and Van Emmerik and Michaels and Bongers. In reviewing their work on pathological gait patterns from a dynamical systems perspective, Wagenaar and Van Emmerik suggest that these gait patterns can be adequately characterized in terms of the phase relations between arm and leg movements as well as between pelvic and thoracic rotations. They seek to identify the intrinsic dynamics of these phase relations using walking velocity as the primary control parameter. In so doing, they are confronted with the problem of how to construct dynamical equations of motion (or potential functions) that capture the changes in multiple phase relations as a function of the control parameter. This problem is amplified by the fact that some of the observed transitions in these phase relations seemed to be abrupt and others continuous, while not all transitions were accompanied by systematic changes in the standard deviations of the relative phase measures in question. It remains to be seen, therefore, to what extent the intrinsic dynamics of individual patients can be formally assessed and serve as a means to classify these patients in a therapeutically useful way. With regard to the topic of the special issue, Wagenaar and Van Emmerik suggest that perceptual information in the form of auditory or visually presented rhythms may be beneficial to the organization of gait patterns. Whereas the authors expect improvement of performance using these rhythms as control parameters, it might be the case that persistent learning effects will only be achieved when some form of behavioural information is provided, that is to say, information that specifies in which direction the intrinsic coordination dynamics have to change. Michaels and Bongers examine the relationship between movement preparation (as indexed by reaction time) and continuous perception-movement patterns. Subjects were instructed to push a button as quickly as possible in reaction to an auditory stimulus, while rhythmically tracking an oscillating visual signal. The main findings were that reaction time depended on the phase of the movement (and not the phase of the signal), that reaction time was longer at higher tracking frequencies than at lower

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frequencies, and that reaction time was longer for anti-phase than for in-phase tracking. The latter two findings are interpreted in terms of the constraints imposed on the execution of a discrete movement by a rhythmic perception-movement pattern with frequency-dependent and mode-dependent coupling strength. On this interpretation, shorter reaction times are associated with stronger coupling between the tracking movements and the motion of the signal. No independent measure of coupling strength, however, was calculated, which renders the interpretation rather tentative. Although it is known in the context of bimanual coordination that the stability of relative phase is a function of both frequency and coordinative mode, it is an open question if this was also the case in the present task conditions, particularly in view of the rather low frequencies used and the small variation thereof (1.00 vs. 1.25 Hz). The tentative character of the proposed explanation is amplified by the fact that the dependency of reaction time on response phase did not match the dependency of the standard deviation of the phase difference between the movement of the arm and the signal motion on response phase. Still, this work is interesting in that it examines for the first time (as far as we know) the effects of the stability of perception-movement cycles on dual-task performance and its attentional demands. As is apparent from the preceding discussion, it will be important in the further development of this approach to formally assess the intrinsic dynamics of the single and dual (coupled) task space and its sensitivity to parametric influences.

5. Other scales of analysis So far, we focused the discussion on the behavioural level at which the phenomena of perception and movement occur. To date, both the ecological approach and the dynamical systems approach to movement coordination have been concerned predominantly with phenomena at this molar level of analysis. Ideally, theories of the relationship between movement and perception are accompanied with complementary theories of sensorimotor integration at the level of the nervous system. Probably the most important theory to date of how motor and sensory systems interleave in the production of perception-action cycles is Edelman’s (1987) theory of neuronal group selection. According to Edelman, perception-action cycles belong to the class of global functions, i.e. “activities leading to categorization, memory, learning, and behavioural perfor-

