Emergent motor timing enhances time perception

Summary

Precise timing underlies many behaviors, from musical performance to navigating a dynamic environment. This study examined how stable temporal patterns that emerge during goal-directed movements influence timing acuity in perceptual discrimination. Rather than relying on explicitly timed actions, we used a self-paced throwing task in which temporal structure develops implicitly with practice. Across three experiments, participants were trained for four days, developing stable motor timing reflected in consistent “ball release times.” This emergent timing selectively enhanced sensitivity to matching temporal intervals in a perceptual discrimination task. Importantly, this effect was not explained by perceptual learning and persisted over several weeks, suggesting a durable motor-perceptual linkage. The results point to a shared representation of time in action and perception, an emergent timing primitive that arises through experience in spatiotemporal movements. These findings shed light on how motor learning can shape temporal perception in ecologically relevant contexts, with implications for rehabilitation and sensorimotor integration.

Graphical abstract

Highlights

• •Stable motor timing enhances perceptual sensitivity to matched intervals
• •Self-paced movement induces a shared temporal structure for action and perception
• •Perceptual gains persist beyond training, suggesting durable motor–perceptual links
• •Implicit timing in motor learning shapes temporal perception without explicit cues

Neuroscience; Behavioral neuroscience; Cognitive neuroscience; Psychology

Introduction

One notion that probably all neuroscientists, cognitive scientists, and experimental psychologists agree upon is that behavior comprises perceptual, cognitive, and motor systems, each divided into functionally relevant subdomains.¹ While few would claim that these domains are strictly independent, in practice, they nevertheless tend to be studied in isolation. This “silo” approach reifies these (sub-)systems as distinct entities that are expected to have identifiable biological substrates. This leaves behind the fact that in real-life behaviors, motor circuits operate smoothly in concert with perceptual and cognitive systems.^2,3,4,5,6 Time seems to be the “glue” that seamlessly unites these domains: we coordinate movements to external events with strikingly accurate timing; we perceive others and communicate by generating and interpreting temporally patterned sounds in speech.⁷ The synchronization of perceptual, cognitive, and motor processes is at the root of all successful behavior. Here, we embraced this interconnection and explicitly examined how timing in the motor and perceptual systems is tightly intertwined.⁸

Prior studies have demonstrated extremely precise timing in skilled movements: for example, professional table tennis players hit a ball within a time window of 4 ms⁹; a baseball batter can see a pitch, start a swing, and get the bat at the right place and time within less than 600 ms.¹⁰ The notion that coordinated behavior relies upon an internal representation of time, a “clock,” has been germane to numerous lines of research. Many psychological approaches developed models of clock-like timing, especially for time perception.^{11,12,13,14,15,16,17,18,19}

However, there has also been growing concern over the clock metaphor in human motor performance. Over the past decades, research in motor neuroscience has recognized that movement control is unlikely to be a solely top-down cortically controlled process. Rather, it is a dynamic process arising from all levels of the neuromechanical system. Any movement not only unfolds over time, but is also constrained by limits set by the limb system and the task.^20,21 While the spatiotemporal pattern of a new movement skill is initially highly variable in space and time, this variability attenuates with practice.^22,23,24 Importantly, over many repetitions, movement timing can develop a stable pattern. Turvey and colleagues have argued that temporal regularities in motor coordination are emergent properties of a self-organizing dynamic system.^25,26 From this perspective, movements do not require a timekeeper. Rather, timing is implicit and manifests via a dynamic process that evolves within the complex neuromechanical system.

One intriguing question would be whether such stable spatiotemporal patterns in movement can also impact the perception of temporal intervals. Relatively little attention has been paid to the active contribution of neuromotor processes to the perception of time, because studies on time perception have typically used movements only to mark the endpoints of a timed process. Put in simple terms, the implicit assumption has been that the brain controls when and how to move, and the motor system generates an output in accord with these cortical timing commands.^{10,27,28,29,30}

A growing body of research has, however, identified a link between motor timing and time perception. Keele et al. were the first to report a positive correlation between time perception and simple motor tasks.³¹ Using rhythmic single-finger tapping, individuals who displayed larger timing variability also demonstrated lower acuity in time perception. Ivry and Hazeltine showed that variability in both perception and action tasks increased similarly over increasing temporal intervals.³² In addition, simultaneous movements can not only create biased time estimates, but can also make them more precise.^19,30 Neural data also revealed that similar brain regions, such as motor circuits in the supplementary motor area (SMA) and subcortical regions, are involved both in time perception and motor timing via cortico-striato-thalamic connections.^33,34,35 Collectively, these findings support a close connection between motor and perceptual timing.

While previous research has not fully resolved whether perceptual and motor systems merely represent time in a similar fashion or whether they share a common mechanism,^36,37 this study aims to take a one step forward by directly juxtaposing motor and perceptual tasks to test whether temporal patterns that were developed through motor practice transfer to perceptual time judgments. According to theories of learning, transfer to another situation is facilitated by the similarity between the two situations or substrates.^38,39,40 Simply put, if there is nothing in common, information learned in one situation will not be of any value in the other situation. We hypothesized that as spatiotemporal patterns in skilled movements emerge from basic dynamic processes during practice, this emergent timing serves as an amodal “primitive” that pervades perceptual and possibly also cognitive processes. It is worth noting that previous research found that improved perceptual sensitivity was context-specific and, as such, did not generalize to other perceptual tasks.^41,42 Therefore, without a shared timing mechanisms, any direct effect of motor timing on perceptual timing is unlikely.

To evaluate the hypothesis of an amodal timing primitive, we employed a virtual throwing task, called skittles, where motor timing emerged as a by-product of goal achievement (Figure 1). Skittles is a virtual target-oriented throwing task similar to the American playground game tetherball (Figure 1A). In this virtual version of the game (Figure 1B), each throw is an independent and discrete event (Figure 1C). Success depends solely on the angle and velocity at the moment of ball release (Figure 1D). Participants were instructed to hit the target as often as possible. Critically, they received no instructions regarding motor timing, such as when to release the ball or the duration of the throwing movements, as these were not relevant for success (Figure 1E). In direct succession to the motor session, we employed a time-interval discrimination task (Figure 2) to investigate whether the temporal patterns emerging in the increasingly stable throwing movements of skittles influenced the auditory discrimination of similar temporal intervals. To prevent any perceptual learning component, we provided no feedback on the time-interval performance and also limited the number of trials to those minimally required for reliable discrimination evaluation.

Figure 1.

The throwing task skittles and its motor timing

(A) Model of the skittles task.

(B) Experimental setup of the virtual skittles task. The lever height was adjusted so that the upper arm formed a 45$°$ angle relative to the trunk. The participant grasped a real ball that was fixed at the distal end of the lever. The virtual ball was released, i.e., “thrown” toward a target, by lifting the index finger from a force sensor. Angular displacements of the lever arm were measured at 1000 Hz by an optical encoder. The display showed the paddle representing the arm, and the starting position. The ball, shown as a small white circle, detached after release and traversed around the red center post to hit a target shown as a yellow circle.

(C) Top-down view of the skittles workspace. The larger red circle is the post, the small yellow circle is the target, and the pink bar is the lever arm. Errors were defined as the minimum distance between the target and the ball trajectory. Two ball trajectories (dashed lines) pass within the 1 cm error threshold, regarded a successful hit; the third ball trajectory (solid line) exemplifies an unsuccessful throw, with the error defined at the trajectory’s minimum distance to the target.

(D) Solution space of the skittles task, spanned by angle and velocity of the arm at ball release. The green band denotes the solution manifold, comprising all angle and velocity combinations, where the throw results in errors below the 1 cm threshold. Two representative arm trajectories and their ball releases are plotted (red and blue lines); the white dots represent the ball releases. The orange color shading codes the error. The release point on the red trajectory resulted in a large error, while the release point on the blue trajectory was a successful hit as it intersected with the solution manifold.

(E) Velocity profile of the arm trajectory of two successive throws with the landmarks onset, ball release, and offset. The red dot indicates the ball release moment at trial n and trial n+1. Two intervals of potential salience were defined: ball-release time and movement time.

Figure 2.

