A Mathematical Perspective on Neurophenomenology

Abstract: 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.

• The paper introduces a novel mathematical formalization that models first-person experience as probabilistic beliefs.
• It quantifies individual differences in phenomenology by linking subjective states to neural dynamics using Bayesian mechanisms.
• The study bridges qualitative and quantitative methods, paving the way for testable predictions in consciousness research.

A Mathematical Perspective on Neurophenomenology

Summary

This paper proposes a novel approach to neurophenomenology by utilizing mathematical tools to conceptualize the alignment between first-person experience and neural dynamics. The authors explore the integration of phenomenological methods, known for qualitative data generation, with neuroscientific techniques that quantify brain activity within the framework of Bayesian mechanics, predictive processing, and the free energy principle. This innovative perspective allows for a rigorous formalization of phenomenological content and provides insights into how first-person experiences may be modeled as probabilistic beliefs.

Core Contributions

1. Mathematical Formalization: The study offers a mathematical formalization of first-person experiences, conceptualizing them as probability distributions or beliefs. These beliefs encode an organism's best estimates regarding its internal and external states, including uncertainties.
2. Quantifying Phenomenological Differences: The authors introduce mathematical tools to quantify individual differences in phenomenology, developing hypotheses regarding the metabolic costs of phenomenology and the subjective experience of time.
3. Generative Passages: The paper conceptualizes the bidirectional relations between first-person phenomenological descriptions and third-person empirical measurements, particularly neural dynamics. This is achieved via the Bayesian mechanics framework and its predictive processing models.
4. Methodological Implications for Future Work: The framework establishes a foundation for studying cognitive phenomena and motivates further research into the constraints on empirical data, offering a robust platform for future empirical investigations.

Implications and Future Directions

This work sets the stage for a more integrated approach to understanding human consciousness, aligning computational models closely with biological data. The authors assert that this framework may also reinvigorate interest in consciousness studies by offering testable predictions derived from the quantitative analysis of phenomenology. Future research could involve empirical studies to validate the proposed mathematical models and extend their implications to domains such as cognitive neuroscience and artificial intelligence.

Furthermore, this research lays the groundwork for individually specific models of conscious experience that can accommodate the complexity and variability of subjective states among different subjects. It also suggests that the principles outlined here may be applied to enhance machine understanding of human cognition, providing valuable insights that bridge perception, cognition, and behavior.

Finally, the paper challenges traditional dichotomies between first-person and third-person data, instead advocating for a sophisticated and integrative methodological approach that uses active inference and Bayesian frameworks to explore the complex interactions between subjective and objective realms, promising scalable insights for both theoretical exploration and practical modeling in neuroscience and AI.