Measuring the Representation of 1-Second Through a Temporal Generalization Task with Repetitive Stimulus

doi:10.21203/rs.3.rs-4702930/v1

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Measuring the Representation of 1-Second Through a Temporal Generalization Task with Repetitive Stimulus

https://doi.org/10.21203/rs.3.rs-4702930/v1

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People retrieve the duration of a 1-second interval from long-term memory to measure supra-second intervals. Although some studies assert that the long-term representation of 1-s (hereafter L1S) is unreliable, the timing literature also indicates a significant correlation between the peak alpha frequency, a stable biomarker, and the precision of the L1S. The present study compared the L1S in time generalization tasks involving different structures. Results revealed that stimulus repetition yielded higher temporal precision, albeit with more overestimation. The precision of the L1S remained stable over two successive days while its accuracy changed systematically. In addition, participants exhibited greater precision when retrieving 1-s from long-term memory (i.e., the L1S) than short-term memory (i.e., the S1S). We propose that the precision of L1S (rather than S1S) could be an individual trait. Additionally, we suggest that L1S (~ 1200 ms) could be the boundary (turning point) between sub- and supra-second time perception. These suggestions provide new perspectives and potential for future research in human timing behavior.

Chronometric intervals, particularly seconds, are crucial in modern life due to the prevalence of analog and digital clocks. In the past, 1-s was defined as 1/(24×60×60) of a day. However, in 1967, the International Committee of Weights and Measures redefined a second as the duration of 9,192,631,770 cycles of radiation produced by the transition between two energy levels of a Cesium-133 atom ¹. Despite its exact definition in physics, people often perceive and understand seconds through everyday experiences. For example, microwave ovens produce 1-s auditory sounds, and intersections use visual 1-s countdowns to prioritize pedestrians ². People retrieve the stored representation of 1-s from long-term memory to measure or produce supra-second intervals, commonly through second-based counting ³. The counting strategy alleviates the impact of memory on the overall variability in timing processes because individuals remember the specific counted number instead of relying on an interval representation ^4–6. As the 1-s serves as a fundamental unit for supra-second intervals, assessing the human capacity to gauge this subjective interval is advantageous.

We name the subjective representation of a 1-s interval the “Long-term representation of 1-Second (L1S).” “Long-term” in L1S indicates that there exists within an individual’s mind a representation of 1 second even without having reexperienced it for a long period. In contrast, we use the term “Short-term representation of 1-Second (S1S)” to refer to the representation of the recently experienced 1-s interval through the presentation, during the encoding phase of a temporal task, of a 1-sec interval. Hence, individuals retrieve the L1S from the long-term memory while the S1S from the short-term memory ⁷. They bring the retrieved L1S or S1S to the working memory as a 1-s interval to be used in ongoing time measurement procedures.

Psychophysical ^8–11, psychopharmacological ^12–14, neuroimaging ^15–19, and patient studies ^9,15,20–24 categorize intervals into sub- and supra-second. Sub-second intervals rely more on automatic and sensory-based processes, whereas supra-second intervals benefit more from higher-level cognitive functions ^3,25. However, there is still some ambiguity when it comes to defining intervals around 1-s, with studies introducing a range between one and two seconds as the intersection point ^3,26–28. For example, discriminating brief auditory intervals may require adopting an explicit counting strategy for intervals longer than 1.2 seconds, as discrimination becomes more challenging beyond this point. This suggests that long intervals may exceed a critical cognitive capacity ^{25,26,28–30}.

