Impossible integration of size and weight

Abstract

Some of the most striking phenomena in visual perception are “impossible figures”—objects or scenes that could never exist in real life, such as a staircase that ascends in every direction, or a triangle with three 90° sides. How pervasive are such experiences in the mind? Specifically, could there be impossible multisensory experiences? Here, we explore one such example that is both (i) phenomenologically striking, and (ii) theoretically significant for notions of perception as rational Bayesian inference. In the Size-Weight Illusion, a smaller object is perceived as heavier than an objectively-equally-weighted larger object. This illusion, though not “impossible”, is puzzling: typically, our interpretation of new data is attracted towards our priors, but the size-weight illusion instead seems to involve repulsion from our priors; faced with ambiguous sensory evidence (i.e., two equally massive objects), we experience the object we expected to be lighter as heavier. Can the insight from this illusion be used to create an impossible perceptual experience? In three experiments, subjects were shown three visually identical boxes in a stack, and were asked to compare the weight of all three boxes lifted together vs. the top box lifted alone. Unbeknownst to them, the top box contained 250g of copper, while the other two boxes were empty. Which felt heavier? As in the classic size-weight illusion, the single top box felt heavier than all three combined—no matter whether the subjects hefted the boxes themselves (Exp.1), had them placed on their hands (Exp.2), or lifted them with strings rather than grasping the boxes directly (Exp.3). However, this outcome is impossible: A subset (box A alone) could never weigh more than its superset (boxes A, B, and C together). Evidently, the mind tolerates not only improbable, but also impossible, integration of information across modalities—and in a way one can feel for oneself.