Formalization of Consciousness as a Complex Dynamical System using Quantum Chaos Theory

Abstract

This paper proposes a novel mathematical framework for understanding consciousness, framing it as a complex dynamical system governed by principles of quantum chaos. The core argument centers on the hypothesis that subjective experience emerges from the intricate, non-linear dynamics of the brain, specifically driven by seemingly random fluctuations exhibiting sensitive dependence on initial conditions – a hallmark of quantum chaos. We formalize this concept using mathematical tools from dynamical systems theory and quantum chaos, aiming to provide a rigorous, albeit speculative, model for consciousness. The framework incorporates key elements such as Lyapunov exponents, fractal dimensions, and the concept of 'information' within the chaotic system to represent aspects of subjective experience. This approach seeks to bridge the gap between neuroscience and quantum physics, suggesting that consciousness isn't merely a product of classical computation but rather a fundamentally quantum phenomenon. The presented model highlights the potential role of decoherence and its influence on the system's evolution, ultimately leading to the emergence of a unified, integrated experience. Further research is warranted to explore the implications of this framework for understanding disorders of consciousness and the nature of reality itself.