Only a few studies address the cue question of the representation of 1-s. Grondin et al. (2020) ⁴ endeavored to estimate the duration of the L1S by adjusting the duration of a sound to match the L1S and producing intervals of 10 seconds by counting from 1 to 11. However, estimations did not consistently align with a 1-s duration and exhibited considerable variability, challenging the assumption of a precise representation of 1-s. Moreover, Rioux et al. (2023) ³¹ investigated the L1S using a time production task, exploring the influence of kinesthetic and auditory factors on interval production. Their findings underscored the instability of the representation of the L1S. While the variability and inconsistency observed in these studies suggest that humans may lack a precise perception of 1-s, noteworthy results emerged in our previous study ³²; there are significant correlations between the L1S (as the reference interval) and alpha peak characteristics through a time generalization task. This raises the question of why, although the peak alpha frequency qualifies as a stable neurophysiological trait marker ³³ linked to L1S ³², previous studies disagreed with the L1S reliability. Is this because the L1S is unstable in nature, or is it because of task conditions? This apparent paradox motivated the present investigation of the human L1S.

We can find in the literature addressing time perception in pathologies estimates of 1-s. Perbal et al. (2003) ³⁴ and Mioni et al. (2013) ³⁵ compared 1-s in TBI and control groups. The former authors used a 1-s finger-tapping task and found that the TBI group overproduced the L1S (1,039 ms) while the control group underproduced the L1S (863 ms). Nonetheless, this 176 ms discrepancy did not differ significantly between patients and controls; the authors attributed this nonsignificant result to the great variability in L1S productions. However, the relative variability of the 1-s tempo rate did not differ across the two groups. TBI patients did not produce more variable L1Ss than control subjects. In the Mioni et al. (2013) study, the TBI cohort showed lower accuracy rates on the time reproduction and time discrimination tasks than the control cohort, but both groups showed equivalent performance on the time production task. For the time reproduction and production tasks, the TBI and control cohorts equally underproduce 1000 ms durations, with an average absolute error of 403 ms across both groups. Although the TBI patients were less accurate than controls, the direction of their errors was similar.

In a somewhat related investigation, Mioni et al. (2016) ³⁶ compared clinical samples, including individuals with anxiety and depression, to a control cohort in 1-s reproduction and production tasks (45 trials involving holding the spacebar). Results revealed that production was less accurate and precise than reproduction, where participants underproduced the 1-s interval. Another study rather compared different age groups. Using a finger-tapping task to produce 30 s, Turgeon and Wing (2012) ³⁷ found that both older and younger healthy participants overproduced a 1-s interval (1,318 and 1,028 ms, respectively).

In this study, we aimed to measure the accuracy and precision (the criterion variables) of the human representation of 1-s in several temporal generalization tasks with varying task demands (Fig. 1A). Firstly, we examined the impact of stimulus repetitions on the L1S (the long-term representation of 1-s). Indeed, it is known that presenting a sequence of intervals instead of a single interval improves duration discrimination ³⁸. Secondly, we investigated the stability of the L1S over one day. If L1S is stable, variability and accuracy should remain the same. Lastly, we will directly compare an L1S condition, which involves retrieving 1-s from long-term memory, with an S1S condition, which involves retrieving 1-s from short-term memory.

Participants

Power analyses for two-tailed paired-samples t-test and repeated measure ANOVA (which were planned to be used in this study) indicated a 34- and 7-subject appropriateness, respectively [G*Power software (version 3.1.9.4) ³⁹, statistical power = 0.8, alpha = 0.05, and medium effect size d = 0.5 ⁴⁰].

We invited students and staff of the University of Isfahan to participate in the experiments. We had three entrance criteria: normal or corrected to normal visual ability, age (18–45 years), and normal mental abilities. For the latter criterion, we selected those who reported no neurological or psychiatric disorders and no medication consumption affecting the nervous system. They were also informed that participation required attendance on two consecutive days[1] , with approximately 60 and 30 minutes on the first and second day, respectively.

In the final sample, we had a group of 48 participants (25 women, 23 men, median age: 23, range: 18–43 years) which was not only in line with the desired power, alpha, and effect size but also in line with the number of counterbalanced orders. In Day 1, we needed to counterbalance four blocks that demanded a multiple of 24 orders (= 4!).

