Evidence Accumulation in the Magnitude System

Abstract

Perceptual interferences in the estimation of quantities (time, space and numbers) have been interpreted as evidence for a common magnitude system. However, if duration estimation has appears sensitive to spatial and numerical interferences, space and number estimation tend to be resilient to temporal manipulations. These observations question the relative contribution of each quantity in the elaboration of a representation in a common mental metric. Here, we elaborated a task in which perceptual evidence accumulated over time for all tested quantities (space, time and number) in order to match the natural requirement for building a duration percept. For this, we used a bisection task. Experimental trials consisted of dynamic dots of different sizes appearing progressively on the screen. Participants were asked to judge the duration, the cumulative surface or the number of dots in the display while the two non-target dimensions varied independently. In a prospective experiment, participants were informed before the trial which dimension was the target; in a retrospective experiment, participants had to attend to all dimensions and were informed only after a given trial which dimension was the target. Surprisingly, we found that duration was resilient to spatial and numerical interferences whereas space and number estimation were affected by time. Specifically, and counter-intuitively, results revealed that longer durations lead to smaller number and space estimates whether participants knew before (prospectively) or after (retrospectively) a given trial which quantity they had to estimate. Altogether, our results support a magnitude system in which perceptual evidence for time, space and numbers integrate following Bayesian cue-combination rules.

SMA Selectively Codes the Active Accumulation of Temporal, Not Spatial, Magnitude

“…By contrast, probe distance was overestimated when probe duration was relatively shorter than the sample. In fact, this surprising result also confirms prior findings: Lambrechts et al (2013) found that the shorter the duration of a dynamic display, the larger the accumulated surface size was estimated to be. It was suggested that, in dynamic displays, when judgments of spatial or numerical magnitude depend on the integration of information over time, shorter stimulus durations lead to a higher concentration of spatial information per unit time, leading participants to overestimate spatial size (Lambrechts et al, 2013).…”

“…Furthermore, in a follow-up study, Droit-Volet (2010) showed that the perceptual distortions induced by click trains, which were thought to be specific to the temporal domain, also applied to spatial and numerical judgments but only if these stimuli were presented sequentially and their individual magnitudes accumulated. More recently, Lambrechts, Walsh, and Van Wassenhove (2013) found that, if spatial and numerical information was presented in a similarly dynamic (i.e., sequential) way to temporal information, then duration judgments were unaffected by the size or number of stimuli, contrary to many previous findings that size (Xuan, Zhang, He, & Chen, 2007) or number (Dormal, Seron, & Pesenti, 2006) distorts estimates of duration. These behavioral findings suggest that, when timing is compared with another magnitude dimension that is equally sequential or dynamic, then psychophysical differences in judgments of duration versus other magnitudes are no longer seen.…”

“…However, several authors have found evidence for asymmetric interference between magnitude dimensions, with spatial (Magnani et al, 2014;Mendez, Prado, Mendoza, & Merchant, 2011;Casasanto & Boroditsky, 2008) or numerical (Dormal et al, 2006) magnitude influencing temporal perception more than temporal magnitude influences spatial or numerical perception. However, this asymmetry may be less evident when both spatial and temporal dimensions are equally dynamic (Lambrechts et al, 2013;Droit-Volet et al, 2008), suggesting that the cumulative nature of temporal processing plays an important role in these effects. Our own behavioral data support this interpretation: The relative magnitude of the task-irrelevant dimension induced spatial, as well as temporal, distortions of our dynamic stimuli.…”

“…The percentage of correct responses in each bin was calculated and analyzed using a 2 × 5 repeatedmeasures ANOVA with task (temporal/spatial) and relative magnitude (probe shorter/longer than sample) as within-subject factors. Finally, we used data from the three dynamic blocks to explore possible influences of stimulus distance on the subjective perception of duration (Casasanto & Boroditsky, 2008;Xuan et al, 2007) or of stimulus duration on the subjective perception of distance (Lambrechts et al, 2013). This time, temporal trials were binned as a function of the relative distance of probe to sample stimuli.…”

Cross-dimensional magnitude interaction is modulated by representational noise: Evidence from space-time interaction

“…The account has received empirical support from behavioural demonstrations that different magnitude dimensions functionally interact with each other in perception (Meck, Church, & Gibbon, 1983;Lorenco & Longo, 2010;Martin et al, 2017;Lambrechts, Walsh, & van Wassenhove, 2013;Riemer, Diersch, Bublatzky, Wolbers, 2016) and recruit overlapping neural substrates (see Bueti & Walsh, 2009, for a review). On this account, a perceived duration is lengthened in the presence of a longer length (relative to a shorter one) because when both the duration and the length are mapped onto the common metric, the greater value of a longer length (relative to a shorter one) can pull on the duration value as a result of interference, resulting in a longer perceived duration.…”