The number-time interaction depends on relative magnitude in the suprasecond range

Number-time interaction: Search for a common magnitude system in a cross-modal setting

A theory of magnitude (ATOM) suggests that a generalized magnitude system in the brain processes magnitudes such as space, time, and numbers. Numerous behavioral and neurocognitive studies have provided support to ATOM theory. However, the evidence for common magnitude processing primarily comes from the studies in which numerical and temporal information are presented visually. Our current understanding of such cross-dimensional magnitude interactions is limited to visual modality only. However, it is still unclear whether the ATOM-framework accounts for the integration of cross-modal magnitude information. To examine the cross-modal influence of numerical magnitude on temporal processing of the tone, we conducted three experiments using a temporal bisection task. We presented the numerical magnitude information in the visual domain and the temporal information in the auditory either simultaneously with duration judgment task (Experiment-1), before duration judgment task (Experiment-2), and before duration judgment task but with numerical magnitude also being task-relevant (Experiment-3). The results suggest that the numerical information presented in the visual domain affects temporal processing of the tone only when the numerical magnitudes were task-relevant and available while making a temporal judgment (Experiments-1 and 3). However, numerical information did not interfere with temporal information when presented temporally separated from the duration information (Experiments-2). The findings indicate that the influence of visual numbers on temporal processing in cross-modal settings may not arise from the common magnitude system but instead from general cognitive mechanisms like attention and memory.

Attention mediates the influence of numerical magnitude on temporal processing

The processing of time and numbers has been fundamental to human cognition. One of the prominent theories of magnitude processing, a theory of magnitude (ATOM), suggests that a generalized magnitude system processes space, time, and numbers; thereby, the magnitude dimensions could potentially interact with one another. However, more recent studies have found support for domain-specific magnitude processing and argued that the magnitudes related to time and number are processed through distinct mechanisms. Such mixed findings have raised questions about whether these magnitudes are processed independently or share a common processing mechanism. In the present study, we examine the influence of numerical magnitude on temporal processing. To investigate, we conducted two experiments using a temporal comparison task, wherein we presented positive and negative numerical magnitudes (large and small) in a blocked (Experiment-1) and intermixed manner (Experiment-2). Results from experiment-1 suggest that numerical magnitude affects temporal processing only in positive numbers but not for negative numbers. Further, results from experiment-2 indicate that the polarity (positive and negative) of the numbers influences temporal processing instead of the numerical magnitude itself. Overall, the current study seems to suggest that cross-domain interaction of magnitudes arises from attentional mechanisms and may not need to posit a common magnitude processing system.

Numerical Magnitude Affects Accuracy but Not Precision of Temporal Judgments

A Theory of Magnitude (ATOM) suggests that space, time, and quantities are processed through a generalized magnitude system. ATOM posits that task-irrelevant magnitudes interfere with the processing of task-relevant magnitudes as all the magnitudes are processed by a common system. Many behavioral and neuroimaging studies have found support in favor of a common magnitude processing system. However, it is largely unknown whether such cross-domain monotonic mapping arises from a change in the accuracy of the magnitude judgments or results from changes in precision of the processing of magnitude. Therefore, in the present study, we examined whether large numerical magnitude affects temporal accuracy or temporal precision, or both. In other words, whether numerical magnitudes change our temporal experience or simply bias duration judgments. The temporal discrimination (between comparison and standard duration) paradigm was used to present numerical magnitudes (“1,” “5,” and “9”) across varied durations. We estimated temporal accuracy (PSE) and precision (Weber ratio) for each numerical magnitude. The results revealed that temporal accuracy (PSE) for large (9) numerical magnitude was significantly lower than that of small (1) and identical (5) magnitudes. This implies that the temporal duration was overestimated for large (9) numerical magnitude compared to small (1) and identical (5) numerical magnitude, in line with ATOM’s prediction. However, no influence of numerical magnitude was observed on temporal precision (Weber ratio). The findings of the present study suggest that task-irrelevant numerical magnitude selectively affects the accuracy of processing of duration but not duration discrimination itself. Further, we argue that numerical magnitude may not directly affect temporal processing but could influence via attentional mechanisms.

Number is special: time, space, and number interact in a temporal reproduction task

Space, time, and number are among fundamental aspects of behavior and reasoning about the environment. Recent studies have shown that these dimensions highly interact with each other. To explain such interaction, two theories have been proposed: A Theory of Magnitude (ATOM), which posits the existence of a common magnitude system, and Conceptual Metaphor Theory (CMT), which proposes abstract domains such as time and number are mapped through more concrete domains such as space. The present study investigates the interaction of number, time and space in a single experimental paradigm using a temporal reproduction task with a visuospatial component. We also investigated whether mathematical education and continuous involvement with calculations and numbers change the processing precision related to number, time, and space. Two groups of students in mathematics (n = 28) and Persian literature (n = 28) participated in a time reproduction task. The stimuli included Arabic numbers 1, 2, 8, and 9, which were presented to the participants over short (300, 400, 500 ms) and long durations (1000, 1100, 1200 ms) on both sides (left and right) of the monitor. The interaction effect of spatialـnumerical and temporal-numerical was found to be significant. There was no overall time-space interaction, but the triple interaction effect between number, time, and space was significant suggesting the existence of a common representational system. This main result was slightly in line with recent proposed theories. Furthermore, the results showed that the main effect of group was not significant. In addition, we found that among the three factors (number, time, and space) the effect of number is more prominent, i.e., when number disappeared the interaction effect was not observed. The results also suggest that the nature of interactions between these factors is not influenced by cognitive and educational factors. The findings of the study are finally discussed in terms of symmetrical or asymmetrical cross-dimensional influences within the frameworks of ATOM and CMT theories.

Bidirectional examination of the interaction between time and numerosity corroborates that numerosity influences time estimation but not vice versa

There has been great interest in the idea that time, number, and space share a common magnitude system. However, only a handful of studies examined bidirectional interaction between time and number and the results varied depending on the specifics of the methods and stimulus properties of each study. The present study investigated bidirectional interaction between time and number using estimation tasks. We used duration (Experiment 1) and numerosity (Experiment 2) estimation tasks to investigate the effect of numerosity-on-duration and duration-on-numerosity estimation. The results from the two experiments demonstrated that numerosity influences duration processing but not vice versa; that is, there was unidirectional interaction between numerosity and time. The duration of stimulus presentation was overestimated for stimuli larger in (task-irrelevant) numerosity. Possible mechanisms underlying the unidirectional interaction between time and number are discussed.

A Bayesian Perspective on Accumulation in the Magnitude System

Several theoretical and empirical work posit the existence of a common magnitude system in the brain. Such a proposal implies that manipulating stimuli in one magnitude dimension (e.g. duration in time) should interfere with the subjective estimation of another magnitude dimension (e.g. size in space). Here, we asked whether a generalized Bayesian magnitude estimation system would sample sensory evidence using a common, amodal prior. Two psychophysical experiments separately tested participants on their perception of duration, surface, and numerosity when the non-target magnitude dimensions and the rate of sensory evidence accumulation were manipulated. First, we found that duration estimation was resilient to changes in surface and numerosity, whereas lengthening (shortening) the duration yielded under- (over-) estimations of surface and numerosity. Second, the perception of surface and numerosity were affected by changes in the rate of sensory evidence accumulation, whereas duration was not. Our results suggest that a generalized magnitude system based on Bayesian computations would minimally necessitate multiple priors.