Constrained paths based on the Farey sequence in learning to juggle.

In this article we report the results of a study conducted to investigate the learning dynamics of three-ball juggling from the perspective of frequency locking. Based on the Farey sequence, we predicted that four stable coordination patterns, corresponding to dwell ratios of 0.83, 0.75, 0.67, and 0.50, would appear in the learning process. We examined the learning process in terms of task performance, taking into account individual differences in the amount of learning. We observed that the participants acquired individual-specific coordination patterns in a relatively early stage of learning, and that those coordination patterns were preserved in subsequent learning, even though performance in terms of number of successful consecutive throws increased substantially. This increase appeared to be related to a reduction in spatial variability of the juggling movements. Finally, the observed coordination patterns were in agreement with the predicted patterns, with the proviso that the pattern corresponding to a dwell ratio of 0.50 was not realized and only a hint of evidence was found for the dwell ratio of 0.67. This implies that the dwell ratios of 0.83 and 0.75 in particular exhibited a stable coordination structure due to strong frequency locking between the temporal variables of juggling.