Multiple time scales and subsystem embedding in the learning of juggling.

To gain insight into the multiform dynamics and integration of remote yet pertinent subsystems into the performance of complex perceptual-motor skills, we recently conducted a series of longitudinal and cross-sectional experiments on the acquisition of 3-ball cascade juggling in which we measured, next to the ball trajectories, postural sway, eye and head movements and respiration. The aim of the present paper is to review the main results and theoretical implications of these experimental studies for understanding skill acquisition. As regards the evolution of the quality of the juggling itself, we found that only certain aspects of throwing and catching were adjusted, while the goal behavior of sustained juggling (operationalized as the number of consecutive throws) and the degree of frequency and phase locking between the ball trajectories, indexing pattern stability, increased monotonically. The latter three aspects evolved at different rates, reflecting the existence of a temporal hierarchy in learning. Postural sway exhibited initial manifestations of task-specific, possibly mechanically induced, modes of 3:1 and 3:2 frequency locking with the ball trajectories and only few transitions between those modes. Functional stability appeared to be enhanced during practice by minimizing the sway amplitudes rather than by adjusting the sway dynamics itself. Eye and point-of-gaze movements also showed instances of 3:1 and 3:2 frequency locking with the ball trajectories; especially establishing a 3:1 locking (horizontal eye movements) appeared to be important. Expert behavior suggested that extended practice promotes reliance on multiple sources of information, allowing the proficient juggler to switch adaptively between functional organizations involving distinct perceptual systems. No consistent coordination between breathing and juggling was found. It was concluded that multiform dynamics, involving hierarchically ordered time scales, underlie the acquisition of complex skills and that the subsystems subserving realization of the task goal become assembled and embedded in a task- and subsystem-specific manner.

[1]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[2]  N. A. Bernstein Dexterity and Its Development , 1996 .

[3]  D. Bramble,et al.  Mammalian locomotor-respiratory integration: implications for diaphragmatic and pulmonary design. , 1993, Science.

[4]  K. Mardia Statistics of Directional Data , 1972 .

[5]  S. Swinnen,et al.  Acquiring bimanual skills: contrasting forms of information feedback for interlimb decoupling , 1993 .

[6]  D. Sternad,et al.  Decomposition of variability in the execution of goal-oriented tasks: three components of skill improvement. , 2004, Journal of experimental psychology. Human perception and performance.

[7]  Aaron D. Wyner,et al.  Claude Elwood Shannon: Collected Papers , 1993 .

[8]  Gregor Schöner,et al.  The uncontrolled manifold concept: identifying control variables for a functional task , 1999, Experimental Brain Research.

[9]  Peter J. Beek,et al.  The Science of Juggling , 1995 .

[10]  R A Heath,et al.  The influence of motor system degradation on the control of handwriting movements: a dynamical systems analysis. , 2003, Human movement science.

[11]  Andreas Daffertshofer,et al.  Dynamical coupling between locomotion and respiration , 2004, Biological Cybernetics.

[12]  M. Bonsignore,et al.  Ventilation and entrainment of breathing during cycling and running in triathletes. , 1998, Medicine and science in sports and exercise.

[13]  J. Kelso,et al.  Evolution of behavioral attractors with learning: nonequilibrium phase transitions. , 1992 .

[14]  Andreas Daffertshofer,et al.  Spatio-temporal patterns of encephalographic signals during polyrhythmic tapping , 2000 .

[15]  T. Stukel,et al.  Ventilatory responses and entrainment of breathing during rowing. , 1991, Medicine and science in sports and exercise.

[16]  H. Haken Principles of brain functioning , 1995 .

[17]  Peter J. Beek,et al.  Spatiotemporal variability in cascade juggling , 1996 .

[18]  Benoît G. Bardy,et al.  Postural coordination modes considered as emergent phenomena , 1999 .

[19]  J. Jacques Temprado,et al.  A novice-expert comparison of (intra-limb) coordination subserving the volleyball serve , 1997 .

[20]  P J Beek,et al.  Coupling of breathing and movement during manual wheelchair propulsion. , 2001, Journal of experimental psychology. Human perception and performance.

