Memory retrieval as a p-adic dynamical system

We propose a mathematical model of the memory retrieval process based on dynamical systems over a metric space of p-adic numbers representing a configuration `space of ideasʹ in which two ideas are close if they have a sufficiently 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 deeper understanding of the process itself. The dynamical system is assumed to be located in a blackbox processing unit (the `subconsciousʹ) and controlled by an interface control unit (the `consciousʹ) that fixes parameters in the dynamical system and starts its iteration by sending an initial generating idea to it. We show that even simple p-adic dynamical systems admit behavioral scenarios that could explain some of the essential features of the human memory retrieval process.