Earlier . . .
Today . . .
* For a connection with I Ching geometry, see a different 8×8 array.
Saturday, May 10, 2025
Friday, May 9, 2025
Pictures at 11: M24.space
The new URL m24.space forwards to . . .
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.
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”
Friday, April 18, 2025
A Koan for Rockwell (Sam, not Norman)
Q — "Is the Eightfold Way the same as the Yellow Brick Road?"
A — "No. The former is the Klein Quartic, the latter the Klein Quadric."
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Sunday, April 6, 2025
The Klein Space Breakthrough
Scholium on today's "Winner's Circle" post —
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Friday, March 28, 2025
Early James† Reads Krysten Ritter*
"You are everywhere and nowhere.
You melt into the crowd. Swipe your boarding pass
over the small red laser beam and hear its reassuring beep.
You board the plane and take your first-class seat.
You lift into the air."
— Ritter, Krysten. Retreat: A Novel (p. 260).
HarperCollins. Kindle Edition.
† "I've got this problem when I'm reading a book.
Know there's an ending, so I can't help but look."
* See this morning's Ritter post.
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Monday, March 24, 2025
A Combinatorial Configuration
Related art —
From "Self-Dual Configurations and Regular Graphs" by H. S. M. Coxeter,
Bulletin of the American Mathematical Society, Vol. 56 (1950), pp. 413-455
For a related combinatorial configuration, take Oxbury's "16 lines"
to be the the 16 dots above and take the "8 points of intersection"
to be the four squares
234, 1234, 124, 24
23, 123, 12, 2
3, 13, 1, 0
34, 134, 14, 4
along with the four diamonds
234, 23, 3, 34
1234, 123, 13, 134
124, 12, 1, 14
24, 2, 0, 4.
Then each "line" is on two "points" and each "point" on
four "lines."
Note that these eight "points" — the four squares and the four diamonds
of Coxeter's figure — form the rows and columns of the following matrix:
| 234 | 1234 | 124 | 24 |
| 23 | 123 | 12 | 2 |
| 3 | 13 | 1 | 0 |
| 34 | 134 | 14 | 4 |
Related reading: Points with Parts .
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Wednesday, March 12, 2025
Dirac, Kummer, Hudson, and the 16 Points
From the January 2025
Bulletin of the American Mathematical Society :
Some background for the above article's conclusion —
For some related material . . .
Search for "Hudson Kummer Quartic" in Log24.
A song for Singer . . .
"I've got this problem when I'm reading a book
Know there's an ending, so I can't help but look"
— Early James, "I Got This Problem" lyrics
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Wednesday, March 5, 2025
Welcome to Klein Space*
"You meet people on their plane of reality"
— White Lotus posture teacher, 2025
* For a rather different Klein space, click here.
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