Linking the Structure of Neuronal Mechanisms to the Structure of Qualia

Structural descriptions of qualitative aspects of conscious experience (qualia) offer a rigorous empirical approach to study consciousness. An important outcome of this approach is that structural descriptions of qualia are formalized as mathematical objects. Mathematical structures describing qualia can be mapped to mathematical structures derived from brain activity and its underlying neuronal connectivity. That is, rather than merely identifying the co-occurrence of specific neuronal activity patterns with specific qualia — correlates of consciousness — we can aim to derive general mathematical mappings that map between qualia and neuronal mechanisms. Such mathematical mappings between neuronal mechanisms and qualia seem consistent with other laws of nature, such as how E=mc² maps mass to energy. Here, we survey key literature that led up to, or follows this structural approach, to assess the current state of the field. We first explicate the historic arc from psychophysics and the neuroscience of consciousness toward structural approaches to qualia. We then critically examine classical attempts of formalizing qualia structure, such as the textbook model of musical chroma (Shepard's pitch helix) and visual color space. We then explore what is known about the structure of their neuronal correlates. We then extend this analysis to visual similarity spaces, including face space and more general image spaces. Finally, we consider ongoing efforts, suggesting that exact experimental comparisons between qualia, analyzed with rigorous mathematics result in an “enriched psychophysics” that expands single-valued measures to much richer scientific exploration.