All participants provided written informed consent before the study, which was conducted in accordance with the Declaration of Helsinki and approved by the Ethical Committee of the University of Isfahan.

Temporal tasks

We used temporal generalizations, a variant of the comparison interval task, with various structures. In a standard temporal generalization task, the standard duration (‘S’, equivalent to the point of objective equality, POE) is typically presented multiple times at the beginning of either the experiment or block of trials to allow the participants to encode its duration into memory ^41,42. They then receive, in each trial of the test phase, a comparison duration ($\:{C}_{i}$) around the S and judge whether this $\:{C}_{i}$ is the same as the standard or different, responding with “yes” (same) or “no” (different), respectively. Researchers can then calculate the accuracy and the precision of time perception from the distribution of relative “yes” responses over the $\:{C}_{i}$s ⁴³. In a temporal generalization task, the responses are non-directional (same/different or yes/no), making the task resistant to response bias compared to tasks requiring a directional response ⁴⁴ (i.e., longer/shorter in another form of comparison tasks called time bisection task ⁴⁵).

We utilized a temporal generalization task similar to that used in Mokhtarinejad et al. because that task structure led to significant correlations between L1S and alpha peak (a biomarker) characteristics ³²: a one-inch white disc appeared on the grey computer screen while blinking every “comparison interval” (regularly repetitive stimulus) during each trial (Fig. 1B). Marking the comparison intervals with a continuous white disc made it a filled interval task. In a filled interval, a continuous stimulus defines the duration of the interval, while in an empty interval, two short markers mark the start and end of the interval.

It is normal to select a symmetric range of comparison intervals around the standard interval ⁴³, but our previous study showed that participants barely selected 500 ms and 600 ms as L1S (standard interval: the participant’s representation of 1-s retrieved from their long-term memory). Hence, we adopted comparison intervals ($\:{C}_{i}$) that lasted from 700 to 1500 ms (instead of 500 to 1500 ms) in 100-ms steps. The duration of comparison intervals was randomized from trial to trial but equiprobable (eight for each block). We used just one comparison interval in a trial, but the comparison interval may change in the next trial. For instance, the white disc blinked every 1300 ms in a given trial. After the participant's response (i.e., “yes”: the stimulus blinked every L1S versus “no”: the stimulus did not blink every L1S), the trial terminated. The stimulus reappeared after a random 1- to 3-sec inter-trial interval (ITI), blinking with another comparison interval (e.g., 800 ms) until the response. The participants counted on a second basis to judge whether the stimulus was blinking every second (actually every L1S) or not.

We selected different numbers of comparison stimulus presentations, each allocated to a separate block: 1 (one presentation, i.e., without repetitions: without blinking), 3, 5, and free repetitions. We named the corresponding temporal generalization tasks L1S1[2], L1S3, L1S5, and L1SF, where the last letter indicates the number of stimulus presentations in all trials of a block (Fig. 1C). Participants were instructed to press the correspondent key (“M” for “Mi-paziram” and “N” for “Nemi-paziram” representing “accept” or “reject” as their L1S in Persian) only after the designated presentations in L1S1 (one), L1S3 (three), and L1S5 (five). The response keys (“M” and “N”) were accessible after the stimulus completed its number of presentations. In contrast, in the L1SF condition, the stimulus was presented repeatedly until the participants pressed either of the response keys. Participants were asked to respond quickly from the time the response keys (“M” and “N”) became accessible.

Participants also performed a standard temporal generalization task: an S1SF task (F: free repetition) (Fig. 1A and Fig. 1B). At the beginning of this block, they were presented with the white disc blinking every 1000 ms and were asked to encode its duration as the standard interval in short-term memory (encoding phase). They then performed a temporal generalization task with the S1S as the standard interval (test phase). Thus, in the S1SF task, the target interval was a currently encoded 1-s retrieved from the short-term memory, whereas, in L1S tasks, the target interval was the 1-s retrieved from the long-term memory ³².

