The Mind-Brain Relationship as a Mathematical Problem

This paper aims to frame certain fundamental aspects of the human mind (content and meaning of mental states) and foundational elements of brain computation (spatial and temporal patterns of neural activity) so as to enable at least in principle their integration within one and the same quantitative representation. Through the history of science, similar approaches have been instrumental to bridge other seemingly mysterious scientific phenomena, such as thermodynamics and statistical mechanics, optics and electromagnetism, or chemistry and quantum physics, among several other examples. Identifying the relevant levels of analysis is important to define proper mathematical formalisms for describing the brain and the mind, such that they could be mapped onto each other in order to explain their equivalence. Based on these premises, we overview the potential of neural connectivity to provide highly informative constraints on brain computational process. Moreover, we outline approaches for representing cognitive and emotional states geometrically with semantic maps. Next, we summarize leading theoretical framework that might serve as an explanatory bridge between neural connectivity and mental space. Furthermore, we discuss the implications of this framework for human communication and our view of reality. We conclude by analyzing the practical requirements to manage the necessary data for solving the mind-brain problem from this perspective.