Timing and Phase Locking in Cascade Juggling

A natural-physical approach is pursued in uncovering basic timing and phase relations in human rhythmic movement. The approach is based on the theory of nonlinear oscillatory motion, entrained by continuously and discretely distrib- uted forcing. In the context of juggling three balls in a figure-eight pattern, a preliminary modeling attempt of the cyclical hand motion suggested that the dynamics underwriting juggling are captured best by a discretely kicked, highly nonlinear, self-sustained oscillator. Discretely kicked, nonlinear oscillators may be characterized by regime diagrams that depict the periodic (phase-locked) and quasiperiodic (not phase-locked) regimes in which the system can operate depending on the magnitude of the kicks. This article provides evidence for 2-quasiperiodicity and near, but not perfect, phase locking between tl/tf and tu/tf (where tl is the mean time that the hands move loaded with a ball, tu is the mean time that the hands move empty, and tf is the mean flight time of the balls). Jugglers perform along the boundaries of Arnol'd tongues (representing complete phase locking) in a regime diagram without actually entering into them. With the help of Denjoy's decomposition of phase modulation into a fast and a slow mode, the deviation from the potential minimum defined by complete phase locking can be understood. The frequency ratios within the continuous relative phase between the two juggling hands reveal a Farey type of phase-locking structure, allowing a qualitative insight into which regimes jugglers position themselves when asked to speed up or slow down their act. Modulation of the hand movements increases when timing constraints become more severe (e.g., when the number of balls in the air increases). The modified standard map promises to he an adequate tool in analyzing the phase progression in juggling. All in all, the results favor an understanding of rhythmic movement in terms of discretely forced, nonlinear dynamics, rather than fully autonomous, self-sustaining oscillators.     

Coordination changes in the early stages of learning to cascade juggle

The experiment was setup to examine the coordination changes in assembling the movement form of 3-ball cascade juggling. Eight adult participants learned to juggle over 4 weeks of practice. Juggling scores were recorded at each session and performance was videotaped at eight selected sessions for purposes of movement analysis. Once the basic spatial and temporal constraints on cascade juggling were satisfied, and the figure-8 juggling mode was established, temporal modulations of the relative motions of the hands were emphasized. All participants learned to juggle and the increase over practice in the number of consecutive balls caught was best fit with a power law. The non-proportional rate of performance increment was consistent with the qualitative changes in the form of the hand and ball movement kinematics that occurred over practice.     

Temporal and spatial factors reflecting performance improvement during learning three-ball cascade juggling

Beek and van Santvoord [Beek, P. J., & van Santvoord, A. A. M. (1992). Journal of Motor Behavior, 24, 85-94] proposed a three-stage model of learning to juggle based on group analyses of temporal measures. Here, we examined in detail how the temporal and spatial features of juggling evolved in eight individual participants progressing from the second to the third stage of learning. During the second stage, the dwell ratio, defined as the ratio of the time that the juggler holds a ball between catch and toss and the hand cycle time (HCT), was stable when it was about 0.83. The subjects with a dwell ratio near this value and controlled throws exhibited stable juggling, whereas the subjects with a dwell ratio of 0.80 or smaller exhibited unstable juggling. Compared to the former group, the latter group had a longer time from the throw of a ball to the arrival at its zenith (TZ), and a shorter time between the arrival of an airborne ball at its zenith and the subsequent throw (IZR). The latter group also exhibited larger variability in the dwell ratio and IZR. With practice, the subjects appropriated, on average, the duration of TZ and IZR to the dwell ratio and improved the ability to accurately throw balls by changing the motions of the limb segments involved. Although these changes helped to stabilize the performance during the second stage, the variability problem was not sufficiently resolved. Only two out of eight subjects passed on to the third stage by the last (10th) Session. They achieved small variability in IZR, dwell ratio, and flight paths of the ball while juggling with short HCTs and small dwell ratios. These results suggest that the reduction of variability in these variables was essential to pass on to the third stage.     

