How a target’s speed influences the extent to which the time or place at which it is intercepted is adjusted

Participants stood in front of a large screen and tried to intercept moving targets by lifting their right index finger off an indicated starting point, 20 cm below the centre of the screen, and tapping on the target. The target moved to the right at a constant velocity, 40 cm above the starting point (Fig. 2). Participants had to wait for the moving target to appear before lifting their finger. To interpret participants’ adjustments to their ongoing or subsequent movements, we have to know how much they should have adjusted. We therefore artificially introduced a need to adjust the movement by having the moving target jump along its path.

There were two experiments, that mainly differed in the timing of the jump. In Experiment 1, the jump was initiated as soon as the participant’s finger left the outline of the starting point, so there was ample time to adjust the ongoing movement (Brenner et al. 2023). In Experiment 2, the jump was initiated when the participant’s finger was within 5 cm of the target’s path. Considering a delay of between 22 and 60 ms from the moment the requirements were met to an actual change occurring on the screen (Brenner and Smeets 2022), the target jump was only visible on the screen near the moment the finger hit the screen. Thus, participants could not adjust their ongoing movement. But they could use the feedback to adjust the next trial. Experiment 2 included a control in which participants were encouraged to change the moment rather than the position at which they intercepted the target by indicating about where the target had to be hit.

Fig. 2figure 2

Schematic representation of a participant in Experiment 1. Each trial started with the participant placing his or her right index finger at the starting point (red disk). Briefly after that, a black, moving target disk appeared. The task was to tap on the target disk

Participants

There were 44 participants in Experiment 1, 24 in the main part of Experiment 2, and 17 in the control of Experiment 2. Most were between 18 and 30 years old, but a few were older (up to 65 years old). There were slightly more females than males (about 60%). They all had normal or corrected-to-normal vision, and none had evident motor abnormalities.

Stimuli and experiments

The experiments were conducted in a normally illuminated room. Images were back-projected at 120 Hz and a resolution of 800 × 600 pixels onto a large screen (Techplex 150; 1.25 m x 1.00 m) that was tilted backward by 30° (Fig. 2). The main difference between the trials within each experiment was the target’s speed. There were slow targets and fast targets. Details of the target speeds and the targets’ lateral starting positions, as well as other differences between the experiments are summarised in Table 1 and Fig. 3. In the next paragraphs, we will explain the origin of these differences. Each experiment consisted of two or three blocks of trials.

In Experiment 1 we considered that participants might move slowly to have more time to adjust the ongoing movement. Therefore, we let the targets appear quite far to the left of the starting point. To make this possible, we placed the starting point 40 cm to the right of the screen centre. Since participants did not move slowly in Experiment 1, we placed the starting point only 20 cm to the right of the screen centre in Experiment 2. The starting point was larger in Experiments 2 than in Experiment 1 (Fig. 3). The reason for having a small starting point in Experiment 1 is that in that experiment the finger leaving the starting point initiated the target jump, so a smaller starting point ensures a more consistent timing across trials. In Experiment 2 the size of the starting point is irrelevant, so we selected a size that made it easy for participants to initiate trials. In the control of Experiment 2, we indicated a region within which participants had to hit the target to evaluate whether participants can adjust the timing of their movements more when they are discouraged to change where they hit the target.

The lateral position at which the target appeared was attuned to the target’s speed such that the target would be hit within about the same region of the screen when moving fast as when moving slowly. The change in the starting point’s colour between Experiments 1 and 2 was unintentional, and is presumably irrelevant. The target size intentionally changed in Experiment 2. It was larger in the control of Experiments 2 than in Experiment 1 to ensure that participants hit an acceptable number of targets (and so did not get too frustrated by target jumps that they could not compensate for). In the main part of Experiment 2 we equated performance rather than target size between slow and fast targets. To achieve this, targets initially had a diameter of 2 cm, but the diameter was multiplied by 1.1 every time the participant missed a target, and it was divided by 1.1 every time the participant hit the target. This was done separately for slow and fast targets (that were presented in separate blocks). Thus, on average, participants hit about half the targets. As it is more difficult to hit faster targets, we anticipated that fast targets would on average be larger than small ones. We increased the difference in speed between slow and fast targets after Experiment 1, because in Experiment 2 we expected to see changes to the next movement rather than to the current one, and adjustments to the next movement are usually incomplete (van Beers 2009).

