Beware bisection: the direction of time-numerosity interactions depends on objective reference

In time perception studies, one of the most commonly employed tasks across humans and animals is temporal bisection. In this task, subjects must classify intervals presented into "short" and "long" duration categories. Crucially, this classification can be done either in reference to explicitly learned "anchors", or in a "reference-free" mode in which no anchors are provided and the subject must use an implicit standard - the so-called "partition variant". Previous work has demonstrated identical performance and modeling between the anchored and partition variants leading to the conclusion that both variants use a common mechanism. Here we report on a series of findings that critically challenge this assumption in which we, quite accidentally, found that the partition variant produces opposite results on a common task - the time-numerosity interaction, in which more numerous dot arrays are associated with longer perceived durations. Instead, we find that the partition variant induces the opposite pattern, where larger numerosities are associated with a shorter reported duration. We suggest this change in direction is the result of the comparison being made, as we tested other tasks (discrimination, reproduction, anchor variant) and found the oft-reported finding of larger numerosities inducing longer reported durations. We further provide a model in which numerosity induces a lengthening of the criterion itself, which can explain the bidirectionality of the effect. We conclude that the partition variant of temporal bisection, while similar to the anchor variant, may provide substantially different results and caution researchers on drawing conclusions based on this task alone and without additional tasks for verification.