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
Kahneman and Tversky distinguished System 1 (our intuitive, prejudicial, unconsciously answering mind) and System 2 (our rational, conceptual, consciously questioning mind). We introspect a System 3 (our cognizant, deliberate, willfully investigating mind) which matches up System 1 (what we know) and System 2 (what we don't know) and then chooses which system to apply. We model these three minds as three matrix operations (transpose, conjugate and conjugate transpose) acting on the Hamiltonian H of a noninteracting free fermion, a solipsistic Self. H is characterized by the quantum symmetries (time reversal, charge conjugation, parity) that it satisfies, and these symmetries may be analyzed as mappings (reversion, conjugation, involution) fixing a Clifford algebra. We interpret the Clifford algebra Cl(k) as modeling k perspectives which the Chevalley action pairs up into shifts in perspectives with an additional metaperspective when k is odd. Cl(k) manifest eightfold real Bott periodicity. These eight structures (k=0,1,2,3,4,5,6,7) define the dynamics of assembling perspectives, the ways of dividing everything into k perspectives, the mental contexts for the most abstract issues: God, order, existence, participation, knowledge, decision-making, morality, logic. 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.
This presentation is based on my unpublished paper, An Allegory: The Solipsistic Self as the Hamiltonian of a Noninteracting Fermion, which I wrote in 2025.
In 2017, I gave two presentations on describing human experience in terms of three levels of awareness ("three minds") and eight mental contexts ("divisions of everything"). Here are the text and slides:
- Time and Space as Representations of Decision-Making
- Consciousness as the Social Awareness Schema of a Disembodying Mind
At Theory Translator, I have curated 388 examples of the "three minds", the three levels of awareness (answering, questioning, investigating), from the history of culture and the evolution of biology.
This last year, I have studied how spin representations manifest eightfold real Bott periodicity. This has yielded further insights on how the divisions of everything are expressed mathematically.
Spin representations are typically constructed by considering the action (described by Claude Chevalley) of vectors {$v\in V$} (understood as raising or lowering operators) acting on monomials {$w_{j_1}w_{j_2}\cdots w_{j_r}\in \wedge^\bullet W$}, with generators {$w_{j_1},w_{j_2},\dots ,w_{j_r}\in W \subset V$}. Specifically, given a complex vector space {$V$} with a quadratic form {$Q$}, we break up {$V=W\oplus W^*\oplus U$}, where {$W\cap W^*=\emptyset$} are dual vector spaces, maximal totally isotropic subspaces of {$V$} with regard to {$Q$}. If {$V$} is odd-dimensional, then additionally it has a one-dimensional subspace {$U$}, and otherwise, {$U=\{0\}$}. We can further consider monomials in the complex Clifford algebra {$Cl(V,Q)$} as similarly acting on monomials in the exterior algebra {$\wedge^\bullet W$}. We identify the spin algebra {$\frak{sp}$}{$(n)$} with the bivectors in {$Cl(V,Q)$} and whose action on the spin space {$\wedge^\bullet W$} yields the spin representations. This action is described in Wikipedia: Spin representation.