Time-interval discrimination task

(A) Trial structure. Participants compared the time intervals of two pairs of beep sounds and reported whether the comparison interval was “shorter” or “longer” than the standard interval. The Δt for every standard-interval t condition was determined by a QUEST+ procedure.

(B) Estimation of the auditory discrimination threshold. Threshold is defined as ½ × (the distance between the stimulus value at 84% “longer” response and the stimulus value at 16% “longer” response), which corresponds to 1 SD of the fitted cumulative normal function. A cartoon psychometric function is shown for illustrative purposes, including threshold and SD.

In principle, temporal patterns during skittles could emerge in both ball-release times and the overall throwing movement durations (Figure 1E). We did not have a priori hypotheses about whether one or both would selectively influence subsequent perceptual time-interval discrimination. In a series of three experiments, we evaluated whether and how the temporal intervals developed during training, such as ball-release time and movement time, influenced a corresponding auditory time interval discrimination.

In Experiment 1, we demonstrated that with throwing practice, participants acquired a stable motor pattern which, in turn, enhanced their sensitivity to time-interval discrimination, specifically in relation to ball-release time. However, within each individual, we did not observe a linear relation between an individual’s improvement in throwing and their perceptual discrimination sensitivity. We conjectured that this lack of a strong dependency might be due to some participants exhibiting relatively atypical throwing actions, which did not display the typical profile of a ballistic throw (see supplemental information, Method S1, and Figures S1–S3: Differences in Throwing Strategies in Experiments 1 and 2).

To address this conjecture, Experiment 2 introduced a variation of the throwing task eliciting a different temporal pattern, resulting in more typical velocity profiles of ballistic throwing movements. Both at the group level and at the individual level, these throwing movements gave rise to much stronger relations between the temporal profile of the trained movement and the enhanced sensitivity to time-interval discrimination, specifically linked to ball-release time. Within individuals, they showed that the more they improved their throwing movements, the better their time perception became over days. We also demonstrated that this motor-perceptual timing association persisted for several weeks.

In addition, Experiment 3 confirmed that without throwing practice, simply repeating the same time-interval discrimination task across multiple days did not lead to perceptual improvements. Therefore, the findings from Experiments 1 and 2 could not be solely attributed to the mere repetition of motor and perceptual tasks across days. Together, this study provides strong evidence that improved motor timing can enhance the discrimination of similar time intervals, consistent with the notion of an emergent timing primitive, suggesting the need for further investigation into the underlying mechanisms.

Results

Experiment 1: Training in motor timing enhances time perception

Experiment 1 investigated whether throwing practice in skittles (Figure 1) increased the sensitivity of time-interval discrimination (Figure 2) and, if so, whether this enhancement was selectively linked to the timing of the practiced movement. Our hypothesis was that with training a self-paced goal-oriented movement, a stable temporal structure emerges that embraces both the motor and perceptual domains and therefore enhances the perceptual discrimination of this interval. Consistent with advances in motor neuroscience,^43,44 we posit that such a stable temporal structure is a dynamic primitive governing both motor and perceptual processes.

Participants practiced throwing a ball to hit a target skittle in a virtual environment over multiple days. They were asked to start each throw from a rest position, indicated on the display by a line to match with the manipulandum (Figure 1B). There were no explicit instructions on the timing of the action: participants could choose their preferred velocity profile and initiate the ball throw at their self-chosen pace. The only instruction was to throw the virtual ball to hit the virtual skittle as accurately as possible. Figure 1C illustrates the x-y coordinates of the workspace as a top-down view with 3 exemplary ball trajectories traversing around the center post; the target is the small yellow circle at the left. Importantly, the task has redundancy: infinitely many arm trajectories with infinitely many combinations of angle and velocity at ball release can lead to task success. However, for each arm angle and velocity at release, the error was fully determined. Figure 1D shows the solution space of the task as it is spanned by the angle and velocity of the arm at ball release. The color codes the error, with darker shades of orange indicating larger errors. The green band comprises all angle-velocity combinations at ball release that lead to errors less than 1 cm from the target center, i.e., it denotes the solution manifold. The red trajectory from early practice had a ball release in the orange-colored area that resulted in a large error; the blue trajectory from later practice resulted in zero error as the ball release occurred directly when intersecting the solution manifold.

An important feature of the skittles task is that different arm movements can result in the same error or target hit, and the same arm trajectories could result in different errors when the ball was released earlier or later. Critical for the analyses below is that task success is determined only by the angle and velocity at ball release and not by the time interval from onset to ball release. Despite this redundancy, previous work already showed that individuals tended to converge toward a preferred trajectory with a relatively invariant temporal pattern, becoming a stable pattern, i.e., a dynamic primitive.⁴⁵

To determine how the timing of the movement evolved, the trajectory of the arm, specifically its velocity profile, was analyzed. Figure 1E shows an exemplary arm trajectory over two successive throws, n and n+1. The trajectory at both throws reveals a relatively invariant temporal pattern: following the onset of the movement, the velocity increased and the ball was released in the vicinity of peak velocity. Then, the arm velocity decreased as the participant resumed the start position for the next throw. This time profile was parsed into two intervals: 1) ball-release time, defined as the interval between the movement onset and ball release; 2) movement time, defined as the interval between movement onset and offset.

Following each throwing session, participants performed the time-interval discrimination task, in which they compared the intervals of two pairs of tones and reported which interval was longer by pressing one of the two keys; no performance feedback was given.³¹ The first pair was the standard interval t, which was pre-determined based on the temporal intervals measured in the motor task, e.g., ball-release time and movement time (Figure 2). The second pair formed the comparison interval, which was either shorter or longer than the standard interval (±Δt) based on a Bayesian adaptive procedure called QUEST+.⁴⁶ Each standard interval was tested separately in a different block to estimate the duration discrimination threshold. There were 10 practice trials plus 70 experimental trials per block. To assess the reliability of participants’ discrimination thresholds across days and standard durations, we analyzed the mean and standard deviation of final posterior distributions from the Quest+ algorithm. The results confirmed that it consistently converged on stable parameter estimates for each standard interval across days⁴⁶ (see supplemental information, Method S2, and Figures S4 and S5: Analysis of Posterior Distributions from Quest+ Algorithm).

On Day 1, participants performed the time-interval discrimination task with three standard intervals. Two were associated with the motor timing intervals extracted from the skittles task, and one was an unrelated control interval (Figure 3). According to our pilot results, the standard intervals in Experiment 1 were set to 500 ms (linked to the ball-release time), 800 ms (linked to the movement time), and 300 ms (unrelated time). On Days 2–5, participants practiced skittles with 320 trials on each day, which took approximately 30min. Following each motor training session, participants performed the auditory duration discrimination task as on Day 1.

Figure 3.

Timeline of the motor and perceptual tasks across the five daily sessions in Experiment 1

On Day 1, the baseline of the time-interval discrimination threshold was measured. From Day 2 to Day 5, participants first performed the motor task and then the time-interval discrimination task in each of the five daily sessions.

Does timing in the goal-directed motor task stabilize and affect perceptual timing?

A first assessment of throwing performance verified that participants learnt and improved in the task over the 4 practice days. Two metrics evaluated performance changes with practice: the success rate of hitting the target and the error. Success rate was defined as the percentage of throws that achieved an error below the threshold of 1 cm (touching the target). Performance error was defined as the minimum distance between the target and the ball’s trajectory, regardless of its location in work space (Figure 1C). As shown in Figure 4, over the course of practice, the success rate increased significantly, supported by a one-way repeated-measures ANOVA with Day as the main factor, F(3,69) = 29.241, p < 0.001, η² = 0.594. Concomitantly, a second ANOVA for performance error revealed a significant decrease, F(3,69) = 46.737, p < 0.001, η² = 0.700.

Figure 4.

Motor performance in Experiment 1

(A) Success rate.

(B) Performance error.

Error bars represent the standard error across participants.

The next important question was whether a temporal pattern emerged in the kinematics of the throwing movement. Figure 5A shows the mean durations of the two different segments, ball-release time and movement time, of the arm trajectory across Days 2–5. Even though participants could throw and hit the target with infinitely many different arm trajectories, they settled on a stable movement time with a relatively stable ball-release interval. The ball-release time was around 500 ms, although it exhibited a minor increase throughout the practice from 512 to 535 ms. A one-way repeated-measures ANOVA was weakly significant, F(3,60) = 3.443, p = 0.044, η² = 0.147. The movement time settled on 693 ± 20 ms on Day 1 and remained consistent across days (p = 0.765).

