Constructive Biology means understanding biological mechanisms through building systems that exhibit life-like properties. Applications include learning engineering tricks from biological system, as well as the validation in biological modeling. In particular, biological system in the course of development and experience become temporally grounded. Researchers attempting to transcend mere reactivity have been inspired by the drives, motivations, homeostasis, hormonal control, and emotions of animals. In order to contextualize and modulate behavior, these ideas have been introduced into robotics and synthetic agents, while further flexibility is achieved by introducing learning. Broadening scope of the temporal horizon further requires post-reactive techniques that address not only the action in the now, although such action may perhaps be modulated by drives and affect. Support is needed for expressing and benefitting from pats experiences, predictions of the future, and form interaction histories of the self with the world and with other agents. Mathematical methods provide a new way to support such grounding in the construction of post-reactive systems. Moreover, the communication of such mathematical encoded histories of experience between situated agents opens a route to narrative intelligence, analogous to communication or story telling in societies.