This study presents a theory of paramediation: the process by which algorithms govern human activity by arranging perceptible phenomena, according to parameters that structure how these phenomena emerge in correlation with human activity. It begins by identifying a tendency in existing research to conceptualize algorithms as representational and regulatory media, and it identifies how alternative theoretical conceptions of algorithms challenge this tendency by developing a phenomenology of algorithm operations. The theory of paramediation is proposed to analyze this phenomenological dimension, how it is designed, and its implications for the way we conceptualize algorithmic governance. Through illustrative case studies, participant interviews, and the production of an interactive game, the study interrogates implications of a theory of paramediation for studying, designing, and critiquing algorithmic media. It concludes that the power of paramediation cannot be checked by evaluating its epistemic validity, but by developing a plurality of practices for interpreting algorithm logic and data.