Learning the cascade juggle: a dynamical systems analysis

How beginning jugglers discover the temporal constraints governing the juggling workspace while learning to juggle three balls in a cascade pattern was the subject of this investigation. On the basis of previous theoretical and experimental work on expert jugglers, we proposed a three-stage model of the learning process, for which objective evidence was sought. The first stage consists of learning to accommodate the real-time requirements of juggling, as expressed in Shannon's equation of juggling, which states that, averaged over time, the cycle time of the hands should be a fixed proportion of the cycle time of the balls. The second stage of learning consists of discovering the primary frequency lock of.75 between the shorter term dynamical regime underlying the repetitive subtask of transporting a ball and the longer term dynamical regime underlying the total hand loop cycle. The third and last stage of learning consists of discovering the principles of frequency modulation from.75 to lower (averaged) values of the proportion of time that a hand carries a ball during the total hand cycle time. Twenty subjects were taught to juggle three balls in a cascade pattern. Ten subjects were trained with the aid of an instructor and a metronome, and 10 with the instructor only. The metronome proved to be of no particular additional help, but the timing results obtained were in agreement with the proposed three stages of learning. The picture that emerged from this study was that learning a new motor skill involves the discovery of invariance's or fixed points in the perceptual-motor workspace associated with that skill, from which excursions can be made and the skill further refined. Because these fixed points afford stability of operation, discovering them logically and factually precedes the acquisition of the functional adaptability and flexibility of operation ("flair") inherent to frequency modulation.     

Phasing and the Pickup of Optical Information in Cascade Juggling

Four experiments were conducted to examine the relationship between the phasing of hand movements and the pickup of optical information in cascade juggling. Three jugglers of intermediate skill juggled three balls while wearing liquid crystal (LC) glasses that opened and closed at preset intervals. The first experiment, in which the duration of the viewing window was gradually reduced to zero, revealed a preference for seeing the segment of the ball flight following the zenith in one subject; such a preference was hinted at in the other two subjects. The second experiment, in which the tachistoscopic rhythm of the glasses was perturbed, showed that, in the case of a stable phase lock, the phasing of the hand movements was adjusted to restore the visibility of the segment following the zenith when it was lost. The third experiment, however, revealed that, after practice, the jugglers did not become better attuned to the optical information contained in this segment. The fourth experiment, in which two jugglers per- formed a cascade together while viewing the ball flights intermittently, suggested that haptic information about the trajectories of the balls to be caught is not necessary for subsequent catching: Optical information picked up during brief intervals of viewing was sufficient to perform the task equally well as when they juggled alone (i.e., when haptic information about the throws was available). Although, admittedly, the results raised only a tip of the veil covering the perceptual basis of juggling, they testify to the potential power of the new technique that was used to let subjects themselves reveal what optical information is relevant for performance.     

Does transfer of training help children learn juggling?

The effectiveness of four different learning sequences in teaching juggling to 5th grade students was investigated. Practice schedules using combinations of scarves, weighted scarves, beanbags, and balls allowed both identical task elements and learners' time-on-task to be varied during a 3-wk. practice period. The exclusive use of beanbags for practice, prior to testing with balls, resulted in significantly better juggling scores than did the other combinations. While transfer of training occurred for other groups, the amount of students' time-on-task during practice appeared to be a strong influence on final performance.     

Pattern Stability and Error Correction During In-Phase and Antiphase Four-Ball Juggling

The authors studied pattern stability and error correction during in-phase and antiphase 4-ball fountain juggling. To obtain ball trajectories, they made and digitized high-speed film recordings of 4 highly skilled participants juggling at 3 different heights (and thus different frequencies). From those ball trajectories, the authors determined and analyzed critical events (i.e., toss, zenith, catch, and toss onset) in terms of variability of point estimates of relative phase and temporal correlations. Contrary to common findings on basic instances of rhythmic interlimb coordination, in-phase and antiphase patterns were equally variable (i.e., stable). Consistent with previous findings, however, pattern stability decreased with increasing frequency. In contrast to previous results for 3-ball cascade juggling, negative lag-one correlations for catch-catch intervals were absent, but the authors obtained evidence for error corrections between catches and toss onsets. That finding may have reflected participants' high skill level, which yielded smaller errors that allowed for corrections later in the hand cycle.     

Pattern stability and error correction during in-phase and antiphase four-ball juggling

The authors studied pattern stability and error correction during in-phase and antiphase 4-ball fountain juggling. To obtain ball trajectories, they made and digitized high-speed film recordings of 4 highly skilled participants juggling at 3 different heights (and thus different frequencies). From those ball trajectories, the authors determined and analyzed critical events (i.e., toss, zenith, catch, and toss onset) in terms of variability of point estimates of relative phase and temporal correlations. Contrary to common findings on basic instances of rhythmic interlimb coordination, in-phase and antiphase patterns were equally variable (i.e., stable). Consistent with previous findings, however, pattern stability decreased with increasing frequency. In contrast to previous results for 3-ball cascade juggling, negative lag-one correlations for catch-catch intervals were absent, but the authors obtained evidence for error corrections between catches and toss onsets. That finding may have reflected participants' high skill level, which yielded smaller errors that allowed for corrections later in the hand cycle.     

