Numerical magnitude affects temporal memories but not time encoding

Previous research has suggested that the perception of time is influenced by concurrent magnitude information (e.g., numerical magnitude in digits, spatial distance), but the locus of the effect is unclear, with some findings suggesting that concurrent magnitudes such as space affect temporal memories and others suggesting that numerical magnitudes in digits affect the clock speed during time encoding. The current paper reports 6 experiments in which participants perceived a stimulus duration and then reproduced it. We showed that though a digit of a large magnitude (e.g., 9), relative to a digit of a small magnitude (e.g., 2), led to a longer reproduced duration when the digits were presented during the perception of the stimulus duration, such a magnitude effect disappeared when the digits were presented during the reproduction of the stimulus duration. These findings disconfirm the account that large numerical magnitudes accelerate the speed of an internal clock during time encoding, as such an account incorrectly predicts that a large numerical magnitude should lead to a shorter reproduced duration when presented during reproduction. Instead, the findings suggest that numerical magnitudes, like other magnitudes such as space, affect temporal memories when numerical magnitudes and temporal durations are concurrently held in memory. Under this account, concurrent numerical magnitudes have the chance to influence the memory of the perceived duration when they are presented during perception but not when they are presented at the reproduction stage.