Classical and quantum dynamics on p-adic trees of ideas

Area of Science:

• Cognitive Science
• Mathematical Psychology
• Theoretical Physics

Background:

• Current models of cognition lack a unified mathematical framework.
• Understanding the interplay between unconscious and conscious processes is a significant challenge.
• The role of quantum mechanics in cognitive functions remains largely unexplored.

Purpose of the Study:

• To develop novel mathematical models for unconscious and conscious information processing.
• To introduce a quantum cognitive mechanics framework generalizing classical cognitive mechanics.
• To explore potential applications in explaining psychological phenomena and biological processes.

Main Methods:

• Utilizing p-adic number representations for mental spaces.
• Generalizing Newton's mechanics to classical cognitive mechanics for unconscious thought.
• Generalizing the pilot wave model to quantum cognitive mechanics for conscious thought.
• Introducing a 'conscious force' as a quantum information force.

Main Results:

• Mathematical formalization of unconscious thinking via classical cognitive mechanics.
• Mathematical formalization of conscious thinking via quantum cognitive mechanics.
• Identification of classical and quantum information forces governing cognitive systems.
• Potential for a unified mathematical foundation for diverse psychological phenomena.

Conclusions:

• The proposed p-adic models offer a novel mathematical basis for understanding cognition.
• Quantum cognitive mechanics provides a framework for conscious thought and its associated forces.
• The models may bridge the gap between physiological processes and mental states.
• This work opens avenues for modeling collective consciousness and conscious evolution.