The Imminence Mapping Anticipates

Abstract

I present a new mathematical formulation of anticipation. A brief introduction to the theory of set-valued mappings culminates in a special specimen, the imminence mapping ${\text{Imm}}_{\,N}$ of a natural system N. For each process f in N, the set ${\text{Imm}}_{\,N} \left( f \right)$ encompasses all possible further actions arising from f, which one may consider the ‘imminence’ of f. The imminence mapping definitively characterizes N as a complex relational network of interacting processes and their entailed potentialities. A natural system N is an anticipatory system if it contains an internal predictive model of itself and its environment, and in accordance with the model’s predictions antecedent actions are taken. Consequent manifestations of the internal predictive model of an anticipatory system are thus embodied in the system’s imminence, whence the imminence mapping, among all that it entails, eminently anticipates.