The world shows some degree of invariance, and we perceive this invariance despite a lot of variation generated locally by our movements, changes in illumination, and the way in which our sense organs react to stimulation. Generally, philosophy and psychology each explain our perception of invariance through the notion of ‘perceptual constancy’. According to the traditional definition, perceptual constancies are capacities to perceive the objective (i.e., perceiver- and context-independent) local properties of external objects despite variation in the stimulation of sensory (...) organs. In this paper, we argue that the traditional understanding of perceptual constancy should be expanded to include a broader range of phenomena connected to the perception of invariance. Our argument starts from an odd activity: pole balancing. Balancing a pole-shaped object (e.g., a broomstick) on the palm of your hand in order to maintain it in an upright position requires (multimodal) perception and continuous tracking (within a certain range) of a particular kind of global invariant feature in the world. By examining this activity and its connection to the notion of perceptual constancy as it is traditionally understood, we propose an alternative account with the goal of clarifying the relationship between the alleged mechanisms underlying constancy and the philosophical implications of the phenomenon. (shrink)