Or… "Mathematics for Language Animals: A Unifying Framework"
Friday, October 3, 2025
Sunday, July 20, 2025
Eddington Elegy
The properties of the mathematical structures in yesterday's post
"Philosophy for Eddington" are those of the Dirac matrices discussed
by Arfken. An elegy for Arfken —
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Tuesday, September 17, 2024
Six to Nine, My Dear Watson … Continues.
Continued from August 9, 2024.
Today 's previous post was on Ch. 6 of Selig's Geometric Fundamentals.
Ch. 9 is on Clifford Algebra.
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Thursday, August 29, 2024
Fearful Symmetry
Peter Woit this afternoon on "The Terrifying Power of Mathematics" —
"… the quantum field theory of fields satisfying the Dirac equation.
Here there’s a standard apparatus of how to calculate given in
every quantum field theory textbook. These standard calculations
involving Dirac gamma-matrices fit well with Feynman’s 'physicists
finding they have the correct equations without understanding them
have been so terrified they give up trying to understand them'."
For a definition of these matrices, see . . .
Weisstein, Eric W. "Dirac Matrices."
From MathWorld — A Wolfram Web Resource.
https://mathworld.wolfram.com/DiracMatrices.html —
"The Dirac matrices are a class of 4×4 matrices which arise
in quantum electrodynamics. There are a variety of different
symbols used, and Dirac matrices are also known as
gamma matrices or Dirac gamma matrices."
For related religious remarks, see "Physics for Poets"
( Log24, April 20, 2022 ).
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Wednesday, October 4, 2023
Clearwater Revival
"You can ponder perpetual motion
Fix your mind on a crystal day
Always time for a good conversation
There's an ear for what you say"
— "Up Around the Bend" lyrics
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Saturday, November 12, 2022
“Dirac’s Hidden Geometry”
See also other Log24 posts tagged Dirac and Geometry.
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Thursday, April 21, 2022
Wednesday, April 20, 2022
Physics for Poets
Excerpt from a long poem by Eliza Griswold —
The square array above does not contain Arfken's variant
labels for ρ1, ρ2, and ρ3, although those variant labels were
included in Arfken's 1985 square array and in Arfken's 1985
list of six anticommuting sets, copied at MathWorld as above.
The omission of variant labels prevents a revised list of the
six anticommuting sets from containing more distinct symbols
than there are matrices.
Revised list of anticommuting sets:
α1 α2 α3 ρ2 ρ3
γ1 γ2 γ3 ρ1 ρ3
δ1 δ2 δ3 ρ1 ρ2
α1 γ1 δ1 σ2 σ3
α2 γ2 δ2 σ1 σ3
α3 γ3 δ3 σ1 σ2 .
Context for the poem: Quark Rock.
Context for the physics: Dirac Matrices.
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Monday, October 21, 2019
Algebra and Space… Illustrated.
Related entertainment —
Detail:
George Steiner —
"Perhaps an insane conceit."
Perhaps.
See Quantum Tesseract Theorem .
Perhaps Not.
See Dirac and Geometry .
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Wednesday, October 9, 2019
The Joy of Six
Note that in the pictures below of the 15 two-subsets of a six-set,
the symbols 1 through 6 in Hudson's square array of 1905 occupy the
same positions as the anticommuting Dirac matrices in Arfken's 1985
square array. Similarly occupying these positions are the skew lines
within a generalized quadrangle (a line complex) inside PG(3