[21]  Karl M Newell,et al.  Task goals and change in dynamical degrees of freedom with motor learning. , 2003, Journal of experimental psychology. Human perception and performance.

[22]  Karl M. Newell,et al.  The acquisition of coordination: Preliminary analysis of learning to write , 1989 .

[23]  Geoffrey P. Bingham,et al.  Task-specific devices and the perceptual bottleneck☆ , 1988 .

[24]  J. Collins,et al.  Upright, correlated random walks: A statistical-biomechanics approach to the human postural control system. , 1995, Chaos.

[25]  P. Bernasconi,et al.  Analysis of co‐ordination between breathing and exercise rhythms in man. , 1993, The Journal of physiology.

[26]  D J Sanderson,et al.  Ventilation and locomotion coupling in varsity male rowers. , 1999, Journal of applied physiology.

[27]  P. Beek,et al.  Learning the cascade juggle: a dynamical systems analysis. , 1992, Journal of motor behavior.

[28]  J. Kelso,et al.  Learning as change of coordination dynamics: theory and experiment. , 1992, Journal of motor behavior.

[29]  Andreas Daffertshofer,et al.  Principal components in three-ball cascade juggling , 2000, Biological Cybernetics.

[30]  P Era,et al.  Postural stability and skilled performance--a study on top-level and naive rifle shooters. , 1996, Journal of biomechanics.

[31]  A. Williams,et al.  Visual search strategy, selective attention, and expertise in soccer. , 1998, Research quarterly for exercise and sport.

[32]  K. M. Newell,et al.  Stochastic processes in postural center-of-pressure profiles , 2006, Experimental Brain Research.

[33]  Marc H. Raibert,et al.  Legged Robots That Balance , 1986, IEEE Expert.

[34]  K. Newell,et al.  Dimensional change in motor learning. , 2001, Human movement science.

[35]  R. Bootsma,et al.  Dynamics of human postural transitions. , 2002 .

[36]  M. Turvey,et al.  Temporal patterning in cascade juggling. , 1992, Journal of experimental psychology. Human perception and performance.

[37]  D. Bramble,et al.  Running and breathing in mammals. , 1983, Science.

[38]  B G Bardy,et al.  Level of gymnastic skill as an intrinsic constraint on postural coordination. , 1999, Journal of sports sciences.

[39]  G. Schöner Recent Developments and Problems in Human Movement Science and Their Conceptual Implications , 1995 .

[40]  J. Kohl,et al.  Effect of coupling the breathing- and cycling rhythms on oxygen uptake during bicycle ergometry , 2004, European Journal of Applied Physiology and Occupational Physiology.

[41]  G. Schöner,et al.  Learning and recall in a dynamic theory of coordination patterns , 1989, Biological Cybernetics.

[42]  Andreas Daffertshofer,et al.  Learning to juggle: on the assembly of functional subsystems into a task-specific dynamical organization , 2003, Biological Cybernetics.

[43]  K. Newell,et al.  Time scales in motor learning and development. , 2001, Psychological review.

[44]  J. Kelso,et al.  Coordination dynamics of learning and transfer: collective and component levels. , 1997, Journal of experimental psychology. Human perception and performance.

[45]  M. Turvey,et al.  Intermediate motor learning as decreasing active (dynamical) degrees of freedom , 1998 .

[46]  Peter J. Beek,et al.  Phasing and the Pickup of Optical Information in Cascade Juggling , 1994 .

[47]  P. Beek,et al.  The coupling between point-of-gaze and ballmovements in three-ball cascade juggling: the effects of expertise, pattern and tempo , 2002, Journal of sports sciences.

[48]  Gregor Schöner,et al.  Identifying the control structure of multijoint coordination during pistol shooting , 2000, Experimental Brain Research.

[49]  A. Daffertshofer,et al.  Multiple time scales and multiform dynamics in learning to juggle. , 2004, Motor control.

[50]  A. Daffertshofer,et al.  Multivariate Ornstein-Uhlenbeck processes with mean-field dependent coefficients: application to postural sway. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.