Richard Feynman’s Classification and First Principles of Studying Natural Phenomena

This Chapter is devoted to the formulation of “Richard Feynman’s Classification of Three Stages of Cognition of Natural Phenomena”, as well as to the application of this classification to the following three examples, namely: (1) the phenomenon of light refraction at the air–water boundary and (2) the laws of conservation of energy, momentum and angular momentum. Particular attention is paid to the application of “Richard Feynman’s ClassificationRichard Feynman’s Classification of Three Stages of Cognition of Natural Phenomena” to (3) the discovery of the place and hexagonal grid cells in the brain, which was awarded the 2014 Nobel Prize in Physiology and Medicine. The problem of grid cells in the brain is considered with taking into account: the experimental studies that led to the emergence of hexagons in the human and animal brain, discussion of the problem of generation and propagation an action potential along nerve fibers, physical parameters of the human brain and its medical applications in the method of hyperthermia for the treatment of malignant tumors, theoretical considerations using a certain analogyAnalogy between grid and Benard cells between grid cells in the brain and Abrikosov’s vortexAbrikosov vortices in superconductors lattice in superconductors of the 2nd type, and hexagonal graphene and dimensional crossover. Moreover, the main purpose of this Chapter is to use the fluctuation theory of phase transitions to formulate the first principleFirst principles of grid cells emergence of the emergence of hexagonal grid cells in the brain and, generally speaking, the first principle for the hexagon formation in different objects of inanimate and living nature. Our original theoretical findings are the following: (a) Polyakov’s conformal invariance hypothesisPolyakov conformal invariance hypothesis is violated for a system of grid cells in the brain; (b) the grid cells system in the brain belongs to the universality classConcept of universality classes including the 3D Ising model in a magnetic field as well as a real classical liquid–vapor system; (c) to formulate the first principle for a reliable theoretical justification of the emergence of hexagonal grid cells in the brain, it is necessary to use the fluctuating part of Gibbs thermodynamic potentialGibbs thermodynamic potential (the Ginzburg–Landau HamiltonianGinzburg–Landau Hamiltonian) for a systemLandau with chemical reactions.