Goal-directed imitation: the means to an end

The effects of goal-directed imitation and observational learning were examined whilst learning a goal-directed motor skill (three-ball cascade juggling). An observational learning (OL) group observed a model and a control (CON) group received minimal verbal instructions regarding how to hold and release the juggling balls. The OL group performed more juggling cycles across practice and retention than the CON group. In addition, the OL group's upper limb coordination and ball flight trajectory pattern were more similar to the model's movements than the CON group. These data show that when the to-be-learnt movement pattern and end-goal are not specified by the task's mechanical constraints, or can be achieved by modifying a pre-existing motor skill, individuals have difficulty learning on the basis of discovery processes alone. Under these circumstances, observational learning is effective because it conveys to the individual the specific means by which the end-goal can be achieved. These findings lead us to suggest that when the end-goal and the means to achieve the end-goal are directly linked, the means are given sufficient weight in the goal hierarchy such that the model's movement is imitated.     

Multiple information sources in interceptive timing

This study was designed to explore the limitations of tau (τ) as an explanatory construct for the timing of interceptive action. This was achieved by examining the effects of environmental structure and binocular vision on the timing of the grasp in a simple one-handed catch. In two experiments, subjects were required to catch luminous balls of different diameters (4, 6, 8 and 10 cm) in a completely darkened room. In the first experiment the influence of the presence vs. absence of an environmental background structure (both under monocular viewing) was tested, and in the second experiment the influence of monocular vs. binocular vision was examined. It was found that irrespective of the presence of environmental structure, an effect of ball size occurred in the monocular viewing conditions. That is, in monocular viewing conditions the grasp was initiated and completed earlier for the larger balls as compared to the smaller ones, while in the binocular viewing condition subjects behaved in accordance with a constant time to contact strategy: no effects of ball size were found. It is concluded that under binocular viewing a binocular information source is used, while in the monocular viewing condition a lower order information source like image size or image velocity is probably involved.     

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.     

The Effect of Load Uncertainty on Neuromotor Control in Catching: Gender Differences and Short Foreperiods

Abstract

To reveal how the CNS copes with load uncertainty in catching, electromyography (EMG) was recorded in 15 females and 14 males while catching visually identical balls of known and unknown weights under varied (1–10?s) and constant (1?s) foreperiods (warning time). EMG integrals, which represented total muscle activity, were computed for three time intervals prior to the catch (anticipatory), and one interval after (compensatory). Load uncertainty caused the CNS to utilize an anticipatory strategy in several muscles, primarily during the ball-flight interval, characterized by preparation to catch balls of unknown weight by utilizing an average of 99.7% of the muscle activation used to catch the heaviest ball under the known weight condition. The constant 1?s foreperiod, which permitted precise temporal anticipation of ball release, did not influence the anticipatory strategy adopted by the CNS to cope with load uncertainty. There were no observed differences in the neuromotor control used by men and women to manage load uncertainty in catching, although there was an interesting difference in the way men and women employed the triceps to prepare to catch balls of a known weight.     

Timing the Selection of Information During Rhythmic Catching

Catching a ball requires that information be available close to the catch but early enough for prospective or corrective control. In the present experiment, 6 participants were asked to throw and catch a ball continuously for 1 min while wearing liquid-crystal goggles that restricted viewing to specific amounts of time at specific intervals. Participants were free to select the information by varying the frequency and phasing of throwing relative to the goggles. Video analysis revealed that they elected a frequency of throwing that matched the goggle frequency and chose to view the ball at or around its zenith. Earlier portions of the ball's trajectory were viewed as the goggle frequency increased. Despite variations in the viewing location, participants elected to view the ball on average 365 ms before the catch. Analysis of the hand's trajectory further revealed that the time interval (M = 82 ms) between the ball's zenith and the initiation of the final motion of the hand toward the catch did not vary as a function of the frequency of throwing. The authors conclude that the timing constraints imposed by the hand's movement are the basis for the selection of information for catching.     

The influence of juggling on mental rotation performance in children with spina bifida

This study examined the influence of juggling training on mental rotation ability in children with spina bifida. Children between the ages of 8 and 12 solved a chronometric mental rotation test. Half of the children received juggling training (EG) over an 8week time period; the other half did not receive training (CG). Afterwards, all participants completed the mental rotation test again. Children of the EG showed a significant decrease in reaction time and an increase in mental rotation speed compared to the control group. This indicates that juggling improves the rotation in the mental rotation process in children with spina bifida.     

