Saturday, May 9, 2026
Sunday, October 19, 2025
Annals of Dark Comedy
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Sunday, August 10, 2025
AI as Hype Tool: A Mathematical Tapestry
From the previous post's new Microsoft Copilot report on
the Cullinane diamond theorem —
"What emerges is a tapestry where geometry, algebra,
combinatorics, and visual art are tightly interwoven."
For a soundtrack . . .
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Friday, July 18, 2025
Thursday, July 17, 2025
Entity Song
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Sunday, May 4, 2025
Thursday, September 12, 2024
The Fourth
Three properties of space — interlocking, interlacing, interweaving.
— "One, two, three … but where is the fourth?"
— "Socrates, the fourth, intertwining, is at . . .
http://m759.net/wordpress/?p=93725 ."
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Tuesday, January 23, 2024
Interweaving
In memory of the "Thomas Crown Affair" director, who
reportedly died at 97 on Saturday, Jan. 20 —
See as well . . .
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Friday, June 10, 2022
Songlines.space
To me, the new URL "Songlines.space" suggests both the Outback
and the University of Western Australia. For the former, see
"'Max Barry' + Lexicon" in this journal. For the latter, see SymOmega.
The new URL forwards to a combination of these posts.
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Friday, December 10, 2021
Unhinged Melody
The time of the previous post was 4:46 AM ET today.
Fourteen minutes later —
"I'm a groupie, really." — Murray Bartlett in today's online NY Times
The previous post discussed group actions on a 3×3 square array. A tune
about related group actions on a 4×4 square array (a Galois tesseract ) . . .
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Thursday, December 9, 2021
Tune for a Matrix Dance
"… inextricably intertwined in the fate of the Matrix …."
See as well The Eddington Song in this journal.
(The "intertwining" part is at Sex Textiles (March 26, 2021).)
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Thursday, July 15, 2021
Dramarama Continues . . .
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Friday, March 26, 2021
Sex Textiles: Introduction to Symplectic* Finite Geometry
Another concept from The New York Times today: intertwining —
“The historical achievements and experiences of women and men
are like the intertwined warp and weft threads of a woven fabric.”
— Virginia Postrel in a NY Times opinion piece today.
From Postrel’s Web page —
* See (for instance) A Picture Show for Quanta Magazine.
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Thursday, March 4, 2021
Continuity
Actually, Dirac “bridged math and physics” much earlier —
“Spinors, which are a kind of square root of vectors, had been introduced
in algebra and also in physics as part of Paul Dirac’s theory of the electron.
A spin structure on a manifold allows such square roots to exist.”
— Quanta Magazine today, article by Daniel S. Freed
See The Eddington Song and . . .
Poetic paraphrase —
“How can we tell the singer from the song?”
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Monday, September 7, 2020
A Discovery of Space
Fiction set in Duke Humfrey's Reading Room at
the Bodleian Library, University of Oxford:
|
"I walked quickly through the original, fifteenth-century part of the library, past the rows of Elizabethan reading desks with their three ascending bookshelves and scarred writing surfaces. Between them, Gothic windows directed the reader’s attention up to the coffered ceilings, where bright paint and gilding picked out the details of the university’s crest of three crowns and open book and where its motto, 'God is my illumination,' was proclaimed repeatedly from on high."
— Harkness, Deborah. A Discovery of Witches: |
Related non-fiction about an event on Jan. 26, 2019 —
Meanwhile, elsewhere —
A later ad for the Lyche exhibition —
See as well some posts about the Eddington song —
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Monday, December 30, 2019
“Welcome to Scotland.”
John Brown, Astronomer Royal for Scotland,
reportedly died there in the early morning
of Saturday, November 16, 2019.
See also Alasdair Gray and Eddington Song —
in particular, Logic in the Spielfeld.
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Saturday, November 16, 2019
Logic in the Spielfeld
"A great many other properties of E-operators
have been found, which I have not space
to examine in detail."
— Sir Arthur Eddington, New Pathways in Science ,
Cambridge University Press, 1935, page 271.
The following 4×4 space, from a post of Aug. 30, 2015,
may help:
The next time she visits an observatory, Emma Stone
may like to do a little dance to …
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Sunday, September 15, 2019
Changes Interlock
"Changes interlock…." — John Dewey
Indeed they do.
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Friday, July 12, 2019
Instrumental
The title is from a New York Times correction in the previous post.
Piano roll for "I am sixteen going on seventeen" —
Backstory: Posts tagged Root Circle.
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Monday, February 25, 2019
Saturday, January 26, 2019
In Memory of a Composer
who reportedly died early today in Paris, a tribute from
those who wrote the English lyrics for "Windmills of Your Mind" —
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Wednesday, January 23, 2019
Decorated
For those who prefer more elaborate decorations —
1. A Facebook image from last August …
2. The Facebook glider suggests a tune from "The Thomas Crown Affair"
(1968) that appeared in a Dec. 16, 2018 post on Christianity and
"interlocking names"—
The revised lyrics describe a square space.
3. An even more elaborate square space:
the Dance of the Snowflakes from
Balanchine's version of The Nutcracker —
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Sunday, December 16, 2018
Wednesday, November 21, 2018
Opening Credits
From Log24 on Friday, Nov. 16 —
This evening's New York Times on an opening-credits designer,
Pablo Ferro, who reportedly died at 83 on Friday, Nov. 16 —
An example of Ferro's later work in film —
Musical accompaniment from Sunday morning —
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Tuesday, November 20, 2018
Logos
Musical accompaniment from Sunday morning —
Update of Nov. 21 —
The reader may contrast the above Squarespace.com logo
(a rather serpentine version of the acronym SS) with a simpler logo
for a square space (the Galois window ):
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Sunday, November 18, 2018
Space Music
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Friday, November 20, 2015
Anticommuting Dirac Matrices as Skew Lines
(Continued from November 13)
The work of Ron Shaw in this area, ca. 1994-1995, does not
display explicitly the correspondence between anticommutativity
in the set of Dirac matrices and skewness in a line complex of
PG(3,2), the projective 3-space over the 2-element Galois field.
Here is an explicit picture —
References:
Arfken, George B., Mathematical Methods for Physicists , Third Edition,
Academic Press, 1985, pages 213-214
Cullinane, Steven H., Notes on Groups and Geometry, 1978-1986
Shaw, Ron, "Finite Geometry, Dirac Groups, and the Table of
Real Clifford Algebras," undated article at ResearchGate.net
Update of November 23:
See my post of Nov. 23 on publications by E. M. Bruins
in 1949 and 1959 on Dirac matrices and line geometry,
and on another author who gives some historical background
going back to Eddington.
Some more-recent related material from the Slovak school of
finite geometry and quantum theory —
The matrices underlying the Saniga paper are those of Pauli, not
those of Dirac, but these two sorts of matrices are closely related.
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