Spatial distances affect temporal prediction and interception

The purpose of the present study was to test whether the well-established perceptual kappa effect also impacts interception performance. In a first experiment, the traditional kappa design was adapted to a temporal prediction task. In a second experiment, additional modifications of the task allowed to assess the kappa effect in motor interception. In line with the kappa effect, participants’ temporal prediction increased with increasing distance between stimuli in Exp. 1. Similarly, in Exp. 2 the timing of interception was affected by the distance between stimuli. Specifically, participants intercepted the target stimulus later when distances between stimuli increased (kappa effect)1,2,13with an exception for the largest spatial interval (350 px).

Importantly, there is some evidence that the temporal ISI moderated the kappa effect in Exp. 2. For some comparisons the effects seem to diminish or even reverse (see Supplementary Fig. S1). Additionally, there was an overall trend in the interception task (Exp. 2) that participants temporally overshot short and undershot long ISIs, potentially indicating a tendency towards the center. This might reflect an overall increased uncertainty in the interception paradigm compared to the temporal prediction task, in which the temporal intervals were generally overshot but less so for longer temporal ISIs. We neither had a priori hypotheses concerning the outcome of these additional, exploratory analyzes nor are we aware of evidence providing robust support for these initial empirical findings. It follows that future research is needed to examine the potential impact of temporal ISIs on the kappa effect.

Together, the effects found in both experiments are in line with previous research on the kappa effect showing that temporal intervals between a sequence of stimuli are judged to have a longer duration when the stimuli are more distant1,2,13,14. Therefore, our findings extend earlier research by showing that the kappa effect transfers to motor actions. More specifically, adding to earlier reported effects on motor sequence learning8,9, the current findings reveal an impact of kappa effects—and hence spatiotemporal biases—on temporal prediction and motor interception performance. The findings also enrich current debates about the coupling of perception and action15,16,17 and the impact of illusions, in particular, visual illusions such as the Müller-Lyer and Ebbinghaus illusions on motor performance for which some studies reported no evidence18,19positive evidence20,21,22 and even mixed evidence23.

When comparing the size of the temporal errors between Exp. 1 and Exp. 2 (see Fig. 2), it becomes apparent that the size of temporal errors in the mere prediction task was almost twice as large as the temporal errors in the interception task. This may be at least partially explained by previous research on time to contact estimations showing that a purely temporal response towards motion objects (similar to Exp. 1) does not exclusively depend on temporal, but also speed information24. If true, then it is reasonable to assume that participants may have used and perhaps integrated velocity, timing and spatial cues to perform the interception task in Exp. 2. In addition, the interceptive movement itself and/or its effects (ie the cursor moving across the screen) are likely to have provided additional online feedback allowing to update the interceptive movement, thereby contributing to smaller temporal errors.

Importantly, the additional analyzes reported in the supplement indicate that the temporal error was nearly identical between experiments for the shorter temporal ISIs. With increasing time between stimulus presentations, the temporal error was then reduced, more so in the interception task (Exp. 2) which even results in undershooting. As indicated above, this finding might be interpreted as an overall tendency to the center (reacting later for short and earlier for long temporal ISIs) which could reflect higher uncertainty in the interception task.

Overall, the finding that participants reacted too late contrasts with studies on synchronizing actions with events25 or reproduction of rhythms26. This highlights the different demands of such tasks. When participants perform an action repeatedly and try to temporally synchronize it with a stimulus signal, the action performance tends to precede the stimulus event. This finding is interpreted as supporting the Paillard-Fraisse hypothesis27 which states that temporal events are temporally ordered according to the temporal succession of their representational codes in the brain. Due to longer processing times for distal events (eg, sensory information from hand to brain) compared to fast processing of auditory or even visual stimuli, actions must be executed in advance to temporally synchronize both codes. However, this preceded timing is typically established after a few repeated taps, which are not typically included in the analyzes of the asynchrony. As the current task only allowed one tap per trial, no sensory feedback for following taps within a trial of the same temporal ISI was available. In general, the current task does not allow to test for brain-code coincidence as for the event in which the participant clicks, no stimulus event is presented. This might explain why we did not find participants to react early in the current task.

Importantly, the results should be discussed in the context of the framework on representational (or ‘explicit’) vs. emergent (or ‘implicit’) timing28 which states that different timing processes can be dissociated across various tasks29.30. Representational timing refers to an explicit representation of a temporal goal and was found to be prevalent in movement initiation, whereas implicit timing was shown for movement duration where timing emerges through the control of other kinetic factors such as movement speed28,31. In implicit timing tasks, timing can be seen as a result of controlling movements, without the explicit goal of reaching a point in time in mind28.

