How does it feel? Passage of time judgments in speeded RT performance

The mean range of individual RT distributions was 1792 ms (SD = 1045 ms), with a mean minimum of 389 ms (SD = 97 ms) and a mean maximum of 2181 ms (SD = 1083 ms). The ANOVA for mean RT revealed significant main effects of numerical distance, F(1, 50) = 94.00, p < 0.001, η_p² = 0.65, and notation, F(1, 50) = 124.02, p < 0.001, η_p² = 0.71. RTs were longer for close numbers (895 ms) than for far numbers (801 ms), and also longer for words (1011 ms) than for digits (691 ms). The interaction did not reach significance, F(1, 50) = 3.98, p = 0.051, η_p² < 0.07. As can be seen in Fig. 1, IRTs and reversed POT judgments showed a similar pattern as RTs. For further analyses, the POT scores were therefore reversed (from 1 = very fast to 5 = very slowly). The ANOVA for the temporal judgments also showed significant main effects of numerical distance, F(1, 50) = 57.73, p < 0.001, η_p² = 0.54, and notation, F(1, 50) = 27.98, p < 0.001, η_p² = 0.37. The main effect of type of judgment was not significant, F(1, 50) = 3.09, p = 0.085, η_p² = 0.06. In contrast to the RT results, there was also a significant interaction between numerical distance and notation, F(1, 50) = 6.27, p = 0.016, η_p² = 0.11. For the temporal judgments, the effect of numerical distance was larger for digits than for words (0.018 vs. 0.011). Importantly, the three way-interaction between numerical distance, notation and type of judgment was not significant, F(1, 50) = 1.19, p = 0.281, η_p² = 0.02, just as the two-way interactions including type of judgment, both ps ≥ 0.257.

In addition to the numerical distance and notation effects, Fig. 1 suggests also an effect of numerical size, especially in the IRT pattern (middle panel). Therefore, we conducted additional individual regression analyses with numerical size as predictor and RT, IRT and POT as outcome variables. These analyses revealed significant positive standardized slopes for RT (M = 0.047, p = 0.004) and IRT (M = 0.255, p < 0.001) but not for POT judgments (M = 0.012, p = 0.739). This was confirmed by a one-way ANOVA comparing the slopes across all three outcome variables, which revealed a significant main effect of outcome variable, F(2, 100) = 19.03, p < 0.001, η_p² = 0.28. Post-hoc Tukey contrasts indicated significant differences between the RT and POT slopes (p < 0.001) and between the IRT and POT slopes (p < 0.001), but no difference between the RT and POT slopes (p = 0.684). It is important to note that these analyses relied on the combined RT data from both introspective (IRT and POT) conditions. The same regression analysis for RT based on only IRT and only POT trials showed significant slopes for IRT trials (M = 0.063, p = 0.002) but not for POT trials (M = 0.036, p = 0.053). A direct comparison of the slopes in the two instrospective conditions, however, did not yield a significant difference, t(50) = 1.44, p = 0.156.

Figure 2 shows the relationship between RT and temporal judgments. The graphs of the functions for IRT and reversed POT judgments look strikingly similar. Accordingly, the LME model analysis yielded no significant main effect or interaction including the factor type of judgment, all ps ≥ 0.104. As expected, RT was a significant predictor, β = 0.58, t(48.7) = 11.61, p < 0.001. There were two other significant predictors, namely numerical distance, β = 0.07, t(8155) = 3.08, p = 0.002, and the interaction between RT and notation, β = 0.12, t(7960) = 4.18, p < 0.001, all other ps ≥ 0.297. As can be seen in Fig. 2, the graphs of the functions were shifted toward longer IRTs and slower POT jugments for close numbers. Addtionally, the slopes of the functions seem to be slightly steeper for digits than for words.

In the present study, we explored the experience of the passage of time in a speeded reaction time task. We were able to replicate the previous results by Corallo and colleagues (2008) that duration judgments (introspective RTs) reflected the effects of numerical distance and notation on RT. POT judgments showed a very similar pattern, with a slower passage of time for more difficult numerical comparisons (close vs. far numbers, words vs. digits). The LME model analysis revealed that both temporal judgments were influenced by numerical distance as well as objective task duration (i.e. RT), with relatively longer IRTs and slower POT judgments for more difficult comparisons.

Our results additionally showed an effect of numerical size on RT and IRT, with longer RTs and IRTs for comparisons with increasing size (i.e., the size effect; e.g. Verguts & Van Opstal, 2005), whereas there was no such effect for POT judgments. Importantly, although the size effect was much more pronounced in IRTs, it occurred also in RTs (a size effect can also be seen in both measures in Fig. 1 of Corallo et al., 2008). This suggests that the size effect in IRTs does not simply reflect a response bias induced by the numerical size of the presented numbers (e.g., a tendency to place the marker on the VAS more to the right for larger numbers corresponding with the increasing scale or tick labels of the VAS from left to right). Nevertheless, the size effect was significantly larger for IRT than for RT, and there was no significant difference between the effect for RT and POT judgments. This suggests that the numerical labeling of the VAS, or maybe even the numerical nature of the IRT estimate as such, might have played a role in the pronounced size effect in IRTs (there was no such labeling of the POT scale). Overall, it remains somewhat unclear to us how reliable the present size effects are, and how possible differences between IRT and POT results could be interpreted.

