Consciousness and Mathematics: A Number Theoretic Approach to Modelling Reality

Abstract

This research analyses the fundamentals of numbers for interpreting consciousness and reality. Complementing Gödel’s incompleteness theorems, we adopted number theory to explore non-referential and self-referential constructs. By examining consciousness, causation, and fundamental mathematical models of reality, we analysed stages of cognition and the emergence of self-referencing as a limitation, which brings incompleteness and undecidability to a framework. By postulating prime numbers as a non-referential fundamental basis, the study underscores their critical role in forming a complete and decidable framework for understanding consciousness and reality. We develop a framework that establishes composite numbers as secondary constructs dependent on prime numbers. Based on the foundation of prime numbers, we explored natural numbers, consisting of even and odd numbers. We analysed Goldbach conjecture and discussed the limitations of mathematical modelling based on our analysis of primes and natural numbers. Our analysis suggests that decomposing numerical systems into non-referential and self-referential components can transcend the limitations of modelling consciousness and reality. Our framework offers a profound foundation for modelling and interpreting consciousness and reality, bridging the gap between consciousness, causation, and mathematics.