Our physical bodies play a central role in shaping human experience in the world, understanding of the world, and interactions in the world. This paper draws on theories of embodiment — from psychology, sociology, and philosophy — synthesizing five themes we believe are particularly salient for interaction design: thinking through doing, performance, visibility, risk, and thick practice. We introduce aspects of human embodied engagement in the world with the goal of inspiring new interaction design approaches and evaluations that better integrate the physical and computational worlds. Author Keywords Embodiment, bodies, embodied interaction, ubiquitous

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In 4 experiments, the authors explored the role of visual layout in rule-based syntactic judgments. Participants judged the validity of a set of algebraic equations that tested their ability to apply the order of operations. In each experiment, a nonmathematical grouping pressure was manipulated to support or interfere with the mathematical convention. Despite the formal irrelevance of these grouping manipulations, accuracy in all experiments was highest when the nonmathematical pressure supported the mathematical grouping. The increase was significantly greater when the correct judgment depended on the order of operator precedence. The result that visual perception impacts rule application in mathematics has broad implications for relational reasoning in general. The authors conclude that formally symbolic reasoning is more visual than is usually proposed.