Math 4 Wisdom. "Mathematics for Wisdom" by Andrius Kulikauskas.

I want to overview my results and my research how Bott periodicity models introspection

Overviews: Modeling introspection, Bott periodicity flavors, Bott periodicity models divisions, Divisions
Expositions: Investigating Bott periodicity, Modeling Introspected Contexts With Mutually Anticommuting Linear Complex Structures, Bott periodicity for Clifford algebra maniacs, Bott periodicity for octonion maniacs, Artificial general intelligence presentation, Modeling the self
Key topics: Hamiltonians, Quantum symmetries, CT groups, Antiautomorphisms, Lie group embeddings, Lie algebra decomposition, Super division algebras, Super Brauer Group, Clifford algebras, Symmetric spaces, Octonions, Binomial Bott, KTheory, Dynkin diagrams, Spinors, Random matrices, Krebs cycle, NSpheres, Linear complex structures
Related topics: Symmetry fibrations, Topological invariants, Homotopy groups, String theory, 24 Cell

An Allegory: The Solipsistic Self as the Hamiltonian of a Noninteracting Fermion

Bott Periodicity Models Consciousness? Preliminary Exploration

Modeling Introspection

Express my goals.

Goals

I wish to model

The structure of each division of everything
- The perspectives, the shifts in perspective, and their relationships.
Why the division of everything into eight perspectives collapses into a division of everything into zero perspectives.
How the three minds acts as operators adding a perspective, a perspective on a perspective, and a perspective on a perspective on a perspective.

Models

The Structure of a Division of Everything

The Chevalley action explains how an ordered set of generators of {$W$} (an ordered set of shifts in perspective) is acted upon by a basis element of {$V$} (a perspective), or a bivector - a generator of the Lie algebra for the spin group, or a monomial of basis elements.

This has us think of a division of everything as an ordered set of shifts in perspectives with perhaps an additional perspective left over.

The Three Minds

The three minds are given by three interpretations for a Hamiltonian {$H$}.

It can be interpreted as the transpose {$H=G^T$}. This is the first mind. It corresponds to {$ABC\rightarrow CBA$} and time reversal.
It can be interpreted as the conjugate {$H=G^*$}. This is the second mind. It corresponds to {$ABC\rightarrow (-A)(-B)(-C)$} and charge conjugation.
It can be interpreted as self-adjoint {$H=H^\dagger$}. This is the third mind. It corresponds to {$ABC\rightarrow (-A)(-B)(-C)$} and mirror symmetry.

The three minds are given by quantum symmetries and related Clifford algebra mappings.

Unconscious	Accessible	Time reversal	usual antilinear	{$U_TH^*U_T^\dagger=H$}	Reversing antiautomorphism	{$ABC\rightarrow CBA$}
Conscious	Inaccessible	Charge conjugation, particle-hole	transposing linear	{$U_CH^*U_C^\dagger=-H$}	Conjugation antiautomorphism	{$ABC\rightarrow (-C)(-B)(-A)$}
Consciousness	Definite	Parity, space reversal, sublattice symmetry	transposing antilinear	{$U_SHU_S^\dagger=-H$}	Involution automorphism	{$ABC\rightarrow (-A)(-B)(-C)$}

We can translate various concepts between quantum symmetries and the Clifford algebra mappings

{$H^*=H^T$} conjugation or transpose	reversion {$ABC\rightarrow CBA$}
{$-H$} transposing	reflection of generators
{$H$} antilinear	?

Study Varlamov 2001, Varlamov 2004.

Consider how time reversal (forwards to backwards) can be identified with space reversal (positive to negative) if we add an extra dimension.

Consider how the quantum symmetry {$T$} or {$C$} squaring to {$+1$} or {$-1$} expressing unconsciousness and consciousness, and how that interacts with the quantum symmetry, as in "consciously inaccessible".