We chose an inter-stimulus interval (ISI) of 17 ms, equal to one period of the monitor refreshing (refresh rate = 60 Hz) as the blinking period. Although this interval is very brief and close to the threshold of human visual perception ⁴⁶, all participants were able to detect it in the laboratory's dimly lit environment (please also refer to the supplementary section of Mokhtarinejad et al., 2024 ³²). We chose this short ISI to simulate the temporal characteristics of the second counter of physical clocks (i.e., tick-tocks).

Procedure

Participants visited the Isfahan Cognitive Laboratory on two consecutive days. They sit comfortably 60 cm from the computer screen (LED, vertical refresh rate = 60 Hz, Resolution = 1024×768, 9×7 inch²). We provided oral instructions for each task before performance, ensuring participants understood them.

Participants underwent training for each L1S task on the first day until they indicated they understood the goal, which took two to six minutes. They then completed all L1S tasks (L1S1, L1S3, L1S5, and L1SF) (Fig. 1B) in four separate blocks (Fig. 1A). We counterbalanced the four tasks across participants: Each order was assigned once to a male and once to a female. An additional female filled a vacant position originally intended for a male. After completing all blocks on the first day, participants were asked to identify the task they believed they performed best regarding minimum fatigue and maximum concentration. On the second day (Fig. 1A), the participants successively performed an L1SF and an S1SF task.

Data analyses

We analyzed the data in terms of the point of subjective equality (PSE) as a criterion for accuracy and the Weber ratio (WR) as a criterion for variability/precision ⁴⁷. The PSE represents the mean of an individual's representation of 1-s [i.e., point of objective equality (POE)]. The closer the PSE is to the POE, the more accurate the participant's timing behavior ⁴³.

We used the waveform moment analysis (WMA), a nonparametric statistical method, to calculate the PSE and WR, the criterion variables ⁴⁸. The number of “yes” responses to the corresponding comparison interval ($\:{C}_{j}$) divided by the number of related trials in a block, 8 in this study, were calculated as $\:{f}_{j}$ [Equation (1)]. Then, $\:{f}_{j}$s were transformed into a probability distribution, as shown in Eq. (2). Finally, PSE and WR were calculated according to the Eq. (3) and Eq. (4), respectively.

$$\mathop p\nolimits_{j} =\frac{{\mathop f\nolimits_{j} }}{{\sum {\mathop f\nolimits_{j} } }}$$

$$PSE=\sum {\mathop p\nolimits_{j} \mathop C\nolimits_{j} }$$

$$WR=\frac{{0.6745\sqrt {\sum {\mathop p\nolimits_{j} {{\left( {\mathop C\nolimits_{j} - PSE} \right)}^2}} } }}{{PSE}}$$

We employed SPSS Statistics (version 26) to analyze outcomes and Microsoft Excel (Professional Plus, 2019) to improve visualization. We initially looked for outliers so that we could remove them and obtain normal data distributions. For the data on the first day, we used rmANOVAs to examine the effect of the number of stimulus repetitions on PSE and WR. We then conducted paired t-tests and Pearson correlation analyses to assess the stability of the PSE and WR of L1SF across two consecutive days. Regarding data collected on the second day, we performed paired t-tests and Pearson correlation analyses to compare the PSEs and WRs of the L1SF versus S1SF.

Figure 2 presents the relative acceptance of a comparison interval as the standard for all temporal generalization tasks. Table 1 displays descriptive data for all tasks, with N representing the number of participants after removing outliers to obtain Shapiro-Wilk p-values higher than 0.05.

