Strongly anticipatory systems-that is, systems which use models of themselves for their further development-and which additionally may be able to run hyperincursive routines-that is, develop only with reference to their future states-cannot exist in res extensa, but can only be envisaged in res cogitans. One needs incursive routines of cogitantes to instantiate these systems. Unlike historical systems (with recursion), these hyper-incursive routines generate redundancies by opening horizons of other possible states. Thus, intentional systems can enrich our perceptions of the cases that have happened to occur. The perspective of hindsight codified at the above-individual level enables us furthermore to intervene technologically. The theory and computation of anticipatory systems have made these loops between supra-individual hyper-incursion, individual incursion (in instantiation), and historical recursion accessible for modeling and empirical investigation.