Time reproduction, bisection and doubling: a novel paradigm to investigate the effect of the internal clock on time estimation

Time perception is an automatic process, but the accuracy in expressing temporal judgment differs among individuals, also in accordance with external environment and internal conditions (Matthews & Meck, 2016). Time scans the moments in our existence, so that the ability to correctly estimate a time interval is crucial for our daily activities (Kononowicz et al., 2018). Given its transversal impact on all our experiences, time perception is one of the topic most investigated in psychology, physiology and neuroscience (Grondin, 2008), nevertheless it still remains controversial. Indeed, conversely to other psychological dimensions, time perception poses a number of unique challenges: for instance—differently from other senses (vision, hearing, smell, etc.)—neither a specific organ nor a single cerebral area have been identified as responsible for time processing (Vroomen & Keetels, 2010). Moreover, varying scales (i.e., from milliseconds to decades) make it really complicated the conceptualization of a single neural substrate or a simple information processing framework of timing (Buonomano, 2007). Nevertheless, different models for time processing have been proposed in the literature. Among these, the Scalar Expectancy Theory, SET (Gibbon et al., 1984a, 1984b), is considered one of the most prominent theoretical accounts of timing. The theory integrates different aspects of human cognition with the psychophysical properties of timing, proposing three interrelated stages of analyses. In particular, the first stage (clock) would be associated with timing: here, an internal pacemaker (counter) would monitor the passage of time. Then, the second stage (memory) would be responsible for a storage of the information just processed, allowing a subjective experience of time. Lastly, the third stage (decision) would be related to the response, thanks to a comparison between the current-objective time and the remembered-subjective time, allowing the selection of an appropriate outcome. Over the past 2 decades, attempts have been made also in identifying brain systems involved in temporal processing, and links have been established between the SET model and neuroanatomical structures undelaying each cognitive stage. The basal ganglia, especially the striatum and pallidum, have been identified as two pivotal hubs of the early raw representation of the temporal interval (Lemoine et al., 2021; Malapani et al., 1998), representing the counter in the SET model (clock stage). Then, the prefrontal cortex would be responsible for the discrimination between internal and external information (Mammarella et al., 2017) and for the raw representation for all the duration of the time interval (Brody et al., 2003), and it would send the processed representation of the interval to the posterior cortex (i.e., inferior parietal lobule and medial temporal lobe; Leon & Shadlen, 2003; Prete et al., 2021), where the final representation of time intervals would be measured, quantified and stored in memory (memory stage). Finally, within the frontoparietal network, the system would compare the new interval with intervals previously stored in memory, and this comparison would drive the behavior (decision stage). This pioneering model has received support also in recent years (Prete et al., 2021) and it has been also integrated, for instance, in a very recent biophysical model (Zemlianova et al., 2022), suggesting the existence of multiple units, allowing the temporal analysis to be translated into the spatial domain, which in turn translates count to a time estimate.

A shared substrate for both temporal and spatial encoding is the basis of another authoritative model proposed by Walsh (Walsh, 2003), aiming to explain the processing of magnitude in general. In fact, Walsh proposed that a common neural substrate exists for time, space and numbers, involving a frontoparietal network. A mole of evidence further validated such model, both at behavioral and cerebral levels, using different paradigms and tasks (Fias, 1996; Macnamara et al., 2018; Prete, 2020; Prete & Tommasi, 2020; Prete et al., 2021), also revealing that duration estimates can vary according to task demands (Droit-Volet et al., 2011). In this model, a left-to-right mental representation is hypothesized, corresponding to a small-to-large distribution of quantities (Dehaene et al., 1993; Walsh, 2003), which has been labeled Mental Number Line (MNL). In the MNL, quantities would be mentally placed from the leftmost to the rightmost portion of a horizontal hypothetical line, in accordance with their smaller/larger quantities, respectively. In this view, independently from the specific content of the magnitude (time, space, and so on), when we are asked to processed quantities, we would automatically place smaller/larger quantities on this MNL, according to their relative weight (from left: smaller, to right: larger). Accordingly, a specific Mental Time Line (MTL) has been proposed, corresponding to the same left-to-right mental representation for small-to-large time intervals, respectively (Droit-Volet & Coull, 2015).

