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Research program

Bott Periodicity: Unfolding of Thinking-in-Parallel

Grothendieck's six operations - Six representations of divisions

Topologies - one-many-all

• Fivesome
  • The five conics - Fivesome
  • Logical connectives - Fivesome
  • Fivefold classification of Sheffer polynomials of A-type zero - Fivesome
• Sixsome ?
• Logical square (and related logic - nonempty (closed) vs. empty (open) system - entropy) - Sevensome-eightsome

Adjoint string of length N - Division of everything into N perspectives

Exact strings.

The cube 8 divisions, 6 conceptions, 12 circumstances.

Understand intuitively

• How could finite exact sequences or perhaps finite strings of adjoint functors model mental chambers, which is to say, holistic cognitive frameworks, divisions of the brain's global workspace, or simply metaphysical divisions of everything?
• How could we classify strings of adjoint functors?
• How could the eightfold Bott periodicity and/or the classification of real Clifford algebras model how our mind proceeds from one mental chamber to another? Walking through the chambers of the mind.
• Why are there four classical families of Lie groups and Lie algebras? and how might they ground four kinds of geometry: affine, projective, conformal, symplectic?
• In any system, how could the Poincare group model the relations between such four geometries? And how could we model the additional conditions by which a system comes into being?
• How might the degrees of freedom in the gauge theories of the Standard Model

Bott periodicity - Eight-cycle of divisions

• Clifford algebras - clock shifts - consciousness

Sevensome

Shu-Hong's equation. Mobius transformations.

I want to be able to describe the cognitive foundations that account for logic.

Seven-eight kinds of duality. Reps of Sn and GLn. Schur-Weyl duality.

I would like to understand the various kinds of opposites in math and classify them.

Understand the Basics of Logic and Truth. I have made some progress in describing such foundations for truth: Truth as the Admission of Self- Contradiction. Which is to say, truth is inherently unstable and tentative, the relation of a level with a metalevel.

Divisions of everything: Exact Sequences

Divisions of everything: Adjunctions

Exact sequences of length n <=> Divisions of everything into N perspectives

Divisions of everything: Spin

Elementary particles

• Higgs - spin 0 - onesome
• Matter (leptons, quarks) - spin 1/2 - twosome
• Force carrying bosons - spin 1 - threesome
• spin 3/2 - not known to exist - foursome (knowledge)
• Graviton - spin 2 - fivesome

Divisions of everything: Bott periodicity

Bott Periodicity <=> The eight-cycle of divisions of everything

Operations

Norman Anderson's theory and modeling thinking fast and slow.

• Investigating examples of what the operations model.
• Shu-Hong Zhu and the sevensome

Visualizations - unconscious and conscious

Six representations

Grothendieck's six operations, the natural bases of the symmetric functions, Hopf algebras.

Twelve circumstances

One, all, many

SU(2) normal form