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Although previous research has suggested that examining the interplay between internal and external representations can benefit our understanding of the role of information visualization (InfoVis) in human cognitive activities, there has been little work detailing the nature of internal representations, the relationship between internal and external representations and how interaction is related to these representations. In this paper, we identify and illustrate a specific kind of internal representation, mental models, and outline the high-level relationships between mental models and external visualizations. We present a top-down perspective of reasoning as model construction and simulation, and discuss the role of visualization in model based reasoning. From this perspective, interaction can be understood as active modeling for three primary purposes: external anchoring, information foraging, and cognitive offloading. Finally we discuss the implications of our approach for design, evaluation and theory development.