Andrius Kulikauskas: I am working on a presentation for the 2026 Models of Consciousness conference.
Modeling Introspection with Clifford Algebras: 3 Levels of Awareness and 8 Mental Contexts
Consciousness studies favor concrete experience, consciousness of apples. Alternatively, introspection lets us ignore all we know (the prejudices of our intuitive, unconscious answering mind) and all we don't know (the preconceptions of our rational, conscious questioning mind) and contemplate (with our cognizant, deliberate, willful investigating mind) abstract mental contexts, the frameworks of perspectives which align questioning and answering. Existence, as a context, supposes two perspectives: the possiblity that opposites coexist (as with free will) and the actuality where they don't (as with fate). Participation supposes a learning cycle of three perspectives: we take a stand, follow through, and reflect, as with the scientific method. Knowledge supposes four levels: How leads to What, and then Why leads to Whether. We describe the structures of mental contexts for contemplating God, order, existence, participation, knowledge, decision-making, morality and logic. We model these eight structures with Clifford algebras manifesting eightfold real Bott periodicity. We identify perspectives with anticommuting generators (reflections), and shifts in perspectives with ordered pairs of generators (rotations). Three levels of awareness (answering, questioning, investigating) act on the sequence of all shifts in perspectives, such as a_1a_2a_3. Answering reverses a_3a_2a_1, questioning conjugates (-a_3)(-a_2)(-a_1), investigating reflects (-a_1)(-a_2)(-a_3). The number of perspectives, k modulo 8, determines which of these actions yields a positive sign (direct experience) or negative sign (reflected experience). This yields a dynamics of assembly, which is complete precisely when k modulo 8 equals 0. Replicating such introspection would explore human experience as a dialogue of three levels of awareness.
- The conceptual frameworks are presented in Time and Space as Representations of Decision Making
- 386 examples of the three levels of awareness are presented at Theory Translator
- The mathematical model in terms of Bott periodicity of Clifford algebras and quantum symmetries is presented in An Allegory: The Solipsistic Self as the Hamiltonian of a Noninteracting Fermion
My proposed talk considers Bott periodicity of spin representations to further distill the underlying mechanisms and how they express the conceptual frameworks. Here are some pages where I'm working on that.