A Mathematical Perspective on Neurophenomenology

In the context of consciousness studies, a key challenge is how to rigorously conceptualise first-person phenomenological descriptions of lived experience and their relation to third-person empirical measurements of the activity or dynamics of the brain and body. Since the 1990s, there has been a coordinated effort to explicitly combine first-person phenomenological methods, generating qualitative data, with neuroscientific techniques used to describe and quantify brain activity under the banner of "neurophenomenology". Here, we take on this challenge and develop an approach to neurophenomenology from a mathematical perspective. We harness recent advances in theoretical neuroscience and the physics of cognitive systems to mathematically conceptualise first-person experience and its correspondence with neural and behavioural dynamics. Throughout, we make the operating assumption that the content of first-person experience can be formalised as (or related to) a belief (i.e. a probability distribution) that encodes an organism's best guesses about the state of its external and internal world (e.g. body or brain) as well as its uncertainty. We mathematically characterise phenomenology, bringing to light a tool-set to quantify individual phenomenological differences and develop several hypotheses including on the metabolic cost of phenomenology and on the subjective experience of time. We conceptualise the form of the generative passages between first- and third-person descriptions, and the mathematical apparatus that mutually constrains them, as well as future research directions. In summary, we formalise and characterise first-person subjective experience and its correspondence with third-person empirical measurements of brain and body, offering hypotheses for quantifying various aspects of phenomenology to be tested in future work.