Table 1

The table provides descriptive data on PSEs (point of subjective equality) and WRs (Weber ratio). Some data were deleted (see column N) to achieve a normal distribution.
	Standard interval	Dependent variable	N	Mean (SD)
First day	L1S	PSE1	48	1147 (135)
		PSE3	48	1197 (134)
		PSE5	46	1223 (123)
		PSEF	43	1256 (97)
		WR1	48	0.115 (0.025)
		WR3	48	0.100 (0.030)
		WR5	44	0.085 (0.022)
		WRF	46	0.083 (0.023)
Second day	L1S	PSEF	46	1195 (125)
	L1S	WRF	48	0.087 (0.029)
	S1S	PSEF	48	1057 (119)
	S1S	WRF	48	0.105 (0.030)

Number of repetitions (L1S tasks of the first day)

One-sample t-tests demonstrated that all PSEs were significantly longer than 1000 ms (p < 0.001). RmANOVAs revealed a significant change in PSE [Greenhouse-Geisser F(2.191, 92.041) = 20.408, p < 0.001, η²_p = 0.327] across different number of repetitions. Post hoc Bonferroni tests indicated a significant difference between L1S1 and all other L1S tasks (p < 0.001) and also between L1S3 and L1SF tasks (p = 0.019). Furthermore, PSEs for all L1S tasks were significantly correlated (p < 0.001), and a linear contrast effect was observed across PSE values [F(1, 42) = 25.461, p < 0.001, η²_p = 0.377], suggesting that the PSE increased linearly with the lower-to-higher number of repetitions. However, although the average number of stimulus repetitions in L1SF (3.88 ± 0.47 over 3465 trials) was lower than that of L1S5 (i.e., 5), the PSE for L1SF lay beyond that of L1S5. RmANOVAs also showed a significant change in WR [F(3,129) = 38.080, p < 0.001, η²_p = 0.470] across different numbers of repetitions. Post hoc Bonferroni tests revealed a significant difference between all WRs (p < 0.022) except L1SF and L1S5 (p = 1.000). Furthermore, WRs for all L1S tasks were significantly correlated (p < 0.001), and a linear contrast effect was observed across WR values [F(1, 43) = 69.425, p < 0.001, η²_p = 0.618], indicating that the WR decreased linearly with a lower-to-higher number of repetitions with the WR of the L1SF as the minimum.

L1SF (first day) vs. L1SF (second day)

Concerning the use of the same L1SF task on the first and second days, paired t-tests showed a significant decrease from the first day to the second day in PSE [t(43) = -4.006, p < 0.001] but no significant change in WR [t(46) = 0.853, p = 0.398]. The correlation between PSEs was significant (r = 0.734, p < 0.001), as was the correlation between WRs (r = 0.570, p < 0.001).

L1SF (second day) vs. S1SF (second day)

On the second day, the L1SF and S1SF tasks were carried out. Analyses showed that there was a significant decrease in PSE from L1SF to S1SF [t(45) = -5.897, p < 0.001]. However, there was a significant increase in WR [t(47) = 4.003, p < 0.001]. The correlation between PSEs was not significant (r = 0.275, p = 0.173), but the correlation between WRs was significant (r = 0.540, p < 0.001). Additionally, it was observed that the PSE increased significantly over the trials: from the first trial to the last trial (PSE = 0.77 n + 1038, linear R² = 0.12, n: the trial number from 1 to 72). This trend was not significant in any other temporal generalization task for PSEs and WRs (linear R² < 0.04).

It is worth interpreting the results based on timing models. Amongst, the scalar expectancy theory (SET) ^49,50 has been very popular. According to the SET, when encoding the 1-s interval of the actual clock into the working memory, an accumulator counts the number of a pacemaker’s pulses corresponding to the duration of the observing 1-s. The content of the accumulator (i.e., the number of counted pulses) is then stored in the short-term (i.e., S1S task) and subsequently in the long-term memory (i.e., L1S task). In each trial of the test phase, participants are presented with a comparison interval (from 700 ms to 1500 ms, with 100 ms steps), where they should judge its duration. They achieve this by measuring the number of transferred pulses, similar to the encoding phase, to extract the content of the accumulator for the comparison interval. By the end of the trial, they compare the current content of the accumulator (for comparison interval) with the previously encoded content of the accumulator (the S1S or L1S, regarding the duration between encoding and test phase) to make a decision: acceptance or rejection. In essence, the L1S task involves accessing the long-term memory, while the S1S task involves accessing the short-term memory to retrieve the content of the accumulator.