Experimental setup and measurements

An infrared camera system (Optotrak 3020, Northern Digital, Waterloo, Ontario) was placed at about shoulder height to the left of the screen (Fig. 2). It measured the position of a marker (an infrared light emitting diode) attached to the nail of the participants’ right index finger at 500 Hz. At the beginning of each block of each experiment, participants aligned the Optotrak’s coordinate system with the screen by placing their right index finger on four small dots at the corners of an imaginary 60 cm x 50 cm rectangle at the centre of the screen. The marker’s positions when the finger was on the four dots were used to express later finger movements with respect to the screen, automatically correcting for the fact that the marker was attached to the fingernail rather than to the tip of the finger.

To know where the finger is with respect to the moving target, we also had to synchronize the measured marker positions with the presentation of the images of the moving target. For this, we presented a flash at the top-left corner of the screen at the moment a new target appeared. A similar flash was presented at the moment the target jumped. About 1 ms after the flash stimulated a sensor that was placed in the path of the light projected towards the top-left corner of the screen, a second marker attached to the left side of the screen stopped emitting infrared light for about 10 ms. This second marker ‘disappearing’ in the Optotrak measurements was used to synchronize the timing of the finger movements with the images. It did so to within 2 ms.

Fig. 3figure 3

Schematic representation of the experiments (not to scale) showing the colours and diameters (Ø) of the starting points and targets. The target and finger are shown at the moment that the target jumped (jumps to the right are shown, but the target could also jump to the left). The grey disks represent earlier target positions. In Experiment 1 the target jumped as soon as the finger started moving, so there was enough time to adjust the ongoing movement. In Experiment 2 it jumped just before the finger tapped the screen. We anticipated that participants would respond to the resulting error by changing the way they moved on the next trial. The target diameter was adjusted to achieve 50% successful trials for both target speeds. In the control Experiment the target size was fixed and the target had to be intercepted within a green, square interception zone (centred 5 cm to the right of the centre of the starting point). The background was white rather than grey to make the interception zone easier to see. Further details are given in Table 1

A tap on the screen was detected when the finger was less than 0.5 cm above the screen, and its deceleration in the direction of the screen (or acceleration away from the screen) was larger than either 50 m/s2 (Experiment 1) or 40 m/s2 (Experiment 2). We reduced the threshold after Experiment 1 because sometimes participants tapped too gently. When they do so we can recover the moment of the tap during the analysis, but the participant does not receive the appropriate feedback. In Experiment 1 this is not really a problem, but in Experiment 2 seeing the tapping error is obviously critical.

Once a tap was detected, we determined whether the target was hit by comparing the position of the finger at the moment of the tap with the position of the target at that moment. If the finger hit the screen before the target jump was visible on the screen (because the last 5 cm of the finger’s movement was covered within the delay) the feedback was determined using what the target’s position would have been if it had already jumped. A target was considered to have been hit if the participant’s fingertip (as determined from the position of the marker) was within the outline of the target at the moment of the tap. If so, the participant heard a sound and the target stopped on the screen at the position at which it was hit (due to the delay it was actually presented at several positions along its original path after being hit, but then jumped back to precisely where it had been at the moment of the tap; participants did not notice this). If participants missed the target, no acoustic feedback was provided and the target deflected away from the finger at 1 m/s (so if participants tapped below and to the right of the target, the disk moved up and to the left from where it had been at the moment of the tap). The static (if the target was hit), deflected (if it was missed), or continuing (if no tap was detected) target disappeared after 500 ms if it had not moved off the screen before then. In the control of Experiment 2, the sound indicating that the target had been hit successfully only sounded if the tap was within the indicated hitting region. If the target was hit outside this region it did stop moving, but there was no sound.

