Log24

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(3,2).

Anticommuting Dirac matrices as spreads of projective lines

Related narrative The "Quantum Tesseract Theorem."

Wednesday, February 27, 2019

Construction of PG(3,2) from K6

Filed under: General,Geometry — Tags: , , — m759 @ 11:38 AM

From this journal on April 23, 2013

IMAGE- Geometry of the Six-Set, Steven H. Cullinane, April 23, 2013

From this journal in 2003

From Wikipedia on Groundhog Day, 2019

Tuesday, February 26, 2019

Annals of Philology

Filed under: General — Tags: — m759 @ 11:05 PM

"What kind of person bokehs an inscape?"

— Question adapted from the weblog Barefooted Philologists

An illustration (click to enlarge) —

Citation

Filed under: General — Tags: , , , — m759 @ 12:00 PM

Some related material in this journal — See a search for k6.gif.

Some related material from Harvard —

Elkies's  "15 simple transpositions" clearly correspond to the 15 edges of
the complete graph K6 and to the 15  2-subsets of a 6-set.

For the connection to PG(3,2), see Finite Geometry of the Square and Cube.

The following "manifestation" of the 2-subsets of a 6-set might serve as
the desired Wikipedia citation —

See also the above 1986 construction of PG(3,2) from a 6-set
in the work of other authors in 1994 and 2002 . . .

IMAGE- Dolgachev and Keum, coordinatization of the 4x4 array in 'Birational Automorphisms of Quartic Hessian Surfaces,' AMS Transactions, 2002

Monday, February 18, 2019

Sacerdotal K6, Continued

Filed under: General,Geometry — Tags: , — m759 @ 12:12 PM

From yesterday's post on sacerdotal jargon

A related note from May 1986 —

Sunday, February 17, 2019

Sacerdotal K6

Filed under: General,Geometry — Tags: , — m759 @ 7:35 PM

From a recently created Wikipedia article —

See also Sacerdotal Jargon (Log24, Dec. 5, 2002).

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