In this framework, the present study was aimed to evaluate whether time representation might be considered a dynamic dimension which might be potentially affected by the environment requests, starting from the hypothesis of a MTL. In particular, we introduced a novel paradigm to test time perception, asking participants either to reproduce, bisect or double a given interval duration (the reference interval). We expected that, in accordance with the left-to-right disposition of quantities (Dehaene et al., 1993; Droit-Volet & Coull, 2015; Walsh, 2003), participants would underestimate the duration when they would be required to bisect the test interval (with smaller quantities mentally placed on the leftmost portion of the MTL), and that they would overestimate the duration when required to double the test interval (with larger quantities mentally placed on the rightmost portion of the MTL), with respect to the duration of the reference stimulus. The reproduction condition (same duration for reference and test interval) was used as a control condition to quantify the objective skill to process time, which would be based on the three stages suggested by the SET model (Gibbon et al., 1984a, 1984b). The paradigm can be considered as a revisitation of the classical paradigms in which participants are asked to categorize a second (test) stimulus as same or different in duration with respect to a first (reference) stimulus (Capizzi et al., 2022; Prete et al., 2021). Furthermore, this comparison task has been already used only in reproduction paradigms (reference and test stimuli had the same duration), and in bisection paradigms (test stimuli lasting a half than the reference one; Kopec & Brody, 2010). In the present study, instead, participants were asked to actively “produce” a specific time interval, which could be the same (reproduction), a half (bisection) or twice (doubling) in duration with respect to a reference interval. A correlation analysis is also carried out among the three tasks (reproduction, bisection and doubling) to verify the possibility of an overall ability in mental time manipulation: we expected that a better performance in reproducing time intervals can correlate with a better performance in manipulating the same intervals (bisection and doubling). Furthermore, besides introducing the doubling condition and the active adjustment task, we also measured handedness, anxiety and personality traits in a sample of healthy participants. In fact, a possible influence of handedness on the processing of magnitudes has been suggested (Serrien & Spapé, 2022), including time (Hancock, 2011), and a very recent study based on the SET model revealed that, for instance, in older adults, the accuracy in time scanning would be compromised due to a slower clock (stage 1 of the SET model), accumulating less pulses, and leading to a slower scanning of time intervals (stages 2 and 3; Capizzi et al., 2022; Droit-Volet et al., 2019). Moving from these premises, we wondered whether more anxious participants have a faster clock, resulting in more pulses accumulated and thus in a faster subjective scanning of time: we expected anxiety as a predictor of the accuracy in timing paradigms, hypothesizing a wider underestimation of intervals in participants with higher anxiety scores, with faster counter resulting in anticipatory responses. Finally, starting from some evidence of a different time processing in accordance with some personality traits (in particular: neuroticism, Witowska et al., 2020; and extraversion, Bisson & Grondin, 2020; Rammsayer, 1997), we also administered a personality questionnaire to verify whether specific personality traits could be associated with a better performance in time processing. It has been found that higher levels in psychoticism and emotional instability (neuroticism) are related to higher overestimation of time intervals (Kirkcaldy, 1984), and that higher levels of extroversion lead to a greater error rate in time judgments, so that it has been proposed that extravert individuals generate an active inhibition processing more quickly, and that they also switch-off this inhibition more slowly, than introvert persons (Eysenck, 1959). Starting from these findings, we hypothesized larger errors in time estimation for participants with higher levels of neuroticism and extraversion, and—conversely—a better performance in participants with higher scores in conscientiousness, due to a higher control of the internal clock.