The result that difficult numerical comparisons were associated with a slower passage of time is in contrast to the results of Martinelli and Droit-Volet (2022b) in the seconds and minutes range with a different task. In their study, participants performed a series of working memory tasks (i.e., reproduction of 2- or 6-digit sequences) and were then asked to judge the passage of time. The series consisted of either 4 or 12 digit sequences and there was a fixed 500 ms response window, in which partcipants had to type in the sequence. This means that the interval to be judged included idle time as well as time filled with task performance, and the relationship between them was reciprocal. That is, the longer it took participants to respond in the working memory task the shorter the idle time in between subsequent tasks. Unfortunately, the authors only reported performance accuracy; however, it is very likely that more difficult and longer sequences resulted in longer RTs as well as typing times. As a consequence, the POT judgments in their study might be more related to the differences in idle time than to the difficulty of the task. A second possibility why we observed a different effect of task difficulty on POT judgments is that our difficulty mainpulations also affected the to be judged time interval, whereas it was constant in Martinelli and Droit-Volet’s study. As a third possibility, the longer overall task processing time in their study compared to the millisecond RTs in our study might have induced a qualitatively different experience of the passage of time. As already mentioned in the Introduction, it is possible that an awareness of the passage of time does not emerge in the millisecond range and therefore participants need to infer it from other factors, as for example, from IRTs.

In contrast to the effects of task difficulty, the present results seem to be consistent with Martinelli and Droit-Volet’s (2022b) observations regarding stimulus duration. In their study, longer stimulus duration and a longer time range (minutes vs. seconds range) resulted in slower POT judgments. In the present study, we considered RT rather than the presentation duration of the number stimuli, which was always 300 ms, as stimulus duration. Nevertheless, POT judgments were clearly affected by RT in the same direction as in Martinelli and Droit-Volet’s study. Since in the present study task difficulty also affected the “stimulus duration”, one might suspect that stimulus duration was the only factor affecting POT judgments. The LME model analysis, however, showed that POT judgments were affected by numerical distance beyond the POT-RT relationship, and the effect was still opposite to the difficulty effect in Martinelli and Droit-Volet’s study.

Previous studies have suggested that duration estimates and POT judgments can be distinguished, when time intervals in the seconds range are to be judged (e.g., Droit-Volet & Wearden, 2016; Droit-Volet et al., 2017), but that they are related when longer intervals in the minutes range are considered (Droit-Volet et al., 2017; Martinelli & Droit-Volet, 2022a). The present results clearly show that duration and POT judgments are very similar, if not interchangeable, when the to be judged temporal interval is very short (in the millisecond range) and filled with active task processing. This suggests that both temporal judgments rely on the same underlying mechanism in this time range. Possibly, in this situation POT judgments are inferred from duration judgments. However, it is also possible that both judgments are inferred or at least biased from factors other than temporal information, as for example from the feeling of difficulty or the knowledge about task difficulty (see e.g., Bratzke & Bryce, 2019; Bryce & Bratzke, 2014).

The present research is subject to several limitations. First, the durations we studied were filled with task processing and task difficulty directly affected the to be judged durations. This situation differs from more common time perception paradigms, in which participants judge the duration of a fixed set of durations (conveyed by a certain stimulus), which they perceive more or less passively. It remains an open question whether the present results generalize to this rather passive perceptual timing task. Second, we were not able to directly analyse the relationship between IRTs and POT judgments, for example, via correlational analyses. This was not possible because we did not assess the two measures within the same trial to avoid possible response biases (e.g. a tendency to indicate the same position on the two scales). Third, one could argue that the VAS method used in the present study is not one of the standard methods to assess duration estimates (as e.g. verbal estimation or temporal reproduction; see Grondin, 2008). However, we consider the VAS as a variant of the verbal estimation method (the estimate is indicated on the scale instead of typed in or spoken aloud), and a previous introspective RT study by Bryce and Bratzke (2015) yielded very similar results with the VAS and the temporal reproduction method. We are therefore reasonably confident that the present duration estimates are not dependent on the use of the VAS method. Finally, in the present study we used a prospective timing task, that is, participants knew in advance that they had to provide temporal judgments after each numerical comparison. Results might be different in a retrospective paradigm, where participants do not know about the temporal task in advance and therefore likely do not attend to time to the same degree. Studying the retrospective paradigm is of course rather uneconomic, especially with rather short durations. Nevertheless, Martinelli and Droit-Volet (2022a) investigated duration and POT judgments with relatively short (20–45 s) and long (80–180 s) durations (viewing an image) under prospective and retrospective conditions. They observed that the more participants attended to time the more slowly time seemed to pass and that even in the retrospective condition participants indicated that they had paid attention to time, even though to a lesser extend (a difference of about 0.3 on a 7-point Likert scale between the pro- and retrospective condition for short durations).

In conclusion, the present study yielded very similar results for duration estimates and POT judgments when participants judged their own reaction time performance in a numerical comparison task. The effects of task difficulty were reflected in both temporal judgments, with longer duration estimates and slower POT judgments for more difficult numerical comparisons. The present results suggest that these two different aspects of temporal experience (duration vs. passage of time) are almost indistinguishable in the millisecond range, at least when participants judge their own reaction time in a cognitive task.