This chapter champions the notion of ‘strange’, paradoxical, level-crossing feedback loops as a means to address the shortcomings of information-processing approaches to cognition, especially as applied to musical improvisation. It highlights the inherent challenges of studying improvisation and consciousness, and suggests ways that embodied and enactive theories of cognition, and emerging ideas in predictive processing and social psychology, may offer productive ways to understand mind and consciousness, and the dynamics of collective musical improvisation. Improvising music together, the chapter argues, involves joint action, embodied coordination, collective attention, and shared intention in ways that challenge conventional understandings of cognition and consciousness.