Experiences of time and temporalities in contemporary life are analysed, with Floridi’s conception of the infosphere as a central concept. The effects of instantaneous communication and digital information are shown to result not simply in the obvious acceleration of many aspects of life, but in multiple temporalities. The informational spaces of Floridi’s hyperhistorical time form a new time-based society, with our informational activities expressed in linear, cyclic, re-cyclic, and iterative processes. Examples from the information sciences, particularly information seeking and “slow information,” are given, and an outline model for time literacy is presented.