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.     

The generalized optic acceleration cancellation theory of catching

The generalized optic acceleration cancellation (GOAC) theory of catching proposes that the path of a fielder running to catch a ball is determined by the attempt to satisfy 2 independent constraints. The 1st is to keep the angle of elevation of gaze to the ball increasing at a decreasing rate. The 2nd is to control the rate of horizontal rotation necessary to maintain fixation on the ball. Depending on the lateral velocity of the ball relative to the fielder, this rate may be zero or constant at a negative or positive value. The authors show that a simulated fielder implementing the GOAC strategy follows a path indistinguishable from that of real fielders running to catch balls thrown on the same trajectories.     

Assume a Spherical Chicken: Analytic Constraints,Inertia Tensor Information,and Wielded Rod Length Perception

Information associated with the inertia tensor is the preeminent explanation for haptic perception of object properties, notably wielded rod length. Critics counter that tensorial-based information requires non-tensorial supplementation (mass, torque). However, those critiques omit important constraints. With relevant constraints included, the inertia tensor alone completely specifies rod length. I list constraints inherent (but tacit) in haptic rod length perception, and show that object properties associated with the inertia tensor are invariant, even with constraints removed, by involving (a) longitudinal moment equivalents for rod mass and (b) derivatives of moments with respect to varying rotation axes. Analytic outcomes show tensorial-based information is a robust basis for wielded rod length perception, and suggest open questions for empirical exploration.     

Multiple role juggling and daily mood states in working mothers: an experience sampling study

The effects of multiple role juggling (i.e., simultaneously attending to demands of different roles) on daily mood states of employed mothers were examined. Ss completed activity and mood questionnaires 8 times a day for 8 days. Multiple role juggling had immediate negative effects on task enjoyment and mood. However, contrast effects and habituation to role juggling occurred when mood and satisfaction were examined over time. Furthermore, mood states tended to spill over from one episode to the next within a day, but contrast effects were found across days. These results reflect the complex nature of psychological adjustment to multiple role occupancy.     

Planning and on-line control of catching as a function of perceptual-motor constraints

Two experiments were conducted in order to investigate the adaptability and associated strategies of the human perceptuo-motor system to deal with changing constraints. In a catching task, perceptual-motor constraints were internally controlled by coupling movement onset of the catch and the illumination circuit in the lab: upon the first movement of the catcher, all lights went out within 3 ms. The authors studied (a) how much movement time catchers prefer if no visual information is available after movement onset, and (b) how movement execution changes under such temporal constraints. It was hypothesised that, in order to accomplish successful catching behaviour, (1) movement initiation would be postponed in order to allow sufficient information uptake before the lights went out, and (2) an alternative control strategy would have to be mobilised, since on-line control becomes inappropriate when catching in the dark. In the first experiment, the adaptation process to the light-dark paradigm was investigated. In the second experiment, the conclusions from experiment 1 were challenged under varying ball speeds. In order to maintain catching performance, subjects initiated the catch approximately 280 ms before ball-hand contact. Next to changes in temporal structure of the catch and subtle kinematic adaptations, evidence for a change in the control mode emerged: while an on-line control strategy was adopted under normal illumination, catching movements seemed to be executed as planned in advance when catching in the dark. Additionally, perceptual constraints seem to determine the time of movement initiation, rather than motor constraints. These results emphasize the capability of the human perceptuo-motor system to adjust promptly to new task constraints.     

The Optics and Actions of Catching Fly Balls: Zeroing Out Optical Acceleration

Advancing or retreating so as to maintain a projectile's constant vertical optical velocity was suggested by Chapman (1968) as a possible basis for locomotion in ball catching. Three experiments examined this thesis. In Experiments I and 2, the positions of balls and catchers were videotaped to see if the movements of the catchers canceled optical acceleration. Such canceling was indeed observed until just prior to the catch for hand-thrown balls (Experiment 1). The monocular availability of the information predicts success with monocular viewing, confirmed in Experiment 2 with machine-thrown balls. In Experiment 3, observers judged whether a ball (represented as a moving dot on a computer screen) would land at, in front of, or behind them. Performance was above chance, but only some observers used acceleration. Together, the experiments provide broad, though not unequivocal, support for the utilization of optical acceleration to guide locomotion in catching.