Figure 5.

Timing in motor performance in Experiment 1

(A) Motor timing durations of the two motor intervals, ball-release time, and movement time.

(B) Variability of timing of the two movement intervals (coefficient of variation of ball-release time and movement time).

In both panels, the colors of the dots mark the daily sessions, and the error bars denote the standard error of the mean across participants.

To evaluate whether the temporal pattern of the throwing movements became more stable, i.e., less variable with practice, the variability of ball-release time and movement time was estimated by the coefficient of variation (Figure 5B). The same one-way ANOVA supported the expected declines in variability for both ball-release time, F(3,60) = 6.302, p < 0.001, η² = 0.208), and movement time, F(3, 60) = 3.594, p = 0.031, η² = 0.13. This practice-induced decrease in variability was consistent with previous studies using the skittles paradigm and is also a fundamental finding in motor learning research.^22,24

Of primary interest was understanding how motor timing influenced time-interval discrimination. To explore this, we calculated the Weber fraction, which is the ratio between the estimated discrimination threshold and the standard interval (see Figure 2). A smaller Weber fraction indicates better discrimination. Figure 6A presents the Weber fractions averaged over all participants for the 3 discrimination intervals across the 5 days. The inspection of this figure suggests that the discrimination of the 500 ms interval, corresponding to the ball-release time, improved the most. To assess the Weber fractions over practice, we employed linear mixed models to analyze performance in the three intervals separately. The model was constructed with Day as the fixed effect, and intercepts for participants were included as random effect. As the main interest of the analyses was the trend across days and to keep the model simple and computationally efficient, the slope of the Day effect was fixed across participants. A negative slope indicates that as days progressed, the discrimination threshold decreased, suggesting an improvement in sensitivity to time perception with training.

Figure 6.

Perceptual performance quantified by the Weber fraction in Experiment 1

(A) Weber fraction for the time-interval discrimination threshold of each standard interval across Days 1–5. Smaller Weber fractions indicate better perceptual performance. The slopes of the linear regressions for each standard interval were averaged with error bars representing the standard error across participants.

(B) The linear mixed model applied to the Weber fraction of the standard interval of 500 ms across Days 1–5. The gray lines represent the model’s fixed effect, and the shaded areas indicate the 95% confidence interval of the model prediction.

(C) Regression slopes of Weber fraction for each standard interval. A negative slope indicates that time perception improved with training. The different shades of blue denote the different participants. Only the interval of 500 ms, which was linked to ball-release time, showed a significant reduction. Error bars represent the 95% confidence interval of the estimated parameters. ∗ p < 0.05.

(D) The linear mixed model applied to the relation between the Weber fraction of the standard interval of 300 ms and the ball-release time variability across Days 2–5.

(E) The linear mixed model applied to the relation between the Weber fraction of the standard interval of 500 ms and the ball-release time variability across Days 2–5.

(F) The linear mixed model applied to the relation between the Weber fraction of the standard interval of 800 ms and the ball-release time variability across Days 2–5.

(G) Participant averages of the regression slopes between the ball-release time variability and the Weber fraction of each standard interval. Error bars represent the 95% confidence interval of the estimated parameters. The differences are not significant.

Data and fitted curves for individual participants are available in the data and code availability section.

Figure 6B illustrates the results of the standard interval of 500 ms, where the slope was significant (β = −0.0142). In contrast, the slopes for 300 ms and 800 ms intervals were not significant (all p > 0.28). Figure 6C summarizes the slopes obtained for all three intervals, pooled over individuals. The average slope for the 500 ms interval was significantly different from zero: β = −0.0142 with [-0.0021, −0.0263] as the 95% confidence interval, t(90) = −2.356, p = 0.021); there was no significant change in discrimination for the 300 ms and 800 ms intervals (all p > 0.281). This is a first indication that ball-release time, not movement time, was a salient interval of the throwing action that influences the temporal discrimination of this similar interval.

We conducted the same linear mixed model analyses to determine if performance error, success rate, or movement time predicted the change in the Weber fractions for the three different time intervals. Results showed that there was no significant correlation between performance error and the Weber fraction (all p > 0.15), nor between success rate and the Weber fraction (all p > 0.07), nor between movement time and the Weber fraction (all p > 0.3).

To investigate whether the stabilization of an individual’s motor timing, indicated by decreasing variability in ball-release times, correlated with enhanced perceptual sensitivity over time, a linear mixed model examined whether a reduction in ball-release time variability predicted a decrease in the Weber fraction across Days 2–5 for each individual. The model included ball-release time variability as fixed effects, with participant intercepts as a random effect. Figure 6D illustrates the relationship between ball-release time variability and the Weber fraction for all individuals. None of the three intervals showed a significant within-individual relationship (Figures 6D, 6E, and 6F). A summary of these findings is provided in Figure 6G.

We tested one additional question: given that the individually preferred ball-release times did not uniformly converge to 500 ms, does closeness of the actual ball-release time to the tested 500 ms interval lead to stronger perceptual discrimination? To this end, we correlated the individually averaged ball-release times with the corresponding Weber fractions. The correlations did not identify a significant effect (p = 0.978, rho = 0.0061). Note that given the single Weber fraction, we had to average the ball release times within participants, which reduced the power of this analysis.

To better understand this lack of within-individual relations, we inspected the throwing trajectories of the arm again. Sometimes, the velocity profile of a single throw exhibited two peaks, which is not typical for a ballistic throwing action. Further, the ball release sometimes occurred after the peak velocity, which is also very unusual.⁴⁷ This may have been due to the start location for the arm that was selected to elicit movements in the vicinity of 500 ms. In pilot studies, we had attempted to create an arm-target constellation that would elicit a ball-release time of 500 ms as this interval is frequently studied in timing studies. However, it seemed that for throwing movements, this is a relatively long duration and therefore caused the observed deviations from the typical ballistic movement profile. We therefore reasoned that the lack of the correlation of timing variability with the Weber fraction at the individual level might be due to this atypical throwing imposed by the start and target locations in this experiment (see supplemental information, Method S1, and Figures S1–S3: Differences in Throwing Strategies in Experiments 1 and 2).

In sum, our first study found that when participants practiced throwing, they settled into a stable temporal pattern. Directly after this practice, they exhibited enhanced sensitivity to the time interval prominent in the throwing action, which was the 500 ms interval closest to the ball-release time. For movement time and the unrelated interval, no improvements were observed. This result suggested that while multiple motor timing patterns emerged overall, only the selected timing of the ball release influenced perceptual discrimination.

Experiment 2: Converging evidence: Selective improvement of perceptual timing linked to ball-release time

Experiment 2 aimed to replicate and further investigate the unique link observed in Experiment 1 between perception and motor performance. Specifically, we examined whether this link is driven by ball-release time, rather than uniquely associated with the 500 ms standard interval. To test whether perceptual timing improvements are tied to an interval matched with ball-release time, we modified the skittles task to create a different spatiotemporal profile of throwing movements. In this version, participants had to throw the ball at a different angle and velocity from Experiment 1 to be successful, resulting in ball-release times around 300 ms (Figure 1E). This faster ball-release time reflected a more typical throwing action compared to the slower action in Experiment 1, which allowed us to determine whether typical throwing actions established an even closer link between performance improvements and temporal sensitivity Therefore, Experiment 2 could provide converging evidence and serve as an active control, verifying the specific relation between perceptual timing discrimination and timing in the throwing action.

To demonstrate that perceptual timing improved only for an interval matched with the motor timing structure, the starting position of the arm was set at a different arm angle to elicit a ball-release time of around 300 ms (Figures 1B and 1C). This was explored in pilot studies that also analyzed the arm trajectories to ensure that the throwing actions were ballistic, i.e., with a single velocity peak and ball release prior to or at this peak. Consequently, the time-interval discrimination task included the new ball-release time (300 ms), the new movement time (600 ms), and a control interval (1000 ms), unrelated to the modified throwing action. All experimental procedures remained the same.

