Sensorimotor experience and its metrics: informational geometry and the temporal horizon

We introduce metrics on sensorimotor experience at various temporal scales based on informationtheory. Sensorimotor variables through which the experience of an agent flows are modeled as information sources in the sense of Shannon information theory. Information distance between the constellation of an embodied agent's sensorimotor variables at different moments in time can be taken variable-by-variable or between entire sets of such variables to yield two classes of metrics on sensorimotor experience: the temporal experiential information distance and the Hausdorff metric on experience. Unlike mutual information, these measures each satisfy the metric axioms and thus induce a geometry on the space of experiences with the same temporal scope. Continuity of maps between experiential spaces as well as robotic applications and extensions are discussed.