Time processing is a complex ability, susceptible of inter-individual differences: subjective experience of time can differ from objective time, and it can also differ among persons. In the present study, we investigated not only the ability to reproduce, after a brief delay, the time interval just experienced, but also the ability to mentally manipulate this time interval, by asking participants to reproduce it as either lasting a half of time or twice with respect to the reference interval. The first result of the present study is that participants correctly reproduced a short time interval (from 1500 to 5000 ms), confirming a kind of internal clock which keeps track of time. Positive correlations among the three conditions (reproduction, bisection and doubling), moreover, confirm an overall ability in mentally manipulating time intervals. In accordance with the SET model (Gibbon et al., 1984a, 1984b), we can conclude that in this condition all the three stages included in the model correctly run: the internal counter (clock) monitor the passage of time (stage 1), it allows a storage of the information just processed into the memory (stage 2), and after a comparison between the current-objective time and the remembered-subjective time, the appropriate response is selected and produced (step 3).

Second, the present results also showed that such a model is valid only in the Reproduction condition, when the interval just experienced has to be reproposed with its exact duration. However, when participants were asked to mentally manipulate the interval duration, they overestimated time intervals when they should mentally bisect the durations, but they underestimated them when they should mentally double the durations. This pattern of results revealed not only that the internal clock can be useful when time has to be linearly scanned, but also that it can fail when time has to be mentally manipulated, furthermore it appears to be in contrast with a Mental Time Line (Droit-Volet & Coull, 2015). According to the MTL, in fact, we expected a shift on the left side of the hypothetical mental line during bisection (when the time interval must be mentally divided by two), leading to an underestimation, and a shift on the right side of the MTL during doubling (when the time interval must be mentally multiplicated for two), with a consequent overestimation. We speculate that this pattern can be due to the fact that a left-to-right mental disposition of time (MTL) occurs mainly in perceptual tasks, whereas in the present task, in which a short-term retention is required, information stored in memory is not subjected to this kind of mental spatialization. We hypothesized, instead, that the convergence of the performance toward a middle interval (i.e., underestimation during bisection and overestimation during doubling) could be viewed as a kind of aftereffect. In this perspective, when required to reproduce an interval longer than that just presented (doubling condition), participants tend to mentally shorten the estimated duration, whereas when required to reproduce an interval shorter than that just presented (bisection condition), they tend to lengthen the estimated duration. A similar pattern has been widely documented when participants are asked to compare two intervals and to decide whether the second is shorter/longer than the first one (e.g., Heron et al., 2012; Li et al., 2017): in this condition, it has been found that after being adapted to a long/short reference stimulus, the following test stimulus is judged as shorter/longer than the first one, respectively (Li et al., 2017; Prete et al., 2021). The present results can be viewed in this framework: starting from the correct performance during the Reproduction condition, showing that participants are able in internally scanning the time, we can speculate that in the Bisection condition, participants mentally transformed the perceived reference duration into a shorter duration (half of the reference), conversely in the Doubling condition they mentally transformed the perceived reference duration into a longer duration (twice the reference). Thus, we propose that the short-term retention in memory of these transformed durations (until the response is given, stage 2 of the SET model) acts as a kind of imagined adaptor, leading to the same kind of aftereffect described in perceptual tasks.

Finally, the present results showed that neither age nor scholarity affect the performance, even if it has to be highlighted that the sample tested in the present study is highly homogeneous in both of these variables, and the same is true for handedness, with only 4 left-handed participants. Moreover, no effect of anxiety scores emerged from the present results, confirming previous evidence (Kelly, 2000). However, some personality traits explained the performance in the Bisection condition. It is interesting in this regard to highlight that also the specific effect of personality traits found here largely confirmed previous evidence: for instance, a study involving male participants revealed that, when required to reproduce target intervals, extraverts tended to overestimate time and to make less accurate time judgments when compared to introverts, whereas participants with higher psychoticism scores were less prone to overestimate time intervals and showed better accuracy of temporal reproduction than those with lower psychoticism scores (Rammsayer, 1997). The present results confirm a significant effect of personality traits, at least in time bisection, confirming the central role of extraversion and openness to experience on time processing (see also (Bisson & Grondin, 2020).