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mance permitting adaptation and survival ( . . . >. Such activities depend as much upon the morphology of non-neural structures in the phenotype as upon the brain” (Edelman, 1987, p. 209). A key thought in Edelman’s theory is that, during phylogenesis and ontogenesis, the brain learns about the non-neural structures that it serves. Important ingredients of this process are the development and tuning of many local motor and sensory re-entrant maps that allow for the efficient and flexible (adaptive) realization of the global functions of perception and action. We find it intriguing to discuss the contribution of Van Ingen Schenau et al. to this special issue in the light of Edelman’s ideas. Bi- and monoarticular muscles may be viewed as specific evolutionary solutions to the requirement of generating, in multijoint movements, the specific patterns of joint moments that are necessary to generate appropriate segmental accelerations and/or to exert appropriately directed forces on the environment. After having elucidated the differential role of mono- and biarticular muscles in multijoint tasks, Van Ingen Schenau et al. provide arguments that the control of these types of muscles is based on different parallel, but interacting, control processes and different sources of sensory information. Monoarticular muscles are deemed to be functionally grouped into simple synergies via central structures, whereas biarticular muscles are less rigidly controlled by central structures and depend more on feedback of peripheral afferents. In terms of Edelman’s theory this would imply that the sensory and motor maps for monoarticular muscles are more specific and more rigidly connected than the maps for biarticular muscles. That is to say, the latter would anticipate tuning of muscle activation on the basis of peripheral feedback mechanisms (cf. Greene, 1972). Hence, the stability and flexibility of the performance of multijoint tasks might be reflected in the differential plasticity of the different sensorimotor connections. Regardless of how these specific speculations will stand the test of time, the general message of Van Ingen Schenau et al. surely will, namely that the relationship between sensory and motor processes at the neurophysiological scale of analysis is as intimate as the relationship between perception and movement at the molar scale.

6. Consoling

remark

All in all, we feel reassured to conclude that the topic of this special issue is of great current interest. The duality between information and

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dynamics will probably haunt us (either in upright position or turned upside down) as long as we work on the relationship between perception and movement. The question is whether this is undesirable. We would like to argue that scientific progress often benefits from seemingly unreconcilable dilemmas such as nature-nurture, wave-particle, mind-body or, for that matter, information-dynamics. After having become tired with an inconclusive dialogue, the scientific community might reside for a while to a principle of complementarity (Pattee, 19771, but, at the same time, will continue to seek new ways to conceptualize the duality. Thus, thanks to the absence of definite solutions, such deep problems may serve as catalysts for scientific progress and innovation. We would be pleased if readers of this special issue will recognize this statement between its lines.

Acknowledgment P.J. Beek’s participation part, by a National Science

in the writing of this article was supported, Foundation Grant (BSN-9109880).

in

References Beek, P.J. and W.J. Beek, 1988. Tools for constructing dynamical models of rhythmic movement. Human Movement Science 7, 301-342. Beek, P.J. and G.P. Bingham, 1991. Task-specific dynamics and the study of perception and action: A reaction to von Hofsten (1989). Ecological Psychology 3, 35554. Bingham, G.P., 1987. Dynamical systems and event perception: A working paper. Perception-Action Workshop Review 2, 4-14. Bootsma, R.J. and P.C.W. van Wieringen, 1990. Timing an attacking forehand drive in table tennis. Journal of Experimental Psychology: Human Perception & Performance 16, 21-29. Edelman, G.M., 1987. Neural Darwinism: The theory of neuronal group selection. New York: Basic Books. Fowler, CA. and M.T. Turvey, 1978. ‘Skill acquisition: an event approach with special reference to searching for the optimum of a function of several variables’. In: G.E. Stelmach (Ed.), Information processing in motor control and learning (pp. l-40). New York: Academic Press. Gibson, J.J.. 1979. The ecological approach to visual perception. Boston, MA: Houghton Mifflin. Greene. P.H., 1972. ‘Problems of organization of motor systems’. In: R. Rosen and F. Snell (Eds.), Progress in theoretical biology, Vol. 2 (pp. 303-338). New York: Academic Press. Haken, H.. J.A.S. Kelso and H. Bunz, 1985. A theoretical model of phase transitions in human hand movements. Biological Cybernetics 51, 347-356. Kugler, P.N. and M.T. Turvey, 1987. Information, natural law, and the self-assembly of rhythmic movement. Hillsdale, NJ: Erlbaum.

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