Evidence accumulation in the magnitude system.

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.