Number of repetitions

Results from the experiment on the first day show that stimulus repetition significantly affects how long people perceive it to last. The PSE shifted towards higher values with stimulus repetition (L1S1: 1147 ms, L1S3: 1197 ms, L1S5: 1223 ms, L1SF: 1256 ms). However, there were no significant differences between 3 and 5 and also between 5 and free repetitions. To explain this shift, let us consider a simple example involving a nonrepetitive 1000 ms empty interval and suppose that people estimate it as lasting 1-s. If we replace the empty interval with a 1000 ms filled interval, the perceived duration might be 1100 ms (overestimation). Then, people might judge a 900 ms interval as 1-s in the comparison task instead. This effect is called the filled duration illusion ^51,52. According to the SET, filled intervals lead to a higher pacemaker speed, which shifts the PSE to the left (decrease); with a higher pace of the pacemaker, participants choose shorter comparison intervals as their L1S. More complex effects may be related to the division of attention ⁵², while another possibility is that filled and empty intervals have different switch latencies ⁵³. Participants in this study considered an 1147 ms filled stimulus as their L1S in the L1S1 task (i.e., without repetition). The filled duration illusion, thus, suggests that their actual representation of 1-s (L1S) was longer than 1147 ms. In contrast, stimulus repetitions shifted the PSE towards higher values. Therefore, the repetition had an opposite effect on the PSE compared to the filled duration illusion. Consequently, the L1S (average over all participants) would be somewhere between 1147 ms and 1256 ms, which is surprisingly close to the turning point (~ 1200 ms and not 1000 ms) identified as the boundary between sub- and supra-second intervals ^25,26,54. Even in the literature on animal timing, 1.2 seconds is identified as one of the local maxima on the time continuum for sensitivity to time ⁵⁵. It suggests that the L1S (the interval that people employ in the counting strategy) may be the turning point that separates sub- and supra-second intervals. However, this interval is not the same for everyone but an individual point. When we discuss the S1SF task, we will return to why the L1S is higher than 1000 ms.

The results also indicated that the precision of the L1S increased significantly by using a repetitive stimulus; a higher number of repetitions leads to higher precision (but no difference between L1S5 and L1SF). The positive effect of repetition on temporal precision is in line with previous studies, which showed that stimulus repetition helps participants measure an interval more precisely ^38,54,56. With repetition, the decision-making stage (the last stage in SET) could compare more options (e.g., 5 in L1S5) with the L1S duration. If the decision stage were unsure about the stimulus duration, it would lean on the following stimulus presentation in the trial. This dynamic could explain why the percentage of ‘yes’ responses was higher in L1S1 than in the repetitive stimulus (44% for L1S1, 40%, 36%, and 36% for L1S3, L1S5, and L1SF, respectively). However, people need more repetitions for comparison intervals near their L1S rather than intervals far from their L1S [refer to the supplementary part of Mokhtarinejad et al. (2024) ³²]. Therefore, it would be more practical to use an L1SF instead of an L1S5 task because free repetition of stimulus is more flexible in task performance. The flexibility in L1SF may explain why 80% of participants reported this task as the most convenient task.