Table 1 Blocks, trials and target detailsProcedure

At a random moment between 0.6 and 1.2 s after participants placed their finger on the starting point, the starting point disappeared and the target disk appeared. If the finger left the starting point before the target appeared, the target did not appear, and the finger had to move back to the starting point to restart the waiting period. In half the trials the target jumped to the left and in the other half it jumped to the right. The idea was to compare participants’ fingers movements after leftward and rightward target jumps to identify how movements changed in response to seeing the target at a different position than anticipated. By doing so for targets moving at two different velocities, we aimed to determine whether participants rely more on changing the timing (when they tapped) than the position (where on the screen they tapped) when the target moved faster. The target jumps were always much smaller than the diameter of the target (Fig. 3). We know that people respond to even smaller jumps (Brenner et al. 2023). The target jumped as often to the left as to the right for each target speed, and the leftward and rightward jumps were always randomly interleaved. In Experiment 1 we presented slow and fast targets in separate blocks of 80 trials each, as well as randomly interleaved in a block of 160 trials (Table 1). In Experiment 2, we only presented slow and fast targets in separate blocks, because we expected the clearest influence on the next trial when the target was moving in the same way. In all cases, the order of the blocks was counterbalanced across participants. Participants could rest for a few minutes between the blocks.

Data analysis

We determined the fraction of targets that were hit for each speed in each experiment, but other than that we made no distinction between hits and misses. Thus, we determined the time taken on each trial as the time from when the target appeared until the finger hit the screen, irrespective of whether or not the target was hit. Our main measure was the extent to which people adjusted where (position) and when (timing) they hit the screen. By comparing adjustments to leftward and rightward target jumps, we isolated responses to the ‘errors’ introduced by such jumps from other aspects of the movement. Experiment 1 examines changes to the ongoing movement, so we compared movements in which the target jumped leftward and rightward. Experiment 2 examines changes on subsequent movements, so we compared movements in which the target had jumped leftward and rightward during the previous trial. In both cases there is reason to believe that participants will change either the position, or the timing, or both (Brenner et al., 2015, 2023). Our prediction was that people would adjust the timing more (and position less) for faster targets.

Since the time (t) and lateral position (x) of the tap may gradually shift during the experiment as participants become more accustomed to the task, get tired, or learn from feedback on previous trials, we quantified the responses to the jumps that we introduced as the change relative the previous trial, rather than as changes relative to average behaviour. So, for each trial n, we calculated the signed trial-to-trial change in the lateral position of the tap on the screen (\(\:\varDelta\:_\)) and in the time taken (\(\:\varDelta\:_\)):

$$\:\varDelta\:_=_-_$$

(1)

$$\:\varDelta\:_=_-_$$

(2)

we related these changes to the direction of the jump on the current trial in Experiment 1, and to that on the previous trial in Experiment 2. Thus, if the target jumped to the left on trial n of Experiment 1, the values of \(\:\varDelta\:_\) and \(\:\varDelta\:_\) were considered to be responses to leftward jumps. If it jumped to the right, they were considered to be responses to rightward jumps. Similarly, if the target jumped to the left on trial n−1 of Experiment 2, the values of \(\:\varDelta\:_\) and \(\:\varDelta\:_\) were considered to be responses to leftward jumps. If it jumped to the right, they were considered to be responses to rightward jumps. In both cases, we then determined the median value for leftward and rightward jumps for each participant. We did so separately for blocked and interleaved trials in Experiment 1. We determined the median rather than the mean so that we do not need to worry about outliers. Our estimate of participants’ adjustments is half the difference between their median changes after rightward and leftward jumps. We divided these median changes by 1 cm (for the change in position) or the time it took the target to move 1 cm (for the change in timing) to express the changes in position and timing as fractions of the adjustment that is required to fully compensate for the target jump.

We predict that participants will adjust the timing more and the position less for fast targets than for slow targets. To test this prediction, we compared the difference between the changes in timing and position (expressed as fractions of the required adjustments) for slow and fast targets. We tested the hypotheses that this difference would be larger (more positive) for fast targets, indicating that participants rely more on adjusting the timing for fast targets, using paired one-sided t-tests. To get more insight in the way movements are adjusted, we also plot the means of the median changes (across participants), both as fractions of the values needed to compensate for the jump, and in terms of the actual changes (in mm for position and ms for timing). Since full compensation could be achieved by many combinations of adjustments to the timing and to the position of the tap, we plot the mean values of both adjustments with 95% confidence ellipses (across participants’ median values) for the combined means. Doing so can inform us on the extent to which differences between participants in the extent to which the time or position of the tap are adjusted are due to differences in the overall amount of compensation, or to differences in the way in which the compensation is achieved.

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