In accord with Experiment 1, participants again improved their performance in target hitting, as evidenced by a significantly increasing success rate across practice days, F(3,69) = 12.783, p < 0.001, η² = 0.357, and a decreasing performance error, F(3,69) = 19.398, p < 0.001, η² = 0.458 (Figures 7A and 7B). These results were obtained using one-way repeated-measures ANOVA with days as a within-participant factor.

Figure 7.

Motor performance in Experiment 2

(A) Success rate over days.

(B) Performance error over days.

In both panels, color indicates the days and the error bars represent the standard error of the mean across participants.

Figure 8A shows the mean durations of the two segments of the arm trajectory, ball-release time, and movement time, across Days 2–5. As can be seen, the ball-release time and the movement time settled to durations of approximately 350 and 550 ms, respectively. The one-way ANOVA ascertained that both time intervals did not change significantly across practice days (all p > 0.6).

Figure 8.

Timing in motor performance in Experiment 2

(A) Durations of the two motor intervals, ball-release time, and movement time.

(B) Variability of the two movement intervals quantified by the coefficient of variation.

In both panels, the color of the dots corresponds to the daily sessions. Error bars represent the standard error across the means of participants.

To evaluate the stability of the temporal pattern in the throwing movement across days, the variability in ball-release time and movement time was analyzed using the coefficient of variation (Figure 8B). The one-way repeated-measures ANOVA confirmed the expected reductions in variability for both ball-release time, F(3,69) = 14.230, p < 0.001, η² = 0.382, and movement time, F(3,69) = 6.451, p = 0.003, η² = 0.219, which was consistent with Experiment 1.

Next, we investigated how motor timing affected the time-interval discrimination of the three standard intervals, 300 ms, 600 ms, and 1000 ms. Of interest was whether, as in Experiment 1, Weber fractions for the standard interval of 300 ms, linked to ball-release time, would improve following motor training. Figure 9A summarizes the changes in the Weber fractions for all participants for the three tested time intervals over 5 days. There was a marked decrease in the Weber fraction for 300 ms, while the other two intervals showed less change.

Figure 9.

Perceptual performance quantified by the Weber fraction in Experiment 2

(A) Weber fraction for the time-interval discrimination threshold of each standard interval across Days 1–5. Smaller Weber fractions indicate better perceptual performance.

(B) The linear mixed model applied to the Weber fraction of the standard interval of 300 ms across Days 1–5. The gray lines represent the model’s fixed effect, and the shaded areas indicate the 95% confidence interval of the model prediction.

(C) Participant averages of the regression slopes of the Weber fraction for each standard interval. A negative slope indicates that time perception improved with training. Only the interval of 300 ms, which is linked to ball-release time, showed a significant reduction. Error bars represent the 95% confidence interval of the estimated parameters. ∗∗∗ p < 0.001.

(D) The linear mixed model applied to the relation between the Weber fraction of the standard interval of 300 ms and the ball-release time variability across Days 2–5.

(E) The linear mixed model applied to the relation between the Weber fraction of the standard interval of 600 ms and the ball-release time variability across Days 2–5.

(F) The linear mixed model applied to the relation between the Weber fraction of the standard interval of 1000 ms and the ball-release time variability across Days 2–5.

(G) Participant averages of the regression slopes applied to the relation between the ball-release time variability and the Weber fraction of each standard interval. Error bars represent the 95% confidence interval of the estimated parameters. ∗∗∗ p < 0.001. Data and fitted curves for individual participants are available in the data and code availability section.

For each standard interval, the change in Weber fractions over the 5 days was evaluated by a linear mixed model, with Day as a fixed effect and Participant as a random effect. Figure 9B illustrates that participants significantly decreased the threshold of time-interval discrimination for the 300 ms interval, the interval linked with ball-release time: slope = −0.0204 ± 0.0074, t(101) = −5.431, p < 0.001. There were no changes in the two other time intervals (all p > 0.18). Figure 9C summarizes the regression slopes for the three intervals by aggregating the means of all participants: the negative slope for the 300 ms interval was significantly different from zero. Therefore, this result confirmed that ball-release time was consistently linked with improvements in perceptual timing discrimination, as seen for the 500 ms interval in Experiment 1 (Figure 6C).

The next objective was to determine whether this faster and more ballistic throwing action of 300 ms strengthened the link between stabilized performance and discrimination sensitivity, i.e., a correlation between ball-release time variability and the Weber fraction. Once again, a linear mixed model examined this relation. Figures 9D–9F illustrate the linear regressions applied to the Weber fractions for the three standard intervals for all participants. The positive regression slopes for the 300 ms interval supported that lower ball-release variability was associated with smaller Weber fractions, slope = 0.286, confidence interval = [0.126, 0.447], t(82) = 3.56, p < 0.001. This enhancement was not observed for the two other intervals. Figure 9G summarizes the regression slopes for all tested time intervals with the 95% confidence intervals, verifying that this positive relation was only evident for the 300 ms standard interval discrimination. These results supported that a more stable temporal structure in the throwing action enhanced temporal discrimination, not only at the group level, but also at the individual level.

In summary, after extended throwing practice, participants showed improved sensitivity in discriminating time intervals, specifically for the 300 ms interval that was close to the ball-release time. Furthermore, within individuals, the stability of motor timing was positively correlated with time-interval discrimination, a finding that went beyond the results from Experiment 1. This strengthened relation may be attributed to the more ballistic throwing movements in Experiment 2. These results provide the first empirical evidence that improvements in motor timing can enhance time perception sensitivity through a shared, amodal timing mechanism.

Does the Temporal Coupling between Action and Perception Persist in the Long Term?

The retention of a motor skill or of a perceptual ability over a longer period has received relatively little systematic study, even though lasting skill is the holy grail of any teaching, coaching, and clinical intervention. In motor control, it has been shown that the temporal patterns in movement skills have indeed remarkable persistence. One study of a bimanual polyrhythmic task showed that individuals not only stabilized their idiosyncratic temporal patterns over 20 practice sessions, but that the fine-grained spatiotemporal pattern then also persisted for 6 months and in three of four cases, for 8 years after the end of practice.^48,49 For a visuomotor task, it was shown that motor learning and its association with external sensory stimuli also persisted for an extended time.⁵⁰ Bolstered by these findings, we examined whether coupling between action and perception timing, and the amodal timing primitive, could also persist in the longer term.

After the five sessions of Experiment 2 were completed, we asked some of the participants to return for a retention session. Based on their availability, 11 participants returned after a period between 6 and 91 days following the last experimental day, i.e., after 22.9 ± 7.7 days. In the retention session, all participants performed one session of the identical skittles task followed by the same time-interval discrimination task. We reasoned that: 1) the temporal structure, or dynamic primitive, formed by the throwing practice, was encoded into long-term memory together with the action, and 2) as the motor timing was maintained, the improved perceptual acuity persisted together with it.

To evaluate how well participants retained their learned throwing skill, we first regressed the ball-release time variability against the motor sessions on Days 2–5 for each individual. The derived regression equation served as a reference to compare the retention day’s performance to previous performance. Figure 10A shows how the retention performance of an individual compares to the regression of the previous performance. A day of 5 indicated that the learned motor skill was fully recovered on the retention day without loss. Figure 10B shows ball-release time variability averaged across participants within the confidence band, including the average day of the retention performance. Interestingly, motor performance was very close to Day 5, the last training day (4.75 ± 0.26 s.e.), indicating that the learned throwing skill almost fully persisted.

Figure 10.

Retention performance is evaluated by variability of ball-release time

(A) For each individual, linear regressions on ball-release time variability across Days 2–5 determined the day on which performance was similar to the retention day. The equation of the example regression was: y = −0.05× + 0.38.

(B) Average ball-release time variability with regression: y = −0.05× + 0.40, and retained day (4.75 ± 0.26 s.e.).

(C) Averaged Weber fraction of the 300 ms interval with regression: y = −0.02× + 0.2, and retained day (3.89 ± 1.21 s.e.).

The gray-shaded areas in (B) and (C) represent the 95% confidence interval of the best-fit line.

