Quantum Gravity-Dark Energy as Zero-Infinity (Coded as 0-1) Duals 20: Unit Ball in Functional Analysis

From Osher Doctorow mdoctorow@xxxxxxxxxxx

We've seen that probability-statistics has 1 representing (coding for)
infinity since there is nothing "more certain" than absolute certainty
up to a set of probability 0, and from previous threads as well as some
parts of this one a similar situation holds with infinitesimal
rotations, population proportions and similar things in Logistic
Differential equations, scaled/normalized variables throughout physics
and mathematics, convergent series (the ratio test, etc.), etc.

Many physicists and mathematicians are under the impression that
algebraic topology and algebraic geometry of string/Superstring/Brane
theory and Loop Quantum Gravity (LQG) have the main momentum in
mathematical and theoretical physics at present, but in fact Functional
Analysis is arguably more pervasive and more frequent if we include all
its subtypes and concepts.

Functional Analysis differs from Algebraic Topology and Algebraic
Geometry in that the former is oriented toward the following
fundamentally (among others):

A. The unit ball
B. Eigenvalues/eigenvectors and their spectral generalizations
C. Diagonals (sets of elements of form (x, x) )
D. The identity and/or zero element and its small neighborhoods.
E. Continuity and differentiability and integrability (discreteness
occurs but is not one of the guiding principles).
F. Unification of Real, Complex, Quaternionic, etc. Analysis,
Probability-Statistics, Physics Experiment (in applications including
Scattering Theory), Combinatorics/Number Theory/Arithmetic,
Differential Equations, Geometry, Topology, Control/Feedback.

Osher Doctorow

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