An Examination of Learning Using Fourier Analysis of Mathematical Models of Consciousness

Abstract

The concept of consciousness remains quite possibly the ultimate mystery for humanity. It is somehow linked to the ability to learn and experience the external environment. The process of learning is of utmost importance to any species and yet remains largely not understood. While many experts from varying fields throughout history have attempted to quantify and measure learning, all failed to capture the process with a mathematical explanation. The purpose of this paper is to present three different models of consciousness and their related Fourier transform and evaluate the ability of each to capture some of the behavior that is understood about the conscious experience. There is some evidence that the experience of consciousness as a function of time can be measured in an expression of phase. With this hypothesis, the technique of Fourier transform becomes a useful tool to examine a mathematical model of consciousness that can be transformed from the phase plane to the linearization of time. This paper summarizes some current research on consciousness and learning and perception of time. This paper then presents three different models of consciousness represented as a pulse function, Dirac Delta function, and exponential decay function and examines each model utilizing Fourier transform. Finally, this paper concludes that the intersection between psychology, neuroscience and cognitive science can be made by utilizing analysis tools in the field of applied mathematics.