Correspondingly, we evaluated how much of their improved time perception of the 300 ms interval participants maintained. To this end, the Weber fractions of the 300 ms time interval were regressed against the 5 days of Experiment 2. As before, the derived regression equations served to determine on which day performance was equal to the retention day’s performance. Figure 10C shows the level of retention of the Weber fraction in the 300 ms standard interval averaged across participants. Time perception performance on the retention day was the same as on Day 3.89 ± 1.21s.e.

In sum, these retention results of Experiment 2 demonstrated that the temporal pattern in the motor action was indeed encoded together with the associated perceptual acuity. The findings established that with throwing practice, participants enhanced the sensitivity of time interval discrimination, and this enhanced sensitivity was selectively linked to the timing of the trained movement. Together, our results corroborated evidence that improved motor timing can be associated with enhanced time-interval discrimination sensitivity, probably mediated by a timing primitive.

Experiment 3: Motor training is necessary to improve time perception

It is important to note that in all temporal perception experiments, we restricted the number of trials to 70 per standard interval, unlike conventional perceptual learning studies that typically involve thousands of trials.⁴² Furthermore, participants did not receive any error feedback. These short sessions without feedback were chosen to capture transfer effects from the motor to the perceptual tasks in both Experiments 1 and 2 to reduce any sort of temporal learning from the perceptual task itself. Therefore, we reasoned that without motor practice, perceptual sensitivity was unlikely to improve solely through perceptual learning, regardless of the intervals. To test this expectation, Experiment 3 involved another group of 15 participants who performed only the time interval discrimination task over 5 days, in an identical fashion as in Experiment 2. We did not expect to see any enhanced performance, specifically not in the standard interval of 300 ms.

Indeed, participants did not improve their sensitivity to time-interval discrimination in the three standard intervals. Figure 11A shows that discrimination sensitivity for all three standard intervals was comparable to Experiment 2. The same linear mixed model of the Weber fractions for each standard interval over the 5 days indicated that the effect of Day for 300 ms was not significantly different from zero, slope = −0.0085 ± 0.0118, t(72) = −1.435, p = 0.156 (Figure 11B), similar to 600 and 1000 ms (all p > 0.15). The slopes of all participants for each standard interval are summarized in Figure 11C, showing no significant difference from zero (see supplemental information, Method S3, and Figure S6: Weber Fraction across Days in Experiment 3).

Figure 11.

Perceptual discrimination performance in Experiment 3

(A) Weber fraction for each standard interval on Days 1–5. The regression slopes for each standard interval were estimated from a linear mixed model.

(B) The linear mixed model applied to the Weber fraction of the standard interval of 300 ms across Days 1–5.

(C) Slopes of Weber fractions changed over time, estimated with a linear mixed model; error bars represent 95% confidence intervals.

In sum, Experiment 3 showed that without throwing practice, participants did not demonstrate any improvements in discrimination sensitivity across all intervals. These findings provide further evidence that the enhanced sensitivity to the salient interval in motor performance was likely induced by motor training, rather than by perceptual learning. However, Experiment 3 could not entirely rule out the possibility that passive exposure to a temporal structure of repeated throwing in each trial might have contributed to the improvement observed in Experiments 1 and 2. Nonetheless, this appeared to be less likely since participants in Experiments 1 and 2 were both exposed to the temporal structure related to movement time. This repeated exposure, which also stabilized over days, did not result in improved perceptual discrimination. Therefore, repeated exposure to a temporal structure alone is not sufficient for transfer. Rather, it is the repeated exposure to task-relevant motor timing that leads to perceptual improvement.

Discussion

This study examined how implicit temporal structure established and stabilized during extended practice of a throwing task influenced the discrimination ability in an auditory time discrimination task. That timing cuts across perceptual and motor processes, i.e., timing is not domain-specific, has already been shown in several previous studies.^30,51,52 However, this study adds several essential new findings to this emerging body of understanding. Our study established that a temporal pattern emerging in the context of a goal-directed, but otherwise completely untimed motor skill can selectively enhance perceptual discrimination. Specifically, our results demonstrated that it was the time from onset to ball release that most affected perceptual discrimination. We conjectured that the significance of ball-release time likely stems from its critical role in the throwing action. However, it is important to note that ball-release time does not directly determine performance success. Future research is needed to further explore the underlying mechanisms linking stable spatiotemporal coordination patterns with enhanced sensitivity to temporal intervals during stabilized motor behavior.

Goal-directed task with implicit timing

Our investigation of emergent motor timing in a goal-oriented movement deviated significantly from most timing experiments as our participants did not produce specific “empty” temporal intervals in a laboratory task such as tapping. This is an essential step beyond previous work. Unlike in laboratory tasks, most movements in the real world are not timed by an external metronome, but timing arises in the context of other goals. When you drink a glass of wine, you reach for the glass, lift and tilt it, carefully controlling the angle of the glass to drink without spilling. The goal is defined by the actor’s intention to drink and is evaluated by the outcome of the action. When actions are repeated many times, the temporal pattern stabilizes. Actions typically happen at a timescale of a 500–1500 ms, determined by the extrinsic task constraints, such as the distance between the hand and the glass and the mouth. The kinematic and dynamic characteristics, i.e., movement and forces of the arm and hand in space and time, require a precisely orchestrated pattern of muscle activity guided by proprioceptive and visual information.^53,54 Notably, these actions are also constrained by the weight of the glass, the amount of wine in it, and the physics of the fluid moving in the glass. Spatiotemporal structure emerges at the interface of kinematics, dynamics, and intentions.

To capture these complex interactions inherent to any real-life action, we employed the task of throwing a ball to hit a target. The experimental paradigm skittles could also capitalize on previous research that developed the virtual implementation based on the dynamics of the real task.^55,56 This task provided an opportunity to examine emergent spatiotemporal patterns, i.e., motor timing, as a by-product of the goal achievement within given task constraints. This task had redundancy, i.e., any performance error could be achieved with mathematically infinite arm trajectories and ball releases. As mentioned, ball-release times do not directly correspond to the error, as different ball-release times can be associated with the same error (see supplemental information, Method S4: Variability in Execution Does Not Necessarily Predict Variability in Task Error). Nevertheless, previous research already reported that even in completely self-paced movements, a stable throwing pattern emerged over repeated throwing actions.⁵⁷ With this motor task, this research created a bridge between motor neuroscience and perceptual psychology using insights from motor control to address the question of time perception.

Experimental demonstration of a link via a multi-session learning study

Our participants practiced the task for four daily sessions, each comprising 320 trials. With such extended practice, we monitored the emergence of a stable spatiotemporal pattern that was coupled with testing perceptual sensitivity for related temporal intervals. This experimental design established a direct link between emerging motor timing and its gradual influence on perceptual sensitivity. This procedure differs from earlier studies that supported a direct connection by demonstrating deficits in both time perception and production in patients.^28,58 Similarly, in neurologically healthy individuals, the relation between motor timing and perceptual timing has only been demonstrated via correlation analyses. For instance, the discrimination of temporal intervals, presented by brief auditory stimuli, was correlated with successive finger taps separated by the same temporal interval.^59,60 Even when the development of motor timing was the focus, it was triggered by an explicit timing instruction without any other motor goal.¹⁰ While revealing, such correlational evidence leaves open the possibility that perceptual and motor systems represent time merely in a similar fashion, or that they only share a common mechanism.^36,61 The current multi-session design demonstrated how stabilizing temporal features in motor performance across daily practice concordantly improved temporal representations in a perception task.

Specificity and longevity of action-perception coupling

It is worth emphasizing that this enhanced sensitivity was specific to the ball-release time, a time that was salient to the success of target-oriented throwing. The results in Experiments 1 and 2 corroborated that the transfer from motor timing to perceptual discrimination was temporally specific to this interval. Experiment 3 established that it was not the result of general learning of the time perception task. Furthermore, in Experiment 2, within individuals, the selective enhancement in time perception correlated with the decrease in ball-release time variability: the more stable the motor timing became, the more accurate was the perception of the same interval. This correlation between motor-timing variability and perceptual discrimination suggested that there is a shared temporal mechanism between perception and movement, regardless of the complexity of the motor tasks.

