The study of time perception has demonstrated the complex interplay of spatiotemporal information in the brain. As temporal processes are linked to their embodied experience of the environment (Safaie et al., 2020), analyzing the spatial dimension in the study of time perception can provide a powerful tool for understanding the underlying mechanisms that allow us to comprehend the external world. Time and space are two aspects of the physical world that frame our experience of the world. The perception of time and space occurs in an interrelated fashion in human cognition, and recent research shows a growing interest in understanding the underlying mechanisms of their relationship (Goldreich, 2007; Robinson and Wiener, 2021; Schroeger et al., 2022; Whitaker et al., 2022). It has been suggested that time perception occurs through spatialization of time intervals in the face of movement-based events of the world (Robbe, 2023). Such spatialization could be seen in the way we have tied the perception of time to space by devising various types of clocks to keep track of the passage of time.

In modern science, time and space have been represented with measurable proxies imbued with operational definitions, i.e., time and distance intervals, respectively (Buzsáki and Llinás, 2017), which provide a framework for studying and quantifying these abstract concepts. This has made possible the study of the relationship between time and space perception. A variety of time-space interactions in the human perceptual system has been observed. For example, spatiotemporal interference is one such interaction where spatial information can distort the perception of temporal information and vice versa (Vidaud-Laperrière et al., 2022). Peri-saccadic spatiotemporal compression is another phenomenon that serves as evidence of common mechanisms in the perception of time and space (Morrone et al., 2005).

A Theory of Magnitude (ATOM) proposed by Walsh (2003) suggests that the brain has a core common magnitude system for time, space, and quantity. According to this theory, the neural mechanisms underlying the perception of time, space, and quantity are intertwined, and the brain processes these dimensions in a unified manner. This theory has been supported by empirical evidence from studies that have shown that the perception of time and space share common neural substrates (Casasanto and Boroditsky, 2008; Howard et al., 2014; Cai and Connell, 2016; Chen et al., 2021; Cui et al., 2022; Jie and Youguo, 2023). A recent meta-analysis of neuroimaging studies (Cona et al., 2021) has suggested that there is a common system of brain regions that are activated during both time and space processing, including bilateral insula, the pre-supplementary motor area (pre-SMA), the right frontal operculum, and intraparietal sulci. At the neuronal level, it has been observed that spatial information could at least be partially derived from temporal information (Burgess et al., 2011).

Despite these findings, the precise nature and the extent to which these perceptual domains share common mechanisms remain unknown. This has spurred several investigations into better understanding the relationship between time and space (Abramson et al., 2023; Schonhaut et al., 2023). Most studies to date have approached the question in terms of the interferences that occur between perceptual domains (Marcos and Genovesio, 2017; Martin et al., 2017; Üstün et al., 2022). We attempted to approach this question by utilizing behavioral modeling and model comparison.

A Bayesian understanding of timing has revealed that the interaction of the temporal context and the internal ongoing processes culminates in the calibration of estimated intervals (Sadibolova and Terhune, 2022) in the form of perceptual biases. Such a formulation of interval timing presents us with two stages in the process of timing, i.e., the measurement (perception) and the reproduction (action) phases of interval timing (Jazayeri and Shadlen, 2010). The link between the measurement and the reproduction is actualized by an estimation function in the observer model. Based on the nature of the observer model (ideal vs. non-ideal), the estimation functions differ. Bayesian least squares (BLS) and maximum likelihood estimation (MLE) estimators have been used in the literature as prior-dependent and prior-independent functions, respectively (Jazayeri and Shadlen, 2010). The Bayesian perspective has also been explored in human spatial navigation (Petzschner and Glasauer, 2011; Thurley and Schild, 2018). Thus, the probabilistic nature of spatiotemporal information could be well captured by an optimum-seeking system which combines experience-dependent information with contextual noisy measurements to generate an estimate of various facets of time and space. It remains unclear whether the perceptual biases in time and space are both attributable to the prior information.

In this study, we compared how spatial and temporal measurements are implemented by probing sources of variability in the process of time and distance measurement and reproduction, within a probabilistic framework. We used saccadic eye movement as the effector to reproduce presented time/distance intervals. In each block, the subjects had to reproduce the presented time/distance interval by making a saccade to a predefined target in case of time reproduction or to a point on a predefined line to reproduce the presented distance. We showed that the perceptual biases in time perception are explained by prior-dependent computations, as previously shown in the literature. On the other hand, we cast doubt on the contribution of prior information to the observed perceptual biases in space perception.

