|
|
  |
|
| |||||||||||||||||||||||||||||||||
|
|||||||||||||||||||||||||||||||||
|
Bifurcations and Self-Organized
Criticality in Motor Learning |
 |
||||||||||||||||||||||||||||||||
|
There are two categorically different
motor learning phenomena: acquiring a never-produced-before new
motor task and improving an already-acquired-motor coordination
performance. Most of the theoretical and empirical research
literature in motor learning has been concerned with the latter
phenomenon although emergence of new coordination patterns of
movement maybe the most commonly encountered situation in practice
and also the most interesting condition in motor learning. From the
attractor dynamics framework of dynamical systems theory, the
qualitative changes in movement organization are reflections of
bifurcations between attractor organization and the transient
phenomena associated with moving toward and away from the
fixed-point dynamics. Hereby the fixed point dynamics corresponds to
the movement patterns performed before learning got started and the
learning goal that will be approached through practice. In the HKB model (Haken, Kelso, & Bunz, 1985), an inversed pitchfork bifurcation was observed when the relative phase of the two finger movement switched from anti-phase to in-phase as the frequency of the oscillatory movement exceeds a critical value. For the motor learning situation, practice time has been identified as the relevant control parameter that is closely related to the skill level of the performer. Within the framework of attractor dynamics, we modeled one motor learning task, the “roller ball task”, by the dynamics involving two fixed points namely initial failure to perform the task and eventual success after sufficient practice time. We showed that we can observe a transition in coordination mode between these two fixed points that was preceded by enhanced performance variability (Liu, Mayer-Kress, & Newell, 2006). Although practice time is a relevant control parameter in the motor learning process, the observation that different roller balls took different amount of practice trials for the coordination transition to occur indicating that task difficulty may also play a role in modulating the learning dynamics (cf. Guadagnoli & Lee, 2004). At a given level of task difficulty, increasing practice time may lead to the transition from the “failure” mode to the “success” mode; increasing the task difficulty however, may reach a point where the “success” mode is no longer stable and a transition to the “failure” mode occurs. By introducing the second control parameter, task difficulty, as a dual to the practice time, we were able to demonstrate the repeated coordination transitions from the same individual performer. Many natural systems exhibit the phenomenon of self-organized criticality where the system spontaneously develops into a critical state (Bak, 1996) and minor perturbations can lead to a qualitative change of behavior (phase transition/bifurcation/catastrophe – e.g., Guastello, 1984; Haken, Kelso, & Bunz, 1985; Van Der Maas & Molenaar, 1992). In the classic example of sand pile behavior, grains are randomly dropped onto a surface. |
As the pile grows, avalanches occur with
frequency and size that increases with its control parameter, the
slope of the pile. It is the slope of the sand pile, when it reaches
the critical value, that triggers avalanches of any admissible size.
The condition of criticality is self organized in the sense that it
is attractive in the space of the control parameter, namely slope:
To achieve criticality it is not necessary to fine-tune the control
parameter but to merely add grains of sand. In the motor learning process, a critical condition is the point where a learner experiences the transition from failure to success during practice. The increasing practice time during learning can be considered in the same way that grains of sand are added to the sand pile. Once the critical point is reached and avalanches occurs the slope of the sand pile will be reduced to the sub-critical level. This corresponds to the widely observed phenomenon that unsupervised learners universally increase the task difficulty once the task at a lower difficulty level is securely mastered. Continuing dropping the grains of sand will build up the slope of the pile again until reaching the next critical point. For the case of motor learning, continuing practicing which is equivalent to reducing task difficulty will lead to the transition of coordination mode therefore successfully performing the task. Once the successful performance is obtained the success rate of performing the task will increase to the maximum level until the task difficulty is raised again. The dual control parameters of the learning dynamics form a control space which determines the critical condition of the dynamics. When the skill level is low (lack of practice) or the task difficulty is high the probability of success is very low therefore making a less effective leaning process due to loss of motivation, never realizing a success or forgetting what successful performance feels like. On the other hand, when the success probability is very high the challenge and the motivation will be reduced (Atkinson, 1957) therefore influence the learning effect as well. We predict that when the learner has control over the selected task difficulty during practice, that there would exist an attractive critical manifold in the skill/difficulty space that has the optimal success rate of 50 %. By way of the roller ball task and the dual control parameters, we were able to demonstrate that self-organized criticality practice condition provided a higher improvement rate in performance outcome than a traditional progressively increasing difficulty condition. We also observed a close to 50% success rate in the self-organized criticality practice condition as theoretically predicted. We also could show that a properly oriented cusp manifold in the sense of catastrophe theory (Thom, 1972) will allow us to construct the critical parameter combinations in the control space. Preliminary experimental data are very well in agreement with this theoretical framework. How can these findings benefit the sport science practitioner and their coaches? On an informal level, experienced coaches certainly were aware of “skill matching difficulty” principles. Here we put this concept into a more quantitative formal context that might make it possible to anticipate when these conditions will be reached and therefore help organizing and optimizing individualized practice schedules. |
||||||||||||||||||||||||||||||||
|
|
|||||||||||||||||||||||||||||||||