This individual connection between motor stability and perceptual discrimination was not observed in Experiment 1. We conjectured that the stronger results in Experiment 2 were due to the nature of the throwing action. Throwing involves a fast ballistic movement with a single peak in velocity and the release is at this peak or shortly before. Due to experimental set-up, Experiment 1 elicited a movement that often exhibited two peaks and the ball release came after the peak of the arm velocity, which is atypical for throwing (see supplemental information, Method S1, and Figures S1–S3: Differences in Throwing Strategies in Experiments 1 and 2).⁴⁵

It is also worth noting that in our study, only the ball-release interval, and not the others, was the critical duration that shows improvement. We did not know a priori whether it would be movement time, i.e., the rhythmicity of successive throwing actions or, as it turned out, the time from movement onset to ball release that would be the salient interval. Interestingly, the timing of the arm trajectory was not what directly led to low errors. Hitting errors are determined by angle and velocity at ball release, independent of the ball-release time, while the timing of the arm movement arose from the entire task constellation. However, we have yet to determine the underlying mechanisms for such specificity. One conjecture could be that the ball release in the skittles task involved a time interval that participants actively controlled. Future research could explore other critical factors.

In addition, the improved time-interval discrimination persisted together with the improved sensorimotor skill for a relatively long period of time, although perceptual timing sensitivity decayed faster than that of motor timing. This remarkable persistence comported with a prior longitudinal case study demonstrating that temporal patterns in a bimanual polyrhythmic task were retained even for 6 months and 8 years after the end of practice.⁶² The results are also in accord with a previous study showing that visuomotor learning and its arbitrary association with external sensory stimuli was retained for a longer term.⁵⁰ However, no one has shown that perceptual discrimination would persist with the retained motor timing in the longer term. This latter result has important implications for our overall hypothesis that dynamic timing primitives may underlie the observed phenomena.

Embodied cognition

Our findings are consistent with research on embodied cognition that has endowed the motor system with a more critical role in higher-level perceptual and cognitive functions.^63,64,65 Perceptual and cognitive processes are assumed to be grounded in and co-determined by our bodily interactions with the environment.^65,66,67,68 Research from this perspective has already documented that transfer from perception to action exists, for instance in the form of observational motor learning.⁵ However, transfer from action to perception has received much less attention, although empirical evidence supports that self-generated action and action experience can modulate perception and cognition.^{69,70,71,72,73,74} Such action-perception transfer is also compatible with the ideomotor theory stating that the observer can activate their internal representations of actions that are represented in the same format as perceived events. Thus, the final stages of perception and the initial stages of action control share a common coding.^37,75,76

Dynamic primitives in motor control and perception

Our observations also match a perspective that has come to the fore in movement neuroscience over the past decades: coordination is achieved via dynamic primitives.^43,77,78,79 Several research lines have converged to recognize that the control of our high-dimensional motor system is unlikely to exclusively rely on top-down processes. Instead, motor control is a dynamic process arising from multiple interacting modules distributed across the complex neuromechanical system. These subsystems, or “dynamic primitives,” are established through practice and become building blocks for the execution of complex actions.^80,81 Dynamic primitives are stable attractors that unfold over time, partly shaped by the mechanical properties of the limbs, especially when allowed to evolve in a self-paced manner. In this skittles task, humans swing their arm and release the ball at a time between 300 and 700 ms after initiation, and never after 5s, nor after 100 ms, given that the arm has to accelerate to a suitable ball release velocity. Hence, spatiotemporal patterns arise from basic physical constraints and dynamic neuromechanical processes. Temporal structure is not explicitly controlled; timing is implicit.

Further, it is generally agreed upon that highly practiced skills settle into a repeatable, sometimes almost stereotypic and idiosyncratic spatiotemporal patterns. Thus, stability with an implicit temporal structure is a core feature of skilled movements.⁵⁷ Our experiments showed this stabilization of the throwing action by tracking the decreasing variability across practice days. These observations of stable but spatiotemporally bounded patterns are consistent with a basic fact in physics: A nonlinear dynamic system, such as the human neuromotor system, tends to form a stable equilibrium or attractor states, with timing arising from the system’s properties.⁸² Two main types of stable attractors are distinguished: fixed points, i.e., a single equilibrium point, or limit cycles, i.e., a periodic equilibrium state.⁸³ There is accumulating evidence that discrete and rhythmic movements map onto these stable attractors. For example, research on bimanual coordination has provided firm support that rhythmic movements are competently modeled by stable limit cycle dynamics.^44,83,84,85 Recent neural work also demonstrated that the primary motor cortex (M1) and SMA exhibit constrained neural dynamics during motor preparation and rhythmic behaviors. This evidence suggests that neuronal populations in motor regions, which may be utilized for perceptual timing, develop stereotyped routines that reduce internal noise.^86,87

A previous study on the skittles task showed that repeated throwing actions developed a preferred inter-throw rhythm with dynamic stability.⁵⁷ Other studies showed that complex, skilled behaviors are a combination of these dynamic primitives.^83,88 We believe that the throwing movements in the current experiments are consistent with a stable attractor, a dynamic primitive, established over the neuromuscular substrate. The transfer to perceptual discrimination suggests that such attractors are not confined to the neuromotor system, but also affect and include other brain areas.^8,12 We suggest to interpret them as “amodal timing primitives.”

We conclude with the thesis that emergent motor timing manifests via a dynamic primitive in the neuromuscular system and serves as an amodal “timing primitive” that pervades perceptual and, maybe, even cognitive systems. Clearly, its presence in cortical dynamics has yet to be shown. Future work is needed to corroborate this notion beyond behavioral experiments to include neuroimaging and computational modeling. Recent strides in motor neuroscience about manifolds in population dynamics of motor cortical neurons generate optimism that this avenue might give more fruitful and supportive insights.

Limitations of the study

While the current study focuses on perceptual sensitivity, it is important to acknowledge broader considerations in modeling and interpreting learning dynamics. We modeled changes across training days using a linear trend to capture overall improvements in discrimination thresholds. However, learning trajectories may follow nonlinear patterns, and future studies could evaluate this possibility by modeling training day as a categorical variable. Additionally, although not a focus here, future research could examine whether and how motor experience influences the point of subjective equality (PSE). Such work could help determine whether emergent motor timing alters not only sensitivity but also perceived duration itself. For example, systematically manipulating temporal structure or feedback in motor training tasks could test whether perceptual biases emerge alongside precision gains. This line of inquiry would further elucidate the mechanisms by which motor experience shapes temporal perception.

Resource availability

Lead contact

Further information and requests for resources should be directed to and will be fulfilled by the lead contact, Joo-Hyun Song (joo-hyun_song@brown.edu).

Materials availability

This study did not generate new unique reagents.

Data and code availability

• •Data: All behavior data from the experiments are publicly available as of the date of publication. Accession numbers are listed in the key resources table.
• •Code: All original code has been deposited at Zenodo and is publicly available as of the date of publication. DOIs are listed in the key resources table. All the software used in the article are listed in the key resources table.
• •Additional information: Any additional information required to reanalyze the data reported in this article is available from the lead contact upon request.

Acknowledgments

This work was supported by NSF BCS-1555006, NSF BCS-2341363 and BCS-2043328 to J.H.S., NSF BCS-2043318 to D.S., and by the National Natural Science Foundation of China (32300868) to Z.Z. We thank Ms. Carissa Aekins for her assistance with data collection in Experiment 1 and Drs. Leslie Welch, Tri Nguyen and Helene Serre for their insightful discussions during the revision process.

Author contributions

J.G., D.S., and J.H.S. designed the tasks. J.G. collected the data. J.G., Z.Z., and M.M. conducted the data analysis. J.G., Z.Z., D.S., and J.H.S. drafted the article. J.H.S., Z.Z., and D.S. revised the article.

Declaration of interests

The authors declare no competing interests.

