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Bott periodicity, Physics

Random matrices

Random matrices

• Random matrix ensembles are based on orthogonal matrices (of various kinds) because they are symmetric matrices (in the relevant sense) whose individual entries can be changed arbitrarily without affecting that condition, which they continue to satisfy. That is perhaps the whole point. Orthogonality grounds the symmetry, which respects itself upon multiplication, which can thus support arbitrary changes. Thus this is the condition for compatibility with arbitrary change in a particular entry. How does this relate to divisions of everything?
• How can random matrices model biological processes such as molecular collisions?
• Philip Cohen, Fabio Deelan Cunden, Neil O’Connell. Moments of discrete orthogonal polynomial ensembles. Related to random matrix theory.

Randomness

• How is randomness related to the Riemann Hypothesis?
• Forms of matter express geometry as uniformity and give rise to mass behavior even randomness.
• Entropy - physics is related to symmetry - Shannon entropy is related to information. And how does that relate to randomness?
• Symmetry breaking - choosing one possibility. From symmetry breaking randomness appears and information is constructed. Deterministic is replaced by irreversibility.
• Randomness as derived from a wall that allows for independent events, as with the other, or with transcendence.
• Randomness as lack of knowledge.
• Note that the weak force is a link between the two universes. It grounds radiation which is a source of randomness and is essential for evolution. We can consider how an adjunctions with a randomness functor could relate the two universes. Randomness is based on ignorance. A mirror universe establishes a basic level of ignorance.
• Choice in an eight-track mind is modeled by the random matrix ensembles.