While computational models of human music making are a hot research topic, the human side of computer-based music making has been largely neglected. What are our cognitive processes like when we create musical algorithms, and when we compose and perform with them? Musical human–algorithm interaction involves embodied action, perception and interaction, and some kind of internalization of the algorithms in the performer’s mind. How does the cognitive relate to the physical here? Departing from the age-old mind–body problem, this chapter tries to answer these questions and review relevant research, drawing from a number of related fields, such as musical cognition, cognition and psychology of programming, embodied performance, and neurological research, as well as from the author’s personal experience as an artist working in the field.