STAR★Methods

Key resources table

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Deposited data
Behavioral data	This paper	Zenodo: https://doi.org/10.5281/zenodo.14913669
Software and algorithms
Codes for presenting individual data	This paper	Zenodo: https://doi.org/10.5281/zenodo.14913669
MATLAB R2023b	MathWorks	https://www.mathworks.com/products/matlab.html
mQUESTPlus: A MATLAB implementation of QUEST+	Watson46	https://github.com/brainardlab/mQUESTPlus

Experimental model and study participant details

Participants

In Experiment 1, 25 participants (13 females; mean age = 22.56 years) were recruited; for Experiment 2, another cohort of 25 participants (14 females; mean age = 25.04 years) were recruited. Eleven participants (7 females; mean age = 22.64 years) who completed the 5-day training session of Experiment 2 were recalled to perform a one-day retention session. For the control Experiment 3, 15 new participants (8 females; mean age = 23.00 years) were recruited. In each experiment, the sample size was determined on the basis of the effect size needed to achieve 90% statistical power, as determined with a one-sample t-test on preliminary data. All participants signed the informed consent form prior to the experiment and were compensated with $10/h after completing the experimental sessions. They had normal or corrected-to-normal vision and were naive to the aim of the study. All procedures were approved by the Northeastern University Institutional Review Board (IRB#08-09-12) and conducted in accordance with the Code of Ethics of the World Medical Association (Declaration of Helsinki) for research involving human participants. All research was carried out in compliance with the approved IRB guidelines. Informed consent was obtained from all participants.

Participant elimination

The throwing action was not explicitly timed, because the emphasis was on allowing participants to stabilize their self-paced action to a relatively invariant spatiotemporal pattern with practice. A previous study on the same skittles task documented how participants not only stabilized their discrete throwing actions, but also fell into a continuous rhythmic sequence of movements.⁵⁷ This observation is consistent with the notion of dynamic primitives that arise with practice. As the present study wanted to isolate salient intervals, participants were asked to initialize each throw from a designated rest position, i.e., with zero velocity and acceleration, i.e., establish a discrete attractor. Despite the instruction, some participants fell into a rhythm, connecting successive throws into a continuous stream of actions. For the current objective, these participants were eliminated, because the determination of the two intervals, ball release time and movement time, was problematic for such a continuous action. Further, as we argued previously, a continuous rhythmic movement differs in its dynamic structure from a discrete movement: a rhythmic movement establishes a limit cycle, which is a different dynamic primitive than a fixed-point attractor that may underlie a discrete movement.^83,84 Hence, these actions should be paired with a different discrimination task.

To identify these continuous throwing actions, we computed “dwell time” between the successive throws. The onset of a throw was indicated when the velocity surpassed 5deg/s for 10 ms and the acceleration exceeded 50deg/s² for 10 ms.⁴⁵ When the onset of a new trial could not be distinguished from the end of the previous one, dwell time was zero. If dwell time was zero in more than 20% of the 320 trials (throws) of a participant in one daily session, then this participant was eliminated from further analysis. Note that for the subsequent regressions across days, 3 days of data were not sufficient. With this procedure, 3 participants were excluded from Experiment 1 (leaving n = 22), and 1 participant from Experiment 2 (leaving n = 24).

Following this elimination, the perception data of the remaining participants were also screened for potential problems. Inspection of the generated stimuli revealed that the Quest+ procedure occasionally elicited a sequence of invariant stimuli regardless of the response. To identify such sequences of invariant stimuli, entropy analysis was applied to each block of 70 stimuli. An entropy value below 2.5 signaled that the stimuli did not vary based on the participants’ responses.⁸⁹ If more than one day contained flawed interval sequences, the specific interval condition was eliminated. If more than 80% of stimuli (56 of 70 forced-choice judgments) were flawed, the entire block was eliminated. In Experiment 1, one participant had to be removed in total (reducing the number of participants to n = 21) and for one additional participant, the 500 ms condition had to be removed (n = 20). For the 800 ms condition, five subjects were eliminated (n = 16). In Experiment 2, 2 participants were removed in the 300 ms condition (n = 22), while the 600 and 1000 ms conditions did not require any eliminations (n = 24). In Experiment 3, 1 participant had to be removed in total (n = 14).

After these eliminations, Experiment 1 included 21, 20, 16 participants in the 300, 500, 800 ms perception conditions, respectively. Experiment 2 included 22, 24, 24 participants in the 300, 600, and 1000 ms perception conditions, respectively. Experiment 3 included 14 participants in all conditions.

Method details

Experiment 1

Motor task

The task, called Skittles, is a target-oriented throwing action similar to the American playground game tetherball (Figure 1A). In the real game, the player throws a ball that is attached via a string to a vertical post to hit one or more target skittles on the far side.^57,90 This task was implemented as a virtual game, where the target and the workspace were shown to the participant as a top down view (Figure 1B). The throwing movement was simplified to a single-joint forearm rotation in the horizontal plane; the ball release was triggered by extending the index finger from a ball attached to the lever arm that simulated the opening of the hand to throw the ball. The participants saw their own arm movements as a rotating purple bar at the bottom of the projection screen (40 cm length) together with the virtual white ball (10 cm diameter) after release as it traversed around the red post (50 cm diameter), hitting or missing the yellow target (10 cm diameter).

Participants stood 1.5 m in front of a large backprojection screen (2 × 2 m) and rested their forearm on a lever arm and performed extension movements in the horizontal plane to throw the ball. The height of the lever arm was individually adjusted so that the subject’s upper arm had a 45° angle with respect to the trunk. Angular displacements of the lever arm were measured by an optical encoder (BEI Sensors, Goleta, CA) with a sampling rate of 1000 Hz. The participant grasped a wooden ball that was fixed at the distal end of the lever to “throw” the ball to hit a target. A force sensor (Interlink Electronics, Camarillo, CA) attached to the ball was closed when pressing the index finger onto it; finger extension opened the contact and triggered the release of the virtual ball on the screen. The angular position and angular velocity of the arm movement at the moment of ball release were used to calculate the ball trajectory. Using these as initial conditions, the ball’s trajectory was simulated to traverse around the post in an elliptic trajectory toward the target on the opposite side (Figure 1B).

The ball’s trajectory was generated by a simple 2D model where the ball was attached to two orthogonal springs that held the ball at its equilibrium position at the post in the center of the workspace, defined as x = y = 0. The equations for the ball movements after release in x- and y-direction were:

$$x\left(\mathrm{t}\right)={\mathrm{A}}_{\mathrm{x}}\sin \left(\omega \mathrm{t}+{\mathrm{\phi }}_{\mathrm{x}}\right){\mathrm{e}}^{-\frac{\mathrm{t}}{\mathrm{\tau }}}$$ (Equation 1)

$$y\left(\mathrm{t}\right)={\mathrm{A}}_{\mathrm{y}}\sin \left(\omega \mathrm{t}+{\mathrm{\phi }}_{\mathrm{y}}\right){\mathrm{e}}^{-\frac{\mathrm{t}}{\mathrm{\tau }}}$$ (Equation 2)

$\mathrm{\omega }$ represented the natural frequency of the springs; the amplitudes A_x and A_y, as well as the phases ${\mathrm{\phi }}_{\mathrm{x}}$ and ${\mathrm{\phi }}_{\mathrm{y}}$ of the springs resulted from the ball’s angle and angular velocity at release. The ball motions were lightly damped by the exponential term to approximate realistic motion, where τ denoted the relaxation time of the decay.

Figure 1C illustrates the x-y coordinates of the workspace and three exemplary ball trajectories traversing around the center post; the target is the small yellow circle at the left. The delay between data sampling and visual display were within the refresh rate of the computer, which was 13 ms. The throwing action had redundancy: mathematically infinitely many combinations of angle and velocity that initiated the ball release could achieve zero error or any other given error value. This feature is summarized in the solution space spanned by release angle and velocity (Figure 1D): the green U-shaped band is the set of all angle-velocity combinations that hit the target successfully with errors <1.0 cm; this is called the solution manifold. The orange shades encode the error that the ball trajectory would have achieved for all other relase combinations; the black area comprises releases that hit the center post. The nonlinear geometry of the solution manifold was determined by the target location in the workspace. Small changes in target location could generate qualitatively different solution manifolds, requiring different throwing strategies.

Metrics of task performance and motor execution

As measures of task achievement, both the success rate and performance error were calculated in each block. The success rate, a binary measure for each trial, indicated the percentage of throws with a performance error below the threshold of 1.0 cm; the error represented a finer-grained metric that was defined as the minimum distance between the target and the ball trajectory.

