Memory retrieval as a p-adic dynamical system

We propose a mathematical model of the memory retrieval process based on dy namical systems over a metric space of p-adic numbers representing a config uration 'space of ideas' in which two ideas are close if they have a suffic iently long common root. Our aim is to suggest a new way of conceptualizing human memory retrieval that might be useful for simulation purposes or for the construction of artificial intelligence devices, as well as for a deep er understanding of the process itself. The dynamical system is assumed to be located in a blackbox processing unit (the 'subconscious') and controlle d by an interface control unit (the 'conscious') that fixes parameters in t he dynamical system and starts its iteration by sending an initial generati ng idea to it. We show that even simple p-adic dynamical systems admit beha vioral scenarios that could explain some of the essential features of the h uman memory retrieval process. (C) 1999 Elsevier Science Ireland Ltd. All r ights reserved.