The role of morphological 'computation' in embodied cognition is usually addressed from the perspective of individual agents, i.e. how do an agent's bodily materials, movements, etc contribute to its cognitive processes. But the body of course also plays a crucial role in many social interactions, not least the communication/recognition of intentions between interacting agents. The talk how this affects human-machine interactions in cases where the interacting agents' morphologies are radically different (e.g. people interacting with cars) as well as cases where morphologies have superficial similarities (e.g. human-humanoid interaction), but the underlying bodily processes are fundamentally different.