Stability over two days

The PSE (extracted from L1SF tasks) decreased significantly from the first day to the second day [t(43) = 4.006, p < 0.001]. According to the SET, this may be due to a change in the content of the accumulator (corresponding to the L1S) during the one-day inter-experiment period. Participants may consciously or unconsciously experience the 1-s outside the laboratory during this period. Additionally, the presence of other tasks could also be a contributing factor ¹⁷ because participants had performed a time production task before the L1SF task on the second day. Nevertheless, the first interpretation is that the PSE is an unstable measure. We accept this point of view; therefore, the PSE for L1S is very vulnerable. However, this interpretation warrants careful consideration; if PSE was truly unstable, a random (non-directional) alteration in PSEs (where the paired t-test is significant but the correlation is nonsignificant) would be expected. In contrast, the one-directional shift confirmed by a robust significant correlation (r = 0.734, p < 0.001, where 74% of participants demonstrated a decrease in the PSE) suggests another reason behind this decreasing shift. Employing rm ANOVA with time as the main factor on L1SF tasks, future studies could explore whether the PSE converges toward a constant value (indicative of practice effects) or exhibits random fluctuations over time (suggesting inherent instability of the PSE).

Concerning variability (precision), our first guess was that the WR of L1SF would decrease from the first day to the second day (p t-test < 0.05, p correlation < 0.05) because of a practice effect. Another assumption was that WR would not be a stable measure (p t-test < 0.05, p correlation > 0.05). However, the WRs of the two days were correlated (r = 0.573, p < 0.001), and this parameter remained stable [t(47) = 0.853, p = 0.398]. It shows that the extracted WR from (at least) an L1SF task may be a stable measure, possibly an “individual psychological trait.” Given the role of the alpha peak in determining the precision of time perception, particularly 1-s perception in an L1SF task ³², and because the alpha peak is a stable individual neurophysiological marker ³³, the stability of the precision of 1-s perception in the L1SF task could be explicable; the pacemaker rate is a function of peak alpha frequency ³², which is a stable biomarker ³³.

L1SF vs. S1SF

It was predictable that the PSE would approach 1000 ms from the L1SF to the S1SF task, given that the content of the accumulator had been updated to the real 1-s in the encoding phase of the S1SF task. However, the intriguing observation was that their updated PSEs tended to increase during the S1SF task performance (linear R² = 0.12) which is equivalent to a decreasing trend in the content of the accumulator. No significant trend was observed for PSEs or WRs in other (L1S) tasks (linear R² < 0.04). This trend suggests that one psychological second is an increasing function of physical time from the time that one encodes it in their memory; individuals may update their PSE every time they observe a real second counter, but then it increases over time. The content of the accumulator reduces during conveying from the short- to the long-term memory. It may be the reason why the PSE for the L1S1 task (nonrepetitive stimulus) was significantly higher than 1000 ms.

Considering the increasing trend of the PSE, experiments in which individuals stay in isolated environments without clock cues for long periods are worth mentioning. In such environments, the long-term representation of 1-s has shown a progressive increase within months of cave isolation, sometimes even doubling ^57–59. The reduced external cues in a cave environment increase the PSE ⁶⁰. Using the S1SF task in our experiment, the PSE showed the same increasing trend in just about five minutes (an interval much smaller than some months) after the encoding phase of 1000 ms. As the subject’s perception of 1000 ms increased by ~ 10% just in ~ five minutes (the S1SF task in this study) and doubled during some months in cave experiments ^57–59, an asymptotical increasing trend could fit the human representation of 1-s as a function of actual time.

Another unexpected result was that the participants were more precise in retrieving 1-s from their long-term memory (L1SF task) than short-term memory (S1SF task). This finding leads us to interpret that the content of the accumulator (for the 1-s) is less variable in the long-term than in the short-term memory. It may be because when one was retrieving the content of the accumulator from short-term memory (i.e., S1S), the content of the accumulator from long-term memory (i.e., L1S) systematically and unconsciously leaked into the working memory (two paragraphs ago). This systematic leakage entrained the S1S toward the L1S from the first to the last (i.e., 72nd ) trial, underscoring the robustness of the representation of 1-s.

