Monday, March 23, 2026
Flashback: The Newman Prize
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Sunday, March 22, 2026
Welcome to the Hotel Redacted
260322-Little_Darling-at-The_Hotel_Redacted.jpg —
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Social Media Hotel Post* —
“Let Your Love Story Unfold”
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“Let Your Love Story Unfold”
“Let Your Love Story Unfold”
The Salinger Files:
Dramarama Meets Bananarama in . . .
A Perfect Day for Redaction
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Dramarama Meets Bananarama in . . .
A Perfect Day for Redaction
Dramarama Meets Bananarama in . . .
A Perfect Day for Redaction
Tuesday, March 3, 2026
Blood Moon at Sunrise
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Sunday, March 1, 2026
Friday, November 14, 2025
A Moduli Space
On the Miracle Octad Generator of R. T. Curtis —
|
December 2025 Notices of the American Mathematical Society Jarod Alper, "Evolution of Stacks and Moduli" — "By a moduli space, we mean a geometric space whose points are in 'natural' bijection (more on what we mean by 'natural' in a moment) with isomorphism classes of your favorite mathematical objects, for example, Riemann surfaces or vector bundles on a fixed space. A moduli space is a solution to the classification problem: it packages all of the data of the geometric objects into a single space, a mathematical catalogue where any object can be located by selecting the corresponding point." |
Analogous notions:
Klein Space and Klein Quadric in this journal.
The Source:
Related art from a Log24 post of July 1, 2018 —
Greg Egan’s animated image of the Klein quartic —
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Wednesday, October 8, 2025
Cube-Brick Columns
This post was suggested by yesterday's update to
the "Analogy Between Analogies" post of October 6.
The reason for the above columns . . .
The action of S8 on the rows of an 8-row 3-column matrix
000
001
010
011
100
101
110
111
is intimately connected, via the 30 labelings of a Fano plane
and via the Klein quadric in PG(5, 2), with the action of a
group of order 322,560 on the 16 squares of a 4×4 array.
See Conwell, 1910 [1] and the Log24 tag 105 partitions.
1. Conwell, George M. “The 3-Space PG(3, 2) and Its Group.”
Annals of Mathematics, vol. 11, no. 2, 1910, pp. 60–76.
JSTOR, https://doi.org/10.2307/1967582.
For those who prefer narratives to mathematics: The Cubes.
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Thursday, October 2, 2025
Wednesday, October 1, 2025
For Wallace Stevens’s Birthday — October 2.
Posts now tagged Incipient Colorings.
Some related mathematics:
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Sunday, September 28, 2025
For Day 28 of September 2025: Fundamental Structures
http://m759.net/wordpress/?s="Ron+Shaw" —
The Klein quadric as background for
the Miracle Octad Generator of R. T. Curtis —
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Saturday, September 27, 2025
Four-Color Monolith
Those who find Kubrick's black 2001 monolith too dark
may prefer a more colorful image, taken from yesterday's
post on the Klein correspondence —
|
When?
Going to dark bed there was a square round Where?
— Ulysses , conclusion of Chapter 17. |
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Friday, September 26, 2025
On the Klein Correspondence in Finite Geometry
Illustration using Cullinane's four-color decomposition theorem —
" … fare forward, voyager . . . ." — T. S. Eliot
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Wednesday, September 24, 2025
The Mind Trick in the Attic
"In my experience, every kind of writing requires
some kind of self-soothing Jedi mind trick, and,
when it comes to essay composition,
this rectangle is mine."
— Zadie Smith in The New Yorker, Sept. 22, 2025.
A mind trick that is perhaps less self-soothing —
The dimensional reduction above, from six affine dimensions over
GF(2) to four dimensions, is, like a similar reduction in the previous post,
done by considering only even-sized subsets, then considering as elements
only the boundaries between these subsets and their complements . . .
and the Galois (XOR) sums of those boundaties.
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Annals of Dimensional Reduction:
“Six Dimensions into Three”
http://m759.net/wordpress/?s="six+dimensions+into+three"
The above link is for fans of Richard J. Trudeau's "Story Theory of Truth."
And then from pure mathematics, there is the reduction from eight dimensions
into six of Diamond Theory, in passing from the eight-dimensional affine space
over the two-element Galois field to the six-dimensional affine space used in
Diamond Theory to represent the five-dimensional projective space PG(5,2).
