Biological systems exist under circumstances of it-reversibility that make them fundamentally different from inanimate matter (distinguishing them for in-stance as subject to development, damage and death). Individual historical memory and story-telling are ca-pacities useful in coping with this irreversibility. Such mechanisms may for embodied agents contribute to -- or may be even be necessary for -- competence in social intelligence. Structuring historical memories connects to an area of algebra called global semigroup theory, which allows one to construct expressions in 'algebras of time ) that can support recording events of fundamental signifi-cance to an agent. This may include records of in-ternal changes (e.g. in motivational, goal, emotional, cognitive, body image, perceptual states, knowledge of other entities) as weU as external changes (location, objects or other agents in the environment, physical conditions of local environment) that provide ground-ing for the representation. The models of change and time selected can be different depending on what is important to the agent. Communicating knowledge of other minds could be modelled in this framework by the passing of alge-braic expressions (in a historical 'expanded' semi-group) which record changes in the life-long learning or experience of another agent. This would correspond to revealing one’s autobiography or, more generally, to telling a story.