Finally, the best predictor for both Bisection and Doubling is anyway the performance in the Reproduction condition. This evidence further supports the abovementioned idea of a functioning clocker, which is at the basis for the correct performance in the Reproduction condition, and agrees with the idea that it is not time scanning the issue leading to a wrong performance in the other two conditions: a person who performs well in the Reproduction has high timing skill. The issue at the basis of the incorrect performance during the Bisection and the Doubling would be an adaptation to the correctly imagined intervals, which have been either bisected or doubled, which in turn leads to the overestimation or underestimation of the test interval. This idea is also in line with the positive correlations found among the three tasks, revealing that participants with a good performance in time reproduction have a good performance in both time bisection and doubling. Further studies are needed to verify such a conclusion, also due to the fact that the active reproduction of a perceived time interval is a poorly exploited paradigm, since the most exploited task in this domain is the passive judgment of the length of a test stimulus as shorter/longer with respect to a reference. Furthermore, even if the bisection procedure has been already used in previous studies, to our knowledge, no previous tasks have been carried out in which participants are asked to actively reproduce a test stimulus lasting twice than the reference. For all these reasons, the present results must be considered an interesting starting point for further explorations of this still debated framework, which is so crucial in our everyday life.

In the context of time perception, several studies have been shown how mental representation of a given interval might be modulated by multiple factors such as mood (Fayolle et al., 2014) and cognitive load (Block & Gruber, 2014). These studies described time perception as a dynamic dimension which might be sensitive to both environment request and specific situation. Moreover, over the last 10 years, psychologists have become increasingly interested in what we might call “time illusions”, which consists in a misrepresentations or manipulations of some temporal aspect of a situation (Jaffe, 2018). In our study, even though participants were able to replicate the time interval accurately, a significant overestimation and underestimation was present when they were asked to bisect or double the time duration. This progressive shift of the internal clock might suggest that, once created, the mental representation of a given interval would be affected by either a bisection or a doubling task where the participants are asked to manipulate the time efference copy to efficiently respond to environment requests. Interestingly, the error was strongly related to the direction of the time projection with participants that either under or overestimate, depending on whether they were asked to bisect or double the time interval. Previous studies reported this effect of direction for other cognitive domains, such as space perception (Bradshaw et al., 1987), which shares neural substrates with time representation (Walsh, 2003). Indeed, numerous findings have shown how, depending on conditions, our brain fails to correspond the time’s true nature (Treisman, 1999). Internal and external factors affect the processing of the metaphysical representation of a given interval and it seems that the brain would be able to counterbalanced accordingly with the situation (Yarrow et al., 2001). Such compensation can lead us into error which might assume different direction (under/overestimation) depending on environment request.

This study showed that brief time intervals can be correctly reproduced after a short delay, providing a further support for an internal clock keeping track of time. The mental manipulation of time—required to bisect and to double the same time intervals—is possibly based on the same cognitive mechanism, as suggested by the positive correlations among the performance collected in each of these tasks, but it does not exactly correspond to the same internal clock. In the present study, in fact, participants overestimated and underestimated time when required to bisect and to double the intervals, respectively. This evidence suggests an adaptation mechanism, according to which the mental representation of time acts as an imagined adaptor, influencing the following response. Finally, the present results also revealed that neither age/scholarity nor anxiety affect time processing, but they showed a role of some personality traits (i.e., extraversion and openness to experience) on time bisection. This last evidence needs to be further investigated in the attempt to shed light on the specific mechanisms underlying this peculiar task. It is surprising in fact to note that personality traits do not affect either time reproduction or doubling, possibly suggesting specific mechanisms—and leading to also hypothesize specific cerebral circuits—involved in this task. This speculation must be specifically investigated both at a cognitive and at a cerebral level, but the results found here suggest this possibility. As specified above, caution is needed concerning the null effects of the demographic data on time processing due to the high homogeneity of the sample tested. In particular, it would be interesting to investigate how time processing change during lifespan, the possible difference between women and men in time manipulation, as well as the possible effect of field of study (scientific vs. humanistic) on time scanning, and following studies should involve participants with different background and demographic features to disentangle the role of such individual features on a domain which is so crucial in our daily life such as time processing.