This article describes and compares two approaches that can be used to build artificial systems that users tend to recognize as agents, based on a review of two systems previously built by the authors. One system, an interactive musical instrument, is a typical artificial intelligence (AI) implementation, based on the technique of constraint programming. The other, a dancing robot, is a typical artificial life (AL) endeavor, specified as a non-linear dynamical system. Although very different in their design, we found that both systems have the same goal of compromising autonomy and reactivity in their user interaction. They elicit interaction and—we argue here—an elusive feeling of agency , because they are neither too predictable nor too random. Creating and controlling such a compromise in a programmatic way is not a trivial problem: we find that both approaches (AI and AL) raise similar pragmatic problems that are in fact rooted in human perception science. Psychological experimentation is needed to clarify the relation between the internal dynamics of the artificial systems and the ongoing feeling of agency (or absence thereof) imparted in their human user. As a first step toward such experimentation, we derive a minimal mathematical model which subsumes both implementations and abstracts them from their respective contexts of music and dance. This model is similar to a Van der Pol oscillator, forced by an input signal coupled to its output in a non-programmatic way. It isolates two critical variables controlling the illusion of agency: the model’s sampling rate and the polynomial order of its reactive term.
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