The attention hypothesis of temporal binding. (a) Attention in outcome binding. The distribution of attention around the clock rim, at the time close to the event requiring a timing report, receives modulation from both action and action outcome. When the sound time is reported, attention increases only after the onset of the sound in the sound only condition. In the action sound condition, attention is activated prior to the sound onset due to action. The difference in the attention distribution between the two conditions can lead to the difference in the reported clock hand position at the time of sound onset (i.e. outcome binding). (b) Attention in action binding. When the action time is reported, the sound in the action sound condition is an extra cue for attention activation compared to the action only condition. Therefore, there is more attention in the action sound condition than the action only condition at clock hand positions after the sound play time, leading to a later reported clock hand position in the action sound time (i.e. action binding). Please refer to the text for detailed information. A stands for the actual clock hand position when the keypress is made, and A’ is the reported A from participants. S stands for the actual clock hand position when the sound is played, and S’ is the reported S from participants.

Trial structure in the AS condition. (a) Each trial started with the clock hand rotating from a random angle. After at least 1000 ms, a voluntary keypress triggered a 250 ms delayed sound. The clock hand continued rotating for another random period between 750 and 1250 ms after sound onset. In timing report trials, participants moved the clock hand back to its position at sound play. In visual probe trials (all 6 probe locations illustrated) and catch trials, participants reported if a visual probe was detected. The imaginary dotted white square (not shown during the testing) illustrates the eye movement control area in Experiment 2 (eyes moving out of this area would lead to trial abortion). In the SO condition, everything was the same except that no keypress was required. (b) A visual probe was presented in each visual probe trial at one of 6 possible locations, which also corresponded to 6 different time points. The position where the clock hand pointed to at the time of sound play was defined as 0° position (0 ms). −50° position (−250 ms) corresponds to the location where the clock hand pointed to when a keypress was made in the AS condition. There were 3 probe locations before 0° and 3 probe locations after 0°. Note that the visual probe was made salient only for the purpose of illustration. SO: sound only condition; AS: action sound condition.

Changed attention distribution and its relevance to outcome binding. (a-b) Results from Experiment 1. a) Individual sound time report in each condition; b) Detection rate of visual probes as a function of condition and probe location. Attention was activated by the keypress in AS condition and by the sound in the SO condition (note that there was no keypress in the SO condition). Bars represent ± 1 standard error. Asterisks indicate significant differences between two conditions at the indicated probe location (false discovery rate adjusted over 6 comparisons). (c-d) Results from Experiment 2 with eye movement control. (e-f) Results from Experiment 3 with eye movement control. An VS condition replaced the SO condition. AS: action sound condition; SO: sound only condition; VS: vibration sound condition.

Similar attention mechanism in action binding. (a) Attention was measured at 11 locations (time points) following the keypress. (b) Individual reported keypress time in each condition. (c) Detection rate of visual probes as a function of condition and probe location. Bars represent ± 1 standard error. AS: action sound condition; AO: action only condition.

Modelling temporal binding with the attention measure. (a) Illustration of the timing report modelling in the outcome binding task. (b-d) Modelling results for outcome binding (Experiments 1-3 combined). b) Scatter plot of the correlation between the modelled timing report and the actual timing report in the AS condition; c) Scatter plot of the correlation between the modelled timing report and the actual timing report in the SO and VS conditions; d) Scatter plot of the correlation between the modelled outcome binding effect and the actual outcome binding effect. (e-g) Modelling results for action binding (Experiment 4). e) Scatter plot of the correlation between the modelled timing report and the actual timing report in the AS condition; f) Scatter plot of the correlation between the modelled timing report and the actual timing report in the AO condition; g) Scatter plot of the correlation between the modelled action binding effect and the actual action binding effect. (h-k) Box-plots of the actual binding effect and the modelled binding effect for all 4 experiments. Asterisks above indicate significant binding effects. Asterisks below indicate significant differences in the size of actual and modelled binding effects. n.s.: not statistically significant.