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 Haptic Magnetism, 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.