New interactions are often developed by mimicking the real world. Therefore, many researchers in haptics have focused on creating a realistic experience of contact between users and objects. However, dispensing with mimicry may allow us to develop novel haptic interactions. We present <italic>Haptic Magnetism</italic>, an interaction modality that delivers sensations of distant objects through tactile stimulation and enables interactions through pseudo-magnetic attraction and repulsion. To show the feasibility of Haptic Magnetism, we designed 12 pseudo-magnetic stimuli and assessed them in two studies. In the first study, we show that participants gain a sense of distant objects. In the second study, we evaluate a subset of stimuli to show that participants can interact with the objects based on experiences of pseudo-magnetic attraction and repulsion. Finally, we discuss how Haptic Magnetism supports guiding movements, nudging users, and revealing affordances.