General notes

The results of this study are quite practical regarding the precision of L1S. Although individuals retrieved 1-s from their long-term memory (in the L1SF task), they were significantly more precise than when they retrieved 1-s from their short-term memory (in the S1SF task). This difference can be attributed to the fact that the information in the long-term memory is more consolidated than information in the short-term memory. During an S1SF task, the encoded temporal information of the recently trained 1-s (stored in the short-term memory) may interfere with the encoded temporal information of the L1S (stored in long-term memory), leading to an increasing trend in PSE during the S1SF task and undermining the WR (i.e., increasing variability). Consequently, we should consider an individual’s L1S as a more precise interval than the S1S, suggesting that the precision of L1S (extracted from an L1SF task) be considered an individual trait for humans in time experiments.

It is important to highlight two key differences in our experimental approach compared to previous studies. First, we utilized temporal generalization tasks that do not require motor actions. While many previous studies used time production tasks, which can introduce errors related to motor actions and attention, our focus on temporal generalization tasks offers a different perspective ^{4,31,34–37,61}. Second, we implemented repetitive stimuli, particularly in the L1SF task. Previous studies, such as that by Grondin et al. (2020) ⁴, utilized a method of adjustments that did not require motor actions before decision-making, but their stimuli were not repetitive. This difference could potentially make judgments more challenging, as the stimulus appeared in a non-repetitive manner. These differences may explain why previous studies have considered L1S as an unreliable measure ^{4,26,31,36,62}.

Finally, because 80% of participants in this study reported free repetitions as more convenient and easier to concentrate on with less boredom, we propose using free repetition (L1SF) in future studies. This approach would be more practical, especially in studies involving children, the elderly, individuals with ADHD, and those prone to anxiety, who may be less inclined to complete tasks with rigorous instructions. This recommendation is not only based on the results of this study but also on the overall practicality of free repetition compared to predefined repetitions.

Repeating a stimulus in a temporal generalization task is crucial for measuring a 1-s interval more precisely. Our study found that people are more precise in measuring 1-s when retrieving it from long-term memory (L1S) rather than short-term memory (S1S). The precision of 1-s retrieved from long-term memory (L1S) remains consistent over 24 hours, while the precision of 1-s retrieved from short-term memory (S1S) remains inconsistent even over some minutes. This led us to introduce the precision of the L1S, a stable trait if measured by an L1SF task. However, it is important to note that these results do not hold for the accuracy of L1S, which demands future investigations.

Data Availability Statement

The authors will make the raw data supporting this article's conclusions available without undue reservation.

Author Contributions

EM conceptualized and designed the study, developed computerized tasks, performed the experiments, analyzed the data, interpreted the results, wrote the manuscript, and is responsible for the final version of the manuscript. AG conceptualized and designed the study, analyzed the data, interpreted the results, and edited the manuscript. MT conceptualized the study and edited the manuscript. M.N. and S.G. reviewed and edited the manuscript. All authors approved the final version of the manuscript.

Conflict of Interest

The authors declare that the research was conducted without any commercial or financial relationships that could potentially create a conflict of interest.

Acknowledgments

We want to express our gratitude to Farshid Adavi for his assistance during the task design, to Faezeh Sharifi for her help with data collection, and to all the participants who volunteered for the experiments.

Funding

No funding.

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Participants also performed a retrospective estimation and a time production task on Day 2 of the experiment, but the results will be reported in another study.
So, L1S is an interval (the participant’s representation of one second retrieved from their long-term memory), while L1S3, for example, is a temporal generalization task in which the standard interval is the participant’s L1S, and each comparison interval is presented three times.

No competing interests reported.

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Measuring the Representation of 1-Second Through a Temporal Generalization Task with Repetitive Stimulus

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Abstract

Figures

Introduction

Method

Participants

Temporal tasks

Procedure

Data analyses

Results

Number of repetitions (L1S tasks of the first day)

L1SF (first day) vs. L1SF (second day)

L1SF (second day) vs. S1SF (second day)

Discussion

Number of repetitions

Stability over two days

L1SF vs. S1SF

General notes

Conclusion

Declarations

References

Footnotes

Additional Declarations

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