Human memory as a $p$-adic dynamic system

We propose a mathematical model of the human memory-retrieval process based on dynamic systems over a metric space of $p$-adic numbers. The elements of this space represent ideas. We assume that two ideas are close if they have a sufficiently long initial segment in common. We also assume that this dynamic system is located in the subconscious and is controlled by the conscious, which specifies the system parameters and provides the ideas that initiate the iteration of the dynamic system. We show that even simple $p$-adic dynamic systems describe essential features of the human memory-retrieval process.