For the identification of the onset and offset of each throw, the angular position was first smoothed using a Savitzky-Golay filter with a 2nd-order polynomial and a window length of 100 ms. Subsequently, the angular velocity of each data point was calculated as the slope of a linear fit to 20 smoothed data samples prior to the current data point; acceleration was then estimated using the same linear fit applied to the 20 velocity samples prior to the time point of interest. The onset of each throw was indicated when the acceleration exceeded 20% of the peak acceleration of the same trial in the direction of arm extension. The offset of each throw was determined as the moment that the hand reached the maximum extension for the first time.

This delimited time profile was parsed into two segments: (1) ball-release time, defined as the interval between the movement onset and the moment of ball release, and (2) movement time, defined as the interval between movement onset and offset (Figure 1E). We also calculated the mean and the variability of these intervals of each participant across the 320 trials of each daily session; variability was quantified by the coefficient of variation (standard deviation of the durations divided by their mean). Note that motor learning is commonly gauged by the reduction in variability with training.^24,36 It is also important to keep in mind that due to the redundancy of the task, variability of the ball-release time does not need to be the same as the variability of the error. In fact, this relation between execution variables and the result variable has been the subject of a lot of theorizing in human motor control research. Several methodological approaches have been developed to gain insight into control principles from the differing distributions of these two variable types.^91,92,93

Time-interval discrimination task

Participants compared the time-intervals of two pairs of tones: a standard and a comparison interval (Figure 2A). In one block the standard interval t was fixed, whereas the second comparison interval was either shorter or longer than the standard interval, t ± Δt ms, where t is the target interval, Δt equals to half of this interval. Participants reported which pair of tones had the longer interval by a keypress; they did not receive any error feedback to avoid any learning (Keele et al., 1985). The threshold of each standard interval was estimated by a Bayesian adaptive procedure available in the software package QUEST+ (Watson, 2017). QUEST+ selected a difference between two intervals (±Δt) for the next trial based on the key press responses in all past trials. Generally, for each trial, the prior of the interval is a normal distribution with the mean set at t ± Δt/2 ms and standard deviation between 0 and t/2. The probability of the keypress response for all Δt’s was fitted with this cumulative normal distribution. After each keypress, ±Δt of the next trial was computed by maximizing the posterior density of responses obtained from all previous trials. The comparison interval for the next trial was then determined as t ± Δt. After all trials, a maximum likelihood (ML) fit of a sigmoidal function was applied on all responses (Figure 2B). The time-interval discrimination threshold was the estimated standard deviation of the ML-fitted psychometric function.

Note that in contrast to conventional perceptual learning studies that typically involve thousands of trials,⁴² we utilized the psychophysical paradigm as a transfer test. Therefore, we deliberately aimed to minimize perceptual learning by restricting the number of trials to 70 per interval. This approach mitigated the potential confounding effects of perceptual learning and helped focus on the specific transfer effects. For the same reason, we did not provide any feedback about the correctness of the response.

Procedure

All participants performed 5 daily sessions (Figure 3). On Day 1, they performed only the time-interval discrimination task to obtain a baseline measurement. This perceptual task comprised 3 standard intervals, 2 of which were associated with 2 movement intervals extracted from the spatiotemporal pattern of the arm movement (Figure 1E); one additional control interval was unrelated to the movement times. The standard intervals were determined in pilot tests with a separate group of participants. According to the pilot results, the standard intervals were set to 500 ms (linked to the ball-release time), 800 ms (linked to the movement time), 300 ms (unrelated time). On Days 2–5, participants first performed the skittles task with 320 trials/throws per day.

To ensure that participants performed separate throwing actions, we asked them to start their throwing movement from a standardized arm position (Figure 1B: starting line). Over practice, participants were expected to stabilize their spatiotemporal pattern of the arm movement (Figure 1E). Following each throwing session, they continued with the perceptual discrimination task with the same intervals as on Day 1. The QUEST+ procedure for each standard interval on each day included 70 trials. A prior 10-trial QUEST+ procedure with an unrelated 300 ms standard interval was used on Day 1 for a practice block. Specifically, for 300 ms, the mean was set at 225 and 375 ms and the standard deviation were between 0 and half of the interval; the standard deviation ranged from 0 to 150 ms. This information means that the discrimination threshold for 300 ms ranged from 0 to 150 ms, and the Weber fraction ranged between 0 and 0.5.

In the perception task, discrimination performance was compared across different standard intervals by computing the Weber fraction. The Weber fraction was defined as the ratio of the estimated discrimination threshold over its standard interval (Equation 3):

$$Weberfraction=\frac{\text{threshold}}{\text{standard}\text{interval}}$$ (Equation 3)

A smaller Weber fraction corresponds to better discrimination. This threshold was compared between the different intervals. It was also regressed against motor timing variability to evaluate the influence of the stability of motor timing on the timing sensitivity.

Experiment 2

Tasks and procedures

The same skittles and time-interval discrimination task were used as in Experiment 1, except for the following modifications: In the skittles task, the starting line was modified to afford more ballistic throwing movements with ball releases that could hit the target. Figure 1B shows the two starting lines for Experiment 1 and 2. Experiment 2 afforded a shorter arm movement before releasing the ball. In the time-interval discrimination task, the three standard intervals were altered to match the new movement intervals: 300 ms (linked to the ball-release time), 600 ms (linked to the movement time), and 1000 ms (unrelated time).

After participants finished all 5 sessions, we asked them to return for a retention session. Eleven participants returned after after 6–91 days, with an average retention time of 22.9 ± 7.69 s.e. days. This time period between the last practice and the retention session was based on the availability of each participant. Upon return, they performed one session of the identical Skittles task followed by the same time-interval discrimination task. All other procedures were identical to those in Experiment 1.

Experiment 3

Tasks and procedures

This experiment did not include any motor practice. All procedures of the perceptual discrimination task were identical to those in Experiment 1 and 2; the three standard intervals were also the same. All data analysis and statistics were performed as in Experiment 1 and 2.

Quantification and statistical analysis

Statistical testing

The results of motor performance, success rate and error and motor timing and its variability, were subjected to one-way repeated-measures ANOVA with Day as a fixed factor and participants as random factor, partial η² was calculated as a measure of effect size. ANOVAs were preferred over regressions as previous work has shown that motor learning in this task tended to follow an exponential time course.^45,94

The perception data were analyzed by linear mixed-effect models (LMM). The first model examined the gradual improvements in Weber fraction, treating Day as a continuous variable. This approach allowed us to assess how changes in motor performance and its influence on time perception evolved over time. We acknowledge that treating day as a continuous predictor assumes a linear trend, which may not fully reflect the true shape of the learning trajectory. However, this linear approximation offers a conservative and interpretable starting point for capturing the overall direction of change.

The model was constructed with Weber fraction ($y_{weber}$) as output and practice Day as fixed effects. Intercepts for participants were included as random effect:

$$y_{weber}={\beta }_0+{\beta }_1{x}_{day}+Z{u}_{participant}+\epsilon \text{,}$$ (Equation 4)

where $y_{weber}$ is the outcome variable, ${\beta }_0$ is the overall intercept, ${\beta }_1$ is the fixed effect coefficient, Z include the random intercepts for all participants ($u_{participant}$), ε is the residual error term. We also use an LMM model on Weber fraction and motor timing variability with Weber fraction ($y_{weber}$) as output and ball release CV ($x_{releaseCV}$) as fixed effects. Again, intercepts for participants were included as random effect:

$$y_{weber}={\beta }_0+{\beta }_1{x}_{releaseCV}+Z{u}_{participant}+\epsilon$$ (Equation 5)

where the variables have the same meaning as the previous one.

All data processing was conducted in MATLAB, and the statistical analyses were carried out with the MATLAB Statistics and Machine Learning Toolbox. The linear mixed model was conducted with the MATLAB function fitlme. All error bars in the figures represented the standard error of the mean (s.e.) or 95% confidence intervals of estimated parameter value upon specification. We also reported the ANOVA results of the LMM and the model fit indices (marginal R² and conditional R²) in the supplemental information, Method S5, and Tables S1 and S2: Summary of Statistical Results of the Linear Mixed-Effects Models.

Published: August 14, 2025