This paper takes its cue from recent work in nonhuman geographies that has sought to think about the relationship between the human and nonhuman topologically. While nonhuman geographies have well‐developed analyses of the topologies of regions and networks, recent work is supplementing these with other topological understandings. Yet, this work can be taken further. To this end, this paper explores the relationship between the human and nonhuman, through a discussion of animals, affects and psychic space. It offers a topological reading of two of Freud's case studies: Emmy von N. and the Wolfman. The paper highlights the twists and turns of affect and psychic space in these cases. It shows that the difference between the human and the nonhuman can be radically uncertain at the very same time that human distinctiveness is being given certain forms. Using the topological figure of the Möbius strip, this paper shows that, while animals and humans might appear on the same topological surface, distinctions between them are not collapsed or fused or flattened. This has implications for how humans are understood to be entangled in nonhuman worlds; entanglements that, it is argued, are always filtered through the beastly mind.