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Andrius: My thoughts and questions for John.

Boundary between self and world

2x2 matrices can model the boundary between the self and the world. The self wants to filter out many causes from the outside but wants to also recognize some so that it can prepare for them and respond to them. So that relates to John's extradynamical model. But it also relates to linear complex structures, how they evenly divide the self and the world, and raise the question, which is the self and which is the world? The self is everything, thus the gap between total symmetry and structured symmetry. This models both the self and the world. But the world is furthermore what is deeper, the unexposed structure, the complement (within the eightsome) of the division of everything. Or is it the other way around? Are they both the self, the explicit self and the implicit self? And where is the spirit.

Double cover

{$SO(3)$} and {$SU(2)$} have the same Lie algebra but globally they are different Lie groups. What is the basis for that difference? Do they parametrize the angle at different speeds? Can that account for the difference in the speed of time between classical and quantum physics? Could that be related to random matrix ensembles and culling? And to the Hamiltonians related to symmetric spaces?

Random ensembles

• Wigner had the idea that one could understand much about a complex system by considering a Hamiltonian randomly selected from an ensemble of Hamiltonians, where there is a probability distribution on the ensemble. Could this be related to evolution?

Unitary representations

• The fact that the Lorentz transformations do not have finite dimensional unitary representations suggests that perhaps that is what drives culling, as a finite dimensional universe grows in dimensions, in perspectives.
• Could this relate to Bott periodicity growing the universe as the number of generators increases but the structure collapses?

Wigner's Theorem

• How does it relate CPT symmetry to the foundations of quantum physics?
• How is Wigner's theorem related to his work on random matrices?

Mass

• How is mass (and frequency) related to localization? and to the distinction between what it is (its own inertia) and what is everything else (the gravitational field)? as with fermions.
• Do bosons contribute to gravity?