We investigated the similarities and differences in the perception of time and space, as two components of the “A Theory of Magnitude” (ATOM) proposal (Walsh, 2003). Our investigation was motivated by the evidence regarding various encoding schemes that are recruited for time and space across different parts of the brain (Kraus et al., 2013; Marcos et al., 2017; Abramson et al., 2023). To achieve this goal, we designed two magnitude reproduction tasks and made them as much similar in terms of stimuli and procedure as possible. We used the observer model, which (Jazayeri and Shadlen, 2010) had used, with two different estimators [Bayesian least square (BLS) vs. maximum likelihood estimator (MLE)] to our behavioral data. We showed that adding another parameter (α) to the classic Bayesian observer model (Jazayeri and Shadlen, 2010) resulted in better fits regardless of the estimator used. We added α to the ideal observer model in order to capture the heterogeneity of perception of time and space in population (Matthews and Meck, 2014).

We showed that in the time domain, models that take priors into account (i.e., BLS_2p and BLS_3p) outperformed those that do not (i.e., MLE_2p and MLE_3p). In the space domain, it remains inconclusive whether MLE_3p or BLS_3p better captures our data. Since both of these two models in the space domain fitted data well, we chose BLS_3p to compare the time and space with the same model. Given that a probabilistic framework explained both time and space, we believe there is a general computation principle in both domains. Although time and space perception abide by shared principles, based on our observation, we believe that this probabilistic computation is applied differently in these two domains: time perception is prior-dependent, while we cannot say the same for space perception.

Our results are corroborated by studies that have shown an effect of global context in time. We provide evidence of the effect of global context on space perception in line with previous works as well (Martin et al., 2017; Sadibolova and Terhune, 2022; Wang et al., 2023). However, we also show that not taking into account the prior would also describe the data equally well. The lack of difference between prior-dependent and prior-independent models in explaining the data in space perception points out to a new challenge in the study of space perception. Space takes different meanings in cognitive experiments (eccentricity in the retinotopic map, surface, distance in navigation, etc.). It may be that priors have an effect on some measures of space and not on the other. Or maybe, the degree of effect varies in different spatial contexts.

Our results are supported by biological evidence as well. A recent meta-analysis has shown that although time and space perception share common regions in the brain, their processing might be separated by an anatomical anterior-posterior gradient (Cona et al., 2021). Dissociable neural indices for time and space have also been found in human electroencephalography (EEG) data (Robinson and Wiener, 2021). Neural recordings from prefrontal cortex (PFC) and temporal lobe in epileptic patients found neurons that encode time-only, space-only or both time and space. In non-human primates, researchers found that neurons in the PFC that encode time and space have a small overlap with each other (Marcos et al., 2017) and the commonality may be at the level of goal coding. These results can be explained by the recent proposal that the brain uses distinct mechanisms to measure temporal and spatial magnitudes and combines them in a unimodal estimate through another mechanism (Gladhill et al., 2022).

In the time domain, we observed in subjects with the lowest and the highest α values, α captured the overall overestimation (Subject No. 3, Supplementary Figure 2) and underestimation (Subject No. 17, Supplementary Figure 3) in time reproduction behavior, respectively. We suggest that α represents the speed of an internal clock (Meck, 1983). Research has shown that people experience the passage of time in different ways and the speed of the internal clock varies in population (Wearden et al., 1999; Allman et al., 2014). Some attempts have been made to use drift diffusion models (DDM) to describe data from timing tasks (Simen et al., 2011). In line with this view, we can reformulate time reproduction as a decision of when to act. The timing of a decision has been studied extensively in the decision-making literature by incorporating an evidence-independent urgency signal to the accumulation of evidence (Cisek et al., 2009; Carland et al., 2016; Ferrucci et al., 2021). An alternative interpretation of α in the perception time is that α could be representative of an urgency signal. The heterogeneity that we found in the performance of our subjects in time reproduction might be linked to their different levels of urgency to act.