See other posts tagged Klein Space.
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“Six Dimensions into Three”
“Six Dimensions into Three”
Monday, September 22, 2025
Patterns: “Perceived Coherence”
From a Log24 post of Oct. 22, 2015 —
Software writer Richard P. Gabriel describes some work of design
philosopher Christopher Alexander in the 1960s at Harvard:
The above 35 strips are, it turns out, isomorphic to
the 35 points of of the Klein quadric over GF(2).
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Sunday, September 21, 2025
Saturday, September 20, 2025
Matrix Design Resurrections: Adventures in Klein Space*
http://m759.net/wordpress/?s=Matrix+Design
http://m759.net/wordpress/?s=Matrix+Resurrections
"Been there, done that." — John Wick
* See as well the above Klein date —
Dec. 19, 2021 — in this journal.
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Tuesday, August 26, 2025
Using AI for Search:
Combinatorial Partitions as Projective Lines …
Within the Klein Quadric
Some backstory: yesterday's post "Using AI: Search vs. Chat."
Vide a PDF of the complete Grok report —
In its five-and-a-half-minute research and reasoning process
Grok was able to reference a post from this weblog, but it missed
the correct answer to the prompt — Cullinane's "four-color
decomposition theorem" in the following weblog image:
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Combinatorial Partitions as Projective Lines …
Within the Klein Quadric
Combinatorial Partitions as Projective Lines …
Within the Klein Quadric
Monday, August 25, 2025
Using AI: Search vs. Chat
Adapted song lyric —
"I used Chat, Chat used me, neither one cared."
What if we read the above machine-boilerplate "Comments Off"
remark ending a May 6 Log24 post as a dramatist's note?
Related reading —
https://www.nytimes.com/2025/08/08/technology/
ai-chatbots-delusions-chatgpt.html —
"Over 21 days of talking with ChatGPT, an otherwise
perfectly sane man became convinced that he was
a real-life superhero. We analyzed the conversation.
. . . We received a full export of all of Allan Brooks’s conversations
with an OpenAI chatbot and analyzed a subset of the conversations
starting from May 6, 2025, when he began the chat about pi."
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Thursday, August 14, 2025
The Klein Quadric and 105 Lines
Earlier Log24 posts tagged 105 Partitions suggest a look at . . .
Version 4 of the above paper is at https://arxiv.org/abs/2105.13798.
See also this journal on the Version 2 date — April 9, 2022 —
a post titled Academic Rhetoric on visual diagrams in mathematics.
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The Perspective That Passeth Understanding
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Saturday, May 10, 2025
Six-Set and Eight-Set:
I Ching* and Brick Space
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I Ching* and Brick Space
I Ching* and Brick Space
Friday, May 9, 2025
Pictures at 11: M24.space
The new URL m24.space forwards to . . .
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Tuesday, May 6, 2025
Grok 3 “Deeper Search” on
the Klein Correspondence and the MOG*
https://x.com/i/grok/share/6S3wugra7IfdMQGn0AvDjEC5V .
|
Conclusion "In conclusion, the Klein correspondence and the MOG are intricately linked through Conwell's correspondence, which aligns partitions of an 8-set with lines in PG(3,2), forming the backbone of the MOG's construction. This relationship enables the MOG to effectively study the Mathieu group M24 and related structures, bridging geometric and combinatorial mathematics. The detailed exploration reveals the depth of this connection, highlighting its significance in advanced mathematical research as of May 6, 2025." — Grok 3 "Deeper Search" |
* The "Miracle Octad Generator" of R. T. Curtis.
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the Klein Correspondence and the MOG*
the Klein Correspondence and the MOG*
Saturday, May 3, 2025
The Corner Pocket
"The tip of his cue struck the cue ball,
the cue ball hit the three, and the three-ball,
red and silent, rolled up the green table,
hit the cushion, rolled gently down, and
into the corner pocket."
— Ending of The Hustler , by Walter Tevis
(New York: Harper & Brothers, 1959).
The plot, and the ending, of the book differ
somewhat from those of the picture.
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Wednesday, April 30, 2025
Klein Space Breakthrough —
“Aus dem stillen Raume”
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“Aus dem stillen Raume”
“Aus dem stillen Raume”