What Does Nature Have to Say About My Sheffer Polynomials Video?
Channel: Math 4 Wisdom
Date: 11/01/2023

Physicist Thomas Gajdosik (Vilnius University) and mathematician John Harland (Palomar College) joined me, Andrius Kulikauskas (Math 4 Wisdom), on December 19, 2022 for a livelier discussion of my video "Sheffer Polynomials: Combinatorial Space for Quantum Physics".
https://www.math4wisdom.com/wiki/Exposition/20221122SpaceBuilders

Topics include:
0:00 Bijection, induction, constructivity and nonconstructivity within the proof.
8:30 My debate with Thomas: Should free space be thought of as a distinguished compartment?
19:00 Laguerre polynomials - free space A(t) and compartments u(t) are basically the same - free space is bound space.
25:00 Does the generalized linear model give ways of comparing free space A(t) and compartments xu(t)?
29:50 Relating a compartment in discrete combinatorial space with intervals in the continuum between zeroes of an orthogonal polynomial.
42:50 Andrius's attempt to state that relation.  
49:00 Thomas about orthogonal polynomials as simply tools for physicists.
51:00 John hopes that the combinatorics could address problems of renormalization.
52:00 John's perspective on infinite dimensional space and reducing it to finite dimensional parts.
54:10 Andrius: Combinatorial interpretation has us listen to what nature has to say. (Manet's painting "The Luncheon on the Grass")
56:00 Combinatorial space as not infinite but "as big as it needs to be" and how that addresses renormalization.
1:03:30 The three-dimensionality of space as a consequence of the recurrence relation for orthogonal polynomials relating three terms.
1:09:00 John on the idea of a universal covering space for combinatorial expressions.
1:12:00 John asks if Sheffer polynomials are the only ways to encode partitions of a set.

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