In the space domain, we made the same observation regarding α. However, the majority of subjects had α values under 1 (median of 0.9 for the distribution of α) which translates into an overall underestimation tendency in distance reproduction. This observation is in line with previous report of an average undershoot of about 10% of target eccentricity in peripheral saccades (Vitu et al., 2017).

We observed that w_m and w_r, model parameters representing the level of variability, were lower in space than in time models. We also found that w_m was not correlated between time and space which hints at the possibility of different measurement mechanisms in the two domains. One explanation for the observed difference in w_m between the two domains could be that there are various sources of variability for time and space, and the measurement and reproduction of space goes under less noisy stages (or processed further). This difference between time and space can be due to how these dimensions are represented in the brain. We believe that given that brain has many retinotopic maps in which spatial relations such as eccentricity, and distance are coded (Felleman and Van Essen, 1991), it has the power to reduce noise at the level of measurement. On the other hand, time has very few chronotopic maps (Protopapa et al., 2019), so the perception of time would be subject to more noise than space. At the motor level, it has long been known that the primate brain has a dedicated system for saccadic eye movement that direct eyes to different locations (Rucci et al., 2007). This system is very precise in transforming static visual scenes into spatiotemporal signals for the brain to structure the spatial maps of the environment (Rucci and Poletti, 2015). We believe that that is the reason why where to look is less noisy than when to look.

We can compute distance based on information from both egocentric cues (i.e., navigation) and distance from fovea (allocentric, i.e., making a saccade) (Feigenbaum and Rolls, 1991; Sabes et al., 2002; Olson, 2003). Distance reproduction tasks so far have mostly focused on egocentric representation as studies have been conducted in virtual reality settings (Maruhn et al., 2019; Zhang et al., 2021). We used a task design in which the perceived and reproduced distances represent the allocentric mapping of spatial information. In recent years, research has found that there are neurons that encode egocentric spatial representations and also represent allocentric spatial relations in primate hippocampal formation (Baraduc et al., 2019; Courellis et al., 2019) driven by saccadic eye movements during visual exploration of environment (Killian et al., 2012). Because of this similarity, we believe our results could generalize to tasks that measure the egocentric encoding of distance.

We observed that as the eccentricity of stimulus increased, the subjects overestimated time intervals, as represented in different (not statistically though) α values obtained from models fitted based on eccentricities we had in our task. We also showed that the fitted parameters to timing data in different eccentricities are not generalizable to other eccentricities, as shown in the deterioration of the goodness-of-fit metric. This finding is in line with the previous observations that as the distance between two visual stimuli, with a constant stimulus onset asynchrony, increases, the perceived duration between these two stimuli also increases. This effect is known as Kappa (Jones and Huang, 1982; Vidaud-Laperrière et al., 2022). On the other hand, the reproduced distances as a function of delay were not different. This observation is unexpected given the literature on the relation of working memory and the anti-saccade task which shows the deterioration of task performance as a function of delay interval (Munoz and Everling, 2004; Meier et al., 2018). We think that the maximum delay duration that we used (1.6 s) is not long enough to manifest the interference effect of time on space.

We do not know that if BLS_3p would be a better fit than BLS_2p to previously reported data in time domain like the ones from Jazayeri and Shadlen (2010). But although they trained subjects to have a stable performance before their main task, we did not have that training. They also provided feedback regarding the precision of performance to their subjects on each trial, which we did not have that either. So, although we cannot extend our modeling works to theirs, our model is more powerful in dealing with not giving feedback and also not requiring subjects to be heavily trained. Given that our model can accommodate data collection with minimum training, we believe it can be applied more easily in populations for which data collection is an obstacle, like children or people with neurological or psychiatric disorders. Meanwhile, note that we only used three intervals for both time and space (nine conditions) to keep the duration for completing both tasks manageable. We are aware that three intervals might not be enough to generalize our results to larger range of time or space, or other models, that we have not used here, might explain these data more comprehensively. Given the literature on time and space perception, we think this possibility is not likely, but needs further investigation.

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

The studies involving humans were approved by the School of Cognitive Sciences, Institute for Research in Fundamental Sciences (IPM). The studies were conducted in accordance with the local legislation and institutional requirements. The participants provided their written informed consent to participate in this study.

SS: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Supervision, Validation, Visualization, Writing – original draft, Writing – review & editing. MS: Conceptualization, Methodology, Project administration, Supervision, Validation, Writing – review & editing.