Here we used the wording ‘temporal representation’ suggesting that explicit timing was addressed. And indeed, when comparing the current task to those of previous experiments, more similarities between explicit timing and interception/temporal prediction than for implicit timing can be identified: Temporal prediction and interception with a mouse (touchpad) both require movement initiation (similar to tapping or intermittent circle drawing) instead of continuous movements as in the implicit continuous circle drawing task. Additionally, the concrete temporal intervals directly relate to the pauses implied in tapping or even intermittent circle drawing both representing explicit timing. If true, the action-based kappa effect, as assessed in the current study, might rely on explicit representation of timing meaning that the presented results do not necessarily transfer to implicit timing tasks. This is especially important, given that other interception tasks such as catching a ball have been suggested to be driven by implicit time encoding28. For instance, a goalkeeper catching a ball might translate his main goal of reaching a certain location in time into subgoals, like increasing movement velocity. This subgoal might be actively controlled to implicitly achieve the timing goal. Importantly, time encoding might even have differed between the two experiments: Similarities to the explicit tapping task are especially evident for Exp. 1 on temporal prediction. In contrast, one might argue that Exp. 2 which assessed manual interception might have triggered implicit timing by, for instance, controlling movement velocity. If true this would suggest that kappa affects both components, explicit representations, and implicit timing (or related components of movement control). Nevertheless, this conclusion is only speculative and a profound evaluation on the paradigm and the implied temporal processes is needed.

Another finding of the interception task was that with increasing temporal ISIs participants overshot the target location less, which may be interpreted as a reversed tau effect, and therefore contrasts with the previously reported perceptual tau effects3.4. While an inverted kappa effect has already been reported for auditory stimuli32, to our knowledge, this is the first time, an inverted tau effect was found. However, given that for several localization biases also inverted effects (ie biases in the opposite direction) have been reported, it might not be surprising to find such an inversion also for the tau effect. For instance, in contrast with the Representational Momentum effect, typically showing that a target’s movement offset location is overshot33,34researchers have repeatedly reported an opposite effect, called the offset-repulsion effect35,36. Similarly, seemingly contradictory findings have been reported for movement onset locations described as the Fröhlich effect37—that is, the perceived onset location of stimuli in motion is shifted in motion direction—or its’ inversion, the onset-repulsion effect38. The original kappa and tau effects (but not their inversions), are often explained by models assuming that expectations about an underlying motion with constant velocity between presentations (slow speed priors) account for the biases39,40. A novel theoretical account, referred to as the speed prior hypothesis41,42, which is also based on prior speed expectations likewise predicts and explains the reversed findings for several biases. This includes the aforementioned offset and onset repulsion effects, but also the inverted versions of kappa and tau effects. In specific, similar to the slow speed hypothesis, this hypothesis predicts smaller/larger spatial and shorter/longer temporal intervals depending on participants’ expectations about the speed (priors), which may be different from the actual speed. Most importantly, it also accounts for possible inversions of the effects, depending on the velocity range administered in the task (ie, the combination of temporal and spatial intervals). For slower presented speeds, a positive relationship between speed and the amount of overshooting is expected (length extension), while as soon as reaching a certain speed (half the speed of the prior), the overshooting should be reduced with increasing speed and even result in undershooting when exceeding the prior speed41,42. It is conceivable that the chosen temporal and spatial intervals in the current study perhaps met the reversal point for the kappa effects, therefore first resulting in a positive effect and then, for longer spatial intervals (where the speed exceeded half of the prior speed) an inversion of this relationship. In addition, the speed prior hypothesis41,42 may also explain the inverted tau effect: If the chosen spatial and temporal intervals resulted in a ‘medium’ speed range (ie, speeds between half of the prior speed and the prior speed), this should have resulted in the observed inverted tau effect.

Finally, next to the many advantages of online studies, like access to a larger and more diverse sample, more efficient/economic use of resources, and reduction or even elimination of experimenter effects43, they also have a few limitations such as no or less control over participants’ behavior during experimentation, used screen sizes, the distance between participants and their screens and the fact whether they finally used a mouse or touchpad for performing the interception task. In Exp. 1 and Exp. 2, 24 out of 57 and 32 out of 53 respectively, participants reported to have used a computer mouse. Concerning the control of participants’ behavior, for instance, a few participants additionally reported that they produced rhythmical sounds with their mouths to support their performance in the temporal task. However, despite these challenges and potential limitations, we deem it unlikely that such behaviors account for our results and findings because we not only found the predicted kappa effects, but we also replicated it across two separate online experiments. Comparisons of online and lab-based studies, so far revealed similar results, emphasizing the validity of web experiments in cognitive and perceptual research44. Regardless, we call for more research examining spatiotemporal biases in interception performance that allows for better controlled and ecologically more valid motor responses such as interceptive movements in a Virtual Reality setting.

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